E R E W h e r e D o We S t a n d ?
edited by Paul De Grauwe
Seminar Series
Exchange Rate ...

Author:
Paul De Grauwe

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E R E W h e r e D o We S t a n d ?

edited by Paul De Grauwe

Seminar Series

Exchange Rate Economics

CESifo Seminar Series edited by Hans-Werner Sinn Inequality and Growth: Theory and Policy Implications Theo S. Eicher and Stephen J. Turnovsky, editors Public Finance and Public Policy in the New Century Sijbren Cnossen and Hans-Werner Sinn, editors Spectrum Auctions and Competition in Telecommunications Gerhard Illing and Ulrich Kluh, editors Managing EU Enlargement Helge Berger and Thomas Moutos, editors European Monetary Integration Hans-Werner Sinn, Mika Widgre´n, and Marko Ko¨thenbu¨rger, editors Measuring the Tax Burden on Capital and Labor Peter Birch Sørensen, editor A Constitution for the European Union Charles B. Blankart and Dennis C. Mueller, editors Labor Market Institutions and Public Regulation Jonas Agell, Michael Keen, and Alfons Weichenrieder, editors Venture Capital, Entrepreneurship, and Public Policy Vesa Kanniainen and Christian Keuschnigg, editors Exchange Rate Economics: Where Do We Stand? Paul De Grauwe, editor

Exchange Rate Economics: Where Do We Stand?

edited by Paul De Grauwe

The MIT Press Cambridge, Massachusetts London, England

( 2005 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email [email protected] or write to Special Sales Department, The MIT Press, 5 Cambridge Center, Cambridge, MA 02142. This book was set in Palatino on 3B2 by Asco Typesetters, Hong Kong, and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Exchange rate economics : where do we stand? / edited by Paul De Grauwe. p. cm. — (CESifo seminar series) Selected papers from seminars hosted by CESifo, an international network of economists supported jointly by the Center for Economic Studies at Ludwig-MaximiliansUniversita¨t, Munich, and the Ifo Institute for Economic Research. Includes bibliographical references and index. ISBN 0-262-04222-3 (alk. paper) 1. Foreign exchange rates—Congresses. 2. Foreign exchange rates—Econometric models—Congresses. I. Grauwe, Paul De. II. Series. HG3851.E894 2005 2004056463 332.40 56—dc22 10 9 8

7 6 5

4 3 2 1

Contents

Contributors vii Series Foreword ix Introduction xi 1

Are Different-Currency Assets Imperfect Substitutes?

1

Martin D. D. Evans and Richard K. Lyons 2

Volume and Volatility in the Foreign Exchange Market: Does It Matter Who You are? 39 Geir H. Bjønnes, Dagﬁnn Rime, and Haakon O. Aa. Solheim

3

A Neoclassical Explanation of Nominal Exchange Rate Volatility 63 Michael J. Moore and Maurice J. Roche

4

Real Exchange Rates and Nonlinearities

87

Mark P. Taylor 5

Heterogeneity of Agents and the Exchange Rate: A Nonlinear Approach 125 Paul De Grauwe and Marianna Grimaldi

6

Dynamics of Endogenous Business Cycles and Exchange Rate Volatility 169 Volker Bo¨hm and Tomoo Kikuchi

vi

7

Contents

The Euro, Eastern Europe, and Black Markets: The Currency Hypothesis 207 Hans-Werner Sinn and Frank Westermann

8

What Do We Know about Recent Exchange Rate Models? In-Sample Fit and Out-of-Sample Performance Evaluated

239

Yin-Wong Cheung, Menzie D. Chinn, and Antonio Garcia Pascual 9

The Euro–Dollar Exchange Rate: Is it Fundamental?

277

Mariam Camarero, Javier Ordo´n˜ez, and Cecilio Tamarit 10 Dusting off the Perception of Risk and Returns in FOREX Markets 307 Phornchanok J. Cumperayot Index

339

Contributors

Geir Bjønnes Stockholm Institute for Financial Research and Norwegian School of Management Volker Bo¨hm University of Bielefeld, Germany Mariam Camarero Jaume I University Yin-Wong Cheung University of California, Santa Cruz Manzie D. Chinn University of California, Santa Cruz and NBER Phornchanok Cumperayot Chulalongkorn University, Erasmus University Rotterdam Paul De Grauwe University of Leuven Martin Evans Georgetown University and NBER Marianna Grimaldi Sveriges Riksbank, Stockholm Tomoo Kikuchi University of Bielefeld, Germany

Richard Lyons University of California, Berkeley and NBER Michael Moore Queen’s University, Belfast Javier Ordo´n˜ez Jaume I University Antonio Garcia Pascual IMF and University of Munich Dagﬁnn Rime Norges Bank (Central Bank of Norway) and Stockholm Institute for Financial Research Maurice Roche National University of Ireland Hans-Werner Sinn CESifo, Munich Haakon Solheim Norwegian School of Management and Statistics Norway Cecilio Tamarit University of Valencia Mark Taylor University of Warwick, Coventry Frank Westermann CESifo, Munich

CESifo Seminar Series in Economic Policy

The book is part of the CESifo Seminar Series in Economic Policy, which aims to cover topical policy issues in economics from a largely European perspective. The books in this series are the products of the papers presented and discussed at seminars hosted by CESifo, an international research network of renowned economists supported jointly by the Center for Economic Studies at Ludwig-Maximilians University, Munich, and the Ifo Institute for Economic Research. All publications in this series have been carefully selected and refereed by members of the CESifo research network. Hans-Werner Sinn

Introduction

Like the movements of the major exchange rates, exchange rate economics has gone through long cycles. In the 1970s during the early stage of the postwar experience with ﬂoating exchange rates, economists enthusiastically proposed simple models to explain and to predict exchange rates. These models were all based on simple analytical tools. One strand of literature used the quantity theory of money and purchasing power parity, describing the long-run equilibrium relation of money, prices, and the exchange rate, and some simple assumptions about price inertia in the short run. The most celebrated model in this vein undoubtedly was the Dornbusch model (Dornbusch 1976). Another strand of literature started from the portfolio balance model and added a dynamics linking the supply of net foreign assets to the current account (Kouri 1976; Branson 1977). During a conference on ﬂexible exchange rates in Stockholm in 1975 there was a strong feeling among the participants that major theoretical breakthroughs in exchange rate modeling had been achieved. The feeling of optimism, even elation, that was present was not very different from the feelings of elation during a speculative bubble in ﬁnancial markets. The theoretical bubble burst in the early 1980s, when Meese and Rogoff published their well-known empirical evaluation of the existing exchange rate models (Meese and Rogoff 1983). The results were devastating for all the existing theoretical models. These models appeared to have no predictive power compared to a simple alternative model, the random walk. Despite the fact that occasionally some researchers claimed to have found models that would outperform the random walk (e.g., Mark 1995), it appeared that these positive results were very sensitive to the sample periods selected in these studies (Faust

xii

Introduction

et al. 2001). This conclusion is conﬁrmed by chapter 8 of this book in which Yin-Wong Cheung, Menzie Chinn, and Antonio Garcia Pascual analyze a larger spectrum of economic models of the exchange rates than in the original Meese and Rogoff studies, conﬁrming that none of these models outperform the random walk. It has often been noted that economic models tend to withstand the test against the random walk better when used for long-term predictions (see Mark 1995). This was sometimes interpreted to mean that the economic models of the exchange rates were not that bad after all. But this was only superﬁcially so. The truth is that the Meese-Rogoff empirical evaluation loads the dice against the random walk model. The reason is that when out of sample forecasts of the exchange rates are made with the economic models, the realized values of the exogenous variables are used, while the forecasts with the random walk model do not have this information. As the horizon of the forecasts increases, the handicap of the random walk forecasts (as compared to the forecasts with the economic models) increases. Thus much of the superior predictive performance of economic models over longer horizons is due to a statistical construction favoring these models. After the intellectual crash of the early 1980s triggered by the Meese and Rogoff empirical studies, theoretical modeling of exchange rates came to a virtual standstill for a decade. Few economists dared to develop exchange rate models, let alone test these models with empirical data. This lasted until the early 1990s when a turnaround was in the making. This turnaround came about as a result of several new developments. First, new theoretical insights were gained about the microstructure of the ﬁnancial markets. These insights were ﬁrst applied in stock markets, and later introduced in the analysis of the foreign exchange markets. Pioneering work in this area was done by Richard Lyons (Lyons 1999). This led to a ﬂourishing new literature that concentrated on the question of how information is transmitted in the market when agents have private information. This literature was a major breakthrough compared to the previous one in which representative agents use the same public information. It led to exciting new insights into the functioning of the foreign exchange market. The ﬁrst two chapters of this book testify for this. The ﬁrst chapter by Evans and Lyons uses insights from the microstructure literature and comes to the conclusion that the portfolio balance theory is surprisingly alive, that there are economically meaningful effects arising from the imperfect substitutability be-

Introduction

xiii

tween domestic and foreign assets even in a world of highly integrated ﬁnancial markets. The authors conclude that this has important implications for the ability of the monetary authorities to intervene successfully in the foreign exchange markets. The second chapter is in the same vein. It analyzes the importance of trading ﬂows and ﬁnds that the effects of these ﬂows differ as between the type of agents who initiate these ﬂows. This suggests that heterogeneous expectations are important in the understanding of the dynamics in the foreign exchange markets. Another equally important theoretical development occurred in the 1990s and gave a new boost to the theoretical analysis of the exchange rate. This is the new open economy macroeconomics pioneered by Obstfeld and Rogoff in the mid-1990s (Obstfeld and Rogoff 1996). This theoretical development started from the idea that macroeconomic analysis should be ﬁrmly grounded on a microeconomic foundation. This led to macroeconomic models in which all decisions of agents are based on explicit utility maximization in a multi-period setup. Any assumption deviating from this paradigm was branded as an intolerable ad hoc assumption. A new fundamentalism took over the profession and led to a large literature in which the implications of this paradigm were analyzed. It also led to a large literature analyzing the exchange rate, an example of which is to be found in chapter 3 of this book. In this chapter Michael Moore and Maurice Roche present a micro-founded macro model explaining the volatility of the exchange rate in such a framework. Not surprisingly, in such a world of fully informed rational agents the high volatility of the nominal exchange rate must be based on real exchange rate variability. The authors identify the source of this variability in the variability of the marginal rate of substitution between home and foreign goods, which in turn arises from an externality in habit persistence. There is no doubt that by its insistence on logical consistency and intellectual rigor, the new open economy macroeconomics provides new avenues of sophisticated research opportunities for young economic graduates. Up to now, however, this research has not led to the formulation of many empirical propositions that could lead to a refutation of these models. As a result it is still unclear whether this approach has a sufﬁciently strong scientiﬁc foundation. After all, the success of a theory should be judged by its capacity to stand empirical tests, and not by its logical consistency or its intellectual rigour.

xiv

Introduction

Scepticism about the ability of the rational expectations–fully informed agent paradigm has led researchers into other directions. One such direction recognizes that agents use different information sets, and thus not all can be rational in the sense of using all available information. Note that this is also implicit in the microstructure literature that was discussed earlier. Such a world of heterogeneous agents creates a rich dynamics of exchange rate movements, as is shown in the chapter of De Grauwe and Grimaldi. In this chapter, chartists and fundamentalists interact and create a dynamics that in many respects resembles the dynamics observed in the foreign exchange market (systematic disconnection of the exchange rate from its fundamental, excess volatility, fat tails, volatility clustering). Similar results are found in chapter 6 where Volker Bo¨hm and Tomoo Kikuchi analyze the connection between the business cycle ﬂuctuation and the ﬂuctuations in the exchange rate. Much remains to be done in the modeling of the foreign exchange markets. This is very clear from the empirical studies collected in this volume. Chapter 4 written by Mark Taylor documents the strong nonlinearities that exist in the dynamic adjustment of the real exchange rate toward its equilibrium value. The author suggests that these nonlinearities can only be understood by introducing transactions costs into our models. These transactions costs create a band of inaction of the arbitrage opportunities in the goods markets. As a result the real exchange rate will react in a nonlinear way to the size of the shocks; namely the speed of adjustment of the real exchange rate toward its equilibrium value increases with the size of the initial disturbance. Econometric techniques have not stood still. New and powerful techniques have been developed allowing researchers to devise better empirical tests. These techniques have also inﬂuenced the empirical analysis of the exchange rates. Several chapters in this book use these state of the art econometric techniques to subject the exchange rates to an empirical analysis. In chapter 7 Hans-Werner Sinn and Frank Westermann subject the dollar/DM and the dollar/euro exchange rates to an empirical analysis. Using a modiﬁed portfolio balance model that takes into account the link with the money market, they come to the conclusion that the depreciation of the euro during the period 1999 to 2001 and its subsequent recovery was very much inﬂuenced by the shifts in the demand for marks in central and eastern Europe. The last two chapters contain a similar quest for underlying fundamentals of the exchange rates. In chapter 8 Camarero, Ordonez, and

Introduction

xv

Tamarit use dynamic panel data econometrics to measure the importance of a number of fundamental economic variables. The authors come to the conclusion that these fundamental economic variables contain useful information to understand the movements of the exchange rate. The extent to which these fundamental economic variables can be used for predictive purposes remains an open question, however. In the last chapter Cumperayot adds another dimension to the analysis. She argues persuasively that in order to explain the movements of the exchange rates, not only the traditional macroeconomic variables such as the money stocks, inﬂation, and output matter. Macroeconomic uncertainty is of equal importance. Therefore the author uses measures of macroeconomic uncertainty and ﬁnds that variations in this uncertainty explains a signiﬁcant part of the ﬂuctuations of the exchange rate around its fundamentals. The chapters of this book reﬂect the very divergent paradigms now in use in the economics profession. Some chapters are grounded on the paradigm of the representative and fully informed rational agent. Other chapters rely on a paradigm of heterogeneity of agents who use different and incomplete sets of information. These differences in the fundamental paradigms lead to different insights and heated discussions among their proponents. These differences may also lead to the impression that macro and monetary analysis is in a state of crisis. To a certain extent this is also the case. At the same time the competition between these different paradigms is a source of new debates and insights that hopefully will lead to a new synthesis allowing us to better understand and predict the movements in the exchange rate. References Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84: 1161–76. Branson, W. 1977. Asset markets and relative prices in exchange rate determination. Sozialwissenschaftliche Annalen 1, 67–80. Faust, J., J. Rogers, and J. Wright. 2001. Exchange rate forecasting: The errors we’ve really made. International Finance Discussion Papers, no. 739. Board of Governors of the Federal Reserve System. Kouri, P. 1976. The exchange rate and the balance of payments in the short run and in the long run. Scandinavian Journal of Economics 78, 280–304.

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Introduction

Lyons, R. 1999. The Microstructure Approach to Exchange Rates. Cambridge: MIT Press. Mark, N. 1995. Exchange rates and fundamentals: Evidence on long horizon predictability. American Economic Review 85: 201–18. Meese, R., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Obstfeld, M., and K. Rogoff. 1996. Foundations of International Macroeconomics. Cambridge: MIT Press.

Exchange Rate Economics

1

Are Different-Currency Assets Imperfect Substitutes? Martin D. D. Evans and Richard K. Lyons

The idea that different-currency assets are imperfect substitutes occupies an important place within exchange rate economics.1 It is still invoked, for example, for why sterilized intervention can be effective. And theoretical work continues to rely on this assumption.2 Yet supportive empirical evidence is scant.3 This chapter addresses the gap between theory and empirics. We test imperfect substitutability in a new, more powerful way and ﬁnd it strongly supported. Empirical work on imperfect substitutability in foreign exchange falls into two groups: (1) tests using measures of asset supply and (2) tests using measures of central bank asset demand. We address the demand side, but we examine demand by the public broadly rather than focusing on demand by central banks. Under ﬂoating rates, changing public demand has no direct effect on monetary fundamentals, current or future. This provides an opportunity to test for price effects from imperfect substitutability. Because data on public trades became available only recently (due to the advent of electronic trading), this strategy is feasible for the ﬁrst time. The discriminating power of our approach arises from avoiding difﬁculties inherent in past approaches. The asset-supply approach, for example, has low power because measuring supplies is notoriously difﬁcult. First, one must determine which measure of supply is the most appropriate. (There is considerable debate in the literature about this issue; e.g., see Golub 1989.) Then, for any given measure, the consistency of data across countries is a concern. Finally, these data are available only at lower frequencies (e.g., quarterly or monthly) and are rather slow-moving, making it difﬁcult to separate the effects of changing supply from the many other forces moving exchange rates. The central bank demand approach—an ‘‘event study’’ approach— may also have limited statistical power because central bank trades in

2

M. D. D. Evans and R. K. Lyons

major markets are relatively few and are small relative to public trading. For example, the average US intervention reported by Dominguez and Frankel (1993b) is only $200 million, or roughly one-thousandth of the daily spot volume in either of the two largest markets. (Since then, US intervention has been larger, typically in the $300 million to $1.5 billion range, but market volume has been higher too; see Edison 1998.) Studies using this latter approach are more successful in ﬁnding portfolio balance effects (e.g., Loopesko 1984; Dominguez 1990; Dominguez and Frankel 1993a). Nevertheless, results using this approach are not exclusively positive (e.g., Rogoff 1984) and the extent these event studies pertain to price effects from portfolio shifts in the broader market is not clear. The ‘‘micro portfolio balance model’’ we develop embeds both Walrasian features (as in the traditional portfolio balance approach) and features more familiar to models from microstructure ﬁnance. Regarding the latter, the model clariﬁes the role played by order ﬂow in conveying information about shifts in traders’ asset demands.4 Beyond this clariﬁcation, two analytical results in particular are important guideposts for our empirical analysis: (1) order ﬂow’s effect on price is persistent as long as public demand for foreign currency is less than perfectly elastic (even when beliefs about future interest rates are held constant), and (2) in the special case where central bank trades are sterilized, conducted anonymously, and convey no policy signal, the price impact of these trades is indistinguishable from that of public trades.5 The latter result links our analysis directly to intervention operations of this type. We establish three main results. First, testable implications of our model are borne out: we ﬁnd strong evidence of price effects from imperfect substitutability. The portfolio balance approach—with its rich past but lack of recent attention—may warrant some fresh consideration. Second, we provide a precise estimate of the immediate price impact of trades: 0.44 percent per $1 billion (of which about 80 percent persists indeﬁnitely). Our third result speaks to intervention policy. (As noted above, our price impact estimate is applicable to central bank trades as long as they are sterilized, secret, and provide no signal.) Estimates suggest that central bank intervention of this type is most effective at times when the ﬂow of macroeconomic news is strong. The remainder of the chapter is in ﬁve sections. Section 1.1 introduces our trading-theoretic approach to measuring price impact. Section 1.2

Are Different-Currency Assets Imperfect Substitutes?

3

presents our micro portfolio balance model. Section 1.3 describes the data. Section 1.4 presents model estimates and discusses their implications (e.g., for central bank intervention). Section 1.5 concludes. 1.1

A Trading-Theoretic Approach to Imperfect Substitutability

This section links the traditional macroeconomic approach to exchange rates to microeconomic theories of asset trading. This is useful for two main reasons. First, theories of asset trading provide greater resolution on how trades affect price. By greater resolution, we mean that individual channels within the macro approach can be broken into separate subchannels. These subchannels are themselves empirically identiﬁable. Second, a trading-theoretic approach establishes that most channels through which trades—including intervention—affect price involve information asymmetry. Impounding dispersed information in price is an important function of the trading process (which our model is designed to capture). Within macroeconomics, central bank (CB) currency demand affects price through two channels: imperfect substitutability and asymmetric information. Distinct modeling approaches are used to examine these two channels. For the ﬁrst channel, imperfect substitutability, macro analysis is based on the portfolio balance approach. Models within this approach are most useful for analyzing intervention that is sterilized and conveys no information (signal) about future monetary policy. Macro analysis of the second channel, asymmetric information, is based on the monetary approach. These models are most useful for analyzing intervention that conveys information about current policy (unsterilized intervention) or future policy (sterilized intervention with signaling). This channel captures the CB’s superior information about its own policy intentions. Let us examine these two macro channels within a trading-theoretic approach. 1.1.1

Imperfect Substitutability

In contrast to macro models, which address imperfect substitutability at the marketwide level only, theories of asset trade address imperfect substitutability at two levels. The ﬁrst level is the dealer level. Dealers—being risk averse—need to be compensated for holding positions they would not otherwise hold. This requires a temporary risk premium, which takes the form of a price-level adjustment. This price

4

M. D. D. Evans and R. K. Lyons

adjustment is temporary because this risk premium is not necessary once positions are shared with the wider market. In trading-theoretic models, price effects from this channel are termed ‘‘inventory effects.’’ These effects dissipate quickly in most markets because full risk sharing occurs rapidly (e.g., within a day).6 Within trading models, imperfect substitutability also operates at a second level, the marketwide level. At this level the market as a whole—being risk averse—needs to be compensated for holding positions it would not otherwise hold.7 This too induces a risk premium, which elicits a price-level adjustment. Unlike price adjustment at the ﬁrst level of imperfect substitutability, price adjustment at this second level is persistent (because risk is fully shared at this level). This is precisely the price adjustment that macro models refer to as a portfolio balance effect. The ﬁrst of these two levels of imperfect substitutability is not present within the macro approach. Indeed, use of the term imperfect substitutability within that approach refers to the second level only. The logic among macroeconomists for addressing only the second level is that effects from the ﬁrst level are presumed ﬂeeting enough to be negligible at longer horizons. This is of course an empirical question—one that our trading-theoretic approach allows us to address in a rigorous way. Moreover our modeling of this channel provides a more disciplined way to understand why part of intervention’s effect on price is ﬂeeting (and what determines the duration of this part of the effect). Below we test empirically whether either or both of these two levels of imperfect substitutability are present. If the ﬁrst level is present—the dealer level—then FX trades should have an impact on the exchange rate, but the effect should be temporary. We term this effect a ‘‘temporary portfolio balance channel.’’ If the second level is present—the marketwide level—then trades should have persistent impact. We term this effect a ‘‘persistent portfolio balance channel.’’ 1.1.2

Asymmetric Payoff Information

Theories of asset trading provide a third channel through which trades affect price—asymmetric payoff information (e.g., see Kyle 1985; Glosten and Milgrom 1985).8 If trades convey future payoff information (sometimes referred to as ‘‘fundamentals’’ in exchange rate economics), then they will have a second persistent effect on price beyond the persistent portfolio balance effect noted above. (For example, in equity markets managers of ﬁrms have inside information about earnings,

Are Different-Currency Assets Imperfect Substitutes?

5

and their trades can convey this information.) Unsterilized interventions are an example of currency trades that convey payoff information (i.e., information about current interest rates). Another example is sterilized intervention that signals future interest rate changes. In foreign-exchange markets, however, trades by market participants other than central banks (the public) do not in general convey payoff information: under ﬂoating-rate regimes, public trades have no direct effect on monetary fundamentals (money supplies, interest rates, and by extension, future price levels).9 For these trades, then, the payoff-information channel is not operative. This presents an opportunity to use public trades to test for the presence of the two types of portfolio balance effect. 1.2

A Micro Portfolio Balance Model

The model is designed to show how the trading process reveals information contained in order ﬂow. At a micro level, it is the ﬂow of orders between dealers that is particularly important: public trades are not observable marketwide but are subsequently reﬂected in interdealer trades, which are observed marketwide. Once observed, this information is impounded in price. This information is of two types, corresponding to the two portfolio balance effects outlined in the previous section: information about temporary portfolio balance effects and information about persistent portfolio balance effects. To understand these different portfolio balance effects, consider the model’s basic structure. At the beginning of each day, the public and central bank place orders in the foreign exchange market. (These orders are stochastic and are not publicly observed.) Initially dealers take the other side of these trades—shifting their portfolios accordingly. To compensate the (risk-averse) dealers for the risk they bear, an intraday risk premium arises, producing a temporary portfolio balance effect on price. The size of this price effect depends on the size of the realized order ﬂow. This is the ﬁrst of the two information types conveyed by order ﬂow. To understand the second, ﬁrst note that at the end of each day, dealers pass intraday positions on to the public (consistent with empirical ﬁndings that dealers end their trading day with no position; see Lyons 1995 and Bjonnes and Rime 2003). Because the public’s (nonstochastic) demand at the end of the day is not perfectly elastic—that is, different-currency assets are imperfect substitutes in the macro sense—beginning-of-day orders have portfolio balance effects that

6

M. D. D. Evans and R. K. Lyons

persist beyond the day. Thus the price impact of these risky positions is not diversiﬁed away even when they are shared marketwide.10 The size of this price effect too is a function of the size of the beginningof-day order ﬂow. This is the second of the two information types conveyed by order ﬂow. 1.2.1

Speciﬁcs

Consider an inﬁnitely lived, pure-exchange economy with two assets, one riskless and one risky, the latter representing foreign exchange.11 Each day, foreign exchange earns a payoff R, publicly observed, which is composed of a series of random increments: Rt ¼

t X

DRi :

ð1Þ

i¼1

The increments DR are iid normal, Nð0; sR2 Þ. We interpret the increments as the ﬂow of public macroeconomic information (e.g., interest rate changes). The foreign exchange market has three participant types: dealers, customers, and a central bank. The N dealers are indexed by i. There is a continuum of customers (the public), indexed by z A ½0; 1. Dealers and customers all have identical negative exponential utility deﬁned over periodic wealth. Central bank trades are described below. Within each day t there are four rounds of trading: Round 1: Dealers trade with the central bank and public. Round 2: Dealers trade among themselves (to share inventory risk). Round 3: Rt is realized and dealers trade among themselves a second time. Round 4: Dealers trade again with the public (to share risk more broadly). The timing of events within each day is shown in ﬁgure 1.1, which also introduces our notation. 1.2.2

Central Bank Trades

To accommodate analysis of intervention, we include trades by a central bank. The intervention we consider is of a particular type, equivalent in its features to public trades: intervention that is sterilized, secret

Are Different-Currency Assets Imperfect Substitutes?

7

Figure 1.1 Daily timing

(anonymous and unannounced), and conveys no signal of future monetary policy.12 More speciﬁcally, each day, one dealer is selected at random to receive an order from the central bank. To maintain anonymity, the CB order is routed to the selected dealer via an agent. Let It denote the intervention on day t, where It < 0 denotes a CB sale (dealer purchase). The central bank order arrives with the public orders at the end of round 1. The CB trade is distributed normally: It @ Nð0; sI2 Þ.13 Because the CB trade is sterilized and conveys no signal, It and the daily interest increments DRt are uncorrelated (at all leads and lags). Secret intervention insures that only the dealer who receives the CB trade observes its size (though not its source). A CB trade is, under these circumstances, indistinguishable from other customer orders.14 1.2.3

Trading Round 1

At the beginning of each day t, each dealer simultaneously and independently quotes a scalar price to the public and central bank.15 We denote this round-1 price of dealer i as P1i . (We suppress unnecessary notation for day t; as we will see, it is the within-day rounds—the subscripts—that capture the model’s economics.) This price is conditioned on all information available to dealer i. Each dealer then receives from the public a net customer order, C1i , that is executed at his quoted price P1i ; C1i < 0 denotes a net customer sale (dealer i purchase). Each of these N customer-order realizations is distributed normally, C1i @ Nð0; sC2 Þ. They are uncorrelated across dealers and uncorrelated with the payoff R. These orders represent portfolio shifts by the public, for example, coming from changing hedging demands, changing transactional demands, or changing risk

8

M. D. D. Evans and R. K. Lyons

preferences. Their realizations are not publicly observed. At the time the customer orders are received, one dealer also receives the intervention trade. 1.2.4

Trading Round 2

Round 2 is the ﬁrst of two interdealer trading rounds. Each dealer simultaneously and independently quotes a scalar price to other dealers at which he agrees to buy and sell (any amount), denoted P2i . These interdealer quotes are observable and available to all dealers in the market. Each dealer then simultaneously and independently trades on other dealers’ quotes. Orders at a given price are split evenly between dealers quoting that price. Let T2i denote the net interdealer trade initiated by dealer i in round two. At the close of round 2, all agents observe a noisy signal of interdealer order ﬂow from that period: X2 ¼

N X

T2i þ n;

ð2Þ

i¼1

where n @ Nð0; sn2 Þ, independently across days. The model’s difference in transparency across trade types corresponds well to institutional reality: customer–dealer trades in major foreign-exchange markets (round 1) are not generally observable, whereas interdealer trades do generate signals of order ﬂow that can be observed publicly.16 1.2.5

Trading Round 3

Round 3 is the second of the two interdealer trading rounds. At the outset of round 3 the payoff increment DRt is realized and the daily payoff Rt is paid (both observable publicly). As in round 2, each dealer then simultaneously and independently quotes a scalar price to other dealers at which he agrees to buy and sell (any amount), denoted P3i . These interdealer quotes are observable and available to all dealers in the market. Each dealer then simultaneously and independently trades on other dealers’ quotes. Orders at a given price are split evenly between dealers quoting that price. Let T3i denote the net interdealer trade initiated by dealer i in round 3. At the close of round 3, all agents observe interdealer order ﬂow from that period:

Are Different-Currency Assets Imperfect Substitutes?

X3 ¼

N X

T3i :

9

ð3Þ

i¼1

Note that this round-3 order ﬂow is observed without noise, unlike the noisy order ﬂow signal observed in round 2 (equation 2). The idea here is a natural one: dealers’ beliefs about random customer demands in round 1 become more precise over successive interdealer trading rounds (these beliefs are due to learning from interdealer trades). Of course, the observation process is not noiseless. We use this more extreme assumption for technical convenience. If dealer updating were Bayesian in round 3, as it is in the round 2, then prices set in round 4 will introduce some noise in the risk sharing between dealers and the nondealer public (described below). This noise would not alter the basic economics of the model, nor the basic structure of the model’s solution as presented in proposition 1 below. 1.2.6

Trading Round 4

In round 4, dealers share overnight risk with the nondealer public. Unlike round 1, the public’s trading in round 4 is nonstochastic. Initially each dealer simultaneously and independently quotes a scalar price P4i at which he agrees to buy and sell any amount. These quotes are observable and available to the public. The mass of customers on the interval ½0; 1 is large (in a convergence sense) relative to the N dealers. This implies that the dealers’ capacity for bearing overnight risk is small relative to the public’s capacity. By this assumption, dealers set prices optimally such that the public willingly absorbs dealer inventory imbalances, and each dealer ends the day with no net position (which is common practice among actual spot foreign-exchange dealers). These round-4 prices are conditioned on the interdealer order ﬂow X3 , described in equation (3). We will see that this interdealer order ﬂow informs dealers of the size of the total position that the public needs to absorb to bring the dealers back to a position of zero. To determine the round-4 price—the price at which the public willingly absorbs the dealers’ aggregate position—dealers need to know (1) the size of that aggregate position and (2) the risk-bearing capacity of the public. We assume the latter is less than inﬁnite. Speciﬁcally, given negative exponential utility, the public’s total demand for foreign exchange in round 4 of day t, denoted C4 , is proportional to the expected return on foreign exchange conditional on public information:

10

M. D. D. Evans and R. K. Lyons

C4 ¼ gðE½P4; tþ1 þ Rtþ1 j W 4; t P4; t Þ;

ð4Þ

where the positive coefﬁcient g captures the aggregate risk-bearing capacity of the public (g ¼ y is inﬁnitely elastic demand), and W 4; t includes all public information available for trading in round 4 of day t. 1.2.7

Equilibrium

The dealer’s problem is deﬁned over six choice variables, the four scalar quotes P1i ; P2i ; P3i , and P4i , and the two dealer’s interdealer trades T2i and T3i . Appendix A provides details of the model’s solution. Here we provide some intuition. Consider the four quotes P1i ; P2i ; P3i , and P4i . No arbitrage ensures that at any given time all dealers will quote a common price: quotes are executable by multiple counterparties, so any difference across dealers would provide an arbitrage opportunity. Hereafter we write P1 ; P2 ; P3 , and P4 in lieu of P1i ; P2i ; P3i , and P4i . It must also be the case that if all dealers quote a common price, then that price must be conditioned on common information only. Common information arises at three points: at the end of round 2 (order ﬂow X2 ), at the beginning of round 3 (payoff R), and at the end of round 3 (order ﬂow X3 ). The price for round-4 trading, P4 , reﬂects the information in all three of these sources. The following optimal quoting rules specify when the common-information variables ðX2 ; X3 ; DRÞ are impounded in price. These quoting rules describe a linear, Bayes-Nash equilibrium. Proposition 1 Dealers in our micro portfolio balance model choose the following quoting rules, where the parameters l2 ; l3 ; d, and f are all positive: P2 P1 ¼ 0; P3 P2 ¼ l2 X2 ; P4 P3 ¼ l3 X3 þ dDR fðP3 P2 Þ: For intuition on these quoting rules, note that the price change from round 1 to round 2 is zero because no additional public information is observed from round-1 trading (neither customer trades nor the CB trade are publicly observed). The change in price from round 2 to round 3, l2 X2 , is driven by public observation of the interdealer order ﬂow X2 . X2 here serves as an information aggregator. Speciﬁcally, it aggregates dispersed information about privately observed trades of

Are Different-Currency Assets Imperfect Substitutes?

11

the public and CB. The value l2 X2 is the price adjustment required for market clearing—it is a risk premium that induces dealers to absorb the round-1 ﬂow from the public and CB (that round-1 ﬂow equaling P i i C1 þ I). The price change from round 3 to round 4 includes both pieces of public information that arise in that interval: X3 and DR. The second round of interdealer ﬂow X3 conveys additional information about round-1 ﬂow (from the public and CB) because it does not include noise. The payoff increment DR will persist into the future, and therefore must be discounted into today’s price. The third component of the price change from round 3 to 4 is dissipation of a temporary portfolio balance effect that arose between rounds 2 and 3. Speciﬁcally, part of the risk premium that l2 X2 represents is a temporary premium that induces dealers to hold risky positions intraday. The endof-day price P4 does not include this because dealers hold no positions overnight. The persistent portion of the portfolio balance effect arises in this model because interdealer order ﬂow informs dealers about the portfoP lio shift ð i C1i þ IÞ that must be absorbed at day’s end by the public. If the end-of-day public demand were perfectly elastic, order ﬂow would still convey information about the portfolio shift, but the shift would not affect the end-of-day price. This persistent portfolio balance effect is the same in the model regardless of whether the initial order ﬂow came from the public or the central bank. Thus CB trades of the type we consider here have the same effect on price as a customer order of the same size—both induce the same portfolio shift at day’s end by the public. 1.3 1.3.1

Empirical Analysis Data

The dataset contains time-stamped, tick-by-tick observations on actual transactions for the largest spot market—DM/$—over a four-month period, May 1 to August 31, 1996. These data are the same as those used by Evans (2002), and the reader is referred to that paper for additional detail. The data were collected from the Reuters Dealing 2000-1 system via an electronic feed customized for the purpose. Dealing 2000-1 is the most widely used electronic dealing system. According to Reuters, over 90 percent of the world’s direct interdealer transactions take place through the system.17 All trades on this system take the

12

M. D. D. Evans and R. K. Lyons

form of bilateral electronic conversations. The conversation is initiated when a dealer uses the system to call another dealer to request a quote. Users are expected to provide a fast two-way quote with a tight spread, which is in turn dealt or declined quickly (i.e., within seconds). To settle disputes, Reuters keeps a temporary record of all bilateral conversations. This record is the source of our data. (Reuters was unable to provide the identity of the trading partners for conﬁdentiality reasons.) For every trade executed on D2000-1, our data set includes a timestamped record of the transaction price and a bought/sold indicator. The bought/sold indicator allows us to sign trades for measuring order ﬂow. This is a major advantage: we do not have to use the noisy algorithms used elsewhere in the literature for signing trades. One drawback is that it is not possible to identify the size of individual transactions. For model estimation, order ﬂow is therefore measured as the difference between the number of buyer-initiated and sellerinitiated trades.18 The variables in our empirical model are measured hourly. We take the spot rate, as the last purchase-transaction price (DM/$) in hour h, Ph . (With roughly 1 million transactions per day, the last purchase transaction is generally within a few seconds of the end of the hour. Using purchase transactions eliminates bid-ask bounce.) Order ﬂow, Xh , is the difference between the number of buyer- and seller-initiated trades (in hundred thousands, negative sign denotes net dollar sales) during hour h. We also make use of three further variables to measure the state of the market: trading intensity, Nh , measured by the gross number of trades during hour h; price dispersion, sh , measured by the standard deviation of all transactions prices during hour h, and the number of macroeconomic announcements, Ah . These announcements comprise all those reported over the Reuter’s News service that relate to macroeconomic data for the United States or Germany. The source is Olsen Associates (Zurich) (for details, see, e.g., Andersen and Bollerslev 1998). Although trading can take place on the D2000-1 system 24 hours a day, 7 days a week, the vast majority of transactions in the DM/$ take place between 6 am and 6 pm, London time, Monday through Friday. Although the results we report below are based on this subsample, they are quite similar to results based on the 24-hour trading day (as noted below). This subsample still leaves us with vast number of trades, providing us with considerable power to test for effects from portfolio balance.

Are Different-Currency Assets Imperfect Substitutes?

1.3.2

13

The Empirical Model

Our model is speciﬁed with each day split into four trading rounds. We now develop an empirical implementation for examining the model’s implications in hourly data. Let rj ð yh Þ denote the probability that the market will move from round j to j þ 1 between the end of hours h and h þ 1, when the state of the market at the end of hour h is yh .19 Given these transition probabilities, the probability that the market will be in round j at the end of hour h, pj ðYh1 Þ, is deﬁned recursively as pj ðYh1 Þ ¼ rj1 ð yh1 Þpj1 ðYh2 Þ þ ½1 rj ð yh1 Þpj ðYh2 Þ;

ð5Þ

where Yh ¼ f yh ; yh1 ; . . .g denotes current and past states of the market. According to proposition 1, prices change when the market moves from rounds 2 to 3, and from rounds 3 to 4. Let DPh and DRh respectively denote the change in price and the ﬂow of macroeconomic information between the end of hours h 1 and h. With the aid of the probabilities rj ð yh1 Þ and pj ðYh1 Þ, we can derive the probability distribution of hourly price changes as shown in table 1.1. Rows II and III of table 1.1 identify the price change associated with the market moving into round 3 and into round 4 between the end of hours h 1 and h respectively. In the former case, the price change is proportional to order ﬂow during the hour. In the latter, the price change depends on order ﬂow and macroeconomic information during the hour, and a lagged price change DPhk , for k > 0. The length of the lag k equals the number of hours the market spends in round-3 trading before moving to round 4. The probabilities in the right-hand column are complicated functions of rj ð yhl Þ for j ¼ 1; 2; 3; 4, and l > 0 and so depend on the past states of the market, Yh1 ¼ f yh1 ; yh2 ; . . .g (see appendix B for details). In the special case where the probability of moving from round 3 to round 4, r3 ð yh1 Þ, equals one, k must also equal one, and the probabilities simplify to Table 1.1 Distribution of hourly price changes DPh : Hourly price change

Probability

I

0

yI ðYh1 Þ

II

l2 X h

yII ðYh1 Þ

III

l3 X h fDPhk þ dDRh

yIII; k ðYh1 Þ

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M. D. D. Evans and R. K. Lyons

yI ðYh1 Þ ¼ 1 yII ðYh1 Þ yIII; 1 ðYh1 Þ; yII ðYh1 Þ ¼ r2 ð yh1 Þp2 ðYh1 Þ; yIII; 1 ðYh1 Þ ¼ r2 ðyh2 Þp2 ðYh2 Þ: Our empirical model is derived from the distribution of hourly price changes. Speciﬁcally, let Wh ¼ fXh ; Yh1 ; DPh1 ; DPh2 ; . . .g denote the information set spanned by current order ﬂow, past states of the market, and past hourly price changes. The observed hourly price change can be written as DPh ¼ E½DPh j Wh þ hh ;

ð6Þ

where hh is the expectational error in hour h. Since the ﬂow of macroeconomic information in hour h, DRh , is orthogonal to Wh , this error includes DRh . To complete the empirical model, we need the conditional expectation from the distribution of hourly price changes. For the special case noted above where r3 ð yh1 Þ ¼ 1, this expectation is given by E½DPh j Wh ¼ b 1 ðYh1 ÞXh þ b2 ðYh1 ÞDPh1

ð7Þ

and b 2 ðYh1 Þ ¼ with b1 ðYh1 Þ ¼ l2 yII ðYh1 Þ þ l3 yIII; 1 ðYh1 Þ fyIII; 1 ðYh1 Þ. Hourly price-change dynamics can therefore be represented by DPh ¼ b 1 ðYh1 ÞXh þ b2 ðYh1 ÞDPh1 þ hh :

ð8Þ

In the more general case where r3 ðyh1 Þ a 1, the equation for price changes contains more than one lag of past price changes on the righthand side (see appendix B for details). These lags are not statistically signiﬁcant in our data. We therefore focus attention on equation (8), which takes the form of a regression with state-dependent coefﬁcients. 1.3.3

Causality

A common critique of empirical models along the lines of equation (8) is based on the following alternative hypothesis: public information causes positively correlated adjustment in both price and order ﬂow, with no causal relationship between price and order ﬂow themselves. For example, macroeconomic news that is positive for the dollar causes the DM price of a dollar to go up and causes a relative increase in transactions initiated by dollar buyers. (This alternative hypothesis

Are Different-Currency Assets Imperfect Substitutes?

15

is distinct from the reverse causality hypothesis under which price increases cause buyer-initiated transactions—i.e., positive feedback trading. Evans and Lyons 2002b reject the hypothesis that positive feedback trading accounts for the positive correlation between interdealer FX order ﬂow and price changes.) Though intuitively appealing, this hypothesis of correlation without causation is inconsistent with rational expectations. As long as expectations are rational, public news does not produce the positive concurrent correlation between order ﬂow and price changes that one ﬁnds empirically. The reason is because—under rational expectations— public information is impounded in price instantaneously. At the new price, which embeds all the public information, there is no longer motivation for dollar buying relative to dollar selling. True, the change in price level may induce trading (i.e., unsigned volume), due perhaps to portfolio rebalancing, but one would not expect good news for the dollar to produce positive order ﬂow on average (a relative increase in transactions initiated by dollar buyers). Consider the possibility that all market participants do not interpret public macro news the same way (in terms of its implication for the exchange rate). This is a departure from traditional modeling of public information in exchange rate economics. Under this scenario, pricesetting market-makers who need to clear the market need to determine the interpretations of other market participants (which they cannot know a priori, by assumption). How might they learn them? The answer from microstructure theory is that they learn from the sequence of submitted orders over time. In this case, price instantaneously adjusts to the market-maker’s rational expectation of the mean market interpretation, and then goes through a period of gradual adjustment to the sequence of transacted orders. Thus, in this (again, nontraditional) setting, causality in part goes directly from public news to price and in part goes from public news to order ﬂow to price. Though catalyzed by public information, it is not the case that there is no causal relationship between price and order ﬂow. 1.4

Results and Implications

Estimation of our micro portfolio balance model allows us to answer three key questions. First, is there support for portfolio balance in the data? Though existing negative results have led to the view that portfolio balance theory is moribund, past work may suffer from low

16

M. D. D. Evans and R. K. Lyons

power (as noted in the introduction). Second, do trades have both temporary and persistent portfolio balance effects? Third, does the price impact of trades depend on the state of the market? This last question is central to identifying states in which intervention is most effective. 1.4.1

Model Estimates

Our estimation strategy proceeds in two stages. First, we estimate a constant-coefﬁcient version of equation (8) and test for state dependency in the coefﬁcients. As we will see, the coefﬁcients in this model accord with portfolio balance predictions in terms of sign and signiﬁcance. The estimated coefﬁcients also accord with our model in that they are indeed state dependent. This latter result motivates the second stage of our strategy, namely, estimation of the precise nature of this state dependency (using nonparametric kernel regressions). Table 1.2 presents results from the ﬁrst stage of our estimation: the constant-coefﬁcient model. Both contemporaneous order ﬂow Xh and lagged price change DPh1 —the two core variables in our model— have the predicted signs and are signiﬁcant. (Though constants do not arise in our derivation, for robustness we also estimate the model with constants; they are insigniﬁcant.) A coefﬁcient on order ﬂow Xh of 0.26 translates into price impact of about 0.44 percent per $1 billion.20 (The magnitude is similar when we use log price change as the dependent variable, as can be seen in table 1.4 of the appendix.) A coefﬁcient on lagged price change of 0.2 implies that 1/1.2, or 83 percent of the impact effect of order ﬂow persists indeﬁnitely. Thus we are ﬁnding evidence of both types of portfolio effect noted in row I: the temporary portfolio balance channel and the persistent portfolio balance channel. Though the temporary channel is clearly present, the permanent channel accounts for the lion’s share of order ﬂow’s price effect (it is also, we would argue, the more important economically). As pointed out by the referee, the temporary channel implies proﬁtable trading strategies, at least at high frequencies, so it is useful to consider just how proﬁtable this would be given our estimates and given realistic transaction costs. (Of course, the reason these temporary price effects arise in the model is that they represent compensation to dealers for bearing intraday risk, i.e., they are risk premia. Hence profitability is not the only criterion for judging their realism. Nevertheless, if the implied proﬁts are large, then the idea that they represent a premium for bearing risk becomes less tenable.) As a back-of-the-envelope

Are Different-Currency Assets Imperfect Substitutes?

17

Table 1.2 Estimates of micro portfolio balance model (constant coefﬁcients), DPh ¼ b 1 Xh þ b 2 DPh1 þ hh Diagnostics Xh I

0.258

DPh1

DPh2

0.203

(13.205) II

Xh1

R2 0.212

0.225

0.173 0.061

0.437

0.071 0.020

; : bð1 þ DÞ D a 0: ð22Þ Figures 6.2 and 6.3 provide a geometric description of the determination of the bond price under demand rationing. At ~s, young consumers are completely rationed. For D > 0, two situations are possible, one with and without complete rationing of young consumers. At s1 , young consumers are completely rationed and invest their entire net income in the bond market. At s2 , they are only partially rationed and invest their remaining income after consumption. The equilibrium bond price in all possible cases is determined by the function

Endogenous Business Cycles and Exchange Rate Volatility

179

Figure 6.3 Bond market equilibrium for D > 0

8 ð1 cðR e ÞÞð1 taxÞðbd þ xE þ gÞ > > ; y d a yðaÞ; > e Þð1 taxÞÞÞ > bðtax þ Dð1 cðR > > > > < yðaÞð1 taxÞ g þ bd þ Ex tax yðaÞ y d > yðaÞ; ; ; s ¼ SðvÞ :¼ min > bð1 þ DÞ bD D > 0; > > > > > yðaÞð1 taxÞ > y d > yðaÞ; > : ; bð1 þ DÞ D a 0: ð23Þ Together with the results from the determination of output and employment one obtains the following lemma: Lemma 1 Given the parameters ðg; tax; d; D; Lmax ; EÞ, any temporary state vector v :¼ ða; b; x; R e Þ g 0 induces a unique positive temporary feasible allocation ð y; LÞ given by equations (18) and (19) and a positive market clearing bond price by equation (23), if D > 1. The functions Y; L; S are continuous and piecewise differentiable functions of the state vector v. Figure 6.4 depicts the partition of the state space into the regions of the three regimes. Its characteristics can be derived from equations (18), (19), and (23) directly. The area of the possible Keynesian unemployment regime (marked K) is deﬁned by all values ðb; a; xÞ A Rþ3

V. Bo¨hm and T. Kikuchi

180

Figure 6.4 Partition of state space into three regimes

behind the plane bcde and below the surface abe. Above the surface abe and above the plane befgh lie all states of the classical unemployment regime C, while below the plane befgh are all repressed inﬂation states of the regime I. 6.3

Dynamics and Expectations Formation

Existence and uniqueness of temporary feasible states provide the basis for a well deﬁned forward recursive structure deﬁning the dynamic development of the economy over time. This requires the description of the dynamical evolution of all state variables of a dynamical system in the mathematical sense. The dynamic equations for the real wage and real bonds are derived ﬁrst. The dynamics of the exchange rate and the expectations processes are discussed afterward. 6.3.1

Adjustment of Prices and Wages

Any temporary state vector v ¼ ðb; a; x; R e Þ uniquely determines the state of the economy for given parameters which in most cases is not

Endogenous Business Cycles and Exchange Rate Volatility

181

the Walrasian equilibrium. This means that quantity constraints occur on the labor and/or on the commodity market which lead to price and/or wage adjustment at the end of the period according to the size of rationing. The adjustments are assumed to follow the so-called law of supply and demand. This means that if supply exceeds demand in a market, its price goes down, and vice versa. One possible formulation of this principle uses the deﬁnition of disequilibrium signals for the labor market s l A ½1; 1 and for the goods market sc A ½1; 1, measuring the sign and the size of rationing. Their dependence on the temporary state vector v ¼ ðb; a; x; R e Þ is described by two functions s l and s c : 4 ! ½1; þ1 : s c ¼ s c ðvÞ; s c : Rþþ 4 ! ½1; þ1 : s l ¼ s l ðvÞ: s l : Rþþ

The signs of the signals correspond to the signs of the respective excess demand functions. On the basis of any pair of disequilibrium signals ðstc ; stl Þ in period t, a price adjustment function P and a wage adjustment function W are deﬁned to obtain P : ½1; 1 ! ð1; þyÞ;

ptþ1 ¼ 1 þ Pðstc Þ; pt

ð24Þ

W : ½1; 1 ! ð1; þyÞ;

wtþ1 ¼ 1 þ Wðstl Þ: wt

ð25Þ

P and W are continuous, strictly monotonically increasing, and satisfy Wð0Þ ¼ Pð0Þ ¼ 0. Together with the signaling function they induce two mappings for price P :¼ P s c and wage W :¼ W s l adjustment: ptþ1 ¼ pt ½1 þ Pðs c ðvt ÞÞ ¼ pt ð1 þ Pðvt ÞÞ;

ð26Þ

wtþ1 ¼ wt ½1 þ Wðs l ðvt ÞÞ ¼ wt ð1 þ Wðvt ÞÞ:

ð27Þ

If one uses a linear adjustment rule, too much instability of interior steady states with frequent divergence to the boundary is created. The following nonlinear functional form of price and wage adjustment will be used in the numerical simulations below. ! 8 > yðaÞ eff y > > if y d > y > > y y > > otherwise : k tanh y

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182

with 0 < g < 1 and 0 < k < 1 as adjustment speeds and yðaÞ eff as the modiﬁed effective aggregate demand. This is deﬁned as yðaÞ eff :¼ yðaÞð1 taxÞcðR e Þ þ bðs þ dÞ þ g þ Ex;

ð29Þ

satisfying y eff ðaÞ > yðaÞ. Given the disequilibrium signals the tangent hyperbolic function delivers a symmetric price and wage adjustment downward and upward with a maximum derivative equal to one. If K or K X I holds, excess supply in the commodity market gives a downward pressure for the price. If y d ¼ y ¼ y, meaning if C X K holds, the commodity market is in equilibrium and there is no price adjustment. In all other cases, meaning if I, C or C X I holds, there is excess demand in the commodity market and an upward pressure for the price. Apart from the situation when y d ¼ y max < y the signal functions s l ðvÞ and s c ðvÞ are continuous.3 Applying the same principle to the labor market, one obtains 8 L Lmax > > if Lmax > L; > l tanh < Lmax ð30Þ WðvÞ ¼ > L L > > otherwise; : m tanh L with 0 < l < 1 and 0 < m < 1 as adjustment speeds. If I or K X I holds, excess demand in the labor market gives an upward pressure for the wage rate. If Lmax ¼ L ¼ L; that is, if C X I holds, the labor market is in equilibrium and there is no wage adjustment. In all other cases (C, K or C X K) there is excess supply in the labor market and a downward pressure for the price. Together the two adjustment functions imply the dynamic equation for the real wage atþ1 ¼ at

1 þ Wðvt Þ : 1 þ Pðvt Þ

ð31Þ

The assumptions concerning bond market equilibrium imply that total ﬁnal bond holdings by young consumers in period t are equal to Btþ1 ¼ Bt ð1 þ DÞ. Therefore the dynamics of real bonds are given by btþ1 ¼ bt

1þD : 1 þ Pðvt Þ

ð32Þ

Endogenous Business Cycles and Exchange Rate Volatility

6.3.2

183

Uncovered Interest Parity and Expectations Formation

One of the interpretations of the uncovered interest parity (UIP) is that of a condition of expected no arbitrage to hold in perfect international capital markets. When applying the UIP to a dynamic model, it is important to take proper account of the sequential structure of the available information and of expectations formation. Let r f denote the nominal rate of return for holding foreign assets. Under the UIP expected returns on domestic and foreign capital markets are assumed to be the same. When purchasing foreign bonds in t, the amount of domestic investment has to be converted at the spot exchange rate Xt into the foreign currency. One period later the principle and the interest have to be reconverted into domestic currency at the future spot exchange rate Xtþ1 . Thus, under expected no arbitrage, the expected returns denominated in either currency have to be the same, implying the following form of the UIP, 1 þ rt;e tþ1 ¼ ð1 þ r f Þ

Xt;e tþ1 : Xt

ð33Þ

Rearranging terms one obtains an equation determining the nominal exchange rate Xt ¼ Xt;e tþ1

1 þ rf 1 þ rt;e tþ1

ð34Þ

as a function of expectations formed prior to the realization of the current exchange rate. Thus the sequential structure of the expectations formation implicit in the condition of the UIP reveals that the dynamic equation determining the actual exchange rate is a function of expectations alone independent of the previous actual exchange rate. Moreover, when forming expectations for t þ 1 agents can use observable information only up to t 1, implying a so called ‘‘expectational lead’’ for the functional relationship.4 Figure 6.5 shows the timing of expectations and of exchange rate determination under UIP. In most models imposing the UIP, it is assumed that agents have perfect foresight with respect to the exchange rate, a property that can be guaranteed here by deriving an explicit perfect forecasting rule. Considering the timing of expectations formation, the perfect foresight e property implies that the difference between the forecast Xt1; t made in

V. Bo¨hm and T. Kikuchi

184

Figure 6.5 Timing of expectations and exchange rates under UIP

t 1 and the actual value Xt must be equal to zero. Put differently, one must have Xt;e tþ1

1 þ rf e Xt1; t ¼ 0: 1 þ rt;e tþ1

Solving for Xt;e tþ1 yields the unique explicit functional form of the perfect predictor c for the exchange rate: e e Xt;e tþ1 ¼ c ðXt1; t ; rt; tþ1 Þ :¼

1 þ rt;e tþ1 e Xt1; t : 1 þ rf

ð35Þ

Therefore the assumption of perfect foresight together with UIP requires that the prediction of the exchange rate is a function of previous predictions and not of previous exchange rates. In other words, the prediction of the exchange rate today guarantees that the prediction of yesterday will be correct.5 As for the exchange rate, one could ask whether it is possible to derive a perfect predictor as well for the expectations formation for the domestic rate of return r e as well as for the inﬂation rate y e . In principle, this might be possible using the techniques from Bo¨hm and Wenzelburger (2004). However, at this stage an explicit solution for a perfect predictor cannot be calculated due to the nonlinearities of the equations and to the dependence on the state variables involved. Therefore an adaptive (but not perfect) forecasting rule will be used for the domestic rate of return and for the inﬂation rate. Observe, however, that the resulting dynamics will, in general, depend on the choice of the adaptive scheme. Let st1 denote the purchase price for bonds, st the selling price, and d the dividend payment. Then the rate of return on domestic bonds effective in period t is given by

Endogenous Business Cycles and Exchange Rate Volatility

rt ¼

d þ st 1: st1

185

ð36Þ

The forecasting rule for the rate of return is assumed to follow the simple adaptive principle rt;e tþ1 ¼ rt1 , inducing a predictor cr of the form rt;e tþ1 ¼ cr ðst1 ; st2 Þ :¼

d þ st1 1: st2

ð37Þ

Notice that two special features are present in any adaptive scheme using past data. First, resulting from the sequential structure, the prediction rt;e tþ1 has to be made prior to the realization of the bond price st , implying that the value for rt is not available as information. Second, the deﬁnition of rt1 implies an additional delay of order two with respect to bond prices, thus increasing the dimensionality of the dynamical system. Similarly assume that the adaptive scheme for prices deﬁnes the expected inﬂation rate yt;e tþ1 :¼ pt;e tþ1 = pt 1 for period t þ 1 as a function of the last t b 1 inﬂation rates: yt;e tþ1 ¼ Cðyt ; . . . ; ytt1 Þ

with ytkþ1 :¼

ptkþ1 1; ptk

k ¼ 1; . . . ; t: ð38Þ

The function C : ð1; yÞ t ! ð1; yÞ is assumed to be continuous satisfying the following property: Cðy; y; . . . ; yÞ ¼ y

Ey > 1:

ð39Þ

The class of such functions includes most of the commonly used adaptive prediction mechanisms with ﬁnite memory. 6.3.3

Dynamical System

It is apparent that the evolution of the economic model will be governed by an interaction of the adjustment equations with the expectations formation rules inducing two strong expectations feedbacks. These are decisive in the stability and in the long-run behavior of the economy. Combining the dynamic equations for the domestic economy with the appropriate mappings for the expectations processes c ; cr , and C for the expected inﬂation rate, the expected interest rate, and for the exchange rate

V. Bo¨hm and T. Kikuchi

186

e e Xt;e tþ1 ¼ c ðXt1; t ; rt; tþ1 Þ;

rt;e tþ1 ¼ cr ðst1 ; st2 Þ; yt;e tþ1 ¼ Cðyt ; . . . ; ytt1 Þ; Rt;e tþ1 :¼

ð40Þ

1 þ rt;e tþ1 ; 1 þ yt;e tþ1

one obtains as the vector of state variables e vt ¼ ðbt ; at ; xt1; t ; st1 ; st2 ; yt ; . . . ; ytt1 Þ e e where xt1; t ¼ Xt1; t =pt . Then the dynamical system is deﬁned by the following mapping:

btþ1 ¼ Bðvt Þ :¼

bt ð1 þ DÞ ; 1 þ Pðvt Þ

atþ1 ¼ Aðvt Þ :¼ at xt;e tþ1 ¼ Fðvt Þ :¼

1 þ Wðvt Þ ; 1 þ Pðvt Þ

e xt1; 1 þ rt;e tþ1 t ; 1 þ Pðvt Þ 1 þ r f

ð41Þ

st ¼ Sðvt Þ; ytþ1 ¼ 1ðvt Þ :¼ Pðvt Þ: The vector of past bond prices and past inﬂation rates ðst1 ; st2 ; yt ; . . . ; ytt1 Þ is just shifted by one time step. Therefore the dynamic e behavior of the economy is described by a sequence fbt ; at ; xt1; t ; st1 ; T st2 ; yt ; . . . ; ytt1 gt0 implying that the state space of the dynamical system equal is a subset of R 5þt . The system exhibits a highly nonlinear structure. This arises not only from the many nonlinear functional relationships but also from the regime switching that occurs induced by the temporary state variables. In the case of a Cobb-Douglas utility function, which implies a constant marginal propensity to consume with no domestic expectations feedback, the dynamical system has dimension ﬁve with a one-period delay in the bond price. Figure 6.6 illustrates the sequential structure when there is no expectations feedback on domestic consumption, where the solid arrows identify the individual mappings of (41). Figure 6.7 illustrates the time one map of the dynamical system (41). The vertical arrows indicate that the expectation of inﬂation rates, of interest rates, and of exchange rates at time t

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Figure 6.6 Sequential structure of prices, exchange rates, and expectations under UIP

Figure 6.7 Structure of time one map

for period t þ 1 are formed on the basis of past realizations of the economic variables. On the other hand, the allocation and the corresponding rationing situation at t depend on these forecasts. It is obvious that the system possesses a lag structure: the bond price, the inﬂation rate, and the expectation of the exchange rate inﬂuence the actual market process at least over two periods. 6.3.4

Stationary States

Due to the high dimensionality of the dynamical system (41), it is apparent that a full analytic characterization of its stationary states

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and their stability properties may be beyond reach. Fortunately, many features for the associated model of a closed economy are well understood (see Bo¨hm, Lohmann, and Lorenz 1997 and Kaas 1995) and some of them carry over directly to the small open economy case, as those stated in the next lemma. Note that all forecasting rules of the model imply perfect foresight in steady states. Lemma 2 Given a feasible list of the parameters ðg; tax; D; r f ; Lmax ; EÞ of the system (41), let ðb; a; y; s; xÞ g 0 denote a stationary state with perfect foresight. Then: 1. 1 < y < 0 if and only if D < 0, and the state is of the Keynesian unemployment type K, 2. y ¼ 0 if and only if D ¼ 0, and the state is of the Walrasian type W, 3. y > 0 if and only if D > 0 and the state is of the repressed inﬂation type I. In other words, the sign of the policy parameter D determines uniquely the type of an interior long-run disequilibrium state independent of the speciﬁc functional forms and the mechanisms. This is one of the fundamental insights into the structural features of this class of models. As a consequence this implies among other things that the local stability properties of any stationary state are regime speciﬁc.6 6.4

Numerical Analysis

For the numerical analysis it is necessary to use speciﬁc functional forms for the intertemporal preferences and for the technology as the ones introduced above. Those have proved to generate tractable results for the closed economy model. Therefore, for the remainder of this chapter, consider the economy with intertemporal preferences of the CES type (1) with r ¼ 0, isoelastic production (7), and with hyperbolic price and wage adjustments of the form (28) and (30). The assumption on preferences eliminates the expectations feedback on domestic consumption implying a constant propensity to consume and no role for the inﬂation predictor C. Therefore the dimension of the dynamical system is ﬁve with the state variables ðb; a; s2 ; s1 ; x e Þ. Even for this special case a full derivation of the eigenvalues when D 0 0 has not yet been obtained. The following partial results and numerical simulations are designed to demonstrate that

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1. there is wide (robust) conﬁrmation of excess volatility of exchange rates compared to domestic real variables in the nonperiodic as well as in the periodic case, 2. the closed economy exhibits period doubling bifurcations for some large sets of parameters while for other ranges of parameters fold bifurcations (saddle-point properties) seem to be the cause of the nonperiodic ﬂuctuations, 3. there is a general overall loss of stability of the domestic economy after introducing foreign demand. 6.4.1

Bifurcation Analysis

Table 6.1 provides a complete list of all parameters used. For this analysis the numerical investigations were restricted to the relationship Table 6.1 Standard parameter set Parameter

Description/origin

Value

g

Adjustment speed pt

0.2

k

Adjustment speed pt

0.2

l

Adjustment speed wt

0.2

m

Adjustment speed wt

0.2

g

Government demand

0.3

tax

Income tax rate

0.3

D

New issues of bonds

0.05

d

Nominal interest

0.01

A

Scaling parameter

1

b

Elasticity of production

Lmax

Constant labor supply

1

d r

Time discount factor Parameter of substitution

1 0

t

Expectational lag

rf E

Foreign rate of return Foreign demand for goods

0.01 0.1

b0

Initial real bond

0.6

a0

Initial real wage

0.6

s0

Initial bond price

0.75

x0e

Initial real expected exchange rate

0.5

Different values

10

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between the production elasticity and the adjustment speeds, since this unveils already some new and important qualitative features. For all time series results the same values were used for the adjustment speeds in analyzing the inﬂuence of four different values of the labor elasticity. Openness and Loss of Stability It is known from the closed economy analogue with money only that the occurrence of endogenous business cycles and bifurcations in such non-Walrasian models is caused by a combination of the adjustment speeds of prices and wages and the labor demand elasticity given by 1=ðB 1Þ (see Kaas 1995). This elasticity becomes large for values of the production elasticity B close to one. The same phenomenon occurs here as well, but with some substantial differences to the closed economy. When E > 0, unstable steady states and non periodic behavior predominate for the open economy where the closed economy would exhibit stable steady states for the same set of parameter values. This is caused primarily by the perfect predictor in conjunction with the UIP assumption. Taken by itself ﬁrst-order effects of the exchange rate tend to induce a derivative equal to plus one near the steady state equivalent to a saddle type property. If second-order effects are positive there will be at least one root larger than one. This is precisely the reason why in the original model by Dornbusch (1976) the steady state is a saddle under the UIP hypothesis since there secondary effects are ignored. Proposition 1 There exists a large critical set of parameter values ðg; tax; D; r f ; Lmax Þ for which the stationary states of the system (41) undergo a period doubling bifurcation when E ¼ 0. When E > 0, there exists a large open set of parameter values such that the stationary states are locally unstable and the system displays ﬁnite as well as complex cycles. Figure 6.8 shows a distinctive destabilizing effect of international trade under UIP. While for the closed economy ﬁgure 6.8a the typical period doubling bifurcation and endogenous cycles occur only for very high values of B, ﬁgure 6.8b shows a large range of low B for which the open economy exhibits endogenous cycles. For high values the bifurcation scenarios appear to be very similar. Figure 6.9 provides evidence of the robustness of the bifurcation scenario of ﬁgure 6.8 in the form of a so-called cyclogram over B and

Endogenous Business Cycles and Exchange Rate Volatility

Figure 6.8 Bifurcation diagram for a

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Figure 6.9 Cyclogram for a

adjustment speeds g ¼ k ¼ l ¼ m simultaneously. A cyclogram is a qualitative multidimensional bifurcation diagram. For each pair of parameters ðB; g ¼ k ¼ l ¼ mÞ the respective color assignment indicates the order of the cycle of the limiting behavior of the system. According to the codes given in ﬁgure 6.10 the color ‘‘yellow’’ indicates nonperiodic limiting behavior. One easily veriﬁes the features of the bifurcation diagram ﬁgure 6.8 by traversing horizontally at the value g ¼ k ¼ l ¼ m ¼ 0:2 in ﬁgure 6.9. Figure 6.8b and ﬁgure 6.9b show that nonperiodic behavior predominates when E > 0. Most important,

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Figure 6.10 Color code for cyclogram

however, the two subﬁgures reveal that for the closed economy the production elasticity alone determines the bifurcation points, whereas for the open economy there is a stability trade-off (nonvertical boundary of the yellow/red region) between the elasticity of production and the adjustment speeds. Exchange Rate Volatility ^t :¼ Xtþ1 =Xt denote the growth ^ t :¼ wtþ1 =wt , p^t :¼ ptþ1 = pt , and X Let w factors of wages, prices, and of the nominal exchange rates respectively. The time series in ﬁgure 6.11 show the typical comovements of the growth factors of the domestic variables, which move procyclically with the bond price as well. B ¼ 0:5 induces a very long ﬁnite cycle, while B ¼ 0:7 shows a quasi-periodic or complex time series. Notice that the exchange rate ﬂuctuates substantially more than the other variables. In addition ﬁgures 6.12 and 6.13 and table 6.2 provide statistical information of the long-run behavior, conﬁrming the higher volatility of the exchange rate by a distinctively higher standard deviation. For an investigation of the bifurcation effects induced by the elasticity of production we consider two further cases. For B ¼ 0:958 the limiting behavior is described by a complex (nonperiodic) orbit with time series given in ﬁgure 6.14a, while for B ¼ 0:96 the limiting behavior of the economy is a ﬁnite cycle of order three as one observes in ﬁgure 6.14b. These ﬁgures portray typical time series of the rates of change showing very clearly the higher volatility of the exchange rate as compared to the domestic variables, especially the price level. Figures 6.15, 6.16, and table 6.3 supply additional evidence of the distinct volatility ^ -p^-space, the features by showing a projection of the attractor into the X marginal densities (histograms) of the exchange rate, of the rate of inﬂation, as well as a table of descriptive statistics. These indicate that: price and exchange rate changes do not reveal a clear cut long-run correlation;

194

Figure 6.11 ^ ; p^, and w ^ for relatively low values of B Time series of X

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Figure 6.12 ^ -^ Attractor plots in X p space for relatively low values of B

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196

Figure 6.13 ^ for relatively low values of B Density plots of X

Table 6.2 ^ ; p^, and w ^ for relatively low values of B Descriptive statistics X B ¼ 0:5

B ¼ 0:7

Variable

Mean

Standard deviation

Mean

Standard deviation

^ X p^

1.0532

0.0831

1.0514

0.0551

1.0504

0.0306

1.0513

0.0177

^ w

1.0504

0.0299

1.0501

0.0171

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Figure 6.14 ^ ; p^, and w ^ for high values of B Time series of X

197

198

Figure 6.15 ^ -^ Attractor plots in X p space for high values of B

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Figure 6.16 ^ and p^ for B ¼ 0:958 Density plots of X

Table 6.3 ^ ; p^, and w ^ for high values of B Descriptive statistics X B ¼ 0:958

B ¼ 0:96

Variable

Mean

Standard deviation

^ X p^

1.0670

0.1956

0.7669

1.1451

0.4689

0.3281

1.0500

0.0072

0.1203

1.0501

0.0183

0.6365

^ w

1.0527

0.0752

0.2174

1.0558

0.1076

0.6422

Skewness

Mean

Standard deviation

Skewness

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Figure 6.17 ^ and p^ for B ¼ 0:958 Cumulative marginal distribution function of w

the standard deviation of the growth factor of the exchange rate is roughly twenty-ﬁve times as large as that of domestic prices;

the skewness of the exchange rate and of prices are positive while the skewness of wages is negative.

The calculation of the associated cumulative marginal distribution ^ Þ and Fð p^Þ yields the two curves depicted in ﬁgure 6.17. functions Fðw These curves indicate that there is always a positive inﬂation and that the probability of increasing wage rate is almost 0.6. Therefore about

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60 percent of the simulated trajectory is located in the repressed inﬂation regime, I (i.e., with full employment and demand rationing), while the others will be of the Keynesian and of the classical type. Finally, there seems to be a positive correlation between domestic prices and wages for relatively low values of B and a negative correlation for higher values (see ﬁgure 6.18 for B ¼ 0:5; 0:7; 0:958; 0:96). The higher variance for wages relative to that for prices is linked to the high value of B. 6.5

Conclusions

The results of this chapter provide a ﬁrst explicit account of possible dynamics of a small open economy in its relationship to perfect international capital markets under the UIP hypothesis. They show that the structural nonlinear relationships between asset markets and real markets can generate permanent endogenous ﬂuctuations. These are the result of the interaction of a strong expectations feedback with sluggish domestic price and wage adjustments under fully competitive/ price-taking behavior in all markets. No elements of market imperfections are present. Moreover the cyclical recurrence arises within a deterministic model when no random perturbations are present. The numerical analysis shows examples which conﬁrm some typical empirically observed high volatility of the nominal exchange rate relative to that of domestic variables. This result directs us closer toward a possible answer to one of the pricing puzzles. The model demonstrates that the channels between domestic real markets and competitive international ﬁnancial markets induce clear dynamic correlations between real and monetary phenomena whose qualitative properties depend heavily on particular structurally given values of the domestic economy, especially the elasticity of production. It has to be taken as one of the surprising ﬁndings that the introduction of competitive international capital markets within this class of models under the UIP hypothesis induces strong destabilizing forces often making stable regular periodic behavior impossible. With these results further research should investigate the structural relationships between domestic macroeconomic variables and international capital markets as well as its policy implications. Moreover a more detailed analytical investigation of the stability properties of this class of dynamic models will identify better the sources of the volatility and of the ﬂuctuations.

202

Figure 6.18 ^ -^ Attractor plots in w p space

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Endogenous Business Cycles and Exchange Rate Volatility

Figure 6.18 (continued)

203

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Notes The research for this chapter is part of the project Endogene stochastische Konjunkturtheorie von Realgu¨ter—und Finanzma¨rkten supported by the Deutsche Forschungsgemeinschaft under contract number Bo. 635/9–1,3. We are indebted to J. Wenzelburger and T. Pampel for useful discussions and M. Meyer for computational assistance. We acknowledge discussions with A. Fo¨rster at the initial stage of the project. 1. The model of a closed economy with instantaneous bond market clearing possesses essentially the same temporal and dynamic structure as the one with money alone. 2. The parameter B chosen for the speciﬁc form should not be confused with the nominal stock of bonds denoted Bt . 3. Note that if we assume the price adjustment function to be continuous at y d ¼ y max < y , there is no price adjustment in commodity market even though the commodity market is not in equilibrium. To avoid this, we assume that s l ðvÞ > s c ðvÞ in this particular case. See Bo¨hm, Lohmann, and Lorenz (1997) for details. 4. Such expectational leads with independence occur in a natural way in many intertemporal equilibrium models when the sequential structure of the expectations formation process is made explicit. 5. This special property of the perfect predictor follows directly from the two structural properties of the exchange rate mapping (34), the presence of an expectational lead and of the independence of the previous actual exchange rate (for a general treatment, see Bo¨hm and Wenzelburger 2004). 6. Note that there is no stationary state of the classical type C since the real wage a always decreases in that regime.

References Barro, R. J., and H. I. Grossman. 1971. A general disequilibrium model of income and employment. American Economic Review 61: 82–93. Benassy, J.-P. 1975. Neo-Keynesian disequilibrium theory in a monetary economy. Review of Economic Studies 42: 503–23. Betts, C., and M. B. Devereux. 2000. Exchange rate dynamics in a model of pricing-tomarket. Journal of International Economics 50: 215–44. Bo¨hm, V. 1993. Recurrence in Keynesian macroeconomic models. In F. Gori, L. Geronazzo, and M. Galeotti, eds., Nonlinear Dynamics in Economics and Social Sciences. Heidelberg: Springer-Verlag. Bo¨hm, V., M. Lohmann, and H.-W. Lorenz. 1997. Dynamic complexity in a Keynesian macroeconomic model—Revised version. Discussion Paper 288. Department of Economics, University of Bielefeld. Bo¨hm, V., and J. Wenzelburger. 2004. Expectational leads in economic dynamical systems. In International Symposia in Economic Theory and Econometrics, vol. 14. Amsterdam: Elsevier, pp. 333–61.

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Chari, V., P. Kehoe, and E. McGrattan. 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69: 533–63. Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84(6): 1161–76. Kaas, L. 1995. Steady states and local bifurcations in a dynamic disequilibrium model. Discussion Paper 300. Department of Economics, University of Bielefeld. Kollmann, R. 2001. The exchange rate in a dynamic-optimizing business cycle model with nominal rigidities: A quantitative investigation. Journal of International Economics 55: 243–62. Lane, P. R. 2001. The new open economy macroeconomics: A survey. Journal of International Economics 54: 235–66. Malinvaud, E. 1977. The Theory of Unemployment Reconsidered. Oxford: Blackwell. Mundell, R. 1968. International Economics. New York: Macmillian. Neary, J. P. 1990. Neo-Keynesian macroeconomics in an open economy. In F. van der Ploeg, ed., Advanced Lectures in Quantitative Economics. New York: Academic Press. Obstfeld, M., and K. Rogoff. 1995. Exchange rate dynamics redux. Journal of Political Economy 103: 624–60. Obstfeld, M., and K. Rogoff. 2001. The six major puzzles in international macroeconomics: Is there a common cause? In B. S. Bernanke and K. Rogoff, eds., NBER Macroeconomics Annual 2000, Cambridge: MIT Press. Rogoff, K. 1996. The purchasing power parity puzzle. Journal of Economic Literature 34: 647–68. Rogoff, K. 1998. Perspectives on exchange rate volatility. In M. Feldstein, ed., International Capital Flows. Chicago: University of Chicago Press. Svensson, L. E. O., and S. Wijnbergen. 1989. Excess capacity, monopolistic competition, and international transmission of money disturbances. Economic Journal 99: 785–805.

7

The Euro, Eastern Europe, and Black Markets: The Currency Hypothesis Hans-Werner Sinn and Frank Westermann

Speculating with the euro has been disappointing for many professional investors because the movements of the exchange rate did not seem to follow conventional wisdom. The euro declined when the US economy went into recession, and it began to rise when the European stock marked slumped in early 2002. In this chapter we elaborate on an explanation that one of us had suggested in two newspaper articles.1 According to this explanation the euro weakened before the physical currency conversion because holders of black money and eastern Europeans ﬂed from the old European currencies, and it strengthened thereafter because these groups of money holders developed a new interest in the euro.2 Although we regard an episode in economic history, we also attempt to contribute to the theory of the exchange rate by explicitly introducing currency stocks in addition to interest-bearing assets in the international portfolio of wealth owners. The inclusion of currency stocks is a simple, though uncommon, extension of the portfolio balance approach. It leads to an explanation for the negative correlation of the stock of deutschmarks in circulation and the value of the deutschmark, which Frankel (1982, 1993) once called the ‘‘mystery of the multiplying marks.’’ Also, by this means, we can modify traditional interpretations of the portfolio balance approach, leading to new kinds of predictions for the exchange rate. By the portfolio balance approach, it is often argued that the exchange rate is the relative price of interest-bearing assets and thus reﬂects the proﬁtability of the economies involved. Given the stocks of these assets, an increase in the proﬁt expectations for US ﬁrms, for example, implies a change in the desired composition of the portfolio in the direction of US assets. Since the composition of the portfolio cannot

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change in the short run, the dollar appreciates until any preference for portfolio restructuring in the aggregate disappears. The problem with this interpretation is not only that it no longer ﬁtted when the US slump began in 2000 or when European share prices fell, but also that it abstracts from the role of currency in the portfolios of international investors. After all, the exchange rate is the relative price of two currencies rather than shares, and shares have their own prices, which are quoted instantaneously at the stock exchange. When share prices are ﬂexible, a proﬁt or demand based portfolio interpretation cannot easily explain the exchange rate because there are two prices for shares, one of which seems to be redundant. If, for example, the proﬁt expectations of the new economy are captured by the Nasdaq, there is no need for the price of the dollar to capture them too. To determine the exchange rate in the presence of ﬂexible share prices, other assets whose prices are not ﬂexible are required. In the formal model derived below, interest-bearing assets whose rates of return are controlled by a central bank via passive interventions and money balances whose rates of return are ﬁxed at a level of zero are considered in addition to stocks. We use this model to develop a new theory of the exchange rate that we call the ‘‘currency hypothesis.’’ This is because we see the exchange rate basically as the ratio of marginal utilities of money holding. By the currency hypothesis we are able to explain the startling empirical development of the euro exchange rate with a changed demand for money balances. It is well known that the traditional portfolio balance model, which does not contain national money balances, has been relatively unsuccessful in explaining the exchange rate (Taylor 1995). Our version of the portfolio balances model reconciles the theory with the development of different exchange rates. In particular, we use it to explain the development of the deutschmark–dollar exchange rate in the period from the fall of the Iron Curtain to the physical introduction of the euro. It is this period that is identiﬁed by a unique historical experiment that creates huge shifts in the demand for deutschmarks. 7.1

Eurosclerosis, New Economy, and the Euro

To detect the ﬂaw of traditional exchange rate explanations it is useful to start with the development of the euro. Figure 7.1 depicts the time path of the euro in terms of dollars from 1990 to July 2002. A synthetic

The Euro, Eastern Europe, and Black Markets

209

Figure 7.1 The development of the euro. Exchange rates are monthly data, while PPPs are given at an annual frequency. Different PPPs are computed with respect to the different consumption baskets in the United States, the OECD, and Germany. The latest data point is from July 1, 2002, with a value of 0.989 for the euro. (Sources: Federal Reserve Bank of St. Louis, Economic and Financial database, www.stls.frb.org/fred/; March 2002, and CESifo homepage, www.cesifo.de.)

euro was constructed for the years before 1999 by way of an ofﬁcial ﬁnal exchange rate with the deutschmark. The diagram also shows the purchasing power parity (PPP) in accord with OECD, US, and German commodity baskets. As the ﬁgure shows, the euro was strong, hovering around the upper PPP bound, until 1996. From 1997 onward it began a decline only to recover in February 2002, which was the month when the conversion of the old euro currencies into the physical euro was completed. Many reasons for the long period of decline in the value of the euro are given in the literature, including labor market rigidities,3 the European welfare net,4 the Kosovo war,5 Italy’s ability to violate the Maastricht rules,6 the excellent growth performance of the US economy,7 and the initially high US interest rates.8 However, the most frequent argument, which also underlies some of the media assessments, is the high volume of capital ﬂows into the United States in recent years, in particular, the high volume of direct investment ﬂowing into the new American economy.9 We call this the economic prosperity view. As ﬁgure 7.2 shows, capital ﬂows into the United States were huge in the 1990s, and they have continued to increase until 2002, reaching

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Figure 7.2 Capital imports into the United States and current account deﬁcit. FDI ¼ Foreign direct investment. The current account is deﬁned as the sum of the capital account and the balance of payments (which is near 0 in the United States). The capital account is the sum of net direct investment, net portfolio investment and other investment. Other investment includes international credit and repayments of credits, participation of governments in international organizations and international real estate purchases. (Source: IMF, International Financial Statistics, CD-ROM, March 2001.)

a level of more than 4 percent of US GDP. In most years the capital ﬂow was predominantly portfolio rather than direct investment, but in 1998 and 1999 the direct investment was also substantial, peaking at about a third of total US capital imports. In view of the size of the US capital imports it is understandable that many observers have attributed the strength of the dollar to the prosperous investment opportunities in the new American economy, and in contrast to the meagre outlook for an apparently desolate Europe suffering from a socalled Eurosclerosis. However, there are two problems with this interpretation: a possible confusion between supply and demand and a theoretical mistake in the reasoning underlying the economic prosperity view. Let us consider these problems in more detail. The economic prosperity view implicitly uses the traditional portfolio balance model that threatens the exchange rate in terms of the relative prices of European and American assets.10 Capital ﬂow into the

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United States is assumed to result from an increase in demand for American assets by European investors. The increase in demand, it argues, drives up the value of the dollar because the price of the dollar is the price of American assets. However, if an observable capital ﬂow results in Europeans buying American assets, the reason could also be an increase in the supply of such assets. The supply of American assets is equivalent to an excess of planned investments over planned savings, and this is the same thing as a planned current account deﬁcit or an excess of planned commodity imports over exports. A planned current account deﬁcit is a net supply of American assets in the international capital markets. If the planned current account deﬁcit goes up and if the price of the dollar is the price of American assets, the value of the dollar will fall rather than rise as capital ﬂows into the US increase. As usual, an increase in trading volume in a market says little about whether this increase is demand or supply driven. The signal for it being demand driven is the strength of the dollar. However, this is not a compelling argument for the economic prosperity view. As we will see, there are other reasons for the dollar’s strength, and there are two empirical observations that support the supply-side rather than the demand-side explanation of the capital ﬂows. The startling decline in savings by US households is one of these observations. At the start of the 1990s the savings rate was about 5 percent; then it fell continually until in 1999 and 2000 it became negative.11 By contrast, the euroland savings rate was nearly 11 percent in 2000. The negative savings rate meant that American households were no longer buying assets but were selling them to ﬁnance their excess absorption in resources. Given the high American investment volume, the increase in the current account deﬁcit and the increase in the supply of assets in international capital markets were the only way to replace the American lack of savings. This development is illustrated in ﬁgure 7.3. A further piece of information that contradicts the economic prosperity view is the poor performance of the US stock market in 1999 and early 2000. If the economic prosperity view is correct, not only the dollar but also American share prices should have increased relative to their European counterparts. But this was not the case as was already pointed out by De Grauwe (2000). Although the European stock market index performed better than the American one, the dollar was rising. A similar phenomenon occurred in the ﬁrst half of 2002.

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Figure 7.3 Savings rates compared. The savings rate is deﬁned as private household savings divided by disposable household income. (Source: OECD Economic Outlook, OECD Statistical Compendium, CD-ROM.)

Newspapers attributed the new strength of the euro to a growing disinterest in American shares, but in fact the European share prices fell sharply relative to American share prices in the same period. 7.2

The Flaw in the Theoretical Argument

A larger problem with the economic prosperity view and the traditional portfolio balance model is that it does not seem to have a theoretical basis. The exchange rate is the price of a currency, and not the price of shares or other interest-bearing assets. It is true that the price of the dollar is a component of the price of American shares, if seen from the viewpoint of European investors, but the US share price itself is another component. This is a trivial but important point that may ultimately contribute to unraveling the puzzle. Suppose that the return on US investment rises because of the new economy effect or for whatever other reason. This increase will raise demand for US shares among European investors and raise the price of American shares compared to the prices of European shares. But does this call for a revaluation of the dollar? Why is it not enough if the dollar price of American shares goes up relative to the euro price

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of European shares? Obviously there are two relative prices for the same thing, and one is redundant. The traditional portfolio balance approach downplays the redundancy problem by assuming that the rates of return for the trading countries’ assets are ﬁxed or determined by monetary policy.12 The only way to reach a portfolio equilibrium, namely a situation where the aggregate of all investors is content with the assets they possess, is an exchange rate adjustment. However, if share prices are ﬂexible, the exclusive focus on the exchange rate adjustment in the establishment of a portfolio equilibrium no longer makes sense. The necessary amendments of the traditional portfolio balance model can best be understood by following the layman’s argument for why a higher demand for US shares by European investors will drive up the share prices. It goes as follows: The investors sell their European shares in Europe against euros, and then they sell the euros obtained against dollars in the currency exchange market in order to use these dollars for the purchase of American shares. As this involves a demand for dollars and a supply of euros, so it is maintained, the value of the euro in terms of dollars must fall. The fallacy of this view is that it overlooks the implications of the additional demand for US shares on share prices and the repercussions on foreign exchange markets. In the short run the volume of outstanding US shares is given. Thus the portfolio reshufﬂing planned by European investors will be possible only to the extent that American investors are crowded out and give their shares to the Europeans. The American investors, on the other hand, may not wish to keep the dollars they receive but to buy other things instead. If it is shares, they will go abroad because only there do they ﬁnd the supply they need to satisfy their demand, and in particular, they will go to Europe where shares are cheap because they are sold by the European investors. Thus they will supply the dollars they received from the European investors in the currency exchange market and feed the demand for euros instead. If the original purchase of dollars drove up the dollar, this will instead drive up the euro and eliminate the effect on the exchange rate. With the passage of time the crowding out of American share holders will become weaker because the share price increase induces an additional ﬂow of new issues of shares to ﬁnance more investment. However, because an increase in planned net investment is equivalent to an increase in the planned current account deﬁcit, this will not

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generate a positive revaluation effect on the dollar. It will, however, imply a smaller share price increase. The real possibility to generate a revaluation effect is if the crowdedout American shareholders do not go into foreign shares because they have a home bias in their preferences. There are two alternatives. One is that the crowded-out American shareholders prefer to go into US money instead of European shares. This is the clearest case where a revaluation of the dollar occurs. However, it hardly supports the naive view that an increased demand for American assets drives up the dollar simply because there is a transitional demand for dollars in the process of portfolio conversion. The alternative is that the crowded-out American shareholders prefer to go into American bonds instead of European shares. If the central bank does not stabilize the interest rate by open market operations, this will drive down the interest rate and crowd out previous bondholders. If these then choose European bonds or shares instead of the American bonds they sold, there is again a countervailing supply of dollars in the exchange market. However, if the central bank stabilizes the interest rate by selling bonds and buying the dollars that the crowded-out shareholders do not want, the countervailing effect will be mitigated, and on balance, an appreciation of the dollar will remain. The lesson from these considerations is that the dollar appreciates when more dollars are demanded or fewer dollars are supplied, not when more American interest-bearing assets are demanded. It is surprising how frequently this simple fact has been overlooked in the literature on the determinants of the exchange rate. One of the reasons why the layman’s argument overlooks the possible repercussions resulting from the actions of crowded-out shareholders is that it focuses on transitional demand and supply ﬂows in the currency exchange markets rather than on ultimate preferences for stocks of assets such as shares, bonds, and currencies. To analyze what is happening to the exchange rate, we need a portfolio balance model enriched with stock demands for domestic and foreign currency. According to such a model, the interest rate, the price of shares, and the exchange rate are determined by the need to equate desired with actual wealth portfolios. At any point in time the actual portfolio of assets is given in the aggregate, and thus a desire to restructure this portfolio cannot be fulﬁlled. Instead, asset prices, rates of return, and exchange rates have to adjust until people’s preferences ﬁt the given actual stocks of assets available, notwithstanding the fact

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that from a microeconomic point of view, it is always possible to adjust the portfolio to the preferences. A Friedmanian thought experiment exempliﬁes the merit of a currency-augmented portfolio balance approach in the present case. Suppose that the European investors who wish to replace their European shares with American ones pack these shares into coffers, ﬂy to the United States, and negotiate directly with the American shareholders. They then ﬁnd an exchange rate between European and American shares, and hence relative rates of return, at which the American shareholders are willing to participate in the deal. In general equilibrium, this direct deal cannot result in any exchange rate other than the one brought about by a transitional conversion of European shares into euros, of euros into dollars, and of dollars into US shares. Thus the thought experiment conﬁrms that the dollar–euro exchange rate cannot be effected if the American shareholders who sold their shares are happy to hold European shares instead. If the dollar appreciates, it must be because American shareholders are not happy with all the European shares they purchased and convert them into other assets in a way that increases the demand for of US money balances or reduces the supply of such money balances. As explained above, the ﬁrst of these cases is the straightforward move from European shares into American money. The second case results from the wish to convert European shares into American bonds (or bills). If this induces the Fed to supply more bonds and reduce the stock of currency in circulation so as to defend the short-term interest rate, US currency will become more scarce and the dollar will appreciate. 7.3

Why Money Matters

To clarify the role of currency in the determination of the exchange rate more formally, we now specify a simple two-country portfolio balance model with a representative international investor who chooses among three types of assets in each of the two countries: shares S, bonds (or bills) B, and money M.13 The two countries are the United States and Europe. In a market equilibrium the share prices, the exchange rate, and the interest rates are determined so as to equate the desired portfolio structure resulting from the investor’s optimization to the actual one, which is taken as given.14

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The units of account for measuring the volumes of shares, bonds, and money are the respective national currencies. The volume of shares S is expressed in terms of the nominal share value. The market value of a share is a multiple P of the nominal value. We call this multiple the share price. When r denotes the rate of return on nominal share values, r S is the dividends distributed and r=P is the effective rate of return on shares (without a potential return from share appreciation). Let i denote the rate of interest on bonds. Variables that refer to the United States are labeled with an asterisk; variables without an asterisk refer to Europe and are expressed in terms of euros. The exchange rate e is the price of euros in terms of dollars. The representative international investor is meant to reﬂect the aggregate of all wealthly Americans and Europeans. He optimizes his portfolio for a given investment period, which may or may not be part of a multiple-period setting. At the beginning of the period he has a given endowment of assets that constitutes his total wealth W in terms of euros, but he chooses to re-optimizes his portfolio structure, taking the two share prices, the exchange rate, and the two interest rates as given.15 The investor’s budget constraint in terms of euro expenses for the six types of assets available is W ¼ S

P 1 1 þ B þ M þ SP þ B þ M: e e e

ð1Þ

Note that the choice of nume´raire is arbitrary but meaningless. Nothing would change by choosing the dollar as the nume´raire. Among other things, the investor’s decisions depend on expectations of end-of-period share prices and of the end-of-period exchange rate, which we denote P~ and ~e. The model predicts that changed expectations about these variables will immediately translate into their current counterparts, but we ﬁx the expectations throughout this chapter in order to concentrate on the fundamentals affecting the exchange rate. Our discussion focuses on changed stocks of assets due to government policies, changed real returns, and changed preferences for certain types of assets, given the expectations. The investor’s utility is assumed to be given by the sum of end-of-period wealth plus a liquidity service ! s S P~ b B m M ~ U ; ; ; sSP; bB; mM ; ~e ~e ~e

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which depends on the respective expected stock values S P~=~e; B =~e; M =~e; SP~; B, and M.16 The liquidity service is meant to capture all considerations important for the choice of assets other than their contribution to the pecuniary return, including risk characteristics, Baumol-Tobin type transactions costs, the timing of planned commodity purchases, and the like. The Greek symbols s ; b ; m ; s; b, and m denote parameters of the utility function, which allow us in a simple fashion to represent arbitrary preference changes including those that generate cross-price effects among different assets. We assume that U is an increasing, separable, and strictly concave function and that the parameters are unity before a preference change takes place. Formally, the investor’s decision can be depicted by maximizing the Lagrangean 1 1 1 L ¼ S ðP~ þ r Þ þ B ð1 þ i Þ þ M þ SðP~ þ rÞ þ Bð1 þ iÞ þ M ~e ~e ~e ! s S P~ b B m M þU ; ; ; sSP~; bB; mM ~e ~e ~e P 1 1 þl WS B M SP B M e e e with respect to the six different asset volumes considered in the model. Here the ﬁrst line is end-of-period wealth in terms of euros, the second gives the liquidity services, and the third contains the investor’s budget constraint where l is the Lagrangean multiplier. The marginal conditions resulting from this optimization approach are e P~ ð1 þ s US Þ þ r ¼ l; ~e P

ð2Þ

e ð1 þ i þ b UB Þ ¼ l; ~e

ð3Þ

e ð1 þ m UM Þ ¼ l; ~e

ð4Þ

P~ð1 þ sUS Þ þ r ¼ l; P

ð5Þ

1 þ i þ bUB ¼ l;

ð6Þ

and

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1 þ mUM ¼ l:

ð7Þ

These equations are similar insofar as they all show that in the optimum the sum of each asset’s own rate of return factor plus the marginal liquidity service, possibly corrected by a growth factor reﬂecting the expected exchange rate adjustment, equals a common yardstick, the Lagrangean multiplier l. In the case of US shares (2), the rate of return factor is a combination of the growth factor of the dollar in terms of euros, e=~e, of the growth factor of the US share price, P~=P , and the effective rate of return on US shares, r =P . In the case of dollar currency (4), the rate of return factor is just the growth factor of the dollar in terms of euros, and in the case of euro currency, it is simply one. The other cases should be self-explanatory. In general, an asset’s pecuniary rate of return factor is smaller, the larger this asset’s marginal liquidity service. As the rate of return on shares tends to be higher than that on bonds and the latter higher than that on cash, the marginal liquidity services will presumably follow the adverse ordering. Let a bar above a variable indicate the given asset stocks in the economy. The investor’s wealth in terms of euros with which he enters the period is then determined by S

P 1 1 þ B þ M þ SP þ B þ M 1 W: e e e

ð8Þ

Equations (1) through (8) deﬁne the demand functions for all six assets. The asset prices, the exchange rate, and the interest rate follow if we assume that, for each asset, demand equals supply: S ¼ S ; B ¼ B ; M ¼ M ; S ¼ S; B ¼ B; M ¼ M:

ð9Þ

In total, there are now 14 equations, one of which is redundant. They explain six asset stocks, two interest rates, two share prices, one exchange rate, the Lagrangean multiplier, and the wealth level, in a total of 13 variables. There is no need to explicitly solve for all of these variables because a number of useful observations can easily be derived by inspecting the equations. One concerns the economic prosperity view. Suppose that s in equation (2) increases and/or s in equation (5) declines while the marginal utilities of money holding remain constant. Equations (4) and (7) then ﬁx the exchange rate e and the Lagrangean multiplier l. As US and US are ﬁxed by the given levels of S and S, it follows from (2) and (5) that the changed preferences for share holdings will be accommo-

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dated only by an increase in the price of US shares P and/or a decline in the price of European shares P. No exchange rate movements are necessary to maintain a portfolio equilibrium. Changes in the nominal rates of return r and r in favor of American assets would, as the reader can easily verify for himself, have very similar effects. If the money demands do not change, they would not, as the economic prosperity view predicts, result in an appreciation of the dollar but, once again, only in an increase in the US share price relative to the European one. A similar remark applies to the rates of interest on bonds. Again, the exchange rate e and the Lagrangean multiplier l are ﬁxed by (4) and (7) independently of these interest rates. An increase in the preference for US bonds as reﬂected by an increase in b will, according to (3), only result in a fall in the US interest rate, and similarly an increase in the preference for European bonds will reduce the European interest rate according to (6) without affecting the exchange rate. The crucial equations for the determination of the exchange rate are (4) and (7). Together they imply that the value of the euro is explained by the marginal liquidity services of euros and dollars in the international wealth portfolio: e ¼ ~e

1 þ mUM : 1 þ m UM

ð10Þ

No pecuniary rates of return of the assets on which the portfolio balance approach focuses enter this formula, since these rates are endogenous to the market equilibrium. This reiterates the point made above, which is less trivial than it sounds: the currency exchange rate is the exchange rate between two types of money, and not the exchange rate between interest-bearing assets. The remarkable aspect of these neutrality results is that preference changes concerning interest-bearing assets will result in price and rate of return changes that are large enough to compensate for these changes but do not affect the exchange rate. For exchange rate movements to come along with such preference changes, it would be necessary that preference changes for money balances be involved too. Consider, for example, the home bias discussed in the previous section implying that crowded-out American shareholders like to go into American money. In the aggregate model considered here, this can be captured by the assumption that the increased preference for American

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shares comes along with an increased preference for US money, meaning an increase of m . According to equation (10) this would indeed imply a weakening of the euro. Thus far we assumed that the stocks of assets are given in the portfolios and that the pecuniary rates of return are ﬂexible. Rate of return adjustments will then be able to accommodate the preference changes with regard to bonds and shares but not with regard to money holdings, because the pecuniary return of money is ﬁxed at zero. Only a changed preference for money holding needs an exchange rate adjustment to keep the desired portfolio structure in line with the given actual one. Things are different, though, when other rates of return are ﬁxed too. The relevant case here is that the two central banks ﬁx the national interest rates and accommodate any changes in preferences for money and bonds with appropriate open market policies that change the composition of the outstanding stocks of bonds and money balances. This will affect the marginal liquidity services of money balances and will have repercussions on the exchange rate according to equation (10). From equations (3), (4), (6), and (7) it follows that the national interest rates are given by i ¼ m UM b UB

and

i ¼ mUM bUB :

ð11Þ

Given the stocks of money and bonds and hence given UM ; UB ; UM , and UB , a national interest rate obviously decreases with a decrease in the preference for the respective national money (decrease of m or m) and/or an increase in the preference for national bonds (increase of b and b), as was explained. To prevent this from happening and to ﬁx the interest rates, the central banks have to accept any exchange between the national stocks of money and bonds that the public wants to carry out at the given interest rates; that is, they have to intervene passively by supplying more of the respective stock in demand and withdrawing the other one from the market. Passive intervention of this type will make the exchange rate reactive to changed preferences for bond holdings and protect it partly from changes in the preference for money holdings. Consider, for example, the case of an increased preference for US bonds, as is reﬂected by an increase in b . To avoid a decrease in the US interest rate, the Federal Reserve Bank will react by selling bonds against US currency, which increases UM and lowers e according to (10). The dollar appreciates after an increase in the demand for US bonds. Similarly a depreciation

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of the euro, e, could be brought about by a reduced preference for European bonds if the European Central Bank ﬁxed the interest rate by buying bonds and selling euros—or, as discussed in the previous section, by an increased preference for American bonds which the Fed accommodates with a contractionary open market policy. Things would be similar if the central banks intervened also to keep the effective rate of return on shares constant, but of course they don’t. This is the crucial point overlooked in the existing portfolio balance literature. If the central bank intervenes only to keep the interest rate constant and if no more than the preference for shares changes as is reﬂected by s and s, equations (2) through (7) continue to ensure an isolation of the exchange rate. This conﬁrms the above criticism of the economic prosperity explanation of the euro’s weakness and of the traditional portfolio-balance approach as such. Even when the central bank intervenes passively to keep the interest rate constant, changes in proﬁt expectations, in preferences for share holdings, or in preferences for direct investment cannot inﬂuence the exchange rate unless they also imply changes in preferences for bonds or money balances. Let us now discuss the reason why a passive intervention might partially protect the exchange rate against changes in liquidity preferences. Suppose that the preference for euro currency declines, as is represented by a reduction of m. According to (10), this will depreciate the euro, and according to (11), it will reduce the European interest rate. To prevent the interest reduction, the European Central Bank will buy back money balances against private bonds. In itself, this will increase UM and increase e, meaning it will stabilize the exchange rate. The stabilization will not be perfect, though, because the increase in the stock of bonds results in a reduction in the marginal utility from bond holding, UB . According to (11), a constancy of the interest rate therefore implies that the marginal utility from money holding, mUM , will not be pushed back to where it was before the preference change and that there is a negative net effect on the euro. This can also be seen by deriving a modiﬁed interest parity condition from equations (3) and (6), which relates the exchange rate to the national interest rates and the marginal liquidity premia for bonds:17 e ¼ ~e

1 þ i þ bUB : 1 þ i þ b UB

ð12Þ

As the passive intervention triggered off by the decline in m increases the stock of bonds held by the public, B, and thus reduces the bonds’

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marginal liquidity service UB , equation (12) ensures that the net effect on the exchange rate is negative. A similar result holds for an increase in m . As the reader may verify for himself, a negative net effect on e and a decrease of M can also result from an increase in the preference for dollar currency if the dollar interest rate is given. The effect has a certain similarity with an active intervention in the exchange market. If such an intervention is sterilized in the sense that it leaves the interest rates ﬁxed in the two countries, it will involve a sale of dollar currency and dollar bonds against euro currency and euro bonds so as to keep the respective national differences in the marginal liquidity services of money and bonds constant, as is indicated by (11). The decline in the marginal utility of US bonds, and the respective increase in the marginal utility of European bonds that results from this change in the structure of the market portfolio, raises the fraction on the right-hand side of (12) and hence the value of the euro.18 It is a common feature of the active and passive interventions that a decline in the stock of euro currency exhibits a positive effect on the value of the euro. However, the distinguishing feature is that this effect comes independently when the central bank intervenes actively in the foreign exchange market while it is only an induced compensating effect, which cannot offset the primary effect when the central bank intervenes passively by ﬁxing the interest rate. Thus the correlation between the stock of euro currency and the value of the euro should be negative in the case of active intervention with a given interest rate, and positive in the case of passive intervention after a change in the currency preference. As we showed above that a negative correlation would also characterize the case of passive intervention after a change in bond preferences, it seems that the sign of the correlation between the currency stocks and the exchange rate might be a clue for ﬁnding the causes of the weak euro.19 It is essential for our theory that American and European bonds be imperfect substitutes in the international portfolio. If they were perfect substitutes, a preference shift would be made from European to American currency. The shift would be accommodated by a contractionary open market policy in Europe and an expansionary one in the United States, so as to keep the interest rates constant and not affect the exchange rate. The simplest way to depict this possibility in our model would be to assume that bonds do not deliver marginal liquidity services in addition to their pecuniary return, such that b UB ¼ bUB ¼ 0.

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Equations (10) through (12) would then imply that ﬁxing the interest rates eliminates any effect of a changed preference for money holding on the exchange rate. Similarly equation (12) would imply that the ECB tried the impossible when it intervened in the foreign exchange market to stabilize the euro without changing the European interest rate. However, we ﬁnd it hard to believe that bonds denominated in different currencies and separated by a ﬂexible and risky currency exchange rate will even come close to being perfect substitutes. This is the old dichotomy between the portfolio balance and the monetary approaches, which can only be solved empirically. Feldstein and Horioka (1980) and Dooley, Frankel, and Mathieson (1987) have argued that a high correlation between savings and investment points to a rather limited international substitutability of assets, and within our model we will also be able to provide supporting evidence for a limited substitutability.20 If American and European bonds are perfect substitutes, the value of the euro and the stock of euro currency should be uncorrelated both in the presence of demand and supply shocks if one controls for the interest rates. On the other hand, if they are imperfect substitutes, then controlling for the interest rates, there should be a negative correlation when supply shocks dominate and a positive correlation if demand shocks dominate. These are clearcut predictions, and we will show that during the historical period considered there was indeed a very signiﬁcant positive correlation. 7.4

Black Money and Deutschmarks Circulating Abroad

The deutschmark provides a particularly striking example of the positive correlation between the stock of currency in circulation and the foreign exchange value of this currency: in the late 1980s and early 1990s the Bundesbank and the public had regularly been surprised, if not alarmed, by the fact that the German monetary base grew much more rapidly than was anticipated, typically exceeding the projection corridor the Bundesbank had published. During this period there was a persistent revaluation pressure for the deutschmark. The pressure even led to the collapse of EMS in 1992, which implied a sudden revaluation of the deutschmark relative to most of the European currencies and the dollar.21 Since 1997, however, this trend has been reversed (see ﬁgure 7.1), and so has the trend in the growth rate of money balances. When the external value of the deutschmark began to decline,

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Figure 7.4 German currency in circulation (monthly data, billion). (Source: Deutsche Bundesbank homepage, 2002.)

the growth rate of the German monetary base began to decline relative to its trend, and during the year 2000 even the base itself began to fall with a gradually accelerating speed. Figure 7.4 illustrates this development. The development of the stock of all euro currencies, as depicted in ﬁgure 7.5, paralleled that of the stock of deutschmark currency. No econometric approach is need to uncover the movements. Obviously the stock of euro currencies in circulation was falling against the trend from about 370 billion @ to about 250 billion @, which is a decline of 120 billion @ or one-third. This is ten times more than the numbers monetary theorists usually try to interpret. The numbers are also huge if compared with previous intervention and speculation volumes. George Soros is said to have succeeded to tilt the EMS with only a few billion pounds, and the ECB’s frequent interventions to stabilize the euro had probably not exceeded 4 billion euros in total. It can only be guessed what the reasons for the euro currencies returning to the ECB were. We believe that it has do to with the announcement and anticipation of the physical currency conversion, which induced a ﬂight from euro currencies into other assets including other currencies. There are two categories of ﬂight money: deutsch-

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Figure 7.5 Euro zone currency in circulation (monthly data, billion). (Sources: September 1997–May 2002 Deutsche Bundesbank (2002), January 1990–August 1997 Ifo estimate based on monthly changes.)

marks that were legally and illegally held for transactions purposes outside Germany, and stocks of black money denominated in all euro currencies that were held by west Europeans. Other reasons that relate to the more technical aspects of the currency conversion could have been important in the very last moment before the conversion, but the deviation from the trend began too early for these reasons to have a considerable explanatory weight. The ﬁrst category must have been substantial because the German currency was the only one among the euro currencies that served as a means of transactions in other countries, in particular, in eastern Europe and Turkey but also in other parts of the world. In a Bundesbank discussion paper published by Seitz (1995), the accumulated stock of deutschmark currency outside Germany was estimated to be between 60 and 90 billion in 1995, which is equivalent to 30 to 45 billion @. At the time this number was between 25 and 35 percent of the German monetary base and between 10 and 15 percent of the monetary base of what later would be the euro countries.22 The deutschmarks circulating abroad began to return after the ﬁrm announcement of the currency union at the Dublin meeting in 1996. Foreign money holders had heard about the abolishment of the

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deutschmark and were afraid of sustaining a conversion loss. Even in Germany, many people were afraid of losing part of their wealth, despite the frequent advertising campaigns for the euro. The uncertainty of ordinary people elsewhere in the world must have been much bigger, since they were not informed about the conditions of the conversion and probably wondered what all this euro business was about. No doubt they heard that the deutschmark was to be abolished in 2002 and had wind of the talk about a new currency replacing it. But they did not know who would carry out the conversion, what the exchange rate would be, and what commission fees would be charged. Those people afraid of sustaining a loss continued to hoard deutschmarks and hurried into the dollar or other currencies, including their own, which were free of this kind of uncertainty. The recipients of the deutschmarks, typically banks and other ﬁnancial institutions, then returned the deutschmarks to the Bundesbank in exchange for interestbearing assets, typically short-term securities that were counted as part of M3. It is interesting in this regard that that the ECB announced in its Bulletin of November 2001 a redeﬁnition of its stock of M3 because a growing proportion of such securities had been accumulated by foreigners and was nevertheless counted as part of M3. Short-term securities with a maturity of up to two years that were being held by foreigners were decided no longer to be included in the deﬁnition of M3. According to the ECB’s own information this amounted to an adjustment of the published increments of M3 on the order of 40 billion @ in one year. An analogous comparison between the old and new M3 ﬁgures for the period back to January 1999 shows that the effect could even have been on the order of 100 billion @. It is unclear how much of this can be attributed to the returning deutschmarks, but the ﬁgures must be seen as a clue to the forces at work. Further evidence comes from two surveys. One was conducted by us, using the Ifo Institute’s Economic Survey International, a quarterly transnational poll among country experts. We asked 150 experts in eastern Europe, typically economists working for international companies, about a potential shift in the interest of ordinary people from the deutschmark to the dollar. Of the 71 people from 15 countries who responded to the poll, a majority of 54 percent reported that the public showed a growing interest in the dollar, 78 percent thought that the public had not been sufﬁciently informed about the introduction of the euro, and another 54 percent said that the public was at least partially

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worried about losses if they did not soon exchange their German marks into a permanent currency such as the dollar. Another, much more extensive survey with thousands of east Europeans was conducted by the Austrian Central Bank (Stix 2001). The survey was taken at various times over two years in Croatia, Hungary, Slovenia, the Czech Republic, and Slovakia. It afﬁrmed that the decline of the share of D-mark in circulation in the total euro money supply was due to the deutschmarks returning from abroad and that as late as May 2001 no less than 41 percent of the holders of deutschmarks who had made up their minds planned to exchange their stocks not into euros but into other currencies. Let us now turn to the second reason for the ﬂight of cash, namely the ﬂight of black money in the run-up to the physical conversion of euro currencies. According to the European laws against money laundering the ofﬁcial conversion of larger sums of old cash into euros was not possible without registration. People who held stocks of black European monies therefore had to ﬁnd ways to gradually convert them outside the banking system before the ofﬁcial conversion date, but they could not convert them into the euro because this currency existed only in a virtual form. Thus they had to go into the dollar, the pound, or other currencies that were not part of the euro group, and the sellers of these international currencies then exchanged the surplus stocks of euro currencies against interest-bearing assets that, after a substitution chain, ultimately came from ECB, which tried to stabilize the interest rate as explained above. Unfortunately, no ofﬁcial statistics are available that allow a precise distinction between the two sources of the decline in currencies as depicted by ﬁgures 7.4 and 7.5. Neither black stocks of money balances nor currency stocks held in eastern Europe are easily observable. Nevertheless, there is indirect evidence that provides rough estimates of the relative magnitudes involved. Consider ﬁrst the results of Schneider and Ernste (2000) on the size of the black economy in Europe. According to these authors, the share of the black economy in the euro countries is about 14 percent of the actual GDP including the black activities. Based on this ﬁgure and the trend value of 370 billion euro, as shown in ﬁgure 7.5, the potential stock of black currency at the time of currency conversion can be expected to have been 52 billion @ or more. Figures 7.4 and 7.5 make it clear that roughly this sum could have contributed to the net decline of the currency in circulation until the

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time of physical currency conversion. As the results of Schneider and Ernste reveal that Germany’s black market share in GDP is close to the European average and as German GDP is about 31 percent of the total of all euro countries, the reduction in the stock of deutschmarks in circulation would have had to be 31 percent of 120 billion @, in other words, 36 billion @ if it was exclusively explained by the black market effect. However, ﬁgure 7.5 reveals that the decline against the trend of the stock of deutschmarks in circulation was much higher, about 90 billion @. This clearly points to the importance of the eastern European effect. Assuming that the 30 billion @ decline of non-German currency in circulation, revealed by ﬁgures 7.5 and 7.6, can be explained fully by the black market effect 23 in the non-German euro countries, which produce 69 percent of the GDP and should therefore hold 69 percent of the stock of black money, the total black market effect for all euro countries can be taken to be about 45 billion @. Thus the remainder of the total decline of 120 billion @, which is 75 billion @, can be seen to reﬂect the stock of deutschmark currency that returned from eastern Europe and other parts of the world, or did not ﬂow there in the ﬁrst place because of the expected euro introduction. These are only rough estimates. Whatever the true relative importance of the two effects may be, the fact that ordinary people outside Germany and west European holders of black money had lost their interest in euro currencies in the run-up to the currency conversion is beyond doubt. There was exactly the kind of reduced preference for euros that was modeled by a decline of the utility parameter m in the previous section. Our theory indicates that this reduced preference would have lowered the value of the euro and the European interest rate if the ECB had not intervened. The euro and the interest rate would have adjusted such that the existing stocks of money balances continued to be held in the international wealth portfolio. However, the ECB intervened passively so as to stabilize the interest rate. As explained in the theory section, this mitigated the decline of the euro without eliminating it, while the stock of circulating currency fell. The mechanism through which this actually happened is that the euro currency held by foreigners and black market agents went to international ﬁnancial agencies (banks and investors) that held both euro and dollar currencies. Some of the dollars delivered by these agencies may have come from the Fed in exchange for US securities and some of the euros received by them went to ECB in exchange for

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European securities. In the end, the euro declined, and there was less US currency and more European currency in the international portfolio of these ﬁnancial agencies, and more US currency and less European currency in the aggregate international portfolio of all private agents taken together, including eastern Europeans and black market agents. This interpretation ﬁts the observed decline of the stock of outstanding deutschmarks as shown in ﬁgures 7.4 and 7.5 and the simultaneous decline of the euro as shown in ﬁgure 7.1. It even ﬁts the rise of the euro after February 2002 when the currency conversion was completed (see ﬁgure 7.1). As was predicted by us in the journal articles and other contributions,24 currency demand by eastern Europeans and holders of black money went up immediately after the physical conversion, forcing the ECB to pump more money into the economy so as to maintain its interest target, and the euro began to appreciate rapidly, taking by surprise the analysts who believed in a correlation between the strong US recovery and the value of the dollar. The development after the physical currency conversion mirrors that of the virtual conversion before it: the euro has been gradually taking the places emptied by the old euro currencies, in particular, the place of the deutschmark in eastern Europe. In a recent paper the ECB (Padua-Schioppa 2002) estimated that until May 2002 no less than 18 billion @ were transferred to countries in eastern Europe. The fall of the Iron Curtain bolstered the deutschmark in the early 1990s. Fear of its conversion into the euro weakened it after 1997 and with it the euro itself. By the same logic, the euro has started to gain strength in the period since the conversion. 7.5

A Quantitative Assessment of the Effect

An important question is whether a decline of the monetary base by about 120 billion @ against the trend can cause effects large enough to explain the actual exchange rate movements. The search for its answer requires an empirical determination of the corresponding reaction coefﬁcients. Here we take two different approaches. First, we review the evidence from recent studies of micro data on the effect of money demand on the exchange rate. Second, we estimate a modiﬁed portfolio balance model, using macro data. Recent contributions by Evans and Lyons (1999, 2001) on the ‘‘micro structure of the exchange rate’’ conclude that each billion of additional sterilized dollar currency demand raises the dollar exchange rate by up

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to half a cent in the short run and about 30 cents in the long run. If these ﬁgures apply equally to the euro, then our theory explains the depreciation of the euro by about 36 cents in the period 1997 to 2000. This is extremely close to the actual depreciation, which was 34 cents during this period. In order to assess the co-movement of the exchange rate and relative money supplies from macro data, we now analyze empirically the determinants of the exchange rate. The question in the context of our model is whether the currency in circulation has a signiﬁcant positive partial effect on the exchange rate of the euro in the presence of the other variables. The co-integration technique is used to study the empirical long-run relationship among the ﬁve variables relevant to our model: the exchange rate, relative money supplies, relative interest rates, relative bonds, and relative share prices. We analyze the comovements for the period from 1984 to the end of 2001 for German, Japanese, UK, and Swiss exchange rates with respect to the United States. The Johansen (1991) procedure is used to test for the presence of cointegration.25 The Johansen test results are reported in panel A of table 7.1, along with the robustness of this model and some econometric issues. The long-run coefﬁcients in the table were the exchange rates normalized to one. All variables are deﬁned as in the theoretical model above. The empirical results are consistent with our impression from the data analysis and the discussion in the previous sections. We ﬁrst focus on the long-run coefﬁcients. In all countries, except Switzerland, which used to control money supply rather than interest rates, the currency in circulation has a positive effect on the exchange value of the domestic currency. Because American and European bonds are perfect substitutes, this contradicts the view that a policy of ﬁxing the interest rates eliminates the effect of currency demand changes on the exchange rate. The positive correlation between the monetary base and the foreign exchange value of the currency had also been observed in earlier work by Frankel (1982, 1993), who called it the ‘‘mystery of the multiplying marks’’ and attributed it to model misspeciﬁcations or wealth effects in the monetary model of the exchange rate. Indeed, the positive correlation seems puzzling if the monetary base is seen as resulting from a supply policy of the central bank and active interventions. However, according to our model, the positive correlation has a straightforward explanation in the historical episode considered here if variations in the

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Table 7.1 Currency augmented portfolio balance model Johansen co-integration results, 1984:1 to 2001:4 Variable

GER

UK

JAP

SWI

A. Long-run coefﬁcients tr

80.57

62.18

82.55

115.25

cv

68.52

47.21

68.52

68.52

0.804 (0.414)

1.622 (0.219)

0.145 (0.993)

7.825 (9.145)

(1.943)

(7.386)

(0.146)

(0.856)

0.009

0.013

0.014

0.109

(0.014)

(0.006)

(0.085)

(0.166)

(0.680)

(2.090)

(0.166)

(0.659)

ln M ln M

ln i ln i

ln B ln B

0.129 (0.197) (0.654)

ln P ln P

1.179

0.079

0.024

2.443

(0.164)

(2.636)

(0.151)

(0.926)

0.025

3.970

(0.257)

(0.091)

(0.153)

(5.247)

(4.580)

(0.874)

(0.164)

(0.756)

0.134

0.239

0.003

0.009

(0.044) (3.009)

(0.106) (2.247)

(0.001) (1.838)

(0.020) (0.448)

B. Reversion coefﬁcients Dðln eÞ

Dðln M ln M Þ

Dðln i ln i Þ

Dðln B ln B Þ

0.140

0.988

(0.081)

(0.191)

(0.026)

(3.922)

(1.725)

(5.168)

(0.119)

0.240

1.166

3.855

0.150

(0.457)

(1.569)

(2.718)

(0.378)

(0.524)

(0.743)

(1.418)

(0.396)

0.019

0.022

0.036

(0.035)

(0.189)

(0.012)

(0.120)

(3.000)

(0.550) Dðln P ln P Þ

0.003

0.155 (0.039)

0.060

0.176

0.158

0.092

(0.062)

(0.059)

(0.397)

(0.026)

(0.972)

(2.961)

(0.399)

(3.496)

Note: Bond data were not available for the United Kingdom. The Swiss data start in 1989, as stock market data were not available before. tr denotes the likelihood ratio test statistic for the null hypothesis of zero cointegrating vectors against the alternative of one cointegrating vector. The asymptotic critical values are denoted by ‘‘cv.’’ In all cases, except for Switzerland, there exists only one cointegrating vector. Standard errors and tstatistics are in parentheses.

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foreign and black market demand for a country’s currency are taken into account. The other estimates are also broadly in line with our theoretical model. The positive effect of the interest rate (for Germany, Japan, and Switzerland) on the value of the domestic currency can have two explanations. One is that it results from an increased preference for the domestic currency which, as indicated by (10) and (11), will imply a revaluation and an increase of the interest rate if the central bank does not intervene. The other is that the central bank actively intervenes by tightening the money supply. According to (11), this increases the difference of the marginal liquidity premia of money and bonds and hence the interest rate, and according to (10), it implies a revaluation. Bonds have a smaller negative effect in Germany, although it is not statistically signiﬁcant and may be the counterpart of the positive effect of money holdings, since interventions imply that bonds and money balances vary inversely. The signiﬁcant negative coefﬁcient of share prices supports the puzzle established by De Grauwe (2000), that the value of an economy’s currency varies inversely with its prosperity, which is the opposite of what the economic prosperity view predicts. By our model, the explanation for the negative correlation is that domestic shareholders whose preferences imply a home bias switch between domestic shares and domestic money, depending on the information they receive. This changes the marginal liquidity premium on domestic money balances conversely to share prices. According to equation (10) the domestic currency appreciates when share prices are low, and vice versa. Given the co-integration result, we use a vector error correction model to explore the reaction to a deviation from the long-run equilibrium.26 The responses of each of the variables to deviations from the long-run equilibrium are captured by the revision coefﬁcients reported in table 7.1. In the cases of Germany, the United Kingdom, and Japan, the exchange rate and the relative money bases react to the deviations from the equilibrium, while most others do not. It is known from the work of Meese and Rogoff (1983) and Taylor (1995) that the empirical research on exchange rate determination suffers from instability of the parameters over time, and poor out-ofsample performance. This problem also applies to our empirical exercise. In order to check the robustness of our estimation procedures, a set of appropriate tests was performed, using several estimation proce-

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dures that addressed econometric problems associated with this type of regression exercise. For example, we estimated an ARCH model, correcting for conditional heteroscedasticity, examined alternative lag structures in the co-integration exercise, and implemented an instrumental variables approach, aiming to reduce the endogeneity problem by way of lagged values as instruments. While most of our variables were affected by these alternative speciﬁcations, our main variable of interest, the relative money stocks, remained remarkably robust, exhibiting in most cases the signiﬁcant positive correlation with the exchange rate predicted by our theory. 7.6

Conclusions

In this chapter we provide a criticism of the portfolio balance approach, and we attempt to develop a new theory of the exchange rate that we call the currency hypothesis. We take an explicit two-country portfolio model with money, bonds, and shares and show that there is little reason to expect the demand for shares to translate into the exchange rate because this demand is already reﬂected in the share price. We argue that what counts most is the stock demand for money in the narrow sense of the word. The exchange rate is the price of one type of money in terms of another and not the price of interest-bearing assets, as both portfolio managers and economists who developed the portfolio balances approach have claimed. This theoretical result is conﬁrmed by a number of empirical tests of exchange rates among various currencies. The tests demonstrated a strong and robust positive correlation between a country’s stock of currency in circulation and the respective exchange value of this currency. Our currency hypothesis is motivated historically by our observing the movements of the exchange value of the deutschmark and the euro from the time of the fall of the Iron Curtain to the physical conversion of the euro. We explain these co-movements in quantitative terms, using the ‘‘microstructure of the exchange rate’’ approach. With the fall of the Iron Curtain, the deutschmark became popular in eastern Europe in the early 1990s, leading to an unprecedented monetary expansion and the appreciation crisis of 1992. Fear of loss in its conversion into the euro reduced the demand for deutschmarks and weakened both the deutschmark and the euro after 1997. By the same logic, and predicted accurately by us in earlier contributions on this topic, the

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euro has gained in strength since the time of the physical conversion. A good reason for the appreciation of the euro is that it is ideally suited for black market operations and is ﬁnding friends in eastern Europe and elsewhere. Notes Earlier work along these lines was presented at a workshop on Exchange Rate and Monetary Policy Issues in Vienna, April 2001, and at the CESifo Macro and International Finance Area Conference in Munich, May 2001. We gratefully acknowledge useful comments by Paul De Grauwe, Walter Fisher, Huntley Schaller, and Haakon Solheim. 1. Hans-Werner Sinn, Handelsblatt, November 6, 2000, Financial Times, April 4, 2001, and Su¨ddeutsche Zeitung, April 6, 2000. See also Paul Krugman’s comment on Sinn in New York Times, April 1, 2001, and Bundesbank Gescha¨ftsbericht of April 4, 2001. 2. Alternative explanations can be found in Alquist and Chinn (2002) and Corsetti (2000). 3. Economist, June 5, 1999, p. 13; April 20, 2000, pp. 25–26. Der Spiegel, October 2000, ‘‘Interner Bericht des Finanzministeriums fordert tiefgreifende Reformen zur Stabilisierung des Euro.’’ 4. Economist, June 5, 1999, p. 14. 5. ECB, Monthly Bulletin, June 1999, p. 39. 6. Ibid. 7. Ibid. 8. Der Spiegel, online, Interview with Karl Otto Po¨hl, June 19, 2000. 9. ‘‘Interner Bericht des Finanzministeriums . . . ,’’ ibid. See also ‘‘Prospects for sustained growth in the Euro area,’’ ch. 2, European Economy, vol. 71, 2000. Ofﬁce for Ofﬁcial Publications of the EC, Luxembourg, pp. 62–67. 10. The literature ranges from Branson (1977), Branson, Halttunen, and Masson (1977), Branson and Henderson (1985), Girton and Henderson (1976), and Henderson (1980) to Dooley and Isaard (1982), Sinn (1983a), MacDonald and Taylor (1992), and Mann and Meade (2002), to mention only a few of the relevant papers. For a description of current research and further references, see Isaard (1995). 11. The ofﬁcially measured savings rate does not include capital gains. This is not a problem in the present context where the savers’ willingness to absorb assets offered in the capital market is concerned. 12. See note 8. 13. We also formulated a more elaborate model distinguishing, among other things, between American and European investors, but the more parsimonious model presented here is sufﬁcient for the points we wish to make. 14. An increase in the portfolio volume will not affect share prices, interest rates, and the exchange rate if preferences are homothetic and growth does not change the actual portfolio structure. For simplicity we assume that this is the case.

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15. This is the general structure of a multi-period stochastic portfolio decision problem. See Sinn (1983b) for a more extensive elaboration on this problem. Here we cut things short by considering one period only and simplifying the utility function. 16. See Fried and Howitt (1983) for a discussion of the potential liquidity services and a formulation along these lines. 17. Equation (12) speciﬁes the interest rates rather than the exchange rates when the respective asset stocks are given and the ECB does not intervene. According to (3) and (6), in equilibrium the interest rates on American and European bonds have to adjust such that they complement the marginal liquidity services of bonds to generate the required overall return factor l. This then automatically satisﬁes the interest parity condition without giving equation (12) much explanatory power for the determination of the exchange rate. When central banks intervene passively to ﬁx the interest rates, the explanatory power increases. Although (12) refers to the spot rate e, it can also be used to determine the forward rate e~f by way of the covered interest parity condition ~e f ¼ e ð1 þ i Þ=ð1 þ iÞ. The forward rate is not the same as the expected future spot rate. The relationship between these rates is found by substituting (12) into the preceding equation: e~f ¼ e~

1 þ bUB =ð1 þ iÞ : 1 þ b UB =ð1 þ i Þ

This expression shows that a reduced preference for euro currency combined with the adjustment to the interest rate reduces the euro’s forward rate relative to its expected future spot rate without affecting the forward premium or the swap rate. 18. In practice, the interventions by the ECB involved the sale of US treasury bonds, which required the Fed to react with an expansionary open market policy increasing the money supply so as to avoid an increase in the US interest rate. 19. It should be noted that the positive correlation between the stock of money balances and the foreign exchange value of this money that the currency hypothesis predicts refers to high-powered base money (M0) rather than broader money aggregates. There are two reasons why an extension of the argument to M1, M2, or M3 is not possible. First, demand, savings, and time deposits may be implicitly or explicitly interest bearing and may therefore classify as part of B rather than M in our model. Second, even if demand deposits and cash are considered as close substitutes by the public, M1 may not be positively correlated with M0. Suppose that the demand for euro cash declines. In that case, the cash will return to the banks in exchange for demand deposits. The money multiplier will increase and induce the banks to expand M1 by giving out more loans to their clients. This will contribute to the decline in the marginal utility of money and the downward effects on the exchange rate and the interest rate. Thus, before and without passive intervention by the ECB, there is a negative correlation between M1 and the exchange rate and none between M0 and the exchange rate. If the ECB intervenes to reestablish the targeted interest level, it can only partly offset the exchange rate effect, and it reduces M0 as was shown above. However, the net effect on M1 will be unclear. Indeed, M1 remained remarkably stable during the collapse of euro base money in the years before currency conversion. 20. See also chapter 1 by Evans and Lyons in this volume. 21. For analyses of this episode see Eichengreen and Wyplosz (1993), De Grauwe (1994), and Sinn (1999).

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22. No less than 60 percent of the US monetary base is said to circulate outside the United States (see Porter and Judson 1996). The outstanding deutschmarks were a source of a signiﬁcant seignorage proﬁt made by the Bundesbank, as was calculated by Sinn and Feist (1997, 2000). When the euro was introduced, the deutschmark constituted a much larger fraction of the euro-11 monetary base than the share in the ECB proﬁt remittances, which was only 31 percent, according to the average of Germany’s GDP and population shares. Sinn and Feist calculated that this implied a seignorage loss which was equivalent to a one-off capital levy of nearly 60 billion DM or 30 billion @ on the German Bundesbank. 23. It is also possible that some of the decline was due to other, more technical, reasons such as the ordinary citizen’s attempt to minimize the stock of money balances at the time of currency conversion. However, all countries would have been affected in proportion to their GDP size. In this case the idiosynchratic component of the reduction in money demand applied to Germany was on the order of 75 billion @. Note that our estimates of the composition of the decline in money balances have only an informative character. None of our arguments for why a decline in money balances reduces the exchange value depends on the causes of this decline. 24. See, in particular, the articles in Handelsblatt and Financial Times published in 2000, as cited in note 1, as well as Sinn and Westermann (2001). 25. All series are nonstationary in levels and stationary in ﬁrst differences. We let xt be a 5 1 vector containing the variables fe; ln M–ln M ; ln i–ln i ; ln B–ln B ; ln P–ln P g. The Johansen test statistics are devised from the sample canonical correlations (Anderson 1958; Marinell 1995) between Dxt and xtp , where t is time and p denotes the lag length, adjusting for all intervening lags. To implement the procedure, we ﬁrst obtain the least squares residuals from Dxt ¼ m1 þ

p1 X

Gj Dxtj þ e1t ;

j¼1

xtp ¼ m2 þ

p1 X

Gj Dxtj þ e2t ;

j¼1

where m1 and m2 are constant vectors, G is a matrix of parameters, and e1 amd e2 are vectors of the error terms. The lag parameter p is identiﬁed by the Akaike information criterion. Next, we compute the eigenvalues, l1 b b ln , of W21 W1 11 W12 with respect to W22 and the associated eigenvectors, n1 ; . . . ; nn , where the moment matrices Wlm ¼ T 1

X

e^t e^t0

t

for l; m ¼ 1; 2, and n is the dimension of xt (i.e., n ¼ 5 in this exercise). l1 . . . ln are the squared canonical correlations between Dxt and xtp , adjusting for all intervening lags. The trace statistic, tr ¼ T

n X

lnð1 lj Þ;

j¼rþ1

where 0 a r a n, tests the hypothesis that there are at most r cointegration vectors. The eigenvectors, n1 ; . . . ; nr are sample estimates of the co-integration vectors. 26. Speciﬁcally, the changes in each of the ﬁve variables are modeled using Dxt ¼ Pp m þ j¼1 Gj Dxtj þ aect1 þ et , where ect is the error correction term.

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References Alquist, R., and M. D. Chinn. 2001. Tracking the euro’s progress. International Finance 3: 357–74. Alquist, R., and M. D. Chinn. 2002. Productivity and the euro–dollar exchange rate puzzle. NBER Working Paper 8824. Branson, W. H. 1977. Asset markets and relative prices in exchange rate determination. Sozialwissenschaftliche Annalen des Institutes fu¨r Ho¨here Studien, Vienna, A, 1: 69–89. Branson, W. H., H. Halttunen, and P. Masson. 1977. Exchange rates in the short run: The dollar–deutschmark rate. European Economic Review 10: 303–24. Branson, W. H., and D. Handerson. 1985. The speciﬁcation and inﬂuence of asset markets. In R. Jones and P. Kenen, eds., Handbook of International Economics, vol. 2. Amsterdam: North-Holland. Corsetti, G. 2000. A perspective on the euro. CESifo Forum 2(2): 32–36. De Grauwe, P. 1994. Towards EMU without EMS. Economic Policy 18: 147–85. De Grauwe, P. 2000. The euro in search of fundamentals. Paper presented at the CESifo conference on Issues of Monetary Integration in Europe. December 2000. Dooley, M. P., and P. Isard. 1982. A portfolio balance rational expectations model of the dollar–mark exchange rate. Journal of International Economics 12: 257–76. Dooley, M. P., J. Frankel, and D. Mathieson. 1997. International capital mobility: What do saving-investment correlations tell us? IMF Staff Papers 34: 503–30. Evans, M. D., and R. K. Lyons. 2001. Order ﬂow and exchange rate dynamics. Journal of Political Economy 110: 170–80. Evans, M. D., and R. K. Lyons. 2001. Portfolio balance, price impact and sterilized intervention. NBER Working Paper 7317. Evans, M. D. D., and R. K. Lyons. 2002. Are different currency assets imperfect substitutes? CESifo, Venice Summer Institute 2001. Workshop on Exchange Rate Modelling. Venice International University, San Servolo, July 13–14, 2002. Eichengreen,. B., and Ch. Wyplosz. 1993. The unstable EMS. Brookings Papers on Economic Activity 1: 51–143. Feldstein, M., and C. Horioka. 1980. Domestic saving and international capital ﬂows. Economic Journal 90: 314–29. Frankel, J. A. 1982. The mystery of the multiplying marks: A modiﬁcation of the monetary model. Review of Economics and Statistics 64: 515–19. Frankel, J. A. 1993. Monetary and portfolio-balance models of exchange rates. In J. A. Frankel, ed., On Exchange Rates. Cambridge: MIT Press, pp. 95–115. Fried, J., and P. Howitt. 1983. The effects of inﬂation on real interest rates. American Economic Review 73(5): 968–80. Girton, L., and D. W. Henderson. 1976. Financial capital movements and central bank behavior in a two-country, short-run portfolio balance. Journal of Monetary Economics 76: 33–61.

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Henderson, D. W. 1980. The dynamic effects of exchange market intervention: Two extreme views and a synthesis. In H. Frisch and G. Schwo¨diauer, eds., The Economics of Flexible Exchange Rates. Supplement to Kredit und Kapital 6: 156–209. Isard, P. 1995. Exchange Rate Economics. Cambridge: Cambridge University Press. MacDonald, R., and M. P. Taylor. 1993. The monetary approach to the exchange rate: Rational expectations, long-run equilibrium and forecasting. IMF Staff Papers 40: 89–107. Mann, C., and E. E. Meade. 2002. Home bias, transactions costs, and prospects for the euro: A more detailed analysis. Institute for International Economics Working Paper 02-3. Meese, R. A., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Padoa-Schioppa, T. 2002. The euro goes east. Lecture at the 8th Dubrovnik Economic Conference. June 29, 2002. Porter, R., and R. Judson. 1996. The location of US currency: How much is abroad? Federal Reserve Bulletin 82: 883–903. Schneider, F., and D. H. Ernste. 2000. Shadow economies: size, causes, and consequences. Journal of Economic Literature 38: 77–114. Seitz, F. 1995. Der DM-Umlauf im Ausland. Volkswirtschaftliche Forschungsgruppe der Deutschen Bundesbank. Bundesbank Diskussionspapier 1/95. Sinn, H.-W. 1983a. International capital movements, ﬂexible exchange rates, and the IS-LM model: A comparison between the portfolio-balance and the ﬂow hypotheses. Weltwirtschaftliches Archiv 119: 36–63. Sinn, H.-W. 1983b. Economic Decisions under Uncertainty. Amsterdam: North-Holland. Sinn, H.-W. 1999. International implications of German uniﬁcation. In A. Razin and E. Sadka, eds., The Economics of Globalization. Cambridge: Cambridge University Press, pp. 33–58. Sinn, H.-W., and H. Feist. 1997. Eurowinners and eurolosers: The distribution of seignorage wealth in EMU. European Journal of Political Economy 13: 665–89. Sinn, H.-W., and H. Feist. 2000. Seignorage wealth in the eurosystem: Eurowinners and eurolosers revisited. CESifo Discussion Paper 353. Sinn, H.-W., and F. Westermann. 2001. Why has the euro been falling? An investigation into the determinants of the exchange rate. NBER Working Paper 8352, CESifo Working Paper 493. Stix, H. 2001. Survey results about foreign currency holdings in ﬁve central and eastern European countries: A note. CESifo Forum 2(3): 41–48. Taylor, M. P. 1995. The economics of exchange rates. Journal of Economic Literature 33: 13– 47.

8

What Do We Know about Recent Exchange Rate Models? In-Sample Fit and Out-of-Sample Performance Evaluated Yin-Wong Cheung, Menzie D. Chinn, and Antonio Garcia Pascual

In contrast to the intellectual ferment that followed the collapse of the Bretton Woods era, the 1990s were marked by a relative paucity of new empirical models of exchange rates. The sticky-price monetary model of Dornbusch and Frankel remained the workhorse of policyoriented analyses of exchange rate ﬂuctuations among the developed economies. However, while no completely new models were developed, several approaches gained increased prominence. Some of these approaches were inspired by new empirical ﬁndings, such as the correlation between net foreign asset positions and real exchange rates. Others, such as those based on productivity differences, were grounded in an older theoretical literature but given new respectability by the new international macroeconomics (Obstfeld and Rogoff 1996) literature. None of the empirical models, however, were subjected to rigorous examination of the sort that Frankel (1979) and Meese and Rogoff (1983a, b) conducted in their seminal works. Consequently, instead of re-examining the usual suspects—the ﬂexible price monetary model, purchasing power parity, and the interest differential1 —we vary the set of performance criteria and expand the set to include the mean squared error, and the direction-of-change statistic. The later dimension is potentially more important from a market timing perspective, besides serving as another indicator of forecast attributes. To summarize, in this study, we compare exchange rate models along several dimensions: Four models are compared against the random walk. Only one of the structural models—the benchmark sticky-price monetary model of Dornbusch and Frankel—has been the subject of previous systematic

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Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

analyses. The other models include one incorporating productivity differentials in a fashion consistent with a Balassa-Samuelson formulation, an interest rate parity speciﬁcation, and a representative behavioral equilibrium exchange rate model. The behavior of US dollar-based exchange rates of the Canadian dollar, British pound, German mark, Swiss franc, and Japanese yen are examined. We also examine the corresponding yen-based rates to ensure that our conclusions are not driven by dollar speciﬁc results.

The models are estimated in two ways: in ﬁrst-difference and error correction speciﬁcations.

In sample ﬁt is assessed in terms of how well the coefﬁcient estimates conform to theoretical priors.

Forecasting performance is evaluated at several horizons (1-, 4and 20-quarter horizons), for a recent period not previously examined (post-1992).

We augment the conventional metrics with a direction-of-change statistic and the ‘‘consistency’’ criterion of Cheung and Chinn (1998).

In accordance with previous studies, we ﬁnd that no model consistently outperforms a random walk according to the mean squared error criterion at short horizons. However, at the longest horizon we ﬁnd that the proportion of times the structural models incorporating long-run relationships outperform a random walk is more than would be expected if the outcomes were merely random. Using a 10 percent signiﬁcance level, a random walk is outperformed 17 percent of the time along a MSE dimension and 27 percent along a direction of change dimension. In terms of the ‘‘consistency’’ test of Cheung and Chinn (1998), we obtain slightly less positive results. The actual and forecasted rates are cointegrated more often than would occur by chance for all the models. While in many of these cases of cointegration, the condition of unitary elasticity of expectations is rejected; only about 5 percent fulﬁll all the conditions of the consistency criteria. We conclude that the question of exchange rate predictability remains unresolved. In particular, while the oft-used mean squared error criterion provides a dismal perspective, criteria other than the conventional ones suggest that structural exchange rate models have some usefulness. Furthermore, structural models incorporating restrictions at long horizons tend to outperform random walk speciﬁcations.

In-Sample Fit and Out-of-Sample Performance Evaluated

8.1

241

Theoretical Models

The universe of empirical models that have been examined over the ﬂoating rate period is enormous. Consequently any evaluation of these models must necessarily be selective. The models we have selected are prominent in the economic and policy literature, and readily implementable and replicable. To our knowledge, with the exception of the sticky-price model, they have also not previously been evaluated in a systematic fashion. We use the random walk model as our benchmark naive model, in line with previous work, but we also select one model—the Dornbusch (1976) and Frankel (1979) model—as a representative of the 1970s vintage models. The sticky-price monetary model can be expressed as follows: ^ t þ b2 y^t þ b 3 ^it þ b4 p^t þ ut ; st ¼ b 0 þ b 1 m

ð1Þ

where s is exchange rate in log, m is log money, y is log real GDP, i and p are the interest and inﬂation rate, respectively, the caret (^) denotes the intercountry difference, and ut is an error term. The characteristics of this model are well known, so we will not devote time to discuss the theory behind the equation. We will observe, however, that the list of variables included in (1) encompasses those employed in the ﬂexible price version of the monetary model, as well as the micro-based general equilibrium models of Stockman (1980) and Lucas (1982). Second, we assess models that are in the Balassa-Samuelson vein, in that they accord a central role to productivity differentials in explaining movements in real, and hence also nominal, exchange rates (see Chinn 1997). Such models drop the purchasing power parity assumption for broad price indexes and allow the real exchange rate to depend on the relative price of nontradables, itself a function of productivity ðzÞ differentials. A generic productivity differential exchange rate equation is ^ þ b2 y^ þ b3 ^i þ b 5^zt þ ut : st ¼ b 0 þ b 1 m

ð2Þ

The third set of models we examine we term the ‘‘behavioral equilibrium exchange rate’’ (BEER) approach. We investigate this model as a proxy for a diverse set of models that incorporate a number of familiar relationships. A typical speciﬁcation is ^ t þ b 7 ^rt þ b 8 g^debtt þ b9 tott þ b10 nfat þ ut ; st ¼ b0 þ p^t þ b6 o

ð3Þ

242

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

where p is the log price level (CPI), o is the relative price of nontradables, r is the real interest rate, gdebt is the government debt to GDP ratio, tot is the log terms of trade, and nfa is the net foreign asset ratio. A unitary coefﬁcient is imposed on p^t . This speciﬁcation can be thought of as incorporating the Balassa-Samuelson effect, the real interest differential model, an exchange risk premium associated with government debt stocks, and additional portfolio balance effects arising from the net foreign asset position of the economy.2 Evaluation of this model can shed light on a number of very closely related approaches, including the macroeconomic framework of the IMF (Isard et al. 2001) and Stein’s NATREX (Stein 1999). The empirical determinants in both approaches overlap with those of the speciﬁcation in equation (3). Models based on this framework have been the predominant approach to determining the level at which currencies will gravitate to over some intermediate horizon, especially in the context of policy issues. For instance, the behavioral equilibrium exchange rate approach is the model that is most used to determine the long-term value of the euro. The ﬁnal speciﬁcation assessed is not a model per se; rather it is an arbitrage relationship—uncovered interest rate parity: stþk st ¼ ^it; k ;

ð4Þ

where ^it; k is the interest rate of maturity k. Unlike the other speciﬁcations, this relation does not need to be estimated in order to generate predictions. Interest rate parity at long horizons has recently gathered empirical support (Alexius 2001; Chinn and Meredith 2002), in contrast to the disappointing results at the shorter horizons. MacDonald and Nagayasu (2000) have also demonstrated that long-run interest rates can predict exchange rate levels. On the basis of these ﬁndings, we anticipate that this speciﬁcation will perform better at the longer horizons than at the shorter.3 8.2 8.2.1

Data and Full-Sample Estimation Data

The analysis uses quarterly data for the United States, Canada, the United Kingdom, Japan, Germany, and Switzerland over the 1973:2 to

In-Sample Fit and Out-of-Sample Performance Evaluated

243

Figure 8.1 German mark–US dollar exchange rate

2000:4 period. The exchange rate, money, price and income variables are drawn primarily from the IMF’s International Financial Statistics. The productivity data were obtained from the Bank for International Settlements, while the interest rates used to conduct the interest rate parity forecasts are essentially the same as those used in Chinn and Meredith (2002). See appendix A for a more detailed description. The out-of-sample period used to assess model performance is 1993:1 to 2000:4. Figures 8.1 and 8.2 depict, respectively, the dollar based German mark and yen exchange rates, with the vertical line indicating the beginning of the out-of-sample period. The out-ofsample period spans a period of dollar depreciation and then sustained appreciation.4 8.2.2

Full-Sample Estimation

Two speciﬁcations of the theoretical models were estimated: (1) an error correction speciﬁcation, and (2) a ﬁrst-differences speciﬁcation. Since implementation of the error correction speciﬁcation is relatively involved, we will address the ﬁrst-difference speciﬁcation to begin

244

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Figure 8.2 Japanese yen–US dollar exchange rate

with. Consider the general expression for the relationship between the exchange rate and fundamentals: st ¼ Xt G þ ut ;

ð5Þ

where Xt is a vector of fundamental variables under consideration. The ﬁrst-difference speciﬁcation involves the following regression: Dst ¼ DXt G þ ut :

ð6Þ

These estimates are then used to generate forecasts one and many quarters ahead. Since these exchange rate models imply joint determination of all variables in the equations, it makes sense to apply instrumental variables. However, previous experience indicates that the gains in consistency are far outweighed by the loss in efﬁciency, in terms of prediction (Chinn and Meese 1995). Hence we rely solely on OLS. One exception to this general rule is the UIP model. In this case the arbitrage condition implies a relationship between the change in the exchange rate and the level of the interest rate differential. Since no long-run condition is implied, we simply estimate the UIP relationship as stated in equation (4).

In-Sample Fit and Out-of-Sample Performance Evaluated

8.2.3

245

Empirical Results

The results of estimating the sticky-price monetary model in levels are presented in panel A of table 8.1. Using the 5 percent asymptotic critical value, we ﬁnd that there is evidence of cointegration for the dollarbased exchange rates for all currencies save one. The German mark stands out as a case where it is difﬁcult to obtain evidence of cointegration; we suspect that this is largely because of the breaks in the series for both money and income associated with the German reuniﬁcation. The evidence for cointegration is more attenuated when the ﬁnite sample critical values (Cheung and Lai 1993) are used. Then only the Canadian dollar and yen have some mixed evidence in favor of cointegration. This ambiguity is useful to recall when evaluating the estimates for the British sterling; the coefﬁcient estimates do not conform to those theoretically implied by the model, as the coefﬁcients of money, inﬂation and income are all incorrectly signed (although the latter two are insigniﬁcantly so). Only the interest rate coefﬁcient is signiﬁcant and correctly signed. In contrast, both the yen and franc broadly conform to the monetary model. Money and inﬂation are correctly signed, while interest rates enter in correctly only for the yen. Finally, the Canadian dollar presents some interesting results. The coefﬁcients are largely in line with the monetary model, although the income coefﬁcient is wrongly signed, with economic and statistical signiﬁcance. The use of the ﬁrst-difference speciﬁcation is justiﬁed when there is a failure to ﬁnd evidence of cointegration (the German mark), or alternatively one suspects that estimates of the long-run coefﬁcients are insufﬁciently precisely estimated to yield useful estimates. In panel B of table 8.1, the results from the ﬁrst-difference speciﬁcation are reported. A general ﬁnding is that the coefﬁcients do not typically enter with both statistical signiﬁcance and correct sign. One partial exception is the interest differential coefﬁcient. Higher interest rates, if all else constant is held constant, appear to appreciate the currency in four of ﬁve cases, although the yen–dollar rate estimate is not statistically signiﬁcant. The British sterling–dollar rate estimate is positive (while the inﬂation rate coefﬁcient is not statistically signiﬁcant), a ﬁnding that is more consistent with a ﬂexible price monetary model than a stickyprice one. Otherwise, the ﬁt does not appear particularly good. These mixed results are suggestive of alternative approaches; the ﬁrst we examine is the productivity-based model. Our interpretation

246

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.1 Full-sample estimates of sticky-price model Sign

BP/$

Can$/$

DM/$

SF/$

Yen/$

A. In levels a Cointegration (asy)

1, 1

3, 1

0, 0

1, 1

1, 1

Cointegration (fs)

0, 0

1, 0

0, 0

0, 0

0, 1

Money

[þ]

Income

[]

Interest rate

[]

Inﬂation rate B. In ﬁrst differences

[þ]

2.89*

1.10*

2.14*

3.61*

1.29

(1.01)

(0.25)

(0.74)

(0.74)

(0.96)

9.70*

0.93

(1.87)

(1.87)

19.49*

6.44*

(4.01)

(3.27)

(4.14)

(5.73)

(4.72)

7.11

10.74*

24.29*

40.96*

26.56*

(4.60)

(3.11)

(4.27)

(6.79)

(4.03)

0.16 (0.22)

0.02 (0.14)

0.44 (0.24)

[þ]

0.21 (0.12)

0.00 (0.06)

Income

[]

2.02*

0.48

Inﬂation rate

5.86

(1.72) 2.09

0.77 (1.97) 17.11*

b

Money

Interest rate

1.10

1.64 (3.94)

[] [þ]

0.51

0.59

(0.42)

(0.29)

(0.43)

(0.52)

0.83*

0.42*

0.91*

0.82*

(0.41)

(0.10)

(0.45)

(0.37)

0.15 (0.48)

0.07 (0.20)

0.00 (0.39) 0.28 (0.33)

1.26

1.29

0.32

(1.09)

(0.81)

(0.44)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes two lags of ﬁrst differences. The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

In-Sample Fit and Out-of-Sample Performance Evaluated

247

of the model simply augments the monetary model with a productivity variable. The results for this model are presented in table 8.2. From the asymptotic critical values, the evidence of cointegration in panel A of table 8.2 is comparable to that reported in panel A of table 8.1. For both the British sterling and Canadian dollar, there is evidence of multiple cointegrating vectors. However, in using the ﬁnite sample critical values, we ﬁnd that the number of implied vectors drops to one (or zero) in this case. In all cases the interest coefﬁcient is correctly signed, and signiﬁcant in most cases. Furthermore the money and inﬂation variables are correctly signed in most cases. The productivity coefﬁcients are signiﬁcant and consistent with the productivity in three cases—the Swiss franc, German mark, and yen. The latter two currencies have previously been found to be inﬂuenced by productivity trends.5 Estimates of the ﬁrst-difference speciﬁcations do not yield appreciably better results than their sticky-price counterparts. Interest differentials tend to be important, once again, while productivity fails to evidence any signiﬁcant impact for three of ﬁve rates. To the extent that one thinks that productivity is a slowly trending variable that inﬂuences the real exchange rate over long periods, this result is unsurprising. While this variable has the correct sign for the German mark– dollar rate, it has the opposite for the sterling–dollar rate. The Canadian dollar appears to be as resilient to being modeled using this productivity speciﬁcation as the others. Chen and Rogoff (2002) have asserted that the Canadian dollar is mostly determined by commodity prices; hence it is not surprising that both models fail to have any predictive content. The BEER model results are presented in table 8.3. There are no estimates for the Swiss franc and the yen because we lack quarterly data on government debt and net foreign assets. Overall, the results are not uniformly supportive of the BEER approach.6 Although there are some instances of correctly signed coefﬁcients, none show up correctly signed across all three currencies. Moving to a ﬁrst-difference speciﬁcation does not improve the results. Besides those on the relative price and real interest rate differentials, very few coefﬁcient estimates are in line with model predictions. For the DM/$ rate, the real interest rate and debt variables possess the correctly signed coefﬁcients, as do the relative price and net foreign assets for the Canadian dollar, but these appear to be isolated instances.7

248

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.2 Full-sample estimates of productivity model Sign

BP/$

Can$/$

DM/$

SF/$

Yen/$

Cointegration (asy)

1, 2

2, 2

0, 0

1, 1

1, 1

Cointegration (fs)

0, 0

1, 0

0, 0

0, 0

0, 1

A. In levels a

Money Income Interest rate Inﬂation rate Productivity

[þ] [] [] [þ] []

0.97*

6.81*

0.62*

2.00*

0.18

(0.47)

(1.45)

(0.33)

(0.30)

(0.54)

4.11*

25.76*

0.68

(1.23)

(6.62)

(0.81)

10.63*

34.53*

9.35*

3.67

(1.65)

(11.16)

(2.57)

(2.54)

(2.67)

9.86*

70.63*

9.18*

15.36*

12.09*

(1.63)

(12.00)

(1.85)

2.79

(2.49)

3.56* (0.68)

16.78* (5.60)

5.66* (1.11)

4.43* (1.46)

2.65* (0.76)

0.16

0.01

1.04 (0.76)

2.77* (1.29) 12.07*

B. In ﬁrst differences b Money

[þ]

0.40* (0.16)

Income

[]

1.59* (0.39)

Interest rate

[]

0.57 (0.46)

Inﬂation rate

[þ]

1.10* (0.50)

Productivity

[]

1.11* (0.21)

0.00 (0.06) 0.47

(0.22) 0.51

(0.14)

0.43 (0.24)

0.70

0.00

(0.29)

(0.43)

(0.51)

(0.40)

0.42*

0.91*

0.82*

(0.10)

(0.45)

(0.41)

1.26

1.19

0.37

(1.09)

(0.81)

(0.45)

5.66*

0.25

0.32

(1.11)

(0.21)

(0.31)

0.08 (0.20) 0.03 (0.15)

0.28 (0.32)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes two lags of ﬁrst differences. The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

In-Sample Fit and Out-of-Sample Performance Evaluated

249

Table 8.3 Full-sample estimates of BEER model Sign

BP/$

Can$/$

DM/$

Cointegration (asy)

2, 2

4, 2

1, 1

Cointegration (fs)

1, 2

2, 1

0, 0 9.38*

A. In levels a

Relative price Real interest rate Debt Terms of trade Net foreign assets

[] [] [þ] [] []

1.27*

1.05*

(0.38)

(0.34)

3.13*

2.03*

(1.07)

(0.91)

1.06*

2.62*

0.04

(0.30)

(0.51)

(0.72)

0.92

0.75*

(1.36) 2.37 (2.09)

0.13

(0.82)

(0.24)

(1.04)

5.65* (0.56)

1.39* (0.40)

4.88* (0.76)

0.44*

0.38

B. In ﬁrst differences b Relative price

[]

0.55 (0.56)

Real interest rate

[]

0.17 (0.16)

Debt

[þ]

0.38 (0.27)

Terms of trade Net foreign assets

[] []

(0.17)

(0.59)

0.15

1.04*

(0.11)

(0.34)

0.18

1.52*

(0.22)

(0.64)

0.09

0.02

0.59*

(0.31)

(0.06)

(0.27)

2.61*

1.19*

3.14*

(0.49)

(0.25)

(0.72)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes 2 lags of ﬁrst differences (4 lags for DM). The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

250

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.4 Uncovered interest parity estimates BP/$

Can$/$

DM/$

SF/$

Yen/$

2.19*

0.48*

0.70

1.28*

2.99*

(1.08)

(0.51)

(1.04)

(0.96)

Horizon 3 month

(1.09)

Adj R 2

0.04

0.00

0.01

0.01

0.06

SER

0.21

0.08

0.26

0.29

0.28

1.42* (0.99)

0.61* (0.49)

0.58* (0.66)

1.05* (0.52)

2.60* (0.69)

1 year Adj R 2

0.06

0.03

0.00

0.04

0.17

SER

0.11

0.04

0.14

0.14

0.13

5 year

0.44

0.24

0.52

1.18*

1.19

(0.36)

(0.47)

(0.75)

(0.97)

(0.38)

Adj R 2

0.02

0.00

0.02

0.04

0.13

SER

0.04

0.02

0.06

0.04

0.05

Note: OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ k 1). SER is standard error of regression. * indicates signiﬁcantly different from unity at the 5 percent marginal signiﬁcance level.

Although we do not use estimated equations to conduct the forecasting of the UIP model, it is informative to consider how well the data conform to the UIP relationship. As is well known, at short horizons, the evidence in favor of UIP is lacking.8 The results of estimating equation (4) are reported in table 8.4. Consistent with Chinn and Meredith (2002), the short-horizon data (1 quarter and 4 quarter maturities) provide almost uniformly negative coefﬁcient estimates, in contradiction to the implication of the UIP hypothesis. At the ﬁve-year horizon, the results are substantially different for all cases, save the Swiss franc. Now all the coefﬁcients are positive; moreover in no case except the franc is the coefﬁcient estimate signiﬁcantly different from the theoretically implied value of unity. 8.3 8.3.1

Forecast Comparison Estimation and Forecasting

We adopt the convention in the empirical exchange rate modeling literature of implementing ‘‘rolling regressions.’’ That is, estimates are applied over a given data sample, out-of-sample forecasts produced,

In-Sample Fit and Out-of-Sample Performance Evaluated

251

then the sample is moved up, or ‘‘rolled’’ forward one observation before the procedure is repeated. This process continues until all the out-of-sample observations are exhausted. This procedure is selected over recursive estimation because it is more in line with previous work, including the original Meese and Rogoff paper. Moreover the power of the test is kept constant as the sample size over which the estimation occurs is ﬁxed, rather than increasing as it does in the recursive framework. The error correction estimation involves a two-step procedure. In the ﬁrst step, the long-run cointegrating relation implied by (5) is identiﬁed using the Johansen procedure, as described in section 8.2. The esti~ Þ is incorporated into the error correction mated cointegrating vector ðG term, and the resulting equation ~ Þ þ ut st stk ¼ d0 þ d1 ðstk Xtk G

ð7Þ

is estimated via OLS. Equation (7) can be thought of as an error correction model stripped of the short-run dynamics. A similar approach was used in Mark (1995) and Chinn and Meese (1995), except for the fact that, in those two cases, the cointegrating vector was imposed a priori. One key difference between our implementation of the error correction speciﬁcation and that undertaken in some other studies involves the treatment of the cointegrating vector. In some other prominent studies (MacDonald and Taylor 1994) the cointegrating relationship is estimated over the entire sample, and then out-of-sample forecasting undertaken, where the short-run dynamics are treated as time varying but the long-run relationship is not. While there are good reasons for adopting this approach—in particular, one wants to use as much information as possible to obtain estimates of the cointegrating relationships—the asymmetry in the estimation approach is troublesome, and makes it difﬁcult to distinguish quasi–ex ante forecasts from true ex ante forecasts. Consequently our estimates of the longrun cointegrating relationship vary as the data window moves. It is also useful to stress the difference between the error correction speciﬁcation forecasts and the ﬁrst-difference speciﬁcation forecasts. In the latter, ex post values of the right-hand side variables are used to generate the predicted exchange rate change. In the former, contemporaneous values of the right-hand side variables are not necessary, and the error correction predictions are true ex ante forecasts. Hence we

252

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

are affording the ﬁrst-difference speciﬁcations a tremendous informational advantage in forecasting.9 8.3.2

Forecast Comparison

To evaluate the forecasting accuracy of the different structural models, the ratio between the mean squared error (MSE) of the structural models and a driftless random walk is used. A value smaller (larger) than one indicates a better performance of the structural model (random walk). We also explicitly test the null hypothesis of no difference in the accuracy of the two competing forecasts (structural model vs. driftless random walk). In particular, we use the Diebold-Mariano statistic (Diebold and Mariano 1995), which is deﬁned as the ratio between the sample mean loss differential and an estimate of its standard error; this ratio is asymptotically distributed as a standard normal.10 The loss differential is deﬁned as the difference between the squared forecast error of the structural models and that of the random walk. A consistent estimate of the standard deviation can be constructed from a weighted sum of the available sample autocovariances of the loss differential vector. Following Andrews (1991), a quadratic spectral kernel is employed, together with a data-dependent bandwidth selection procedure.11 We also examine the predictive power of the various models along different dimensions. One might be tempted to conclude that we are merely changing the well-established ‘‘rules of the game’’ by doing so. However, there are very good reasons to use other evaluation criteria. First, there is the intuitively appealing rationale that minimizing the mean squared error (or relatedly mean absolute error) may not be important from an economic standpoint. A less pedestrian motivation is that the typical mean squared error criterion may miss out on important aspects of predictions, especially at long horizons. Christoffersen and Diebold (1998) point out that the standard mean squared error criterion indicates no improvement of predictions that take into account cointegrating relationships vis a` vis univariate predictions. But surely any reasonable criteria would put some weight on the tendency for predictions from cointegrated systems to ‘‘hang together.’’ Hence, our ﬁrst alternative evaluation metric for the relative forecast performance of the structural models is the direction-of-change statistic, which is computed as the number of correct predictions of the direction of change over the total number of predictions. A value above

In-Sample Fit and Out-of-Sample Performance Evaluated

253

(below) 50 percent indicates a better (worse) forecasting performance than a naive model that predicts the exchange rate has an equal chance to go up or down. Again, Diebold and Mariano (1995) provide a test statistic for the null of no forecasting performance of the structural model. The statistic follows a binomial distribution, and its studentized version is asymptotically distributed as a standard normal. Not only does the direction-of-change statistic constitute an alternative metric, it is also an approximate measure of proﬁtability. We have in mind here tests for market-timing ability (Cumby and Modest 1987).12 The third metric we used to evaluate forecast performance is the consistency criterion proposed in Cheung and Chinn (1998). This metric focuses on the time series properties of the forecast. The forecast of a given spot exchange rate is labeled as consistent if (1) the two series have the same order of integration, (2) they are cointegrated, and (3) the cointegration vector satisﬁes the unitary elasticity of expectations condition. Loosely speaking, a forecast is consistent if it moves in tandem with the spot exchange rate in the long run. Cheung and Chinn (1998) provide a more detailed discussion on the consistency criterion and its implementation. 8.4 8.4.1

Comparing the Forecast Performance The MSE Criterion

The comparison of forecasting performance based on MSE ratios is summarized in table 8.5. The table contains MSE ratios and the pvalues from ﬁve dollar-based currency pairs, four structural models, the error correction and ﬁrst-difference speciﬁcations, and three forecasting horizons. Every cell in the table has two entries. The ﬁrst one is the MSE ratio (the MSEs of a structural model to the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value of the hypothesis that the MSEs of the structural and random walk models are the same. Because of the lack of data, the behavioral equilibrium exchange rate model is not estimated for the dollar–Swiss franc, dollar–yen exchange rates, and all yen-based exchange rates. Altogether there are 153 MSE ratios. Of these 153 ratios, 90 are computed from the error correction speciﬁcation and 63 from the ﬁrst-difference one. Note that in the tables only ‘‘error correction speciﬁcation’’ entries are reported for the interest rate parity model. This model is not

254

Table 8.5 MSE ratios from the dollar-based and yen-based exchange rates Speciﬁcation Panel A ECM

S–P

IRP

PROD

BP/$ 1.0469 0.3343

1.0096 0.6613

1.0795 0.1827

4

1.0870 0.5163

0.7696 0.3379

20

0.4949 0.1329

0.9810 0.9581

1 4

1

20 Panel B ECM

FD

BEER

S–P

IRP

PROD

1.1597 0.0909

BP/yen 0.9709 0.5831

1.0421 0.6269

1.0266 0.7905

1.1974 0.2571

1.5255 0.0001

1.1466 0.3889

1.0008 0.9975

1.4142 0.3171

0.7285 0.5225

1.2841 0.4016

1.2020 0.1302

0.7611 0.5795

1.7493 0.0295

1.0357 0.7095

1.1678 0.4255

1.8876 0.0092

0.9655 0.7175

1.0000 1.0000

1.2691 0.3260 6.0121 0.0000

1.3830 0.1038 2.2029 0.0021

3.7789 0.0004 18.370 0.0000

1.1191 0.6543 4.5445 0.0000

1.1114 0.6886 4.7881 0.0000

CAN$/yen

CAN$/$ 1

1.0365 0.3991

1.0849 0.0316

1.0537 0.3994

1.2644 0.0018

0.9617 0.2537

1.0096 0.8710

0.9948 0.9269

4

1.0681 0.2531

1.0123 0.9592

1.1194 0.2015

1.5570 0.0002

0.9716 0.7037

1.0045 0.9814

1.1185 0.4038

20

0.6339 0.0248

0.1881 0.0001

1.0204 0.9276

1.7609 0.0302

1.1694 0.2747

0.6462 0.4125

4.8827 0.1130

1

1.0474 0.6214 0.9866 0.9531

1.0842 0.3971 1.0519 0.8232

0.5424 0.1544 1.2907 0.5046

1.0106 0.9144 1.1578 0.5751

4

0.9827 0.8456 1.1663 0.5827

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

Horizon

Panel C ECM

FD

4.7274 0.0000

12.181 0.0000

12.12 0.0000

DM/yen

DM/$ 0.9990 0.5440

1.0705 0.0383

0.9867 0.5858

1.0810 0.1951

1.0447 0.3200

0.9662 0.4790

0.9983 0.0528

4

0.9967 0.5861

1.2090 0.0694

0.9298 0.2956

1.0484 0.3109

1.0006 0.5779

0.8571 0.3238

1.0003 0.7265

20

1.0242 0.0004

1.0073 0.9354

1.0410 0.0030

0.6299 0.0891

1.0034 0.6003

0.5485 0.0480

0.9921 0.1126

1

1.0354 0.3020 1.1184 0.2019

1.1208 0.1959 1.1782 0.0029

0.4649 0.0009 0.3331 0.0059

1.0227 0.7181 1.0859 0.1849

1.0060 0.9219 1.0045 0.9625

2.0817 1.1915

1.9828 0.0000

1.2906 0.2550

0.9521 0.7217

0.8569 0.3572

20 Panel D

FD

0.2937 0.1018

1

4

ECM

0.2051 0.0318

SF/yen

SF/$ 0.9784 0.7773

1.1101 0.0692

1.1200 0.1614

0.9961 0.9333

0.9985 0.9522

1.0515 0.2892

4

0.8864 0.4152

1.2871 0.0689

1.0409 0.7438

1.0627 0.2595

0.9276 0.3983

1.0140 0.7786

20

1.2873 0.1209

1.4894 0.0000

0.9651 0.8684

0.8331 0.2925

0.9031 0.4856

0.9216 0.1019

1

1.3115 0.1641

1.3891 0.1734

0.9350 0.1643

0.9338 0.1765

4

1.6856 0.0774

1.8437 0.0713

1.0114 0.8595

0.9666 0.7366

20

5.6773 0.0000

5.9918 0.0000

0.9208 0.0000

0.8852 0.0001

255

1

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

256

Table 8.5 (continued) Horizon

IRP

PROD

0.9821 0.8799 0.8870 0.6214

1.0681 0.2979 1.2047 0.2862

0.9973 0.9647 0.9460 0.7343

20

0.8643 0.4299

0.9824 0.9661

0.8500 0.3856

1

1.0022 0.9840

0.9456 0.4427

4

1.0240 0.8207

1.0624 0.5342

20

2.7132 0.0000

2.2586 0.0001

Panel E ECM

BEER

S–P

IRP

PROD

Yen/$ 1 4

Note: The results are based on dollar-based and yen-based exchange rates and their forecasts. Each cell has two entries. The ﬁrst is the MSE ratio (the MSEs of a structural model to the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value of the hypothesis that the MSEs of the structural and random walk models are the same (Diebold and Mariano 1995). The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. Due to data unavailability, the BEER model was not estimated for the Japanese yen and Swiss franc.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

In-Sample Fit and Out-of-Sample Performance Evaluated

257

estimated; rather the predicted spot rate is calculated using the uncovered interest parity condition. To the extent that long-term interest rates can be considered the error correction term, we believe this categorization is most appropriate. Overall, the MSE results are not favorable to the structural models. Of the 153 MSE ratios, 109 are not signiﬁcant (at the 10 percent signiﬁcance level), and 44 are signiﬁcant. That is, for the majority of the cases one cannot differentiate the forecasting performance between a structural model and a random walk model. For the 44 signiﬁcant cases, there are 32 cases in which the random walk model is signiﬁcantly better than the competing structural models and only 11 cases in which the opposite is true. As 10 percent is the size of the test and 12 cases constitute less than 10 percent of the total of 153 cases, the empirical evidence can hardly be interpreted as supportive of the superior forecasting performance of the structural models. One caveat is necessary, however. When one restricts attention to the long-horizon forecasts, it turns out that those incorporating long-run restrictions outperform a random walk more often than would be expected to occur randomly: ﬁve out of 30 cases, or 17 percent, using a 10 percent signiﬁcance level. Inspecting the MSE ratios, one does not observe many consistent patterns, in terms of outperformance. It appears that the BEER model does not do particularly well except for the DM/$ rate. The interest rate parity model tends to do better at the 20-quarter horizon than at the 1- and 4-quarter horizons—a result consistent with the well-known bias in forward rates at short horizons. In accordance with the existing literature, our results are supportive of the assertion that it is very difﬁcult to ﬁnd forecasts from a structural model that can consistently beat the random walk model using the MSE criterion. The current exercise further strengthens the assertion as it covers both dollar- and yen-based exchange rates and some structural models that have not been extensively studied before. 8.4.2

The Direction-of-Change Criterion

Table 8.6 reports the proportion of forecasts that correctly predicts the direction of the exchange rate movement and, underneath these sample proportions, the p-values for the hypothesis that the reported proportion is signiﬁcantly different from 0.5. When the proportion statistic is signiﬁcantly larger than 0.5, the forecast is said to have the ability to predict the direct of change. On the other hand, if the statistic is

258

Table 8.6 Direction-of-change statistics from the dollar-based and yen-based exchange rates Speciﬁcation Panel A ECM

S–P

IRP

PROD

BEER

S–P

IRP

PROD

BP/$ 0.5312 0.7236

0.4849 0.8618

0.5313 0.7237

0.4062 0.2888

BP/yen 0.5625 0.4795

0.4546 0.6015

0.6563 0.0771

4

0.5862 0.3531

0.5455 0.6015

0.4483 0.5775

0.3448 0.0946

0.5517 0.5774

0.6364 0.1172

0.5517 0.5775

20

0.8461 0.0125

0.7273 0.0090

0.7692 0.0522

0.3846 0.4053

0.5384 0.7815

0.5758 0.3841

0.2308 0.0522

1

0.5937 0.2888

0.4688 0.7237

0.4062 0.2888

0.5937 0.2888

0.4375 0.4795

4

0.5517 0.5774 0.3076 0.1655

0.5172 0.8527 0.1539 0.0126

0.3448 0.0946 0.3076 0.1655

0.6551 0.0946 0.0000 0.0000

0.5862 0.3532 0.0000 0.0000

1

20 Panel B ECM

FD

CAN$/yen

CAN$/$ 1

0.4062 0.2888

0.3939 0.2230

0.3438 0.0771

0.3125 0.0338

0.5937 0.2888

0.4849 0.8618

0.6250 0.1573

4

0.4827 0.8526

0.4242 0.3841

0.4828 0.8527

0.1724 0.0004

0.6206 0.1936

0.5758 0.3841

0.5172 0.8527

20

0.7692 0.0522

1.0000 0.0000

0.4615 0.7815

0.0769 0.0022

0.5384 0.7815

0.7273 0.0090

0.2308 0.0522

1

0.5312 0.7236 0.7586 0.0053

0.5625 0.4795 0.7241 0.0158

0.6250 0.1573 0.5862 0.3531

0.5000 1.0000 0.5172 0.8526

4

0.4375 0.4795 0.4828 0.8527

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

Horizon

Panel C ECM

FD

0.0000 0.0000

0.3077 0.1655

0.3076 0.1655 DM/yen

DM/$ 0.5000 1.0000

0.3030 0.0236

0.3750 0.1573

0.5625 0.4795

0.6250 0.1573

0.5152 0.8618

0.5000 1.0000

4

0.5517 0.5774

0.3030 0.0236

0.3103 0.0411

0.4827 0.8526

0.4137 0.3531

0.6667 0.0555

0.3793 0.1937

20

0.0769 0.0022

0.5152 0.8618

0.2308 0.0522

0.2307 0.0522

0.6923 0.1655

0.8485 0.0001

0.6154 0.4054

1

0.5000 1.0000 0.3448 0.0946

0.4063 0.2888 0.2759 0.0158

0.8125 0.0004 0.7931 0.0015

0.4687 0.7236 0.4827 0.8526

0.5000 1.0000 0.4483 0.5775

0.0769 0.0022

0.0769 0.0023

0.3076 0.1655

0.3076 0.1655

0.4615 0.7815

20 Panel D

FD

1.0000 0.0000

1

4

ECM

1.0000 0.0000

SF/yen

SF/$ 0.5625 0.4795

0.3030 0.0236

0.5625 0.4795

0.6562 0.0771

0.6061 0.2230

0.4688 0.7237

4

0.5517 0.5774

0.3636 0.1172

0.5517 0.5775

0.4827 0.8526

0.5758 0.3841

0.4138 0.3532

20

0.5384 0.7815

0.4546 0.6698

0.6923 0.1655

0.5384 0.7815

0.5000 1.0000

0.6154 0.4054

1

0.4062 0.2888

0.4375 0.4795

0.5937 0.2888

0.6875 0.0339

4

0.4137 0.3531

0.5172 0.8527

0.5517 0.5774

0.5862 0.3532

20

0.2307 0.0522

0.2308 0.0522

0.5384 0.7815

0.6154 0.4054

259

1

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

260

Table 8.6 (continued) Horizon

IRP

PROD

0.6562 0.0771 0.5517 0.5774

0.3636 0.1172 0.5152 0.8618

0.5625 0.4795 0.4828 0.8527

20

0.7692 0.0522

0.5152 0.8618

0.6923 0.1655

1

0.6875 0.0338

0.6563 0.0771

4

0.6551 0.0946

0.6207 0.1937

20

0.0000 0.0000

0.0000 0.0000

Panel E ECM

BEER

S–P

IRP

PROD

Yen/$ 1 4

Note: The table reports the proportion of forecasts that correctly predict the direction of the dollar-based and yen-based exchange rate movements. Under each direction-of-change statistic, the p-values for the hypothesis that the reported proportion is signiﬁcantly different from 0.5 is listed. When the statistic is signiﬁcantly larger than 0.5, the forecast is said to have the ability to predict the direct of change. If the statistic is signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrstdifference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. Due to data unavailability, the BEER model was not estimated for the Japanese yen and Swiss franc.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

In-Sample Fit and Out-of-Sample Performance Evaluated

261

signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. If a model consistently forecasts the direction of change incorrectly, traders can derive a potentially proﬁtable trading rule by going against these forecasts. Thus, for trading purposes, information regarding the signiﬁcance of ‘‘incorrect’’ prediction is as useful as the one of ‘‘correct’’ forecasts. However, in evaluating the ability of the model to describe exchange rate behavior, we separate the two cases. There is mixed evidence on the ability of the structural models to correctly predict the direction of change. Among the 153 direction-ofchange statistics, 23 (27) are signiﬁcantly larger (less) than 0.5 at the 10 percent level. The occurrence of the signiﬁcant outperformance cases is slightly higher (15 percent) than the one implied by the 10 percent level of the test. The results indicate that the structural model forecasts can correctly predict the direction of the change, although the proportion of cases where a random walk outperforms the competing models is higher than what one would expect if they occurred randomly. Let us take a closer look at the incidences in which the forecasts are in the right direction. About half of the 23 cases are in the error correction category (12). Thus it is not clear if the error correction speciﬁcation— which incorporates the empirical long-run relationship—is a better speciﬁcation for the models under consideration. Among the four models under consideration, the sticky-price model has the highest number (10) of forecasts that give the correct directionof-change prediction (18 percent of these forecasts), while the interest rate parity model has the highest proportion of correct predictions (19 percent). Thus, at least on this count, the newer exchange rate models do not signiﬁcantly edge out the ‘‘old fashioned’’ sticky-price model save perhaps the interest rate parity condition. The cases of correct direction prediction appear to cluster at the long forecast horizon. The 20-quarter horizon accounts for 10 of the 23 cases while the 4-quarter and 1-quarter horizons have, respectively, 6 and 7 direction-of-change statistics that are signiﬁcantly larger than 0.5. Since there have been few studies utilizing the direction-of-change statistic in similar contexts, it is difﬁcult to make comparisons. Chinn and Meese (1995) apply the direction-of-change statistic to three-year horizons for three conventional models, and ﬁnd that performance is largely currency-speciﬁc: the no-change prediction is outperformed in the case of the dollar–yen exchange rate, while all models are outperformed in the case of the dollar–sterling rate. In contrast, in our study at the 20quarter horizon, the positive results appear to be concentrated in the

262

Table 8.7 Cointegration between exchange rates and their forecasts Speciﬁcation Panel A ECM

FD

Horizon

S–P

IRP

PROD

BEER

S–P

1

BP/$ 2.12

4

14.25*

2.41

19.26*

BP/yen 8.70

5.35

5.06

4.88

5.72

6.98

18.13*

26.54*

3.99

7.26

20

9.69*

8.71

16.45*

6.54

6.27

5.25

1

8.51

19.05*

7.66

15.85*

5.50

4

8.30

7.32

4.53

5.34

5.38

20

2.78

7.73

1.87

8.77

8.80

ECM

FD

FD

4.02

CAN$/yen

CAN$/$ 1

6.74

6.03

3.41

6.32

6.94

6.59

7.77

4 20

6.31 6.58

5.87 7.03

1.97 8.96

5.80 4.53

2.85 7.22

4.18 9.51

1.13 4.29

1

14.42*

15.60*

12.53*

15.07*

13.87*

4

10.97*

7.22

6.22

5.64

4.20

20

3.87

4.08

1.93

6.31

6.50

Panel C ECM

PROD

DM/yen

DM/$ 1

2.78

11.18*

3.11

8.38

2.43

5.71

5.57

4

4.74

11.72*

2.83

6.42

14.77*

4.39

9.50

20

1.17

1.01

11.09*

3.30

7.12

13.97*

1 4

14.99* 8.37

7.21 7.36

7.63 3.02

14.28* 42.41*

16.37* 3.58

20

1.37

1.20

5.17

5.55

5.84

6.45

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Panel B

IRP

ECM

FD

1.08

6.88

3.24

—

5.12

2.76

10.31*

4

22.52*

6.84

34.23*

—

1.57

108.57*

3.25

20

0.69

6.93

0.49

—

4.05

4.72

1

2.73

1.02

—

4.40

47.89*

4

5.21

1.65

—

1.81

3.10

20

2.90

2.78

—

7.83

7.01

Panel E ECM

FD

SF/yen

SF/$ 1

6.39

Yen/$ 1 4

14.82* 5.73

12.20* 10.93*

4.84 5.33

— —

20

14.99*

1.05

13.16*

—

1

20.48*

25.39*

—

4

5.61

42.86*

—

20

15.06*

13.17*

—

Note: The table reports the Johansen maximum eigenvalue statistic for the null hypothesis that a dollar-based (or a yen-based) exchange rate and its forecast are not cointegrated. * indicates the 10% marginal signiﬁcance level. Tests for the null of one cointegrating vector were also conducted, but in all cases the null was not rejected. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. The dash indicates that the statistics were not generated due to unavailability of data.

In-Sample Fit and Out-of-Sample Performance Evaluated

Panel D

263

264

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

yen–dollar and Canadian dollar–dollar rates.13 It is interesting to note that the direction-of-change statistic works for the interest rate parity model almost only at the 20-quarter horizon, thus mirroring the MSE results. This pattern is entirely consistent with the ﬁnding that uncovered interest parity holds better at long horizons. 8.4.3

The Consistency Criterion

The consistency criterion only requires the forecast and actual realization comove one-to-one in the long run. One could argue that the criterion is less demanding than the MSE and direction-of-change metrics. Indeed, a forecast that satisﬁes the consistency criterion can (1) have a MSE larger than that of the random walk model, (2) have a directionof-change statistic less than 0.5, or (3) generate forecast errors that are serially correlated. However, given the problems related to modeling, estimation, and data quality, the consistency criterion can be a more ﬂexible way to evaluate a forecast. In assessing the consistency, we ﬁrst test if the forecast and the realization are cointegrated.14 If they are cointegrated, then we test if the cointegrating vector satisﬁes the ð1; 1Þ requirement. The cointegration results are reported in table 8.7. The test results for the ð1; 1Þ restriction are reported in table 8.8. Thirty-eight of 153 cases reject the null hypothesis of no cointegration at the 10 percent signiﬁcance level. Thus 25 percent of forecast series are cointegrated with the corresponding spot exchange rates. The error correction speciﬁcation accounts for 20 of the 38 cointegrated cases and the ﬁrst-difference speciﬁcation accounts for the remaining 18 cases. There is no evidence that the error correction speciﬁcation gives better forecasting performance than the ﬁrst-difference speciﬁcation. Interestingly the sticky-price model garners the largest number of cointegrated cases. There are 54 forecast series generated under the sticky-price model. Fifteen of these 54 series (i.e., 28 percent) are cointegrated with the corresponding spot rates. Twenty-six percent of the interest rate parity and 24 percent of the productivity model are cointegrated with the spot rates. Again, we do not ﬁnd evidence that the recently developed exchange rate models outperform the ‘‘old’’ vintage sticky-price model. The yen–dollar has 10 out of the 15 forecast series that are cointegrated with their respective spot rates. The Canadian dollar–dollar pair, which yields relatively good forecasts according to the direction-

In-Sample Fit and Out-of-Sample Performance Evaluated

265

of-change metric, has only 4 cointegrated forecast series. Evidently the forecasting performance is not just currency speciﬁc; it also depends on the evaluation criterion. The distribution of the cointegrated cases across forecasting horizons is puzzling. The frequency of occurrence is inversely proportional to the forecasting horizons. There are 19 of 51 one-quarter ahead forecast series that are cointegrated with the spot rates. However, there are only 11 of the 4-quarter ahead and 8 of the 20-quarter ahead forecast series that are cointegrated with the spot rates. One possible explanation for this result is that there are fewer observations in the 20-quarter ahead forecast series, and this effects the power of the cointegration test. The results of testing for the long-run unitary elasticity of expectations at the 10 percent signiﬁcance level are reported in table 8.8. The condition of long-run unitary elasticity of expectations, that is, the ð1; 1Þ restriction on the cointegrating vector, is rejected by the data quite frequently. The ð1; 1Þ restriction is rejected in 33 of the 38 cointegration cases. That is 13 percent of the cointegrated cases display long-run unitary elasticity of expectations. Taking both the cointegration and restriction test results together, 3 percent of the 153 cases meet the consistency criterion. 8.4.4

Discussion

Several aspects of the foregoing analysis merit discussion. To begin with, even at long horizons, the performance of the structural models is less than impressive along the MSE dimension. This result is consistent with those in other recent studies, although we have documented this ﬁnding for a wider set of models and speciﬁcations. Groen (2000) restricted his attention to a ﬂexible price monetary model, while Faust et al. (2001) examined a portfolio balance model as well; both remained within the MSE evaluation framework. Expanding the set of criteria does yield some interesting surprises. In particular, the direction-of-change statistics indicate more evidence that structural models can outperform a random walk. However, the basic conclusion that no economic model is consistently more successful than the others remains intact. This, we believe, is a new ﬁnding. Even if we cannot glean from this analysis a consistent ‘‘winner,’’ it may still be of interest to note the best and worst performing combinations of model/speciﬁcation/currency. The best performance on the MSE criterion is turned in by the interest rate parity model at the

266

Table 8.8 Results of ð1; 1Þ restriction test Speciﬁcation Panel A ECM

Horizon 1 4 20

FD

— —

445.3 0.00

— —

— —

4

— — — —

Panel B

39.66 0.00

— —

1

20

ECM

BP/$ — —

IRP

PROD

BEER

— —

0.32 0.57

— —

19.99 0.00

S–P

IRP

PROD

BP/yen — —

— —

— —

49.55 0.00

— —

— —

— —

— —

458.91 0.00

— —

— —

1.56 0.21

— —

24.73 0.00

— —

— — — —

— — — —

— — — —

— — — —

CAN$/yen

CAN$/$ 1

— —

— —

— —

— —

— —

— —

— —

4

— —

— —

— —

— —

— —

— —

— —

20

— —

— —

— —

— —

— —

— —

— —

15.73 0.00 — —

1263 0.00 — —

17.17 0.00 — —

1 4

16.58 0.00 132.5 0.00

28.50 0.00

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

— —

1

— —

4 20

Panel C ECM

FD

1

164.5 0.00

— —

— —

— —

— —

— —

— —

392.97 0.00

— —

— —

11.20 0.00

— —

— —

— —

— —

— —

— —

535.13 0.00 — — — —

— — — —

20

— —

— —

— —

1

— — 3.34 0.06

5.06 0.02

3.40 0.06 3.88 0.04

— — 3.40 0.07 — — — —

— — SF/yen

SF/$

4

— — DM/yen

6.73 0.00 — —

Panel D

FD

— —

DM/$

4

ECM

— —

— —

— —

— —

— —

— —

313.12 0.00

— —

— —

— —

— —

— —

— — — —

9.77 0.00

4.56 0.03

— —

1

— —

— —

— —

31.07 0.00

4

— —

— —

— —

— —

20

— —

— —

— —

— —

267

20

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

268

Table 8.8 (continued) Horizon

Panel E ECM

IRP

PROD

62.10 0.00 — —

209.36 0.00 33.58 0.00

— — — —

876.4 0.00

— —

1916 0.00

BEER

S–P

IRP

PROD

Yen/$ 1 4 20 1 4 20

0.582 0.445 — — 436.4 0.00

1.03 0.31 1.14 0.29 289.22 0.00

Note: The likelihood ratio test statistic for the restriction of ð1; 1Þ on the cointegrating vector and its p-value are reported. The test is only applied to the cointegration cases present in table 8.3. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

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20-quarter horizon for the Canadian dollar–yen exchange rate, with a MSE ratio of 0.19 ( p-value of 0.0001). The worst performances are associated with ﬁrst-difference speciﬁcations; in this case the highest MSE ratio is for the ﬁrst differences speciﬁcation of the sticky-price exchange rate model at the 20-quarter horizon for the Canadian dollar– US dollar exchange rate. However, the other catastrophic failures in prediction performance are distributed across ﬁrst-difference speciﬁcations of the various models, so the key determinant in this pattern of results appears to be the difﬁculty in estimating stable short-run dynamics. (We take here into account the fact that these predictions utilize ex post realizations of the right-hand side variables.) Overall, the inconstant nature of the parameter estimates appears to be closely linked with the erratic nature of the forecasting performance. This applies to the variation in long-run estimates and reversion coefﬁcients, but perhaps most strongly to the short-run dynamics obtained in the ﬁrst-differences speciﬁcations. 8.5

Concluding Remarks

In this chapter we systematically assess the in-sample ﬁt and out-ofsample predictive capacities of models developed during the 1990s. These models are compared along a number of dimensions, including econometric speciﬁcation, currencies, and differing metrics. Our investigation does not reveal that any particular model or any particular speciﬁcation ﬁt the data well, in terms of providing estimates in accord with theoretical priors. Of course, this ﬁnding is dependent on a very simple speciﬁcation search, and we used theory to discipline variable selection and information criteria to select lag lengths. On the other hand, some models seem to do well at certain horizons, for certain criteria. Indeed, it may be that one model will do well for one exchange rate and not for another. For instance, the productivity model does well for the mark–yen rate along the direction-of-change and consistency dimensions (although not by the MSE criterion), but that same conclusion cannot be applied to any other exchange rate. Similarly we fail to ﬁnd any particular model or speciﬁcation that out-performed a random walk on a consistent basis. Again, we imposed the disciplining device of using a given speciﬁcation, and a given out-of-sample forecasting period. Perhaps most interestingly,

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there is little apparent correlation between how well the in-sample estimates accord with theory and out-of-sample prediction performance. The only link between in-sample and out-of-sample performance is an indirect one, for the interest parity condition. It is well known that interest rate differentials are biased predictors of future spot rate movements at short horizons. However, the improved predictive performance at longer horizons does accord with the fact that uncovered interest parity is more likely to hold at longer horizons than at short horizons. In sum, while the results of our study have been fairly negative regarding the predictive capabilities of newer empirical models of exchange rates, in some sense we believe the ﬁndings pertain more to difﬁculties in estimation, rather than the models themselves. And this may point the direction for future research avenues.15 Appendix A: Data Unless otherwise stated, we use seasonally adjusted quarterly data from the IMF International Financial Statistics ranging from the second quarter of 1973 to the last quarter of 2000. The exchange rate data are end of period exchange rates. Money is measured as narrow money (essentially M1), with the exception of the United Kingdom, where M0 is used. The output data are measured in constant 1990 prices. The consumer and producer price indexes also use 1990 as base year. The three-month, annual, and ﬁve-year interest rates are end-ofperiod constant maturity interest rates and are obtained from the IMF country desks. See Meredith and Chinn (1998) for details. Five-year interest rate data were unavailable for Japan and Switzerland; hence data from Global Financial Data http://www.globalﬁndata.com/ were used, speciﬁcally, ﬁve-year government note yields for Switzerland and ﬁve-year discounted bonds for Japan. The productivity series are labor productivity indexes, measured as real GDP per employee, converted to indexes (1995 ¼ 100). These data are drawn from the Bank for International Settlements database. The net foreign asset (NFA) series is computed as follows. Using stock data for year 1995 on NFA (Lane and Milesi-Ferretti 2001) at http://econserv2.bess.tcd.ie/plane/data.html, and ﬂow quarterly data from the IFS statistics on the current account, we generated quarterly stocks for the NFA series (with the exception of Japan, for which there is no quarterly data available on the current account).

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To generate quarterly government debt data, we follow a similar strategy. We use annual debt data from the IFS statistics, combined with quarterly government deﬁcit (surplus) data. The data source for Canadian government debt is the Bank of Canada. For the United Kingdom, the IFS data are updated with government debt data from the public sector accounts of the UK Statistical Ofﬁce (for Japan and Switzerland, we have very incomplete data sets, and hence no behavioral equilibrium exchange rate models are estimated for these two countries). Appendix B: Evaluating Forecast Accuracy The Diebold-Mariano statistics (Diebold and Mariano 1995) are used to evaluate the forecast performance of the different model speciﬁcations relative to that of the naive random walk. Given the exchange rate series xt and the forecast series yt , the loss function L for the mean square error is deﬁned as Lðyt Þ ¼ ðyt xt Þ 2 :

ðA1Þ

Testing whether the performance of the forecast series is different from that of the naive random walk forecast zt is equivalent to testing whether the population mean of the loss differential series dt is zero. The loss differential is deﬁned as dt ¼ Lðyt Þ Lðzt Þ:

ðA2Þ

Under the assumptions of covariance stationarity and short-memory for dt , the large-sample statistic for the null of equal forecast performance is distributed as a standard normal, and can be expressed as d qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ; PT PðT1Þ ðdt dÞðdtjtj dÞ 2p t¼ðT1Þ lðt=SðTÞÞ t¼jtjþ1

ðA3Þ

where lðt=SðTÞÞ is the lag window, SðTÞ is the truncation lag, and T is the number of observations. Different lag-window speciﬁcations can be applied, such as the Barlett or the quadratic spectral kernels, in combination with a data-dependent lag-selection procedure (Andrews 1991). For the direction-of-change statistic, the loss differential series is deﬁned as follows: dt takes a value of one if the forecast series correctly predicts the direction of change, otherwise it will take a value of zero.

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Hence a value of d signiﬁcantly larger than 0.5 indicates that the forecast has the ability to predict the direction of change; on the other hand, if the statistic is signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. In large samples, the studentized version of the test statistic, d 0:5 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ; 0:25=T

ðA4Þ

is distributed as a standard normal. Notes We thank, without implicating, Jeff Frankel, Fabio Ghironi, Jan Groen, Lutz Kilian, Ed Leamer, Ronald MacDonald, John Rogers, Lucio Sarno, Torsten Slok, Frank Westermann, seminar participants at Academia Sinica, Boston College, UCLA, and participants at CESIfo conference on Exchange Rate Modeling: Where Do We Stand? for helpful comments, and Jeannine Bailliu, Gabriele Galati, and Guy Meredith for providing data. The ﬁnancial support of faculty research funds of the University of California, Santa Cruz is gratefully acknowledged. 1. A recent review of the empirical literature on the monetary approach is provided by Neely and Sarno (2002). 2. See Clark and MacDonald (1999), Clostermann and Schnatz (2000), Yilmaz and Jen (2001), and Maeso-Fernandez et al. (2001) for recent applications of this speciﬁcation. On the portfolio balance channel, Cavallo and Ghironi (2002) provide a role for net foreign assets in the determination of exchange rates in the sticky-price optimizing framework of Obstfeld and Rogoff (1995). 3. Despite this ﬁnding, there is little evidence that long-term interest rate differentials— or equivalently long-dated forward rates—have been used for forecasting at the horizons we are investigating. One exception from the professional literature is Rosenberg (2001). 4. The ﬁndings reported below are not very sensitive to the forecasting periods (Cheung, Chinn, and Garcia Pascual 2002). 5. For the pound, the productivity coefﬁcient is incorrectly signed, although this ﬁnding is combined with a very large (and correctly signed) income coefﬁcient, which suggests some difﬁculty in disentangling the income from productivity effects. 6. Overall, the interpretation of the results is complicated by the fact that, for the level speciﬁcations, multiple cointegrating vectors are indicated using the asymptotic critical values. The use of ﬁnite sample critical values reduces the implied number of cointegrating vectors, as indicated in the second row, to one or two vectors. Hence we do not believe the assumption of one cointegrating vector does much violence to the data. 7. One substantial caveat is necessary at this point. BEER models have almost uniformly been couched in terms of multilateral exchange rates; hence the interpretation of the BEERs in a bilateral context does not exactly replicate the experiments conducted by BEER exponents. On the other hand, the fact that it is difﬁcult to obtain the theoretically

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implied coefﬁcient signs suggests that some searching is necessary in order to obtain a ‘‘good’’ ﬁt. 8. Two recent exceptions to this characterization are Flood and Rose (2002) and Bansal and Dahlquist (2000). Flood and Rose conclude that UIP holds much better for countries experiencing currency crises, while Bansal and Dahlquist ﬁnd that UIP holds much better for a set of non-OECD countries. Neither of these descriptions applies to the currencies examined in this study. 9. We opted to exclude short-run dynamics in equation (7) because, on the one hand, the use of equation (7) yields true ex ante forecasts and makes our exercise directly comparable with, for example, Mark (1995), Chinn and Meese (1995), and Groen (2000), and on the other, the inclusion of short-run dynamics creates additional demands on the generation of the right-hand-side variables and the stability of the short-run dynamics that complicate the forecast comparison exercise beyond a manageable level. 10. In using the DM test, we are relying on asymptotic results, which may or may not be appropriate for our sample. However, generating ﬁnite sample critical values for the large number of cases we deal with would be computationally infeasible. More important, the most likely outcome of such an exercise would be to make detection of statistically signiﬁcant out-performance even more rare, and leaving our basic conclusion intact. 11. We also experimented with the Bartlett kernel and the deterministic bandwidth selection method. The results from these methods are qualitatively very similar. In appendix B we provide a more detailed discussion of the forecast comparison tests. 12. See also Leitch and Tanner (1991), who argue that a direction of change criterion may be more relevant for proﬁtability and economic concerns, and hence a more appropriate metric than others based on purely statistical motivations. 13. Using Markov switching models, Engel (1994) obtains some success along the direction of change dimension at horizons of up to one year. However, his results are not statistically signiﬁcant. 14. The Johansen method is used to test the null hypothesis of no cointegration. The maximum eigenvalue statistics are reported in the manuscript. Results based on the trace statistics are essentially the same. Before implementing the cointegration test, both the forecast and exchange rate series were checked for the Ið1Þ property. For brevity, the Ið1Þ test results and the trace statistics are not reported. 15. Our survey is necessarily limited, and we leave open the question of whether alternative statistical techniques can yield better results, for example, nonlinearities (Meese and Rose 1991; Kilian and Taylor 2001), fractional integration (Cheung 1993), and regime switching (Engel and Hamilton 1990), cointegrated panel techniques (Mark and Sul 2001), and systems-based estimates (MacDonald and Marsh 1997).

References Alexius, A. 2001. Uncovered interest parity revisited. Review of International Economics 9(3): 505–17. Andrews, D. 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817–58.

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Bansal, R., and M. Dahlquist. 2000. The forward premium puzzle: Different tales from developed and emerging economies. Journal of International Economics 51(1): 115–44. Cavallo, M., and F. Ghironi. 2002. Net foreign assets and the exchange rate: Redux revived. Mimeo NYU and Boston College. February. Chen, Y.-C., and K. Rogoff. 2003. Commodity currencies. Journal of International Economics 60(1): 133–60. Cheung, Y.-W. 1993. Long memony in foreign exchange rate. Journal of Business and Economic Statistics 11(1): 93–102. Cheung, Y.-W., and K. S. Lai. 1993. Finite-sample sizes of Johansen’s likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics 55(3): 313–28. Cheung, Y.-W., and M. Chinn. 1998. Integration, cointegration, and the forecast consistency of structural exchange rate models. Journal of International Money and Finance 17(5): 813–30. Cheung, Y.-W., M. Chinn, and A. G. Pascual. 2002. Empirical exchange rate models of the 1990s: Are any ﬁt to survive? NBER Working Paper 9393. Chinn, M. 1997. Paper pushers or paper money? Empirical assessment of ﬁscal and monetary models of exchange rate determination. Journal of Policy Modelling 19(1): 51–78. Chinn, M., and R. Meese. 1995. Banking on currency forecasts: How predictable is change in money? Journal of International Economics 38(1–2): 161–78. Chinn, M., and G. Meredith. 2002. Testing uncovered interest parity at short and long horizons during the post–Bretton Woods era. Mimeo. Santa Cruz, CA. Christoffersen, P. F., and F. X. Diebold. 1998. Cointegration and long-horizon forecasting. Journal of Business and Economic Statistics 16: 450–58. Clark, P., and R. MacDonald. 1999. Exchange rates and economic fundamentals: A methodological comparison of Beers and Feers. In J. Stein and R. MacDonald, eds., Equilibrium Exchange Rates. Boston: Kluwer, pp. 285–322. Clostermann, J., and B. Schnatz. 2000. The determinants of the euro–dollar exchange rate: Synthetic fundamentals and a non-existing currency. Konjunkturpolitik 46(3): 274–302. Cumby, R. E., and D. M. Modest. 1987. Testing for market timing ability: A framework for forecast evaluation. Journal of Financial Economics 19(1): 169–89. Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84: 1161–76. Diebold, F., and R. Mariano. 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13: 253–65. Engel, C. 1994. Can the Markov switching model forecast exchange rates? Journal of International Economics 36(1–2): 151–65. Engel, C., and J. Hamilton. 1990. Long swings in the exchange rate: Are they in the data and do markets know it? American Economic Review 80(4): 689–713. Faust, J., J. Rogers, and J. Wright. 2003. Exchange rate forecasting: The errors we’ve really made. Journal of International Economics 60(1): 35–59.

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Flood, R., and A. Rose. 2002. Uncovered interest parity in crisis. IMF Staff Papers 49(2): 252–66. Frankel, J. A. 1979. On the mark: A theory of ﬂoating exchange rates based on real interest differentials. American Economic Review 69: 610–22. Groen, J. J. 2000. The monetary exchange rate model as a long-run phenomenon. Journal of International Economics 52(2): 299–320. Isard, P., H. Faruqee, G. R. Kinkaid, and M. Fetherston. 2001. Methodology for current account and exchange rate assessments. IMF Occasional Paper 209. Kilian, L., and M. Taylor. 2003. Why is it so difﬁcult to beat the random walk forecast of exchange rates. Journal of International Economics 60(1): 85–107. Lane, P., and G. Milesi-Ferretti. 2001. The external wealth of nations: Measures of foreign assets and liabilities for industrial and developing. Journal of International Economics 55: 263–94. Leitch, G., and J. E. Tanner. 1991. Economic forecast evaluation: Proﬁts versus the conventional error measures. American Economic Review 81(3): 580–90. Lucas, R. 1982. Interest rates and currency prices in a two-country world. Journal of Monetary Economics 19(3): 335–59. MacDonald, R., and J. Nagayasu. 2000. The long-run relationship between real exchange rates and real interest rate differentials. IMF Staff Papers 47(1): 116–28. MacDonald, R., and M. P. Taylor. 1994. The monetary model of the exchange rate: Longrun relationships, short-run dynamics and how to beat a random walk. Journal of International Money and Finance 13(3): 276–90. Maeso-Fernandez, F., C. Osbat, and B. Schnatz. 2001. Determinants of the euro real effective exchange rate: A BEER/PEER approach. ECB Working Paper 85. Mark, N. 1995. Exchange rates and fundamentals: Evidence on long horizon predictability. American Economic Review 85: 201–18. Mark, N., and D. Sul. 2001. Nominal exchange rates and monetary fundamentals: Evidence from a small post–Bretton Woods panel. Journal of International Economics 53(1): 29–52. Meese, R., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Meese, R., and A. K. Rose. 1991. An empirical assessment of non-linearities in models of exchange rate determination. Review of Economic Studies 58(3): 603–19. Neely, C. J., and L. Sarno. 2002. How well do monetary fundamentals forecast exchange rates? Federal Reserve Bank of St. Louis Review 84(5): 51–74. Obstfeld, M., and K. Rogoff. 1996. Foundations of International Macroeconomics. Cambridge: MIT Press. Rosenberg, M. 2001. Investment strategies based on long-dated forward rate/PPP divergence. FX Weekly (New York: Deutsche Bank Global Markets Research, April 27), pp. 4–8.

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Stein, J. 1999. The evolution of the real value of the US dollar relative to the G7 currencies. In J. Stein and R. MacDonald, eds., Equilibrium Exchange Rates. Boston: Kluwer, pp. 67–102. Stockman, A. 1980. A theory of exchange rate determination. Journal of Political Economy 88(4): 673–98. Yilmaz, F., and S. Jen. 2001. Correcting the US dollar—A technical note. Morgan Stanley Dean Witter ( June 1).

9

The Euro–Dollar Exchange Rate: Is It Fundamental? Mariam Camarero, Javier Ordo´n˜ez, and Cecilio Tamarit

The evolution of the euro exchange rate vis-a`-vis the main international currencies, and particularly, the US dollar, has given rise to a growing literature. Contrary to the more or less general expectations of appreciation, the euro has been in its ﬁrst three years of existence depreciating against the dollar. Many arguments have been given in search of fundamentals, but the results are up to now puzzling (e.g., see De Grauwe 2000 or Meredith 2001). Two arguments can be put forth to support this fact. First, an analysis based on fundamentals cannot be performed on a short-term basis. Although the operators in the money markets seem to be working in a chartist world, from a policyoriented view the data span has to be long enough to capture the longrun equilibria relationships, and the econometric framework based on cointegration is the most appropriate methodology for this purpose. Second, and related to the preceding argument, the absence of historical data for the euro makes it necessary to use aggregate variables in order to expand the series backward (ECB 2000). This ‘‘synthetic’’ euro and the aggregate euro area variables have an important qualiﬁcation: they summarize the evolution of the legacy currencies that developed in the framework of rather heterogeneous economic environments.1 This heterogenous character and its contribution to the ‘‘strength’’ of the euro were pointed out by De Grauwe (1997). In this chapter we propose a complementary approach that shows how to overcome these problems. Our main attempt will be to compare the behavior of the bilateral real exchange rates for the individual euro-area countries in a panel with the performance of a model estimated using aggregate euro-area variables for the period 1970 to 1998 in terms of quarterly data. To make the results fully comparable, we restrict the countries analyzed to those with information available for the whole period. Concerning the econometric techniques applied, we ﬁrst use the

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pooled mean group (PMG) estimator proposed by Pesaran, Shin, and Smith (1999) for nonstationary regressors and estimate a panel for a group of euro-area currencies. This method constrains the long-run coefﬁcients to be identical but allows error variances and short-run parameters to differ. By this method we also will be able to capture the long-run relationships consistently with the medium- and long-run orientation of the fundamental exchange rate models and the objectives of European monetary policy. Also it should enable us to understand the different responses of the euro-area countries. Second, we estimate an aggregate bilateral model for the euro–dollar real exchange rate. We use the standard Johansen cointegration analysis method to arrive at the long-run determinants of the real exchange rate based on the current values of the variables. With this framework we are further able to test for regime shifts or structural breaks. However, we must bear in mind that these changes can only be detected with a signiﬁcant delay. Thus, even if the creation of the European Monetary Union has provoked a change in regime, it is still too early to be able to detect it using the available techniques. The remainder of the chapter is organized as follows. In section 9.1 we provide an overview of the recent empirical literature on the issue of exchange rate determination in the euro case. In section 9.2, we describe the theoretical models and in section 9.3 present the econometric results. Finally, in section 9.4 we report the main results and conclusions. 9.1

Recent Empirical Literature2

A traditional starting point for estimating equilibrium exchange rate has been the PPP theory, either in its absolute or relative version. However, due to a different bulk of factors well documented in the literature, the speed of adjustment of the current value of exchange rate to the long-run equilibrium is very slow. Therefore other approaches have been implemented over time. Basically these approaches can be classiﬁed in accord with two strands of literature: fundamental equilibrium exchange rate (FEER) or behavioral equilibrium exchange rates (BEER).3 The caveat to the ﬁrst approach is its normative nature. This is due to the fact that under the FEER approach the exchange rate has to be consistent with internal and external balance. Thus we think, as Clark and MacDonald (1999) point out, that the behavioral approach may be a better empirical approach to exchange rate modeling

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because the computation is based on current levels of the fundamental factors. The problem is to determine the correct combination of fundamental variables, and the answer is largely empirical. Over the past two years different econometric techniques were implemented in several studies in line with the behavioral approach. Alberola et al. (1999) using cointegration techniques for individual currencies as well as for a panel of currencies found only a long-run relationship with net foreign assets and relative sectoral prices (the Balassa-Samuelson effect), and Ledo and Taguas (1999) found that the deviations from PPP can be explained largely by productivity differentials and interest rate differentials in an error correction model. Additionally Closterman and Schnatz (2000) found an equilibrium relationship for the bilateral euro–dollar exchange rate that includes the productivity differential, the interest rate differential, the real oil price, and the relative ﬁscal position. Makrydakis et al. (2000) found a relation with the productivity differential and the real interest rate differential as in Alquist and Chinn (2001). Finally Maeso-Ferna´ndez et al. (2001) found the euro to be mainly affected by productivity developments, real interest rate differentials, and external shocks due to oil dependence of the euro area. All the models taken together appear to encompass useful information, so any assessment about the evolution of the real exchange rate should start to build in some way on this broad-based multifaceted range of analysis (ECB 2002). 9.2

Theoretical Models: An Eclectic Nested Approach

As in the euro–dollar case discussed above, the most recent empirical evidence on real exchange rates has not been able to secure a position among traditional theoretical models. In his search of an answer to the problems associated with modeling exchange rates and, in particular, real exchange rates, MacDonald (1998) has proposed an eclectic approach to model real exchange rates. Meese and Rogoff (1988), in their study of the link between real exchange rates and real interest rate differentials, have tried to solve some of the problems related to the monetary models. They deﬁne the real exchange rate, qt , as qt 1 et pt þ pt , where et is the price of a unit of foreign currency in terms of domestic currency and pt and pt are the logarithms of domestic and foreign prices. Three assumptions are made: ﬁrst, that when a shock occurs, the real exchange rate returns to its equilibrium value at a constant rate; second, that the long-run real exchange rate, q^t , is a

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nonstationary variable; ﬁnally, that uncovered real interest rate parity is fulﬁlled. Combining the three assumptions above, the real exchange rate can be expressed in the following form: qt ¼ jðR t R t Þ þ q^t ;

ð1Þ

where R t and R t are, respectively, the real foreign and domestic interest rates for an asset of maturity k. This leaves relatively open the question of which are the determinants of q^t , which is a nonstationary variable. Meese and Rogoff real exchange rate model has been very inﬂuential in the empirical literature. As Edison and Melick (1995) show in their paper, the implementation of the empirical tests depends on the treatment of the expected real exchange rate derived from equation (1). The simplest model will assume that the expected real exchange rate is constant, while the models including other variables will specify it using other determinants. The model was ﬁrst tested, in its simplest version, by Campbell and Clarida (1987) and Meese and Rogoff (1988). The former found little of the movement in real exchange rates to be explained by movements in real interest differentials. Meese and Rogoff (1988), using cointegration techniques (Engle and Granger single-equation tests), could not ﬁnd a long-run relationship between the two variables. However, Baxter (1994) found more encouraging results, and in a recent paper, MacDonald and Nagayasu (2000) tested this relationship for 14 industrialized countries using both long- and short-term real interest rate differentials and time series as well as panel cointegration methods. After obtaining evidence of statistically signiﬁcant long-run relationships and plausible point estimates using panel tests, they concluded that the failure of previous researches was probably due to the estimation method used rather than to any theoretical deﬁciency. In a second group of papers, the assumption that the expected real exchange rate is constant is relaxed, and additional variables are introduced in an attempt to explain it. This approach was ﬁrst introduced by Hooper and Morton (1982), who modeled the expected real exchange rate as a function of cumulated current account. Edison and Pauls (1993) and Edison and Melick (1995) estimate the same model using cointegration techniques. In the second paper they ﬁnd evidence of a cointegrating relationship, after Edison and Pauls (1993) failed to ﬁnd a statistical link between real exchange rates and real interest rates

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using the Engle-Granger methodology. However, the estimated error correction models are more supportive of such a relation. Wu (1999) has recently also obtained good results (even in forecasting ability) for this type of speciﬁcation applied to Germany and Japan in relation to the dollar exchange rate and using the Johansen technique. MacDonald (1998) used this approach, dividing the real exchange rate determinants into two components: the real interest rate differential and a set of fundamentals that explains the behavior of the long-run (equilibrium) real exchange rate, which include productivity differentials, the effect of relative ﬁscal balances on the equilibrium real exchange rate, the private sector savings, and the real price of oil. We will describe this eclectic approach in more detail because it forms the basis of our analysis. MacDonald assumes that PPP holds for nontraded goods, so he arrives at the following expression for the long-run equilibrium real exchange rate:

q^t 1 qtT þ at ðptT ptNT Þ at ðptT ptNT Þ;

ð2Þ

where qtT is the real exchange rate for traded goods; ð ptT ptNT Þ ð ptT ptNT Þ is the relative price of traded to nontraded goods between the home and the foreign country and a and a are the weights. By way of (2), MacDonald identiﬁes two potential sources of variation in the equilibrium real exchange rate: 1. Movements in the relative prices of traded to nontraded goods between the home and foreign country (second and third terms in equation 2). These differences are mostly concentrated in nontraded goods. In particular, according to the traditional Balassa-Samuelson effect, productivity differences in the production of traded goods across countries can introduce a bias in the overall real exchange rate. This is because productivity advances tend to concentrate in the traded goods sectors. Because of the linkages between prices of goods and wages (and wages across sectors), provided that there is internal factor mobility (from the nontraded to the traded goods sectors and conversely), the real exchange rate tends to appreciate in fast growing economies. 2. Nonconstancy of the real exchange rate for traded goods, qtT , (the ﬁrst term in equation 2). Two additional factors may introduce variability in qtT : international differences in savings and investment and changes in the real price of oil.

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a. The real exchange rate for traded goods is also, following MacDonald (1998), a major determinant of the current account and is in turn driven by the determinants of savings and investment. We can separate two variables that may capture this effect: Fiscal policy, whose relation with the real exchange rate depends on the approach. According to the Mundell-Fleming model, an expansionary ﬁscal policy reduces national savings, increases the domestic real interest rate, and generates a permanent appreciation. In contrast, the portfolio balance models consider permanent ﬁscal expansion to cause a decrease in net foreign assets and a depreciation of the currency.

Private sector net savings, whose effect on the real exchange rate is inﬂuenced by demographic factors. This way the cross-country variations of saving rates are seen to affect the relative net foreign asset position.

b. Increases in the real price of oil tends to appreciate the currencies of the net oil exporters or, in general, the currencies of the less energy dependent countries. MacDonald’s proposal does not rely exclusively on the monetary approach to exchange rate determination, although it captures the majority of the fundamental variables mentioned in the literature and makes them compatible with it. Accordingly, the above-mentioned factors can be summarized in the following empirical speciﬁcation: qt ¼ jðR t R t Þ þ q^t ¼ f ððR t R t Þ; ðat at Þ; ðgt gt Þ; oilt ; dnfat Þ; ðÞ

ðÞ

ð=þÞ

ðÞ

ð3Þ

ðÞ

where ðat at Þ is the difference between the domestic and foreign economies productivity,4 ðgt gt Þ is the public expenditure differential, oilt 5 is the real oil price and dnfat is the relative net foreign asset position of the economy. 9.3

Empirical Results

Two different econometric techniques have been applied to the same data set. First, using dynamic panel techniques, we estimate the real exchange rate of the dollar versus a group of seven individual countries. In addition we study separately the euro countries in the sample

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283

from the rest. Second, using time series techniques, we explain the dollar–euro real exchange rate in terms of euro-area aggregated variables. 9.3.1

Panel Analysis: the Dollar in the World

As we noted earlier in our theoretical discussion, we examined a wide set of explanatory (fundamental) variables in order to assess the main factors behind the behavior of the dollar’s real exchange rate. This ﬁrst part of the analysis involves eight countries: the United States as the domestic country, Japan, Canada, the United Kingdom, and four euroarea countries (those with information available for the sample period and variables of interest). As a result in this ﬁrst part of the analysis we do not strictly estimate a model for the dollar versus the euro area. We have chosen to include countries, such as the United Kingdom, Canada, and Japan, that do not participate in EMU in order to capture the behavior of the most important world currencies. Our method in this part of the analysis allows for both group and individual approaches. We consider ﬁrst the entire group of countries (where N ¼ 7) and then divide the panel into the euro area countries (N ¼ 4: Germany, Spain, France, and Italy) and non-euro area countries (N ¼ 3: Canada, Japan, and the United Kingdom). The data are quarterly and the sample goes from 1970:1 to 1998:4.6 In choosing our model speciﬁcation, we tried to follow as close as possible the general to speciﬁc methodology. Our starting point was the models described in the previous section, and to make the estimated models comparable, we used a general speciﬁcation: rerdolit ¼ f ðdproit ; drrit ; oildepit ; dnfait ; dpexit Þ; ðÞ

ðÞ

ðÞ

ðÞ

ðþ=Þ

where rerdolit is the real exchange rate of the dollar versus all the currencies deﬁned as the units of domestic currency necessary to buy a unit of foreign currency in real terms; dproit is the relative productivity of the United States versus that of the other countries: an increase in the value of this variable tends to appreciate the currency; drrit is the real interest rate differential between the United States and the other countries analyzed: an increase in this differential appreciates the currency; oildepit is the real price of oil adjusted by the relative dependency on oil imports by each country compared to that of the United

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States: in this case, the dollar will appreciate when the oil dependency of the foreign countries is increasing; dnfait is the difference in the net foreign asset position over GDP of the United States versus the other countries, and the sign should be negative (the currencies of countries increasing its net foreign asset position tend to appreciate); dpexit is the difference in public expenditure over GDP between the United States and each of the other countries. In the last instance, there are two competing theories explaining the relation of public expenditure to the GDP with respect to the real exchange rate. The relation is positive (depreciation) if the portfolio balance model prevails, but it is negative according to the Mundell-Fleming approach. The models we used are the following:7 Model 1

Eclectic model:

rerdolit ¼ ai þ b 1i drrit þ b2i dpexit þ b3i dproit þ b 4i dnfait þ b5i oildepit : Model 2

Restricted eclectic model:

rerdolit ¼ ai þ b 1i drrit þ b2i dpexit þ b3i dproit þ b 4i dnfait : Model 1 follows the general speciﬁcation described above. Model 2 is a version of model 1 with the oil dependence variable excluded. In what follows, we show how these empirical models were tested. Order of Integration of the Variables Bearing all these considerations in mind, we should start the analysis with the study of the order of integration of the variables. Several panel unit root tests are already available in the literature, from the early works of Levin and Lin (1992)8 to the Im, Pesaran, and Shin (1995) tests. However, because of its higher power we applied the LM test for the null of stationarity proposed by Hadri (2000) with heterogeneous and serially correlated errors. These tests can be considered a panel version of the KPSS tests applied in the univariate context. Hadri (2000) provides two models (with and without a deterministic trend) that can be decomposed into the sum of a random walk and a stationary disturbance term. He tests the null hypothesis that all the variables ðyit Þ are stationary (around deterministic levels or around deterministic trends), so that for the N elements of the panel the variance of the errors is such that 2 2 ¼ ¼ suN ¼0 H0 : su1

ð4Þ

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Table 9.1 Hadri (2000) stationarity tests ðl ¼ 2Þ Variables

hm

ht

rerdolit

23.72**

dpexit

14.30**

262.49**

dnfait

47.05**

1655.32**

dproit drrit

29.79** 18.23**

801.21** 167.71**

oildepit

18.38**

149.01**

175.45**

Note: The statistic hm does not include a time trend, whereas ht does, and both are normally distributed. The two asterisks denote rejection of the null hypothesis of stationarity at 5 percent. The number of lags selected is l ¼ 2. 2 against the alternative H1 : that some sui > 0: This alternative allows for 2 heterogeneous sui across the cross sections and includes the homoge2 neous alternative (sui ¼ su2 for all iÞ as a special case. It also allows for a subset of cross sections to be stationary under the alternative. The two statistics are called hm for the null of stationarity around an intercept and ht when the null is stationarity around a deterministic trend. The results of the tests applied to the four variables are presented in table 9.1. The null hypothesis of stationarity can be easily rejected in the two cases (with and without time trend), so that all the panel variables can be considered nonstationary.

Long-Run Relationships: ‘‘Pooled Mean Group’’ Estimation Results Once we have determined the order of integration of the variables for the analysis of the real exchange rate of the dollar, we can follow the methodology proposed by Pesaran, Shin, and Smith (1999) and compute the pooled mean group estimators.9 This estimation technique is well suited in our case because we are interested in considering different groups of countries and comparing the estimation results (i.e., the whole group, the euro area countries, and the non–euro area countries). The pooled mean group (PMG) estimator involves both pooling and averaging. This estimator allows the intercepts, short-run coefﬁcients, and error variances to differ across groups, but the long-run coefﬁcients are constrained to be the same. Due to the high level of economic integration achieved among the euro-area countries, we chose to impose equality in the long-run parameters (or rather in most of them) but allow the short-run slope coefﬁcients and the dynamic speciﬁcation (i.e., the number of lags included) to differ across groups.

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Then we estimated the panel, using a maximum likelihood approach. The ML estimators that result are the pooled mean group (PMG) estimators. This is because they are both pooled, as implied by the homogeneity restrictions on the long-run coefﬁcients, and averaged across groups to obtain means of the estimated error-correction coefﬁcients and the other short-run parameters of the model. The empirical model takes on the eclectic form presented above, starting with model 1, which includes the main explanatory variables proposed by the literature on real exchange rates. Other theoretical models are restricted versions of model 1. Many empirical speciﬁcations have been estimated and compared through likelihood-based information criteria, such as the AIC and the SBC. In addition in each speciﬁcation we have tested two important questions: the homogeneity restriction using a likelihood ratio test; the existence of discrepancies between the pooled mean group estimates and the mean group estimates, which differ also in the degree of heterogeneity allowed. The Hausman test permits us to decide whether these discrepancies recommend the exclusion of the homogeneity restriction in some of the long-run parameters. Thus the second test complements the ﬁrst one because, if homogeneity is rejected using the LR test, the Hausman test for the individual variables helps identify the variable source of the heterogeneity. Concerning the dynamics of the model, the short-run has been modeled using up to two lags, as derived in the application of the Schwarz Bayesian criterion for lag selection. In the second and third columns of table 9.2 we present the information criteria used in the selection of the two models, and show the corresponding LR homogeneity test results along with the concrete hypotheses tested for the three groups of countries analyzed. In model 1, all the variables were considered, and it has higher AIC and SBC than model 2. No null hypothesis of homogeneity in the long-run parameters could be accepted for any of the groups of countries analyzed (e.g., see, for N ¼ 7, w 2 ð18Þ ¼ 67:81 with a probability of [0.00]). Also the long-run parameter of the variable oildept is nonsigniﬁcant. Where some heterogeneity was allowed, speciﬁcally in the oil dependency variable, the results did not improve.10 Model 2 is a restricted version of model 1, where oildept has been excluded. The information criteria are smaller, and after we imposed the condition that not all the long-run parameters must be equal for all the countries, the restrictions for the rest of the variables in the three

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Table 9.2 Comparison of the speciﬁed models Variables AIC

SBC

LR test

drrt dpext oildt dnfat

dpro t

N¼7 Model 1

1714

1686

w 2 ð18Þ ¼ 67:81½0:00

0

¼E

0

¼E

¼E

Model 2

1691

1665

w 2 ð12Þ ¼ 20:68½0:05**

0

¼E

—

0

¼E

N ¼ 4: Euro-area Model 1

1036

1018

w 2 ð6Þ ¼ 17:95½0:00

0

0

0

¼E

¼E

Model 2

998

982

w 2 ð9Þ ¼ 15:87½0:07**

0

¼E

—

¼E

¼E

w 2 ð6Þ ¼ 11:37½0:07**

0

¼E

—

¼E

0

N ¼ 3: Non-euro Model 1 763.74

748.40

w 2 ð4Þ ¼ 28:51½0:00

0

0

0

¼E

¼E

Model 2

750

w 2 ð4Þ ¼ 8:55½0:07**

0

¼E

—

0

¼E

763

Note: AIC stands for Akaike Information Criterium, SBC for Swartz Bayesian criterium and LR test is the likelihood ratio test for equality of either some or all the long-run parameters (probability values appear in parentheses). Two asterisks denote acceptance of the restriction on the long-run parameters at 5 percent signiﬁcance level. 0 stands for the assumption of different parameter values for all the N members of the panel. The homogeneity hypothesis is represented by the symbols ¼ E.

conﬁgurations could be accepted. For example, for N ¼ 7, the homogeneity restriction is accepted for dprot and dpext ( w 2 ð12Þ ¼ 20:68 with a probability of [0.05]), although it is necessary to allow for some heterogeneity in the real interest rate and in the net foreign asset differential. The estimates and the associated t-statistics are presented in the ﬁrst column of table 9.3, where all variables but drrt are signiﬁcant. It should be noted that the error correction coefﬁcient is highly signiﬁcant and of a reasonable magnitude (0.120). Thus the adjustment toward equilibrium will take approximately two years. In tables 9.4 and 9.5 the information concerns the long-run relations among the countries as well as the misspeciﬁcation tests. As is evident, apart from some normality departures in some of the countries, the individual equations pass the misspeciﬁcation tests. Moreover the R 2 in almost every case (Canada excepted) is over 0.80. The estimated parameters conform to the theory and are of correct sign. Thus the increase in the real interest differential causes the currency to appreciate (b1 < 0). The expansionary ﬁscal policy in the United States relative to the other countries causes the currency (b2 > 0Þ to depreciate, whereas an increase in relative productivity

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Table 9.3 Pooled mean group estimates Variables

All countries ðN ¼ 7Þ

Euro-area ðN ¼ 4Þ

Non-euro ðN ¼ 3Þ

Model 2: rerdolit ¼ ai þ b1i dproit þ b2i drrit þ b 3i dnfait þ b 4i dpexit drrt dpext dprot dnfat ecmt1

0.005 a

0.007 a

0.006 a

0.008 a

(1.58)

(1.92)

(2.38)

(2.23)

0.003 (2.95)

0.003 (2.48)

0.002 (2.09)

0.008 (2.72)

0.749 a

0.851

0.870

(27.02)

(22.34)

(7.12)

0.314

0.288

(5.57)

(6.94)

(6.58)

0.120

0.126

0.134

0.149

(3.83)

(2.99)

(3.15)

(4.77)

0.327 a

0.836 (15.47) 0.266 a (1.59)

Note: Student’s t is in parentheses. Superscript ‘‘a’’ indicates that the corresponding variable was not subject to the restriction of equal long-run parameters for all the members of the group. Thus its estimate is the mean group estimate, instead of the PMGE.

causes the currency (b3 < 0) to appreciate, due to the BalassaSamuelson effect. Finally, an increase in the relative net foreign assets position also induces appreciation (b 4 < 0). Notice that in the long-run parameter estimates of drrt and dnfat , we do not impose equality of all the cross-sectional elements. The individual country estimates are presented in detail in table 9.4. Although with larger N this technique has more advantages, due to our focus on the euro area, we have also estimated the dynamic panel data for the four EMU countries with the information available, as well as for the other three countries considered. The long-run parameters estimates, also presented in table 9.3, are very similar to those obtained for the larger group. Recall from table 9.2 the information criteria (also smaller than in model 1), as well as the LR tests for homogeneity in the long-run parameters, for the euro-area countries. In this case, after imposing that drrt is heterogeneous for the members of the group, we accept the homogeneity of the other three explanatory variables. As an additional test for homogeneity, we used the Hausman test for the variable dprot , which did not accept the similarity between the coefﬁcient estimated using the PMG estimator and the MG estimator, where heterogeneity

N¼7 Countries

drr t

N¼4 dpro t

dnfa t

dpex t

ecm t1

drr t

N¼3 dpro t

dnfa t

dpex t

ecm t1

drr t

dpro t

dnfa t

dpex t

ecm t1

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

Model 2 Germany Spain

0.005

0.851

0.328

0.003

0.120

0.006

0.74

0.288

0.002

0.128

(1.58)

(27.02)

(5.57)

(2.95)

(3.83)

(1.91)

(8.52)

(6.57)

(2.09)

(3.92)

0.0001 (0.08)

France Italy Canada Japan United Kingdom

0.851

0.372

0.003

0.117

(27.02)

(2.81)

(2.95)

(2.99)

0.0001 (0.09)

0.891

0.288

0.002

0.123

(8.39)

(6.57)

(2.09)

(3.10)

0.005

0.851

0.330

0.003

0.215

0.005

0.907

0.288

0.002

0.246

(3.46)

(27.02)

(5.27)

(2.95)

(4.52)

(4.24)

(20.85)

(6.57)

(2.09)

(4.90)

0.004

0.851

0.127

0.003

0.096

0.011

0.454

0.288

0.002

0.039

(1.46)

(27.02)

(1.16)

(2.95)

(2.72)

(1.08)

(1.30)

(6.57)

(2.09)

(1.60)

—

—

—

0.007

0.851

0.350

0.003

(3.73)

(27.02)

(7.07)

(2.95)

0.009

0.851

0.430

0.003

(2.51)

(27.02)

(6.95)

(2.95)

0.003

0.851

0.043

0.003

(2.12)

(27.02)

(2.07)

(2.95)

0.144 —

—

(4.15) 0.126 —

—

—

—

—

(3.33) 0.217 — (3.91)

—

—

—

—

0.008

0.836

0.383

0.007

0.139

(3.79)

(15.47)

(15.47)

(2.72)

(4.18)

0.011

0.836

0.478

0.007

0.100

(2.26)

(15.47)

(5.73)

(2.72)

(2.95)

0.003

0.836

0.063

0.007

0.207

(2.28)

(15.47)

(2.53)

(2.72)

(3.84)

Euro-Dollar Exchange Rate: Is It Fundamental?

Table 9.4 Individual countries estimates

289

M. Camarero, J. Ordo´n˜ez, and C. Tamarit

290

Table 9.5 Individual countries speciﬁcation tests R

2

Correlation

FF

NO

HE

34.03* 36.63*

36.82* 0.03

Model 2 ðN ¼ 7Þ Germany Spain

0.882 0.829

0.71 0.10

17.43* 1.67

France

0.890

0.18

1.87

4.39

1.07

Italy

0.850

3.71

1.21

35.98*

0.08

Canada

0.578

1.28

0.52

2.36

0.13

Japan

0.869

0.01

0.54

5.68

0.00

United Kingdom

0.844

1.09

0.33

25.79*

0.52

is allowed.11 Once the two variables are not constrained to be homogeneous, the model passes the Hausman test. Note that in table 9.3 the estimation results for the two cases are very similar. All the variables are signiﬁcant and the error correction term is slightly larger in the second case. For the other three countries (Canada, Japan, and United Kingdom), the homogeneity of all the variables is rejected. Only after allowing heterogeneity in drrt and dnfat the homogeneity of the other long-run parameters can be accepted. Model 2 and model 1’s AIC and SBC are similar, but only in model 2 the partial homogeneity is accepted after the restrictions are imposed, this being the test w 2 ð4Þ ¼ 8:55 with a probability of [0.07]. Thus model 2 seems adequate also for N ¼ 3. The long-run estimates of the parameters have similar magnitude if compared with the larger model. The only exception is dpext , whose value is 0.008 in contrast with 0.003. The error correction coefﬁcient takes the value of 0.149 and an associated student t of 4.77. 9.3.2

Aggregate European Results: The Euro and the Dollar

The preceding panel analysis gives some clues about the behavior of the dollar in terms of major world currencies. As we expected, the results do not ﬁt a simple model (e.g., the Meese and Rogoff 1988 real interest differential), but a rather eclectic speciﬁcation as it includes variables both from the demand and the supply sides of the economy. In our results the role of productivity differentials supports the fulﬁllment of the Balassa-Samuelson effect. The real interest rate differential

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Table 9.6 Cointegration test statistics r

Eigenvalues

Trace

Trace (R)

Trace 95%

0

0.3748

122.7**

97.28*

94.2

1

0.3420

81.78**

64.86

68.5

2

0.2791

45.36

35.97

47.2

3 4

0.1085 0.0699

16.88 6.883

13.39 5.429

29.7 15.4

5

0.0065

0.571

0.452

3.8

Note: The critical values are given with 95 percent critical values based on a response surface ﬁtted to the results of Osterward-Lenum (1992). (R) stands for the small-sample correction of the trace tests statistics proposed by Reimers (1992). * and ** denotes rejection of the null hypothesis at 5 and 1 percent signiﬁcance level respectively.

is also present, although this is not the exclusive determinant of real exchange rate behavior: the ﬁscal policies and the net foreign assets of the countries are among the explanatory variables. The only variable that did not show a signiﬁcant contribution was the real oil price. The additional conclusion that can be drawn from the dynamic panel analysis is that overall, the model estimated for the dollar real exchange rate does not change much with the different conﬁgurations of the countries (besides the minor exceptions already mentioned). Once the panel analysis has been completed for the European countries separately, we focus on the ‘‘synthetic’’ euro-area variables. The two approaches are complementary as the use of panels allows for heterogeneity. In fact the lack of heterogeneity is one of the main criticisms of aggregate analyses. If the results from these two complementary methodologies do not show important discrepancies, we can be more conﬁdent in using the aggregate series for inference and policy analysis. For this part of the analysis we use the Johansen (1995) method for the estimation and identiﬁcation of cointegrated systems where differentials are no longer calculated for the United States relative to every other country but relative to a representative euro-area variable. First in the analysis we studied the order of integration of the variables, using a stationarity testing strategy in the context of the VAR system. All the variables turned out to be I(1).12 Table 9.6 shows the trace test statistics for the determination of the number of cointegration relationships.13 The Reimers adjusted trace test statistics are also shown. Clearly, the trace test statistic fails to reject the existence of two

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292

cointegration vectors, whereas the Reimers adjusted test fails to reject one cointegration vector. To gain insight on the appropriate number of cointegration vectors, we need to add to this analysis information about the roots of the companion matrix: three are almost unity and other two are pretty close to unity, implying that ﬁve is the number of common stochastic trends. Moreover, for r ¼ 1, the largest roots are removed, leaving no near unit root in the model, so this must be the appropriate choice for r. In addition, from the time path plot for each of the feasible cointegration vectors, only the ﬁrst one seems to be stationary. The recursive analysis of the system provides other useful information regarding the existence of cointegration: the recursive time path of the nonadjusted trace statistic suggests that at most there exist two cointegration vectors though one is the most sensible outcome. From all this evidence, the most feasible choice is the existence of one cointegration vector, that is, p r ¼ 5, where p is the number of common stochastic trends. We can proceed to identify the cointegration vector by imposing the overidentifying restriction that the variable for energy dependence (oildept ) is excluded from the long-run: the LR statistic is w 2 ð1Þ ¼ 3:43 with a probability value of 0.06. The resulting cointegration vector takes the form (standard errors in parentheses): qt ¼ 0:011dpext 0:007drrt 0:77 dprot 0:36 dnfat : ð0:001Þ

ð0:001Þ

ð0:033Þ

ð5Þ

ð0:032Þ

At this stage of the analysis we can already compare the results obtained using the PMG in the dynamic panel with the time series model using aggregate variables. Taking into account the results presented in table 9.3 for model 2, we can observe that the results are very similar. First, the variable relative oil dependency (oildept ) that turned out not to be signiﬁcant in the panel analysis can be also excluded from the time series cointegration vector. Second, the four variables have the same signs even if we are using quite different estimation techniques. Moreover the parameters’ estimates are not very different in magnitude, the only exception being the case of dpext , where the time series value is 0.011 and 0.002 for the panel. In other cases the parameters are almost equal, as for the real interest differential (0.007 for the aggregate model and 0.006 for the panel) or the productivity differential (0.77 in the time series model and 0.749 in the panel).14 Finally, the net foreign asset position is also in a similar range: 0.36 in the aggregate model and 0.288 in the panel.

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Once we have identiﬁed the cointegration vector, we formally test for weak exogeneity of the variables in the system. According to our results all the variables appear to be weakly exogenous with the only exception of the real exchange rate. The joint hypothesis of weak exogeneity and the identifying restrictions on the cointegration space b are accepted: the LR statistic value is w 2 ð6Þ ¼ 11:16 with a probability of 0.08. We present next the error correction model (ECM hereafter) for the univariate partial model (t-values in brackets): Dqt ¼ 0:291 0:375 Ddprot 0:185 Ddprot1 0:105 Ddprot2 ½5:010

½7:675

½2:999

½2:068

0:002 Ddrrt3 0:184 ecmt1 þ et : ½2:002

ð6Þ

½5:007

Misspeciﬁcation tests Residual correlation: Fð5; 76Þ ¼ 1:0856½0:3752 ARCH: Fð4; 73Þ ¼ 0:8310½0:5098 Normality: w 2 ð2Þ ¼ 1:1128½0:5733 Heteroscedaticity (squares): Fð10; 70Þ ¼ 1:0960½0:3774 Heteroscedaticity 1:1588½0:3203

(squares

and

cross

products):

Fð20; 60Þ ¼

In the equation above et is a vector of disturbances and ecmt1 is the cointegration vector (5). None of the misspeciﬁcation tests reported here rejects the null hypothesis that the model is correctly speciﬁed. In addition we apply the Hansen and Johansen (1993) approach to test for parameter instability in the cointegration vector. Speciﬁcally we test both whether the cointegration space and each of the parameters in the cointegration vector are stable. We also test for the stability of the loading parameters. If both a and b appear to be stable, we can conclude that our error correction model is well speciﬁed for the period analyzed. Panel a of ﬁgure 9.1 shows the plot of the test for constancy of the cointegration space. The test statistic has been scaled by the 95 percent quantile in the w 2 -distribution so that unity corresponds to the 5 percent signiﬁcance level. The test statistic for stability is obtained using both the Z-representation and the R-representation of our model. In the former, stability is analyzed by the recursive estimation of the whole model, and in the latter the short-run dynamics are ﬁxed and only the long-run parameters are re-estimated. Thus the

Figure 9.1 Stability of the cointegration space

Euro-Dollar Exchange Rate: Is It Fundamental?

295

R-representation is the relevant one to assess the stability of the cointegration space, which is clearly accepted. Panels b and c of ﬁgure 9.1 show, respectively, the stability tests for each of the beta coefﬁcients and for the loadings to the cointegration vector. In all cases, the recursively estimated coefﬁcients lay within the 95 percent conﬁdence bounds showing a remarkable stability. To summarize, we can conclude that the cointegration space is stable, that is, the long-run parameters as well as the loadings do not show signs of instability. Finally, panel b of ﬁgure 9.2 presents several recursive tests of parameter stability for the parsimonious conditional model. Accordingly, our model is stable not only concerning the cointegration space but also the model as a whole. As for the real exchange rate ECM presented in equation (6), we should note that the error correction parameter presents the correct sign and magnitude (taking into account that the data are quarterly), and passes the Banerjee, Dolado, and Mestre (1992) cointegration test. In addition two of the variables appear in the dynamics of the real exchange rate. The ﬁrst is, with three lags, the real interest rate differential ðdrrt Þ, although it is borderline signiﬁcative. The negative parameter for this variable, as in the panel analysis, is the one expected from the theory. Second is the productivity differential measure, contemporaneous and lagged from one to two periods, with the same negative sign found in the long-run time series analysis and in the panel analysis reported in section 9.3.1 above. The important role that the productivity differential has in driving the system toward the equilibrium should be emphasized and also the fact that the adjustment starts in the same quarter where the shocks have occurred. We can again compare the error correction model of the aggregate European variables with the results for the panel. As in the time series case, the contemporaneous effects coming from the productivity differential are very important and of the same sign (with a t-statistic of 17.56), but the rest of the variables are not signiﬁcant. Concerning the error correction coefﬁcient, its magnitude is smaller in the panel (0.134). Although there is no consensus in the profession on a particular model speciﬁcation of exchange rate equations inspired by the New Open Macroeconomics literature (Sarno 2002), the results obtained in this chapter are compatible with these models. In particular, according to Lane (2002), net foreign assets positions are an important form of

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Figure 9.2 Dynamic forecast and recursive estimation

Euro-Dollar Exchange Rate: Is It Fundamental?

297

international macroeconomic interdependence. The inﬂuence of net foreign asset positions on the values of the real exchange rate has also been studied recently in Cavallo and Ghironi (2002) and Lane and Milesi-Ferretti (2001). In this chapter, we have used the net foreign asset dataset constructed in Lane and Milesi-Ferretti (2001), that is, the ‘‘adjusted cumulative current account,’’ and our results are compatible with the most recent empirical literature besides the previous empirical work.15 To complete our analysis, we check the predictive ability of the euroarea model. Table 9.7 presents ex post and ex ante forecasting results. To compute the ex post forecasts, we left out eight observations (two years) and re-estimated the model. From the one-step static forecast analysis, our model appears to deliver sensible and stable forecasts. The estimates for the dynamic forecast are carried out recursively: the estimation period is successively extended quarter by quarter so that the real exchange rate is forecasted for up to eight quarters into the future. Panel a of ﬁgure 9.2 shows graphically the predictive performance of our model. This graph plots the dynamic forecasts for the period 1997:1 to 1998:4 estimated by full-information maximum likelihood. The forecasts lie within the 95 percent conﬁdence interval, shown by the vertical error bars of plus or minus twice the forecast’s standard error. Moreover the ﬁt of the model is good, and there are no large departures from the actual values. Finally, the forecast quality of our model is also assessed by comparing its forecast accuracy with a random walk model for the real exchange rate. For this purpose we obtain the ratio between the root mean squared error (RMSE) corresponding to our VECM relative to the random walk. If the VECM presents a better predictive performance, that is, lower RMSE, this ratio will be below 1. In addition, following Diebold (1998), we carried out a formal test to gain insight into whether the random walk model can generate signiﬁcantly better forecasts from a statistical point of view. Thus, rejection of the null for this test implies that the random walk model does not provide signiﬁcantly better forecasts than our VECM. Table 9.7 presents the ratio of the two RMSE for a forecast horizon up to eight quarters as well as the signiﬁcance level for the Diebold and Mariano test statistic, which is indicated by asterisks in the third column. By these results the VECM outperforms the random walk model even in the shorter horizons, as can be seen from RMSE ratios, which are well below 1. Moreover the predictive performance of our model is statistically shown, rejecting

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Table 9.7 Static and dynamic forecasting A. One-step (ex post) forecast analysis: 1997:1 to 1998:4 Parameter constancy x1 x2 x3

w 2 ð8Þ ¼ 10:679 [0.2205] w 2 ð8Þ ¼ 8:9096 [0.3500]

Fð8; 73Þ ¼ 1:3349 [0.2402] Fð8; 73Þ ¼ 1:1137 [0.3643]

w 2 ð8Þ ¼ 9:5206 [0.3003]

Fð8; 73Þ ¼ 1:1901 [0.3169]

2

Forecast tests: w ð1Þ Using x1

Using x2

1997:1

3.4134 [0.0647]

2.6766 [0.1018]

1997:2

1.0618 [0.3028]

0.8527 [0.3558]

1997:3

1.3785 [0.2404]

1.0663 [0.3018]

1997:4

0.0069 [0.9337]

0.0062 [0.9369]

1998:1 1998:2

0.2791 [0.5973] 0.0428 [0.8361]

0.2503 [0.6168] 0.0380 [0.8454]

1998:3

3.6488 [0.0561]

3.2989 [0.0693]

1998:4

0.8479 [0.3571]

0.7203 [0.3960]

Forecast horizon

RMSE (ratio)

Signiﬁcance

B. Forecast quality: 1997:1 to 1998:4 1997:1

0.2509

1997:2

0.2176

1997:3

0.1887

1997:4

0.1821

***

1998:1 1998:2

0.1716 0.1676

*** ***

1998:3

0.1665

***

1998:4

0.1728

***

Note: x1 ; x2 , and x3 are indexes of numerical parameter constancy. The former ignores both parameter uncertainty and intercorrelation between forecasts errors at different time periods. x2 is similar to x1 but takes parameter uncertainty into account. x3 takes both parameter uncertainty and intercorrelations between forecasts errors into account. Forecast test are the individual test statistics underlying x1 and x2 . *** stands for 1 percent error probability.

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for all the forecast horizons the superiority of the random walk model with a probability as low as 1 percent. 9.4

Conclusions

In this chapter we apply two different but complementary techniques and approaches to the study of the evolution of the dollar real exchange rate in relation with the euro-area currencies. First, using panel techniques, we study the long-run relationship between the bilateral real exchange rate of the dollar versus the currencies of ﬁve European countries, Canada, and Japan. Second, in a time series framework, we use euro-area aggregate or ‘‘synthetic’’ variables to study the behavior of the dollar–euro real exchange rate. Our aim was to compare the results obtained from the two approaches and for the same time span. Given that the lack of heterogeneity is one of the main criticisms commonly associated with aggregate analyses, in using a panel analysis, we allow for individual country differences. The similarity of the results obtained by the two methods adds robustness to the euro-area measures. Heterogeneity is a feature not evident in other papers dealing with the real exchange rate of the euro. We maintain this distinction in summarizing the most important empirical results. First, concerning the dynamic panel analysis, we use the methodology of Pesaran et al. (1999), which allows for short-run heterogeneity for the individual components of each panel and a formal test of homogeneity in the long-run parameters. We ﬁnd that both the supply- and demand-side factors can be accounted for to explain the bilateral real exchange rate of the US dollar. In particular, the estimated error correction models support a speciﬁcation that includes relative productivity, the real interest rate differential, the difference in public expenditure, and the relative net foreign asset position. This type of relation holds not only for the euro countries but also for the whole group and for the rest-of-the-world countries. We arrived at the same long-run speciﬁcation using the Johansen technique in a time series context. Therefore, we showed that even if we allow a larger degree of heterogeneity in the panel and even if we use different estimation techniques, the results appear to be almost identical. In addition, in the aggregate time series empirical model, the cointegration vector passed all the applied stability tests. Last, the estimated VECM was remarkably predictive in performance and provided better forecasts than the random walk for both the short and the medium terms.

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The long-run results showed the dollar–euro exchange rate to depreciate if American ﬁscal policy becomes more expansionary than European ﬁscal policy. However, productivity growth and real interest rate differentials, together with the accumulated net foreign assets, will appreciate the currency. Appendix: Data Sources We used quarterly data for the period 1970:1 to 1998:4 from France, Germany, Italy, Spain, and the United Kingdom. We included data from the United States (the home country) and Canada and Japan. The data were obtained from the magnetic tapes of the International Monetary Fund International Financial Statistics (IFS) with the exception of employment and oil balances data, which came from the International Sectoral Database (OECD). The net foreign assets data were taken from Lane and Milesi-Ferretti (2001), L-M hereafter. The nominal exchange rate for the euro relative to the US dollar was from the database for European variables of the Banco Bilbao Vizcaya Argentaria (BBVA). The panel data were constructed as follows: rerdolit : Bilateral real exchange rate of the US dollar relative to the other currencies considered. The nominal exchange rate, st , has been deﬁned as currency units of US dollar to purchase a unit of currency j: ! ptUSA rerdolt ¼ log ; j s t pt j

where ptUSA and pt are respectively the CPI for the Unites States and the foreign country. (Source: IFS) drr it : Real interest rate differential. The nominal interest rates are call money rates as deﬁned by the IMF. In order to obtain the real variables, the expected inﬂation rate is the smoothed variable based on CPI indexes using the Hodrick and Prescott ﬁlter: pt ¼

pt pt1 100; pt1

pte ¼ pt ptt ; rrt ¼ rt pte ; j

drret ¼ rrtUSA rrt ;

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301

where pte is expected inﬂation ﬁltered using the HP ﬁlter, ptt is the transitory component of inﬂation, rrtUSA is the American real interest rate, j and rrt the foreign rate. (Source: IFS) dproit : Apparent productivity differential in labor, j

dprot ¼ protUSA prot ; j

where protUSA and prot are respectively the American and the foreign apparent labor productivity. This is calculated as ! j gdpt 1 j prot ¼ log ; j s t employment t

with

gdptUSA ¼ log : employmenttUSA

protUSA

(Source: IFS and OCDE) dpexit : Public expenditure differential, calculated as j

dpext ¼ pextUSA pext ; j

where pextUSA and pext are respectively the American and the foreign government spending. The government spending is calculated relative to GDP: pext ¼

pexnt 100; gdpnt

where pexpnt is nominal public expenditure. (Source: IFS) dnfait : Net foreign assets differential, j

dnfat ¼ rnfatUSA rnfat ; j

where rnfatUSA and rnfat stands respectively for the American and the foreign’s net foreign asset position relative to the GDP in US dollar: j

nfat

j

rnfat ¼

j

gdpt ð1=st Þ

and rnfatUSA ¼

nfatUSA gdptUSA

(Source: L-M)

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302

oildepit : Relative oil dependence, j

oildept ¼

balt brent price 100; USA balt cpitUSA j

where baltUSA and balt are measures of energetic dependence for the United States and the foreign country respectively. This is obtained as balt ¼

Net oil imports : gdpnt

(Source: IFS and OCDE) For the time series analysis, differentials are no longer calculated for the United States relative to every other country but relative to a representative European variable. The latter is obtained as the weighted average of the corresponding national values already used in the panel analysis. The weights are the share of national GDP relative to the GDP for our idyosincratic euro area. The GDP are in constant terms and PPP, as reported by the OECD, the base year being 1993. The bilateral real exchange rate (qt ) of the US dollar relative to the euro is obtained as in the panel, where st is deﬁned as units of dollars required to purchase a euro. The sources for st are BBVA (from 1970:1 to 1997:4) and IFS for the rest of the sample. Notes The authors belong to INTECO, Research Group on Economic Integration, supported by Generalitat Valenciana. They want to acknowledge the ﬁnancial support of the project SEC2002-03651 from the CICYT and FEDER. The computations have been made using two Gauss routines: the pooled mean group estimation program, written by Y. Shin, and NPT 1.3, by Chiang and Kao (2001). The authors are very grateful to all the participants in the CESifo conference on Exchange Rate Modeling: Where Do We Stand? for their comments and, in particular, to the discussant, Jan-Egbert Sturn, and to Paul de Grauwe. The chapter has also beneﬁted from the comments of an anonymous referee. 1. See ECB (2002). 2. For a complete overview of different empirical approaches, see Williamson (1994), and more recently, MacDonald (2000). 3. For simplicity, we are omitting the NATREX and the PEER approaches. We consider the ﬁrst to be clearly connected to the FEER approach and the second to the BEER approach. 4. The breakdown between traded and nontraded goods has not been possible for the sample period, the OECD data available only reaching 1992. 5. Hamilton (1983) found that the energy price can account for innovations in many US macroeconomic variables. Amano and van Norden (1998) ﬁnd a stable link between the

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303

effective real exchange rate of the dollar and the oil price shocks. They also think that these shocks account for most of the major movements in the terms of trade. According to them, the correlations between the terms of trade and the one-period lagged price of oil are 0.57, 0.78, and 0.92 for the United States, Japan, and Germany, respectively. 6. A detailed description of the variables can be found in appendix A. 7. In addition, other speciﬁcations have been estimated in the empirical part of the model. In particular there are the simplest version of the Meese and Rogoff (1988) model (rerdolit ¼ ai þ b 1i drrit Þ and the Rogoff (1992) intertemporal model (rerdolit ¼ ai þ b 1i dpex þ b 2i dproit þ b 3i oildepit Þ. In the ﬁrst case, although the information criteria were encouraging, the model was not very explanatory (with R 2 under 0.10 for the individual countries). As for the Rogoff (1992) model, none of the hypotheses concerning the long-run parameters were accepted, and the information criteria did not recommend its choice. The results, although not reported in this chapter, are available upon request. 8. Finally published as Levin, Lin, and Chu (2002). 9. Groen (2000) and Mark and Sul (2001) have also recently applied panel techniques to estimate models for the dollar exchange rate determination. In particular, Groen (2000) applies a panel version of the Engle and Granger two-step procedure under the homogeneity restriction on the long-run parameters. Mark and Sul (2001) apply dynamic OLS estimators, and also impose homogeneity in the cross sections. 10. All the results concerning this speciﬁcation are available upon request. 11. The p-values associated with the test for each of the variables are the following: dpext [0.40], dnfat [0.51], and dprot [0.00]. 12. The results are available upon request. 13. The model has been speciﬁed with the constant unrestricted. Previous to this choice, the different possible speciﬁcations for the deterministic components were compared using the procedure suggested by Johansen (1996). 14. The magnitude of this parameter also lies in the range commonly found in the empirical literature, as reported by Gregorio and Wolf (1994). According to them, this range is ð0:1; 1:0Þ. 15. We should note that the real exchange rate is deﬁned in our chapter in the opposite way. More precisely, an increase in the real exchange rate corresponds to a real depreciation.

References Alberola, E., S. Cervero, H. Lo´pez, and A. Ubide. 1999. Global equilibrium exchange rates: Euro, dollar, ‘‘ins,’’ ‘‘outs,’’ and other major currencies in a panel cointegration framework. IMF Working Paper 99/175. Alquist, R., and M. D. Chinn. 2002. Productivity and the euro–dollar exchange rate puzzle. NBER Working Paper 8824. Amano, R., and S. van Norden. 1998. Oil prices and the rise and fall of the US real exchange rate. Journal of International Money and Finance 17: 299–316. Banerjee, A., J. J. Dolado, and R. Mestre. 1992. On some simple tests for cointegration: The cost of simplicity. Bank of Spain Working Paper 9302.

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Baxter, M. 1994. Real exchange rates and real interest differentials. Have we missed the business-cycle relationship? Journal of Monetary Economics 33: 5–37. Cavallo, M., and F. Ghironi. 2002. Net foreign assets and the exchange rate: Redux revived. Journal of Monetary Economics 49(5): 1057–97. Campbell, J. Y., and R. H. Clarida. 1987. The dollar and real interest rates. CarnegieRochester Conference Series on Public Policy 27: 103–40. Chiang, M. H., and C. Kao. 2001. Nonstationary panel time series using NPT 1.2. A user guide. Center for Policy Research. Syracuse University. Clark, P. B., and R. MacDonald. 1999. Exchange rates and economic fundamentals: A methodological comparison of BEERs and FEERs. In R. MacDonald and J. L. Stein, eds., Equilibrium Exchange Rates, Norwell, MA: Kluwer Academic Publishers, pp. 285–322. Clostermann, J., and B. Schnatz. 2000. The determinants of the euro–dollar exchange rate: Synthetic fundamentals and a non-existing currency. Konjunkturpolitic, Applied Economics Quarterly 46(3): 274–302. De Grauwe, P. 1997. Exchange rate arrangements between the ins and the outs. In Masson et al., eds., EMU and the International Monetary System. Washington: IMF. De Grauwe, P. 2000. Exchange rates in search of fundamentals: the case of the euro– dollar rate. International Macroeconomics Discussion Paper Series 2575. CEPR. Diebold, F. X. 1998. Elements of Forecasting. Cincinnati, OH: South-Western College Publishing. Gregorio, J., and H. Wolf. 1994. Terms of trade, productivity and the real exchange rate. NBER Working Paper 4807. ECB. 2000. The nominal and real effective exchange rates of the euro. Monthly Bulletin, April. ECB. 2002. Economic fundamentals and the exchange rate of the euro. Monthly Bulletin, April. Edison, H. J., and W. R. Melick. 1995. Alternative approaches to real exchange rates and real interest rates: Three up and three down. International Finance Discussion Paper 518. Board of Governors of the Federal Reserve System. Edison, H. J., and B. D. Pauls. 1993. A re-assessment of the relationship between real exchange rates and real interest rates: 1974–1990. Journal of Monetary Economics 31: 165–87. Groen, J. J. J. 2000. The monetary exchange rate model as a long-run phenomenon. Journal of International Economics 52: 299–319. Hadri, K. 2000. Testing for unit roots in heterogeneous panel data. Econometrics Journal 3: 148–61. Hamilton, J. D. 1983. Oil and the macroeconomy since World War II. Journal of Political Economy 91: 228–48. Hansen, H., and S. Johansen. 1993. Recursive estimation in cointegrated VAR-models. Preprint 1993, n. 1. Institute of Mathematical Statistics. University of Copenhagen. Hooper, P., and J. Morton. 1982. Fluctuations in the dollar: A model of nominal and real exchange rate determination. Journal of International Money and Finance 1: 39–56.

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Im, K., M. H. Pesaran, and Y. Shin. 1995. Testing for unit roots in heterogeneous panels. Department of Applied Economics. University of Cambridge. Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector Auto-regressive Models. Oxford: Oxford University Press. Johansen, S. 1996. Likelihood based inference for cointegration of non-stationary time series. In D. R. Cox, D. Hinkley, and O. E. Barndorff-Nielsen, eds., Likelihood, Time Series with Econometric and Other Applications. London: Chapmann and Hall. Lane, P. R. 2002. Discussion of ‘‘Net foreign assets and the exchange rate: Redux revived’’ by M. Cavallo and F. Ghironi, Carnegie-Rochester Conference on Public Policy, November 2001. Mimeo. http://econserv2.bess.tcd.ie/plane/. Lane, P. R., and G. M. Milesi-Ferretti. 2001. The external wealth of nations: Measures of foreign assets and liabilities in industrial and developing countries. Journal of International Economics 55(2): 263–94. Ledo, M., and D. Taguas. 1999. Un modelo para el do´lar-euro. Situacio´n 6 (diciembre). Servicio de Estudios, BBVA. Levin, A., and C. F. Lin. 1992. Unit root tests in panel data: Asymptotic and ﬁnite-sample properties. UC San Diego, Working Paper 92-23. Levin, A., C. F. Lin, and J. Chu. 2002. Unit root tests in panel data: Asymptotic and ﬁnitesample properties. Journal of Econometrics 108: 1–24. Maeso-Ferna´ndez, F., C. Osbat, and B. Schnatz. 2001. Determinants of the Euro real effective exchange rate: A BEER/PEER approach. ECB Working Paper 85. MacDonald, R. 1998. What determines real exchange rates? The long and the short of it. Journal of International Financial Markets, Institutions and Money 8: 117–53. MacDonald, R. 2000. Concepts to calculate equilibrium exchange rates: An overview. Discussion Paper 3/00. Economic Research Group of the Deustche Bundesbank. MacDonald, R., and J. Nagayasu. 2000. The long-run relationship between real exchange rates and real interest differentials: A panel study. IMF Staff Papers 47: 116–28. Makrydakis, S. P. de Lima, J. Claessens, and M. Kramer. 2000. The real effective exchange rate of the Euro and economic fundamentals: A BEER perspective. Mimeo. European Central Bank. March. Mark, N. C., and D. Sul. 2001. Nominal exchange rates and monetary fundamentals: Evidence from a small post–Bretton Woods panel. Journal of International Economics 53: 29–52. Meese, R., and K. Rogoff. 1988. Was it real? The exchange rate-interest differential relation over the modern ﬂoating-rate period. Journal of Finance 43: 933–48. Meredith, G. 2001. Why has the euro been so weak? IMF Working Paper 01/155. Osterward-Lenum, M. 1992. A note with quantiles of the asymptotic distribution of the LM cointegration rank statistics. Oxford Bulletin of Economics and Statistics 54: 461–72. Pesaran, M. H., Y. Shin, and R. P. Smith. 1999. Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association 94(446): 621–34.

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Reimers, H.-E. 1992. Comparisons of tests for multivariate cointegration. Statistical Papers 33: 335–59. Rogoff, K. 1992. Traded goods consumption smoothing and the random walk behaviour of the real exchange rate. Bank of Japan Monetary and Economic Studies 10: 783–820. Sarno, L. 2002. Toward a new paradigm in open economy modeling: Where do we stand? Federal Reserve Bank of St. Louis Review (May–June): 21–36. Williamson, J. 1994. Estimating Equilibrium Exchange Rates. Washington: Institute for International Economics. Wu, J. L. 1999. A re-examination of the exchange rate-interest differential relationship: Evidence from Germany and Japan. Journal of International Money and Finance 18: 319–36.

10

Dusting off the Perception of Risk and Returns in FOREX Markets Phornchanok J. Cumperayot

After the demise of the Bretton Woods system in early 1973, many industrialized countries turned to a (semi-) ﬂoating exchange rate regime.1 Academics try to explain causes of exchange rate ﬂuctuations and search for policy recommendations. There are numerous papers attempting at explaining the movement of exchange rates.2 Many theoretical versions, however, fail to determine exchange rates in practice. Empirical investigations have been carried out to test the exchange rate theories and the predictability of exchange rates.3 The empirical support for the theories has been rather weak. In this chapter a nonlinear model for exchange rates is proposed, based on the monetary exchange rate theory and the theory of ﬁnancial asset pricing, so as to provide alternative insights about the anomalous behavior of exchange rates. This model is inspired by the pioneering work of Hodrick (1989), who introduced the volatilities of macroeconomic fundamentals in the exchange rate model as additional risk factors. Unlike Hodrick (1989), I incorporate macroeconomic risk into the ﬂexible-price and the sluggish-price monetary models. This allows the long-run and short-run effects of the fundamental uncertainty to be examined. The empirical results are rather striking and supportive compared to those of Hodrick (1989). As I show in this chapter, in the long run the nonlinear model explains how an increase in domestic money supply or a decrease in domestic real income leads to depreciation of the domestic currency, and vice versa for the foreign variables. Time-varying conditional variances of the macroeconomic variables, representing macroeconomic risk, can be related to the deviation of the exchange rate from its fundamental-based value. Macroeconomic uncertainty inﬂuences the perception of FOREX risk and consequently inﬂuences market expectations about compensation for risk bearing. Due to risk aversion,

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high risk is accompanied by high expected future returns, or equivalently a current depreciation of the currency. In the short run, the nonlinear model is shown to provide evidence for correction of equilibrium errors toward the long-run equilibrium. These results indicate that macroeconomic sources of FOREX risk is a missing factor in exchange rate studies and that the monetaryapproach models is potentially still useful. In section 10.1, I give the motivation of my work. In section 10.2, I discuss the nonlinear dynamic model. I report its econometric results in section 10.3, and make some concluding remarks in section 10.4. 10.1

Motivation for the Model

The monetary approach to model exchange rates has been viewed as one of the most dismal failures in modern economics (see Flood and Rose 1999). Nevertheless, it can hardly be denied that for our anticipation of exchange rates we rely on economic fundamentals, and often in the manner predicted by the monetary-based exchange rate models. My work was inspired by Dornbusch (1976) and Hodrick (1989). I use their model for exchange rates to reconsider the expectation assumptions used in the traditional exchange rate models by exploiting the statistical regularity of time-varying conditional variances of fundamental growth rates. As suggested by Dornbusch (1976), a fundamental change from its equilibrium level may cause a short-run overshooting in the exchange rate. Volatility in the macroeconomic variables may consequently induce volatility in the exchange rate. In turn the uncertainty in macroeconomic fundamentals may inﬂuence the perception of risk in the markets, and subsequently through the risk premium it may price returns on the exchange rate, as stated in Hodrick (1989). This seems like a natural way to explain the exchange rate risk premium, as arising from variation in conditional variances of exchange rate returns, but Hodrick (1989) ﬁnds little support for the idea. After more than a decade since his research and almost three decades of ﬂoating exchange rate regime, it is time to reinvestigate the hypothesis in Hodrick (1989). In the literature, exchange rates rely on two factors: the current fundamental levels, f~t , and the expectation of future exchange rates, Et ½etþ1 .4 A general framework of the models in the exchange rate literature can be summarized as shown in Cuthbertson (1999):5

Dusting off the Perception of Risk and Returns in FOREX Markets

309

et ¼ Et ½etþ1 af~t ;

ð1Þ

where et is the logarithm of the nominal exchange rate, f~t represents the fundamentals that may differ in each model, and Et ½ is the conditional expectation operator. Apart from many possible estimation problems,6 as expectations about the future exchange rate are likely to be a self-fulﬁlling prophecy, the expectation formation deserves considerable attention. In the context of the present value relation, it is known that persistent movement in an asset’s expected return tends to have dramatic effects on the asset price, as it makes the price more volatile than in the case of a constant expected return.7 This also holds for the currency price, for which the expected return is represented by the expected price change. However, the source of the expectation variation is an unresolved issue. In this chapter, I provide an alternative explanation for the expectation formation in the exchange rate models. According to the exchange rate literature, the fundamental solution of the exchange rate is determined by the expected present value of macroeconomic fundamentals, discounted at a constant rate (following from Cuthbertson 1999 in this case is equal to one):8 et ¼

y X

aEt ½ f~tþi :

ð2Þ

i¼0

P ~ By comparing this equation (i.e., et ¼ af~t y i¼1 aEt ½ ftþi ) to equation (1), we ﬁnd that the expected future fundamentals are used to determine the expected future exchange rate. However, in practice, the structure of expectation formation is not known, and the inﬁnite horizon is not easily speciﬁed. It is often assumed that the fundamental processes are a random walk process, Et ½xtþ1 xt ¼ 0. As a consequence the models are left with the current values of the fundamentals as representatives of the expected future fundamentals (e.g., see Meese and Rogoff 1983). As there is no expected change in the fundamentals, these rational expectation models imply zero expected exchange rate returns. Yet empirically positive correlations of exchange rate returns are found at short horizons, whereas negative serial correlations are reported at longer horizons (e.g., see Cuthbertson 1999). Moreover there is some evidence for predictability of the exchange rate at long horizons once the fundamentals are brought into the analysis.9 It is unlikely that the expected returns are zero. In particular,

310

Ph. J. Cumperayot

patterns of time variation in the mean and the variance of the fundamental changes have actually been observed. Like exchange rate returns, there is strong evidence of time-varying conditional variances of the fundamentals, although this is not well documented.10 As there exists systematic fundamental volatility, I investigate in this chapter whether the fundamental uncertainty (e.g., through the risk premium) can determine expected exchange rate returns and thus the exchange rate movement. This doctrine is similar to the well-known theme of asset pricing models, such as the capital asset pricing model (CAPM) developed by Markowitz (1959), Sharpe (1964), and Lintner (1965) and the arbitrage pricing theory of Ross (1976). The theory’s goal is mainly to quantify the assets’ equilibrium expected returns from the risk of bearing the assets. To relate exchange rate risk and return, Fama (1984) ﬁnds that the variation in the risk premium in the forward exchange market is more pronounced than the expected depreciation rate (i.e., expected exchange rate return). Frankel and Meese (1987) indicate that changes in conditional variance of the exchange rate have substantial impacts on the level of the exchange rate. Hodrick’s (1989) model theoretically predicts that changes in the macroeconomic variances affect risk premia and therefore, exchange rates. Yet the empirical results are not supportive. 10.2

The Model

The present value of the exchange rate for the ﬂexible-price model can be written as e t ¼ v0

y X

v2i þ v1

y X

i¼0

v2i Et ½ f~tþi ;

ð3Þ

i¼0

~ t ð1 þ gÞ y~t , and m ~ t and y~t are the logarithms of the where f~t ¼ m domestic money supply and real income with respect to the foreign levels. For the sluggish-price model, inertia is introduced into the price mechanism and thus the exchange rate equation. Cuthbertson (1999) shows that with the UIP condition the Dornbusch model gives rise to a form similar to equation (2): et ¼ Q1 et1 þ l

y X i¼0

Q2 Et1 ½~ktþi ;

ðQ1 ; Q2 Þ < 1;

ð4Þ

Dusting off the Perception of Risk and Returns in FOREX Markets

311

where ~kt 1 ð1=jÞ f~t þ ½ð1 yÞ=yj f~t1 . The exchange rate now depends on ~kt , namely current and lagged values of money supply and real income, and on its expected future values.11 Since the exchange rate is a discounted sum of expected future fundamentals (i.e., equations 2, 3, and 4), if the expectation of f~ (or ~k in a case of the sticky-price model) can be speciﬁed, an explicit process of the exchange rate can be found. A number of methods to incorporate the fundamentals’ variances into their expectations are discussed in appendix C. Here we assume that the fundamental series can be explained by their historical values and their time-varying second moment.12 Therefore the expected future fundamentals do not only depend on the current fundamental levels but also the expected variances of the fundamentals, representing the volatility of the fundamentals. An explicit solution of the ﬂexible-price model can then be written as ~ t þ a2 y~t þ a3 hm~ ; t þ a4 hy~; t : e t ¼ a0 þ a1 m

ð5Þ

In addition to the current fundamental values, the exchange rate is determined by time-varying conditional variances of the fundamentals, ht . For the sticky-price model the closed-form solution is ~ t þ b3 y~t þ b4 m ~ t1 þ b5 y~t1 þ b6 hm~ ; t et ¼ b0 þ b1 et1 þ b2 m þ b7 hy~; t þ b8 hm~ ; t1 þ b9 hy~; t1 ;

ð6Þ

in which the present and lagged values of the fundamentals and their time-varying conditional variances are included in the exchange rate determination. The levels of macroeconomic fundamentals are well known to be insufﬁcient for explaining exchange rate movements. In addition to the traditional monetary models, we introduce macroeconomic risk to describe the deviation of the excessive volatile exchange rate relative to the conventional prediction based on economic fundamentals. In this chapter the expectations of future fundamentals are reformulated by exploiting the systematic pattern of fundamental volatility, instead of assuming a random walk process. Equations (5) and (6) similarly predict that, ceteris paribus, an increase in money supply and a decrease in industrial production, relative to the foreign levels, tend to depreciate the domestic currency. Besides, we explain anomalous movements of the exchange rate, relative to the traditional paradigm, by the presence of volatility clusters in the fundamentals.13 To capture

312

Ph. J. Cumperayot

the currency price volatility, time variation in conditional variances of the fundamentals, captured by a GARCHð1; 1Þ model,14 are incorporated to describe expected exchange rate returns. The modiﬁed ﬂexible-price model in equation (5) is used to characterize the long-run equilibrium of exchange rates, while the modiﬁed sticky-price model in equation (6) corrects for fundamental disequilibrium. The idea to examine the long-run impacts of macroeconomic risk on the exchange rate may seem controversial at ﬁrst, as one would think that the exchange rate volatility is considered as a short-term phenomenon and has nothing to do with the long run. In fact, asset pricing models, such as CAPM, are used for the long-run equilibrium price determination. Intuitively the models say that one who holds risky assets expects to be compensated at least in the long run. 10.3

Speciﬁcation and Estimation

With regard to the exchange rate level, although many developments can cause permanent changes in the exchange rate, the cointegration relationship between the spot rates and macroeconomic fundamentals implies that there is some long-run equilibrium relation tying the exchange rate to its macroeconomic fundamentals (see Hamilton 1994).15 Moreover persistent movements in the fundamental volatility are likely to have larger impacts on exchange rate risk and returns than temporary movements. To model the exchange rate, we are therefore concerned with the cointegration among the variables in equation (5), whereas equation (6) is applied as an error-correction model to explain the adjustment toward the long-run equilibrium. Like other macroeconomic studies this empirical study involves nonstationary and trending variables, such as exchange rates, money supply, and industrial production. Furthermore some GARCH series, as a proxy of time variation in conditional variances ht , may appear to be Ið1Þ as the variance process is close to an integrated GARCH model, namely IGARCH. There are several ways to manipulate such series, to use transformations to reduce them to stationarity, such as to use a vector autoregressive (VAR) model or to analyze the relationship between these trending variables. Hodrick (1989) takes ﬁrst differences to make the series stationary. However, in the existence of a cointegration relationship differencing the data might not be appropriate since counterproductively, it would obscure the long-run relationships between the variables.

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313

As mentioned, the latter option allows us to distinguish between a long-run relationship, in which the variables drift together at roughly the same rate, and the short-run dynamics that capture the relationship between deviations of the variables from the long-run trend (see Stock and Watson 1988; Greene 2000). It should also be noted that the analysis involves generated regressors, in the form of the estimated conditional variances. According to Pagan (1984), the two-step procedure to estimate the conditional variances from the ARCH models and exogenously use the estimated variances in the OLS regression can produce consistency in estimated coefﬁcients if the ARCH processes provide consistent estimates of true conditional variances (see also Hodrick 1989). Unlike Hodrick (1989), we will use a GARCHð1; 1Þ model with a student t error distribution to estimate conditional variances ht .16 For the empirical study we take our macroeconomic series from six OECD countries—Canada, France, Italy, Japan, the United Kingdom, and the United States. Our theoretical constructs will focus on exchange rates, money supply, and industrial production.17 To see the role of economic fundamental uncertainty in determining the exchange rate risk and expected returns, we consider the price of a US dollar in terms of the domestic currency, as the US dollar has been recognized as a vehicle currency.18 The US variables are thus treated as foreign variables in the exchange rate models. Hodrick (1989), however, ﬁnds no evidence for fundamental volatility to price exchange rates because of the weak evidence of ARCH in monthly exchange rates. By expanding the period employed in Hodrick (1989), we have stronger evidence of ARCH in monthly observations.19 So we can reexamine the question posed in Hodrick (1989). To investigate the exchange rate determination based on equations (5) and (6), we need to look at the domestic and the foreign variables separately, not in relative terms.20 Thus the regression equations become et ¼ a0 þ a1; d mt þ a1; f mt þ a2; d yt þ a2; f yt þ a3; d ^h m; t þ a3; f ^ h m ; t þ a4; d ^ h y; t þ a4; f ^ h y ; t

ð7Þ

and et ¼ b0 þ b1 et1 þ b2; d mt þ b2; f mt þ b3; d yt þ b3; f yt þ b4; d mt1 þ b4; f mt1 þ b5; d yt1 þ b5; f yt1 þ b6; d ^h m; t

h m ; t þ b7; d ^ h y; t þ b7; f ^ h y ; t þ b8; d ^ h m; t1 þ b6; f ^ þ b8; f ^ h m ; t1 þ b9; d ^ h y; t1 þ b9; f ^ h y ; t1 ;

ð8Þ

314

Ph. J. Cumperayot

where e is the logarithm of the nominal exchange rate (i.e., the price of a unit of foreign currency in terms of domestic currency), x represents a domestic variable, and x represents a foreign (US) variable.21 The method of investigation is as follows: An augmented DickeyFuller test is ﬁrstly applied to test the null hypothesis that the variables in equation (7) contain a unit root, namely using an Ið1Þ series, and whether the series are integrated to the same order. If the variables are integrated to different orders, a cointegration model would not be appropriate. Second, the Johansen (1988) test is used to identify the number of cointegration vectors from groups of the variables. Then, by an augmented Engle and Granger (1987) test, we check if the error term of the cointegration equation is an Ið0Þ series. Later, we advance to a dynamic OLS estimation of equation (7) and the short-run dynamic equation (8). The ﬁrst step is to identify the appropriate degree of differencing for each series. Suppose that the series of interest is zt . Then the augmented Dickey-Fuller test is based on the regression of the following equation, with or without the presence of a trend t: wðLÞDzt ¼ m þ tt þ bzt1 þ ut ; where wðLÞ ¼ In w1 L w2 L 2 wp L p and ut is an error term. This augmented speciﬁcation is used to test the null hypothesis of a unit root in the series, which is H0 : b ¼ 0 against H1 : b < 0. Table 10.1 shows the results from the augmented DickeyFuller tests of the null hypotheses (1) that the logarithmic level of the series is Ið1Þ and (2) that the logarithmic ﬁrst difference of the series contains a unit root. The table displays b^, and throughout this chapter an asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance, respectively. According to table 10.1, the economic series are likely to be Ið1Þ series. At the 1 percent level of signiﬁcance, ﬁrst-differencing is appropriate to induce stationary in the natural logarithms of the exchange rate, money supply, and industrial productivity. The estimated GARCH processes of the macroeconomic variables are shown to be Ið0Þ, except for the estimated series of the French money supply. The estimated GARCH processes of the Canadian money supply and real income exhibit trend stationarity at the 5 percent signiﬁcance level. Therefore the model represented by equation (7) involves the variables that can

Canada Exchange rate Money supply

Italy

Japan

United Kingdom

e

0.709

1.933

1.920

2.338

2.560

De

7.729***

6.873***

6.834***

7.212***

7.458***

m Dm ^hm D^hm

Industrial production

France

1.591

2.200

10.710*** 3.185**

10.997*** 2.400

7.824***

8.639***

0.965 12.714*** 8.218***

3.275* 12.560*** 3.492***

3.366* 9.798*** 4.903***

United States

1.313 7.873*** 4.043***

y

2.403

2.783

3.143

1.108

2.845

2.915

Dy ^hy

6.350***

8.125***

8.754***

5.471***

7.944***

6.461***

3.179**

5.676***

6.538***

3.919***

4.413***

5.563***

D^hy

11.059***

Note: The results are of the augmented Dickey-Fuller unit root test. The test is based on the augmented equation displayed on top of the table. The speciﬁcation, with or without a trend t depending on its signiﬁcance, is used to test the null hypothesis of a unit root in the series (i.e., H0 : b ¼ 0Þ against the alternative hypothesis of no unit root ðH1 : b < 0Þ. The test is applied to the natural logarithmic levels of exchange rate (e), money supply (m), and real income (y), and also to the estimated GARCH series (h) of money growth and income growth. For the series that cannot reject the unit root at the 1 percent level, the test is also applied to ﬁrst differences of these series. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

Dusting off the Perception of Risk and Returns in FOREX Markets

Table 10.1 Results of the augmented Dickey-Fuller unit root test, wðLÞDzt ¼ m þ tt þ bzt1 þ ut

315

316

Ph. J. Cumperayot

Table 10.2 Results of the Johansen cointegration test et ¼ a 0 þ a1; d mt þ a1; f mt þ a2; d yt þ a2; f yt þ a3; d^h m; t þ a3; f ^h m ; t þ a4; d^h y; t þ a4; f ^h y ; t

Hypothesized

Canada

France

Italy

Japan

United Kingdom

2**

1**

1**

1**

2**

Number of ranks Note: The results are of the Johansen cointegration test for the group of the Ið1Þ variables in the modiﬁed ﬂexible-price model (as shown on top of the table). The test is conducted under the null hypothesis that the cointegrating rank is r or lower. The table shows the number of cointegrating vectors, that cannot be rejected. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

individually be either Ið0Þ or Ið1Þ. The modiﬁed exchange rate equation is then tested for a cointegration relationship, that is, if there exists a stationary linear combination of these variables. The Ið0Þ variables are introduced as exogenous regressors in the cointegration function. The second step is to examine if there is any cointegration relationship among these Ið1Þ series. The Johansen (1988) test is used to serve this purpose.22 Table 10.2 reports the number of signiﬁcant cointegration vectors. The likelihood ratio (LR) test can reject the null hypothesis of no cointegration in every country. At the 5 percent signiﬁcance level, the LR test indicates 1 cointegration relationship for France, Italy, and Japan, and 2 cointegration relationships in the case of Canada and the United Kingdom. As the Johansen test predicts cointegration relationship(s) for every country, an alternative method by Engle and Granger (1987) is used to assess whether linear combinations, based on the ﬂexible-price model in equation (7), are stationary. From equation (7), the model for the exchange rate that is suitable for regression analysis can be rewritten as et ¼ a^0 þ a^1; d mt þ a^1; f mt þ a^2; d yt þ a^2; f yt þ a^3; d ^h m; t h m ; t þ a^4; d ^ h y; t þ a^4; f ^ h y ; t þ et ; þ a^3; f ^

ð9Þ

where et is an error term. In equation (9) the cointegration function represents the long-run movement of exchange rates. OLS estimation is applied because it has been proved to yield asymptotically superconsistent estimators when estimating cointegration relationships (see Greene 2000). The Engle and Granger (1987) two-step procedure test is applied to examine the stationarity of the residual term et . To correct for autocorrelation in the equilibrium error series, an augmented Engle and Granger test is based on estimating

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317

Table 10.3 Results of the augmented Engle and Granger cointegration test Det ¼ f0 et1 þ f1 Det1 þ þ et

f^0

Canada

France

Italy

Japan

United Kingdom

3.415**

4.904***

3.722***

3.129**

4.522***

Note: The results are of the augmented Engle and Granger cointegration test on the equilibrium error et . It is to test the signiﬁcance of the null hypothesis that the error series contains a unit root (i.e., H0 : f0 ¼ 0, H1 : f0 < 0). If the null hypothesis cannot be rejected, there is no cointegration relationship. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

Det ¼ f0 et1 þ f1 Det1 þ þ et by the Newey-West approach. If the null hypothesis of a unit root in the residual series (H0 : f0 ¼ 0, H1 : f0 < 0) cannot be rejected, there is no cointegration relationship among the variables in the model. Table 10.3 shows f^0 . Asterisks indicate that the null hypothesis of unit root can be rejected at the 5 percent signiﬁcance level for Canada and Japan, and at the 1 percent level for France, Italy and the United Kingdom. The evidence in tables 10.2 and 10.3 demonstrates the cointegration in these countries. To test our assumption regarding the expectation formation that incorporates macroeconomic uncertainty, we apply the two-step cointegration approach as proposed by Engle and Granger (1987).23 We ﬁrst deal with the modiﬁed ﬂexible-price model and then the modiﬁed sluggish-price model. The Stock and Watson (1993) dynamic OLS estimation method is employed to regress the logarithm of the exchange rate against the logarithms of money supply and industrial production, and the estimated conditional variances—from a GARCHð1; 1Þ model—of the growth rates of money supply and industrial production. The US variables are used as the foreign variables. Although the OLS estimation has proved to asymptotically yield superconsistent estimates, because of the possibility that the explanatory variables are contemporaneously correlated with the disturbance term, the OLS regression coefﬁcients are likely to be inconsistent.24 The dynamic OLS procedure, on the other hand, is robust to small sample size and simultaneity bias. To eliminate the effects of these correlations, we apply the Stock and Watson (1993) dynamic OLS approach by adding the one-period leads and lags of the ﬁrst differences of the regressors mentioned above.25 The method is also known for being a robust single equation that

318

Ph. J. Cumperayot

corrects for stochastic-regressor endogeneity. According to equation (7) the dynamic OLS equation is et ¼ a^0 þ a^1; d mt þ a^1; f mt þ a^2; d yt þ a^2; f yt þ a^3; d ^h m; t þ a^3; f ^h m ; t h y; t þ a^4; f ^ hy ; t þ a^5; d Dmtþ1 þ a^5; f Dmtþ1 þ a^4; d ^ þ a^6; d Dytþ1 þ a^6; f Dytþ1 þ a^7; d D ^ h m; tþ1 þ a^7; f D ^ h m ; tþ1 þ a^8; d D ^h y; tþ1

ð10Þ

þ a^8; f D ^ h y ; tþ1 þ a^9; d Dmt1 þ a^9; f Dmt1 þ a^10; d Dyt1 þ a^10; f Dyt1 þ a^11; d D ^ h m; t1 þ a^11; f D ^ h m ; t1 þ a^12; d D ^h y; t1

þ a^12; f D ^ h y ; t1 þ xt ; where xt denotes the error term. Table 10.4 contains the estimated parameters from equation (10), a^i; d and a^i; f when i ¼ 1; . . . ; 4. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent level of signiﬁcance, respectively. Apart from allowing us to examine the long-run impacts of macroeconomic risk on exchange rates, adding the estimated macroeconomic risk into a cointegration equation may help reduce the problem of omitted variables.26 From table 10.4 the estimated coefﬁcients of money supply and real income have signs as expected in the literature. In the long run an increase in the domestic money supply or a decrease in the foreign money supply tends to depreciate the domestic currency, Table 10.4 Parameters of the modiﬁed ﬂexible-price model et ¼ a^0 þ a^1; d mt þ a^1; f m þ a^2; d yt þ a^2; f y þ a^3; d^h m; t þ a^3; f ^h m ; t þ a^4; d^h y; t þ a^4; f ^h y ; t þ t

Canada

t

France

Italy

Japan

United Kingdom

a^0 a^1; d

3.128***

6.740***

6.210***

7.472***

3.868***

0.116

0.753***

0.929***

0.774***

0.321**

a^1; f a^2; d

0.155**

0.580***

0.666***

1.101***

0.097

0.535**

1.886***

2.056***

0.538**

1.266**

a^2; f a^3; d a^3; f

116.328*** 1356.045**

a^4; d a^4; f

25.750

0.076

178.947***

0.479* 530.64*** 3185.05** 376.15** 6.369

0.693*** 497.51* 4555.66** 46.59** 433.14

1.444*** 224.703* 1840.97 270.166* 555.754**

0.029 877.01** 6340.388*** 172.19* 777.12***

Note: The estimation results are of the modiﬁed ﬂexible-price model, based on the Stock and Watson (1993) dynamic OLS approach. The estimated parameters are a^i; d and a^i; f when i ¼ 1; . . . ; 4. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance respectively.

Dusting off the Perception of Risk and Returns in FOREX Markets

319

except for Canada. Higher domestic output or lower foreign output is likely to appreciate the domestic currency (although there are exceptions for Canada and Japan). For Canada and the United Kingdom, at the 5 percent signiﬁcance level the Wald test cannot reject the null hypothesis that the coefﬁcients of domestic and foreign macroeconomic variables, like money supply and real income, are signiﬁcantly equal. When we restrict the domestic and foreign coefﬁcients of money supply and real income to be equal in these countries, higher money supply or lower real income relative to the US tends to depreciate the domestic currencies while the coefﬁcients of macroeconomic risk are similar to those in table 10.4.27 Signiﬁcantly, an increase in the money supply volatility, both domestic and foreign, depreciates the Canadian dollar but appreciates other currencies. For uncertainty in real income, the results signiﬁcantly show that with an increase in the domestic volatility, the domestic currency depreciates (except in the United Kingdom). In contrast, with an increase in the foreign volatility, the domestic currency appreciates. Higher uncertainty in the US real income or the US money supply raises the expected future returns on US dollars by pushing down the current US dollar price. It consequently causes the domestic currency to appreciate (except in Canada). By the same argument, uncertainty in the domestic real income is positively related to the US dollar exchange rates. It leads to an upward bias in the variation of actual exchange rates from the prediction of the traditional model. From table 10.4, macroeconomic uncertainty, represented by the conditional variances of money supply and real income, relates signiﬁcantly to the deviation of the exchange rate from its fundamentally based value. Uncertainty about the economy appears to lower the demand for the currency and subsequently leads to depreciation, relative to the fundamental benchmark value. From an asset pricing perspective, higher risk should be accompanied by higher expected future returns, leading to a current depreciation of the currency. Theory coherently predicts that higher variability of domestic fundamentals should result in higher current depreciation of the domestic currency. However, the opposite impact can also be observed in some cases of uncertainty in money growth. For every country except Canada, higher volatility in the domestic money supply tends to increase the domestic currency prices. This might be because the volatile money supply (e.g., due to volatile capital ﬂows or active domestic monetary policy) does not necessarily

320

Ph. J. Cumperayot

imply a negative outlook on the domestic currency.28 Because of this positive effect of macroeconomic risk, economic agents prefer to hold their local currencies and will pay a higher price. These cases also reveal a strong preference for domestic currency that is parallel to the equity home bias, meaning the tendency to underinvest in (more attractive) foreign assets, that has been long studied in ﬁnance.29 On the other hand for Canada there exists a negative risk premium toward the US dollar, which shows a positive reaction toward an active US monetary policy.30 The modiﬁed sticky-price model extends the cointegration relationship between the exchange rate and its fundamentals by adding the long-run equilibrium error adjustment. By rearranging equation (8), we obtain a form of the error-correction model: Det ¼ ^b0 þ ^b2; d Dmt þ ^b2; f Dmt þ ^b3; d Dyt þ ^b3; f Dyt þ ^b6; d D ^h m; t þ ^b6; f D ^ h m ; t þ ^b7; d D ^ h y; t þ ^b7; f D ^ h y ; t þ ð^b1 1Þ ( ) et1 c^1; d mt1 c^1; f mt1 c^2; d yt1 c^2; f yt1 þ nt ; h m; t1 c^3; f ^ h m ; t1 c^4; d ^ h y; t1 þ c^4; f ^h y ; t1 ^ c3; d ^ where c^1; d ¼ ð^b4; d þ ^b2; d Þ=ð^b1 1Þ, c^1; f ¼ ð^b4; f þ ^b2; f Þ=ð^b1 1Þ, c^2; d ¼ ð^b5; d þ ^b3; d Þ=ð^b1 1Þ, c^2; f ¼ ð^b5; f þ ^b3; f Þ=ð^b1 1Þ, c^3; d ¼ ð^b8; d þ ^b6; d Þ=ð^b1 1Þ, c^3; f ¼ ð^b8; f þ ^b6; f Þ=ð^b1 1Þ, c^4; d ¼ ð^b9; d þ ^b7; d Þ=ð^b1 1Þ and c^4; f ¼ ð^b9; f þ ^b7; f Þ=ð^b1 1Þ. Provided that the relationship between the exchange rate and the fundamentals is stable, the set of coefﬁcients c in this equation is equivalent to the set of coefﬁcients a in the modiﬁed ﬂexible-price model. Thus we can test the short-run dynamic equation31 Det ¼ ^b0 þ ^b2; d Dmt þ ^b2; f Dmt þ ^b3; d Dyt þ ^b3; f Dyt þ ^b6; d D ^h m; t þ ^b6; f D ^ h m ; t þ ^b7; d D ^ h y; t þ ^b7; f D ^ h y ; t þ ð^b1 1Þet1 þ nt : Note that since ﬁrst differencing is sufﬁcient to produce stationary series and since there exists the cointegration relationship shown in tables 10.2 and 10.3, the residual term nt is an Ið0Þ series. As stated by Greene (2000), the movement of the exchange rate from the previous period associates with the changes in the fundamentals along the long-run equilibrium corrected for the previous deviation

Dusting off the Perception of Risk and Returns in FOREX Markets

321

Table 10.5 Parameters of the modiﬁed sticky-price model Det ¼ ^b0 þ ð^b1 1Þet1 þ ^b2; d Dmt þ ^b2; f Dm þ ^b3; d Dyt þ ^b3; f Dy þ ^b6; d D^h m; t t

t

þ ^b6; f D^h m ; t þ ^b7; d D^h y; t þ ^b7; f D^h y ; t þ nt Canada ^b0 ð^b1 1Þ ^b2; d ^b2; f ^b3; d ^b3; f ^b6; d ^b6; f ^b7; d ^b7; f

France

Italy

Japan 0.002

United Kingdom

0.001

2.37E-4

0.003

0.023**

0.056***

0.027

0.063***

0.087***

0.042 0.055

0.024 0.071

0.083 0.040

0.021 0.189*

0.067 0.003

0.070

0.109

0.009

0.050

0.078

0.207** 9.119

0.502** 10.505

0.481**

0.084

56.871

75.438

0.001

0.675*** 159.643*

138.630

33.414

59.534

210.013

17.408

22.570

3.041

12.068

229.840 10.498

28.122

75.073

4.561

21.820

42.507

Note: The estimation results are of the modiﬁed sticky-price model, based on the linear OLS regression. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance respectively.

from the long-run equilibrium. This equation contains an equilibrium relationship in the ﬁrst two lines and an adjustment for the deviation from the previous equilibrium in the last line. Table 10.5 shows that there exists a correction mechanism of equilibrium errors toward the long-run equilibrium, as ð^b1 1Þ is signiﬁcantly negative, except in the case of Italy. The error correction term, et1 , is signiﬁcantly negative at the 5 percent signiﬁcance level in the case of Canada and at the 1 percent signiﬁcance level for France, Japan, and the United Kingdom. For Italy, at the monthly horizon, the adjustment toward long-run equilibrium is not signiﬁcant but the sign of ð^b1 1Þ is still negative. Furthermore, in the short run, the exchange rate can be signiﬁcantly explained by changes in the US real income. Yet other macroeconomic fundamentals as well as their uncertainty fail to explain the exchange rate in the short run. 10.4

Conclusion

The expectations regarding macroeconomic circumstances can inﬂuence the exchange rate in the manner predicted by the monetary models, but the random walk assumption is too naive for market expectations. In this chapter, I propose an alternative expectation formation process for the macroeconomic variables by introducing

322

Ph. J. Cumperayot

additional risk factors, based on the volatility of the macroeconomic fundamentals. As the fundamentals empirically exhibit a meanreverting process with persistent memory in the standard deviation (representing the adjustment and speed toward the mean), a nonlinearity in the expectation formation process is present. To capture the exchange rate volatility, in addition to the traditional fundamentals, such as money supply and real income, time variation in the second moments of these fundamentals is incorporated to describe the expected exchange rate returns. The result shows signiﬁcant cointegration between the variables in the modiﬁed ﬂexible-price monetary model, as well as a correction of equilibrium errors toward the long-run equilibrium in the modiﬁed sticky-price model. In the long run, an increase in the domestic money supply or a decrease in the foreign money supply tends to depreciate the domestic currency. Higher domestic output or lower foreign output is likely to appreciate the domestic currency. The impacts of macroeconomic sources of risk are also signiﬁcant. In general, uncertainty about the economy lowers the demand for the currency and subsequently depreciates the currency, relative to the fundamental-based value. From an asset pricing perspective, increased risk is accompanied by increased expected future returns, leading to a current depreciation of the currency. The ﬁndings in this chapter indicate that macroeconomic sources of FOREX risk are a missing factor in exchange rate studies and that the monetary exchange rate models are still potentially useful. Appendix A: Data Sources The data applied in this chapter are monthly observations of exchange rates, money supply and industrial production, starting from June 1973 (with the breakdown of the Bretton Woods system) to December 1998. There are six OECD countries studied: Canada, France, Italy, Japan, the United Kingdom, and the United States. Both European and nonEuropean countries, with possible different economic mechanisms, are selected based on the availability of the required data. The US dollar is used as a vehicle currency and the US variables are used as the foreign variables. The main data source is the IMF International Financial Statistics (IFS), except for M1 of the United States. This time series is from the US Federal Reserve Bank at St. Louis. It is compared with available

Dusting off the Perception of Risk and Returns in FOREX Markets

323

quarterly series from the IFS and they are very similar. The US dollar exchange rates (domestic currency prices per one US dollar) from the IFS are coded AE. Monetary aggregation is represented by seasonally unadjusted M1 data from IFS coded 34, except for the United Kingdom. For the purpose of this chapter, liquidity under the central bank’s controllability is preferable. For the United Kingdom, M 0 , is used and coded 59, instead of another available choice M 4 . Seasonally adjusted industrial production, coded 66, is used as a proxy for real income. If necessary, a seasonal adjustment can be made by way of an additive seasonal moving average approach. Appendix B: The Reduced-Form Solutions of the Exchange Rate Models The ﬂexible-price model is derived from the simple quantity equation Mt Vt ¼ Pt Yt . In logarithms, the quantity equation reveals that m t þ vt ¼ pt þ yt ;

ðA1Þ

where mt ; vt ; pt , and yt are the logarithms of the money supply, the money velocity, the price level, and the real income at period t respectively. We can assume that purchasing power parity (PPP) and uncovered interest parity (UIP) hold. The stochastic PPP assumption, which is a more speciﬁc version of the no-arbitrage assumption, is deﬁned as pt ¼ t þ pt þ et þ ot :

ðA2Þ

In equation (A2), et ; pt , and pt are the logarithms of the nominal exchange rate, namely the price of a unit of foreign currency, the domestic price level and the foreign price level respectively. An asterisk denotes a foreign variable, which in this case is a US variable. While t is a constant, ot represents a stationary, zero-mean disturbance term, sometimes referred to as the real exchange rate. According to the UIP condition, the interest rate differential between domestic and foreign assets is supposed to be equal to the expected rate of depreciation of the domestic currency. The expected change in currency price that satisﬁes equilibrium in the capital markets can thus be written as Et ½etþ1 et ¼ it it ;

ðA3Þ

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where it and it are the domestic interest rate and the foreign interest rate respectively. Et ½ is the conditional expectation operator. The velocity of money circulation is presumed to be a stable function of real income and the interest rate. The logarithm of money velocity is linearly speciﬁed as a decreasing function of the logarithm of real income and an increasing function of the interest rate: vt ¼ y gyt þ jit þ $t ;

ðA4Þ

where y is a constant and $t is a stationary, zero-mean disturbance. Suppose that (A1) holds at home and in foreign countries with an identical income elasticity, g, and interest semi-elasticity, j. Combine (A1) with (A2), (A3), and (A4) and rework for the foreign country: et ¼ t þ

1 ð1 þ gÞ j ~t m y~t þ Et ½etþ1 þ et ; 1þj 1þj 1þj

ðA5Þ

where x~t ¼ xt xt and et ¼ $t $t ot . To solve this linear equation with rational expectation, we apply the law of iterated expectations (see Samuelson 1965; Blanchard and Fischer 1993). For simplicity, we rewrite equation (A5) as et ¼ v0 þ v1 f~t þ v2 Et ½etþ1 þ et ;

ðA6Þ

~ t ð1 þ gÞ y~t . where v0 ¼ t, v1 ¼ 1=ð1 þ jÞ, v2 ¼ j=ð1 þ jÞ, and f~t ¼ m Note that v2 ¼ 1 v1 and that v1 and v2 A ð0; 1Þ as 0 < j < 1 (see Flood, Rose, and Mathieson 1991; Flood and Rose 1995). Equation (A6) implies that the exchange rate depends on its expected rate for the next period, Et ½etþ1 , and on the current fundamentals, f~t , with the weights summing up one. According to the law of iterated expectations, we have e t ¼ v0

T X i¼0

v2i þ v1

T X

v2i Et ½ f~tþi þ v2Tþ1 Et ½etþTþ1 þ

i¼0

T X

v2i Et ½etþi :

ðA7Þ

i¼0

We then assume that as the horizon T increases, the exchange rate at T þ 1 periods becomes negligeable, or equivalently the rational bubble shrinks to zero and that Et ½etþi ¼ 0. As T tends to inﬁnity, lim v2Tþ1 Et ½etþTþ1 ¼ 0;

T!y

and the solution becomes

ðA8Þ

Dusting off the Perception of Risk and Returns in FOREX Markets

e t ¼ v0

y X

v2i þ v1

i¼0

y X

v2i Et ½ f~tþi :

325

ðA9Þ

i¼0

This equation is comparable to equation (2), and implies that the elasticity of the exchange rate, with respect to its expected fundamentals, declines as we look farther into the future as lim v2t ¼ 0:

ðA10Þ

t!y

Moreover, for equation (A8) to converge, it requires that the logarithm of fundamentals, f~, grow at rate lower than v1 =ð1 v1 Þ (i.e., 1=j); otherwise, the solution (A9) would be explosive. The sluggish-price model is an extension of the ﬂexible-price model with inertia introduced into the price mechanism, instead of relying on perfectly ﬂexible prices. Empirically there are deviations from purchasing power parity in equation (A2) where ot are large and persistent. There is also strong correlation between nominal and real exchange rates. In Dornbusch’s (1976) sluggish-price model the expected exchange rate return is formed as the discrepancy between the long-run rate e, to which the economy will eventually converge, and the current spot rate e. Mathematically, E½e e ¼ dðe eÞ;

0 < d < 1:

To allow for sticky prices, the Phillips curve equation is substituted in equation (A2) in the place of purchasing power parity (e.g., see Obstfeld and Rogoff 1984; Flood and Rose 1995). It is conventional to assume that in addition to the PPP condition, prices respond to the lagged excess demand in the good markets, yt yt , and shocks to the good markets, gt : ptþ1 pt ¼ mð yt yt Þ þ gt þ Et ½ p^tþ1 p^t ;

0 < m < 1;

ðA11Þ

where y is the long-run output level, gt has zero mean and constant variance, and p^t is the price level at time t if prices were ﬂexible and the good markets cleared. yt yt ¼ Yðet þ pt pt Þ þ Frt :

ðA12Þ

The excess demand is deﬁned as an increasing function of real exchange rate, Y > 0, and a decreasing function of the ex ante expected real interest rate, namely rt 1 it Et ½ ptþ1 pt , F < 0. Thus, by substituting equation (A12) into equation (A11), we get

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ptþ1 pt ¼ m½Yðet þ pt pt Þ þ Frt þ gt þ Et ½ p^tþ1 p^t :

ðA13Þ

Equation (A13) displays the long-run equilibrium (when the purchasing power parity holds and thus, the left-hand side, LHS, is equal to the last term on the right-hand side, RHS) and its short-run dynamics (represented by deviations from the purchasing power parity by the ﬁrst and the second terms on the RHS). As in the long run p^ ¼ p, p^ can be deﬁned by m½Yðet þ pt p^t Þ þ Frt þ gt ¼ 0; and thus pt ptþ1 pt ¼ m½Yðet þ pt pt Þ þ Frt þ gt þ Et ½ptþ1

þ Et ½etþ1 et þ

F 1 Et ½rtþ1 rt þ Et ½ gtþ1 gt : Y mY

Therefore, instead of using the purchasing power parity condition in equation (A2), we substitute the price equation, p~t ¼ pt pt ¼ et þ þ

1 1 1 Et ½etþ1 et þ Et ½ ptþ1 ðptþ1 pt Þ pt Ym Ym Ym

1 F F 1 1 gt ; Et ½rtþ1 rt þ rt þ Et ½gtþ1 gt þ m Y2 Y Ym m2Y2

ðA14Þ

into the money demand equation, derived from the quantity equation (A1) and the assumption of money circulation (A4): ~ t ð1 þ gÞ y~t þ j~it þ $ p~t ¼ m ~ t: Hence 1 ~ t ð1 þ gÞ y~t þ j~it þ $ Et ½etþ1 et ~t et ¼ m Ym

1 1 1 F Et ½ptþ1 ð ptþ1 pt Þ pt þ Et ½rtþ1 rt Ym Ym m Y2

F 1 1 rt gt : Et ½gtþ1 gt 2 2 Y Ym m Y

ðA15Þ

To present the model in a common form as in equation (2), we assume the UIP condition (A3) and the price process in equation (A14). As a consequence the exchange rate equation becomes

Dusting off the Perception of Risk and Returns in FOREX Markets

et ¼ ~kt þ Et ½etþ1 þ

327

ð1 yÞj y ð1 yÞj y þ 1 Et1 ½et et1 þ ct : yj yj ðA16Þ

where ~kt ¼ 1 f~ þ 1y f~ , j t yj t1 1 y ct ¼ j1 pt j1 Et1 ½ pt Wj Et1 ½rt ð1yWÞ yj rt1 j gt1 j Et1 ½gt gt1 ;

~ t ð1 þ gÞ y~t . The coefﬁand the fundamental f~t is deﬁned as f~t ¼ m cients are assigned by y ¼ 1=Ym and W ¼ F=Y. To apply the law of iterated expectations to this second-order difference equation, we deﬁne At ¼ et þ f½ð1 yÞj y þ 1=yjget1 . Equation (A16) can then be rewritten as At ¼ ~kt þ Et1 ½Atþ1

1 Et1 ½et þ kt þ ct ; yj

ðA17Þ

where kt ¼ Et ½etþ1 Et1 ½etþ1 . By the law of iterated expectations, we get At ¼ ~kt þ

T X

Et1 ½~ktþi

i¼1

þ

T X i¼0

Et1 ½ktþi þ

T 1 X Et1 ½etþi þ Et1 ½AtþTþ1 yj i¼0

T X

Et1 ½ctþi :

i¼0

For simplicity, we presume that the expected exchange rate in any one period, namely Et1 ½AtþTþ1 , is only a small component in determining the current spot rate, and it becomes negligeable as the horizon T rises. Furthermore, when i b 0, Et1 ½ktþi ¼ Et1 ½ctþi ¼ 0. As a consequence, as T tends to inﬁnity, the solution becomes et ¼

y y X ð1 þ jÞðy 1Þ 1 X et1 þ ~kt þ Et1 ½~ktþi Et1 ½etþi : yj yj i¼0 i¼1

ðA18Þ

Equation (A18) is like equation (A9) in the ﬂexible-price model, except there is inertia in the exchange rate equation. The exchange rate now depends on ~kt , namely current and lagged values of money supply and income, and its expected future fundamentals. Additionally equation (A18) is rather similar to the sticky-price concept stated earlier and also a solution (4) from Cuthbertson (1999).

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Appendix C: Adding Stochastic Volatility to the Fundamental Expectations There are many ways to incorporate the second moments of the fundamentals into their expectations. In this appendix I show a few possible ways. In developing an explicit solution for the exchange rate, Hodrick (1989) assumes a conditionally lognormal data-generating process for the fundamentals, and applies the fact that if x has a lognormal dis2 tribution with logðxÞ @ Nðm; s 2 Þ, its expectation reads E½x ¼ e mþs =2 . Hence, by loglinearization of his general equilibrium model, we get logðE½xÞ ¼ m þ 12 s 2 , which is explored in Hodrick (1989). We could equivalently adopt the modiﬁed form of uncovered interest parity (UIP) that adjusts for a risk premium, and we could specify a risk premium as a function of time-varying fundamental variances. This is similar to the portfolio balance model, in which the UIP condition incorporates the risk premium as a function of relative asset holding in domestic and foreign bonds. By combining equation (A5) with a modiﬁed version of UIP that has a time-varying risk premium rt , and applying the law of iterated expectations, we can express the exchange rate as ~ tþi bEt ½ y~tþi þ aEt ½ rtþi : et ¼ Et ½m From the equation above, the exchange rates are determined by two components: the expectation regarding the future fundamental values and the expectation regarding risk from holding the currency. Intuitively, a deviation from its expected fundamental value needs an extra compensation. So, using a risk premium, we can characterize risk in the FOREX markets by macroeconomic uncertainty. Another technical approach is to apply Taylor’s theorem. To make our point, we consider money supply process based on Lucas (1982) and Obstfeld (1987). Suppose mt ¼ wt þ mt1 , where mt is the logarithmic level of money supply and wt is the stochastic growth rate of money supply. Obstfeld (1987) assumes that wt exhibits a jump process, meaning wt ¼ dt mt , where dt represents a dummy variable for the occurrence of a Poisson event and mt denotes the volume of change. To describe money growth wt , there are a number of possible Poisson processes, ranging from the simplest one with a constant probability to the one with unstable probability behavior where dt is a Markov chain with an unabsorbing state.

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329

In practice, we know that the logarithmic ﬁrst difference of the fundamentals, mt mt1 ¼ Dmt ¼ dt mt , is likely to be mean reverting. Hence, to proxy the movement of the variable Dmt around its mean, we can apply Taylor’s theorem to an arbitrary function (see Chiang 1984). If the mean is close to zero, we can use Maclaurin’s series by expanding the function around the point Dx ¼ 0. To include the variance term in the fundamental expectation, we can expand the series to the second degree, which is rather conventional for Taylor’s expansion. As a result we can proxy the expected movement of the macroeconomic series by a nonlinear function. Appendix D: The Closed-Form Solutions To introduce time-varying conditional variances of the macroeconomic variables into the exchange rate model, we assume that there is a relationship between the ﬁrst and the second moments of the fundamentals. The fundamentals are assumed to have somewhat similar to ARCH-in-Mean (ARCH-M) processes. The ARCH-M model, initiated by Engle, Lilien, and Robins (1987), is originally used to describe the risk and return relationship of assets, as suggested in ﬁnance theory. For macroeconomic variables, there is rather weak evidence of ARCHM process.32 An approximate linear relationship between the fundamental expectation and its variance is, however, intuitive. Similar to the ARCH-M model, the whole sequence of future fundamentals can be represented by its current value and its variance. If xt is the time series of interest, the model may be written as xtþ1 ¼ g0 þ g1 xt þ g2 htþ1 þ utþ1 ;

ðA19Þ

where x represents a macroeconomic variable, h is the conditional variance of the variable x, presumably time varying, and u is a residual term. As the fundamentals empirically exhibit mean-reverting processes with persistent memory in standard deviations, time variation in the conditional variance may represent the adjustment and speed toward the mean. In equation (29) the ﬁrst component is like a random walk or an AR(1) process, which is often assumed for macroeconomic variables. The second component shows that macroeconomic uncertainty plays a role in the fundamental expectation formations. For example, the fundamental variances may represent economic circumstances, namely

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whether the economy is in volatile or tranquil periods, in which the expectations may be different. In turmoil (disequilibria), the monetary variables, such as money supply and interest rates, may be altered more often, and the state variables, such as income, unemployment rate, and inﬂation rate, may be more volatile than in regular periods. To capture time-varying conditional variances, for simplicity, we use a GARCHð1; 1Þ model: htþ1 ¼ l0 þ l1 ut2 þ l2 ht : A GARCHð1; 1Þ model is often used to capture time-varying conditional variances of economic variables (see Bollerslev 1987). By way of the law of iterated expectations, the expected future fundamentals can be described as Et ½xtþi ¼ g0

i1 X

g1s þ g1i xt þ g2

s¼0

i1 X

g1s Et ½htþis ;

s¼0

ðA20Þ Et ½htþis ¼ l0

is1 X

ðl1 þ l2 Þ k þ ðl1 þ l2 Þ is ht :

k¼0

Reorganizing gives a process of x as a function of its current value and its conditional variance as Et ½xtþi ¼ a0 þ a1 xt þ a2 ht ;

ðA21Þ

where P i1 s P is1 g1 ½g0 þ g2 l0 k¼0 ðl1 þ l2 Þ k , a0 ¼ s¼0 a1 ¼ g1i , P i1 s a2 ¼ g2 s¼0 g1 ½ðl1 þ l2 Þ is . Substitute the expectations for money supply and real income into equation (A9), and rework with inertia in equation (A18). The results are equations (5) and (6), respectively. Notes The author would like to thank Paul de Grauwe, Roy Kouwenberg, Antonio Garcia Pascual, Mark Taylor, and Casper de Vries for useful discussions and thoughtful comments, and also Namwon Hyung for econometric tips. 1. This discussion is based on my doctoral thesis (2002).

Dusting off the Perception of Risk and Returns in FOREX Markets

331

2. For example, for the monetary-approach partial equilibrium models Frenkel (1976), Mussa (1976), and Bilson (1978) discuss the ﬂexible-price model, while Dornbusch (1976), Frankel (1979), Mussa (1979), and Buiter and Miller (1982) consider the stickyprice model. The general equilibrium asset-pricing models are studied by Stockman (1980), Lucas (1982), Svensson (1985a, b), and Hodrick (1989), and extended into the continuous-time stochastic framework by Bakshi and Chen (1997) and Basak and Gallmeyer (1998). 3. Among the empirical studies are those by Frenkel (1976), Bilson (1978), Hodrick (1978, 1989), Meese and Rogoff (1983, 1988), Backus (1984), Meese (1990), MacDonald and Taylor (1994), Chinn and Meese (1995), Mark (1995), and Flood and Rose (1995, 1999). 4. Mathematical applications are partially adopted from Cuthbertson (1999). 5. This equation is derived from the uncovered interest parity (UIP) and from an assumption corresponding to the monetary models that the interest rate differential depends on the fundamentals f~t : it i ¼ af~: t

t

6. For a summary, see Meese (1990). 7. See Campbell, Lo, and MacKinlay (1997, ch. 7). 8. This solution is derived by applying to equation (1) the law of iterated expectations, that is Et ½Etþ1 ½X ¼ Et ½X. Suppose that the discount rate is lower than one, that it is governed by an interest semi-elasticity to money demand smaller than one. The expectation would be assigned a lower exponential weight (to the power i) as looking forward (to time t þ i). From the limit theorem, at inﬁnity T ! y the bubble term (with a weight to the power T þ 1) vanishes (See also Blanchard and Fischer 1993, ch. 5). 9. For instance, MacDonald and Taylor (1994) ﬁnd cointegration between exchange rates and monetary variables in the fundamental exchange rate models. Chinn and Meese (1995), as well as Mark (1995), ﬁnd evidence that for long horizons the monetary-based exchange rate model overcomes the random walk model in predicting exchange rates. Groen (1999) shows that at a pooled time series level, there is cointegration between exchange rates and macroeconomic variables in the monetary model. 10. The exceptions include the studies by Cragg (1982), Engle (1982, 1983), Obstfeld (1987), Hodrick (1989), Arnold (1996), and Bekaert (1996). 11. In appendix B, I provide the derivation (in detail) of the reduced-form solutions of the ﬂexible-price and sluggish-price models. It should be noted that for the sluggish-price model one actually works with a more complex assumption of price inertia. As a result the solution can be tedious (but similar), compared to equation (4). Importantly, it facilitates our closed-form derivation shown next. 12. The argument and derivation are in appendix D. 13. The nonlinearity in the model seems to coincide with the idea of nonlinear bubbles. For example, in Froot and Obstfeld (1991) the bubble is a nonlinear function of stock’s dividend. 14. A GARCHð1; 1Þ model (with a Student’s t distribution, if necessary) is used to capture fundamental uncertainty. The model, originated by Bollerslev (1986), suggests a form of heteroskedasticity in which the conditional variance changes over time as a function of past errors and past conditional variances. Therefore a turbulent (tranquil) period

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is likely to be followed by turbulent (tranquil) periods. Alternatively, regative news has persistent effect in some periods. 15. For empirical results, see, for example, MacDonald and Taylor (1994) and Groen (1999). 16. Hodrick (1989) applies the ARCH-LR test and models fundamental volatility by using an ARCH(1) model with a normal distribution. In contrast, we specify the conditional variance model by using a GARCHð1; 1Þ-t model, suggested in Bollerslev (1987). First, this is because the GARCHð1; 1Þ model is considered to be a parsimonious model of conditional variance that adequately ﬁts many economic time series. See, for example, Bollerslev (1986) for the merit of the GARCHð1; 1Þ model in allowing long memory. Second, heteroskedasticity may be a reason for a heavy-tailed distribution, see, for example, de Haan, Resnick, Rootzen, and de Vries (1989) and Embrechts, Kluppelberg, and Mikosch (1999); Bollerslev (1987) shows the adequacy of the GARCHð1; 1Þ-t model for fat-tail distributed economic series. Additionally my empirical results show highly signiﬁcant GARCH coefﬁcients and signiﬁcantly reject the null hypothesis of normally distributed error terms. 17. For more detail, the reader is referred to appendix A. I also studied Austria, Germany, and the Netherlands. There is no evidence of a cointegration relationship in the Netherlands. However, there are ambiguous cointegration test results between the Johansen (1988) test and the augmented Engle and Granger (1987) test in the case of Austria and Germany. 18. This deﬁnition is given in Krugman and Obstfeld (1997). The US dollar is broadly accepted and held as a ﬁnancial asset. 19. There are many studies investigating ARCH properties in the logarithmic changes in exchange rates. At short horizons, strong ﬁndings in weekly and daily intervals respectively have been reported by Engle and Bollerslev (1986) and Baillie and Bollerslev (1987), but due to temporal aggregation (see Drost and Nijman 1993) rather weak evidence for monthly data has been reported by Baillie and Bollerslev (1989) and Hodrick (1989). Within our sample, we ﬁnd rather strong evidence of ARCH in monthly exchange rate returns and fundamental growth rates. The results of the ARCH(1)-LM test, the ARMAGARCH modeling method and the estimated coefﬁcients of GARCH models are available upon request. 20. These reduced-form equations are the unrestricted monetary models of equations (5) and (6). This follows from the discussion in Meese (1990) and MacDonald and Taylor (1994) regarding the failure of the monetary models due to imposing inappropriate coefﬁcient restrictions. Meese (1990) states that although most models are formulated in relative terms to simplify exposition, in estimation there is no need to impose the constraints on structural parameters. Furthermore MacDonald and Taylor (1994) show that their unrestricted ﬂexible-price monetary model is valid in explaining the long-run exchange rate. 21. If the theoretical speciﬁcations are correct, one would expect the coefﬁcients of domestic and foreign variables to be equal (in absolute term but with opposite signs). In practice, the coefﬁcient restrictions are rejected by the data in three out of ﬁve countries. Only in the case of Canada and the United Kingdom, at the 5 percent signiﬁcance level, the Wald test cannot reject the restriction that the coefﬁcients of the domestic and foreign (US) variables are equal in money supply and real income. 22. For more detail, the reader is referred to Hamilton (1994) and Greene (2000).

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333

23. Based on the method of Engle and Granger (1987), the long-run equilibrium relationship is ﬁrst estimated. The estimated parameters of the cointegration vector are, subsequently, used in the error correction equation. See, for example, Engle and Granger (1987), Phillips and Loretan (1991), and MacDonald and Taylor (1994). The estimated coefﬁcients of the long-run and short-run relationships are presented in tables 10.4 and 10.5, respectively. 24. However, if the explanatory variables and the disturbance term are not independent but they are contemporaneously uncorrelated, the OLS retains its desirable properties; see Dougherty (1992). 25. According to Hamilton (1994), the similar method has been suggested by Saikkonen (1991) and Phillips and Loretan (1991). 26. It should also be stressed that this approach is not exposed to the simultaneity bias. To avoid the simultaneity bias (or other violation of the fourth Gauss-Markov condition, e.g., from stochastic regressors or measurement errors), we use instrumental variables that are highly correlated with the regressors but not correlated to the error terms. In this chapter, rather than using the true conditional variances, whose random components may be correlated with error terms in the exchange rate equation, I use the predicted values of the endogenous explanatory variables, namely the GARCH forecast of volatility. By using the forecasts that are functions of the squared lagged residual and the estimated variances from the previous period, one can eliminate the random components in the fundamentals’ conditional variances. 27. The regression result for Canada is ~ t 0:304~ yt þ 149:477 ^h m; t þ 1739:14 ^h m ; t et ¼ 0:889 þ 0:343 m ^ þ 141:418 h y; t 440:945 hy ; t þ xt : The regression result for the United Kingdom is ~ t 0:566 y~ 1500:33 h^ m; t 5263:13 ^h m ; t et ¼ 0:320 þ 0:119m t

315:254 ^ h y; t 341:454hy ; t þ xt : 28. An increase in risk is not always a bad thing if society at large receives (nonmarketable) gains from the higher risk, as noted in Cumperayot et al. (2000). 29. For example, see Levy and Sarnat (1970) and Solnik (1974). 30. The ambiguous result for the impact of volatile money growth on the exchange rate is an interesting topic for further research. 31. The estimation is based on the two-step method of Engle and Granger (1987). Thus the estimated parameters of the cointegration vector in table 10.4 are used in this errorcorrection model. See, for instance, Engle and Granger (1987) and MacDonald and Taylor (1994). 32. For example, in our data set only Canada and the United Kingdom show weak evidence of this feature.

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Index

Adjusted cumulative current account, 297 Aggregate consumption externality, 65, 81 Aggregate demand, effective, and domestic bond price, 175–76 Allocations, feasible, and bond market equilibrium, 176–80 Arbitrage and fundamentalists, 132 and law of one price, 87–88, 93–94 ARCH-M model, 329 ARCH model(s), 233, 313, 332n.19 ARIMA model, 47 ARMA model, 47, 98 Asset pricing models, 310, 312, 319, 322 Asset-supply approach, 1 Asset trading theories, 3 Asymmetric payoff information, 3, 4–5 Asymptotic theory, for kernel regressions, 29 Balassa-Samuelson formulation or effect, 240, 241, 242, 279, 281, 288, 290–91 Bank for International Settlements, 243, 270 Bank nationality, and volume-volatility relationship, 44, 55, 57, 59 Bank size and volatility, 41 and volume-volatility relationship, 44, 54–55, 58 Bayesian-Nash equilibrium (BNE), 25 Behavioral equilibrium exchange rate (BEER) approach, 241–42, 247, 257, 272– 73n.7, 278 Bifurcation analysis, 189–201 Black money, 207, 225, 227–29 Bond market equilibrium, and feasible allocations, 176–80

Bond price, domestic, and effective aggregate demand, 175–76 Border effect, 92 Bretton Woods system, collapse of, 239, 307, 322 British sterling, in study of exchange rate models, 245, 247, 261 Business cycles, and expectation formation in model, 171 Canada in nonlinear model for exchange rates, 313, 319, 320, 321, 322, 332n.21 in study of euro, 283, 285, 290, 300 Canadian dollar in nonlinear model for exchange rates, 319 in study of exchange rate models, 245, 247, 264, 269 Capital asset pricing model (CAPM), 310, 312 Capital markets, international, 201 Causality, and price-order ﬂow relationship, 14–15 Central bank (CB), 23, 68. See also European Central Bank Central bank (CB) currency demand, and price, 3 Central bank-demand approach, 1, 1–2 Central bank trades, in micro portfolio balance model, 6–7 Chartists and chartism, 128–32, 160, 160– 61 evolutionary stability of, 159–60 and money markets, 277 and simple nonlinear exchange rate model, 135, 137, 149

340

Classical unemployment, 176, 177 Clustering, volatility, 152–55 Cobb-Douglas utility function, 186 Cointegration and long-run equilibria relationships, 277 in nonlinear model, 312, 314, 316, 317, 318, 320, 322 in real-exchange-rate model, 280–81 in study of euro, 292, 293, 295 in study of exchange rate models, 240, 245, 247, 251, 252, 253, 264, 265 Cointegration analysis, 97–100, 147–48, 230, 232, 278, 279. See also Johansen cointegration analysis method, 278, 281, 291, 299 Competitive international capital markets, 201 Consistency test, 240, 253, 264–65 Constant-coefﬁcient model, 16 Consumers, domestic, in model, 171–73 Croatia, and deutschmark holdings, 227 Currency hypothesis, 208, 233 and deutschmark/euro, 223–29 quantitative assessment of, 229–33 and role of money, 215–23 Currency stocks, 207 Czech Republic, and deutschmark holdings, 227 Demand foreign, 174 government, 174 and imperfect substitutability, 1 Deutschmark (German mark) and euro conversion, 223–29, 233 shift of interest from to dollar, 226 stock and value of, 207 in study of exchange rate models, 243, 245, 247 Deutschmark-dollar exchange rate, 208 Dickey-Fuller test, 314 Diebold-Mariano statistic, 252, 253, 271 Different-currency assets, as imperfect substitutes, 1, 5. See also Imperfect substitutability) Direction-of-change statistic, 239, 252–53, 257–61, 264, 265 loss differential series for, 271–72 Disconnect puzzle, 145, 146–48, 161, 170 Dispersion of beliefs, and volumevolatility relationship, 40, 53 DM/$ spot market, 11

Index

Dollar, Canadian. See Canadian dollar Dollar, US. See also United States and euro area currencies, 290–99 and forecasts from monetary vs. random walk model, 79 in nonlinear model for exchange rates, 313 real exchange rate of, 282–90 shift of interest to from deutschmark, 226 Dollar-deutschmark exchange rate, 208 Dollar-deutschmark (DM/$) spot market, 11 Dollar-euro exchange rate, 279, 282–83, 299–300 Domestic bond price, and effective aggregate demand, 175–76 Domestic consumers, in model, 171–73 Domestic production, in model, 173–74 Dornbusch (Dornbush and Frankel) model, xi, 63, 125, 169, 190, 239, 241, 310, 325 Dynamic closed economy model extended to small open economy, 171, 201 behavioral assumptions of, 171–74 dynamics and expectations formation in, 180–88 numerical analysis on, 188–201 temporary feasible states in, 174–80 Dynamic ﬂex price setting, 171 Dynamic general equilibrium models, 170 Eastern Europeans, 207 and deutschmarks, 227, 233 and Euro, 229, 234 ECB (European Central Bank), 221, 224, 227, 228, 229 Eclectic model, 279, 281–82, 284, 286, 290 restricted, 284 ECM (error correction model), 293, 295 Econometrics techniques, xiv Economic prosperity view, 209–12 theoretical ﬂaw in, 212–15 Effective aggregate demand, and domestic bond price, 175–76 Electronic trading and data on public trades, 1 and testing for imperfect substitutability, 22 EMS collapse of, 223 Soros’s tilting of, 224 Equilibrium trading strategies, 27–28

Index

Error correction model (ECM), 293, 295 ESTAR model, 64, 82n.3, 108, 109–10 Estimation, and forecasting, 250–252 Euro, 207, 208–209, 277 and black money, 227–29 depreciation and recovery of, xiv, 233– 34 and deutschmark, 225–27, 233 and economic prosperity view, 209–12, 213 exchange rate for (analysis), 229–33 factors affecting, 279 stock of, 224–25 Euro, study of, 277–78, 299–300 data sources for, 300–302 empirical results in, 282–99 and modeling of real exchange rates, 279–82 Euro-dollar exchange rate, 279, 282–83, 299–300 European Central Bank (ECB), 221, 224, 226, 227, 228, 229. See also at Central bank European Monetary Union, 278 European Union, 69–70. See also speciﬁc countries Eurosclerosis, 210 Excess kurtosis, in exchange rate distributions, 150–52, 161 Excess volatility puzzle, 148–50, 161 Exchange rate(s). See also Nominal exchange rate; Real exchange rate dollar-deutschmark, 208 dollar-euro, 279, 282–83, 299–300 in dynamical system, 185–87 of euro (analysis), 229–33 failure to explain, 307 ﬁxed and ﬂoating (volatility), 81 ﬂoating, 307 in logarithmic form, 96 microstructure of, 229–30, 233 as price of money vs. interest-bearing assets, 212, 233 recent empirical literature on, 278–79 Exchange rate determination, microstructural approaches to, 63 Exchange rate disconnect puzzle. See Disconnect puzzle Exchange rate economics cycles in, xi divergent paradigms in, xv models vs. data in, 63

341

Exchange rate modeling, xi–xiii turnaround in, xii Exchange rate models, 125, 239. See also Dynamic closed economy model extended to small open economy; Micro portfolio balance model; Neoclassical explanation of nominal exchange rate volatility; Nonlinear model for exchange rates; Simple nonlinear exchange rate model eclectic, 279, 281–82, 284, 286, 290 ESTAR, 64, 82n.3, 108, 109–10 evaluation of (Meese and Rogoff), xi, xii, 125 ﬂexible-price, 239, 307, 310–11 (see also Flexible-price model) interest differential, 239 interest rate parity, 257, 261, 265 (see also Interest rate parity speciﬁcation or model) macroeconomic, xiii monetary-based, 125, 308 new approaches to, 125–26 ‘‘News,’’ 125, 148 Obstfeld-Rogoff, 126 portfolio balance, 22, 125, 208 (see also Portfolio balance model or approach) productivity-based, 245, 247, 269 random walk, xi–xii, 63, 78, 97 (see also random walk model) rational expectations efﬁcient market model(s), 125 smooth transition autoregressive (STAR), 107–109 sticky (sluggish)-price, 239, 241, 245, 261, 264, 307 (see also Dornbusch model; Sticky-price monetary models) threshold autoregressive (TAR), 94, 107 UIP, 244, 250, 273n.8 Exchange rate models, study of, 239–42, 265, 269–70 data in, 242–43, 270–71 empirical results of, 245–50 forecast comparison in, 250–69, 271–72 full-sample estimation of, 243–44 Exchange rate predictability, 240 Exchange rate variability, xiii Exchange rate volatility. See Volatility Expectation(s). See also at Rational expectations exchange rates’ reliance on, 308–10 and fundamentals, 311, 328–29

342

Expectation(s) (cont.) inﬂuence of, 321–22 law of iterated expectations, 324, 327 long-run unitary elasticity of, 265 in simple nonlinear exchange rate model, 127 Expectations feedback, in dynamic model, 201 Expectations formation, in dynamic model, 183–85 Expected rate of inﬂation, 185–87 Expected volume, 47 Fat tails, in exchange rate distributions, 150–52, 161 Feasible allocations, and bond market equilibrium, 176–80 Fiscal policy, 282 Fixed-point attractors, and simple nonlinear exchange rate model, 133, 135, 137, 160 Flexible-price model, 239, 307, 310–11 and British sterling-dollar rate estimate, 245 modiﬁed, 312, 317, 320 and nonlinear model for exchange rates, 310–11, 312 reduced form solution of, 323–25, 331n.11 Flight money, 224–25 black money as, 227–29 Floating exchange rate, 81, 307 Forecasting of exchange rates, 78–81 chartists’ rules of, 128–30 in study of euro, 297 in study of exchange-rate models, 250– 69, 271–72 Foreign demand, in model, 174 Forward market and exchange rate, 40 and volatility, 43 Forward swaps, 51 Franc, in study of exchange rate models, 245 France in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 300 Fundamental equilibrium exchange rate (FEER), 278 Fundamentalists, economic, 106, 128, 132, 160

Index

and simple nonlinear exchange rate model, 135, 137 and transactions costs, 132 Fundamental levels, exchange rates’ reliance on, 308–10 ‘‘Fundamentals’’ (future payoff information), 4 Fundamental variables and disconnect puzzle, 146–47, 161, 170 and exchange rate movements, 146 and expectations, 311, 328–29 in nonlinear model for exchange rates, 328, 329 in rational expectations efﬁcient market model, 125 GARCH, 152, 161, 312, 314 GARCH forecast of volatility, 333n.26 GARCH(1,1)-M, 48 GARCH(1,1) model, 47, 152, 312, 317, 330, 331–32n.14 German reuniﬁcation, 245 Germany, in study of euro, 283, 285, 300 Global Financial Data, 270 Global stability of adjustment process, 164n.7 Government demand, in model, 174 Habit model, in model of nominal exchange rate volatility, 65, 72, 73, 78, 79, 81, 83n.15 Habit persistence externality, 64, 65, 67–68 Hausman test, 286, 288, 290 Heterogeneity and aggregate analyses, 291 of beliefs (simple nonlinear model), 127 in panel analyses of euro exchange rate, 299 and volatility, 40, 41 Heterogeneous agents, 106 and exchange rate model, 126 Heterogeneous expectations, xiii ‘‘Hot potato’’ trading, 21 Hungary, and deutschmark holdings, 227 ‘‘Iceberg’’ transport costs, 93 Imperfect substitutability, xii–xiii, 1–2 as intervention condition, 21 and micro portfolio balance model, 5–30 and relation of value of currency to stock of currency, 222–23 trading-theoretic approach to, 3–5

Index

Inﬂation expected rate of, 185–87 and PPP-relationship, 158 repressed, 176, 177 Information. See Private information; Public information Interest differential model, 239 Interest parity, uncovered (UIP), in dynamic model, 183–85, 201 Interest rate expected, 185–87 national, 220–22 Interest rate differential, real, 279, 291 Interest rate parity speciﬁcation or model, 240, 242, 257, 261, 265, 269, 270 International capital markets, competitive, 201 International Comparison Programme (ICP) data set, 90 International Monetary Fund (IMF), 70 International Financial Statistics (IFS), 243, 270, 300, 322 on transportation costs, 92 International risk sharing, 68–69 International Sectoral Database (OECD), 300 International substitutability of assets, 223 Intervention and micro portfolio balance model, 21– 22 trading-theoretic approach to, 23 Intervention policy, 2 Inventory effects, 4 Italy in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 300 Iterated expectations, law of, 324, 327 Japan in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 290, 300 Johansen cointegration analysis method, 278, 281, 291, 299 Johansen test, 98, 230, 314, 316 Kernel estimation, 18–19 Kernel regression, 29–30 Keynesian unemployment, 176, 177 Kurtosis, in exchange rate distributions, 150–52

343

Law of iterated expectations, 324, 327 Law of one price (LOP), 87–93 absolute version of, 87–88 nonlinearities in deviations from, 88, 93– 95 and purchasing power parity, 89–90 relative version of, 88 Linear exchange rate determination models, 69 MacDonald’s hamburgers, product differentiation of across countries, 112n.1 Macroeconomic models, xiii Macroeconomics, open economy, xiii Macroeconomic uncertainty, xv Mean squared error (MSE) criterion, 78, 239, 240, 252, 253–57, 265, 269 Micro portfolio balance model, 2, 5–11, 22–23. See also Portfolio balance model or approach empirical analysis of, 11–15 and kernel regression, 29–30 and log price changes, 30 model solution in, 23–28 results and implications of, 15–22 Microstructure of exchange rate, 229–30, 233 Misalignment problem, 146 Misspeciﬁcation tests, 293 Mixture of distribution hypothesis, 40 Models of exchange rates. See Exchange rate models Monetary-based exchange rate models, 125, 308 Money, in exchange rate determination, 215–23. See also Currency hypothesis; Deutschmark; Dollar, US; Swedish krona (SEK) market; Yen; other currencies MSE (mean squared error) criterion, 78, 239, 240, 252, 253–57, 265 , 269 M3, redeﬁnition of, 226 Mundell-Fleming model or approach, 282, 284 ‘‘Mystery of the multiplying marks,’’ 230 National interest rates, 220–22 Nationality of banks, and volumevolatility relationship, 44, 55, 57, 59 Negative feedback rule, 128, 160

344

Neoclassical explanation of nominal exchange rate volatility, 64 data for, 69–70 model for, 64–69 model calibration in, 70–73 results in, 73–81 ‘‘New open economy macroeconomics,’’ xiii, 63, 170, 170–71 ‘‘News’’ models, 125, 148 Noise traders, 129 Nominal exchange rate. See also Neoclassical explanation of nominal exchange rate volatility and Dornbusch model, 169 and real exchange rate, 87 Nominal exchange rate volatility, neoclassical explanation of. See Neoclassica explanation of nominal exchange rate volatility Nonlinear exchange rate model, simple. See Simple nonlinear exchange rate model Nonlinearity(ies) and deviations from law of one price, 88, 93–95 in real exchange rate movements, 87, 105–11 of transactions costs, 132 Nonlinear model for exchange rates, 307– 308, 321–22 and closed-form solutions, 329–30 data sources for, 322–23 and expectations of future fundamentals, 311 and ﬂexible-price model, 310–11, 312 motivation for, 308–10 speciﬁcation and estimation in, 312–21 and sticky-price model, 311, 312 stochastic volatility added to fundamental expectations in, 328–29 Obstfeld-Rogoff framework of dynamic utility optimization, 125 Obstfeld-Rogoff new open economy macro model, 126 Open economy macroeconomics. See ‘‘New open economy macroeconomics’’ Options, and volatility, 43, 51 Option volume, 49 Order ﬂow and micro portfolio balance model, 2, 5 and price, 15, 21, 22

Index

and swap transaction, 49 vs. trading volume, 33n.4 Orderly market, and intervention, 21–22 Organization for Economic Cooperation and Development (OECD), 70 Panel analysis, 283–290, 299 Partial autocorrelation function (PACF), 113n.20 Payoff information, asymmetric, 3, 4–5 ‘‘Payoffs,’’ 33n.8 Perfect substitutability, and law of one price, 88 Persistent portfolio balance channel, 4, 16 Pooled mean group (PMG), estimator, 277–78, 285–86 Portfolio balance effect, 4 Portfolio balance model or approach, xi, xii, 2, 3, 22, 125, 207–208, 233. See also Micro portfolio balance model and currency hypothesis, 208, 215–23, 229 currency stocks in, 207 theoretical ﬂaw in, 212–15 Positive feedback rule, 128, 160 PPP. See Purchasing power parity Predictability, exchange rate, 240 Price(s) adjustment of (dynamic model), 180–82 and central bank (CB) currency demand, 3 and order ﬂow, 15, 21, 22 Price differentials, and law of one price, 91–92 Price index problems, 89–90 Price stickiness. See Sticky (sluggish)-price monetary models; Sticky prices Pricing-to-market (PTM) theory, 94–95, 112n.3 Pricing puzzles, 170 Private information, xii and weekends, 48 Product differentiation across countries, of MacDonald’s hamburgers, 112 Production, domestic, in model, 173–74 Production economy, and nominal exchange rate volatility, 81–82 Productivity advances, and real exchange rate, 281 Productivity-based model, 245, 247, 269 PTM (pricing-to-market) theory, 94–95, 112n.3

Index

Public demand, and imperfect substitutability, 1 Public information and micro portfolio balance model, 14– 15, 26 and weekends, 48 Purchasing power parity (PPP), xi, 95–96, 278 absolute, 95 and Balassa-Samuelson models, 241 and cointegration and unit root tests, 96– 100, 109 (see also Unit root test) deviations from, 89, 97, 106, 279, 325, 326 and Dornbusch model, 169 and ﬂexible-price model, 323 and law of one price, 87, 89–90 long-span studies of, 101 and nontraded goods, 281 OECD, US, and German, 209 panel data studies of, 102–103 puzzle of, 104–105, 110, 170 and real exchange rate, 87 relative, 95 and sluggish-price model, 325, 326 stochastic assumption of, 323 in study of exchange rate models, 239 Quantity theory of money, xi Quoting strategies, optimal, 25 Random walk model, xi–xii, 63, 78, 97 and closed-form solutions, 329 and cointegration, 98 and euro-area model, 297 and expectations, 311, 321 naı¨ve, 271 and study of exchange rate models, 239, 240, 241, 252, 257, 261, 269 Rate of return adjustments, 220 Rational expectations, and effect of public information, 15 Rational expectations efﬁcient market model, 125 Rational expectations fully informed agent paradigm, xiv Real exchange rate, 87 under ﬁxed vs. ﬂoating regime, 169 modeling of, 279–82 nonlinearities in, 87, 105–11 nonstationarity of, 96, 97, 98, 102 and purchasing power parity puzzle, 104–105

345

testing for stability of, 99–100, 101 Real exchange rate adjustment, nonlinearity in, 87 Real interest rate differential, 279, 291 Redundancy problem, 212–13 Relative proﬁtability of chartism, 130 Reporters, and volatility, 53 Representative behavioral equilibrium exchange rate model, 240 Reservation prices, and volume-volatility relationship, 40 Reverse causality hypothesis, 14–15 Risk and imperfect substitutability, 3–4 in nonlinear model, 307, 312, 320, 328 Risk sharing, international, 68–69 Rolling regressions, 250–51 Sensitivity analysis, for simple nonlinear exchange rate model, 135–40 Short swaps, 60n.1 and volatility, 43, 49, 51 Simple nonlinear exchange rate model, 126–32, 160–61 empirical relevance of, 145–55, 161 and evolutionary stability of chartism, 159–60 and permanent shocks, 141–45 sensitivity analysis of, 135–40 solution of, 133–34 stochastic version of, 140–41 with transactions costs, 132–33 and variance of shocks, 155–58 Simultaneity bias, 333n.26 Slovakia, and deutschmark holdings, 227 Slovenia, and deutschmark holdings, 227 Sluggish-price models. See Dornbusch (Dornbusch and Frankel) model; Sticky (sluggish)-price monetary models Smooth transition autoregressive (STAR) model, 107–109 Soros, George, 224 SPA (superior predictive ability), test of, 80 Spain, in study of euro, 283, 285, 300 Speculators, and volatility, 41 Spot market DM/$, 11 and exchange rate, 40, 49 interdealer transactions in, 34n.17 and volatility, 43 Spot volatility, 49 Spot volumes, and volatility, 51

346

Standard model, in model of nominal exchange rate volatility, 65 STAR (Smooth transition autoregressive) model, 107–109 Stationary states, in dynamical system, 187–88 Sterling (British), in study of exchange rate models, 245, 247, 261 Sticky (sluggish)-price monetary models, 239, 241, 245, 261, 264, 307. See also Dornbusch (Dornbusch and Frankel) model and British sterling-dollar rate estimate, 245 closed-form solution of, 311, 312 modiﬁed, 317, 320 reduced-form solution of, 325–27, 331n.11 Sticky prices, 63, 64, 82, 169, 170, 170–71 Stochastic PPP assumption, 323 Stochastic version of simple nonlinear exchange rate model, 140–41 Stockholm, conference on ﬂexible exchange rates in, xi Stock shares, and portfolio interpretation, 208 Study of exchange rate models. See Exchange rate models, study of Substitutability of assets, imperfect. See Imperfect substitutability Substitutability of assets, international, 223 Superior predictive ability (SPA), test of, 80 Swaps (standard) and exchange rate, 49 and volatility, 43 Swedish krona (SEK) market, and volumevolatility relationship, 39, 40, 58. See also Volume-volatility relationship Swiss franc, in study of exchange rate models, 247, 250 TAR (threshold autoregressive) model, 94, 107 Taylor, Mark, 64 Taylor’s theorem, 328, 329 Temporary ﬁxed-price situations, 171 Temporary portfolio balance channel, 4, 16 Threshold autoregressive (TAR) model, 94, 107

Index

Trading ﬂows, xiii. See also Order ﬂow Trading rounds, in micro portfolio balance model, 7–10 Trading strategies, equilibrium, 27–28 Trading-theoretic approach to imperfect substitutability, 3–5 to intervention, 23 Trading volume, vs. order ﬂow, 33n.4 Transactions costs, xiv, 94, 107, 132–33. See also Arbitrage UIP model, 244, 250, 273n.8 Uncertainty, macroeconomic, xv Uncovered interest parity (UIP), 242. See also UIP model and Dornbusch model, 310 in dynamic model, 171, 183–85, 190, 201 and ﬂexible-price model, 323 and risk premium, 328 Unemployment, classical, 176, 177 Unemployment, Keynesian, 176, 177 United Kingdom in nonlinear model for exchange rates, 313, 319, 321, 322, 332n.21 in study of euro, 283, 285, 290, 300 United States. See also Dollar, US capital ﬂow into (and decline of euro), 209–12 intervention by, 2 in neoclassical explanation, 69 in nonlinear model for exchange rates, 313, 322 savings rate decline in, 211 Unit root test, 97, 100, 101, 102, 103, 104, 107, 109, 110, 111 Variability, exchange rate, xiii VECM, 297, 299 Vector autoregressive (VAR) model, 291, 312 Volatility attempts to explain, 63–64 (see also Neoclassical explanation of nominal exchange rate volatility) in bifurcation analysis, 193–201 and domestic currency prices, 319–20 and risk premium, 308 spot, 49 Volatility clustering, 152–55 Volume-volatility relationship, 39–41, 57– 59 data in study of, 41–48

Index

and expected vs. unexpected volume, 45, 47 results in study of, 48–57 Wages, adjustment of (dynamic model), 180–82 Wholesale price index (WPI), 92, 99 Williamson, John, 146 Yen, in study of exchange rate models, 243, 245, 247, 261, 264, 269

347

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Exchange Rate Economics

CESifo Seminar Series edited by Hans-Werner Sinn Inequality and Growth: Theory and Policy Implications Theo S. Eicher and Stephen J. Turnovsky, editors Public Finance and Public Policy in the New Century Sijbren Cnossen and Hans-Werner Sinn, editors Spectrum Auctions and Competition in Telecommunications Gerhard Illing and Ulrich Kluh, editors Managing EU Enlargement Helge Berger and Thomas Moutos, editors European Monetary Integration Hans-Werner Sinn, Mika Widgre´n, and Marko Ko¨thenbu¨rger, editors Measuring the Tax Burden on Capital and Labor Peter Birch Sørensen, editor A Constitution for the European Union Charles B. Blankart and Dennis C. Mueller, editors Labor Market Institutions and Public Regulation Jonas Agell, Michael Keen, and Alfons Weichenrieder, editors Venture Capital, Entrepreneurship, and Public Policy Vesa Kanniainen and Christian Keuschnigg, editors Exchange Rate Economics: Where Do We Stand? Paul De Grauwe, editor

Exchange Rate Economics: Where Do We Stand?

edited by Paul De Grauwe

The MIT Press Cambridge, Massachusetts London, England

( 2005 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email [email protected] or write to Special Sales Department, The MIT Press, 5 Cambridge Center, Cambridge, MA 02142. This book was set in Palatino on 3B2 by Asco Typesetters, Hong Kong, and was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Exchange rate economics : where do we stand? / edited by Paul De Grauwe. p. cm. — (CESifo seminar series) Selected papers from seminars hosted by CESifo, an international network of economists supported jointly by the Center for Economic Studies at Ludwig-MaximiliansUniversita¨t, Munich, and the Ifo Institute for Economic Research. Includes bibliographical references and index. ISBN 0-262-04222-3 (alk. paper) 1. Foreign exchange rates—Congresses. 2. Foreign exchange rates—Econometric models—Congresses. I. Grauwe, Paul De. II. Series. HG3851.E894 2005 2004056463 332.40 56—dc22 10 9 8

7 6 5

4 3 2 1

Contents

Contributors vii Series Foreword ix Introduction xi 1

Are Different-Currency Assets Imperfect Substitutes?

1

Martin D. D. Evans and Richard K. Lyons 2

Volume and Volatility in the Foreign Exchange Market: Does It Matter Who You are? 39 Geir H. Bjønnes, Dagﬁnn Rime, and Haakon O. Aa. Solheim

3

A Neoclassical Explanation of Nominal Exchange Rate Volatility 63 Michael J. Moore and Maurice J. Roche

4

Real Exchange Rates and Nonlinearities

87

Mark P. Taylor 5

Heterogeneity of Agents and the Exchange Rate: A Nonlinear Approach 125 Paul De Grauwe and Marianna Grimaldi

6

Dynamics of Endogenous Business Cycles and Exchange Rate Volatility 169 Volker Bo¨hm and Tomoo Kikuchi

vi

7

Contents

The Euro, Eastern Europe, and Black Markets: The Currency Hypothesis 207 Hans-Werner Sinn and Frank Westermann

8

What Do We Know about Recent Exchange Rate Models? In-Sample Fit and Out-of-Sample Performance Evaluated

239

Yin-Wong Cheung, Menzie D. Chinn, and Antonio Garcia Pascual 9

The Euro–Dollar Exchange Rate: Is it Fundamental?

277

Mariam Camarero, Javier Ordo´n˜ez, and Cecilio Tamarit 10 Dusting off the Perception of Risk and Returns in FOREX Markets 307 Phornchanok J. Cumperayot Index

339

Contributors

Geir Bjønnes Stockholm Institute for Financial Research and Norwegian School of Management Volker Bo¨hm University of Bielefeld, Germany Mariam Camarero Jaume I University Yin-Wong Cheung University of California, Santa Cruz Manzie D. Chinn University of California, Santa Cruz and NBER Phornchanok Cumperayot Chulalongkorn University, Erasmus University Rotterdam Paul De Grauwe University of Leuven Martin Evans Georgetown University and NBER Marianna Grimaldi Sveriges Riksbank, Stockholm Tomoo Kikuchi University of Bielefeld, Germany

Richard Lyons University of California, Berkeley and NBER Michael Moore Queen’s University, Belfast Javier Ordo´n˜ez Jaume I University Antonio Garcia Pascual IMF and University of Munich Dagﬁnn Rime Norges Bank (Central Bank of Norway) and Stockholm Institute for Financial Research Maurice Roche National University of Ireland Hans-Werner Sinn CESifo, Munich Haakon Solheim Norwegian School of Management and Statistics Norway Cecilio Tamarit University of Valencia Mark Taylor University of Warwick, Coventry Frank Westermann CESifo, Munich

CESifo Seminar Series in Economic Policy

The book is part of the CESifo Seminar Series in Economic Policy, which aims to cover topical policy issues in economics from a largely European perspective. The books in this series are the products of the papers presented and discussed at seminars hosted by CESifo, an international research network of renowned economists supported jointly by the Center for Economic Studies at Ludwig-Maximilians University, Munich, and the Ifo Institute for Economic Research. All publications in this series have been carefully selected and refereed by members of the CESifo research network. Hans-Werner Sinn

Introduction

Like the movements of the major exchange rates, exchange rate economics has gone through long cycles. In the 1970s during the early stage of the postwar experience with ﬂoating exchange rates, economists enthusiastically proposed simple models to explain and to predict exchange rates. These models were all based on simple analytical tools. One strand of literature used the quantity theory of money and purchasing power parity, describing the long-run equilibrium relation of money, prices, and the exchange rate, and some simple assumptions about price inertia in the short run. The most celebrated model in this vein undoubtedly was the Dornbusch model (Dornbusch 1976). Another strand of literature started from the portfolio balance model and added a dynamics linking the supply of net foreign assets to the current account (Kouri 1976; Branson 1977). During a conference on ﬂexible exchange rates in Stockholm in 1975 there was a strong feeling among the participants that major theoretical breakthroughs in exchange rate modeling had been achieved. The feeling of optimism, even elation, that was present was not very different from the feelings of elation during a speculative bubble in ﬁnancial markets. The theoretical bubble burst in the early 1980s, when Meese and Rogoff published their well-known empirical evaluation of the existing exchange rate models (Meese and Rogoff 1983). The results were devastating for all the existing theoretical models. These models appeared to have no predictive power compared to a simple alternative model, the random walk. Despite the fact that occasionally some researchers claimed to have found models that would outperform the random walk (e.g., Mark 1995), it appeared that these positive results were very sensitive to the sample periods selected in these studies (Faust

xii

Introduction

et al. 2001). This conclusion is conﬁrmed by chapter 8 of this book in which Yin-Wong Cheung, Menzie Chinn, and Antonio Garcia Pascual analyze a larger spectrum of economic models of the exchange rates than in the original Meese and Rogoff studies, conﬁrming that none of these models outperform the random walk. It has often been noted that economic models tend to withstand the test against the random walk better when used for long-term predictions (see Mark 1995). This was sometimes interpreted to mean that the economic models of the exchange rates were not that bad after all. But this was only superﬁcially so. The truth is that the Meese-Rogoff empirical evaluation loads the dice against the random walk model. The reason is that when out of sample forecasts of the exchange rates are made with the economic models, the realized values of the exogenous variables are used, while the forecasts with the random walk model do not have this information. As the horizon of the forecasts increases, the handicap of the random walk forecasts (as compared to the forecasts with the economic models) increases. Thus much of the superior predictive performance of economic models over longer horizons is due to a statistical construction favoring these models. After the intellectual crash of the early 1980s triggered by the Meese and Rogoff empirical studies, theoretical modeling of exchange rates came to a virtual standstill for a decade. Few economists dared to develop exchange rate models, let alone test these models with empirical data. This lasted until the early 1990s when a turnaround was in the making. This turnaround came about as a result of several new developments. First, new theoretical insights were gained about the microstructure of the ﬁnancial markets. These insights were ﬁrst applied in stock markets, and later introduced in the analysis of the foreign exchange markets. Pioneering work in this area was done by Richard Lyons (Lyons 1999). This led to a ﬂourishing new literature that concentrated on the question of how information is transmitted in the market when agents have private information. This literature was a major breakthrough compared to the previous one in which representative agents use the same public information. It led to exciting new insights into the functioning of the foreign exchange market. The ﬁrst two chapters of this book testify for this. The ﬁrst chapter by Evans and Lyons uses insights from the microstructure literature and comes to the conclusion that the portfolio balance theory is surprisingly alive, that there are economically meaningful effects arising from the imperfect substitutability be-

Introduction

xiii

tween domestic and foreign assets even in a world of highly integrated ﬁnancial markets. The authors conclude that this has important implications for the ability of the monetary authorities to intervene successfully in the foreign exchange markets. The second chapter is in the same vein. It analyzes the importance of trading ﬂows and ﬁnds that the effects of these ﬂows differ as between the type of agents who initiate these ﬂows. This suggests that heterogeneous expectations are important in the understanding of the dynamics in the foreign exchange markets. Another equally important theoretical development occurred in the 1990s and gave a new boost to the theoretical analysis of the exchange rate. This is the new open economy macroeconomics pioneered by Obstfeld and Rogoff in the mid-1990s (Obstfeld and Rogoff 1996). This theoretical development started from the idea that macroeconomic analysis should be ﬁrmly grounded on a microeconomic foundation. This led to macroeconomic models in which all decisions of agents are based on explicit utility maximization in a multi-period setup. Any assumption deviating from this paradigm was branded as an intolerable ad hoc assumption. A new fundamentalism took over the profession and led to a large literature in which the implications of this paradigm were analyzed. It also led to a large literature analyzing the exchange rate, an example of which is to be found in chapter 3 of this book. In this chapter Michael Moore and Maurice Roche present a micro-founded macro model explaining the volatility of the exchange rate in such a framework. Not surprisingly, in such a world of fully informed rational agents the high volatility of the nominal exchange rate must be based on real exchange rate variability. The authors identify the source of this variability in the variability of the marginal rate of substitution between home and foreign goods, which in turn arises from an externality in habit persistence. There is no doubt that by its insistence on logical consistency and intellectual rigor, the new open economy macroeconomics provides new avenues of sophisticated research opportunities for young economic graduates. Up to now, however, this research has not led to the formulation of many empirical propositions that could lead to a refutation of these models. As a result it is still unclear whether this approach has a sufﬁciently strong scientiﬁc foundation. After all, the success of a theory should be judged by its capacity to stand empirical tests, and not by its logical consistency or its intellectual rigour.

xiv

Introduction

Scepticism about the ability of the rational expectations–fully informed agent paradigm has led researchers into other directions. One such direction recognizes that agents use different information sets, and thus not all can be rational in the sense of using all available information. Note that this is also implicit in the microstructure literature that was discussed earlier. Such a world of heterogeneous agents creates a rich dynamics of exchange rate movements, as is shown in the chapter of De Grauwe and Grimaldi. In this chapter, chartists and fundamentalists interact and create a dynamics that in many respects resembles the dynamics observed in the foreign exchange market (systematic disconnection of the exchange rate from its fundamental, excess volatility, fat tails, volatility clustering). Similar results are found in chapter 6 where Volker Bo¨hm and Tomoo Kikuchi analyze the connection between the business cycle ﬂuctuation and the ﬂuctuations in the exchange rate. Much remains to be done in the modeling of the foreign exchange markets. This is very clear from the empirical studies collected in this volume. Chapter 4 written by Mark Taylor documents the strong nonlinearities that exist in the dynamic adjustment of the real exchange rate toward its equilibrium value. The author suggests that these nonlinearities can only be understood by introducing transactions costs into our models. These transactions costs create a band of inaction of the arbitrage opportunities in the goods markets. As a result the real exchange rate will react in a nonlinear way to the size of the shocks; namely the speed of adjustment of the real exchange rate toward its equilibrium value increases with the size of the initial disturbance. Econometric techniques have not stood still. New and powerful techniques have been developed allowing researchers to devise better empirical tests. These techniques have also inﬂuenced the empirical analysis of the exchange rates. Several chapters in this book use these state of the art econometric techniques to subject the exchange rates to an empirical analysis. In chapter 7 Hans-Werner Sinn and Frank Westermann subject the dollar/DM and the dollar/euro exchange rates to an empirical analysis. Using a modiﬁed portfolio balance model that takes into account the link with the money market, they come to the conclusion that the depreciation of the euro during the period 1999 to 2001 and its subsequent recovery was very much inﬂuenced by the shifts in the demand for marks in central and eastern Europe. The last two chapters contain a similar quest for underlying fundamentals of the exchange rates. In chapter 8 Camarero, Ordonez, and

Introduction

xv

Tamarit use dynamic panel data econometrics to measure the importance of a number of fundamental economic variables. The authors come to the conclusion that these fundamental economic variables contain useful information to understand the movements of the exchange rate. The extent to which these fundamental economic variables can be used for predictive purposes remains an open question, however. In the last chapter Cumperayot adds another dimension to the analysis. She argues persuasively that in order to explain the movements of the exchange rates, not only the traditional macroeconomic variables such as the money stocks, inﬂation, and output matter. Macroeconomic uncertainty is of equal importance. Therefore the author uses measures of macroeconomic uncertainty and ﬁnds that variations in this uncertainty explains a signiﬁcant part of the ﬂuctuations of the exchange rate around its fundamentals. The chapters of this book reﬂect the very divergent paradigms now in use in the economics profession. Some chapters are grounded on the paradigm of the representative and fully informed rational agent. Other chapters rely on a paradigm of heterogeneity of agents who use different and incomplete sets of information. These differences in the fundamental paradigms lead to different insights and heated discussions among their proponents. These differences may also lead to the impression that macro and monetary analysis is in a state of crisis. To a certain extent this is also the case. At the same time the competition between these different paradigms is a source of new debates and insights that hopefully will lead to a new synthesis allowing us to better understand and predict the movements in the exchange rate. References Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84: 1161–76. Branson, W. 1977. Asset markets and relative prices in exchange rate determination. Sozialwissenschaftliche Annalen 1, 67–80. Faust, J., J. Rogers, and J. Wright. 2001. Exchange rate forecasting: The errors we’ve really made. International Finance Discussion Papers, no. 739. Board of Governors of the Federal Reserve System. Kouri, P. 1976. The exchange rate and the balance of payments in the short run and in the long run. Scandinavian Journal of Economics 78, 280–304.

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Lyons, R. 1999. The Microstructure Approach to Exchange Rates. Cambridge: MIT Press. Mark, N. 1995. Exchange rates and fundamentals: Evidence on long horizon predictability. American Economic Review 85: 201–18. Meese, R., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Obstfeld, M., and K. Rogoff. 1996. Foundations of International Macroeconomics. Cambridge: MIT Press.

Exchange Rate Economics

1

Are Different-Currency Assets Imperfect Substitutes? Martin D. D. Evans and Richard K. Lyons

The idea that different-currency assets are imperfect substitutes occupies an important place within exchange rate economics.1 It is still invoked, for example, for why sterilized intervention can be effective. And theoretical work continues to rely on this assumption.2 Yet supportive empirical evidence is scant.3 This chapter addresses the gap between theory and empirics. We test imperfect substitutability in a new, more powerful way and ﬁnd it strongly supported. Empirical work on imperfect substitutability in foreign exchange falls into two groups: (1) tests using measures of asset supply and (2) tests using measures of central bank asset demand. We address the demand side, but we examine demand by the public broadly rather than focusing on demand by central banks. Under ﬂoating rates, changing public demand has no direct effect on monetary fundamentals, current or future. This provides an opportunity to test for price effects from imperfect substitutability. Because data on public trades became available only recently (due to the advent of electronic trading), this strategy is feasible for the ﬁrst time. The discriminating power of our approach arises from avoiding difﬁculties inherent in past approaches. The asset-supply approach, for example, has low power because measuring supplies is notoriously difﬁcult. First, one must determine which measure of supply is the most appropriate. (There is considerable debate in the literature about this issue; e.g., see Golub 1989.) Then, for any given measure, the consistency of data across countries is a concern. Finally, these data are available only at lower frequencies (e.g., quarterly or monthly) and are rather slow-moving, making it difﬁcult to separate the effects of changing supply from the many other forces moving exchange rates. The central bank demand approach—an ‘‘event study’’ approach— may also have limited statistical power because central bank trades in

2

M. D. D. Evans and R. K. Lyons

major markets are relatively few and are small relative to public trading. For example, the average US intervention reported by Dominguez and Frankel (1993b) is only $200 million, or roughly one-thousandth of the daily spot volume in either of the two largest markets. (Since then, US intervention has been larger, typically in the $300 million to $1.5 billion range, but market volume has been higher too; see Edison 1998.) Studies using this latter approach are more successful in ﬁnding portfolio balance effects (e.g., Loopesko 1984; Dominguez 1990; Dominguez and Frankel 1993a). Nevertheless, results using this approach are not exclusively positive (e.g., Rogoff 1984) and the extent these event studies pertain to price effects from portfolio shifts in the broader market is not clear. The ‘‘micro portfolio balance model’’ we develop embeds both Walrasian features (as in the traditional portfolio balance approach) and features more familiar to models from microstructure ﬁnance. Regarding the latter, the model clariﬁes the role played by order ﬂow in conveying information about shifts in traders’ asset demands.4 Beyond this clariﬁcation, two analytical results in particular are important guideposts for our empirical analysis: (1) order ﬂow’s effect on price is persistent as long as public demand for foreign currency is less than perfectly elastic (even when beliefs about future interest rates are held constant), and (2) in the special case where central bank trades are sterilized, conducted anonymously, and convey no policy signal, the price impact of these trades is indistinguishable from that of public trades.5 The latter result links our analysis directly to intervention operations of this type. We establish three main results. First, testable implications of our model are borne out: we ﬁnd strong evidence of price effects from imperfect substitutability. The portfolio balance approach—with its rich past but lack of recent attention—may warrant some fresh consideration. Second, we provide a precise estimate of the immediate price impact of trades: 0.44 percent per $1 billion (of which about 80 percent persists indeﬁnitely). Our third result speaks to intervention policy. (As noted above, our price impact estimate is applicable to central bank trades as long as they are sterilized, secret, and provide no signal.) Estimates suggest that central bank intervention of this type is most effective at times when the ﬂow of macroeconomic news is strong. The remainder of the chapter is in ﬁve sections. Section 1.1 introduces our trading-theoretic approach to measuring price impact. Section 1.2

Are Different-Currency Assets Imperfect Substitutes?

3

presents our micro portfolio balance model. Section 1.3 describes the data. Section 1.4 presents model estimates and discusses their implications (e.g., for central bank intervention). Section 1.5 concludes. 1.1

A Trading-Theoretic Approach to Imperfect Substitutability

This section links the traditional macroeconomic approach to exchange rates to microeconomic theories of asset trading. This is useful for two main reasons. First, theories of asset trading provide greater resolution on how trades affect price. By greater resolution, we mean that individual channels within the macro approach can be broken into separate subchannels. These subchannels are themselves empirically identiﬁable. Second, a trading-theoretic approach establishes that most channels through which trades—including intervention—affect price involve information asymmetry. Impounding dispersed information in price is an important function of the trading process (which our model is designed to capture). Within macroeconomics, central bank (CB) currency demand affects price through two channels: imperfect substitutability and asymmetric information. Distinct modeling approaches are used to examine these two channels. For the ﬁrst channel, imperfect substitutability, macro analysis is based on the portfolio balance approach. Models within this approach are most useful for analyzing intervention that is sterilized and conveys no information (signal) about future monetary policy. Macro analysis of the second channel, asymmetric information, is based on the monetary approach. These models are most useful for analyzing intervention that conveys information about current policy (unsterilized intervention) or future policy (sterilized intervention with signaling). This channel captures the CB’s superior information about its own policy intentions. Let us examine these two macro channels within a trading-theoretic approach. 1.1.1

Imperfect Substitutability

In contrast to macro models, which address imperfect substitutability at the marketwide level only, theories of asset trade address imperfect substitutability at two levels. The ﬁrst level is the dealer level. Dealers—being risk averse—need to be compensated for holding positions they would not otherwise hold. This requires a temporary risk premium, which takes the form of a price-level adjustment. This price

4

M. D. D. Evans and R. K. Lyons

adjustment is temporary because this risk premium is not necessary once positions are shared with the wider market. In trading-theoretic models, price effects from this channel are termed ‘‘inventory effects.’’ These effects dissipate quickly in most markets because full risk sharing occurs rapidly (e.g., within a day).6 Within trading models, imperfect substitutability also operates at a second level, the marketwide level. At this level the market as a whole—being risk averse—needs to be compensated for holding positions it would not otherwise hold.7 This too induces a risk premium, which elicits a price-level adjustment. Unlike price adjustment at the ﬁrst level of imperfect substitutability, price adjustment at this second level is persistent (because risk is fully shared at this level). This is precisely the price adjustment that macro models refer to as a portfolio balance effect. The ﬁrst of these two levels of imperfect substitutability is not present within the macro approach. Indeed, use of the term imperfect substitutability within that approach refers to the second level only. The logic among macroeconomists for addressing only the second level is that effects from the ﬁrst level are presumed ﬂeeting enough to be negligible at longer horizons. This is of course an empirical question—one that our trading-theoretic approach allows us to address in a rigorous way. Moreover our modeling of this channel provides a more disciplined way to understand why part of intervention’s effect on price is ﬂeeting (and what determines the duration of this part of the effect). Below we test empirically whether either or both of these two levels of imperfect substitutability are present. If the ﬁrst level is present—the dealer level—then FX trades should have an impact on the exchange rate, but the effect should be temporary. We term this effect a ‘‘temporary portfolio balance channel.’’ If the second level is present—the marketwide level—then trades should have persistent impact. We term this effect a ‘‘persistent portfolio balance channel.’’ 1.1.2

Asymmetric Payoff Information

Theories of asset trading provide a third channel through which trades affect price—asymmetric payoff information (e.g., see Kyle 1985; Glosten and Milgrom 1985).8 If trades convey future payoff information (sometimes referred to as ‘‘fundamentals’’ in exchange rate economics), then they will have a second persistent effect on price beyond the persistent portfolio balance effect noted above. (For example, in equity markets managers of ﬁrms have inside information about earnings,

Are Different-Currency Assets Imperfect Substitutes?

5

and their trades can convey this information.) Unsterilized interventions are an example of currency trades that convey payoff information (i.e., information about current interest rates). Another example is sterilized intervention that signals future interest rate changes. In foreign-exchange markets, however, trades by market participants other than central banks (the public) do not in general convey payoff information: under ﬂoating-rate regimes, public trades have no direct effect on monetary fundamentals (money supplies, interest rates, and by extension, future price levels).9 For these trades, then, the payoff-information channel is not operative. This presents an opportunity to use public trades to test for the presence of the two types of portfolio balance effect. 1.2

A Micro Portfolio Balance Model

The model is designed to show how the trading process reveals information contained in order ﬂow. At a micro level, it is the ﬂow of orders between dealers that is particularly important: public trades are not observable marketwide but are subsequently reﬂected in interdealer trades, which are observed marketwide. Once observed, this information is impounded in price. This information is of two types, corresponding to the two portfolio balance effects outlined in the previous section: information about temporary portfolio balance effects and information about persistent portfolio balance effects. To understand these different portfolio balance effects, consider the model’s basic structure. At the beginning of each day, the public and central bank place orders in the foreign exchange market. (These orders are stochastic and are not publicly observed.) Initially dealers take the other side of these trades—shifting their portfolios accordingly. To compensate the (risk-averse) dealers for the risk they bear, an intraday risk premium arises, producing a temporary portfolio balance effect on price. The size of this price effect depends on the size of the realized order ﬂow. This is the ﬁrst of the two information types conveyed by order ﬂow. To understand the second, ﬁrst note that at the end of each day, dealers pass intraday positions on to the public (consistent with empirical ﬁndings that dealers end their trading day with no position; see Lyons 1995 and Bjonnes and Rime 2003). Because the public’s (nonstochastic) demand at the end of the day is not perfectly elastic—that is, different-currency assets are imperfect substitutes in the macro sense—beginning-of-day orders have portfolio balance effects that

6

M. D. D. Evans and R. K. Lyons

persist beyond the day. Thus the price impact of these risky positions is not diversiﬁed away even when they are shared marketwide.10 The size of this price effect too is a function of the size of the beginningof-day order ﬂow. This is the second of the two information types conveyed by order ﬂow. 1.2.1

Speciﬁcs

Consider an inﬁnitely lived, pure-exchange economy with two assets, one riskless and one risky, the latter representing foreign exchange.11 Each day, foreign exchange earns a payoff R, publicly observed, which is composed of a series of random increments: Rt ¼

t X

DRi :

ð1Þ

i¼1

The increments DR are iid normal, Nð0; sR2 Þ. We interpret the increments as the ﬂow of public macroeconomic information (e.g., interest rate changes). The foreign exchange market has three participant types: dealers, customers, and a central bank. The N dealers are indexed by i. There is a continuum of customers (the public), indexed by z A ½0; 1. Dealers and customers all have identical negative exponential utility deﬁned over periodic wealth. Central bank trades are described below. Within each day t there are four rounds of trading: Round 1: Dealers trade with the central bank and public. Round 2: Dealers trade among themselves (to share inventory risk). Round 3: Rt is realized and dealers trade among themselves a second time. Round 4: Dealers trade again with the public (to share risk more broadly). The timing of events within each day is shown in ﬁgure 1.1, which also introduces our notation. 1.2.2

Central Bank Trades

To accommodate analysis of intervention, we include trades by a central bank. The intervention we consider is of a particular type, equivalent in its features to public trades: intervention that is sterilized, secret

Are Different-Currency Assets Imperfect Substitutes?

7

Figure 1.1 Daily timing

(anonymous and unannounced), and conveys no signal of future monetary policy.12 More speciﬁcally, each day, one dealer is selected at random to receive an order from the central bank. To maintain anonymity, the CB order is routed to the selected dealer via an agent. Let It denote the intervention on day t, where It < 0 denotes a CB sale (dealer purchase). The central bank order arrives with the public orders at the end of round 1. The CB trade is distributed normally: It @ Nð0; sI2 Þ.13 Because the CB trade is sterilized and conveys no signal, It and the daily interest increments DRt are uncorrelated (at all leads and lags). Secret intervention insures that only the dealer who receives the CB trade observes its size (though not its source). A CB trade is, under these circumstances, indistinguishable from other customer orders.14 1.2.3

Trading Round 1

At the beginning of each day t, each dealer simultaneously and independently quotes a scalar price to the public and central bank.15 We denote this round-1 price of dealer i as P1i . (We suppress unnecessary notation for day t; as we will see, it is the within-day rounds—the subscripts—that capture the model’s economics.) This price is conditioned on all information available to dealer i. Each dealer then receives from the public a net customer order, C1i , that is executed at his quoted price P1i ; C1i < 0 denotes a net customer sale (dealer i purchase). Each of these N customer-order realizations is distributed normally, C1i @ Nð0; sC2 Þ. They are uncorrelated across dealers and uncorrelated with the payoff R. These orders represent portfolio shifts by the public, for example, coming from changing hedging demands, changing transactional demands, or changing risk

8

M. D. D. Evans and R. K. Lyons

preferences. Their realizations are not publicly observed. At the time the customer orders are received, one dealer also receives the intervention trade. 1.2.4

Trading Round 2

Round 2 is the ﬁrst of two interdealer trading rounds. Each dealer simultaneously and independently quotes a scalar price to other dealers at which he agrees to buy and sell (any amount), denoted P2i . These interdealer quotes are observable and available to all dealers in the market. Each dealer then simultaneously and independently trades on other dealers’ quotes. Orders at a given price are split evenly between dealers quoting that price. Let T2i denote the net interdealer trade initiated by dealer i in round two. At the close of round 2, all agents observe a noisy signal of interdealer order ﬂow from that period: X2 ¼

N X

T2i þ n;

ð2Þ

i¼1

where n @ Nð0; sn2 Þ, independently across days. The model’s difference in transparency across trade types corresponds well to institutional reality: customer–dealer trades in major foreign-exchange markets (round 1) are not generally observable, whereas interdealer trades do generate signals of order ﬂow that can be observed publicly.16 1.2.5

Trading Round 3

Round 3 is the second of the two interdealer trading rounds. At the outset of round 3 the payoff increment DRt is realized and the daily payoff Rt is paid (both observable publicly). As in round 2, each dealer then simultaneously and independently quotes a scalar price to other dealers at which he agrees to buy and sell (any amount), denoted P3i . These interdealer quotes are observable and available to all dealers in the market. Each dealer then simultaneously and independently trades on other dealers’ quotes. Orders at a given price are split evenly between dealers quoting that price. Let T3i denote the net interdealer trade initiated by dealer i in round 3. At the close of round 3, all agents observe interdealer order ﬂow from that period:

Are Different-Currency Assets Imperfect Substitutes?

X3 ¼

N X

T3i :

9

ð3Þ

i¼1

Note that this round-3 order ﬂow is observed without noise, unlike the noisy order ﬂow signal observed in round 2 (equation 2). The idea here is a natural one: dealers’ beliefs about random customer demands in round 1 become more precise over successive interdealer trading rounds (these beliefs are due to learning from interdealer trades). Of course, the observation process is not noiseless. We use this more extreme assumption for technical convenience. If dealer updating were Bayesian in round 3, as it is in the round 2, then prices set in round 4 will introduce some noise in the risk sharing between dealers and the nondealer public (described below). This noise would not alter the basic economics of the model, nor the basic structure of the model’s solution as presented in proposition 1 below. 1.2.6

Trading Round 4

In round 4, dealers share overnight risk with the nondealer public. Unlike round 1, the public’s trading in round 4 is nonstochastic. Initially each dealer simultaneously and independently quotes a scalar price P4i at which he agrees to buy and sell any amount. These quotes are observable and available to the public. The mass of customers on the interval ½0; 1 is large (in a convergence sense) relative to the N dealers. This implies that the dealers’ capacity for bearing overnight risk is small relative to the public’s capacity. By this assumption, dealers set prices optimally such that the public willingly absorbs dealer inventory imbalances, and each dealer ends the day with no net position (which is common practice among actual spot foreign-exchange dealers). These round-4 prices are conditioned on the interdealer order ﬂow X3 , described in equation (3). We will see that this interdealer order ﬂow informs dealers of the size of the total position that the public needs to absorb to bring the dealers back to a position of zero. To determine the round-4 price—the price at which the public willingly absorbs the dealers’ aggregate position—dealers need to know (1) the size of that aggregate position and (2) the risk-bearing capacity of the public. We assume the latter is less than inﬁnite. Speciﬁcally, given negative exponential utility, the public’s total demand for foreign exchange in round 4 of day t, denoted C4 , is proportional to the expected return on foreign exchange conditional on public information:

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M. D. D. Evans and R. K. Lyons

C4 ¼ gðE½P4; tþ1 þ Rtþ1 j W 4; t P4; t Þ;

ð4Þ

where the positive coefﬁcient g captures the aggregate risk-bearing capacity of the public (g ¼ y is inﬁnitely elastic demand), and W 4; t includes all public information available for trading in round 4 of day t. 1.2.7

Equilibrium

The dealer’s problem is deﬁned over six choice variables, the four scalar quotes P1i ; P2i ; P3i , and P4i , and the two dealer’s interdealer trades T2i and T3i . Appendix A provides details of the model’s solution. Here we provide some intuition. Consider the four quotes P1i ; P2i ; P3i , and P4i . No arbitrage ensures that at any given time all dealers will quote a common price: quotes are executable by multiple counterparties, so any difference across dealers would provide an arbitrage opportunity. Hereafter we write P1 ; P2 ; P3 , and P4 in lieu of P1i ; P2i ; P3i , and P4i . It must also be the case that if all dealers quote a common price, then that price must be conditioned on common information only. Common information arises at three points: at the end of round 2 (order ﬂow X2 ), at the beginning of round 3 (payoff R), and at the end of round 3 (order ﬂow X3 ). The price for round-4 trading, P4 , reﬂects the information in all three of these sources. The following optimal quoting rules specify when the common-information variables ðX2 ; X3 ; DRÞ are impounded in price. These quoting rules describe a linear, Bayes-Nash equilibrium. Proposition 1 Dealers in our micro portfolio balance model choose the following quoting rules, where the parameters l2 ; l3 ; d, and f are all positive: P2 P1 ¼ 0; P3 P2 ¼ l2 X2 ; P4 P3 ¼ l3 X3 þ dDR fðP3 P2 Þ: For intuition on these quoting rules, note that the price change from round 1 to round 2 is zero because no additional public information is observed from round-1 trading (neither customer trades nor the CB trade are publicly observed). The change in price from round 2 to round 3, l2 X2 , is driven by public observation of the interdealer order ﬂow X2 . X2 here serves as an information aggregator. Speciﬁcally, it aggregates dispersed information about privately observed trades of

Are Different-Currency Assets Imperfect Substitutes?

11

the public and CB. The value l2 X2 is the price adjustment required for market clearing—it is a risk premium that induces dealers to absorb the round-1 ﬂow from the public and CB (that round-1 ﬂow equaling P i i C1 þ I). The price change from round 3 to round 4 includes both pieces of public information that arise in that interval: X3 and DR. The second round of interdealer ﬂow X3 conveys additional information about round-1 ﬂow (from the public and CB) because it does not include noise. The payoff increment DR will persist into the future, and therefore must be discounted into today’s price. The third component of the price change from round 3 to 4 is dissipation of a temporary portfolio balance effect that arose between rounds 2 and 3. Speciﬁcally, part of the risk premium that l2 X2 represents is a temporary premium that induces dealers to hold risky positions intraday. The endof-day price P4 does not include this because dealers hold no positions overnight. The persistent portion of the portfolio balance effect arises in this model because interdealer order ﬂow informs dealers about the portfoP lio shift ð i C1i þ IÞ that must be absorbed at day’s end by the public. If the end-of-day public demand were perfectly elastic, order ﬂow would still convey information about the portfolio shift, but the shift would not affect the end-of-day price. This persistent portfolio balance effect is the same in the model regardless of whether the initial order ﬂow came from the public or the central bank. Thus CB trades of the type we consider here have the same effect on price as a customer order of the same size—both induce the same portfolio shift at day’s end by the public. 1.3 1.3.1

Empirical Analysis Data

The dataset contains time-stamped, tick-by-tick observations on actual transactions for the largest spot market—DM/$—over a four-month period, May 1 to August 31, 1996. These data are the same as those used by Evans (2002), and the reader is referred to that paper for additional detail. The data were collected from the Reuters Dealing 2000-1 system via an electronic feed customized for the purpose. Dealing 2000-1 is the most widely used electronic dealing system. According to Reuters, over 90 percent of the world’s direct interdealer transactions take place through the system.17 All trades on this system take the

12

M. D. D. Evans and R. K. Lyons

form of bilateral electronic conversations. The conversation is initiated when a dealer uses the system to call another dealer to request a quote. Users are expected to provide a fast two-way quote with a tight spread, which is in turn dealt or declined quickly (i.e., within seconds). To settle disputes, Reuters keeps a temporary record of all bilateral conversations. This record is the source of our data. (Reuters was unable to provide the identity of the trading partners for conﬁdentiality reasons.) For every trade executed on D2000-1, our data set includes a timestamped record of the transaction price and a bought/sold indicator. The bought/sold indicator allows us to sign trades for measuring order ﬂow. This is a major advantage: we do not have to use the noisy algorithms used elsewhere in the literature for signing trades. One drawback is that it is not possible to identify the size of individual transactions. For model estimation, order ﬂow is therefore measured as the difference between the number of buyer-initiated and sellerinitiated trades.18 The variables in our empirical model are measured hourly. We take the spot rate, as the last purchase-transaction price (DM/$) in hour h, Ph . (With roughly 1 million transactions per day, the last purchase transaction is generally within a few seconds of the end of the hour. Using purchase transactions eliminates bid-ask bounce.) Order ﬂow, Xh , is the difference between the number of buyer- and seller-initiated trades (in hundred thousands, negative sign denotes net dollar sales) during hour h. We also make use of three further variables to measure the state of the market: trading intensity, Nh , measured by the gross number of trades during hour h; price dispersion, sh , measured by the standard deviation of all transactions prices during hour h, and the number of macroeconomic announcements, Ah . These announcements comprise all those reported over the Reuter’s News service that relate to macroeconomic data for the United States or Germany. The source is Olsen Associates (Zurich) (for details, see, e.g., Andersen and Bollerslev 1998). Although trading can take place on the D2000-1 system 24 hours a day, 7 days a week, the vast majority of transactions in the DM/$ take place between 6 am and 6 pm, London time, Monday through Friday. Although the results we report below are based on this subsample, they are quite similar to results based on the 24-hour trading day (as noted below). This subsample still leaves us with vast number of trades, providing us with considerable power to test for effects from portfolio balance.

Are Different-Currency Assets Imperfect Substitutes?

1.3.2

13

The Empirical Model

Our model is speciﬁed with each day split into four trading rounds. We now develop an empirical implementation for examining the model’s implications in hourly data. Let rj ð yh Þ denote the probability that the market will move from round j to j þ 1 between the end of hours h and h þ 1, when the state of the market at the end of hour h is yh .19 Given these transition probabilities, the probability that the market will be in round j at the end of hour h, pj ðYh1 Þ, is deﬁned recursively as pj ðYh1 Þ ¼ rj1 ð yh1 Þpj1 ðYh2 Þ þ ½1 rj ð yh1 Þpj ðYh2 Þ;

ð5Þ

where Yh ¼ f yh ; yh1 ; . . .g denotes current and past states of the market. According to proposition 1, prices change when the market moves from rounds 2 to 3, and from rounds 3 to 4. Let DPh and DRh respectively denote the change in price and the ﬂow of macroeconomic information between the end of hours h 1 and h. With the aid of the probabilities rj ð yh1 Þ and pj ðYh1 Þ, we can derive the probability distribution of hourly price changes as shown in table 1.1. Rows II and III of table 1.1 identify the price change associated with the market moving into round 3 and into round 4 between the end of hours h 1 and h respectively. In the former case, the price change is proportional to order ﬂow during the hour. In the latter, the price change depends on order ﬂow and macroeconomic information during the hour, and a lagged price change DPhk , for k > 0. The length of the lag k equals the number of hours the market spends in round-3 trading before moving to round 4. The probabilities in the right-hand column are complicated functions of rj ð yhl Þ for j ¼ 1; 2; 3; 4, and l > 0 and so depend on the past states of the market, Yh1 ¼ f yh1 ; yh2 ; . . .g (see appendix B for details). In the special case where the probability of moving from round 3 to round 4, r3 ð yh1 Þ, equals one, k must also equal one, and the probabilities simplify to Table 1.1 Distribution of hourly price changes DPh : Hourly price change

Probability

I

0

yI ðYh1 Þ

II

l2 X h

yII ðYh1 Þ

III

l3 X h fDPhk þ dDRh

yIII; k ðYh1 Þ

14

M. D. D. Evans and R. K. Lyons

yI ðYh1 Þ ¼ 1 yII ðYh1 Þ yIII; 1 ðYh1 Þ; yII ðYh1 Þ ¼ r2 ð yh1 Þp2 ðYh1 Þ; yIII; 1 ðYh1 Þ ¼ r2 ðyh2 Þp2 ðYh2 Þ: Our empirical model is derived from the distribution of hourly price changes. Speciﬁcally, let Wh ¼ fXh ; Yh1 ; DPh1 ; DPh2 ; . . .g denote the information set spanned by current order ﬂow, past states of the market, and past hourly price changes. The observed hourly price change can be written as DPh ¼ E½DPh j Wh þ hh ;

ð6Þ

where hh is the expectational error in hour h. Since the ﬂow of macroeconomic information in hour h, DRh , is orthogonal to Wh , this error includes DRh . To complete the empirical model, we need the conditional expectation from the distribution of hourly price changes. For the special case noted above where r3 ð yh1 Þ ¼ 1, this expectation is given by E½DPh j Wh ¼ b 1 ðYh1 ÞXh þ b2 ðYh1 ÞDPh1

ð7Þ

and b 2 ðYh1 Þ ¼ with b1 ðYh1 Þ ¼ l2 yII ðYh1 Þ þ l3 yIII; 1 ðYh1 Þ fyIII; 1 ðYh1 Þ. Hourly price-change dynamics can therefore be represented by DPh ¼ b 1 ðYh1 ÞXh þ b2 ðYh1 ÞDPh1 þ hh :

ð8Þ

In the more general case where r3 ðyh1 Þ a 1, the equation for price changes contains more than one lag of past price changes on the righthand side (see appendix B for details). These lags are not statistically signiﬁcant in our data. We therefore focus attention on equation (8), which takes the form of a regression with state-dependent coefﬁcients. 1.3.3

Causality

A common critique of empirical models along the lines of equation (8) is based on the following alternative hypothesis: public information causes positively correlated adjustment in both price and order ﬂow, with no causal relationship between price and order ﬂow themselves. For example, macroeconomic news that is positive for the dollar causes the DM price of a dollar to go up and causes a relative increase in transactions initiated by dollar buyers. (This alternative hypothesis

Are Different-Currency Assets Imperfect Substitutes?

15

is distinct from the reverse causality hypothesis under which price increases cause buyer-initiated transactions—i.e., positive feedback trading. Evans and Lyons 2002b reject the hypothesis that positive feedback trading accounts for the positive correlation between interdealer FX order ﬂow and price changes.) Though intuitively appealing, this hypothesis of correlation without causation is inconsistent with rational expectations. As long as expectations are rational, public news does not produce the positive concurrent correlation between order ﬂow and price changes that one ﬁnds empirically. The reason is because—under rational expectations— public information is impounded in price instantaneously. At the new price, which embeds all the public information, there is no longer motivation for dollar buying relative to dollar selling. True, the change in price level may induce trading (i.e., unsigned volume), due perhaps to portfolio rebalancing, but one would not expect good news for the dollar to produce positive order ﬂow on average (a relative increase in transactions initiated by dollar buyers). Consider the possibility that all market participants do not interpret public macro news the same way (in terms of its implication for the exchange rate). This is a departure from traditional modeling of public information in exchange rate economics. Under this scenario, pricesetting market-makers who need to clear the market need to determine the interpretations of other market participants (which they cannot know a priori, by assumption). How might they learn them? The answer from microstructure theory is that they learn from the sequence of submitted orders over time. In this case, price instantaneously adjusts to the market-maker’s rational expectation of the mean market interpretation, and then goes through a period of gradual adjustment to the sequence of transacted orders. Thus, in this (again, nontraditional) setting, causality in part goes directly from public news to price and in part goes from public news to order ﬂow to price. Though catalyzed by public information, it is not the case that there is no causal relationship between price and order ﬂow. 1.4

Results and Implications

Estimation of our micro portfolio balance model allows us to answer three key questions. First, is there support for portfolio balance in the data? Though existing negative results have led to the view that portfolio balance theory is moribund, past work may suffer from low

16

M. D. D. Evans and R. K. Lyons

power (as noted in the introduction). Second, do trades have both temporary and persistent portfolio balance effects? Third, does the price impact of trades depend on the state of the market? This last question is central to identifying states in which intervention is most effective. 1.4.1

Model Estimates

Our estimation strategy proceeds in two stages. First, we estimate a constant-coefﬁcient version of equation (8) and test for state dependency in the coefﬁcients. As we will see, the coefﬁcients in this model accord with portfolio balance predictions in terms of sign and signiﬁcance. The estimated coefﬁcients also accord with our model in that they are indeed state dependent. This latter result motivates the second stage of our strategy, namely, estimation of the precise nature of this state dependency (using nonparametric kernel regressions). Table 1.2 presents results from the ﬁrst stage of our estimation: the constant-coefﬁcient model. Both contemporaneous order ﬂow Xh and lagged price change DPh1 —the two core variables in our model— have the predicted signs and are signiﬁcant. (Though constants do not arise in our derivation, for robustness we also estimate the model with constants; they are insigniﬁcant.) A coefﬁcient on order ﬂow Xh of 0.26 translates into price impact of about 0.44 percent per $1 billion.20 (The magnitude is similar when we use log price change as the dependent variable, as can be seen in table 1.4 of the appendix.) A coefﬁcient on lagged price change of 0.2 implies that 1/1.2, or 83 percent of the impact effect of order ﬂow persists indeﬁnitely. Thus we are ﬁnding evidence of both types of portfolio effect noted in row I: the temporary portfolio balance channel and the persistent portfolio balance channel. Though the temporary channel is clearly present, the permanent channel accounts for the lion’s share of order ﬂow’s price effect (it is also, we would argue, the more important economically). As pointed out by the referee, the temporary channel implies proﬁtable trading strategies, at least at high frequencies, so it is useful to consider just how proﬁtable this would be given our estimates and given realistic transaction costs. (Of course, the reason these temporary price effects arise in the model is that they represent compensation to dealers for bearing intraday risk, i.e., they are risk premia. Hence profitability is not the only criterion for judging their realism. Nevertheless, if the implied proﬁts are large, then the idea that they represent a premium for bearing risk becomes less tenable.) As a back-of-the-envelope

Are Different-Currency Assets Imperfect Substitutes?

17

Table 1.2 Estimates of micro portfolio balance model (constant coefﬁcients), DPh ¼ b 1 Xh þ b 2 DPh1 þ hh Diagnostics Xh I

0.258

DPh1

DPh2

0.203

(13.205) II

Xh1

R2 0.212

0.225

0.173 0.061

0.437

0.071 0.020

; : bð1 þ DÞ D a 0: ð22Þ Figures 6.2 and 6.3 provide a geometric description of the determination of the bond price under demand rationing. At ~s, young consumers are completely rationed. For D > 0, two situations are possible, one with and without complete rationing of young consumers. At s1 , young consumers are completely rationed and invest their entire net income in the bond market. At s2 , they are only partially rationed and invest their remaining income after consumption. The equilibrium bond price in all possible cases is determined by the function

Endogenous Business Cycles and Exchange Rate Volatility

179

Figure 6.3 Bond market equilibrium for D > 0

8 ð1 cðR e ÞÞð1 taxÞðbd þ xE þ gÞ > > ; y d a yðaÞ; > e Þð1 taxÞÞÞ > bðtax þ Dð1 cðR > > > > < yðaÞð1 taxÞ g þ bd þ Ex tax yðaÞ y d > yðaÞ; ; ; s ¼ SðvÞ :¼ min > bð1 þ DÞ bD D > 0; > > > > > yðaÞð1 taxÞ > y d > yðaÞ; > : ; bð1 þ DÞ D a 0: ð23Þ Together with the results from the determination of output and employment one obtains the following lemma: Lemma 1 Given the parameters ðg; tax; d; D; Lmax ; EÞ, any temporary state vector v :¼ ða; b; x; R e Þ g 0 induces a unique positive temporary feasible allocation ð y; LÞ given by equations (18) and (19) and a positive market clearing bond price by equation (23), if D > 1. The functions Y; L; S are continuous and piecewise differentiable functions of the state vector v. Figure 6.4 depicts the partition of the state space into the regions of the three regimes. Its characteristics can be derived from equations (18), (19), and (23) directly. The area of the possible Keynesian unemployment regime (marked K) is deﬁned by all values ðb; a; xÞ A Rþ3

V. Bo¨hm and T. Kikuchi

180

Figure 6.4 Partition of state space into three regimes

behind the plane bcde and below the surface abe. Above the surface abe and above the plane befgh lie all states of the classical unemployment regime C, while below the plane befgh are all repressed inﬂation states of the regime I. 6.3

Dynamics and Expectations Formation

Existence and uniqueness of temporary feasible states provide the basis for a well deﬁned forward recursive structure deﬁning the dynamic development of the economy over time. This requires the description of the dynamical evolution of all state variables of a dynamical system in the mathematical sense. The dynamic equations for the real wage and real bonds are derived ﬁrst. The dynamics of the exchange rate and the expectations processes are discussed afterward. 6.3.1

Adjustment of Prices and Wages

Any temporary state vector v ¼ ðb; a; x; R e Þ uniquely determines the state of the economy for given parameters which in most cases is not

Endogenous Business Cycles and Exchange Rate Volatility

181

the Walrasian equilibrium. This means that quantity constraints occur on the labor and/or on the commodity market which lead to price and/or wage adjustment at the end of the period according to the size of rationing. The adjustments are assumed to follow the so-called law of supply and demand. This means that if supply exceeds demand in a market, its price goes down, and vice versa. One possible formulation of this principle uses the deﬁnition of disequilibrium signals for the labor market s l A ½1; 1 and for the goods market sc A ½1; 1, measuring the sign and the size of rationing. Their dependence on the temporary state vector v ¼ ðb; a; x; R e Þ is described by two functions s l and s c : 4 ! ½1; þ1 : s c ¼ s c ðvÞ; s c : Rþþ 4 ! ½1; þ1 : s l ¼ s l ðvÞ: s l : Rþþ

The signs of the signals correspond to the signs of the respective excess demand functions. On the basis of any pair of disequilibrium signals ðstc ; stl Þ in period t, a price adjustment function P and a wage adjustment function W are deﬁned to obtain P : ½1; 1 ! ð1; þyÞ;

ptþ1 ¼ 1 þ Pðstc Þ; pt

ð24Þ

W : ½1; 1 ! ð1; þyÞ;

wtþ1 ¼ 1 þ Wðstl Þ: wt

ð25Þ

P and W are continuous, strictly monotonically increasing, and satisfy Wð0Þ ¼ Pð0Þ ¼ 0. Together with the signaling function they induce two mappings for price P :¼ P s c and wage W :¼ W s l adjustment: ptþ1 ¼ pt ½1 þ Pðs c ðvt ÞÞ ¼ pt ð1 þ Pðvt ÞÞ;

ð26Þ

wtþ1 ¼ wt ½1 þ Wðs l ðvt ÞÞ ¼ wt ð1 þ Wðvt ÞÞ:

ð27Þ

If one uses a linear adjustment rule, too much instability of interior steady states with frequent divergence to the boundary is created. The following nonlinear functional form of price and wage adjustment will be used in the numerical simulations below. ! 8 > yðaÞ eff y > > if y d > y > > y y > > otherwise : k tanh y

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182

with 0 < g < 1 and 0 < k < 1 as adjustment speeds and yðaÞ eff as the modiﬁed effective aggregate demand. This is deﬁned as yðaÞ eff :¼ yðaÞð1 taxÞcðR e Þ þ bðs þ dÞ þ g þ Ex;

ð29Þ

satisfying y eff ðaÞ > yðaÞ. Given the disequilibrium signals the tangent hyperbolic function delivers a symmetric price and wage adjustment downward and upward with a maximum derivative equal to one. If K or K X I holds, excess supply in the commodity market gives a downward pressure for the price. If y d ¼ y ¼ y, meaning if C X K holds, the commodity market is in equilibrium and there is no price adjustment. In all other cases, meaning if I, C or C X I holds, there is excess demand in the commodity market and an upward pressure for the price. Apart from the situation when y d ¼ y max < y the signal functions s l ðvÞ and s c ðvÞ are continuous.3 Applying the same principle to the labor market, one obtains 8 L Lmax > > if Lmax > L; > l tanh < Lmax ð30Þ WðvÞ ¼ > L L > > otherwise; : m tanh L with 0 < l < 1 and 0 < m < 1 as adjustment speeds. If I or K X I holds, excess demand in the labor market gives an upward pressure for the wage rate. If Lmax ¼ L ¼ L; that is, if C X I holds, the labor market is in equilibrium and there is no wage adjustment. In all other cases (C, K or C X K) there is excess supply in the labor market and a downward pressure for the price. Together the two adjustment functions imply the dynamic equation for the real wage atþ1 ¼ at

1 þ Wðvt Þ : 1 þ Pðvt Þ

ð31Þ

The assumptions concerning bond market equilibrium imply that total ﬁnal bond holdings by young consumers in period t are equal to Btþ1 ¼ Bt ð1 þ DÞ. Therefore the dynamics of real bonds are given by btþ1 ¼ bt

1þD : 1 þ Pðvt Þ

ð32Þ

Endogenous Business Cycles and Exchange Rate Volatility

6.3.2

183

Uncovered Interest Parity and Expectations Formation

One of the interpretations of the uncovered interest parity (UIP) is that of a condition of expected no arbitrage to hold in perfect international capital markets. When applying the UIP to a dynamic model, it is important to take proper account of the sequential structure of the available information and of expectations formation. Let r f denote the nominal rate of return for holding foreign assets. Under the UIP expected returns on domestic and foreign capital markets are assumed to be the same. When purchasing foreign bonds in t, the amount of domestic investment has to be converted at the spot exchange rate Xt into the foreign currency. One period later the principle and the interest have to be reconverted into domestic currency at the future spot exchange rate Xtþ1 . Thus, under expected no arbitrage, the expected returns denominated in either currency have to be the same, implying the following form of the UIP, 1 þ rt;e tþ1 ¼ ð1 þ r f Þ

Xt;e tþ1 : Xt

ð33Þ

Rearranging terms one obtains an equation determining the nominal exchange rate Xt ¼ Xt;e tþ1

1 þ rf 1 þ rt;e tþ1

ð34Þ

as a function of expectations formed prior to the realization of the current exchange rate. Thus the sequential structure of the expectations formation implicit in the condition of the UIP reveals that the dynamic equation determining the actual exchange rate is a function of expectations alone independent of the previous actual exchange rate. Moreover, when forming expectations for t þ 1 agents can use observable information only up to t 1, implying a so called ‘‘expectational lead’’ for the functional relationship.4 Figure 6.5 shows the timing of expectations and of exchange rate determination under UIP. In most models imposing the UIP, it is assumed that agents have perfect foresight with respect to the exchange rate, a property that can be guaranteed here by deriving an explicit perfect forecasting rule. Considering the timing of expectations formation, the perfect foresight e property implies that the difference between the forecast Xt1; t made in

V. Bo¨hm and T. Kikuchi

184

Figure 6.5 Timing of expectations and exchange rates under UIP

t 1 and the actual value Xt must be equal to zero. Put differently, one must have Xt;e tþ1

1 þ rf e Xt1; t ¼ 0: 1 þ rt;e tþ1

Solving for Xt;e tþ1 yields the unique explicit functional form of the perfect predictor c for the exchange rate: e e Xt;e tþ1 ¼ c ðXt1; t ; rt; tþ1 Þ :¼

1 þ rt;e tþ1 e Xt1; t : 1 þ rf

ð35Þ

Therefore the assumption of perfect foresight together with UIP requires that the prediction of the exchange rate is a function of previous predictions and not of previous exchange rates. In other words, the prediction of the exchange rate today guarantees that the prediction of yesterday will be correct.5 As for the exchange rate, one could ask whether it is possible to derive a perfect predictor as well for the expectations formation for the domestic rate of return r e as well as for the inﬂation rate y e . In principle, this might be possible using the techniques from Bo¨hm and Wenzelburger (2004). However, at this stage an explicit solution for a perfect predictor cannot be calculated due to the nonlinearities of the equations and to the dependence on the state variables involved. Therefore an adaptive (but not perfect) forecasting rule will be used for the domestic rate of return and for the inﬂation rate. Observe, however, that the resulting dynamics will, in general, depend on the choice of the adaptive scheme. Let st1 denote the purchase price for bonds, st the selling price, and d the dividend payment. Then the rate of return on domestic bonds effective in period t is given by

Endogenous Business Cycles and Exchange Rate Volatility

rt ¼

d þ st 1: st1

185

ð36Þ

The forecasting rule for the rate of return is assumed to follow the simple adaptive principle rt;e tþ1 ¼ rt1 , inducing a predictor cr of the form rt;e tþ1 ¼ cr ðst1 ; st2 Þ :¼

d þ st1 1: st2

ð37Þ

Notice that two special features are present in any adaptive scheme using past data. First, resulting from the sequential structure, the prediction rt;e tþ1 has to be made prior to the realization of the bond price st , implying that the value for rt is not available as information. Second, the deﬁnition of rt1 implies an additional delay of order two with respect to bond prices, thus increasing the dimensionality of the dynamical system. Similarly assume that the adaptive scheme for prices deﬁnes the expected inﬂation rate yt;e tþ1 :¼ pt;e tþ1 = pt 1 for period t þ 1 as a function of the last t b 1 inﬂation rates: yt;e tþ1 ¼ Cðyt ; . . . ; ytt1 Þ

with ytkþ1 :¼

ptkþ1 1; ptk

k ¼ 1; . . . ; t: ð38Þ

The function C : ð1; yÞ t ! ð1; yÞ is assumed to be continuous satisfying the following property: Cðy; y; . . . ; yÞ ¼ y

Ey > 1:

ð39Þ

The class of such functions includes most of the commonly used adaptive prediction mechanisms with ﬁnite memory. 6.3.3

Dynamical System

It is apparent that the evolution of the economic model will be governed by an interaction of the adjustment equations with the expectations formation rules inducing two strong expectations feedbacks. These are decisive in the stability and in the long-run behavior of the economy. Combining the dynamic equations for the domestic economy with the appropriate mappings for the expectations processes c ; cr , and C for the expected inﬂation rate, the expected interest rate, and for the exchange rate

V. Bo¨hm and T. Kikuchi

186

e e Xt;e tþ1 ¼ c ðXt1; t ; rt; tþ1 Þ;

rt;e tþ1 ¼ cr ðst1 ; st2 Þ; yt;e tþ1 ¼ Cðyt ; . . . ; ytt1 Þ; Rt;e tþ1 :¼

ð40Þ

1 þ rt;e tþ1 ; 1 þ yt;e tþ1

one obtains as the vector of state variables e vt ¼ ðbt ; at ; xt1; t ; st1 ; st2 ; yt ; . . . ; ytt1 Þ e e where xt1; t ¼ Xt1; t =pt . Then the dynamical system is deﬁned by the following mapping:

btþ1 ¼ Bðvt Þ :¼

bt ð1 þ DÞ ; 1 þ Pðvt Þ

atþ1 ¼ Aðvt Þ :¼ at xt;e tþ1 ¼ Fðvt Þ :¼

1 þ Wðvt Þ ; 1 þ Pðvt Þ

e xt1; 1 þ rt;e tþ1 t ; 1 þ Pðvt Þ 1 þ r f

ð41Þ

st ¼ Sðvt Þ; ytþ1 ¼ 1ðvt Þ :¼ Pðvt Þ: The vector of past bond prices and past inﬂation rates ðst1 ; st2 ; yt ; . . . ; ytt1 Þ is just shifted by one time step. Therefore the dynamic e behavior of the economy is described by a sequence fbt ; at ; xt1; t ; st1 ; T st2 ; yt ; . . . ; ytt1 gt0 implying that the state space of the dynamical system equal is a subset of R 5þt . The system exhibits a highly nonlinear structure. This arises not only from the many nonlinear functional relationships but also from the regime switching that occurs induced by the temporary state variables. In the case of a Cobb-Douglas utility function, which implies a constant marginal propensity to consume with no domestic expectations feedback, the dynamical system has dimension ﬁve with a one-period delay in the bond price. Figure 6.6 illustrates the sequential structure when there is no expectations feedback on domestic consumption, where the solid arrows identify the individual mappings of (41). Figure 6.7 illustrates the time one map of the dynamical system (41). The vertical arrows indicate that the expectation of inﬂation rates, of interest rates, and of exchange rates at time t

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Figure 6.6 Sequential structure of prices, exchange rates, and expectations under UIP

Figure 6.7 Structure of time one map

for period t þ 1 are formed on the basis of past realizations of the economic variables. On the other hand, the allocation and the corresponding rationing situation at t depend on these forecasts. It is obvious that the system possesses a lag structure: the bond price, the inﬂation rate, and the expectation of the exchange rate inﬂuence the actual market process at least over two periods. 6.3.4

Stationary States

Due to the high dimensionality of the dynamical system (41), it is apparent that a full analytic characterization of its stationary states

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and their stability properties may be beyond reach. Fortunately, many features for the associated model of a closed economy are well understood (see Bo¨hm, Lohmann, and Lorenz 1997 and Kaas 1995) and some of them carry over directly to the small open economy case, as those stated in the next lemma. Note that all forecasting rules of the model imply perfect foresight in steady states. Lemma 2 Given a feasible list of the parameters ðg; tax; D; r f ; Lmax ; EÞ of the system (41), let ðb; a; y; s; xÞ g 0 denote a stationary state with perfect foresight. Then: 1. 1 < y < 0 if and only if D < 0, and the state is of the Keynesian unemployment type K, 2. y ¼ 0 if and only if D ¼ 0, and the state is of the Walrasian type W, 3. y > 0 if and only if D > 0 and the state is of the repressed inﬂation type I. In other words, the sign of the policy parameter D determines uniquely the type of an interior long-run disequilibrium state independent of the speciﬁc functional forms and the mechanisms. This is one of the fundamental insights into the structural features of this class of models. As a consequence this implies among other things that the local stability properties of any stationary state are regime speciﬁc.6 6.4

Numerical Analysis

For the numerical analysis it is necessary to use speciﬁc functional forms for the intertemporal preferences and for the technology as the ones introduced above. Those have proved to generate tractable results for the closed economy model. Therefore, for the remainder of this chapter, consider the economy with intertemporal preferences of the CES type (1) with r ¼ 0, isoelastic production (7), and with hyperbolic price and wage adjustments of the form (28) and (30). The assumption on preferences eliminates the expectations feedback on domestic consumption implying a constant propensity to consume and no role for the inﬂation predictor C. Therefore the dimension of the dynamical system is ﬁve with the state variables ðb; a; s2 ; s1 ; x e Þ. Even for this special case a full derivation of the eigenvalues when D 0 0 has not yet been obtained. The following partial results and numerical simulations are designed to demonstrate that

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1. there is wide (robust) conﬁrmation of excess volatility of exchange rates compared to domestic real variables in the nonperiodic as well as in the periodic case, 2. the closed economy exhibits period doubling bifurcations for some large sets of parameters while for other ranges of parameters fold bifurcations (saddle-point properties) seem to be the cause of the nonperiodic ﬂuctuations, 3. there is a general overall loss of stability of the domestic economy after introducing foreign demand. 6.4.1

Bifurcation Analysis

Table 6.1 provides a complete list of all parameters used. For this analysis the numerical investigations were restricted to the relationship Table 6.1 Standard parameter set Parameter

Description/origin

Value

g

Adjustment speed pt

0.2

k

Adjustment speed pt

0.2

l

Adjustment speed wt

0.2

m

Adjustment speed wt

0.2

g

Government demand

0.3

tax

Income tax rate

0.3

D

New issues of bonds

0.05

d

Nominal interest

0.01

A

Scaling parameter

1

b

Elasticity of production

Lmax

Constant labor supply

1

d r

Time discount factor Parameter of substitution

1 0

t

Expectational lag

rf E

Foreign rate of return Foreign demand for goods

0.01 0.1

b0

Initial real bond

0.6

a0

Initial real wage

0.6

s0

Initial bond price

0.75

x0e

Initial real expected exchange rate

0.5

Different values

10

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between the production elasticity and the adjustment speeds, since this unveils already some new and important qualitative features. For all time series results the same values were used for the adjustment speeds in analyzing the inﬂuence of four different values of the labor elasticity. Openness and Loss of Stability It is known from the closed economy analogue with money only that the occurrence of endogenous business cycles and bifurcations in such non-Walrasian models is caused by a combination of the adjustment speeds of prices and wages and the labor demand elasticity given by 1=ðB 1Þ (see Kaas 1995). This elasticity becomes large for values of the production elasticity B close to one. The same phenomenon occurs here as well, but with some substantial differences to the closed economy. When E > 0, unstable steady states and non periodic behavior predominate for the open economy where the closed economy would exhibit stable steady states for the same set of parameter values. This is caused primarily by the perfect predictor in conjunction with the UIP assumption. Taken by itself ﬁrst-order effects of the exchange rate tend to induce a derivative equal to plus one near the steady state equivalent to a saddle type property. If second-order effects are positive there will be at least one root larger than one. This is precisely the reason why in the original model by Dornbusch (1976) the steady state is a saddle under the UIP hypothesis since there secondary effects are ignored. Proposition 1 There exists a large critical set of parameter values ðg; tax; D; r f ; Lmax Þ for which the stationary states of the system (41) undergo a period doubling bifurcation when E ¼ 0. When E > 0, there exists a large open set of parameter values such that the stationary states are locally unstable and the system displays ﬁnite as well as complex cycles. Figure 6.8 shows a distinctive destabilizing effect of international trade under UIP. While for the closed economy ﬁgure 6.8a the typical period doubling bifurcation and endogenous cycles occur only for very high values of B, ﬁgure 6.8b shows a large range of low B for which the open economy exhibits endogenous cycles. For high values the bifurcation scenarios appear to be very similar. Figure 6.9 provides evidence of the robustness of the bifurcation scenario of ﬁgure 6.8 in the form of a so-called cyclogram over B and

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Figure 6.8 Bifurcation diagram for a

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Figure 6.9 Cyclogram for a

adjustment speeds g ¼ k ¼ l ¼ m simultaneously. A cyclogram is a qualitative multidimensional bifurcation diagram. For each pair of parameters ðB; g ¼ k ¼ l ¼ mÞ the respective color assignment indicates the order of the cycle of the limiting behavior of the system. According to the codes given in ﬁgure 6.10 the color ‘‘yellow’’ indicates nonperiodic limiting behavior. One easily veriﬁes the features of the bifurcation diagram ﬁgure 6.8 by traversing horizontally at the value g ¼ k ¼ l ¼ m ¼ 0:2 in ﬁgure 6.9. Figure 6.8b and ﬁgure 6.9b show that nonperiodic behavior predominates when E > 0. Most important,

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Figure 6.10 Color code for cyclogram

however, the two subﬁgures reveal that for the closed economy the production elasticity alone determines the bifurcation points, whereas for the open economy there is a stability trade-off (nonvertical boundary of the yellow/red region) between the elasticity of production and the adjustment speeds. Exchange Rate Volatility ^t :¼ Xtþ1 =Xt denote the growth ^ t :¼ wtþ1 =wt , p^t :¼ ptþ1 = pt , and X Let w factors of wages, prices, and of the nominal exchange rates respectively. The time series in ﬁgure 6.11 show the typical comovements of the growth factors of the domestic variables, which move procyclically with the bond price as well. B ¼ 0:5 induces a very long ﬁnite cycle, while B ¼ 0:7 shows a quasi-periodic or complex time series. Notice that the exchange rate ﬂuctuates substantially more than the other variables. In addition ﬁgures 6.12 and 6.13 and table 6.2 provide statistical information of the long-run behavior, conﬁrming the higher volatility of the exchange rate by a distinctively higher standard deviation. For an investigation of the bifurcation effects induced by the elasticity of production we consider two further cases. For B ¼ 0:958 the limiting behavior is described by a complex (nonperiodic) orbit with time series given in ﬁgure 6.14a, while for B ¼ 0:96 the limiting behavior of the economy is a ﬁnite cycle of order three as one observes in ﬁgure 6.14b. These ﬁgures portray typical time series of the rates of change showing very clearly the higher volatility of the exchange rate as compared to the domestic variables, especially the price level. Figures 6.15, 6.16, and table 6.3 supply additional evidence of the distinct volatility ^ -p^-space, the features by showing a projection of the attractor into the X marginal densities (histograms) of the exchange rate, of the rate of inﬂation, as well as a table of descriptive statistics. These indicate that: price and exchange rate changes do not reveal a clear cut long-run correlation;

194

Figure 6.11 ^ ; p^, and w ^ for relatively low values of B Time series of X

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Figure 6.12 ^ -^ Attractor plots in X p space for relatively low values of B

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196

Figure 6.13 ^ for relatively low values of B Density plots of X

Table 6.2 ^ ; p^, and w ^ for relatively low values of B Descriptive statistics X B ¼ 0:5

B ¼ 0:7

Variable

Mean

Standard deviation

Mean

Standard deviation

^ X p^

1.0532

0.0831

1.0514

0.0551

1.0504

0.0306

1.0513

0.0177

^ w

1.0504

0.0299

1.0501

0.0171

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Figure 6.14 ^ ; p^, and w ^ for high values of B Time series of X

197

198

Figure 6.15 ^ -^ Attractor plots in X p space for high values of B

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Figure 6.16 ^ and p^ for B ¼ 0:958 Density plots of X

Table 6.3 ^ ; p^, and w ^ for high values of B Descriptive statistics X B ¼ 0:958

B ¼ 0:96

Variable

Mean

Standard deviation

^ X p^

1.0670

0.1956

0.7669

1.1451

0.4689

0.3281

1.0500

0.0072

0.1203

1.0501

0.0183

0.6365

^ w

1.0527

0.0752

0.2174

1.0558

0.1076

0.6422

Skewness

Mean

Standard deviation

Skewness

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Figure 6.17 ^ and p^ for B ¼ 0:958 Cumulative marginal distribution function of w

the standard deviation of the growth factor of the exchange rate is roughly twenty-ﬁve times as large as that of domestic prices;

the skewness of the exchange rate and of prices are positive while the skewness of wages is negative.

The calculation of the associated cumulative marginal distribution ^ Þ and Fð p^Þ yields the two curves depicted in ﬁgure 6.17. functions Fðw These curves indicate that there is always a positive inﬂation and that the probability of increasing wage rate is almost 0.6. Therefore about

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60 percent of the simulated trajectory is located in the repressed inﬂation regime, I (i.e., with full employment and demand rationing), while the others will be of the Keynesian and of the classical type. Finally, there seems to be a positive correlation between domestic prices and wages for relatively low values of B and a negative correlation for higher values (see ﬁgure 6.18 for B ¼ 0:5; 0:7; 0:958; 0:96). The higher variance for wages relative to that for prices is linked to the high value of B. 6.5

Conclusions

The results of this chapter provide a ﬁrst explicit account of possible dynamics of a small open economy in its relationship to perfect international capital markets under the UIP hypothesis. They show that the structural nonlinear relationships between asset markets and real markets can generate permanent endogenous ﬂuctuations. These are the result of the interaction of a strong expectations feedback with sluggish domestic price and wage adjustments under fully competitive/ price-taking behavior in all markets. No elements of market imperfections are present. Moreover the cyclical recurrence arises within a deterministic model when no random perturbations are present. The numerical analysis shows examples which conﬁrm some typical empirically observed high volatility of the nominal exchange rate relative to that of domestic variables. This result directs us closer toward a possible answer to one of the pricing puzzles. The model demonstrates that the channels between domestic real markets and competitive international ﬁnancial markets induce clear dynamic correlations between real and monetary phenomena whose qualitative properties depend heavily on particular structurally given values of the domestic economy, especially the elasticity of production. It has to be taken as one of the surprising ﬁndings that the introduction of competitive international capital markets within this class of models under the UIP hypothesis induces strong destabilizing forces often making stable regular periodic behavior impossible. With these results further research should investigate the structural relationships between domestic macroeconomic variables and international capital markets as well as its policy implications. Moreover a more detailed analytical investigation of the stability properties of this class of dynamic models will identify better the sources of the volatility and of the ﬂuctuations.

202

Figure 6.18 ^ -^ Attractor plots in w p space

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Figure 6.18 (continued)

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Notes The research for this chapter is part of the project Endogene stochastische Konjunkturtheorie von Realgu¨ter—und Finanzma¨rkten supported by the Deutsche Forschungsgemeinschaft under contract number Bo. 635/9–1,3. We are indebted to J. Wenzelburger and T. Pampel for useful discussions and M. Meyer for computational assistance. We acknowledge discussions with A. Fo¨rster at the initial stage of the project. 1. The model of a closed economy with instantaneous bond market clearing possesses essentially the same temporal and dynamic structure as the one with money alone. 2. The parameter B chosen for the speciﬁc form should not be confused with the nominal stock of bonds denoted Bt . 3. Note that if we assume the price adjustment function to be continuous at y d ¼ y max < y , there is no price adjustment in commodity market even though the commodity market is not in equilibrium. To avoid this, we assume that s l ðvÞ > s c ðvÞ in this particular case. See Bo¨hm, Lohmann, and Lorenz (1997) for details. 4. Such expectational leads with independence occur in a natural way in many intertemporal equilibrium models when the sequential structure of the expectations formation process is made explicit. 5. This special property of the perfect predictor follows directly from the two structural properties of the exchange rate mapping (34), the presence of an expectational lead and of the independence of the previous actual exchange rate (for a general treatment, see Bo¨hm and Wenzelburger 2004). 6. Note that there is no stationary state of the classical type C since the real wage a always decreases in that regime.

References Barro, R. J., and H. I. Grossman. 1971. A general disequilibrium model of income and employment. American Economic Review 61: 82–93. Benassy, J.-P. 1975. Neo-Keynesian disequilibrium theory in a monetary economy. Review of Economic Studies 42: 503–23. Betts, C., and M. B. Devereux. 2000. Exchange rate dynamics in a model of pricing-tomarket. Journal of International Economics 50: 215–44. Bo¨hm, V. 1993. Recurrence in Keynesian macroeconomic models. In F. Gori, L. Geronazzo, and M. Galeotti, eds., Nonlinear Dynamics in Economics and Social Sciences. Heidelberg: Springer-Verlag. Bo¨hm, V., M. Lohmann, and H.-W. Lorenz. 1997. Dynamic complexity in a Keynesian macroeconomic model—Revised version. Discussion Paper 288. Department of Economics, University of Bielefeld. Bo¨hm, V., and J. Wenzelburger. 2004. Expectational leads in economic dynamical systems. In International Symposia in Economic Theory and Econometrics, vol. 14. Amsterdam: Elsevier, pp. 333–61.

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Chari, V., P. Kehoe, and E. McGrattan. 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69: 533–63. Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84(6): 1161–76. Kaas, L. 1995. Steady states and local bifurcations in a dynamic disequilibrium model. Discussion Paper 300. Department of Economics, University of Bielefeld. Kollmann, R. 2001. The exchange rate in a dynamic-optimizing business cycle model with nominal rigidities: A quantitative investigation. Journal of International Economics 55: 243–62. Lane, P. R. 2001. The new open economy macroeconomics: A survey. Journal of International Economics 54: 235–66. Malinvaud, E. 1977. The Theory of Unemployment Reconsidered. Oxford: Blackwell. Mundell, R. 1968. International Economics. New York: Macmillian. Neary, J. P. 1990. Neo-Keynesian macroeconomics in an open economy. In F. van der Ploeg, ed., Advanced Lectures in Quantitative Economics. New York: Academic Press. Obstfeld, M., and K. Rogoff. 1995. Exchange rate dynamics redux. Journal of Political Economy 103: 624–60. Obstfeld, M., and K. Rogoff. 2001. The six major puzzles in international macroeconomics: Is there a common cause? In B. S. Bernanke and K. Rogoff, eds., NBER Macroeconomics Annual 2000, Cambridge: MIT Press. Rogoff, K. 1996. The purchasing power parity puzzle. Journal of Economic Literature 34: 647–68. Rogoff, K. 1998. Perspectives on exchange rate volatility. In M. Feldstein, ed., International Capital Flows. Chicago: University of Chicago Press. Svensson, L. E. O., and S. Wijnbergen. 1989. Excess capacity, monopolistic competition, and international transmission of money disturbances. Economic Journal 99: 785–805.

7

The Euro, Eastern Europe, and Black Markets: The Currency Hypothesis Hans-Werner Sinn and Frank Westermann

Speculating with the euro has been disappointing for many professional investors because the movements of the exchange rate did not seem to follow conventional wisdom. The euro declined when the US economy went into recession, and it began to rise when the European stock marked slumped in early 2002. In this chapter we elaborate on an explanation that one of us had suggested in two newspaper articles.1 According to this explanation the euro weakened before the physical currency conversion because holders of black money and eastern Europeans ﬂed from the old European currencies, and it strengthened thereafter because these groups of money holders developed a new interest in the euro.2 Although we regard an episode in economic history, we also attempt to contribute to the theory of the exchange rate by explicitly introducing currency stocks in addition to interest-bearing assets in the international portfolio of wealth owners. The inclusion of currency stocks is a simple, though uncommon, extension of the portfolio balance approach. It leads to an explanation for the negative correlation of the stock of deutschmarks in circulation and the value of the deutschmark, which Frankel (1982, 1993) once called the ‘‘mystery of the multiplying marks.’’ Also, by this means, we can modify traditional interpretations of the portfolio balance approach, leading to new kinds of predictions for the exchange rate. By the portfolio balance approach, it is often argued that the exchange rate is the relative price of interest-bearing assets and thus reﬂects the proﬁtability of the economies involved. Given the stocks of these assets, an increase in the proﬁt expectations for US ﬁrms, for example, implies a change in the desired composition of the portfolio in the direction of US assets. Since the composition of the portfolio cannot

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change in the short run, the dollar appreciates until any preference for portfolio restructuring in the aggregate disappears. The problem with this interpretation is not only that it no longer ﬁtted when the US slump began in 2000 or when European share prices fell, but also that it abstracts from the role of currency in the portfolios of international investors. After all, the exchange rate is the relative price of two currencies rather than shares, and shares have their own prices, which are quoted instantaneously at the stock exchange. When share prices are ﬂexible, a proﬁt or demand based portfolio interpretation cannot easily explain the exchange rate because there are two prices for shares, one of which seems to be redundant. If, for example, the proﬁt expectations of the new economy are captured by the Nasdaq, there is no need for the price of the dollar to capture them too. To determine the exchange rate in the presence of ﬂexible share prices, other assets whose prices are not ﬂexible are required. In the formal model derived below, interest-bearing assets whose rates of return are controlled by a central bank via passive interventions and money balances whose rates of return are ﬁxed at a level of zero are considered in addition to stocks. We use this model to develop a new theory of the exchange rate that we call the ‘‘currency hypothesis.’’ This is because we see the exchange rate basically as the ratio of marginal utilities of money holding. By the currency hypothesis we are able to explain the startling empirical development of the euro exchange rate with a changed demand for money balances. It is well known that the traditional portfolio balance model, which does not contain national money balances, has been relatively unsuccessful in explaining the exchange rate (Taylor 1995). Our version of the portfolio balances model reconciles the theory with the development of different exchange rates. In particular, we use it to explain the development of the deutschmark–dollar exchange rate in the period from the fall of the Iron Curtain to the physical introduction of the euro. It is this period that is identiﬁed by a unique historical experiment that creates huge shifts in the demand for deutschmarks. 7.1

Eurosclerosis, New Economy, and the Euro

To detect the ﬂaw of traditional exchange rate explanations it is useful to start with the development of the euro. Figure 7.1 depicts the time path of the euro in terms of dollars from 1990 to July 2002. A synthetic

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Figure 7.1 The development of the euro. Exchange rates are monthly data, while PPPs are given at an annual frequency. Different PPPs are computed with respect to the different consumption baskets in the United States, the OECD, and Germany. The latest data point is from July 1, 2002, with a value of 0.989 for the euro. (Sources: Federal Reserve Bank of St. Louis, Economic and Financial database, www.stls.frb.org/fred/; March 2002, and CESifo homepage, www.cesifo.de.)

euro was constructed for the years before 1999 by way of an ofﬁcial ﬁnal exchange rate with the deutschmark. The diagram also shows the purchasing power parity (PPP) in accord with OECD, US, and German commodity baskets. As the ﬁgure shows, the euro was strong, hovering around the upper PPP bound, until 1996. From 1997 onward it began a decline only to recover in February 2002, which was the month when the conversion of the old euro currencies into the physical euro was completed. Many reasons for the long period of decline in the value of the euro are given in the literature, including labor market rigidities,3 the European welfare net,4 the Kosovo war,5 Italy’s ability to violate the Maastricht rules,6 the excellent growth performance of the US economy,7 and the initially high US interest rates.8 However, the most frequent argument, which also underlies some of the media assessments, is the high volume of capital ﬂows into the United States in recent years, in particular, the high volume of direct investment ﬂowing into the new American economy.9 We call this the economic prosperity view. As ﬁgure 7.2 shows, capital ﬂows into the United States were huge in the 1990s, and they have continued to increase until 2002, reaching

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Figure 7.2 Capital imports into the United States and current account deﬁcit. FDI ¼ Foreign direct investment. The current account is deﬁned as the sum of the capital account and the balance of payments (which is near 0 in the United States). The capital account is the sum of net direct investment, net portfolio investment and other investment. Other investment includes international credit and repayments of credits, participation of governments in international organizations and international real estate purchases. (Source: IMF, International Financial Statistics, CD-ROM, March 2001.)

a level of more than 4 percent of US GDP. In most years the capital ﬂow was predominantly portfolio rather than direct investment, but in 1998 and 1999 the direct investment was also substantial, peaking at about a third of total US capital imports. In view of the size of the US capital imports it is understandable that many observers have attributed the strength of the dollar to the prosperous investment opportunities in the new American economy, and in contrast to the meagre outlook for an apparently desolate Europe suffering from a socalled Eurosclerosis. However, there are two problems with this interpretation: a possible confusion between supply and demand and a theoretical mistake in the reasoning underlying the economic prosperity view. Let us consider these problems in more detail. The economic prosperity view implicitly uses the traditional portfolio balance model that threatens the exchange rate in terms of the relative prices of European and American assets.10 Capital ﬂow into the

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United States is assumed to result from an increase in demand for American assets by European investors. The increase in demand, it argues, drives up the value of the dollar because the price of the dollar is the price of American assets. However, if an observable capital ﬂow results in Europeans buying American assets, the reason could also be an increase in the supply of such assets. The supply of American assets is equivalent to an excess of planned investments over planned savings, and this is the same thing as a planned current account deﬁcit or an excess of planned commodity imports over exports. A planned current account deﬁcit is a net supply of American assets in the international capital markets. If the planned current account deﬁcit goes up and if the price of the dollar is the price of American assets, the value of the dollar will fall rather than rise as capital ﬂows into the US increase. As usual, an increase in trading volume in a market says little about whether this increase is demand or supply driven. The signal for it being demand driven is the strength of the dollar. However, this is not a compelling argument for the economic prosperity view. As we will see, there are other reasons for the dollar’s strength, and there are two empirical observations that support the supply-side rather than the demand-side explanation of the capital ﬂows. The startling decline in savings by US households is one of these observations. At the start of the 1990s the savings rate was about 5 percent; then it fell continually until in 1999 and 2000 it became negative.11 By contrast, the euroland savings rate was nearly 11 percent in 2000. The negative savings rate meant that American households were no longer buying assets but were selling them to ﬁnance their excess absorption in resources. Given the high American investment volume, the increase in the current account deﬁcit and the increase in the supply of assets in international capital markets were the only way to replace the American lack of savings. This development is illustrated in ﬁgure 7.3. A further piece of information that contradicts the economic prosperity view is the poor performance of the US stock market in 1999 and early 2000. If the economic prosperity view is correct, not only the dollar but also American share prices should have increased relative to their European counterparts. But this was not the case as was already pointed out by De Grauwe (2000). Although the European stock market index performed better than the American one, the dollar was rising. A similar phenomenon occurred in the ﬁrst half of 2002.

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Figure 7.3 Savings rates compared. The savings rate is deﬁned as private household savings divided by disposable household income. (Source: OECD Economic Outlook, OECD Statistical Compendium, CD-ROM.)

Newspapers attributed the new strength of the euro to a growing disinterest in American shares, but in fact the European share prices fell sharply relative to American share prices in the same period. 7.2

The Flaw in the Theoretical Argument

A larger problem with the economic prosperity view and the traditional portfolio balance model is that it does not seem to have a theoretical basis. The exchange rate is the price of a currency, and not the price of shares or other interest-bearing assets. It is true that the price of the dollar is a component of the price of American shares, if seen from the viewpoint of European investors, but the US share price itself is another component. This is a trivial but important point that may ultimately contribute to unraveling the puzzle. Suppose that the return on US investment rises because of the new economy effect or for whatever other reason. This increase will raise demand for US shares among European investors and raise the price of American shares compared to the prices of European shares. But does this call for a revaluation of the dollar? Why is it not enough if the dollar price of American shares goes up relative to the euro price

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of European shares? Obviously there are two relative prices for the same thing, and one is redundant. The traditional portfolio balance approach downplays the redundancy problem by assuming that the rates of return for the trading countries’ assets are ﬁxed or determined by monetary policy.12 The only way to reach a portfolio equilibrium, namely a situation where the aggregate of all investors is content with the assets they possess, is an exchange rate adjustment. However, if share prices are ﬂexible, the exclusive focus on the exchange rate adjustment in the establishment of a portfolio equilibrium no longer makes sense. The necessary amendments of the traditional portfolio balance model can best be understood by following the layman’s argument for why a higher demand for US shares by European investors will drive up the share prices. It goes as follows: The investors sell their European shares in Europe against euros, and then they sell the euros obtained against dollars in the currency exchange market in order to use these dollars for the purchase of American shares. As this involves a demand for dollars and a supply of euros, so it is maintained, the value of the euro in terms of dollars must fall. The fallacy of this view is that it overlooks the implications of the additional demand for US shares on share prices and the repercussions on foreign exchange markets. In the short run the volume of outstanding US shares is given. Thus the portfolio reshufﬂing planned by European investors will be possible only to the extent that American investors are crowded out and give their shares to the Europeans. The American investors, on the other hand, may not wish to keep the dollars they receive but to buy other things instead. If it is shares, they will go abroad because only there do they ﬁnd the supply they need to satisfy their demand, and in particular, they will go to Europe where shares are cheap because they are sold by the European investors. Thus they will supply the dollars they received from the European investors in the currency exchange market and feed the demand for euros instead. If the original purchase of dollars drove up the dollar, this will instead drive up the euro and eliminate the effect on the exchange rate. With the passage of time the crowding out of American share holders will become weaker because the share price increase induces an additional ﬂow of new issues of shares to ﬁnance more investment. However, because an increase in planned net investment is equivalent to an increase in the planned current account deﬁcit, this will not

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generate a positive revaluation effect on the dollar. It will, however, imply a smaller share price increase. The real possibility to generate a revaluation effect is if the crowdedout American shareholders do not go into foreign shares because they have a home bias in their preferences. There are two alternatives. One is that the crowded-out American shareholders prefer to go into US money instead of European shares. This is the clearest case where a revaluation of the dollar occurs. However, it hardly supports the naive view that an increased demand for American assets drives up the dollar simply because there is a transitional demand for dollars in the process of portfolio conversion. The alternative is that the crowded-out American shareholders prefer to go into American bonds instead of European shares. If the central bank does not stabilize the interest rate by open market operations, this will drive down the interest rate and crowd out previous bondholders. If these then choose European bonds or shares instead of the American bonds they sold, there is again a countervailing supply of dollars in the exchange market. However, if the central bank stabilizes the interest rate by selling bonds and buying the dollars that the crowded-out shareholders do not want, the countervailing effect will be mitigated, and on balance, an appreciation of the dollar will remain. The lesson from these considerations is that the dollar appreciates when more dollars are demanded or fewer dollars are supplied, not when more American interest-bearing assets are demanded. It is surprising how frequently this simple fact has been overlooked in the literature on the determinants of the exchange rate. One of the reasons why the layman’s argument overlooks the possible repercussions resulting from the actions of crowded-out shareholders is that it focuses on transitional demand and supply ﬂows in the currency exchange markets rather than on ultimate preferences for stocks of assets such as shares, bonds, and currencies. To analyze what is happening to the exchange rate, we need a portfolio balance model enriched with stock demands for domestic and foreign currency. According to such a model, the interest rate, the price of shares, and the exchange rate are determined by the need to equate desired with actual wealth portfolios. At any point in time the actual portfolio of assets is given in the aggregate, and thus a desire to restructure this portfolio cannot be fulﬁlled. Instead, asset prices, rates of return, and exchange rates have to adjust until people’s preferences ﬁt the given actual stocks of assets available, notwithstanding the fact

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that from a microeconomic point of view, it is always possible to adjust the portfolio to the preferences. A Friedmanian thought experiment exempliﬁes the merit of a currency-augmented portfolio balance approach in the present case. Suppose that the European investors who wish to replace their European shares with American ones pack these shares into coffers, ﬂy to the United States, and negotiate directly with the American shareholders. They then ﬁnd an exchange rate between European and American shares, and hence relative rates of return, at which the American shareholders are willing to participate in the deal. In general equilibrium, this direct deal cannot result in any exchange rate other than the one brought about by a transitional conversion of European shares into euros, of euros into dollars, and of dollars into US shares. Thus the thought experiment conﬁrms that the dollar–euro exchange rate cannot be effected if the American shareholders who sold their shares are happy to hold European shares instead. If the dollar appreciates, it must be because American shareholders are not happy with all the European shares they purchased and convert them into other assets in a way that increases the demand for of US money balances or reduces the supply of such money balances. As explained above, the ﬁrst of these cases is the straightforward move from European shares into American money. The second case results from the wish to convert European shares into American bonds (or bills). If this induces the Fed to supply more bonds and reduce the stock of currency in circulation so as to defend the short-term interest rate, US currency will become more scarce and the dollar will appreciate. 7.3

Why Money Matters

To clarify the role of currency in the determination of the exchange rate more formally, we now specify a simple two-country portfolio balance model with a representative international investor who chooses among three types of assets in each of the two countries: shares S, bonds (or bills) B, and money M.13 The two countries are the United States and Europe. In a market equilibrium the share prices, the exchange rate, and the interest rates are determined so as to equate the desired portfolio structure resulting from the investor’s optimization to the actual one, which is taken as given.14

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The units of account for measuring the volumes of shares, bonds, and money are the respective national currencies. The volume of shares S is expressed in terms of the nominal share value. The market value of a share is a multiple P of the nominal value. We call this multiple the share price. When r denotes the rate of return on nominal share values, r S is the dividends distributed and r=P is the effective rate of return on shares (without a potential return from share appreciation). Let i denote the rate of interest on bonds. Variables that refer to the United States are labeled with an asterisk; variables without an asterisk refer to Europe and are expressed in terms of euros. The exchange rate e is the price of euros in terms of dollars. The representative international investor is meant to reﬂect the aggregate of all wealthly Americans and Europeans. He optimizes his portfolio for a given investment period, which may or may not be part of a multiple-period setting. At the beginning of the period he has a given endowment of assets that constitutes his total wealth W in terms of euros, but he chooses to re-optimizes his portfolio structure, taking the two share prices, the exchange rate, and the two interest rates as given.15 The investor’s budget constraint in terms of euro expenses for the six types of assets available is W ¼ S

P 1 1 þ B þ M þ SP þ B þ M: e e e

ð1Þ

Note that the choice of nume´raire is arbitrary but meaningless. Nothing would change by choosing the dollar as the nume´raire. Among other things, the investor’s decisions depend on expectations of end-of-period share prices and of the end-of-period exchange rate, which we denote P~ and ~e. The model predicts that changed expectations about these variables will immediately translate into their current counterparts, but we ﬁx the expectations throughout this chapter in order to concentrate on the fundamentals affecting the exchange rate. Our discussion focuses on changed stocks of assets due to government policies, changed real returns, and changed preferences for certain types of assets, given the expectations. The investor’s utility is assumed to be given by the sum of end-of-period wealth plus a liquidity service ! s S P~ b B m M ~ U ; ; ; sSP; bB; mM ; ~e ~e ~e

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which depends on the respective expected stock values S P~=~e; B =~e; M =~e; SP~; B, and M.16 The liquidity service is meant to capture all considerations important for the choice of assets other than their contribution to the pecuniary return, including risk characteristics, Baumol-Tobin type transactions costs, the timing of planned commodity purchases, and the like. The Greek symbols s ; b ; m ; s; b, and m denote parameters of the utility function, which allow us in a simple fashion to represent arbitrary preference changes including those that generate cross-price effects among different assets. We assume that U is an increasing, separable, and strictly concave function and that the parameters are unity before a preference change takes place. Formally, the investor’s decision can be depicted by maximizing the Lagrangean 1 1 1 L ¼ S ðP~ þ r Þ þ B ð1 þ i Þ þ M þ SðP~ þ rÞ þ Bð1 þ iÞ þ M ~e ~e ~e ! s S P~ b B m M þU ; ; ; sSP~; bB; mM ~e ~e ~e P 1 1 þl WS B M SP B M e e e with respect to the six different asset volumes considered in the model. Here the ﬁrst line is end-of-period wealth in terms of euros, the second gives the liquidity services, and the third contains the investor’s budget constraint where l is the Lagrangean multiplier. The marginal conditions resulting from this optimization approach are e P~ ð1 þ s US Þ þ r ¼ l; ~e P

ð2Þ

e ð1 þ i þ b UB Þ ¼ l; ~e

ð3Þ

e ð1 þ m UM Þ ¼ l; ~e

ð4Þ

P~ð1 þ sUS Þ þ r ¼ l; P

ð5Þ

1 þ i þ bUB ¼ l;

ð6Þ

and

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1 þ mUM ¼ l:

ð7Þ

These equations are similar insofar as they all show that in the optimum the sum of each asset’s own rate of return factor plus the marginal liquidity service, possibly corrected by a growth factor reﬂecting the expected exchange rate adjustment, equals a common yardstick, the Lagrangean multiplier l. In the case of US shares (2), the rate of return factor is a combination of the growth factor of the dollar in terms of euros, e=~e, of the growth factor of the US share price, P~=P , and the effective rate of return on US shares, r =P . In the case of dollar currency (4), the rate of return factor is just the growth factor of the dollar in terms of euros, and in the case of euro currency, it is simply one. The other cases should be self-explanatory. In general, an asset’s pecuniary rate of return factor is smaller, the larger this asset’s marginal liquidity service. As the rate of return on shares tends to be higher than that on bonds and the latter higher than that on cash, the marginal liquidity services will presumably follow the adverse ordering. Let a bar above a variable indicate the given asset stocks in the economy. The investor’s wealth in terms of euros with which he enters the period is then determined by S

P 1 1 þ B þ M þ SP þ B þ M 1 W: e e e

ð8Þ

Equations (1) through (8) deﬁne the demand functions for all six assets. The asset prices, the exchange rate, and the interest rate follow if we assume that, for each asset, demand equals supply: S ¼ S ; B ¼ B ; M ¼ M ; S ¼ S; B ¼ B; M ¼ M:

ð9Þ

In total, there are now 14 equations, one of which is redundant. They explain six asset stocks, two interest rates, two share prices, one exchange rate, the Lagrangean multiplier, and the wealth level, in a total of 13 variables. There is no need to explicitly solve for all of these variables because a number of useful observations can easily be derived by inspecting the equations. One concerns the economic prosperity view. Suppose that s in equation (2) increases and/or s in equation (5) declines while the marginal utilities of money holding remain constant. Equations (4) and (7) then ﬁx the exchange rate e and the Lagrangean multiplier l. As US and US are ﬁxed by the given levels of S and S, it follows from (2) and (5) that the changed preferences for share holdings will be accommo-

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dated only by an increase in the price of US shares P and/or a decline in the price of European shares P. No exchange rate movements are necessary to maintain a portfolio equilibrium. Changes in the nominal rates of return r and r in favor of American assets would, as the reader can easily verify for himself, have very similar effects. If the money demands do not change, they would not, as the economic prosperity view predicts, result in an appreciation of the dollar but, once again, only in an increase in the US share price relative to the European one. A similar remark applies to the rates of interest on bonds. Again, the exchange rate e and the Lagrangean multiplier l are ﬁxed by (4) and (7) independently of these interest rates. An increase in the preference for US bonds as reﬂected by an increase in b will, according to (3), only result in a fall in the US interest rate, and similarly an increase in the preference for European bonds will reduce the European interest rate according to (6) without affecting the exchange rate. The crucial equations for the determination of the exchange rate are (4) and (7). Together they imply that the value of the euro is explained by the marginal liquidity services of euros and dollars in the international wealth portfolio: e ¼ ~e

1 þ mUM : 1 þ m UM

ð10Þ

No pecuniary rates of return of the assets on which the portfolio balance approach focuses enter this formula, since these rates are endogenous to the market equilibrium. This reiterates the point made above, which is less trivial than it sounds: the currency exchange rate is the exchange rate between two types of money, and not the exchange rate between interest-bearing assets. The remarkable aspect of these neutrality results is that preference changes concerning interest-bearing assets will result in price and rate of return changes that are large enough to compensate for these changes but do not affect the exchange rate. For exchange rate movements to come along with such preference changes, it would be necessary that preference changes for money balances be involved too. Consider, for example, the home bias discussed in the previous section implying that crowded-out American shareholders like to go into American money. In the aggregate model considered here, this can be captured by the assumption that the increased preference for American

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shares comes along with an increased preference for US money, meaning an increase of m . According to equation (10) this would indeed imply a weakening of the euro. Thus far we assumed that the stocks of assets are given in the portfolios and that the pecuniary rates of return are ﬂexible. Rate of return adjustments will then be able to accommodate the preference changes with regard to bonds and shares but not with regard to money holdings, because the pecuniary return of money is ﬁxed at zero. Only a changed preference for money holding needs an exchange rate adjustment to keep the desired portfolio structure in line with the given actual one. Things are different, though, when other rates of return are ﬁxed too. The relevant case here is that the two central banks ﬁx the national interest rates and accommodate any changes in preferences for money and bonds with appropriate open market policies that change the composition of the outstanding stocks of bonds and money balances. This will affect the marginal liquidity services of money balances and will have repercussions on the exchange rate according to equation (10). From equations (3), (4), (6), and (7) it follows that the national interest rates are given by i ¼ m UM b UB

and

i ¼ mUM bUB :

ð11Þ

Given the stocks of money and bonds and hence given UM ; UB ; UM , and UB , a national interest rate obviously decreases with a decrease in the preference for the respective national money (decrease of m or m) and/or an increase in the preference for national bonds (increase of b and b), as was explained. To prevent this from happening and to ﬁx the interest rates, the central banks have to accept any exchange between the national stocks of money and bonds that the public wants to carry out at the given interest rates; that is, they have to intervene passively by supplying more of the respective stock in demand and withdrawing the other one from the market. Passive intervention of this type will make the exchange rate reactive to changed preferences for bond holdings and protect it partly from changes in the preference for money holdings. Consider, for example, the case of an increased preference for US bonds, as is reﬂected by an increase in b . To avoid a decrease in the US interest rate, the Federal Reserve Bank will react by selling bonds against US currency, which increases UM and lowers e according to (10). The dollar appreciates after an increase in the demand for US bonds. Similarly a depreciation

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of the euro, e, could be brought about by a reduced preference for European bonds if the European Central Bank ﬁxed the interest rate by buying bonds and selling euros—or, as discussed in the previous section, by an increased preference for American bonds which the Fed accommodates with a contractionary open market policy. Things would be similar if the central banks intervened also to keep the effective rate of return on shares constant, but of course they don’t. This is the crucial point overlooked in the existing portfolio balance literature. If the central bank intervenes only to keep the interest rate constant and if no more than the preference for shares changes as is reﬂected by s and s, equations (2) through (7) continue to ensure an isolation of the exchange rate. This conﬁrms the above criticism of the economic prosperity explanation of the euro’s weakness and of the traditional portfolio-balance approach as such. Even when the central bank intervenes passively to keep the interest rate constant, changes in proﬁt expectations, in preferences for share holdings, or in preferences for direct investment cannot inﬂuence the exchange rate unless they also imply changes in preferences for bonds or money balances. Let us now discuss the reason why a passive intervention might partially protect the exchange rate against changes in liquidity preferences. Suppose that the preference for euro currency declines, as is represented by a reduction of m. According to (10), this will depreciate the euro, and according to (11), it will reduce the European interest rate. To prevent the interest reduction, the European Central Bank will buy back money balances against private bonds. In itself, this will increase UM and increase e, meaning it will stabilize the exchange rate. The stabilization will not be perfect, though, because the increase in the stock of bonds results in a reduction in the marginal utility from bond holding, UB . According to (11), a constancy of the interest rate therefore implies that the marginal utility from money holding, mUM , will not be pushed back to where it was before the preference change and that there is a negative net effect on the euro. This can also be seen by deriving a modiﬁed interest parity condition from equations (3) and (6), which relates the exchange rate to the national interest rates and the marginal liquidity premia for bonds:17 e ¼ ~e

1 þ i þ bUB : 1 þ i þ b UB

ð12Þ

As the passive intervention triggered off by the decline in m increases the stock of bonds held by the public, B, and thus reduces the bonds’

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marginal liquidity service UB , equation (12) ensures that the net effect on the exchange rate is negative. A similar result holds for an increase in m . As the reader may verify for himself, a negative net effect on e and a decrease of M can also result from an increase in the preference for dollar currency if the dollar interest rate is given. The effect has a certain similarity with an active intervention in the exchange market. If such an intervention is sterilized in the sense that it leaves the interest rates ﬁxed in the two countries, it will involve a sale of dollar currency and dollar bonds against euro currency and euro bonds so as to keep the respective national differences in the marginal liquidity services of money and bonds constant, as is indicated by (11). The decline in the marginal utility of US bonds, and the respective increase in the marginal utility of European bonds that results from this change in the structure of the market portfolio, raises the fraction on the right-hand side of (12) and hence the value of the euro.18 It is a common feature of the active and passive interventions that a decline in the stock of euro currency exhibits a positive effect on the value of the euro. However, the distinguishing feature is that this effect comes independently when the central bank intervenes actively in the foreign exchange market while it is only an induced compensating effect, which cannot offset the primary effect when the central bank intervenes passively by ﬁxing the interest rate. Thus the correlation between the stock of euro currency and the value of the euro should be negative in the case of active intervention with a given interest rate, and positive in the case of passive intervention after a change in the currency preference. As we showed above that a negative correlation would also characterize the case of passive intervention after a change in bond preferences, it seems that the sign of the correlation between the currency stocks and the exchange rate might be a clue for ﬁnding the causes of the weak euro.19 It is essential for our theory that American and European bonds be imperfect substitutes in the international portfolio. If they were perfect substitutes, a preference shift would be made from European to American currency. The shift would be accommodated by a contractionary open market policy in Europe and an expansionary one in the United States, so as to keep the interest rates constant and not affect the exchange rate. The simplest way to depict this possibility in our model would be to assume that bonds do not deliver marginal liquidity services in addition to their pecuniary return, such that b UB ¼ bUB ¼ 0.

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Equations (10) through (12) would then imply that ﬁxing the interest rates eliminates any effect of a changed preference for money holding on the exchange rate. Similarly equation (12) would imply that the ECB tried the impossible when it intervened in the foreign exchange market to stabilize the euro without changing the European interest rate. However, we ﬁnd it hard to believe that bonds denominated in different currencies and separated by a ﬂexible and risky currency exchange rate will even come close to being perfect substitutes. This is the old dichotomy between the portfolio balance and the monetary approaches, which can only be solved empirically. Feldstein and Horioka (1980) and Dooley, Frankel, and Mathieson (1987) have argued that a high correlation between savings and investment points to a rather limited international substitutability of assets, and within our model we will also be able to provide supporting evidence for a limited substitutability.20 If American and European bonds are perfect substitutes, the value of the euro and the stock of euro currency should be uncorrelated both in the presence of demand and supply shocks if one controls for the interest rates. On the other hand, if they are imperfect substitutes, then controlling for the interest rates, there should be a negative correlation when supply shocks dominate and a positive correlation if demand shocks dominate. These are clearcut predictions, and we will show that during the historical period considered there was indeed a very signiﬁcant positive correlation. 7.4

Black Money and Deutschmarks Circulating Abroad

The deutschmark provides a particularly striking example of the positive correlation between the stock of currency in circulation and the foreign exchange value of this currency: in the late 1980s and early 1990s the Bundesbank and the public had regularly been surprised, if not alarmed, by the fact that the German monetary base grew much more rapidly than was anticipated, typically exceeding the projection corridor the Bundesbank had published. During this period there was a persistent revaluation pressure for the deutschmark. The pressure even led to the collapse of EMS in 1992, which implied a sudden revaluation of the deutschmark relative to most of the European currencies and the dollar.21 Since 1997, however, this trend has been reversed (see ﬁgure 7.1), and so has the trend in the growth rate of money balances. When the external value of the deutschmark began to decline,

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Figure 7.4 German currency in circulation (monthly data, billion). (Source: Deutsche Bundesbank homepage, 2002.)

the growth rate of the German monetary base began to decline relative to its trend, and during the year 2000 even the base itself began to fall with a gradually accelerating speed. Figure 7.4 illustrates this development. The development of the stock of all euro currencies, as depicted in ﬁgure 7.5, paralleled that of the stock of deutschmark currency. No econometric approach is need to uncover the movements. Obviously the stock of euro currencies in circulation was falling against the trend from about 370 billion @ to about 250 billion @, which is a decline of 120 billion @ or one-third. This is ten times more than the numbers monetary theorists usually try to interpret. The numbers are also huge if compared with previous intervention and speculation volumes. George Soros is said to have succeeded to tilt the EMS with only a few billion pounds, and the ECB’s frequent interventions to stabilize the euro had probably not exceeded 4 billion euros in total. It can only be guessed what the reasons for the euro currencies returning to the ECB were. We believe that it has do to with the announcement and anticipation of the physical currency conversion, which induced a ﬂight from euro currencies into other assets including other currencies. There are two categories of ﬂight money: deutsch-

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Figure 7.5 Euro zone currency in circulation (monthly data, billion). (Sources: September 1997–May 2002 Deutsche Bundesbank (2002), January 1990–August 1997 Ifo estimate based on monthly changes.)

marks that were legally and illegally held for transactions purposes outside Germany, and stocks of black money denominated in all euro currencies that were held by west Europeans. Other reasons that relate to the more technical aspects of the currency conversion could have been important in the very last moment before the conversion, but the deviation from the trend began too early for these reasons to have a considerable explanatory weight. The ﬁrst category must have been substantial because the German currency was the only one among the euro currencies that served as a means of transactions in other countries, in particular, in eastern Europe and Turkey but also in other parts of the world. In a Bundesbank discussion paper published by Seitz (1995), the accumulated stock of deutschmark currency outside Germany was estimated to be between 60 and 90 billion in 1995, which is equivalent to 30 to 45 billion @. At the time this number was between 25 and 35 percent of the German monetary base and between 10 and 15 percent of the monetary base of what later would be the euro countries.22 The deutschmarks circulating abroad began to return after the ﬁrm announcement of the currency union at the Dublin meeting in 1996. Foreign money holders had heard about the abolishment of the

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deutschmark and were afraid of sustaining a conversion loss. Even in Germany, many people were afraid of losing part of their wealth, despite the frequent advertising campaigns for the euro. The uncertainty of ordinary people elsewhere in the world must have been much bigger, since they were not informed about the conditions of the conversion and probably wondered what all this euro business was about. No doubt they heard that the deutschmark was to be abolished in 2002 and had wind of the talk about a new currency replacing it. But they did not know who would carry out the conversion, what the exchange rate would be, and what commission fees would be charged. Those people afraid of sustaining a loss continued to hoard deutschmarks and hurried into the dollar or other currencies, including their own, which were free of this kind of uncertainty. The recipients of the deutschmarks, typically banks and other ﬁnancial institutions, then returned the deutschmarks to the Bundesbank in exchange for interestbearing assets, typically short-term securities that were counted as part of M3. It is interesting in this regard that that the ECB announced in its Bulletin of November 2001 a redeﬁnition of its stock of M3 because a growing proportion of such securities had been accumulated by foreigners and was nevertheless counted as part of M3. Short-term securities with a maturity of up to two years that were being held by foreigners were decided no longer to be included in the deﬁnition of M3. According to the ECB’s own information this amounted to an adjustment of the published increments of M3 on the order of 40 billion @ in one year. An analogous comparison between the old and new M3 ﬁgures for the period back to January 1999 shows that the effect could even have been on the order of 100 billion @. It is unclear how much of this can be attributed to the returning deutschmarks, but the ﬁgures must be seen as a clue to the forces at work. Further evidence comes from two surveys. One was conducted by us, using the Ifo Institute’s Economic Survey International, a quarterly transnational poll among country experts. We asked 150 experts in eastern Europe, typically economists working for international companies, about a potential shift in the interest of ordinary people from the deutschmark to the dollar. Of the 71 people from 15 countries who responded to the poll, a majority of 54 percent reported that the public showed a growing interest in the dollar, 78 percent thought that the public had not been sufﬁciently informed about the introduction of the euro, and another 54 percent said that the public was at least partially

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worried about losses if they did not soon exchange their German marks into a permanent currency such as the dollar. Another, much more extensive survey with thousands of east Europeans was conducted by the Austrian Central Bank (Stix 2001). The survey was taken at various times over two years in Croatia, Hungary, Slovenia, the Czech Republic, and Slovakia. It afﬁrmed that the decline of the share of D-mark in circulation in the total euro money supply was due to the deutschmarks returning from abroad and that as late as May 2001 no less than 41 percent of the holders of deutschmarks who had made up their minds planned to exchange their stocks not into euros but into other currencies. Let us now turn to the second reason for the ﬂight of cash, namely the ﬂight of black money in the run-up to the physical conversion of euro currencies. According to the European laws against money laundering the ofﬁcial conversion of larger sums of old cash into euros was not possible without registration. People who held stocks of black European monies therefore had to ﬁnd ways to gradually convert them outside the banking system before the ofﬁcial conversion date, but they could not convert them into the euro because this currency existed only in a virtual form. Thus they had to go into the dollar, the pound, or other currencies that were not part of the euro group, and the sellers of these international currencies then exchanged the surplus stocks of euro currencies against interest-bearing assets that, after a substitution chain, ultimately came from ECB, which tried to stabilize the interest rate as explained above. Unfortunately, no ofﬁcial statistics are available that allow a precise distinction between the two sources of the decline in currencies as depicted by ﬁgures 7.4 and 7.5. Neither black stocks of money balances nor currency stocks held in eastern Europe are easily observable. Nevertheless, there is indirect evidence that provides rough estimates of the relative magnitudes involved. Consider ﬁrst the results of Schneider and Ernste (2000) on the size of the black economy in Europe. According to these authors, the share of the black economy in the euro countries is about 14 percent of the actual GDP including the black activities. Based on this ﬁgure and the trend value of 370 billion euro, as shown in ﬁgure 7.5, the potential stock of black currency at the time of currency conversion can be expected to have been 52 billion @ or more. Figures 7.4 and 7.5 make it clear that roughly this sum could have contributed to the net decline of the currency in circulation until the

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time of physical currency conversion. As the results of Schneider and Ernste reveal that Germany’s black market share in GDP is close to the European average and as German GDP is about 31 percent of the total of all euro countries, the reduction in the stock of deutschmarks in circulation would have had to be 31 percent of 120 billion @, in other words, 36 billion @ if it was exclusively explained by the black market effect. However, ﬁgure 7.5 reveals that the decline against the trend of the stock of deutschmarks in circulation was much higher, about 90 billion @. This clearly points to the importance of the eastern European effect. Assuming that the 30 billion @ decline of non-German currency in circulation, revealed by ﬁgures 7.5 and 7.6, can be explained fully by the black market effect 23 in the non-German euro countries, which produce 69 percent of the GDP and should therefore hold 69 percent of the stock of black money, the total black market effect for all euro countries can be taken to be about 45 billion @. Thus the remainder of the total decline of 120 billion @, which is 75 billion @, can be seen to reﬂect the stock of deutschmark currency that returned from eastern Europe and other parts of the world, or did not ﬂow there in the ﬁrst place because of the expected euro introduction. These are only rough estimates. Whatever the true relative importance of the two effects may be, the fact that ordinary people outside Germany and west European holders of black money had lost their interest in euro currencies in the run-up to the currency conversion is beyond doubt. There was exactly the kind of reduced preference for euros that was modeled by a decline of the utility parameter m in the previous section. Our theory indicates that this reduced preference would have lowered the value of the euro and the European interest rate if the ECB had not intervened. The euro and the interest rate would have adjusted such that the existing stocks of money balances continued to be held in the international wealth portfolio. However, the ECB intervened passively so as to stabilize the interest rate. As explained in the theory section, this mitigated the decline of the euro without eliminating it, while the stock of circulating currency fell. The mechanism through which this actually happened is that the euro currency held by foreigners and black market agents went to international ﬁnancial agencies (banks and investors) that held both euro and dollar currencies. Some of the dollars delivered by these agencies may have come from the Fed in exchange for US securities and some of the euros received by them went to ECB in exchange for

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European securities. In the end, the euro declined, and there was less US currency and more European currency in the international portfolio of these ﬁnancial agencies, and more US currency and less European currency in the aggregate international portfolio of all private agents taken together, including eastern Europeans and black market agents. This interpretation ﬁts the observed decline of the stock of outstanding deutschmarks as shown in ﬁgures 7.4 and 7.5 and the simultaneous decline of the euro as shown in ﬁgure 7.1. It even ﬁts the rise of the euro after February 2002 when the currency conversion was completed (see ﬁgure 7.1). As was predicted by us in the journal articles and other contributions,24 currency demand by eastern Europeans and holders of black money went up immediately after the physical conversion, forcing the ECB to pump more money into the economy so as to maintain its interest target, and the euro began to appreciate rapidly, taking by surprise the analysts who believed in a correlation between the strong US recovery and the value of the dollar. The development after the physical currency conversion mirrors that of the virtual conversion before it: the euro has been gradually taking the places emptied by the old euro currencies, in particular, the place of the deutschmark in eastern Europe. In a recent paper the ECB (Padua-Schioppa 2002) estimated that until May 2002 no less than 18 billion @ were transferred to countries in eastern Europe. The fall of the Iron Curtain bolstered the deutschmark in the early 1990s. Fear of its conversion into the euro weakened it after 1997 and with it the euro itself. By the same logic, the euro has started to gain strength in the period since the conversion. 7.5

A Quantitative Assessment of the Effect

An important question is whether a decline of the monetary base by about 120 billion @ against the trend can cause effects large enough to explain the actual exchange rate movements. The search for its answer requires an empirical determination of the corresponding reaction coefﬁcients. Here we take two different approaches. First, we review the evidence from recent studies of micro data on the effect of money demand on the exchange rate. Second, we estimate a modiﬁed portfolio balance model, using macro data. Recent contributions by Evans and Lyons (1999, 2001) on the ‘‘micro structure of the exchange rate’’ conclude that each billion of additional sterilized dollar currency demand raises the dollar exchange rate by up

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to half a cent in the short run and about 30 cents in the long run. If these ﬁgures apply equally to the euro, then our theory explains the depreciation of the euro by about 36 cents in the period 1997 to 2000. This is extremely close to the actual depreciation, which was 34 cents during this period. In order to assess the co-movement of the exchange rate and relative money supplies from macro data, we now analyze empirically the determinants of the exchange rate. The question in the context of our model is whether the currency in circulation has a signiﬁcant positive partial effect on the exchange rate of the euro in the presence of the other variables. The co-integration technique is used to study the empirical long-run relationship among the ﬁve variables relevant to our model: the exchange rate, relative money supplies, relative interest rates, relative bonds, and relative share prices. We analyze the comovements for the period from 1984 to the end of 2001 for German, Japanese, UK, and Swiss exchange rates with respect to the United States. The Johansen (1991) procedure is used to test for the presence of cointegration.25 The Johansen test results are reported in panel A of table 7.1, along with the robustness of this model and some econometric issues. The long-run coefﬁcients in the table were the exchange rates normalized to one. All variables are deﬁned as in the theoretical model above. The empirical results are consistent with our impression from the data analysis and the discussion in the previous sections. We ﬁrst focus on the long-run coefﬁcients. In all countries, except Switzerland, which used to control money supply rather than interest rates, the currency in circulation has a positive effect on the exchange value of the domestic currency. Because American and European bonds are perfect substitutes, this contradicts the view that a policy of ﬁxing the interest rates eliminates the effect of currency demand changes on the exchange rate. The positive correlation between the monetary base and the foreign exchange value of the currency had also been observed in earlier work by Frankel (1982, 1993), who called it the ‘‘mystery of the multiplying marks’’ and attributed it to model misspeciﬁcations or wealth effects in the monetary model of the exchange rate. Indeed, the positive correlation seems puzzling if the monetary base is seen as resulting from a supply policy of the central bank and active interventions. However, according to our model, the positive correlation has a straightforward explanation in the historical episode considered here if variations in the

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Table 7.1 Currency augmented portfolio balance model Johansen co-integration results, 1984:1 to 2001:4 Variable

GER

UK

JAP

SWI

A. Long-run coefﬁcients tr

80.57

62.18

82.55

115.25

cv

68.52

47.21

68.52

68.52

0.804 (0.414)

1.622 (0.219)

0.145 (0.993)

7.825 (9.145)

(1.943)

(7.386)

(0.146)

(0.856)

0.009

0.013

0.014

0.109

(0.014)

(0.006)

(0.085)

(0.166)

(0.680)

(2.090)

(0.166)

(0.659)

ln M ln M

ln i ln i

ln B ln B

0.129 (0.197) (0.654)

ln P ln P

1.179

0.079

0.024

2.443

(0.164)

(2.636)

(0.151)

(0.926)

0.025

3.970

(0.257)

(0.091)

(0.153)

(5.247)

(4.580)

(0.874)

(0.164)

(0.756)

0.134

0.239

0.003

0.009

(0.044) (3.009)

(0.106) (2.247)

(0.001) (1.838)

(0.020) (0.448)

B. Reversion coefﬁcients Dðln eÞ

Dðln M ln M Þ

Dðln i ln i Þ

Dðln B ln B Þ

0.140

0.988

(0.081)

(0.191)

(0.026)

(3.922)

(1.725)

(5.168)

(0.119)

0.240

1.166

3.855

0.150

(0.457)

(1.569)

(2.718)

(0.378)

(0.524)

(0.743)

(1.418)

(0.396)

0.019

0.022

0.036

(0.035)

(0.189)

(0.012)

(0.120)

(3.000)

(0.550) Dðln P ln P Þ

0.003

0.155 (0.039)

0.060

0.176

0.158

0.092

(0.062)

(0.059)

(0.397)

(0.026)

(0.972)

(2.961)

(0.399)

(3.496)

Note: Bond data were not available for the United Kingdom. The Swiss data start in 1989, as stock market data were not available before. tr denotes the likelihood ratio test statistic for the null hypothesis of zero cointegrating vectors against the alternative of one cointegrating vector. The asymptotic critical values are denoted by ‘‘cv.’’ In all cases, except for Switzerland, there exists only one cointegrating vector. Standard errors and tstatistics are in parentheses.

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foreign and black market demand for a country’s currency are taken into account. The other estimates are also broadly in line with our theoretical model. The positive effect of the interest rate (for Germany, Japan, and Switzerland) on the value of the domestic currency can have two explanations. One is that it results from an increased preference for the domestic currency which, as indicated by (10) and (11), will imply a revaluation and an increase of the interest rate if the central bank does not intervene. The other is that the central bank actively intervenes by tightening the money supply. According to (11), this increases the difference of the marginal liquidity premia of money and bonds and hence the interest rate, and according to (10), it implies a revaluation. Bonds have a smaller negative effect in Germany, although it is not statistically signiﬁcant and may be the counterpart of the positive effect of money holdings, since interventions imply that bonds and money balances vary inversely. The signiﬁcant negative coefﬁcient of share prices supports the puzzle established by De Grauwe (2000), that the value of an economy’s currency varies inversely with its prosperity, which is the opposite of what the economic prosperity view predicts. By our model, the explanation for the negative correlation is that domestic shareholders whose preferences imply a home bias switch between domestic shares and domestic money, depending on the information they receive. This changes the marginal liquidity premium on domestic money balances conversely to share prices. According to equation (10) the domestic currency appreciates when share prices are low, and vice versa. Given the co-integration result, we use a vector error correction model to explore the reaction to a deviation from the long-run equilibrium.26 The responses of each of the variables to deviations from the long-run equilibrium are captured by the revision coefﬁcients reported in table 7.1. In the cases of Germany, the United Kingdom, and Japan, the exchange rate and the relative money bases react to the deviations from the equilibrium, while most others do not. It is known from the work of Meese and Rogoff (1983) and Taylor (1995) that the empirical research on exchange rate determination suffers from instability of the parameters over time, and poor out-ofsample performance. This problem also applies to our empirical exercise. In order to check the robustness of our estimation procedures, a set of appropriate tests was performed, using several estimation proce-

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dures that addressed econometric problems associated with this type of regression exercise. For example, we estimated an ARCH model, correcting for conditional heteroscedasticity, examined alternative lag structures in the co-integration exercise, and implemented an instrumental variables approach, aiming to reduce the endogeneity problem by way of lagged values as instruments. While most of our variables were affected by these alternative speciﬁcations, our main variable of interest, the relative money stocks, remained remarkably robust, exhibiting in most cases the signiﬁcant positive correlation with the exchange rate predicted by our theory. 7.6

Conclusions

In this chapter we provide a criticism of the portfolio balance approach, and we attempt to develop a new theory of the exchange rate that we call the currency hypothesis. We take an explicit two-country portfolio model with money, bonds, and shares and show that there is little reason to expect the demand for shares to translate into the exchange rate because this demand is already reﬂected in the share price. We argue that what counts most is the stock demand for money in the narrow sense of the word. The exchange rate is the price of one type of money in terms of another and not the price of interest-bearing assets, as both portfolio managers and economists who developed the portfolio balances approach have claimed. This theoretical result is conﬁrmed by a number of empirical tests of exchange rates among various currencies. The tests demonstrated a strong and robust positive correlation between a country’s stock of currency in circulation and the respective exchange value of this currency. Our currency hypothesis is motivated historically by our observing the movements of the exchange value of the deutschmark and the euro from the time of the fall of the Iron Curtain to the physical conversion of the euro. We explain these co-movements in quantitative terms, using the ‘‘microstructure of the exchange rate’’ approach. With the fall of the Iron Curtain, the deutschmark became popular in eastern Europe in the early 1990s, leading to an unprecedented monetary expansion and the appreciation crisis of 1992. Fear of loss in its conversion into the euro reduced the demand for deutschmarks and weakened both the deutschmark and the euro after 1997. By the same logic, and predicted accurately by us in earlier contributions on this topic, the

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euro has gained in strength since the time of the physical conversion. A good reason for the appreciation of the euro is that it is ideally suited for black market operations and is ﬁnding friends in eastern Europe and elsewhere. Notes Earlier work along these lines was presented at a workshop on Exchange Rate and Monetary Policy Issues in Vienna, April 2001, and at the CESifo Macro and International Finance Area Conference in Munich, May 2001. We gratefully acknowledge useful comments by Paul De Grauwe, Walter Fisher, Huntley Schaller, and Haakon Solheim. 1. Hans-Werner Sinn, Handelsblatt, November 6, 2000, Financial Times, April 4, 2001, and Su¨ddeutsche Zeitung, April 6, 2000. See also Paul Krugman’s comment on Sinn in New York Times, April 1, 2001, and Bundesbank Gescha¨ftsbericht of April 4, 2001. 2. Alternative explanations can be found in Alquist and Chinn (2002) and Corsetti (2000). 3. Economist, June 5, 1999, p. 13; April 20, 2000, pp. 25–26. Der Spiegel, October 2000, ‘‘Interner Bericht des Finanzministeriums fordert tiefgreifende Reformen zur Stabilisierung des Euro.’’ 4. Economist, June 5, 1999, p. 14. 5. ECB, Monthly Bulletin, June 1999, p. 39. 6. Ibid. 7. Ibid. 8. Der Spiegel, online, Interview with Karl Otto Po¨hl, June 19, 2000. 9. ‘‘Interner Bericht des Finanzministeriums . . . ,’’ ibid. See also ‘‘Prospects for sustained growth in the Euro area,’’ ch. 2, European Economy, vol. 71, 2000. Ofﬁce for Ofﬁcial Publications of the EC, Luxembourg, pp. 62–67. 10. The literature ranges from Branson (1977), Branson, Halttunen, and Masson (1977), Branson and Henderson (1985), Girton and Henderson (1976), and Henderson (1980) to Dooley and Isaard (1982), Sinn (1983a), MacDonald and Taylor (1992), and Mann and Meade (2002), to mention only a few of the relevant papers. For a description of current research and further references, see Isaard (1995). 11. The ofﬁcially measured savings rate does not include capital gains. This is not a problem in the present context where the savers’ willingness to absorb assets offered in the capital market is concerned. 12. See note 8. 13. We also formulated a more elaborate model distinguishing, among other things, between American and European investors, but the more parsimonious model presented here is sufﬁcient for the points we wish to make. 14. An increase in the portfolio volume will not affect share prices, interest rates, and the exchange rate if preferences are homothetic and growth does not change the actual portfolio structure. For simplicity we assume that this is the case.

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15. This is the general structure of a multi-period stochastic portfolio decision problem. See Sinn (1983b) for a more extensive elaboration on this problem. Here we cut things short by considering one period only and simplifying the utility function. 16. See Fried and Howitt (1983) for a discussion of the potential liquidity services and a formulation along these lines. 17. Equation (12) speciﬁes the interest rates rather than the exchange rates when the respective asset stocks are given and the ECB does not intervene. According to (3) and (6), in equilibrium the interest rates on American and European bonds have to adjust such that they complement the marginal liquidity services of bonds to generate the required overall return factor l. This then automatically satisﬁes the interest parity condition without giving equation (12) much explanatory power for the determination of the exchange rate. When central banks intervene passively to ﬁx the interest rates, the explanatory power increases. Although (12) refers to the spot rate e, it can also be used to determine the forward rate e~f by way of the covered interest parity condition ~e f ¼ e ð1 þ i Þ=ð1 þ iÞ. The forward rate is not the same as the expected future spot rate. The relationship between these rates is found by substituting (12) into the preceding equation: e~f ¼ e~

1 þ bUB =ð1 þ iÞ : 1 þ b UB =ð1 þ i Þ

This expression shows that a reduced preference for euro currency combined with the adjustment to the interest rate reduces the euro’s forward rate relative to its expected future spot rate without affecting the forward premium or the swap rate. 18. In practice, the interventions by the ECB involved the sale of US treasury bonds, which required the Fed to react with an expansionary open market policy increasing the money supply so as to avoid an increase in the US interest rate. 19. It should be noted that the positive correlation between the stock of money balances and the foreign exchange value of this money that the currency hypothesis predicts refers to high-powered base money (M0) rather than broader money aggregates. There are two reasons why an extension of the argument to M1, M2, or M3 is not possible. First, demand, savings, and time deposits may be implicitly or explicitly interest bearing and may therefore classify as part of B rather than M in our model. Second, even if demand deposits and cash are considered as close substitutes by the public, M1 may not be positively correlated with M0. Suppose that the demand for euro cash declines. In that case, the cash will return to the banks in exchange for demand deposits. The money multiplier will increase and induce the banks to expand M1 by giving out more loans to their clients. This will contribute to the decline in the marginal utility of money and the downward effects on the exchange rate and the interest rate. Thus, before and without passive intervention by the ECB, there is a negative correlation between M1 and the exchange rate and none between M0 and the exchange rate. If the ECB intervenes to reestablish the targeted interest level, it can only partly offset the exchange rate effect, and it reduces M0 as was shown above. However, the net effect on M1 will be unclear. Indeed, M1 remained remarkably stable during the collapse of euro base money in the years before currency conversion. 20. See also chapter 1 by Evans and Lyons in this volume. 21. For analyses of this episode see Eichengreen and Wyplosz (1993), De Grauwe (1994), and Sinn (1999).

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22. No less than 60 percent of the US monetary base is said to circulate outside the United States (see Porter and Judson 1996). The outstanding deutschmarks were a source of a signiﬁcant seignorage proﬁt made by the Bundesbank, as was calculated by Sinn and Feist (1997, 2000). When the euro was introduced, the deutschmark constituted a much larger fraction of the euro-11 monetary base than the share in the ECB proﬁt remittances, which was only 31 percent, according to the average of Germany’s GDP and population shares. Sinn and Feist calculated that this implied a seignorage loss which was equivalent to a one-off capital levy of nearly 60 billion DM or 30 billion @ on the German Bundesbank. 23. It is also possible that some of the decline was due to other, more technical, reasons such as the ordinary citizen’s attempt to minimize the stock of money balances at the time of currency conversion. However, all countries would have been affected in proportion to their GDP size. In this case the idiosynchratic component of the reduction in money demand applied to Germany was on the order of 75 billion @. Note that our estimates of the composition of the decline in money balances have only an informative character. None of our arguments for why a decline in money balances reduces the exchange value depends on the causes of this decline. 24. See, in particular, the articles in Handelsblatt and Financial Times published in 2000, as cited in note 1, as well as Sinn and Westermann (2001). 25. All series are nonstationary in levels and stationary in ﬁrst differences. We let xt be a 5 1 vector containing the variables fe; ln M–ln M ; ln i–ln i ; ln B–ln B ; ln P–ln P g. The Johansen test statistics are devised from the sample canonical correlations (Anderson 1958; Marinell 1995) between Dxt and xtp , where t is time and p denotes the lag length, adjusting for all intervening lags. To implement the procedure, we ﬁrst obtain the least squares residuals from Dxt ¼ m1 þ

p1 X

Gj Dxtj þ e1t ;

j¼1

xtp ¼ m2 þ

p1 X

Gj Dxtj þ e2t ;

j¼1

where m1 and m2 are constant vectors, G is a matrix of parameters, and e1 amd e2 are vectors of the error terms. The lag parameter p is identiﬁed by the Akaike information criterion. Next, we compute the eigenvalues, l1 b b ln , of W21 W1 11 W12 with respect to W22 and the associated eigenvectors, n1 ; . . . ; nn , where the moment matrices Wlm ¼ T 1

X

e^t e^t0

t

for l; m ¼ 1; 2, and n is the dimension of xt (i.e., n ¼ 5 in this exercise). l1 . . . ln are the squared canonical correlations between Dxt and xtp , adjusting for all intervening lags. The trace statistic, tr ¼ T

n X

lnð1 lj Þ;

j¼rþ1

where 0 a r a n, tests the hypothesis that there are at most r cointegration vectors. The eigenvectors, n1 ; . . . ; nr are sample estimates of the co-integration vectors. 26. Speciﬁcally, the changes in each of the ﬁve variables are modeled using Dxt ¼ Pp m þ j¼1 Gj Dxtj þ aect1 þ et , where ect is the error correction term.

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References Alquist, R., and M. D. Chinn. 2001. Tracking the euro’s progress. International Finance 3: 357–74. Alquist, R., and M. D. Chinn. 2002. Productivity and the euro–dollar exchange rate puzzle. NBER Working Paper 8824. Branson, W. H. 1977. Asset markets and relative prices in exchange rate determination. Sozialwissenschaftliche Annalen des Institutes fu¨r Ho¨here Studien, Vienna, A, 1: 69–89. Branson, W. H., H. Halttunen, and P. Masson. 1977. Exchange rates in the short run: The dollar–deutschmark rate. European Economic Review 10: 303–24. Branson, W. H., and D. Handerson. 1985. The speciﬁcation and inﬂuence of asset markets. In R. Jones and P. Kenen, eds., Handbook of International Economics, vol. 2. Amsterdam: North-Holland. Corsetti, G. 2000. A perspective on the euro. CESifo Forum 2(2): 32–36. De Grauwe, P. 1994. Towards EMU without EMS. Economic Policy 18: 147–85. De Grauwe, P. 2000. The euro in search of fundamentals. Paper presented at the CESifo conference on Issues of Monetary Integration in Europe. December 2000. Dooley, M. P., and P. Isard. 1982. A portfolio balance rational expectations model of the dollar–mark exchange rate. Journal of International Economics 12: 257–76. Dooley, M. P., J. Frankel, and D. Mathieson. 1997. International capital mobility: What do saving-investment correlations tell us? IMF Staff Papers 34: 503–30. Evans, M. D., and R. K. Lyons. 2001. Order ﬂow and exchange rate dynamics. Journal of Political Economy 110: 170–80. Evans, M. D., and R. K. Lyons. 2001. Portfolio balance, price impact and sterilized intervention. NBER Working Paper 7317. Evans, M. D. D., and R. K. Lyons. 2002. Are different currency assets imperfect substitutes? CESifo, Venice Summer Institute 2001. Workshop on Exchange Rate Modelling. Venice International University, San Servolo, July 13–14, 2002. Eichengreen,. B., and Ch. Wyplosz. 1993. The unstable EMS. Brookings Papers on Economic Activity 1: 51–143. Feldstein, M., and C. Horioka. 1980. Domestic saving and international capital ﬂows. Economic Journal 90: 314–29. Frankel, J. A. 1982. The mystery of the multiplying marks: A modiﬁcation of the monetary model. Review of Economics and Statistics 64: 515–19. Frankel, J. A. 1993. Monetary and portfolio-balance models of exchange rates. In J. A. Frankel, ed., On Exchange Rates. Cambridge: MIT Press, pp. 95–115. Fried, J., and P. Howitt. 1983. The effects of inﬂation on real interest rates. American Economic Review 73(5): 968–80. Girton, L., and D. W. Henderson. 1976. Financial capital movements and central bank behavior in a two-country, short-run portfolio balance. Journal of Monetary Economics 76: 33–61.

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Henderson, D. W. 1980. The dynamic effects of exchange market intervention: Two extreme views and a synthesis. In H. Frisch and G. Schwo¨diauer, eds., The Economics of Flexible Exchange Rates. Supplement to Kredit und Kapital 6: 156–209. Isard, P. 1995. Exchange Rate Economics. Cambridge: Cambridge University Press. MacDonald, R., and M. P. Taylor. 1993. The monetary approach to the exchange rate: Rational expectations, long-run equilibrium and forecasting. IMF Staff Papers 40: 89–107. Mann, C., and E. E. Meade. 2002. Home bias, transactions costs, and prospects for the euro: A more detailed analysis. Institute for International Economics Working Paper 02-3. Meese, R. A., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Padoa-Schioppa, T. 2002. The euro goes east. Lecture at the 8th Dubrovnik Economic Conference. June 29, 2002. Porter, R., and R. Judson. 1996. The location of US currency: How much is abroad? Federal Reserve Bulletin 82: 883–903. Schneider, F., and D. H. Ernste. 2000. Shadow economies: size, causes, and consequences. Journal of Economic Literature 38: 77–114. Seitz, F. 1995. Der DM-Umlauf im Ausland. Volkswirtschaftliche Forschungsgruppe der Deutschen Bundesbank. Bundesbank Diskussionspapier 1/95. Sinn, H.-W. 1983a. International capital movements, ﬂexible exchange rates, and the IS-LM model: A comparison between the portfolio-balance and the ﬂow hypotheses. Weltwirtschaftliches Archiv 119: 36–63. Sinn, H.-W. 1983b. Economic Decisions under Uncertainty. Amsterdam: North-Holland. Sinn, H.-W. 1999. International implications of German uniﬁcation. In A. Razin and E. Sadka, eds., The Economics of Globalization. Cambridge: Cambridge University Press, pp. 33–58. Sinn, H.-W., and H. Feist. 1997. Eurowinners and eurolosers: The distribution of seignorage wealth in EMU. European Journal of Political Economy 13: 665–89. Sinn, H.-W., and H. Feist. 2000. Seignorage wealth in the eurosystem: Eurowinners and eurolosers revisited. CESifo Discussion Paper 353. Sinn, H.-W., and F. Westermann. 2001. Why has the euro been falling? An investigation into the determinants of the exchange rate. NBER Working Paper 8352, CESifo Working Paper 493. Stix, H. 2001. Survey results about foreign currency holdings in ﬁve central and eastern European countries: A note. CESifo Forum 2(3): 41–48. Taylor, M. P. 1995. The economics of exchange rates. Journal of Economic Literature 33: 13– 47.

8

What Do We Know about Recent Exchange Rate Models? In-Sample Fit and Out-of-Sample Performance Evaluated Yin-Wong Cheung, Menzie D. Chinn, and Antonio Garcia Pascual

In contrast to the intellectual ferment that followed the collapse of the Bretton Woods era, the 1990s were marked by a relative paucity of new empirical models of exchange rates. The sticky-price monetary model of Dornbusch and Frankel remained the workhorse of policyoriented analyses of exchange rate ﬂuctuations among the developed economies. However, while no completely new models were developed, several approaches gained increased prominence. Some of these approaches were inspired by new empirical ﬁndings, such as the correlation between net foreign asset positions and real exchange rates. Others, such as those based on productivity differences, were grounded in an older theoretical literature but given new respectability by the new international macroeconomics (Obstfeld and Rogoff 1996) literature. None of the empirical models, however, were subjected to rigorous examination of the sort that Frankel (1979) and Meese and Rogoff (1983a, b) conducted in their seminal works. Consequently, instead of re-examining the usual suspects—the ﬂexible price monetary model, purchasing power parity, and the interest differential1 —we vary the set of performance criteria and expand the set to include the mean squared error, and the direction-of-change statistic. The later dimension is potentially more important from a market timing perspective, besides serving as another indicator of forecast attributes. To summarize, in this study, we compare exchange rate models along several dimensions: Four models are compared against the random walk. Only one of the structural models—the benchmark sticky-price monetary model of Dornbusch and Frankel—has been the subject of previous systematic

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analyses. The other models include one incorporating productivity differentials in a fashion consistent with a Balassa-Samuelson formulation, an interest rate parity speciﬁcation, and a representative behavioral equilibrium exchange rate model. The behavior of US dollar-based exchange rates of the Canadian dollar, British pound, German mark, Swiss franc, and Japanese yen are examined. We also examine the corresponding yen-based rates to ensure that our conclusions are not driven by dollar speciﬁc results.

The models are estimated in two ways: in ﬁrst-difference and error correction speciﬁcations.

In sample ﬁt is assessed in terms of how well the coefﬁcient estimates conform to theoretical priors.

Forecasting performance is evaluated at several horizons (1-, 4and 20-quarter horizons), for a recent period not previously examined (post-1992).

We augment the conventional metrics with a direction-of-change statistic and the ‘‘consistency’’ criterion of Cheung and Chinn (1998).

In accordance with previous studies, we ﬁnd that no model consistently outperforms a random walk according to the mean squared error criterion at short horizons. However, at the longest horizon we ﬁnd that the proportion of times the structural models incorporating long-run relationships outperform a random walk is more than would be expected if the outcomes were merely random. Using a 10 percent signiﬁcance level, a random walk is outperformed 17 percent of the time along a MSE dimension and 27 percent along a direction of change dimension. In terms of the ‘‘consistency’’ test of Cheung and Chinn (1998), we obtain slightly less positive results. The actual and forecasted rates are cointegrated more often than would occur by chance for all the models. While in many of these cases of cointegration, the condition of unitary elasticity of expectations is rejected; only about 5 percent fulﬁll all the conditions of the consistency criteria. We conclude that the question of exchange rate predictability remains unresolved. In particular, while the oft-used mean squared error criterion provides a dismal perspective, criteria other than the conventional ones suggest that structural exchange rate models have some usefulness. Furthermore, structural models incorporating restrictions at long horizons tend to outperform random walk speciﬁcations.

In-Sample Fit and Out-of-Sample Performance Evaluated

8.1

241

Theoretical Models

The universe of empirical models that have been examined over the ﬂoating rate period is enormous. Consequently any evaluation of these models must necessarily be selective. The models we have selected are prominent in the economic and policy literature, and readily implementable and replicable. To our knowledge, with the exception of the sticky-price model, they have also not previously been evaluated in a systematic fashion. We use the random walk model as our benchmark naive model, in line with previous work, but we also select one model—the Dornbusch (1976) and Frankel (1979) model—as a representative of the 1970s vintage models. The sticky-price monetary model can be expressed as follows: ^ t þ b2 y^t þ b 3 ^it þ b4 p^t þ ut ; st ¼ b 0 þ b 1 m

ð1Þ

where s is exchange rate in log, m is log money, y is log real GDP, i and p are the interest and inﬂation rate, respectively, the caret (^) denotes the intercountry difference, and ut is an error term. The characteristics of this model are well known, so we will not devote time to discuss the theory behind the equation. We will observe, however, that the list of variables included in (1) encompasses those employed in the ﬂexible price version of the monetary model, as well as the micro-based general equilibrium models of Stockman (1980) and Lucas (1982). Second, we assess models that are in the Balassa-Samuelson vein, in that they accord a central role to productivity differentials in explaining movements in real, and hence also nominal, exchange rates (see Chinn 1997). Such models drop the purchasing power parity assumption for broad price indexes and allow the real exchange rate to depend on the relative price of nontradables, itself a function of productivity ðzÞ differentials. A generic productivity differential exchange rate equation is ^ þ b2 y^ þ b3 ^i þ b 5^zt þ ut : st ¼ b 0 þ b 1 m

ð2Þ

The third set of models we examine we term the ‘‘behavioral equilibrium exchange rate’’ (BEER) approach. We investigate this model as a proxy for a diverse set of models that incorporate a number of familiar relationships. A typical speciﬁcation is ^ t þ b 7 ^rt þ b 8 g^debtt þ b9 tott þ b10 nfat þ ut ; st ¼ b0 þ p^t þ b6 o

ð3Þ

242

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

where p is the log price level (CPI), o is the relative price of nontradables, r is the real interest rate, gdebt is the government debt to GDP ratio, tot is the log terms of trade, and nfa is the net foreign asset ratio. A unitary coefﬁcient is imposed on p^t . This speciﬁcation can be thought of as incorporating the Balassa-Samuelson effect, the real interest differential model, an exchange risk premium associated with government debt stocks, and additional portfolio balance effects arising from the net foreign asset position of the economy.2 Evaluation of this model can shed light on a number of very closely related approaches, including the macroeconomic framework of the IMF (Isard et al. 2001) and Stein’s NATREX (Stein 1999). The empirical determinants in both approaches overlap with those of the speciﬁcation in equation (3). Models based on this framework have been the predominant approach to determining the level at which currencies will gravitate to over some intermediate horizon, especially in the context of policy issues. For instance, the behavioral equilibrium exchange rate approach is the model that is most used to determine the long-term value of the euro. The ﬁnal speciﬁcation assessed is not a model per se; rather it is an arbitrage relationship—uncovered interest rate parity: stþk st ¼ ^it; k ;

ð4Þ

where ^it; k is the interest rate of maturity k. Unlike the other speciﬁcations, this relation does not need to be estimated in order to generate predictions. Interest rate parity at long horizons has recently gathered empirical support (Alexius 2001; Chinn and Meredith 2002), in contrast to the disappointing results at the shorter horizons. MacDonald and Nagayasu (2000) have also demonstrated that long-run interest rates can predict exchange rate levels. On the basis of these ﬁndings, we anticipate that this speciﬁcation will perform better at the longer horizons than at the shorter.3 8.2 8.2.1

Data and Full-Sample Estimation Data

The analysis uses quarterly data for the United States, Canada, the United Kingdom, Japan, Germany, and Switzerland over the 1973:2 to

In-Sample Fit and Out-of-Sample Performance Evaluated

243

Figure 8.1 German mark–US dollar exchange rate

2000:4 period. The exchange rate, money, price and income variables are drawn primarily from the IMF’s International Financial Statistics. The productivity data were obtained from the Bank for International Settlements, while the interest rates used to conduct the interest rate parity forecasts are essentially the same as those used in Chinn and Meredith (2002). See appendix A for a more detailed description. The out-of-sample period used to assess model performance is 1993:1 to 2000:4. Figures 8.1 and 8.2 depict, respectively, the dollar based German mark and yen exchange rates, with the vertical line indicating the beginning of the out-of-sample period. The out-ofsample period spans a period of dollar depreciation and then sustained appreciation.4 8.2.2

Full-Sample Estimation

Two speciﬁcations of the theoretical models were estimated: (1) an error correction speciﬁcation, and (2) a ﬁrst-differences speciﬁcation. Since implementation of the error correction speciﬁcation is relatively involved, we will address the ﬁrst-difference speciﬁcation to begin

244

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Figure 8.2 Japanese yen–US dollar exchange rate

with. Consider the general expression for the relationship between the exchange rate and fundamentals: st ¼ Xt G þ ut ;

ð5Þ

where Xt is a vector of fundamental variables under consideration. The ﬁrst-difference speciﬁcation involves the following regression: Dst ¼ DXt G þ ut :

ð6Þ

These estimates are then used to generate forecasts one and many quarters ahead. Since these exchange rate models imply joint determination of all variables in the equations, it makes sense to apply instrumental variables. However, previous experience indicates that the gains in consistency are far outweighed by the loss in efﬁciency, in terms of prediction (Chinn and Meese 1995). Hence we rely solely on OLS. One exception to this general rule is the UIP model. In this case the arbitrage condition implies a relationship between the change in the exchange rate and the level of the interest rate differential. Since no long-run condition is implied, we simply estimate the UIP relationship as stated in equation (4).

In-Sample Fit and Out-of-Sample Performance Evaluated

8.2.3

245

Empirical Results

The results of estimating the sticky-price monetary model in levels are presented in panel A of table 8.1. Using the 5 percent asymptotic critical value, we ﬁnd that there is evidence of cointegration for the dollarbased exchange rates for all currencies save one. The German mark stands out as a case where it is difﬁcult to obtain evidence of cointegration; we suspect that this is largely because of the breaks in the series for both money and income associated with the German reuniﬁcation. The evidence for cointegration is more attenuated when the ﬁnite sample critical values (Cheung and Lai 1993) are used. Then only the Canadian dollar and yen have some mixed evidence in favor of cointegration. This ambiguity is useful to recall when evaluating the estimates for the British sterling; the coefﬁcient estimates do not conform to those theoretically implied by the model, as the coefﬁcients of money, inﬂation and income are all incorrectly signed (although the latter two are insigniﬁcantly so). Only the interest rate coefﬁcient is signiﬁcant and correctly signed. In contrast, both the yen and franc broadly conform to the monetary model. Money and inﬂation are correctly signed, while interest rates enter in correctly only for the yen. Finally, the Canadian dollar presents some interesting results. The coefﬁcients are largely in line with the monetary model, although the income coefﬁcient is wrongly signed, with economic and statistical signiﬁcance. The use of the ﬁrst-difference speciﬁcation is justiﬁed when there is a failure to ﬁnd evidence of cointegration (the German mark), or alternatively one suspects that estimates of the long-run coefﬁcients are insufﬁciently precisely estimated to yield useful estimates. In panel B of table 8.1, the results from the ﬁrst-difference speciﬁcation are reported. A general ﬁnding is that the coefﬁcients do not typically enter with both statistical signiﬁcance and correct sign. One partial exception is the interest differential coefﬁcient. Higher interest rates, if all else constant is held constant, appear to appreciate the currency in four of ﬁve cases, although the yen–dollar rate estimate is not statistically signiﬁcant. The British sterling–dollar rate estimate is positive (while the inﬂation rate coefﬁcient is not statistically signiﬁcant), a ﬁnding that is more consistent with a ﬂexible price monetary model than a stickyprice one. Otherwise, the ﬁt does not appear particularly good. These mixed results are suggestive of alternative approaches; the ﬁrst we examine is the productivity-based model. Our interpretation

246

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.1 Full-sample estimates of sticky-price model Sign

BP/$

Can$/$

DM/$

SF/$

Yen/$

A. In levels a Cointegration (asy)

1, 1

3, 1

0, 0

1, 1

1, 1

Cointegration (fs)

0, 0

1, 0

0, 0

0, 0

0, 1

Money

[þ]

Income

[]

Interest rate

[]

Inﬂation rate B. In ﬁrst differences

[þ]

2.89*

1.10*

2.14*

3.61*

1.29

(1.01)

(0.25)

(0.74)

(0.74)

(0.96)

9.70*

0.93

(1.87)

(1.87)

19.49*

6.44*

(4.01)

(3.27)

(4.14)

(5.73)

(4.72)

7.11

10.74*

24.29*

40.96*

26.56*

(4.60)

(3.11)

(4.27)

(6.79)

(4.03)

0.16 (0.22)

0.02 (0.14)

0.44 (0.24)

[þ]

0.21 (0.12)

0.00 (0.06)

Income

[]

2.02*

0.48

Inﬂation rate

5.86

(1.72) 2.09

0.77 (1.97) 17.11*

b

Money

Interest rate

1.10

1.64 (3.94)

[] [þ]

0.51

0.59

(0.42)

(0.29)

(0.43)

(0.52)

0.83*

0.42*

0.91*

0.82*

(0.41)

(0.10)

(0.45)

(0.37)

0.15 (0.48)

0.07 (0.20)

0.00 (0.39) 0.28 (0.33)

1.26

1.29

0.32

(1.09)

(0.81)

(0.44)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes two lags of ﬁrst differences. The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

In-Sample Fit and Out-of-Sample Performance Evaluated

247

of the model simply augments the monetary model with a productivity variable. The results for this model are presented in table 8.2. From the asymptotic critical values, the evidence of cointegration in panel A of table 8.2 is comparable to that reported in panel A of table 8.1. For both the British sterling and Canadian dollar, there is evidence of multiple cointegrating vectors. However, in using the ﬁnite sample critical values, we ﬁnd that the number of implied vectors drops to one (or zero) in this case. In all cases the interest coefﬁcient is correctly signed, and signiﬁcant in most cases. Furthermore the money and inﬂation variables are correctly signed in most cases. The productivity coefﬁcients are signiﬁcant and consistent with the productivity in three cases—the Swiss franc, German mark, and yen. The latter two currencies have previously been found to be inﬂuenced by productivity trends.5 Estimates of the ﬁrst-difference speciﬁcations do not yield appreciably better results than their sticky-price counterparts. Interest differentials tend to be important, once again, while productivity fails to evidence any signiﬁcant impact for three of ﬁve rates. To the extent that one thinks that productivity is a slowly trending variable that inﬂuences the real exchange rate over long periods, this result is unsurprising. While this variable has the correct sign for the German mark– dollar rate, it has the opposite for the sterling–dollar rate. The Canadian dollar appears to be as resilient to being modeled using this productivity speciﬁcation as the others. Chen and Rogoff (2002) have asserted that the Canadian dollar is mostly determined by commodity prices; hence it is not surprising that both models fail to have any predictive content. The BEER model results are presented in table 8.3. There are no estimates for the Swiss franc and the yen because we lack quarterly data on government debt and net foreign assets. Overall, the results are not uniformly supportive of the BEER approach.6 Although there are some instances of correctly signed coefﬁcients, none show up correctly signed across all three currencies. Moving to a ﬁrst-difference speciﬁcation does not improve the results. Besides those on the relative price and real interest rate differentials, very few coefﬁcient estimates are in line with model predictions. For the DM/$ rate, the real interest rate and debt variables possess the correctly signed coefﬁcients, as do the relative price and net foreign assets for the Canadian dollar, but these appear to be isolated instances.7

248

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.2 Full-sample estimates of productivity model Sign

BP/$

Can$/$

DM/$

SF/$

Yen/$

Cointegration (asy)

1, 2

2, 2

0, 0

1, 1

1, 1

Cointegration (fs)

0, 0

1, 0

0, 0

0, 0

0, 1

A. In levels a

Money Income Interest rate Inﬂation rate Productivity

[þ] [] [] [þ] []

0.97*

6.81*

0.62*

2.00*

0.18

(0.47)

(1.45)

(0.33)

(0.30)

(0.54)

4.11*

25.76*

0.68

(1.23)

(6.62)

(0.81)

10.63*

34.53*

9.35*

3.67

(1.65)

(11.16)

(2.57)

(2.54)

(2.67)

9.86*

70.63*

9.18*

15.36*

12.09*

(1.63)

(12.00)

(1.85)

2.79

(2.49)

3.56* (0.68)

16.78* (5.60)

5.66* (1.11)

4.43* (1.46)

2.65* (0.76)

0.16

0.01

1.04 (0.76)

2.77* (1.29) 12.07*

B. In ﬁrst differences b Money

[þ]

0.40* (0.16)

Income

[]

1.59* (0.39)

Interest rate

[]

0.57 (0.46)

Inﬂation rate

[þ]

1.10* (0.50)

Productivity

[]

1.11* (0.21)

0.00 (0.06) 0.47

(0.22) 0.51

(0.14)

0.43 (0.24)

0.70

0.00

(0.29)

(0.43)

(0.51)

(0.40)

0.42*

0.91*

0.82*

(0.10)

(0.45)

(0.41)

1.26

1.19

0.37

(1.09)

(0.81)

(0.45)

5.66*

0.25

0.32

(1.11)

(0.21)

(0.31)

0.08 (0.20) 0.03 (0.15)

0.28 (0.32)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes two lags of ﬁrst differences. The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

In-Sample Fit and Out-of-Sample Performance Evaluated

249

Table 8.3 Full-sample estimates of BEER model Sign

BP/$

Can$/$

DM/$

Cointegration (asy)

2, 2

4, 2

1, 1

Cointegration (fs)

1, 2

2, 1

0, 0 9.38*

A. In levels a

Relative price Real interest rate Debt Terms of trade Net foreign assets

[] [] [þ] [] []

1.27*

1.05*

(0.38)

(0.34)

3.13*

2.03*

(1.07)

(0.91)

1.06*

2.62*

0.04

(0.30)

(0.51)

(0.72)

0.92

0.75*

(1.36) 2.37 (2.09)

0.13

(0.82)

(0.24)

(1.04)

5.65* (0.56)

1.39* (0.40)

4.88* (0.76)

0.44*

0.38

B. In ﬁrst differences b Relative price

[]

0.55 (0.56)

Real interest rate

[]

0.17 (0.16)

Debt

[þ]

0.38 (0.27)

Terms of trade Net foreign assets

[] []

(0.17)

(0.59)

0.15

1.04*

(0.11)

(0.34)

0.18

1.52*

(0.22)

(0.64)

0.09

0.02

0.59*

(0.31)

(0.06)

(0.27)

2.61*

1.19*

3.14*

(0.49)

(0.25)

(0.72)

Note: ‘‘Sign’’ indicates coefﬁcient sign implied by theoretical model. * indicates signiﬁcantly different from zero at the 5% marginal signiﬁcance level. Estimates for DM include shift and impulse dummies for German monetary and economic uniﬁcation. a. Long-run cointegrating estimates from Johansen procedure (standard errors in parentheses), where the VECM includes 2 lags of ﬁrst differences (4 lags for DM). The number of cointegrating vectors is implied by the trace and maximal eigenvalue statistics, using the 5% marginal signiﬁcance level; ‘‘asy’’ denotes asymptotic critical values and ‘‘fs’’ denotes ﬁnite sample critical values of Cheung and Lai (1993) that are used. b. OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ 4).

250

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Table 8.4 Uncovered interest parity estimates BP/$

Can$/$

DM/$

SF/$

Yen/$

2.19*

0.48*

0.70

1.28*

2.99*

(1.08)

(0.51)

(1.04)

(0.96)

Horizon 3 month

(1.09)

Adj R 2

0.04

0.00

0.01

0.01

0.06

SER

0.21

0.08

0.26

0.29

0.28

1.42* (0.99)

0.61* (0.49)

0.58* (0.66)

1.05* (0.52)

2.60* (0.69)

1 year Adj R 2

0.06

0.03

0.00

0.04

0.17

SER

0.11

0.04

0.14

0.14

0.13

5 year

0.44

0.24

0.52

1.18*

1.19

(0.36)

(0.47)

(0.75)

(0.97)

(0.38)

Adj R 2

0.02

0.00

0.02

0.04

0.13

SER

0.04

0.02

0.06

0.04

0.05

Note: OLS estimates (Newey-West standard errors in parentheses, truncation lag ¼ k 1). SER is standard error of regression. * indicates signiﬁcantly different from unity at the 5 percent marginal signiﬁcance level.

Although we do not use estimated equations to conduct the forecasting of the UIP model, it is informative to consider how well the data conform to the UIP relationship. As is well known, at short horizons, the evidence in favor of UIP is lacking.8 The results of estimating equation (4) are reported in table 8.4. Consistent with Chinn and Meredith (2002), the short-horizon data (1 quarter and 4 quarter maturities) provide almost uniformly negative coefﬁcient estimates, in contradiction to the implication of the UIP hypothesis. At the ﬁve-year horizon, the results are substantially different for all cases, save the Swiss franc. Now all the coefﬁcients are positive; moreover in no case except the franc is the coefﬁcient estimate signiﬁcantly different from the theoretically implied value of unity. 8.3 8.3.1

Forecast Comparison Estimation and Forecasting

We adopt the convention in the empirical exchange rate modeling literature of implementing ‘‘rolling regressions.’’ That is, estimates are applied over a given data sample, out-of-sample forecasts produced,

In-Sample Fit and Out-of-Sample Performance Evaluated

251

then the sample is moved up, or ‘‘rolled’’ forward one observation before the procedure is repeated. This process continues until all the out-of-sample observations are exhausted. This procedure is selected over recursive estimation because it is more in line with previous work, including the original Meese and Rogoff paper. Moreover the power of the test is kept constant as the sample size over which the estimation occurs is ﬁxed, rather than increasing as it does in the recursive framework. The error correction estimation involves a two-step procedure. In the ﬁrst step, the long-run cointegrating relation implied by (5) is identiﬁed using the Johansen procedure, as described in section 8.2. The esti~ Þ is incorporated into the error correction mated cointegrating vector ðG term, and the resulting equation ~ Þ þ ut st stk ¼ d0 þ d1 ðstk Xtk G

ð7Þ

is estimated via OLS. Equation (7) can be thought of as an error correction model stripped of the short-run dynamics. A similar approach was used in Mark (1995) and Chinn and Meese (1995), except for the fact that, in those two cases, the cointegrating vector was imposed a priori. One key difference between our implementation of the error correction speciﬁcation and that undertaken in some other studies involves the treatment of the cointegrating vector. In some other prominent studies (MacDonald and Taylor 1994) the cointegrating relationship is estimated over the entire sample, and then out-of-sample forecasting undertaken, where the short-run dynamics are treated as time varying but the long-run relationship is not. While there are good reasons for adopting this approach—in particular, one wants to use as much information as possible to obtain estimates of the cointegrating relationships—the asymmetry in the estimation approach is troublesome, and makes it difﬁcult to distinguish quasi–ex ante forecasts from true ex ante forecasts. Consequently our estimates of the longrun cointegrating relationship vary as the data window moves. It is also useful to stress the difference between the error correction speciﬁcation forecasts and the ﬁrst-difference speciﬁcation forecasts. In the latter, ex post values of the right-hand side variables are used to generate the predicted exchange rate change. In the former, contemporaneous values of the right-hand side variables are not necessary, and the error correction predictions are true ex ante forecasts. Hence we

252

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

are affording the ﬁrst-difference speciﬁcations a tremendous informational advantage in forecasting.9 8.3.2

Forecast Comparison

To evaluate the forecasting accuracy of the different structural models, the ratio between the mean squared error (MSE) of the structural models and a driftless random walk is used. A value smaller (larger) than one indicates a better performance of the structural model (random walk). We also explicitly test the null hypothesis of no difference in the accuracy of the two competing forecasts (structural model vs. driftless random walk). In particular, we use the Diebold-Mariano statistic (Diebold and Mariano 1995), which is deﬁned as the ratio between the sample mean loss differential and an estimate of its standard error; this ratio is asymptotically distributed as a standard normal.10 The loss differential is deﬁned as the difference between the squared forecast error of the structural models and that of the random walk. A consistent estimate of the standard deviation can be constructed from a weighted sum of the available sample autocovariances of the loss differential vector. Following Andrews (1991), a quadratic spectral kernel is employed, together with a data-dependent bandwidth selection procedure.11 We also examine the predictive power of the various models along different dimensions. One might be tempted to conclude that we are merely changing the well-established ‘‘rules of the game’’ by doing so. However, there are very good reasons to use other evaluation criteria. First, there is the intuitively appealing rationale that minimizing the mean squared error (or relatedly mean absolute error) may not be important from an economic standpoint. A less pedestrian motivation is that the typical mean squared error criterion may miss out on important aspects of predictions, especially at long horizons. Christoffersen and Diebold (1998) point out that the standard mean squared error criterion indicates no improvement of predictions that take into account cointegrating relationships vis a` vis univariate predictions. But surely any reasonable criteria would put some weight on the tendency for predictions from cointegrated systems to ‘‘hang together.’’ Hence, our ﬁrst alternative evaluation metric for the relative forecast performance of the structural models is the direction-of-change statistic, which is computed as the number of correct predictions of the direction of change over the total number of predictions. A value above

In-Sample Fit and Out-of-Sample Performance Evaluated

253

(below) 50 percent indicates a better (worse) forecasting performance than a naive model that predicts the exchange rate has an equal chance to go up or down. Again, Diebold and Mariano (1995) provide a test statistic for the null of no forecasting performance of the structural model. The statistic follows a binomial distribution, and its studentized version is asymptotically distributed as a standard normal. Not only does the direction-of-change statistic constitute an alternative metric, it is also an approximate measure of proﬁtability. We have in mind here tests for market-timing ability (Cumby and Modest 1987).12 The third metric we used to evaluate forecast performance is the consistency criterion proposed in Cheung and Chinn (1998). This metric focuses on the time series properties of the forecast. The forecast of a given spot exchange rate is labeled as consistent if (1) the two series have the same order of integration, (2) they are cointegrated, and (3) the cointegration vector satisﬁes the unitary elasticity of expectations condition. Loosely speaking, a forecast is consistent if it moves in tandem with the spot exchange rate in the long run. Cheung and Chinn (1998) provide a more detailed discussion on the consistency criterion and its implementation. 8.4 8.4.1

Comparing the Forecast Performance The MSE Criterion

The comparison of forecasting performance based on MSE ratios is summarized in table 8.5. The table contains MSE ratios and the pvalues from ﬁve dollar-based currency pairs, four structural models, the error correction and ﬁrst-difference speciﬁcations, and three forecasting horizons. Every cell in the table has two entries. The ﬁrst one is the MSE ratio (the MSEs of a structural model to the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value of the hypothesis that the MSEs of the structural and random walk models are the same. Because of the lack of data, the behavioral equilibrium exchange rate model is not estimated for the dollar–Swiss franc, dollar–yen exchange rates, and all yen-based exchange rates. Altogether there are 153 MSE ratios. Of these 153 ratios, 90 are computed from the error correction speciﬁcation and 63 from the ﬁrst-difference one. Note that in the tables only ‘‘error correction speciﬁcation’’ entries are reported for the interest rate parity model. This model is not

254

Table 8.5 MSE ratios from the dollar-based and yen-based exchange rates Speciﬁcation Panel A ECM

S–P

IRP

PROD

BP/$ 1.0469 0.3343

1.0096 0.6613

1.0795 0.1827

4

1.0870 0.5163

0.7696 0.3379

20

0.4949 0.1329

0.9810 0.9581

1 4

1

20 Panel B ECM

FD

BEER

S–P

IRP

PROD

1.1597 0.0909

BP/yen 0.9709 0.5831

1.0421 0.6269

1.0266 0.7905

1.1974 0.2571

1.5255 0.0001

1.1466 0.3889

1.0008 0.9975

1.4142 0.3171

0.7285 0.5225

1.2841 0.4016

1.2020 0.1302

0.7611 0.5795

1.7493 0.0295

1.0357 0.7095

1.1678 0.4255

1.8876 0.0092

0.9655 0.7175

1.0000 1.0000

1.2691 0.3260 6.0121 0.0000

1.3830 0.1038 2.2029 0.0021

3.7789 0.0004 18.370 0.0000

1.1191 0.6543 4.5445 0.0000

1.1114 0.6886 4.7881 0.0000

CAN$/yen

CAN$/$ 1

1.0365 0.3991

1.0849 0.0316

1.0537 0.3994

1.2644 0.0018

0.9617 0.2537

1.0096 0.8710

0.9948 0.9269

4

1.0681 0.2531

1.0123 0.9592

1.1194 0.2015

1.5570 0.0002

0.9716 0.7037

1.0045 0.9814

1.1185 0.4038

20

0.6339 0.0248

0.1881 0.0001

1.0204 0.9276

1.7609 0.0302

1.1694 0.2747

0.6462 0.4125

4.8827 0.1130

1

1.0474 0.6214 0.9866 0.9531

1.0842 0.3971 1.0519 0.8232

0.5424 0.1544 1.2907 0.5046

1.0106 0.9144 1.1578 0.5751

4

0.9827 0.8456 1.1663 0.5827

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

Horizon

Panel C ECM

FD

4.7274 0.0000

12.181 0.0000

12.12 0.0000

DM/yen

DM/$ 0.9990 0.5440

1.0705 0.0383

0.9867 0.5858

1.0810 0.1951

1.0447 0.3200

0.9662 0.4790

0.9983 0.0528

4

0.9967 0.5861

1.2090 0.0694

0.9298 0.2956

1.0484 0.3109

1.0006 0.5779

0.8571 0.3238

1.0003 0.7265

20

1.0242 0.0004

1.0073 0.9354

1.0410 0.0030

0.6299 0.0891

1.0034 0.6003

0.5485 0.0480

0.9921 0.1126

1

1.0354 0.3020 1.1184 0.2019

1.1208 0.1959 1.1782 0.0029

0.4649 0.0009 0.3331 0.0059

1.0227 0.7181 1.0859 0.1849

1.0060 0.9219 1.0045 0.9625

2.0817 1.1915

1.9828 0.0000

1.2906 0.2550

0.9521 0.7217

0.8569 0.3572

20 Panel D

FD

0.2937 0.1018

1

4

ECM

0.2051 0.0318

SF/yen

SF/$ 0.9784 0.7773

1.1101 0.0692

1.1200 0.1614

0.9961 0.9333

0.9985 0.9522

1.0515 0.2892

4

0.8864 0.4152

1.2871 0.0689

1.0409 0.7438

1.0627 0.2595

0.9276 0.3983

1.0140 0.7786

20

1.2873 0.1209

1.4894 0.0000

0.9651 0.8684

0.8331 0.2925

0.9031 0.4856

0.9216 0.1019

1

1.3115 0.1641

1.3891 0.1734

0.9350 0.1643

0.9338 0.1765

4

1.6856 0.0774

1.8437 0.0713

1.0114 0.8595

0.9666 0.7366

20

5.6773 0.0000

5.9918 0.0000

0.9208 0.0000

0.8852 0.0001

255

1

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

256

Table 8.5 (continued) Horizon

IRP

PROD

0.9821 0.8799 0.8870 0.6214

1.0681 0.2979 1.2047 0.2862

0.9973 0.9647 0.9460 0.7343

20

0.8643 0.4299

0.9824 0.9661

0.8500 0.3856

1

1.0022 0.9840

0.9456 0.4427

4

1.0240 0.8207

1.0624 0.5342

20

2.7132 0.0000

2.2586 0.0001

Panel E ECM

BEER

S–P

IRP

PROD

Yen/$ 1 4

Note: The results are based on dollar-based and yen-based exchange rates and their forecasts. Each cell has two entries. The ﬁrst is the MSE ratio (the MSEs of a structural model to the random walk speciﬁcation). The entry underneath the MSE ratio is the p-value of the hypothesis that the MSEs of the structural and random walk models are the same (Diebold and Mariano 1995). The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. Due to data unavailability, the BEER model was not estimated for the Japanese yen and Swiss franc.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

In-Sample Fit and Out-of-Sample Performance Evaluated

257

estimated; rather the predicted spot rate is calculated using the uncovered interest parity condition. To the extent that long-term interest rates can be considered the error correction term, we believe this categorization is most appropriate. Overall, the MSE results are not favorable to the structural models. Of the 153 MSE ratios, 109 are not signiﬁcant (at the 10 percent signiﬁcance level), and 44 are signiﬁcant. That is, for the majority of the cases one cannot differentiate the forecasting performance between a structural model and a random walk model. For the 44 signiﬁcant cases, there are 32 cases in which the random walk model is signiﬁcantly better than the competing structural models and only 11 cases in which the opposite is true. As 10 percent is the size of the test and 12 cases constitute less than 10 percent of the total of 153 cases, the empirical evidence can hardly be interpreted as supportive of the superior forecasting performance of the structural models. One caveat is necessary, however. When one restricts attention to the long-horizon forecasts, it turns out that those incorporating long-run restrictions outperform a random walk more often than would be expected to occur randomly: ﬁve out of 30 cases, or 17 percent, using a 10 percent signiﬁcance level. Inspecting the MSE ratios, one does not observe many consistent patterns, in terms of outperformance. It appears that the BEER model does not do particularly well except for the DM/$ rate. The interest rate parity model tends to do better at the 20-quarter horizon than at the 1- and 4-quarter horizons—a result consistent with the well-known bias in forward rates at short horizons. In accordance with the existing literature, our results are supportive of the assertion that it is very difﬁcult to ﬁnd forecasts from a structural model that can consistently beat the random walk model using the MSE criterion. The current exercise further strengthens the assertion as it covers both dollar- and yen-based exchange rates and some structural models that have not been extensively studied before. 8.4.2

The Direction-of-Change Criterion

Table 8.6 reports the proportion of forecasts that correctly predicts the direction of the exchange rate movement and, underneath these sample proportions, the p-values for the hypothesis that the reported proportion is signiﬁcantly different from 0.5. When the proportion statistic is signiﬁcantly larger than 0.5, the forecast is said to have the ability to predict the direct of change. On the other hand, if the statistic is

258

Table 8.6 Direction-of-change statistics from the dollar-based and yen-based exchange rates Speciﬁcation Panel A ECM

S–P

IRP

PROD

BEER

S–P

IRP

PROD

BP/$ 0.5312 0.7236

0.4849 0.8618

0.5313 0.7237

0.4062 0.2888

BP/yen 0.5625 0.4795

0.4546 0.6015

0.6563 0.0771

4

0.5862 0.3531

0.5455 0.6015

0.4483 0.5775

0.3448 0.0946

0.5517 0.5774

0.6364 0.1172

0.5517 0.5775

20

0.8461 0.0125

0.7273 0.0090

0.7692 0.0522

0.3846 0.4053

0.5384 0.7815

0.5758 0.3841

0.2308 0.0522

1

0.5937 0.2888

0.4688 0.7237

0.4062 0.2888

0.5937 0.2888

0.4375 0.4795

4

0.5517 0.5774 0.3076 0.1655

0.5172 0.8527 0.1539 0.0126

0.3448 0.0946 0.3076 0.1655

0.6551 0.0946 0.0000 0.0000

0.5862 0.3532 0.0000 0.0000

1

20 Panel B ECM

FD

CAN$/yen

CAN$/$ 1

0.4062 0.2888

0.3939 0.2230

0.3438 0.0771

0.3125 0.0338

0.5937 0.2888

0.4849 0.8618

0.6250 0.1573

4

0.4827 0.8526

0.4242 0.3841

0.4828 0.8527

0.1724 0.0004

0.6206 0.1936

0.5758 0.3841

0.5172 0.8527

20

0.7692 0.0522

1.0000 0.0000

0.4615 0.7815

0.0769 0.0022

0.5384 0.7815

0.7273 0.0090

0.2308 0.0522

1

0.5312 0.7236 0.7586 0.0053

0.5625 0.4795 0.7241 0.0158

0.6250 0.1573 0.5862 0.3531

0.5000 1.0000 0.5172 0.8526

4

0.4375 0.4795 0.4828 0.8527

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

Horizon

Panel C ECM

FD

0.0000 0.0000

0.3077 0.1655

0.3076 0.1655 DM/yen

DM/$ 0.5000 1.0000

0.3030 0.0236

0.3750 0.1573

0.5625 0.4795

0.6250 0.1573

0.5152 0.8618

0.5000 1.0000

4

0.5517 0.5774

0.3030 0.0236

0.3103 0.0411

0.4827 0.8526

0.4137 0.3531

0.6667 0.0555

0.3793 0.1937

20

0.0769 0.0022

0.5152 0.8618

0.2308 0.0522

0.2307 0.0522

0.6923 0.1655

0.8485 0.0001

0.6154 0.4054

1

0.5000 1.0000 0.3448 0.0946

0.4063 0.2888 0.2759 0.0158

0.8125 0.0004 0.7931 0.0015

0.4687 0.7236 0.4827 0.8526

0.5000 1.0000 0.4483 0.5775

0.0769 0.0022

0.0769 0.0023

0.3076 0.1655

0.3076 0.1655

0.4615 0.7815

20 Panel D

FD

1.0000 0.0000

1

4

ECM

1.0000 0.0000

SF/yen

SF/$ 0.5625 0.4795

0.3030 0.0236

0.5625 0.4795

0.6562 0.0771

0.6061 0.2230

0.4688 0.7237

4

0.5517 0.5774

0.3636 0.1172

0.5517 0.5775

0.4827 0.8526

0.5758 0.3841

0.4138 0.3532

20

0.5384 0.7815

0.4546 0.6698

0.6923 0.1655

0.5384 0.7815

0.5000 1.0000

0.6154 0.4054

1

0.4062 0.2888

0.4375 0.4795

0.5937 0.2888

0.6875 0.0339

4

0.4137 0.3531

0.5172 0.8527

0.5517 0.5774

0.5862 0.3532

20

0.2307 0.0522

0.2308 0.0522

0.5384 0.7815

0.6154 0.4054

259

1

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

260

Table 8.6 (continued) Horizon

IRP

PROD

0.6562 0.0771 0.5517 0.5774

0.3636 0.1172 0.5152 0.8618

0.5625 0.4795 0.4828 0.8527

20

0.7692 0.0522

0.5152 0.8618

0.6923 0.1655

1

0.6875 0.0338

0.6563 0.0771

4

0.6551 0.0946

0.6207 0.1937

20

0.0000 0.0000

0.0000 0.0000

Panel E ECM

BEER

S–P

IRP

PROD

Yen/$ 1 4

Note: The table reports the proportion of forecasts that correctly predict the direction of the dollar-based and yen-based exchange rate movements. Under each direction-of-change statistic, the p-values for the hypothesis that the reported proportion is signiﬁcantly different from 0.5 is listed. When the statistic is signiﬁcantly larger than 0.5, the forecast is said to have the ability to predict the direct of change. If the statistic is signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrstdifference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. Due to data unavailability, the BEER model was not estimated for the Japanese yen and Swiss franc.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

In-Sample Fit and Out-of-Sample Performance Evaluated

261

signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. If a model consistently forecasts the direction of change incorrectly, traders can derive a potentially proﬁtable trading rule by going against these forecasts. Thus, for trading purposes, information regarding the signiﬁcance of ‘‘incorrect’’ prediction is as useful as the one of ‘‘correct’’ forecasts. However, in evaluating the ability of the model to describe exchange rate behavior, we separate the two cases. There is mixed evidence on the ability of the structural models to correctly predict the direction of change. Among the 153 direction-ofchange statistics, 23 (27) are signiﬁcantly larger (less) than 0.5 at the 10 percent level. The occurrence of the signiﬁcant outperformance cases is slightly higher (15 percent) than the one implied by the 10 percent level of the test. The results indicate that the structural model forecasts can correctly predict the direction of the change, although the proportion of cases where a random walk outperforms the competing models is higher than what one would expect if they occurred randomly. Let us take a closer look at the incidences in which the forecasts are in the right direction. About half of the 23 cases are in the error correction category (12). Thus it is not clear if the error correction speciﬁcation— which incorporates the empirical long-run relationship—is a better speciﬁcation for the models under consideration. Among the four models under consideration, the sticky-price model has the highest number (10) of forecasts that give the correct directionof-change prediction (18 percent of these forecasts), while the interest rate parity model has the highest proportion of correct predictions (19 percent). Thus, at least on this count, the newer exchange rate models do not signiﬁcantly edge out the ‘‘old fashioned’’ sticky-price model save perhaps the interest rate parity condition. The cases of correct direction prediction appear to cluster at the long forecast horizon. The 20-quarter horizon accounts for 10 of the 23 cases while the 4-quarter and 1-quarter horizons have, respectively, 6 and 7 direction-of-change statistics that are signiﬁcantly larger than 0.5. Since there have been few studies utilizing the direction-of-change statistic in similar contexts, it is difﬁcult to make comparisons. Chinn and Meese (1995) apply the direction-of-change statistic to three-year horizons for three conventional models, and ﬁnd that performance is largely currency-speciﬁc: the no-change prediction is outperformed in the case of the dollar–yen exchange rate, while all models are outperformed in the case of the dollar–sterling rate. In contrast, in our study at the 20quarter horizon, the positive results appear to be concentrated in the

262

Table 8.7 Cointegration between exchange rates and their forecasts Speciﬁcation Panel A ECM

FD

Horizon

S–P

IRP

PROD

BEER

S–P

1

BP/$ 2.12

4

14.25*

2.41

19.26*

BP/yen 8.70

5.35

5.06

4.88

5.72

6.98

18.13*

26.54*

3.99

7.26

20

9.69*

8.71

16.45*

6.54

6.27

5.25

1

8.51

19.05*

7.66

15.85*

5.50

4

8.30

7.32

4.53

5.34

5.38

20

2.78

7.73

1.87

8.77

8.80

ECM

FD

FD

4.02

CAN$/yen

CAN$/$ 1

6.74

6.03

3.41

6.32

6.94

6.59

7.77

4 20

6.31 6.58

5.87 7.03

1.97 8.96

5.80 4.53

2.85 7.22

4.18 9.51

1.13 4.29

1

14.42*

15.60*

12.53*

15.07*

13.87*

4

10.97*

7.22

6.22

5.64

4.20

20

3.87

4.08

1.93

6.31

6.50

Panel C ECM

PROD

DM/yen

DM/$ 1

2.78

11.18*

3.11

8.38

2.43

5.71

5.57

4

4.74

11.72*

2.83

6.42

14.77*

4.39

9.50

20

1.17

1.01

11.09*

3.30

7.12

13.97*

1 4

14.99* 8.37

7.21 7.36

7.63 3.02

14.28* 42.41*

16.37* 3.58

20

1.37

1.20

5.17

5.55

5.84

6.45

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

Panel B

IRP

ECM

FD

1.08

6.88

3.24

—

5.12

2.76

10.31*

4

22.52*

6.84

34.23*

—

1.57

108.57*

3.25

20

0.69

6.93

0.49

—

4.05

4.72

1

2.73

1.02

—

4.40

47.89*

4

5.21

1.65

—

1.81

3.10

20

2.90

2.78

—

7.83

7.01

Panel E ECM

FD

SF/yen

SF/$ 1

6.39

Yen/$ 1 4

14.82* 5.73

12.20* 10.93*

4.84 5.33

— —

20

14.99*

1.05

13.16*

—

1

20.48*

25.39*

—

4

5.61

42.86*

—

20

15.06*

13.17*

—

Note: The table reports the Johansen maximum eigenvalue statistic for the null hypothesis that a dollar-based (or a yen-based) exchange rate and its forecast are not cointegrated. * indicates the 10% marginal signiﬁcance level. Tests for the null of one cointegrating vector were also conducted, but in all cases the null was not rejected. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4. The dash indicates that the statistics were not generated due to unavailability of data.

In-Sample Fit and Out-of-Sample Performance Evaluated

Panel D

263

264

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

yen–dollar and Canadian dollar–dollar rates.13 It is interesting to note that the direction-of-change statistic works for the interest rate parity model almost only at the 20-quarter horizon, thus mirroring the MSE results. This pattern is entirely consistent with the ﬁnding that uncovered interest parity holds better at long horizons. 8.4.3

The Consistency Criterion

The consistency criterion only requires the forecast and actual realization comove one-to-one in the long run. One could argue that the criterion is less demanding than the MSE and direction-of-change metrics. Indeed, a forecast that satisﬁes the consistency criterion can (1) have a MSE larger than that of the random walk model, (2) have a directionof-change statistic less than 0.5, or (3) generate forecast errors that are serially correlated. However, given the problems related to modeling, estimation, and data quality, the consistency criterion can be a more ﬂexible way to evaluate a forecast. In assessing the consistency, we ﬁrst test if the forecast and the realization are cointegrated.14 If they are cointegrated, then we test if the cointegrating vector satisﬁes the ð1; 1Þ requirement. The cointegration results are reported in table 8.7. The test results for the ð1; 1Þ restriction are reported in table 8.8. Thirty-eight of 153 cases reject the null hypothesis of no cointegration at the 10 percent signiﬁcance level. Thus 25 percent of forecast series are cointegrated with the corresponding spot exchange rates. The error correction speciﬁcation accounts for 20 of the 38 cointegrated cases and the ﬁrst-difference speciﬁcation accounts for the remaining 18 cases. There is no evidence that the error correction speciﬁcation gives better forecasting performance than the ﬁrst-difference speciﬁcation. Interestingly the sticky-price model garners the largest number of cointegrated cases. There are 54 forecast series generated under the sticky-price model. Fifteen of these 54 series (i.e., 28 percent) are cointegrated with the corresponding spot rates. Twenty-six percent of the interest rate parity and 24 percent of the productivity model are cointegrated with the spot rates. Again, we do not ﬁnd evidence that the recently developed exchange rate models outperform the ‘‘old’’ vintage sticky-price model. The yen–dollar has 10 out of the 15 forecast series that are cointegrated with their respective spot rates. The Canadian dollar–dollar pair, which yields relatively good forecasts according to the direction-

In-Sample Fit and Out-of-Sample Performance Evaluated

265

of-change metric, has only 4 cointegrated forecast series. Evidently the forecasting performance is not just currency speciﬁc; it also depends on the evaluation criterion. The distribution of the cointegrated cases across forecasting horizons is puzzling. The frequency of occurrence is inversely proportional to the forecasting horizons. There are 19 of 51 one-quarter ahead forecast series that are cointegrated with the spot rates. However, there are only 11 of the 4-quarter ahead and 8 of the 20-quarter ahead forecast series that are cointegrated with the spot rates. One possible explanation for this result is that there are fewer observations in the 20-quarter ahead forecast series, and this effects the power of the cointegration test. The results of testing for the long-run unitary elasticity of expectations at the 10 percent signiﬁcance level are reported in table 8.8. The condition of long-run unitary elasticity of expectations, that is, the ð1; 1Þ restriction on the cointegrating vector, is rejected by the data quite frequently. The ð1; 1Þ restriction is rejected in 33 of the 38 cointegration cases. That is 13 percent of the cointegrated cases display long-run unitary elasticity of expectations. Taking both the cointegration and restriction test results together, 3 percent of the 153 cases meet the consistency criterion. 8.4.4

Discussion

Several aspects of the foregoing analysis merit discussion. To begin with, even at long horizons, the performance of the structural models is less than impressive along the MSE dimension. This result is consistent with those in other recent studies, although we have documented this ﬁnding for a wider set of models and speciﬁcations. Groen (2000) restricted his attention to a ﬂexible price monetary model, while Faust et al. (2001) examined a portfolio balance model as well; both remained within the MSE evaluation framework. Expanding the set of criteria does yield some interesting surprises. In particular, the direction-of-change statistics indicate more evidence that structural models can outperform a random walk. However, the basic conclusion that no economic model is consistently more successful than the others remains intact. This, we believe, is a new ﬁnding. Even if we cannot glean from this analysis a consistent ‘‘winner,’’ it may still be of interest to note the best and worst performing combinations of model/speciﬁcation/currency. The best performance on the MSE criterion is turned in by the interest rate parity model at the

266

Table 8.8 Results of ð1; 1Þ restriction test Speciﬁcation Panel A ECM

Horizon 1 4 20

FD

— —

445.3 0.00

— —

— —

4

— — — —

Panel B

39.66 0.00

— —

1

20

ECM

BP/$ — —

IRP

PROD

BEER

— —

0.32 0.57

— —

19.99 0.00

S–P

IRP

PROD

BP/yen — —

— —

— —

49.55 0.00

— —

— —

— —

— —

458.91 0.00

— —

— —

1.56 0.21

— —

24.73 0.00

— —

— — — —

— — — —

— — — —

— — — —

CAN$/yen

CAN$/$ 1

— —

— —

— —

— —

— —

— —

— —

4

— —

— —

— —

— —

— —

— —

— —

20

— —

— —

— —

— —

— —

— —

— —

15.73 0.00 — —

1263 0.00 — —

17.17 0.00 — —

1 4

16.58 0.00 132.5 0.00

28.50 0.00

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

— —

1

— —

4 20

Panel C ECM

FD

1

164.5 0.00

— —

— —

— —

— —

— —

— —

392.97 0.00

— —

— —

11.20 0.00

— —

— —

— —

— —

— —

— —

535.13 0.00 — — — —

— — — —

20

— —

— —

— —

1

— — 3.34 0.06

5.06 0.02

3.40 0.06 3.88 0.04

— — 3.40 0.07 — — — —

— — SF/yen

SF/$

4

— — DM/yen

6.73 0.00 — —

Panel D

FD

— —

DM/$

4

ECM

— —

— —

— —

— —

— —

— —

313.12 0.00

— —

— —

— —

— —

— —

— — — —

9.77 0.00

4.56 0.03

— —

1

— —

— —

— —

31.07 0.00

4

— —

— —

— —

— —

20

— —

— —

— —

— —

267

20

In-Sample Fit and Out-of-Sample Performance Evaluated

20

Speciﬁcation

268

Table 8.8 (continued) Horizon

Panel E ECM

IRP

PROD

62.10 0.00 — —

209.36 0.00 33.58 0.00

— — — —

876.4 0.00

— —

1916 0.00

BEER

S–P

IRP

PROD

Yen/$ 1 4 20 1 4 20

0.582 0.445 — — 436.4 0.00

1.03 0.31 1.14 0.29 289.22 0.00

Note: The likelihood ratio test statistic for the restriction of ð1; 1Þ on the cointegrating vector and its p-value are reported. The test is only applied to the cointegration cases present in table 8.3. The notation used in the table is ECM: error correction speciﬁcation; FD: ﬁrst-difference speciﬁcation; S–P: sticky-price model; IRP: interest rate parity model; PROD: productivity differential model; and BEER: behavioral equilibrium exchange rate model. The forecasting horizons (in quarters) are listed under the heading ‘‘horizon.’’ The forecasting period is 1993:1 to 2000:4.

Y.-W. Cheung, M. D. Chinn, and A. G. Pascual

FD

S–P

In-Sample Fit and Out-of-Sample Performance Evaluated

269

20-quarter horizon for the Canadian dollar–yen exchange rate, with a MSE ratio of 0.19 ( p-value of 0.0001). The worst performances are associated with ﬁrst-difference speciﬁcations; in this case the highest MSE ratio is for the ﬁrst differences speciﬁcation of the sticky-price exchange rate model at the 20-quarter horizon for the Canadian dollar– US dollar exchange rate. However, the other catastrophic failures in prediction performance are distributed across ﬁrst-difference speciﬁcations of the various models, so the key determinant in this pattern of results appears to be the difﬁculty in estimating stable short-run dynamics. (We take here into account the fact that these predictions utilize ex post realizations of the right-hand side variables.) Overall, the inconstant nature of the parameter estimates appears to be closely linked with the erratic nature of the forecasting performance. This applies to the variation in long-run estimates and reversion coefﬁcients, but perhaps most strongly to the short-run dynamics obtained in the ﬁrst-differences speciﬁcations. 8.5

Concluding Remarks

In this chapter we systematically assess the in-sample ﬁt and out-ofsample predictive capacities of models developed during the 1990s. These models are compared along a number of dimensions, including econometric speciﬁcation, currencies, and differing metrics. Our investigation does not reveal that any particular model or any particular speciﬁcation ﬁt the data well, in terms of providing estimates in accord with theoretical priors. Of course, this ﬁnding is dependent on a very simple speciﬁcation search, and we used theory to discipline variable selection and information criteria to select lag lengths. On the other hand, some models seem to do well at certain horizons, for certain criteria. Indeed, it may be that one model will do well for one exchange rate and not for another. For instance, the productivity model does well for the mark–yen rate along the direction-of-change and consistency dimensions (although not by the MSE criterion), but that same conclusion cannot be applied to any other exchange rate. Similarly we fail to ﬁnd any particular model or speciﬁcation that out-performed a random walk on a consistent basis. Again, we imposed the disciplining device of using a given speciﬁcation, and a given out-of-sample forecasting period. Perhaps most interestingly,

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there is little apparent correlation between how well the in-sample estimates accord with theory and out-of-sample prediction performance. The only link between in-sample and out-of-sample performance is an indirect one, for the interest parity condition. It is well known that interest rate differentials are biased predictors of future spot rate movements at short horizons. However, the improved predictive performance at longer horizons does accord with the fact that uncovered interest parity is more likely to hold at longer horizons than at short horizons. In sum, while the results of our study have been fairly negative regarding the predictive capabilities of newer empirical models of exchange rates, in some sense we believe the ﬁndings pertain more to difﬁculties in estimation, rather than the models themselves. And this may point the direction for future research avenues.15 Appendix A: Data Unless otherwise stated, we use seasonally adjusted quarterly data from the IMF International Financial Statistics ranging from the second quarter of 1973 to the last quarter of 2000. The exchange rate data are end of period exchange rates. Money is measured as narrow money (essentially M1), with the exception of the United Kingdom, where M0 is used. The output data are measured in constant 1990 prices. The consumer and producer price indexes also use 1990 as base year. The three-month, annual, and ﬁve-year interest rates are end-ofperiod constant maturity interest rates and are obtained from the IMF country desks. See Meredith and Chinn (1998) for details. Five-year interest rate data were unavailable for Japan and Switzerland; hence data from Global Financial Data http://www.globalﬁndata.com/ were used, speciﬁcally, ﬁve-year government note yields for Switzerland and ﬁve-year discounted bonds for Japan. The productivity series are labor productivity indexes, measured as real GDP per employee, converted to indexes (1995 ¼ 100). These data are drawn from the Bank for International Settlements database. The net foreign asset (NFA) series is computed as follows. Using stock data for year 1995 on NFA (Lane and Milesi-Ferretti 2001) at http://econserv2.bess.tcd.ie/plane/data.html, and ﬂow quarterly data from the IFS statistics on the current account, we generated quarterly stocks for the NFA series (with the exception of Japan, for which there is no quarterly data available on the current account).

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To generate quarterly government debt data, we follow a similar strategy. We use annual debt data from the IFS statistics, combined with quarterly government deﬁcit (surplus) data. The data source for Canadian government debt is the Bank of Canada. For the United Kingdom, the IFS data are updated with government debt data from the public sector accounts of the UK Statistical Ofﬁce (for Japan and Switzerland, we have very incomplete data sets, and hence no behavioral equilibrium exchange rate models are estimated for these two countries). Appendix B: Evaluating Forecast Accuracy The Diebold-Mariano statistics (Diebold and Mariano 1995) are used to evaluate the forecast performance of the different model speciﬁcations relative to that of the naive random walk. Given the exchange rate series xt and the forecast series yt , the loss function L for the mean square error is deﬁned as Lðyt Þ ¼ ðyt xt Þ 2 :

ðA1Þ

Testing whether the performance of the forecast series is different from that of the naive random walk forecast zt is equivalent to testing whether the population mean of the loss differential series dt is zero. The loss differential is deﬁned as dt ¼ Lðyt Þ Lðzt Þ:

ðA2Þ

Under the assumptions of covariance stationarity and short-memory for dt , the large-sample statistic for the null of equal forecast performance is distributed as a standard normal, and can be expressed as d qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ; PT PðT1Þ ðdt dÞðdtjtj dÞ 2p t¼ðT1Þ lðt=SðTÞÞ t¼jtjþ1

ðA3Þ

where lðt=SðTÞÞ is the lag window, SðTÞ is the truncation lag, and T is the number of observations. Different lag-window speciﬁcations can be applied, such as the Barlett or the quadratic spectral kernels, in combination with a data-dependent lag-selection procedure (Andrews 1991). For the direction-of-change statistic, the loss differential series is deﬁned as follows: dt takes a value of one if the forecast series correctly predicts the direction of change, otherwise it will take a value of zero.

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Hence a value of d signiﬁcantly larger than 0.5 indicates that the forecast has the ability to predict the direction of change; on the other hand, if the statistic is signiﬁcantly less than 0.5, the forecast tends to give the wrong direction of change. In large samples, the studentized version of the test statistic, d 0:5 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ; 0:25=T

ðA4Þ

is distributed as a standard normal. Notes We thank, without implicating, Jeff Frankel, Fabio Ghironi, Jan Groen, Lutz Kilian, Ed Leamer, Ronald MacDonald, John Rogers, Lucio Sarno, Torsten Slok, Frank Westermann, seminar participants at Academia Sinica, Boston College, UCLA, and participants at CESIfo conference on Exchange Rate Modeling: Where Do We Stand? for helpful comments, and Jeannine Bailliu, Gabriele Galati, and Guy Meredith for providing data. The ﬁnancial support of faculty research funds of the University of California, Santa Cruz is gratefully acknowledged. 1. A recent review of the empirical literature on the monetary approach is provided by Neely and Sarno (2002). 2. See Clark and MacDonald (1999), Clostermann and Schnatz (2000), Yilmaz and Jen (2001), and Maeso-Fernandez et al. (2001) for recent applications of this speciﬁcation. On the portfolio balance channel, Cavallo and Ghironi (2002) provide a role for net foreign assets in the determination of exchange rates in the sticky-price optimizing framework of Obstfeld and Rogoff (1995). 3. Despite this ﬁnding, there is little evidence that long-term interest rate differentials— or equivalently long-dated forward rates—have been used for forecasting at the horizons we are investigating. One exception from the professional literature is Rosenberg (2001). 4. The ﬁndings reported below are not very sensitive to the forecasting periods (Cheung, Chinn, and Garcia Pascual 2002). 5. For the pound, the productivity coefﬁcient is incorrectly signed, although this ﬁnding is combined with a very large (and correctly signed) income coefﬁcient, which suggests some difﬁculty in disentangling the income from productivity effects. 6. Overall, the interpretation of the results is complicated by the fact that, for the level speciﬁcations, multiple cointegrating vectors are indicated using the asymptotic critical values. The use of ﬁnite sample critical values reduces the implied number of cointegrating vectors, as indicated in the second row, to one or two vectors. Hence we do not believe the assumption of one cointegrating vector does much violence to the data. 7. One substantial caveat is necessary at this point. BEER models have almost uniformly been couched in terms of multilateral exchange rates; hence the interpretation of the BEERs in a bilateral context does not exactly replicate the experiments conducted by BEER exponents. On the other hand, the fact that it is difﬁcult to obtain the theoretically

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implied coefﬁcient signs suggests that some searching is necessary in order to obtain a ‘‘good’’ ﬁt. 8. Two recent exceptions to this characterization are Flood and Rose (2002) and Bansal and Dahlquist (2000). Flood and Rose conclude that UIP holds much better for countries experiencing currency crises, while Bansal and Dahlquist ﬁnd that UIP holds much better for a set of non-OECD countries. Neither of these descriptions applies to the currencies examined in this study. 9. We opted to exclude short-run dynamics in equation (7) because, on the one hand, the use of equation (7) yields true ex ante forecasts and makes our exercise directly comparable with, for example, Mark (1995), Chinn and Meese (1995), and Groen (2000), and on the other, the inclusion of short-run dynamics creates additional demands on the generation of the right-hand-side variables and the stability of the short-run dynamics that complicate the forecast comparison exercise beyond a manageable level. 10. In using the DM test, we are relying on asymptotic results, which may or may not be appropriate for our sample. However, generating ﬁnite sample critical values for the large number of cases we deal with would be computationally infeasible. More important, the most likely outcome of such an exercise would be to make detection of statistically signiﬁcant out-performance even more rare, and leaving our basic conclusion intact. 11. We also experimented with the Bartlett kernel and the deterministic bandwidth selection method. The results from these methods are qualitatively very similar. In appendix B we provide a more detailed discussion of the forecast comparison tests. 12. See also Leitch and Tanner (1991), who argue that a direction of change criterion may be more relevant for proﬁtability and economic concerns, and hence a more appropriate metric than others based on purely statistical motivations. 13. Using Markov switching models, Engel (1994) obtains some success along the direction of change dimension at horizons of up to one year. However, his results are not statistically signiﬁcant. 14. The Johansen method is used to test the null hypothesis of no cointegration. The maximum eigenvalue statistics are reported in the manuscript. Results based on the trace statistics are essentially the same. Before implementing the cointegration test, both the forecast and exchange rate series were checked for the Ið1Þ property. For brevity, the Ið1Þ test results and the trace statistics are not reported. 15. Our survey is necessarily limited, and we leave open the question of whether alternative statistical techniques can yield better results, for example, nonlinearities (Meese and Rose 1991; Kilian and Taylor 2001), fractional integration (Cheung 1993), and regime switching (Engel and Hamilton 1990), cointegrated panel techniques (Mark and Sul 2001), and systems-based estimates (MacDonald and Marsh 1997).

References Alexius, A. 2001. Uncovered interest parity revisited. Review of International Economics 9(3): 505–17. Andrews, D. 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817–58.

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Bansal, R., and M. Dahlquist. 2000. The forward premium puzzle: Different tales from developed and emerging economies. Journal of International Economics 51(1): 115–44. Cavallo, M., and F. Ghironi. 2002. Net foreign assets and the exchange rate: Redux revived. Mimeo NYU and Boston College. February. Chen, Y.-C., and K. Rogoff. 2003. Commodity currencies. Journal of International Economics 60(1): 133–60. Cheung, Y.-W. 1993. Long memony in foreign exchange rate. Journal of Business and Economic Statistics 11(1): 93–102. Cheung, Y.-W., and K. S. Lai. 1993. Finite-sample sizes of Johansen’s likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics 55(3): 313–28. Cheung, Y.-W., and M. Chinn. 1998. Integration, cointegration, and the forecast consistency of structural exchange rate models. Journal of International Money and Finance 17(5): 813–30. Cheung, Y.-W., M. Chinn, and A. G. Pascual. 2002. Empirical exchange rate models of the 1990s: Are any ﬁt to survive? NBER Working Paper 9393. Chinn, M. 1997. Paper pushers or paper money? Empirical assessment of ﬁscal and monetary models of exchange rate determination. Journal of Policy Modelling 19(1): 51–78. Chinn, M., and R. Meese. 1995. Banking on currency forecasts: How predictable is change in money? Journal of International Economics 38(1–2): 161–78. Chinn, M., and G. Meredith. 2002. Testing uncovered interest parity at short and long horizons during the post–Bretton Woods era. Mimeo. Santa Cruz, CA. Christoffersen, P. F., and F. X. Diebold. 1998. Cointegration and long-horizon forecasting. Journal of Business and Economic Statistics 16: 450–58. Clark, P., and R. MacDonald. 1999. Exchange rates and economic fundamentals: A methodological comparison of Beers and Feers. In J. Stein and R. MacDonald, eds., Equilibrium Exchange Rates. Boston: Kluwer, pp. 285–322. Clostermann, J., and B. Schnatz. 2000. The determinants of the euro–dollar exchange rate: Synthetic fundamentals and a non-existing currency. Konjunkturpolitik 46(3): 274–302. Cumby, R. E., and D. M. Modest. 1987. Testing for market timing ability: A framework for forecast evaluation. Journal of Financial Economics 19(1): 169–89. Dornbusch, R. 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84: 1161–76. Diebold, F., and R. Mariano. 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13: 253–65. Engel, C. 1994. Can the Markov switching model forecast exchange rates? Journal of International Economics 36(1–2): 151–65. Engel, C., and J. Hamilton. 1990. Long swings in the exchange rate: Are they in the data and do markets know it? American Economic Review 80(4): 689–713. Faust, J., J. Rogers, and J. Wright. 2003. Exchange rate forecasting: The errors we’ve really made. Journal of International Economics 60(1): 35–59.

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Flood, R., and A. Rose. 2002. Uncovered interest parity in crisis. IMF Staff Papers 49(2): 252–66. Frankel, J. A. 1979. On the mark: A theory of ﬂoating exchange rates based on real interest differentials. American Economic Review 69: 610–22. Groen, J. J. 2000. The monetary exchange rate model as a long-run phenomenon. Journal of International Economics 52(2): 299–320. Isard, P., H. Faruqee, G. R. Kinkaid, and M. Fetherston. 2001. Methodology for current account and exchange rate assessments. IMF Occasional Paper 209. Kilian, L., and M. Taylor. 2003. Why is it so difﬁcult to beat the random walk forecast of exchange rates. Journal of International Economics 60(1): 85–107. Lane, P., and G. Milesi-Ferretti. 2001. The external wealth of nations: Measures of foreign assets and liabilities for industrial and developing. Journal of International Economics 55: 263–94. Leitch, G., and J. E. Tanner. 1991. Economic forecast evaluation: Proﬁts versus the conventional error measures. American Economic Review 81(3): 580–90. Lucas, R. 1982. Interest rates and currency prices in a two-country world. Journal of Monetary Economics 19(3): 335–59. MacDonald, R., and J. Nagayasu. 2000. The long-run relationship between real exchange rates and real interest rate differentials. IMF Staff Papers 47(1): 116–28. MacDonald, R., and M. P. Taylor. 1994. The monetary model of the exchange rate: Longrun relationships, short-run dynamics and how to beat a random walk. Journal of International Money and Finance 13(3): 276–90. Maeso-Fernandez, F., C. Osbat, and B. Schnatz. 2001. Determinants of the euro real effective exchange rate: A BEER/PEER approach. ECB Working Paper 85. Mark, N. 1995. Exchange rates and fundamentals: Evidence on long horizon predictability. American Economic Review 85: 201–18. Mark, N., and D. Sul. 2001. Nominal exchange rates and monetary fundamentals: Evidence from a small post–Bretton Woods panel. Journal of International Economics 53(1): 29–52. Meese, R., and K. Rogoff. 1983. Empirical exchange rate models of the seventies: Do they ﬁt out of sample? Journal of International Economics 14: 3–24. Meese, R., and A. K. Rose. 1991. An empirical assessment of non-linearities in models of exchange rate determination. Review of Economic Studies 58(3): 603–19. Neely, C. J., and L. Sarno. 2002. How well do monetary fundamentals forecast exchange rates? Federal Reserve Bank of St. Louis Review 84(5): 51–74. Obstfeld, M., and K. Rogoff. 1996. Foundations of International Macroeconomics. Cambridge: MIT Press. Rosenberg, M. 2001. Investment strategies based on long-dated forward rate/PPP divergence. FX Weekly (New York: Deutsche Bank Global Markets Research, April 27), pp. 4–8.

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Stein, J. 1999. The evolution of the real value of the US dollar relative to the G7 currencies. In J. Stein and R. MacDonald, eds., Equilibrium Exchange Rates. Boston: Kluwer, pp. 67–102. Stockman, A. 1980. A theory of exchange rate determination. Journal of Political Economy 88(4): 673–98. Yilmaz, F., and S. Jen. 2001. Correcting the US dollar—A technical note. Morgan Stanley Dean Witter ( June 1).

9

The Euro–Dollar Exchange Rate: Is It Fundamental? Mariam Camarero, Javier Ordo´n˜ez, and Cecilio Tamarit

The evolution of the euro exchange rate vis-a`-vis the main international currencies, and particularly, the US dollar, has given rise to a growing literature. Contrary to the more or less general expectations of appreciation, the euro has been in its ﬁrst three years of existence depreciating against the dollar. Many arguments have been given in search of fundamentals, but the results are up to now puzzling (e.g., see De Grauwe 2000 or Meredith 2001). Two arguments can be put forth to support this fact. First, an analysis based on fundamentals cannot be performed on a short-term basis. Although the operators in the money markets seem to be working in a chartist world, from a policyoriented view the data span has to be long enough to capture the longrun equilibria relationships, and the econometric framework based on cointegration is the most appropriate methodology for this purpose. Second, and related to the preceding argument, the absence of historical data for the euro makes it necessary to use aggregate variables in order to expand the series backward (ECB 2000). This ‘‘synthetic’’ euro and the aggregate euro area variables have an important qualiﬁcation: they summarize the evolution of the legacy currencies that developed in the framework of rather heterogeneous economic environments.1 This heterogenous character and its contribution to the ‘‘strength’’ of the euro were pointed out by De Grauwe (1997). In this chapter we propose a complementary approach that shows how to overcome these problems. Our main attempt will be to compare the behavior of the bilateral real exchange rates for the individual euro-area countries in a panel with the performance of a model estimated using aggregate euro-area variables for the period 1970 to 1998 in terms of quarterly data. To make the results fully comparable, we restrict the countries analyzed to those with information available for the whole period. Concerning the econometric techniques applied, we ﬁrst use the

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pooled mean group (PMG) estimator proposed by Pesaran, Shin, and Smith (1999) for nonstationary regressors and estimate a panel for a group of euro-area currencies. This method constrains the long-run coefﬁcients to be identical but allows error variances and short-run parameters to differ. By this method we also will be able to capture the long-run relationships consistently with the medium- and long-run orientation of the fundamental exchange rate models and the objectives of European monetary policy. Also it should enable us to understand the different responses of the euro-area countries. Second, we estimate an aggregate bilateral model for the euro–dollar real exchange rate. We use the standard Johansen cointegration analysis method to arrive at the long-run determinants of the real exchange rate based on the current values of the variables. With this framework we are further able to test for regime shifts or structural breaks. However, we must bear in mind that these changes can only be detected with a signiﬁcant delay. Thus, even if the creation of the European Monetary Union has provoked a change in regime, it is still too early to be able to detect it using the available techniques. The remainder of the chapter is organized as follows. In section 9.1 we provide an overview of the recent empirical literature on the issue of exchange rate determination in the euro case. In section 9.2, we describe the theoretical models and in section 9.3 present the econometric results. Finally, in section 9.4 we report the main results and conclusions. 9.1

Recent Empirical Literature2

A traditional starting point for estimating equilibrium exchange rate has been the PPP theory, either in its absolute or relative version. However, due to a different bulk of factors well documented in the literature, the speed of adjustment of the current value of exchange rate to the long-run equilibrium is very slow. Therefore other approaches have been implemented over time. Basically these approaches can be classiﬁed in accord with two strands of literature: fundamental equilibrium exchange rate (FEER) or behavioral equilibrium exchange rates (BEER).3 The caveat to the ﬁrst approach is its normative nature. This is due to the fact that under the FEER approach the exchange rate has to be consistent with internal and external balance. Thus we think, as Clark and MacDonald (1999) point out, that the behavioral approach may be a better empirical approach to exchange rate modeling

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because the computation is based on current levels of the fundamental factors. The problem is to determine the correct combination of fundamental variables, and the answer is largely empirical. Over the past two years different econometric techniques were implemented in several studies in line with the behavioral approach. Alberola et al. (1999) using cointegration techniques for individual currencies as well as for a panel of currencies found only a long-run relationship with net foreign assets and relative sectoral prices (the Balassa-Samuelson effect), and Ledo and Taguas (1999) found that the deviations from PPP can be explained largely by productivity differentials and interest rate differentials in an error correction model. Additionally Closterman and Schnatz (2000) found an equilibrium relationship for the bilateral euro–dollar exchange rate that includes the productivity differential, the interest rate differential, the real oil price, and the relative ﬁscal position. Makrydakis et al. (2000) found a relation with the productivity differential and the real interest rate differential as in Alquist and Chinn (2001). Finally Maeso-Ferna´ndez et al. (2001) found the euro to be mainly affected by productivity developments, real interest rate differentials, and external shocks due to oil dependence of the euro area. All the models taken together appear to encompass useful information, so any assessment about the evolution of the real exchange rate should start to build in some way on this broad-based multifaceted range of analysis (ECB 2002). 9.2

Theoretical Models: An Eclectic Nested Approach

As in the euro–dollar case discussed above, the most recent empirical evidence on real exchange rates has not been able to secure a position among traditional theoretical models. In his search of an answer to the problems associated with modeling exchange rates and, in particular, real exchange rates, MacDonald (1998) has proposed an eclectic approach to model real exchange rates. Meese and Rogoff (1988), in their study of the link between real exchange rates and real interest rate differentials, have tried to solve some of the problems related to the monetary models. They deﬁne the real exchange rate, qt , as qt 1 et pt þ pt , where et is the price of a unit of foreign currency in terms of domestic currency and pt and pt are the logarithms of domestic and foreign prices. Three assumptions are made: ﬁrst, that when a shock occurs, the real exchange rate returns to its equilibrium value at a constant rate; second, that the long-run real exchange rate, q^t , is a

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nonstationary variable; ﬁnally, that uncovered real interest rate parity is fulﬁlled. Combining the three assumptions above, the real exchange rate can be expressed in the following form: qt ¼ jðR t R t Þ þ q^t ;

ð1Þ

where R t and R t are, respectively, the real foreign and domestic interest rates for an asset of maturity k. This leaves relatively open the question of which are the determinants of q^t , which is a nonstationary variable. Meese and Rogoff real exchange rate model has been very inﬂuential in the empirical literature. As Edison and Melick (1995) show in their paper, the implementation of the empirical tests depends on the treatment of the expected real exchange rate derived from equation (1). The simplest model will assume that the expected real exchange rate is constant, while the models including other variables will specify it using other determinants. The model was ﬁrst tested, in its simplest version, by Campbell and Clarida (1987) and Meese and Rogoff (1988). The former found little of the movement in real exchange rates to be explained by movements in real interest differentials. Meese and Rogoff (1988), using cointegration techniques (Engle and Granger single-equation tests), could not ﬁnd a long-run relationship between the two variables. However, Baxter (1994) found more encouraging results, and in a recent paper, MacDonald and Nagayasu (2000) tested this relationship for 14 industrialized countries using both long- and short-term real interest rate differentials and time series as well as panel cointegration methods. After obtaining evidence of statistically signiﬁcant long-run relationships and plausible point estimates using panel tests, they concluded that the failure of previous researches was probably due to the estimation method used rather than to any theoretical deﬁciency. In a second group of papers, the assumption that the expected real exchange rate is constant is relaxed, and additional variables are introduced in an attempt to explain it. This approach was ﬁrst introduced by Hooper and Morton (1982), who modeled the expected real exchange rate as a function of cumulated current account. Edison and Pauls (1993) and Edison and Melick (1995) estimate the same model using cointegration techniques. In the second paper they ﬁnd evidence of a cointegrating relationship, after Edison and Pauls (1993) failed to ﬁnd a statistical link between real exchange rates and real interest rates

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using the Engle-Granger methodology. However, the estimated error correction models are more supportive of such a relation. Wu (1999) has recently also obtained good results (even in forecasting ability) for this type of speciﬁcation applied to Germany and Japan in relation to the dollar exchange rate and using the Johansen technique. MacDonald (1998) used this approach, dividing the real exchange rate determinants into two components: the real interest rate differential and a set of fundamentals that explains the behavior of the long-run (equilibrium) real exchange rate, which include productivity differentials, the effect of relative ﬁscal balances on the equilibrium real exchange rate, the private sector savings, and the real price of oil. We will describe this eclectic approach in more detail because it forms the basis of our analysis. MacDonald assumes that PPP holds for nontraded goods, so he arrives at the following expression for the long-run equilibrium real exchange rate:

q^t 1 qtT þ at ðptT ptNT Þ at ðptT ptNT Þ;

ð2Þ

where qtT is the real exchange rate for traded goods; ð ptT ptNT Þ ð ptT ptNT Þ is the relative price of traded to nontraded goods between the home and the foreign country and a and a are the weights. By way of (2), MacDonald identiﬁes two potential sources of variation in the equilibrium real exchange rate: 1. Movements in the relative prices of traded to nontraded goods between the home and foreign country (second and third terms in equation 2). These differences are mostly concentrated in nontraded goods. In particular, according to the traditional Balassa-Samuelson effect, productivity differences in the production of traded goods across countries can introduce a bias in the overall real exchange rate. This is because productivity advances tend to concentrate in the traded goods sectors. Because of the linkages between prices of goods and wages (and wages across sectors), provided that there is internal factor mobility (from the nontraded to the traded goods sectors and conversely), the real exchange rate tends to appreciate in fast growing economies. 2. Nonconstancy of the real exchange rate for traded goods, qtT , (the ﬁrst term in equation 2). Two additional factors may introduce variability in qtT : international differences in savings and investment and changes in the real price of oil.

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a. The real exchange rate for traded goods is also, following MacDonald (1998), a major determinant of the current account and is in turn driven by the determinants of savings and investment. We can separate two variables that may capture this effect: Fiscal policy, whose relation with the real exchange rate depends on the approach. According to the Mundell-Fleming model, an expansionary ﬁscal policy reduces national savings, increases the domestic real interest rate, and generates a permanent appreciation. In contrast, the portfolio balance models consider permanent ﬁscal expansion to cause a decrease in net foreign assets and a depreciation of the currency.

Private sector net savings, whose effect on the real exchange rate is inﬂuenced by demographic factors. This way the cross-country variations of saving rates are seen to affect the relative net foreign asset position.

b. Increases in the real price of oil tends to appreciate the currencies of the net oil exporters or, in general, the currencies of the less energy dependent countries. MacDonald’s proposal does not rely exclusively on the monetary approach to exchange rate determination, although it captures the majority of the fundamental variables mentioned in the literature and makes them compatible with it. Accordingly, the above-mentioned factors can be summarized in the following empirical speciﬁcation: qt ¼ jðR t R t Þ þ q^t ¼ f ððR t R t Þ; ðat at Þ; ðgt gt Þ; oilt ; dnfat Þ; ðÞ

ðÞ

ð=þÞ

ðÞ

ð3Þ

ðÞ

where ðat at Þ is the difference between the domestic and foreign economies productivity,4 ðgt gt Þ is the public expenditure differential, oilt 5 is the real oil price and dnfat is the relative net foreign asset position of the economy. 9.3

Empirical Results

Two different econometric techniques have been applied to the same data set. First, using dynamic panel techniques, we estimate the real exchange rate of the dollar versus a group of seven individual countries. In addition we study separately the euro countries in the sample

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from the rest. Second, using time series techniques, we explain the dollar–euro real exchange rate in terms of euro-area aggregated variables. 9.3.1

Panel Analysis: the Dollar in the World

As we noted earlier in our theoretical discussion, we examined a wide set of explanatory (fundamental) variables in order to assess the main factors behind the behavior of the dollar’s real exchange rate. This ﬁrst part of the analysis involves eight countries: the United States as the domestic country, Japan, Canada, the United Kingdom, and four euroarea countries (those with information available for the sample period and variables of interest). As a result in this ﬁrst part of the analysis we do not strictly estimate a model for the dollar versus the euro area. We have chosen to include countries, such as the United Kingdom, Canada, and Japan, that do not participate in EMU in order to capture the behavior of the most important world currencies. Our method in this part of the analysis allows for both group and individual approaches. We consider ﬁrst the entire group of countries (where N ¼ 7) and then divide the panel into the euro area countries (N ¼ 4: Germany, Spain, France, and Italy) and non-euro area countries (N ¼ 3: Canada, Japan, and the United Kingdom). The data are quarterly and the sample goes from 1970:1 to 1998:4.6 In choosing our model speciﬁcation, we tried to follow as close as possible the general to speciﬁc methodology. Our starting point was the models described in the previous section, and to make the estimated models comparable, we used a general speciﬁcation: rerdolit ¼ f ðdproit ; drrit ; oildepit ; dnfait ; dpexit Þ; ðÞ

ðÞ

ðÞ

ðÞ

ðþ=Þ

where rerdolit is the real exchange rate of the dollar versus all the currencies deﬁned as the units of domestic currency necessary to buy a unit of foreign currency in real terms; dproit is the relative productivity of the United States versus that of the other countries: an increase in the value of this variable tends to appreciate the currency; drrit is the real interest rate differential between the United States and the other countries analyzed: an increase in this differential appreciates the currency; oildepit is the real price of oil adjusted by the relative dependency on oil imports by each country compared to that of the United

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States: in this case, the dollar will appreciate when the oil dependency of the foreign countries is increasing; dnfait is the difference in the net foreign asset position over GDP of the United States versus the other countries, and the sign should be negative (the currencies of countries increasing its net foreign asset position tend to appreciate); dpexit is the difference in public expenditure over GDP between the United States and each of the other countries. In the last instance, there are two competing theories explaining the relation of public expenditure to the GDP with respect to the real exchange rate. The relation is positive (depreciation) if the portfolio balance model prevails, but it is negative according to the Mundell-Fleming approach. The models we used are the following:7 Model 1

Eclectic model:

rerdolit ¼ ai þ b 1i drrit þ b2i dpexit þ b3i dproit þ b 4i dnfait þ b5i oildepit : Model 2

Restricted eclectic model:

rerdolit ¼ ai þ b 1i drrit þ b2i dpexit þ b3i dproit þ b 4i dnfait : Model 1 follows the general speciﬁcation described above. Model 2 is a version of model 1 with the oil dependence variable excluded. In what follows, we show how these empirical models were tested. Order of Integration of the Variables Bearing all these considerations in mind, we should start the analysis with the study of the order of integration of the variables. Several panel unit root tests are already available in the literature, from the early works of Levin and Lin (1992)8 to the Im, Pesaran, and Shin (1995) tests. However, because of its higher power we applied the LM test for the null of stationarity proposed by Hadri (2000) with heterogeneous and serially correlated errors. These tests can be considered a panel version of the KPSS tests applied in the univariate context. Hadri (2000) provides two models (with and without a deterministic trend) that can be decomposed into the sum of a random walk and a stationary disturbance term. He tests the null hypothesis that all the variables ðyit Þ are stationary (around deterministic levels or around deterministic trends), so that for the N elements of the panel the variance of the errors is such that 2 2 ¼ ¼ suN ¼0 H0 : su1

ð4Þ

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Table 9.1 Hadri (2000) stationarity tests ðl ¼ 2Þ Variables

hm

ht

rerdolit

23.72**

dpexit

14.30**

262.49**

dnfait

47.05**

1655.32**

dproit drrit

29.79** 18.23**

801.21** 167.71**

oildepit

18.38**

149.01**

175.45**

Note: The statistic hm does not include a time trend, whereas ht does, and both are normally distributed. The two asterisks denote rejection of the null hypothesis of stationarity at 5 percent. The number of lags selected is l ¼ 2. 2 against the alternative H1 : that some sui > 0: This alternative allows for 2 heterogeneous sui across the cross sections and includes the homoge2 neous alternative (sui ¼ su2 for all iÞ as a special case. It also allows for a subset of cross sections to be stationary under the alternative. The two statistics are called hm for the null of stationarity around an intercept and ht when the null is stationarity around a deterministic trend. The results of the tests applied to the four variables are presented in table 9.1. The null hypothesis of stationarity can be easily rejected in the two cases (with and without time trend), so that all the panel variables can be considered nonstationary.

Long-Run Relationships: ‘‘Pooled Mean Group’’ Estimation Results Once we have determined the order of integration of the variables for the analysis of the real exchange rate of the dollar, we can follow the methodology proposed by Pesaran, Shin, and Smith (1999) and compute the pooled mean group estimators.9 This estimation technique is well suited in our case because we are interested in considering different groups of countries and comparing the estimation results (i.e., the whole group, the euro area countries, and the non–euro area countries). The pooled mean group (PMG) estimator involves both pooling and averaging. This estimator allows the intercepts, short-run coefﬁcients, and error variances to differ across groups, but the long-run coefﬁcients are constrained to be the same. Due to the high level of economic integration achieved among the euro-area countries, we chose to impose equality in the long-run parameters (or rather in most of them) but allow the short-run slope coefﬁcients and the dynamic speciﬁcation (i.e., the number of lags included) to differ across groups.

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Then we estimated the panel, using a maximum likelihood approach. The ML estimators that result are the pooled mean group (PMG) estimators. This is because they are both pooled, as implied by the homogeneity restrictions on the long-run coefﬁcients, and averaged across groups to obtain means of the estimated error-correction coefﬁcients and the other short-run parameters of the model. The empirical model takes on the eclectic form presented above, starting with model 1, which includes the main explanatory variables proposed by the literature on real exchange rates. Other theoretical models are restricted versions of model 1. Many empirical speciﬁcations have been estimated and compared through likelihood-based information criteria, such as the AIC and the SBC. In addition in each speciﬁcation we have tested two important questions: the homogeneity restriction using a likelihood ratio test; the existence of discrepancies between the pooled mean group estimates and the mean group estimates, which differ also in the degree of heterogeneity allowed. The Hausman test permits us to decide whether these discrepancies recommend the exclusion of the homogeneity restriction in some of the long-run parameters. Thus the second test complements the ﬁrst one because, if homogeneity is rejected using the LR test, the Hausman test for the individual variables helps identify the variable source of the heterogeneity. Concerning the dynamics of the model, the short-run has been modeled using up to two lags, as derived in the application of the Schwarz Bayesian criterion for lag selection. In the second and third columns of table 9.2 we present the information criteria used in the selection of the two models, and show the corresponding LR homogeneity test results along with the concrete hypotheses tested for the three groups of countries analyzed. In model 1, all the variables were considered, and it has higher AIC and SBC than model 2. No null hypothesis of homogeneity in the long-run parameters could be accepted for any of the groups of countries analyzed (e.g., see, for N ¼ 7, w 2 ð18Þ ¼ 67:81 with a probability of [0.00]). Also the long-run parameter of the variable oildept is nonsigniﬁcant. Where some heterogeneity was allowed, speciﬁcally in the oil dependency variable, the results did not improve.10 Model 2 is a restricted version of model 1, where oildept has been excluded. The information criteria are smaller, and after we imposed the condition that not all the long-run parameters must be equal for all the countries, the restrictions for the rest of the variables in the three

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Table 9.2 Comparison of the speciﬁed models Variables AIC

SBC

LR test

drrt dpext oildt dnfat

dpro t

N¼7 Model 1

1714

1686

w 2 ð18Þ ¼ 67:81½0:00

0

¼E

0

¼E

¼E

Model 2

1691

1665

w 2 ð12Þ ¼ 20:68½0:05**

0

¼E

—

0

¼E

N ¼ 4: Euro-area Model 1

1036

1018

w 2 ð6Þ ¼ 17:95½0:00

0

0

0

¼E

¼E

Model 2

998

982

w 2 ð9Þ ¼ 15:87½0:07**

0

¼E

—

¼E

¼E

w 2 ð6Þ ¼ 11:37½0:07**

0

¼E

—

¼E

0

N ¼ 3: Non-euro Model 1 763.74

748.40

w 2 ð4Þ ¼ 28:51½0:00

0

0

0

¼E

¼E

Model 2

750

w 2 ð4Þ ¼ 8:55½0:07**

0

¼E

—

0

¼E

763

Note: AIC stands for Akaike Information Criterium, SBC for Swartz Bayesian criterium and LR test is the likelihood ratio test for equality of either some or all the long-run parameters (probability values appear in parentheses). Two asterisks denote acceptance of the restriction on the long-run parameters at 5 percent signiﬁcance level. 0 stands for the assumption of different parameter values for all the N members of the panel. The homogeneity hypothesis is represented by the symbols ¼ E.

conﬁgurations could be accepted. For example, for N ¼ 7, the homogeneity restriction is accepted for dprot and dpext ( w 2 ð12Þ ¼ 20:68 with a probability of [0.05]), although it is necessary to allow for some heterogeneity in the real interest rate and in the net foreign asset differential. The estimates and the associated t-statistics are presented in the ﬁrst column of table 9.3, where all variables but drrt are signiﬁcant. It should be noted that the error correction coefﬁcient is highly signiﬁcant and of a reasonable magnitude (0.120). Thus the adjustment toward equilibrium will take approximately two years. In tables 9.4 and 9.5 the information concerns the long-run relations among the countries as well as the misspeciﬁcation tests. As is evident, apart from some normality departures in some of the countries, the individual equations pass the misspeciﬁcation tests. Moreover the R 2 in almost every case (Canada excepted) is over 0.80. The estimated parameters conform to the theory and are of correct sign. Thus the increase in the real interest differential causes the currency to appreciate (b1 < 0). The expansionary ﬁscal policy in the United States relative to the other countries causes the currency (b2 > 0Þ to depreciate, whereas an increase in relative productivity

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Table 9.3 Pooled mean group estimates Variables

All countries ðN ¼ 7Þ

Euro-area ðN ¼ 4Þ

Non-euro ðN ¼ 3Þ

Model 2: rerdolit ¼ ai þ b1i dproit þ b2i drrit þ b 3i dnfait þ b 4i dpexit drrt dpext dprot dnfat ecmt1

0.005 a

0.007 a

0.006 a

0.008 a

(1.58)

(1.92)

(2.38)

(2.23)

0.003 (2.95)

0.003 (2.48)

0.002 (2.09)

0.008 (2.72)

0.749 a

0.851

0.870

(27.02)

(22.34)

(7.12)

0.314

0.288

(5.57)

(6.94)

(6.58)

0.120

0.126

0.134

0.149

(3.83)

(2.99)

(3.15)

(4.77)

0.327 a

0.836 (15.47) 0.266 a (1.59)

Note: Student’s t is in parentheses. Superscript ‘‘a’’ indicates that the corresponding variable was not subject to the restriction of equal long-run parameters for all the members of the group. Thus its estimate is the mean group estimate, instead of the PMGE.

causes the currency (b3 < 0) to appreciate, due to the BalassaSamuelson effect. Finally, an increase in the relative net foreign assets position also induces appreciation (b 4 < 0). Notice that in the long-run parameter estimates of drrt and dnfat , we do not impose equality of all the cross-sectional elements. The individual country estimates are presented in detail in table 9.4. Although with larger N this technique has more advantages, due to our focus on the euro area, we have also estimated the dynamic panel data for the four EMU countries with the information available, as well as for the other three countries considered. The long-run parameters estimates, also presented in table 9.3, are very similar to those obtained for the larger group. Recall from table 9.2 the information criteria (also smaller than in model 1), as well as the LR tests for homogeneity in the long-run parameters, for the euro-area countries. In this case, after imposing that drrt is heterogeneous for the members of the group, we accept the homogeneity of the other three explanatory variables. As an additional test for homogeneity, we used the Hausman test for the variable dprot , which did not accept the similarity between the coefﬁcient estimated using the PMG estimator and the MG estimator, where heterogeneity

N¼7 Countries

drr t

N¼4 dpro t

dnfa t

dpex t

ecm t1

drr t

N¼3 dpro t

dnfa t

dpex t

ecm t1

drr t

dpro t

dnfa t

dpex t

ecm t1

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

Model 2 Germany Spain

0.005

0.851

0.328

0.003

0.120

0.006

0.74

0.288

0.002

0.128

(1.58)

(27.02)

(5.57)

(2.95)

(3.83)

(1.91)

(8.52)

(6.57)

(2.09)

(3.92)

0.0001 (0.08)

France Italy Canada Japan United Kingdom

0.851

0.372

0.003

0.117

(27.02)

(2.81)

(2.95)

(2.99)

0.0001 (0.09)

0.891

0.288

0.002

0.123

(8.39)

(6.57)

(2.09)

(3.10)

0.005

0.851

0.330

0.003

0.215

0.005

0.907

0.288

0.002

0.246

(3.46)

(27.02)

(5.27)

(2.95)

(4.52)

(4.24)

(20.85)

(6.57)

(2.09)

(4.90)

0.004

0.851

0.127

0.003

0.096

0.011

0.454

0.288

0.002

0.039

(1.46)

(27.02)

(1.16)

(2.95)

(2.72)

(1.08)

(1.30)

(6.57)

(2.09)

(1.60)

—

—

—

0.007

0.851

0.350

0.003

(3.73)

(27.02)

(7.07)

(2.95)

0.009

0.851

0.430

0.003

(2.51)

(27.02)

(6.95)

(2.95)

0.003

0.851

0.043

0.003

(2.12)

(27.02)

(2.07)

(2.95)

0.144 —

—

(4.15) 0.126 —

—

—

—

—

(3.33) 0.217 — (3.91)

—

—

—

—

0.008

0.836

0.383

0.007

0.139

(3.79)

(15.47)

(15.47)

(2.72)

(4.18)

0.011

0.836

0.478

0.007

0.100

(2.26)

(15.47)

(5.73)

(2.72)

(2.95)

0.003

0.836

0.063

0.007

0.207

(2.28)

(15.47)

(2.53)

(2.72)

(3.84)

Euro-Dollar Exchange Rate: Is It Fundamental?

Table 9.4 Individual countries estimates

289

M. Camarero, J. Ordo´n˜ez, and C. Tamarit

290

Table 9.5 Individual countries speciﬁcation tests R

2

Correlation

FF

NO

HE

34.03* 36.63*

36.82* 0.03

Model 2 ðN ¼ 7Þ Germany Spain

0.882 0.829

0.71 0.10

17.43* 1.67

France

0.890

0.18

1.87

4.39

1.07

Italy

0.850

3.71

1.21

35.98*

0.08

Canada

0.578

1.28

0.52

2.36

0.13

Japan

0.869

0.01

0.54

5.68

0.00

United Kingdom

0.844

1.09

0.33

25.79*

0.52

is allowed.11 Once the two variables are not constrained to be homogeneous, the model passes the Hausman test. Note that in table 9.3 the estimation results for the two cases are very similar. All the variables are signiﬁcant and the error correction term is slightly larger in the second case. For the other three countries (Canada, Japan, and United Kingdom), the homogeneity of all the variables is rejected. Only after allowing heterogeneity in drrt and dnfat the homogeneity of the other long-run parameters can be accepted. Model 2 and model 1’s AIC and SBC are similar, but only in model 2 the partial homogeneity is accepted after the restrictions are imposed, this being the test w 2 ð4Þ ¼ 8:55 with a probability of [0.07]. Thus model 2 seems adequate also for N ¼ 3. The long-run estimates of the parameters have similar magnitude if compared with the larger model. The only exception is dpext , whose value is 0.008 in contrast with 0.003. The error correction coefﬁcient takes the value of 0.149 and an associated student t of 4.77. 9.3.2

Aggregate European Results: The Euro and the Dollar

The preceding panel analysis gives some clues about the behavior of the dollar in terms of major world currencies. As we expected, the results do not ﬁt a simple model (e.g., the Meese and Rogoff 1988 real interest differential), but a rather eclectic speciﬁcation as it includes variables both from the demand and the supply sides of the economy. In our results the role of productivity differentials supports the fulﬁllment of the Balassa-Samuelson effect. The real interest rate differential

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Table 9.6 Cointegration test statistics r

Eigenvalues

Trace

Trace (R)

Trace 95%

0

0.3748

122.7**

97.28*

94.2

1

0.3420

81.78**

64.86

68.5

2

0.2791

45.36

35.97

47.2

3 4

0.1085 0.0699

16.88 6.883

13.39 5.429

29.7 15.4

5

0.0065

0.571

0.452

3.8

Note: The critical values are given with 95 percent critical values based on a response surface ﬁtted to the results of Osterward-Lenum (1992). (R) stands for the small-sample correction of the trace tests statistics proposed by Reimers (1992). * and ** denotes rejection of the null hypothesis at 5 and 1 percent signiﬁcance level respectively.

is also present, although this is not the exclusive determinant of real exchange rate behavior: the ﬁscal policies and the net foreign assets of the countries are among the explanatory variables. The only variable that did not show a signiﬁcant contribution was the real oil price. The additional conclusion that can be drawn from the dynamic panel analysis is that overall, the model estimated for the dollar real exchange rate does not change much with the different conﬁgurations of the countries (besides the minor exceptions already mentioned). Once the panel analysis has been completed for the European countries separately, we focus on the ‘‘synthetic’’ euro-area variables. The two approaches are complementary as the use of panels allows for heterogeneity. In fact the lack of heterogeneity is one of the main criticisms of aggregate analyses. If the results from these two complementary methodologies do not show important discrepancies, we can be more conﬁdent in using the aggregate series for inference and policy analysis. For this part of the analysis we use the Johansen (1995) method for the estimation and identiﬁcation of cointegrated systems where differentials are no longer calculated for the United States relative to every other country but relative to a representative euro-area variable. First in the analysis we studied the order of integration of the variables, using a stationarity testing strategy in the context of the VAR system. All the variables turned out to be I(1).12 Table 9.6 shows the trace test statistics for the determination of the number of cointegration relationships.13 The Reimers adjusted trace test statistics are also shown. Clearly, the trace test statistic fails to reject the existence of two

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292

cointegration vectors, whereas the Reimers adjusted test fails to reject one cointegration vector. To gain insight on the appropriate number of cointegration vectors, we need to add to this analysis information about the roots of the companion matrix: three are almost unity and other two are pretty close to unity, implying that ﬁve is the number of common stochastic trends. Moreover, for r ¼ 1, the largest roots are removed, leaving no near unit root in the model, so this must be the appropriate choice for r. In addition, from the time path plot for each of the feasible cointegration vectors, only the ﬁrst one seems to be stationary. The recursive analysis of the system provides other useful information regarding the existence of cointegration: the recursive time path of the nonadjusted trace statistic suggests that at most there exist two cointegration vectors though one is the most sensible outcome. From all this evidence, the most feasible choice is the existence of one cointegration vector, that is, p r ¼ 5, where p is the number of common stochastic trends. We can proceed to identify the cointegration vector by imposing the overidentifying restriction that the variable for energy dependence (oildept ) is excluded from the long-run: the LR statistic is w 2 ð1Þ ¼ 3:43 with a probability value of 0.06. The resulting cointegration vector takes the form (standard errors in parentheses): qt ¼ 0:011dpext 0:007drrt 0:77 dprot 0:36 dnfat : ð0:001Þ

ð0:001Þ

ð0:033Þ

ð5Þ

ð0:032Þ

At this stage of the analysis we can already compare the results obtained using the PMG in the dynamic panel with the time series model using aggregate variables. Taking into account the results presented in table 9.3 for model 2, we can observe that the results are very similar. First, the variable relative oil dependency (oildept ) that turned out not to be signiﬁcant in the panel analysis can be also excluded from the time series cointegration vector. Second, the four variables have the same signs even if we are using quite different estimation techniques. Moreover the parameters’ estimates are not very different in magnitude, the only exception being the case of dpext , where the time series value is 0.011 and 0.002 for the panel. In other cases the parameters are almost equal, as for the real interest differential (0.007 for the aggregate model and 0.006 for the panel) or the productivity differential (0.77 in the time series model and 0.749 in the panel).14 Finally, the net foreign asset position is also in a similar range: 0.36 in the aggregate model and 0.288 in the panel.

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Once we have identiﬁed the cointegration vector, we formally test for weak exogeneity of the variables in the system. According to our results all the variables appear to be weakly exogenous with the only exception of the real exchange rate. The joint hypothesis of weak exogeneity and the identifying restrictions on the cointegration space b are accepted: the LR statistic value is w 2 ð6Þ ¼ 11:16 with a probability of 0.08. We present next the error correction model (ECM hereafter) for the univariate partial model (t-values in brackets): Dqt ¼ 0:291 0:375 Ddprot 0:185 Ddprot1 0:105 Ddprot2 ½5:010

½7:675

½2:999

½2:068

0:002 Ddrrt3 0:184 ecmt1 þ et : ½2:002

ð6Þ

½5:007

Misspeciﬁcation tests Residual correlation: Fð5; 76Þ ¼ 1:0856½0:3752 ARCH: Fð4; 73Þ ¼ 0:8310½0:5098 Normality: w 2 ð2Þ ¼ 1:1128½0:5733 Heteroscedaticity (squares): Fð10; 70Þ ¼ 1:0960½0:3774 Heteroscedaticity 1:1588½0:3203

(squares

and

cross

products):

Fð20; 60Þ ¼

In the equation above et is a vector of disturbances and ecmt1 is the cointegration vector (5). None of the misspeciﬁcation tests reported here rejects the null hypothesis that the model is correctly speciﬁed. In addition we apply the Hansen and Johansen (1993) approach to test for parameter instability in the cointegration vector. Speciﬁcally we test both whether the cointegration space and each of the parameters in the cointegration vector are stable. We also test for the stability of the loading parameters. If both a and b appear to be stable, we can conclude that our error correction model is well speciﬁed for the period analyzed. Panel a of ﬁgure 9.1 shows the plot of the test for constancy of the cointegration space. The test statistic has been scaled by the 95 percent quantile in the w 2 -distribution so that unity corresponds to the 5 percent signiﬁcance level. The test statistic for stability is obtained using both the Z-representation and the R-representation of our model. In the former, stability is analyzed by the recursive estimation of the whole model, and in the latter the short-run dynamics are ﬁxed and only the long-run parameters are re-estimated. Thus the

Figure 9.1 Stability of the cointegration space

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295

R-representation is the relevant one to assess the stability of the cointegration space, which is clearly accepted. Panels b and c of ﬁgure 9.1 show, respectively, the stability tests for each of the beta coefﬁcients and for the loadings to the cointegration vector. In all cases, the recursively estimated coefﬁcients lay within the 95 percent conﬁdence bounds showing a remarkable stability. To summarize, we can conclude that the cointegration space is stable, that is, the long-run parameters as well as the loadings do not show signs of instability. Finally, panel b of ﬁgure 9.2 presents several recursive tests of parameter stability for the parsimonious conditional model. Accordingly, our model is stable not only concerning the cointegration space but also the model as a whole. As for the real exchange rate ECM presented in equation (6), we should note that the error correction parameter presents the correct sign and magnitude (taking into account that the data are quarterly), and passes the Banerjee, Dolado, and Mestre (1992) cointegration test. In addition two of the variables appear in the dynamics of the real exchange rate. The ﬁrst is, with three lags, the real interest rate differential ðdrrt Þ, although it is borderline signiﬁcative. The negative parameter for this variable, as in the panel analysis, is the one expected from the theory. Second is the productivity differential measure, contemporaneous and lagged from one to two periods, with the same negative sign found in the long-run time series analysis and in the panel analysis reported in section 9.3.1 above. The important role that the productivity differential has in driving the system toward the equilibrium should be emphasized and also the fact that the adjustment starts in the same quarter where the shocks have occurred. We can again compare the error correction model of the aggregate European variables with the results for the panel. As in the time series case, the contemporaneous effects coming from the productivity differential are very important and of the same sign (with a t-statistic of 17.56), but the rest of the variables are not signiﬁcant. Concerning the error correction coefﬁcient, its magnitude is smaller in the panel (0.134). Although there is no consensus in the profession on a particular model speciﬁcation of exchange rate equations inspired by the New Open Macroeconomics literature (Sarno 2002), the results obtained in this chapter are compatible with these models. In particular, according to Lane (2002), net foreign assets positions are an important form of

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Figure 9.2 Dynamic forecast and recursive estimation

Euro-Dollar Exchange Rate: Is It Fundamental?

297

international macroeconomic interdependence. The inﬂuence of net foreign asset positions on the values of the real exchange rate has also been studied recently in Cavallo and Ghironi (2002) and Lane and Milesi-Ferretti (2001). In this chapter, we have used the net foreign asset dataset constructed in Lane and Milesi-Ferretti (2001), that is, the ‘‘adjusted cumulative current account,’’ and our results are compatible with the most recent empirical literature besides the previous empirical work.15 To complete our analysis, we check the predictive ability of the euroarea model. Table 9.7 presents ex post and ex ante forecasting results. To compute the ex post forecasts, we left out eight observations (two years) and re-estimated the model. From the one-step static forecast analysis, our model appears to deliver sensible and stable forecasts. The estimates for the dynamic forecast are carried out recursively: the estimation period is successively extended quarter by quarter so that the real exchange rate is forecasted for up to eight quarters into the future. Panel a of ﬁgure 9.2 shows graphically the predictive performance of our model. This graph plots the dynamic forecasts for the period 1997:1 to 1998:4 estimated by full-information maximum likelihood. The forecasts lie within the 95 percent conﬁdence interval, shown by the vertical error bars of plus or minus twice the forecast’s standard error. Moreover the ﬁt of the model is good, and there are no large departures from the actual values. Finally, the forecast quality of our model is also assessed by comparing its forecast accuracy with a random walk model for the real exchange rate. For this purpose we obtain the ratio between the root mean squared error (RMSE) corresponding to our VECM relative to the random walk. If the VECM presents a better predictive performance, that is, lower RMSE, this ratio will be below 1. In addition, following Diebold (1998), we carried out a formal test to gain insight into whether the random walk model can generate signiﬁcantly better forecasts from a statistical point of view. Thus, rejection of the null for this test implies that the random walk model does not provide signiﬁcantly better forecasts than our VECM. Table 9.7 presents the ratio of the two RMSE for a forecast horizon up to eight quarters as well as the signiﬁcance level for the Diebold and Mariano test statistic, which is indicated by asterisks in the third column. By these results the VECM outperforms the random walk model even in the shorter horizons, as can be seen from RMSE ratios, which are well below 1. Moreover the predictive performance of our model is statistically shown, rejecting

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Table 9.7 Static and dynamic forecasting A. One-step (ex post) forecast analysis: 1997:1 to 1998:4 Parameter constancy x1 x2 x3

w 2 ð8Þ ¼ 10:679 [0.2205] w 2 ð8Þ ¼ 8:9096 [0.3500]

Fð8; 73Þ ¼ 1:3349 [0.2402] Fð8; 73Þ ¼ 1:1137 [0.3643]

w 2 ð8Þ ¼ 9:5206 [0.3003]

Fð8; 73Þ ¼ 1:1901 [0.3169]

2

Forecast tests: w ð1Þ Using x1

Using x2

1997:1

3.4134 [0.0647]

2.6766 [0.1018]

1997:2

1.0618 [0.3028]

0.8527 [0.3558]

1997:3

1.3785 [0.2404]

1.0663 [0.3018]

1997:4

0.0069 [0.9337]

0.0062 [0.9369]

1998:1 1998:2

0.2791 [0.5973] 0.0428 [0.8361]

0.2503 [0.6168] 0.0380 [0.8454]

1998:3

3.6488 [0.0561]

3.2989 [0.0693]

1998:4

0.8479 [0.3571]

0.7203 [0.3960]

Forecast horizon

RMSE (ratio)

Signiﬁcance

B. Forecast quality: 1997:1 to 1998:4 1997:1

0.2509

1997:2

0.2176

1997:3

0.1887

1997:4

0.1821

***

1998:1 1998:2

0.1716 0.1676

*** ***

1998:3

0.1665

***

1998:4

0.1728

***

Note: x1 ; x2 , and x3 are indexes of numerical parameter constancy. The former ignores both parameter uncertainty and intercorrelation between forecasts errors at different time periods. x2 is similar to x1 but takes parameter uncertainty into account. x3 takes both parameter uncertainty and intercorrelations between forecasts errors into account. Forecast test are the individual test statistics underlying x1 and x2 . *** stands for 1 percent error probability.

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for all the forecast horizons the superiority of the random walk model with a probability as low as 1 percent. 9.4

Conclusions

In this chapter we apply two different but complementary techniques and approaches to the study of the evolution of the dollar real exchange rate in relation with the euro-area currencies. First, using panel techniques, we study the long-run relationship between the bilateral real exchange rate of the dollar versus the currencies of ﬁve European countries, Canada, and Japan. Second, in a time series framework, we use euro-area aggregate or ‘‘synthetic’’ variables to study the behavior of the dollar–euro real exchange rate. Our aim was to compare the results obtained from the two approaches and for the same time span. Given that the lack of heterogeneity is one of the main criticisms commonly associated with aggregate analyses, in using a panel analysis, we allow for individual country differences. The similarity of the results obtained by the two methods adds robustness to the euro-area measures. Heterogeneity is a feature not evident in other papers dealing with the real exchange rate of the euro. We maintain this distinction in summarizing the most important empirical results. First, concerning the dynamic panel analysis, we use the methodology of Pesaran et al. (1999), which allows for short-run heterogeneity for the individual components of each panel and a formal test of homogeneity in the long-run parameters. We ﬁnd that both the supply- and demand-side factors can be accounted for to explain the bilateral real exchange rate of the US dollar. In particular, the estimated error correction models support a speciﬁcation that includes relative productivity, the real interest rate differential, the difference in public expenditure, and the relative net foreign asset position. This type of relation holds not only for the euro countries but also for the whole group and for the rest-of-the-world countries. We arrived at the same long-run speciﬁcation using the Johansen technique in a time series context. Therefore, we showed that even if we allow a larger degree of heterogeneity in the panel and even if we use different estimation techniques, the results appear to be almost identical. In addition, in the aggregate time series empirical model, the cointegration vector passed all the applied stability tests. Last, the estimated VECM was remarkably predictive in performance and provided better forecasts than the random walk for both the short and the medium terms.

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The long-run results showed the dollar–euro exchange rate to depreciate if American ﬁscal policy becomes more expansionary than European ﬁscal policy. However, productivity growth and real interest rate differentials, together with the accumulated net foreign assets, will appreciate the currency. Appendix: Data Sources We used quarterly data for the period 1970:1 to 1998:4 from France, Germany, Italy, Spain, and the United Kingdom. We included data from the United States (the home country) and Canada and Japan. The data were obtained from the magnetic tapes of the International Monetary Fund International Financial Statistics (IFS) with the exception of employment and oil balances data, which came from the International Sectoral Database (OECD). The net foreign assets data were taken from Lane and Milesi-Ferretti (2001), L-M hereafter. The nominal exchange rate for the euro relative to the US dollar was from the database for European variables of the Banco Bilbao Vizcaya Argentaria (BBVA). The panel data were constructed as follows: rerdolit : Bilateral real exchange rate of the US dollar relative to the other currencies considered. The nominal exchange rate, st , has been deﬁned as currency units of US dollar to purchase a unit of currency j: ! ptUSA rerdolt ¼ log ; j s t pt j

where ptUSA and pt are respectively the CPI for the Unites States and the foreign country. (Source: IFS) drr it : Real interest rate differential. The nominal interest rates are call money rates as deﬁned by the IMF. In order to obtain the real variables, the expected inﬂation rate is the smoothed variable based on CPI indexes using the Hodrick and Prescott ﬁlter: pt ¼

pt pt1 100; pt1

pte ¼ pt ptt ; rrt ¼ rt pte ; j

drret ¼ rrtUSA rrt ;

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301

where pte is expected inﬂation ﬁltered using the HP ﬁlter, ptt is the transitory component of inﬂation, rrtUSA is the American real interest rate, j and rrt the foreign rate. (Source: IFS) dproit : Apparent productivity differential in labor, j

dprot ¼ protUSA prot ; j

where protUSA and prot are respectively the American and the foreign apparent labor productivity. This is calculated as ! j gdpt 1 j prot ¼ log ; j s t employment t

with

gdptUSA ¼ log : employmenttUSA

protUSA

(Source: IFS and OCDE) dpexit : Public expenditure differential, calculated as j

dpext ¼ pextUSA pext ; j

where pextUSA and pext are respectively the American and the foreign government spending. The government spending is calculated relative to GDP: pext ¼

pexnt 100; gdpnt

where pexpnt is nominal public expenditure. (Source: IFS) dnfait : Net foreign assets differential, j

dnfat ¼ rnfatUSA rnfat ; j

where rnfatUSA and rnfat stands respectively for the American and the foreign’s net foreign asset position relative to the GDP in US dollar: j

nfat

j

rnfat ¼

j

gdpt ð1=st Þ

and rnfatUSA ¼

nfatUSA gdptUSA

(Source: L-M)

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302

oildepit : Relative oil dependence, j

oildept ¼

balt brent price 100; USA balt cpitUSA j

where baltUSA and balt are measures of energetic dependence for the United States and the foreign country respectively. This is obtained as balt ¼

Net oil imports : gdpnt

(Source: IFS and OCDE) For the time series analysis, differentials are no longer calculated for the United States relative to every other country but relative to a representative European variable. The latter is obtained as the weighted average of the corresponding national values already used in the panel analysis. The weights are the share of national GDP relative to the GDP for our idyosincratic euro area. The GDP are in constant terms and PPP, as reported by the OECD, the base year being 1993. The bilateral real exchange rate (qt ) of the US dollar relative to the euro is obtained as in the panel, where st is deﬁned as units of dollars required to purchase a euro. The sources for st are BBVA (from 1970:1 to 1997:4) and IFS for the rest of the sample. Notes The authors belong to INTECO, Research Group on Economic Integration, supported by Generalitat Valenciana. They want to acknowledge the ﬁnancial support of the project SEC2002-03651 from the CICYT and FEDER. The computations have been made using two Gauss routines: the pooled mean group estimation program, written by Y. Shin, and NPT 1.3, by Chiang and Kao (2001). The authors are very grateful to all the participants in the CESifo conference on Exchange Rate Modeling: Where Do We Stand? for their comments and, in particular, to the discussant, Jan-Egbert Sturn, and to Paul de Grauwe. The chapter has also beneﬁted from the comments of an anonymous referee. 1. See ECB (2002). 2. For a complete overview of different empirical approaches, see Williamson (1994), and more recently, MacDonald (2000). 3. For simplicity, we are omitting the NATREX and the PEER approaches. We consider the ﬁrst to be clearly connected to the FEER approach and the second to the BEER approach. 4. The breakdown between traded and nontraded goods has not been possible for the sample period, the OECD data available only reaching 1992. 5. Hamilton (1983) found that the energy price can account for innovations in many US macroeconomic variables. Amano and van Norden (1998) ﬁnd a stable link between the

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303

effective real exchange rate of the dollar and the oil price shocks. They also think that these shocks account for most of the major movements in the terms of trade. According to them, the correlations between the terms of trade and the one-period lagged price of oil are 0.57, 0.78, and 0.92 for the United States, Japan, and Germany, respectively. 6. A detailed description of the variables can be found in appendix A. 7. In addition, other speciﬁcations have been estimated in the empirical part of the model. In particular there are the simplest version of the Meese and Rogoff (1988) model (rerdolit ¼ ai þ b 1i drrit Þ and the Rogoff (1992) intertemporal model (rerdolit ¼ ai þ b 1i dpex þ b 2i dproit þ b 3i oildepit Þ. In the ﬁrst case, although the information criteria were encouraging, the model was not very explanatory (with R 2 under 0.10 for the individual countries). As for the Rogoff (1992) model, none of the hypotheses concerning the long-run parameters were accepted, and the information criteria did not recommend its choice. The results, although not reported in this chapter, are available upon request. 8. Finally published as Levin, Lin, and Chu (2002). 9. Groen (2000) and Mark and Sul (2001) have also recently applied panel techniques to estimate models for the dollar exchange rate determination. In particular, Groen (2000) applies a panel version of the Engle and Granger two-step procedure under the homogeneity restriction on the long-run parameters. Mark and Sul (2001) apply dynamic OLS estimators, and also impose homogeneity in the cross sections. 10. All the results concerning this speciﬁcation are available upon request. 11. The p-values associated with the test for each of the variables are the following: dpext [0.40], dnfat [0.51], and dprot [0.00]. 12. The results are available upon request. 13. The model has been speciﬁed with the constant unrestricted. Previous to this choice, the different possible speciﬁcations for the deterministic components were compared using the procedure suggested by Johansen (1996). 14. The magnitude of this parameter also lies in the range commonly found in the empirical literature, as reported by Gregorio and Wolf (1994). According to them, this range is ð0:1; 1:0Þ. 15. We should note that the real exchange rate is deﬁned in our chapter in the opposite way. More precisely, an increase in the real exchange rate corresponds to a real depreciation.

References Alberola, E., S. Cervero, H. Lo´pez, and A. Ubide. 1999. Global equilibrium exchange rates: Euro, dollar, ‘‘ins,’’ ‘‘outs,’’ and other major currencies in a panel cointegration framework. IMF Working Paper 99/175. Alquist, R., and M. D. Chinn. 2002. Productivity and the euro–dollar exchange rate puzzle. NBER Working Paper 8824. Amano, R., and S. van Norden. 1998. Oil prices and the rise and fall of the US real exchange rate. Journal of International Money and Finance 17: 299–316. Banerjee, A., J. J. Dolado, and R. Mestre. 1992. On some simple tests for cointegration: The cost of simplicity. Bank of Spain Working Paper 9302.

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Baxter, M. 1994. Real exchange rates and real interest differentials. Have we missed the business-cycle relationship? Journal of Monetary Economics 33: 5–37. Cavallo, M., and F. Ghironi. 2002. Net foreign assets and the exchange rate: Redux revived. Journal of Monetary Economics 49(5): 1057–97. Campbell, J. Y., and R. H. Clarida. 1987. The dollar and real interest rates. CarnegieRochester Conference Series on Public Policy 27: 103–40. Chiang, M. H., and C. Kao. 2001. Nonstationary panel time series using NPT 1.2. A user guide. Center for Policy Research. Syracuse University. Clark, P. B., and R. MacDonald. 1999. Exchange rates and economic fundamentals: A methodological comparison of BEERs and FEERs. In R. MacDonald and J. L. Stein, eds., Equilibrium Exchange Rates, Norwell, MA: Kluwer Academic Publishers, pp. 285–322. Clostermann, J., and B. Schnatz. 2000. The determinants of the euro–dollar exchange rate: Synthetic fundamentals and a non-existing currency. Konjunkturpolitic, Applied Economics Quarterly 46(3): 274–302. De Grauwe, P. 1997. Exchange rate arrangements between the ins and the outs. In Masson et al., eds., EMU and the International Monetary System. Washington: IMF. De Grauwe, P. 2000. Exchange rates in search of fundamentals: the case of the euro– dollar rate. International Macroeconomics Discussion Paper Series 2575. CEPR. Diebold, F. X. 1998. Elements of Forecasting. Cincinnati, OH: South-Western College Publishing. Gregorio, J., and H. Wolf. 1994. Terms of trade, productivity and the real exchange rate. NBER Working Paper 4807. ECB. 2000. The nominal and real effective exchange rates of the euro. Monthly Bulletin, April. ECB. 2002. Economic fundamentals and the exchange rate of the euro. Monthly Bulletin, April. Edison, H. J., and W. R. Melick. 1995. Alternative approaches to real exchange rates and real interest rates: Three up and three down. International Finance Discussion Paper 518. Board of Governors of the Federal Reserve System. Edison, H. J., and B. D. Pauls. 1993. A re-assessment of the relationship between real exchange rates and real interest rates: 1974–1990. Journal of Monetary Economics 31: 165–87. Groen, J. J. J. 2000. The monetary exchange rate model as a long-run phenomenon. Journal of International Economics 52: 299–319. Hadri, K. 2000. Testing for unit roots in heterogeneous panel data. Econometrics Journal 3: 148–61. Hamilton, J. D. 1983. Oil and the macroeconomy since World War II. Journal of Political Economy 91: 228–48. Hansen, H., and S. Johansen. 1993. Recursive estimation in cointegrated VAR-models. Preprint 1993, n. 1. Institute of Mathematical Statistics. University of Copenhagen. Hooper, P., and J. Morton. 1982. Fluctuations in the dollar: A model of nominal and real exchange rate determination. Journal of International Money and Finance 1: 39–56.

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Im, K., M. H. Pesaran, and Y. Shin. 1995. Testing for unit roots in heterogeneous panels. Department of Applied Economics. University of Cambridge. Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector Auto-regressive Models. Oxford: Oxford University Press. Johansen, S. 1996. Likelihood based inference for cointegration of non-stationary time series. In D. R. Cox, D. Hinkley, and O. E. Barndorff-Nielsen, eds., Likelihood, Time Series with Econometric and Other Applications. London: Chapmann and Hall. Lane, P. R. 2002. Discussion of ‘‘Net foreign assets and the exchange rate: Redux revived’’ by M. Cavallo and F. Ghironi, Carnegie-Rochester Conference on Public Policy, November 2001. Mimeo. http://econserv2.bess.tcd.ie/plane/. Lane, P. R., and G. M. Milesi-Ferretti. 2001. The external wealth of nations: Measures of foreign assets and liabilities in industrial and developing countries. Journal of International Economics 55(2): 263–94. Ledo, M., and D. Taguas. 1999. Un modelo para el do´lar-euro. Situacio´n 6 (diciembre). Servicio de Estudios, BBVA. Levin, A., and C. F. Lin. 1992. Unit root tests in panel data: Asymptotic and ﬁnite-sample properties. UC San Diego, Working Paper 92-23. Levin, A., C. F. Lin, and J. Chu. 2002. Unit root tests in panel data: Asymptotic and ﬁnitesample properties. Journal of Econometrics 108: 1–24. Maeso-Ferna´ndez, F., C. Osbat, and B. Schnatz. 2001. Determinants of the Euro real effective exchange rate: A BEER/PEER approach. ECB Working Paper 85. MacDonald, R. 1998. What determines real exchange rates? The long and the short of it. Journal of International Financial Markets, Institutions and Money 8: 117–53. MacDonald, R. 2000. Concepts to calculate equilibrium exchange rates: An overview. Discussion Paper 3/00. Economic Research Group of the Deustche Bundesbank. MacDonald, R., and J. Nagayasu. 2000. The long-run relationship between real exchange rates and real interest differentials: A panel study. IMF Staff Papers 47: 116–28. Makrydakis, S. P. de Lima, J. Claessens, and M. Kramer. 2000. The real effective exchange rate of the Euro and economic fundamentals: A BEER perspective. Mimeo. European Central Bank. March. Mark, N. C., and D. Sul. 2001. Nominal exchange rates and monetary fundamentals: Evidence from a small post–Bretton Woods panel. Journal of International Economics 53: 29–52. Meese, R., and K. Rogoff. 1988. Was it real? The exchange rate-interest differential relation over the modern ﬂoating-rate period. Journal of Finance 43: 933–48. Meredith, G. 2001. Why has the euro been so weak? IMF Working Paper 01/155. Osterward-Lenum, M. 1992. A note with quantiles of the asymptotic distribution of the LM cointegration rank statistics. Oxford Bulletin of Economics and Statistics 54: 461–72. Pesaran, M. H., Y. Shin, and R. P. Smith. 1999. Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association 94(446): 621–34.

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Reimers, H.-E. 1992. Comparisons of tests for multivariate cointegration. Statistical Papers 33: 335–59. Rogoff, K. 1992. Traded goods consumption smoothing and the random walk behaviour of the real exchange rate. Bank of Japan Monetary and Economic Studies 10: 783–820. Sarno, L. 2002. Toward a new paradigm in open economy modeling: Where do we stand? Federal Reserve Bank of St. Louis Review (May–June): 21–36. Williamson, J. 1994. Estimating Equilibrium Exchange Rates. Washington: Institute for International Economics. Wu, J. L. 1999. A re-examination of the exchange rate-interest differential relationship: Evidence from Germany and Japan. Journal of International Money and Finance 18: 319–36.

10

Dusting off the Perception of Risk and Returns in FOREX Markets Phornchanok J. Cumperayot

After the demise of the Bretton Woods system in early 1973, many industrialized countries turned to a (semi-) ﬂoating exchange rate regime.1 Academics try to explain causes of exchange rate ﬂuctuations and search for policy recommendations. There are numerous papers attempting at explaining the movement of exchange rates.2 Many theoretical versions, however, fail to determine exchange rates in practice. Empirical investigations have been carried out to test the exchange rate theories and the predictability of exchange rates.3 The empirical support for the theories has been rather weak. In this chapter a nonlinear model for exchange rates is proposed, based on the monetary exchange rate theory and the theory of ﬁnancial asset pricing, so as to provide alternative insights about the anomalous behavior of exchange rates. This model is inspired by the pioneering work of Hodrick (1989), who introduced the volatilities of macroeconomic fundamentals in the exchange rate model as additional risk factors. Unlike Hodrick (1989), I incorporate macroeconomic risk into the ﬂexible-price and the sluggish-price monetary models. This allows the long-run and short-run effects of the fundamental uncertainty to be examined. The empirical results are rather striking and supportive compared to those of Hodrick (1989). As I show in this chapter, in the long run the nonlinear model explains how an increase in domestic money supply or a decrease in domestic real income leads to depreciation of the domestic currency, and vice versa for the foreign variables. Time-varying conditional variances of the macroeconomic variables, representing macroeconomic risk, can be related to the deviation of the exchange rate from its fundamental-based value. Macroeconomic uncertainty inﬂuences the perception of FOREX risk and consequently inﬂuences market expectations about compensation for risk bearing. Due to risk aversion,

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high risk is accompanied by high expected future returns, or equivalently a current depreciation of the currency. In the short run, the nonlinear model is shown to provide evidence for correction of equilibrium errors toward the long-run equilibrium. These results indicate that macroeconomic sources of FOREX risk is a missing factor in exchange rate studies and that the monetaryapproach models is potentially still useful. In section 10.1, I give the motivation of my work. In section 10.2, I discuss the nonlinear dynamic model. I report its econometric results in section 10.3, and make some concluding remarks in section 10.4. 10.1

Motivation for the Model

The monetary approach to model exchange rates has been viewed as one of the most dismal failures in modern economics (see Flood and Rose 1999). Nevertheless, it can hardly be denied that for our anticipation of exchange rates we rely on economic fundamentals, and often in the manner predicted by the monetary-based exchange rate models. My work was inspired by Dornbusch (1976) and Hodrick (1989). I use their model for exchange rates to reconsider the expectation assumptions used in the traditional exchange rate models by exploiting the statistical regularity of time-varying conditional variances of fundamental growth rates. As suggested by Dornbusch (1976), a fundamental change from its equilibrium level may cause a short-run overshooting in the exchange rate. Volatility in the macroeconomic variables may consequently induce volatility in the exchange rate. In turn the uncertainty in macroeconomic fundamentals may inﬂuence the perception of risk in the markets, and subsequently through the risk premium it may price returns on the exchange rate, as stated in Hodrick (1989). This seems like a natural way to explain the exchange rate risk premium, as arising from variation in conditional variances of exchange rate returns, but Hodrick (1989) ﬁnds little support for the idea. After more than a decade since his research and almost three decades of ﬂoating exchange rate regime, it is time to reinvestigate the hypothesis in Hodrick (1989). In the literature, exchange rates rely on two factors: the current fundamental levels, f~t , and the expectation of future exchange rates, Et ½etþ1 .4 A general framework of the models in the exchange rate literature can be summarized as shown in Cuthbertson (1999):5

Dusting off the Perception of Risk and Returns in FOREX Markets

309

et ¼ Et ½etþ1 af~t ;

ð1Þ

where et is the logarithm of the nominal exchange rate, f~t represents the fundamentals that may differ in each model, and Et ½ is the conditional expectation operator. Apart from many possible estimation problems,6 as expectations about the future exchange rate are likely to be a self-fulﬁlling prophecy, the expectation formation deserves considerable attention. In the context of the present value relation, it is known that persistent movement in an asset’s expected return tends to have dramatic effects on the asset price, as it makes the price more volatile than in the case of a constant expected return.7 This also holds for the currency price, for which the expected return is represented by the expected price change. However, the source of the expectation variation is an unresolved issue. In this chapter, I provide an alternative explanation for the expectation formation in the exchange rate models. According to the exchange rate literature, the fundamental solution of the exchange rate is determined by the expected present value of macroeconomic fundamentals, discounted at a constant rate (following from Cuthbertson 1999 in this case is equal to one):8 et ¼

y X

aEt ½ f~tþi :

ð2Þ

i¼0

P ~ By comparing this equation (i.e., et ¼ af~t y i¼1 aEt ½ ftþi ) to equation (1), we ﬁnd that the expected future fundamentals are used to determine the expected future exchange rate. However, in practice, the structure of expectation formation is not known, and the inﬁnite horizon is not easily speciﬁed. It is often assumed that the fundamental processes are a random walk process, Et ½xtþ1 xt ¼ 0. As a consequence the models are left with the current values of the fundamentals as representatives of the expected future fundamentals (e.g., see Meese and Rogoff 1983). As there is no expected change in the fundamentals, these rational expectation models imply zero expected exchange rate returns. Yet empirically positive correlations of exchange rate returns are found at short horizons, whereas negative serial correlations are reported at longer horizons (e.g., see Cuthbertson 1999). Moreover there is some evidence for predictability of the exchange rate at long horizons once the fundamentals are brought into the analysis.9 It is unlikely that the expected returns are zero. In particular,

310

Ph. J. Cumperayot

patterns of time variation in the mean and the variance of the fundamental changes have actually been observed. Like exchange rate returns, there is strong evidence of time-varying conditional variances of the fundamentals, although this is not well documented.10 As there exists systematic fundamental volatility, I investigate in this chapter whether the fundamental uncertainty (e.g., through the risk premium) can determine expected exchange rate returns and thus the exchange rate movement. This doctrine is similar to the well-known theme of asset pricing models, such as the capital asset pricing model (CAPM) developed by Markowitz (1959), Sharpe (1964), and Lintner (1965) and the arbitrage pricing theory of Ross (1976). The theory’s goal is mainly to quantify the assets’ equilibrium expected returns from the risk of bearing the assets. To relate exchange rate risk and return, Fama (1984) ﬁnds that the variation in the risk premium in the forward exchange market is more pronounced than the expected depreciation rate (i.e., expected exchange rate return). Frankel and Meese (1987) indicate that changes in conditional variance of the exchange rate have substantial impacts on the level of the exchange rate. Hodrick’s (1989) model theoretically predicts that changes in the macroeconomic variances affect risk premia and therefore, exchange rates. Yet the empirical results are not supportive. 10.2

The Model

The present value of the exchange rate for the ﬂexible-price model can be written as e t ¼ v0

y X

v2i þ v1

y X

i¼0

v2i Et ½ f~tþi ;

ð3Þ

i¼0

~ t ð1 þ gÞ y~t , and m ~ t and y~t are the logarithms of the where f~t ¼ m domestic money supply and real income with respect to the foreign levels. For the sluggish-price model, inertia is introduced into the price mechanism and thus the exchange rate equation. Cuthbertson (1999) shows that with the UIP condition the Dornbusch model gives rise to a form similar to equation (2): et ¼ Q1 et1 þ l

y X i¼0

Q2 Et1 ½~ktþi ;

ðQ1 ; Q2 Þ < 1;

ð4Þ

Dusting off the Perception of Risk and Returns in FOREX Markets

311

where ~kt 1 ð1=jÞ f~t þ ½ð1 yÞ=yj f~t1 . The exchange rate now depends on ~kt , namely current and lagged values of money supply and real income, and on its expected future values.11 Since the exchange rate is a discounted sum of expected future fundamentals (i.e., equations 2, 3, and 4), if the expectation of f~ (or ~k in a case of the sticky-price model) can be speciﬁed, an explicit process of the exchange rate can be found. A number of methods to incorporate the fundamentals’ variances into their expectations are discussed in appendix C. Here we assume that the fundamental series can be explained by their historical values and their time-varying second moment.12 Therefore the expected future fundamentals do not only depend on the current fundamental levels but also the expected variances of the fundamentals, representing the volatility of the fundamentals. An explicit solution of the ﬂexible-price model can then be written as ~ t þ a2 y~t þ a3 hm~ ; t þ a4 hy~; t : e t ¼ a0 þ a1 m

ð5Þ

In addition to the current fundamental values, the exchange rate is determined by time-varying conditional variances of the fundamentals, ht . For the sticky-price model the closed-form solution is ~ t þ b3 y~t þ b4 m ~ t1 þ b5 y~t1 þ b6 hm~ ; t et ¼ b0 þ b1 et1 þ b2 m þ b7 hy~; t þ b8 hm~ ; t1 þ b9 hy~; t1 ;

ð6Þ

in which the present and lagged values of the fundamentals and their time-varying conditional variances are included in the exchange rate determination. The levels of macroeconomic fundamentals are well known to be insufﬁcient for explaining exchange rate movements. In addition to the traditional monetary models, we introduce macroeconomic risk to describe the deviation of the excessive volatile exchange rate relative to the conventional prediction based on economic fundamentals. In this chapter the expectations of future fundamentals are reformulated by exploiting the systematic pattern of fundamental volatility, instead of assuming a random walk process. Equations (5) and (6) similarly predict that, ceteris paribus, an increase in money supply and a decrease in industrial production, relative to the foreign levels, tend to depreciate the domestic currency. Besides, we explain anomalous movements of the exchange rate, relative to the traditional paradigm, by the presence of volatility clusters in the fundamentals.13 To capture

312

Ph. J. Cumperayot

the currency price volatility, time variation in conditional variances of the fundamentals, captured by a GARCHð1; 1Þ model,14 are incorporated to describe expected exchange rate returns. The modiﬁed ﬂexible-price model in equation (5) is used to characterize the long-run equilibrium of exchange rates, while the modiﬁed sticky-price model in equation (6) corrects for fundamental disequilibrium. The idea to examine the long-run impacts of macroeconomic risk on the exchange rate may seem controversial at ﬁrst, as one would think that the exchange rate volatility is considered as a short-term phenomenon and has nothing to do with the long run. In fact, asset pricing models, such as CAPM, are used for the long-run equilibrium price determination. Intuitively the models say that one who holds risky assets expects to be compensated at least in the long run. 10.3

Speciﬁcation and Estimation

With regard to the exchange rate level, although many developments can cause permanent changes in the exchange rate, the cointegration relationship between the spot rates and macroeconomic fundamentals implies that there is some long-run equilibrium relation tying the exchange rate to its macroeconomic fundamentals (see Hamilton 1994).15 Moreover persistent movements in the fundamental volatility are likely to have larger impacts on exchange rate risk and returns than temporary movements. To model the exchange rate, we are therefore concerned with the cointegration among the variables in equation (5), whereas equation (6) is applied as an error-correction model to explain the adjustment toward the long-run equilibrium. Like other macroeconomic studies this empirical study involves nonstationary and trending variables, such as exchange rates, money supply, and industrial production. Furthermore some GARCH series, as a proxy of time variation in conditional variances ht , may appear to be Ið1Þ as the variance process is close to an integrated GARCH model, namely IGARCH. There are several ways to manipulate such series, to use transformations to reduce them to stationarity, such as to use a vector autoregressive (VAR) model or to analyze the relationship between these trending variables. Hodrick (1989) takes ﬁrst differences to make the series stationary. However, in the existence of a cointegration relationship differencing the data might not be appropriate since counterproductively, it would obscure the long-run relationships between the variables.

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313

As mentioned, the latter option allows us to distinguish between a long-run relationship, in which the variables drift together at roughly the same rate, and the short-run dynamics that capture the relationship between deviations of the variables from the long-run trend (see Stock and Watson 1988; Greene 2000). It should also be noted that the analysis involves generated regressors, in the form of the estimated conditional variances. According to Pagan (1984), the two-step procedure to estimate the conditional variances from the ARCH models and exogenously use the estimated variances in the OLS regression can produce consistency in estimated coefﬁcients if the ARCH processes provide consistent estimates of true conditional variances (see also Hodrick 1989). Unlike Hodrick (1989), we will use a GARCHð1; 1Þ model with a student t error distribution to estimate conditional variances ht .16 For the empirical study we take our macroeconomic series from six OECD countries—Canada, France, Italy, Japan, the United Kingdom, and the United States. Our theoretical constructs will focus on exchange rates, money supply, and industrial production.17 To see the role of economic fundamental uncertainty in determining the exchange rate risk and expected returns, we consider the price of a US dollar in terms of the domestic currency, as the US dollar has been recognized as a vehicle currency.18 The US variables are thus treated as foreign variables in the exchange rate models. Hodrick (1989), however, ﬁnds no evidence for fundamental volatility to price exchange rates because of the weak evidence of ARCH in monthly exchange rates. By expanding the period employed in Hodrick (1989), we have stronger evidence of ARCH in monthly observations.19 So we can reexamine the question posed in Hodrick (1989). To investigate the exchange rate determination based on equations (5) and (6), we need to look at the domestic and the foreign variables separately, not in relative terms.20 Thus the regression equations become et ¼ a0 þ a1; d mt þ a1; f mt þ a2; d yt þ a2; f yt þ a3; d ^h m; t þ a3; f ^ h m ; t þ a4; d ^ h y; t þ a4; f ^ h y ; t

ð7Þ

and et ¼ b0 þ b1 et1 þ b2; d mt þ b2; f mt þ b3; d yt þ b3; f yt þ b4; d mt1 þ b4; f mt1 þ b5; d yt1 þ b5; f yt1 þ b6; d ^h m; t

h m ; t þ b7; d ^ h y; t þ b7; f ^ h y ; t þ b8; d ^ h m; t1 þ b6; f ^ þ b8; f ^ h m ; t1 þ b9; d ^ h y; t1 þ b9; f ^ h y ; t1 ;

ð8Þ

314

Ph. J. Cumperayot

where e is the logarithm of the nominal exchange rate (i.e., the price of a unit of foreign currency in terms of domestic currency), x represents a domestic variable, and x represents a foreign (US) variable.21 The method of investigation is as follows: An augmented DickeyFuller test is ﬁrstly applied to test the null hypothesis that the variables in equation (7) contain a unit root, namely using an Ið1Þ series, and whether the series are integrated to the same order. If the variables are integrated to different orders, a cointegration model would not be appropriate. Second, the Johansen (1988) test is used to identify the number of cointegration vectors from groups of the variables. Then, by an augmented Engle and Granger (1987) test, we check if the error term of the cointegration equation is an Ið0Þ series. Later, we advance to a dynamic OLS estimation of equation (7) and the short-run dynamic equation (8). The ﬁrst step is to identify the appropriate degree of differencing for each series. Suppose that the series of interest is zt . Then the augmented Dickey-Fuller test is based on the regression of the following equation, with or without the presence of a trend t: wðLÞDzt ¼ m þ tt þ bzt1 þ ut ; where wðLÞ ¼ In w1 L w2 L 2 wp L p and ut is an error term. This augmented speciﬁcation is used to test the null hypothesis of a unit root in the series, which is H0 : b ¼ 0 against H1 : b < 0. Table 10.1 shows the results from the augmented DickeyFuller tests of the null hypotheses (1) that the logarithmic level of the series is Ið1Þ and (2) that the logarithmic ﬁrst difference of the series contains a unit root. The table displays b^, and throughout this chapter an asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance, respectively. According to table 10.1, the economic series are likely to be Ið1Þ series. At the 1 percent level of signiﬁcance, ﬁrst-differencing is appropriate to induce stationary in the natural logarithms of the exchange rate, money supply, and industrial productivity. The estimated GARCH processes of the macroeconomic variables are shown to be Ið0Þ, except for the estimated series of the French money supply. The estimated GARCH processes of the Canadian money supply and real income exhibit trend stationarity at the 5 percent signiﬁcance level. Therefore the model represented by equation (7) involves the variables that can

Canada Exchange rate Money supply

Italy

Japan

United Kingdom

e

0.709

1.933

1.920

2.338

2.560

De

7.729***

6.873***

6.834***

7.212***

7.458***

m Dm ^hm D^hm

Industrial production

France

1.591

2.200

10.710*** 3.185**

10.997*** 2.400

7.824***

8.639***

0.965 12.714*** 8.218***

3.275* 12.560*** 3.492***

3.366* 9.798*** 4.903***

United States

1.313 7.873*** 4.043***

y

2.403

2.783

3.143

1.108

2.845

2.915

Dy ^hy

6.350***

8.125***

8.754***

5.471***

7.944***

6.461***

3.179**

5.676***

6.538***

3.919***

4.413***

5.563***

D^hy

11.059***

Note: The results are of the augmented Dickey-Fuller unit root test. The test is based on the augmented equation displayed on top of the table. The speciﬁcation, with or without a trend t depending on its signiﬁcance, is used to test the null hypothesis of a unit root in the series (i.e., H0 : b ¼ 0Þ against the alternative hypothesis of no unit root ðH1 : b < 0Þ. The test is applied to the natural logarithmic levels of exchange rate (e), money supply (m), and real income (y), and also to the estimated GARCH series (h) of money growth and income growth. For the series that cannot reject the unit root at the 1 percent level, the test is also applied to ﬁrst differences of these series. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

Dusting off the Perception of Risk and Returns in FOREX Markets

Table 10.1 Results of the augmented Dickey-Fuller unit root test, wðLÞDzt ¼ m þ tt þ bzt1 þ ut

315

316

Ph. J. Cumperayot

Table 10.2 Results of the Johansen cointegration test et ¼ a 0 þ a1; d mt þ a1; f mt þ a2; d yt þ a2; f yt þ a3; d^h m; t þ a3; f ^h m ; t þ a4; d^h y; t þ a4; f ^h y ; t

Hypothesized

Canada

France

Italy

Japan

United Kingdom

2**

1**

1**

1**

2**

Number of ranks Note: The results are of the Johansen cointegration test for the group of the Ið1Þ variables in the modiﬁed ﬂexible-price model (as shown on top of the table). The test is conducted under the null hypothesis that the cointegrating rank is r or lower. The table shows the number of cointegrating vectors, that cannot be rejected. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

individually be either Ið0Þ or Ið1Þ. The modiﬁed exchange rate equation is then tested for a cointegration relationship, that is, if there exists a stationary linear combination of these variables. The Ið0Þ variables are introduced as exogenous regressors in the cointegration function. The second step is to examine if there is any cointegration relationship among these Ið1Þ series. The Johansen (1988) test is used to serve this purpose.22 Table 10.2 reports the number of signiﬁcant cointegration vectors. The likelihood ratio (LR) test can reject the null hypothesis of no cointegration in every country. At the 5 percent signiﬁcance level, the LR test indicates 1 cointegration relationship for France, Italy, and Japan, and 2 cointegration relationships in the case of Canada and the United Kingdom. As the Johansen test predicts cointegration relationship(s) for every country, an alternative method by Engle and Granger (1987) is used to assess whether linear combinations, based on the ﬂexible-price model in equation (7), are stationary. From equation (7), the model for the exchange rate that is suitable for regression analysis can be rewritten as et ¼ a^0 þ a^1; d mt þ a^1; f mt þ a^2; d yt þ a^2; f yt þ a^3; d ^h m; t h m ; t þ a^4; d ^ h y; t þ a^4; f ^ h y ; t þ et ; þ a^3; f ^

ð9Þ

where et is an error term. In equation (9) the cointegration function represents the long-run movement of exchange rates. OLS estimation is applied because it has been proved to yield asymptotically superconsistent estimators when estimating cointegration relationships (see Greene 2000). The Engle and Granger (1987) two-step procedure test is applied to examine the stationarity of the residual term et . To correct for autocorrelation in the equilibrium error series, an augmented Engle and Granger test is based on estimating

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317

Table 10.3 Results of the augmented Engle and Granger cointegration test Det ¼ f0 et1 þ f1 Det1 þ þ et

f^0

Canada

France

Italy

Japan

United Kingdom

3.415**

4.904***

3.722***

3.129**

4.522***

Note: The results are of the augmented Engle and Granger cointegration test on the equilibrium error et . It is to test the signiﬁcance of the null hypothesis that the error series contains a unit root (i.e., H0 : f0 ¼ 0, H1 : f0 < 0). If the null hypothesis cannot be rejected, there is no cointegration relationship. *, **, and *** indicate signiﬁcance at the 10, 5, and 1 percent levels respectively.

Det ¼ f0 et1 þ f1 Det1 þ þ et by the Newey-West approach. If the null hypothesis of a unit root in the residual series (H0 : f0 ¼ 0, H1 : f0 < 0) cannot be rejected, there is no cointegration relationship among the variables in the model. Table 10.3 shows f^0 . Asterisks indicate that the null hypothesis of unit root can be rejected at the 5 percent signiﬁcance level for Canada and Japan, and at the 1 percent level for France, Italy and the United Kingdom. The evidence in tables 10.2 and 10.3 demonstrates the cointegration in these countries. To test our assumption regarding the expectation formation that incorporates macroeconomic uncertainty, we apply the two-step cointegration approach as proposed by Engle and Granger (1987).23 We ﬁrst deal with the modiﬁed ﬂexible-price model and then the modiﬁed sluggish-price model. The Stock and Watson (1993) dynamic OLS estimation method is employed to regress the logarithm of the exchange rate against the logarithms of money supply and industrial production, and the estimated conditional variances—from a GARCHð1; 1Þ model—of the growth rates of money supply and industrial production. The US variables are used as the foreign variables. Although the OLS estimation has proved to asymptotically yield superconsistent estimates, because of the possibility that the explanatory variables are contemporaneously correlated with the disturbance term, the OLS regression coefﬁcients are likely to be inconsistent.24 The dynamic OLS procedure, on the other hand, is robust to small sample size and simultaneity bias. To eliminate the effects of these correlations, we apply the Stock and Watson (1993) dynamic OLS approach by adding the one-period leads and lags of the ﬁrst differences of the regressors mentioned above.25 The method is also known for being a robust single equation that

318

Ph. J. Cumperayot

corrects for stochastic-regressor endogeneity. According to equation (7) the dynamic OLS equation is et ¼ a^0 þ a^1; d mt þ a^1; f mt þ a^2; d yt þ a^2; f yt þ a^3; d ^h m; t þ a^3; f ^h m ; t h y; t þ a^4; f ^ hy ; t þ a^5; d Dmtþ1 þ a^5; f Dmtþ1 þ a^4; d ^ þ a^6; d Dytþ1 þ a^6; f Dytþ1 þ a^7; d D ^ h m; tþ1 þ a^7; f D ^ h m ; tþ1 þ a^8; d D ^h y; tþ1

ð10Þ

þ a^8; f D ^ h y ; tþ1 þ a^9; d Dmt1 þ a^9; f Dmt1 þ a^10; d Dyt1 þ a^10; f Dyt1 þ a^11; d D ^ h m; t1 þ a^11; f D ^ h m ; t1 þ a^12; d D ^h y; t1

þ a^12; f D ^ h y ; t1 þ xt ; where xt denotes the error term. Table 10.4 contains the estimated parameters from equation (10), a^i; d and a^i; f when i ¼ 1; . . . ; 4. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent level of signiﬁcance, respectively. Apart from allowing us to examine the long-run impacts of macroeconomic risk on exchange rates, adding the estimated macroeconomic risk into a cointegration equation may help reduce the problem of omitted variables.26 From table 10.4 the estimated coefﬁcients of money supply and real income have signs as expected in the literature. In the long run an increase in the domestic money supply or a decrease in the foreign money supply tends to depreciate the domestic currency, Table 10.4 Parameters of the modiﬁed ﬂexible-price model et ¼ a^0 þ a^1; d mt þ a^1; f m þ a^2; d yt þ a^2; f y þ a^3; d^h m; t þ a^3; f ^h m ; t þ a^4; d^h y; t þ a^4; f ^h y ; t þ t

Canada

t

France

Italy

Japan

United Kingdom

a^0 a^1; d

3.128***

6.740***

6.210***

7.472***

3.868***

0.116

0.753***

0.929***

0.774***

0.321**

a^1; f a^2; d

0.155**

0.580***

0.666***

1.101***

0.097

0.535**

1.886***

2.056***

0.538**

1.266**

a^2; f a^3; d a^3; f

116.328*** 1356.045**

a^4; d a^4; f

25.750

0.076

178.947***

0.479* 530.64*** 3185.05** 376.15** 6.369

0.693*** 497.51* 4555.66** 46.59** 433.14

1.444*** 224.703* 1840.97 270.166* 555.754**

0.029 877.01** 6340.388*** 172.19* 777.12***

Note: The estimation results are of the modiﬁed ﬂexible-price model, based on the Stock and Watson (1993) dynamic OLS approach. The estimated parameters are a^i; d and a^i; f when i ¼ 1; . . . ; 4. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance respectively.

Dusting off the Perception of Risk and Returns in FOREX Markets

319

except for Canada. Higher domestic output or lower foreign output is likely to appreciate the domestic currency (although there are exceptions for Canada and Japan). For Canada and the United Kingdom, at the 5 percent signiﬁcance level the Wald test cannot reject the null hypothesis that the coefﬁcients of domestic and foreign macroeconomic variables, like money supply and real income, are signiﬁcantly equal. When we restrict the domestic and foreign coefﬁcients of money supply and real income to be equal in these countries, higher money supply or lower real income relative to the US tends to depreciate the domestic currencies while the coefﬁcients of macroeconomic risk are similar to those in table 10.4.27 Signiﬁcantly, an increase in the money supply volatility, both domestic and foreign, depreciates the Canadian dollar but appreciates other currencies. For uncertainty in real income, the results signiﬁcantly show that with an increase in the domestic volatility, the domestic currency depreciates (except in the United Kingdom). In contrast, with an increase in the foreign volatility, the domestic currency appreciates. Higher uncertainty in the US real income or the US money supply raises the expected future returns on US dollars by pushing down the current US dollar price. It consequently causes the domestic currency to appreciate (except in Canada). By the same argument, uncertainty in the domestic real income is positively related to the US dollar exchange rates. It leads to an upward bias in the variation of actual exchange rates from the prediction of the traditional model. From table 10.4, macroeconomic uncertainty, represented by the conditional variances of money supply and real income, relates signiﬁcantly to the deviation of the exchange rate from its fundamentally based value. Uncertainty about the economy appears to lower the demand for the currency and subsequently leads to depreciation, relative to the fundamental benchmark value. From an asset pricing perspective, higher risk should be accompanied by higher expected future returns, leading to a current depreciation of the currency. Theory coherently predicts that higher variability of domestic fundamentals should result in higher current depreciation of the domestic currency. However, the opposite impact can also be observed in some cases of uncertainty in money growth. For every country except Canada, higher volatility in the domestic money supply tends to increase the domestic currency prices. This might be because the volatile money supply (e.g., due to volatile capital ﬂows or active domestic monetary policy) does not necessarily

320

Ph. J. Cumperayot

imply a negative outlook on the domestic currency.28 Because of this positive effect of macroeconomic risk, economic agents prefer to hold their local currencies and will pay a higher price. These cases also reveal a strong preference for domestic currency that is parallel to the equity home bias, meaning the tendency to underinvest in (more attractive) foreign assets, that has been long studied in ﬁnance.29 On the other hand for Canada there exists a negative risk premium toward the US dollar, which shows a positive reaction toward an active US monetary policy.30 The modiﬁed sticky-price model extends the cointegration relationship between the exchange rate and its fundamentals by adding the long-run equilibrium error adjustment. By rearranging equation (8), we obtain a form of the error-correction model: Det ¼ ^b0 þ ^b2; d Dmt þ ^b2; f Dmt þ ^b3; d Dyt þ ^b3; f Dyt þ ^b6; d D ^h m; t þ ^b6; f D ^ h m ; t þ ^b7; d D ^ h y; t þ ^b7; f D ^ h y ; t þ ð^b1 1Þ ( ) et1 c^1; d mt1 c^1; f mt1 c^2; d yt1 c^2; f yt1 þ nt ; h m; t1 c^3; f ^ h m ; t1 c^4; d ^ h y; t1 þ c^4; f ^h y ; t1 ^ c3; d ^ where c^1; d ¼ ð^b4; d þ ^b2; d Þ=ð^b1 1Þ, c^1; f ¼ ð^b4; f þ ^b2; f Þ=ð^b1 1Þ, c^2; d ¼ ð^b5; d þ ^b3; d Þ=ð^b1 1Þ, c^2; f ¼ ð^b5; f þ ^b3; f Þ=ð^b1 1Þ, c^3; d ¼ ð^b8; d þ ^b6; d Þ=ð^b1 1Þ, c^3; f ¼ ð^b8; f þ ^b6; f Þ=ð^b1 1Þ, c^4; d ¼ ð^b9; d þ ^b7; d Þ=ð^b1 1Þ and c^4; f ¼ ð^b9; f þ ^b7; f Þ=ð^b1 1Þ. Provided that the relationship between the exchange rate and the fundamentals is stable, the set of coefﬁcients c in this equation is equivalent to the set of coefﬁcients a in the modiﬁed ﬂexible-price model. Thus we can test the short-run dynamic equation31 Det ¼ ^b0 þ ^b2; d Dmt þ ^b2; f Dmt þ ^b3; d Dyt þ ^b3; f Dyt þ ^b6; d D ^h m; t þ ^b6; f D ^ h m ; t þ ^b7; d D ^ h y; t þ ^b7; f D ^ h y ; t þ ð^b1 1Þet1 þ nt : Note that since ﬁrst differencing is sufﬁcient to produce stationary series and since there exists the cointegration relationship shown in tables 10.2 and 10.3, the residual term nt is an Ið0Þ series. As stated by Greene (2000), the movement of the exchange rate from the previous period associates with the changes in the fundamentals along the long-run equilibrium corrected for the previous deviation

Dusting off the Perception of Risk and Returns in FOREX Markets

321

Table 10.5 Parameters of the modiﬁed sticky-price model Det ¼ ^b0 þ ð^b1 1Þet1 þ ^b2; d Dmt þ ^b2; f Dm þ ^b3; d Dyt þ ^b3; f Dy þ ^b6; d D^h m; t t

t

þ ^b6; f D^h m ; t þ ^b7; d D^h y; t þ ^b7; f D^h y ; t þ nt Canada ^b0 ð^b1 1Þ ^b2; d ^b2; f ^b3; d ^b3; f ^b6; d ^b6; f ^b7; d ^b7; f

France

Italy

Japan 0.002

United Kingdom

0.001

2.37E-4

0.003

0.023**

0.056***

0.027

0.063***

0.087***

0.042 0.055

0.024 0.071

0.083 0.040

0.021 0.189*

0.067 0.003

0.070

0.109

0.009

0.050

0.078

0.207** 9.119

0.502** 10.505

0.481**

0.084

56.871

75.438

0.001

0.675*** 159.643*

138.630

33.414

59.534

210.013

17.408

22.570

3.041

12.068

229.840 10.498

28.122

75.073

4.561

21.820

42.507

Note: The estimation results are of the modiﬁed sticky-price model, based on the linear OLS regression. An asterisk, two asterisks, and three asterisks indicate signiﬁcance at the 10, 5, and 1 percent levels of signiﬁcance respectively.

from the long-run equilibrium. This equation contains an equilibrium relationship in the ﬁrst two lines and an adjustment for the deviation from the previous equilibrium in the last line. Table 10.5 shows that there exists a correction mechanism of equilibrium errors toward the long-run equilibrium, as ð^b1 1Þ is signiﬁcantly negative, except in the case of Italy. The error correction term, et1 , is signiﬁcantly negative at the 5 percent signiﬁcance level in the case of Canada and at the 1 percent signiﬁcance level for France, Japan, and the United Kingdom. For Italy, at the monthly horizon, the adjustment toward long-run equilibrium is not signiﬁcant but the sign of ð^b1 1Þ is still negative. Furthermore, in the short run, the exchange rate can be signiﬁcantly explained by changes in the US real income. Yet other macroeconomic fundamentals as well as their uncertainty fail to explain the exchange rate in the short run. 10.4

Conclusion

The expectations regarding macroeconomic circumstances can inﬂuence the exchange rate in the manner predicted by the monetary models, but the random walk assumption is too naive for market expectations. In this chapter, I propose an alternative expectation formation process for the macroeconomic variables by introducing

322

Ph. J. Cumperayot

additional risk factors, based on the volatility of the macroeconomic fundamentals. As the fundamentals empirically exhibit a meanreverting process with persistent memory in the standard deviation (representing the adjustment and speed toward the mean), a nonlinearity in the expectation formation process is present. To capture the exchange rate volatility, in addition to the traditional fundamentals, such as money supply and real income, time variation in the second moments of these fundamentals is incorporated to describe the expected exchange rate returns. The result shows signiﬁcant cointegration between the variables in the modiﬁed ﬂexible-price monetary model, as well as a correction of equilibrium errors toward the long-run equilibrium in the modiﬁed sticky-price model. In the long run, an increase in the domestic money supply or a decrease in the foreign money supply tends to depreciate the domestic currency. Higher domestic output or lower foreign output is likely to appreciate the domestic currency. The impacts of macroeconomic sources of risk are also signiﬁcant. In general, uncertainty about the economy lowers the demand for the currency and subsequently depreciates the currency, relative to the fundamental-based value. From an asset pricing perspective, increased risk is accompanied by increased expected future returns, leading to a current depreciation of the currency. The ﬁndings in this chapter indicate that macroeconomic sources of FOREX risk are a missing factor in exchange rate studies and that the monetary exchange rate models are still potentially useful. Appendix A: Data Sources The data applied in this chapter are monthly observations of exchange rates, money supply and industrial production, starting from June 1973 (with the breakdown of the Bretton Woods system) to December 1998. There are six OECD countries studied: Canada, France, Italy, Japan, the United Kingdom, and the United States. Both European and nonEuropean countries, with possible different economic mechanisms, are selected based on the availability of the required data. The US dollar is used as a vehicle currency and the US variables are used as the foreign variables. The main data source is the IMF International Financial Statistics (IFS), except for M1 of the United States. This time series is from the US Federal Reserve Bank at St. Louis. It is compared with available

Dusting off the Perception of Risk and Returns in FOREX Markets

323

quarterly series from the IFS and they are very similar. The US dollar exchange rates (domestic currency prices per one US dollar) from the IFS are coded AE. Monetary aggregation is represented by seasonally unadjusted M1 data from IFS coded 34, except for the United Kingdom. For the purpose of this chapter, liquidity under the central bank’s controllability is preferable. For the United Kingdom, M 0 , is used and coded 59, instead of another available choice M 4 . Seasonally adjusted industrial production, coded 66, is used as a proxy for real income. If necessary, a seasonal adjustment can be made by way of an additive seasonal moving average approach. Appendix B: The Reduced-Form Solutions of the Exchange Rate Models The ﬂexible-price model is derived from the simple quantity equation Mt Vt ¼ Pt Yt . In logarithms, the quantity equation reveals that m t þ vt ¼ pt þ yt ;

ðA1Þ

where mt ; vt ; pt , and yt are the logarithms of the money supply, the money velocity, the price level, and the real income at period t respectively. We can assume that purchasing power parity (PPP) and uncovered interest parity (UIP) hold. The stochastic PPP assumption, which is a more speciﬁc version of the no-arbitrage assumption, is deﬁned as pt ¼ t þ pt þ et þ ot :

ðA2Þ

In equation (A2), et ; pt , and pt are the logarithms of the nominal exchange rate, namely the price of a unit of foreign currency, the domestic price level and the foreign price level respectively. An asterisk denotes a foreign variable, which in this case is a US variable. While t is a constant, ot represents a stationary, zero-mean disturbance term, sometimes referred to as the real exchange rate. According to the UIP condition, the interest rate differential between domestic and foreign assets is supposed to be equal to the expected rate of depreciation of the domestic currency. The expected change in currency price that satisﬁes equilibrium in the capital markets can thus be written as Et ½etþ1 et ¼ it it ;

ðA3Þ

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where it and it are the domestic interest rate and the foreign interest rate respectively. Et ½ is the conditional expectation operator. The velocity of money circulation is presumed to be a stable function of real income and the interest rate. The logarithm of money velocity is linearly speciﬁed as a decreasing function of the logarithm of real income and an increasing function of the interest rate: vt ¼ y gyt þ jit þ $t ;

ðA4Þ

where y is a constant and $t is a stationary, zero-mean disturbance. Suppose that (A1) holds at home and in foreign countries with an identical income elasticity, g, and interest semi-elasticity, j. Combine (A1) with (A2), (A3), and (A4) and rework for the foreign country: et ¼ t þ

1 ð1 þ gÞ j ~t m y~t þ Et ½etþ1 þ et ; 1þj 1þj 1þj

ðA5Þ

where x~t ¼ xt xt and et ¼ $t $t ot . To solve this linear equation with rational expectation, we apply the law of iterated expectations (see Samuelson 1965; Blanchard and Fischer 1993). For simplicity, we rewrite equation (A5) as et ¼ v0 þ v1 f~t þ v2 Et ½etþ1 þ et ;

ðA6Þ

~ t ð1 þ gÞ y~t . where v0 ¼ t, v1 ¼ 1=ð1 þ jÞ, v2 ¼ j=ð1 þ jÞ, and f~t ¼ m Note that v2 ¼ 1 v1 and that v1 and v2 A ð0; 1Þ as 0 < j < 1 (see Flood, Rose, and Mathieson 1991; Flood and Rose 1995). Equation (A6) implies that the exchange rate depends on its expected rate for the next period, Et ½etþ1 , and on the current fundamentals, f~t , with the weights summing up one. According to the law of iterated expectations, we have e t ¼ v0

T X i¼0

v2i þ v1

T X

v2i Et ½ f~tþi þ v2Tþ1 Et ½etþTþ1 þ

i¼0

T X

v2i Et ½etþi :

ðA7Þ

i¼0

We then assume that as the horizon T increases, the exchange rate at T þ 1 periods becomes negligeable, or equivalently the rational bubble shrinks to zero and that Et ½etþi ¼ 0. As T tends to inﬁnity, lim v2Tþ1 Et ½etþTþ1 ¼ 0;

T!y

and the solution becomes

ðA8Þ

Dusting off the Perception of Risk and Returns in FOREX Markets

e t ¼ v0

y X

v2i þ v1

i¼0

y X

v2i Et ½ f~tþi :

325

ðA9Þ

i¼0

This equation is comparable to equation (2), and implies that the elasticity of the exchange rate, with respect to its expected fundamentals, declines as we look farther into the future as lim v2t ¼ 0:

ðA10Þ

t!y

Moreover, for equation (A8) to converge, it requires that the logarithm of fundamentals, f~, grow at rate lower than v1 =ð1 v1 Þ (i.e., 1=j); otherwise, the solution (A9) would be explosive. The sluggish-price model is an extension of the ﬂexible-price model with inertia introduced into the price mechanism, instead of relying on perfectly ﬂexible prices. Empirically there are deviations from purchasing power parity in equation (A2) where ot are large and persistent. There is also strong correlation between nominal and real exchange rates. In Dornbusch’s (1976) sluggish-price model the expected exchange rate return is formed as the discrepancy between the long-run rate e, to which the economy will eventually converge, and the current spot rate e. Mathematically, E½e e ¼ dðe eÞ;

0 < d < 1:

To allow for sticky prices, the Phillips curve equation is substituted in equation (A2) in the place of purchasing power parity (e.g., see Obstfeld and Rogoff 1984; Flood and Rose 1995). It is conventional to assume that in addition to the PPP condition, prices respond to the lagged excess demand in the good markets, yt yt , and shocks to the good markets, gt : ptþ1 pt ¼ mð yt yt Þ þ gt þ Et ½ p^tþ1 p^t ;

0 < m < 1;

ðA11Þ

where y is the long-run output level, gt has zero mean and constant variance, and p^t is the price level at time t if prices were ﬂexible and the good markets cleared. yt yt ¼ Yðet þ pt pt Þ þ Frt :

ðA12Þ

The excess demand is deﬁned as an increasing function of real exchange rate, Y > 0, and a decreasing function of the ex ante expected real interest rate, namely rt 1 it Et ½ ptþ1 pt , F < 0. Thus, by substituting equation (A12) into equation (A11), we get

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ptþ1 pt ¼ m½Yðet þ pt pt Þ þ Frt þ gt þ Et ½ p^tþ1 p^t :

ðA13Þ

Equation (A13) displays the long-run equilibrium (when the purchasing power parity holds and thus, the left-hand side, LHS, is equal to the last term on the right-hand side, RHS) and its short-run dynamics (represented by deviations from the purchasing power parity by the ﬁrst and the second terms on the RHS). As in the long run p^ ¼ p, p^ can be deﬁned by m½Yðet þ pt p^t Þ þ Frt þ gt ¼ 0; and thus pt ptþ1 pt ¼ m½Yðet þ pt pt Þ þ Frt þ gt þ Et ½ptþ1

þ Et ½etþ1 et þ

F 1 Et ½rtþ1 rt þ Et ½ gtþ1 gt : Y mY

Therefore, instead of using the purchasing power parity condition in equation (A2), we substitute the price equation, p~t ¼ pt pt ¼ et þ þ

1 1 1 Et ½etþ1 et þ Et ½ ptþ1 ðptþ1 pt Þ pt Ym Ym Ym

1 F F 1 1 gt ; Et ½rtþ1 rt þ rt þ Et ½gtþ1 gt þ m Y2 Y Ym m2Y2

ðA14Þ

into the money demand equation, derived from the quantity equation (A1) and the assumption of money circulation (A4): ~ t ð1 þ gÞ y~t þ j~it þ $ p~t ¼ m ~ t: Hence 1 ~ t ð1 þ gÞ y~t þ j~it þ $ Et ½etþ1 et ~t et ¼ m Ym

1 1 1 F Et ½ptþ1 ð ptþ1 pt Þ pt þ Et ½rtþ1 rt Ym Ym m Y2

F 1 1 rt gt : Et ½gtþ1 gt 2 2 Y Ym m Y

ðA15Þ

To present the model in a common form as in equation (2), we assume the UIP condition (A3) and the price process in equation (A14). As a consequence the exchange rate equation becomes

Dusting off the Perception of Risk and Returns in FOREX Markets

et ¼ ~kt þ Et ½etþ1 þ

327

ð1 yÞj y ð1 yÞj y þ 1 Et1 ½et et1 þ ct : yj yj ðA16Þ

where ~kt ¼ 1 f~ þ 1y f~ , j t yj t1 1 y ct ¼ j1 pt j1 Et1 ½ pt Wj Et1 ½rt ð1yWÞ yj rt1 j gt1 j Et1 ½gt gt1 ;

~ t ð1 þ gÞ y~t . The coefﬁand the fundamental f~t is deﬁned as f~t ¼ m cients are assigned by y ¼ 1=Ym and W ¼ F=Y. To apply the law of iterated expectations to this second-order difference equation, we deﬁne At ¼ et þ f½ð1 yÞj y þ 1=yjget1 . Equation (A16) can then be rewritten as At ¼ ~kt þ Et1 ½Atþ1

1 Et1 ½et þ kt þ ct ; yj

ðA17Þ

where kt ¼ Et ½etþ1 Et1 ½etþ1 . By the law of iterated expectations, we get At ¼ ~kt þ

T X

Et1 ½~ktþi

i¼1

þ

T X i¼0

Et1 ½ktþi þ

T 1 X Et1 ½etþi þ Et1 ½AtþTþ1 yj i¼0

T X

Et1 ½ctþi :

i¼0

For simplicity, we presume that the expected exchange rate in any one period, namely Et1 ½AtþTþ1 , is only a small component in determining the current spot rate, and it becomes negligeable as the horizon T rises. Furthermore, when i b 0, Et1 ½ktþi ¼ Et1 ½ctþi ¼ 0. As a consequence, as T tends to inﬁnity, the solution becomes et ¼

y y X ð1 þ jÞðy 1Þ 1 X et1 þ ~kt þ Et1 ½~ktþi Et1 ½etþi : yj yj i¼0 i¼1

ðA18Þ

Equation (A18) is like equation (A9) in the ﬂexible-price model, except there is inertia in the exchange rate equation. The exchange rate now depends on ~kt , namely current and lagged values of money supply and income, and its expected future fundamentals. Additionally equation (A18) is rather similar to the sticky-price concept stated earlier and also a solution (4) from Cuthbertson (1999).

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Appendix C: Adding Stochastic Volatility to the Fundamental Expectations There are many ways to incorporate the second moments of the fundamentals into their expectations. In this appendix I show a few possible ways. In developing an explicit solution for the exchange rate, Hodrick (1989) assumes a conditionally lognormal data-generating process for the fundamentals, and applies the fact that if x has a lognormal dis2 tribution with logðxÞ @ Nðm; s 2 Þ, its expectation reads E½x ¼ e mþs =2 . Hence, by loglinearization of his general equilibrium model, we get logðE½xÞ ¼ m þ 12 s 2 , which is explored in Hodrick (1989). We could equivalently adopt the modiﬁed form of uncovered interest parity (UIP) that adjusts for a risk premium, and we could specify a risk premium as a function of time-varying fundamental variances. This is similar to the portfolio balance model, in which the UIP condition incorporates the risk premium as a function of relative asset holding in domestic and foreign bonds. By combining equation (A5) with a modiﬁed version of UIP that has a time-varying risk premium rt , and applying the law of iterated expectations, we can express the exchange rate as ~ tþi bEt ½ y~tþi þ aEt ½ rtþi : et ¼ Et ½m From the equation above, the exchange rates are determined by two components: the expectation regarding the future fundamental values and the expectation regarding risk from holding the currency. Intuitively, a deviation from its expected fundamental value needs an extra compensation. So, using a risk premium, we can characterize risk in the FOREX markets by macroeconomic uncertainty. Another technical approach is to apply Taylor’s theorem. To make our point, we consider money supply process based on Lucas (1982) and Obstfeld (1987). Suppose mt ¼ wt þ mt1 , where mt is the logarithmic level of money supply and wt is the stochastic growth rate of money supply. Obstfeld (1987) assumes that wt exhibits a jump process, meaning wt ¼ dt mt , where dt represents a dummy variable for the occurrence of a Poisson event and mt denotes the volume of change. To describe money growth wt , there are a number of possible Poisson processes, ranging from the simplest one with a constant probability to the one with unstable probability behavior where dt is a Markov chain with an unabsorbing state.

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329

In practice, we know that the logarithmic ﬁrst difference of the fundamentals, mt mt1 ¼ Dmt ¼ dt mt , is likely to be mean reverting. Hence, to proxy the movement of the variable Dmt around its mean, we can apply Taylor’s theorem to an arbitrary function (see Chiang 1984). If the mean is close to zero, we can use Maclaurin’s series by expanding the function around the point Dx ¼ 0. To include the variance term in the fundamental expectation, we can expand the series to the second degree, which is rather conventional for Taylor’s expansion. As a result we can proxy the expected movement of the macroeconomic series by a nonlinear function. Appendix D: The Closed-Form Solutions To introduce time-varying conditional variances of the macroeconomic variables into the exchange rate model, we assume that there is a relationship between the ﬁrst and the second moments of the fundamentals. The fundamentals are assumed to have somewhat similar to ARCH-in-Mean (ARCH-M) processes. The ARCH-M model, initiated by Engle, Lilien, and Robins (1987), is originally used to describe the risk and return relationship of assets, as suggested in ﬁnance theory. For macroeconomic variables, there is rather weak evidence of ARCHM process.32 An approximate linear relationship between the fundamental expectation and its variance is, however, intuitive. Similar to the ARCH-M model, the whole sequence of future fundamentals can be represented by its current value and its variance. If xt is the time series of interest, the model may be written as xtþ1 ¼ g0 þ g1 xt þ g2 htþ1 þ utþ1 ;

ðA19Þ

where x represents a macroeconomic variable, h is the conditional variance of the variable x, presumably time varying, and u is a residual term. As the fundamentals empirically exhibit mean-reverting processes with persistent memory in standard deviations, time variation in the conditional variance may represent the adjustment and speed toward the mean. In equation (29) the ﬁrst component is like a random walk or an AR(1) process, which is often assumed for macroeconomic variables. The second component shows that macroeconomic uncertainty plays a role in the fundamental expectation formations. For example, the fundamental variances may represent economic circumstances, namely

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whether the economy is in volatile or tranquil periods, in which the expectations may be different. In turmoil (disequilibria), the monetary variables, such as money supply and interest rates, may be altered more often, and the state variables, such as income, unemployment rate, and inﬂation rate, may be more volatile than in regular periods. To capture time-varying conditional variances, for simplicity, we use a GARCHð1; 1Þ model: htþ1 ¼ l0 þ l1 ut2 þ l2 ht : A GARCHð1; 1Þ model is often used to capture time-varying conditional variances of economic variables (see Bollerslev 1987). By way of the law of iterated expectations, the expected future fundamentals can be described as Et ½xtþi ¼ g0

i1 X

g1s þ g1i xt þ g2

s¼0

i1 X

g1s Et ½htþis ;

s¼0

ðA20Þ Et ½htþis ¼ l0

is1 X

ðl1 þ l2 Þ k þ ðl1 þ l2 Þ is ht :

k¼0

Reorganizing gives a process of x as a function of its current value and its conditional variance as Et ½xtþi ¼ a0 þ a1 xt þ a2 ht ;

ðA21Þ

where P i1 s P is1 g1 ½g0 þ g2 l0 k¼0 ðl1 þ l2 Þ k , a0 ¼ s¼0 a1 ¼ g1i , P i1 s a2 ¼ g2 s¼0 g1 ½ðl1 þ l2 Þ is . Substitute the expectations for money supply and real income into equation (A9), and rework with inertia in equation (A18). The results are equations (5) and (6), respectively. Notes The author would like to thank Paul de Grauwe, Roy Kouwenberg, Antonio Garcia Pascual, Mark Taylor, and Casper de Vries for useful discussions and thoughtful comments, and also Namwon Hyung for econometric tips. 1. This discussion is based on my doctoral thesis (2002).

Dusting off the Perception of Risk and Returns in FOREX Markets

331

2. For example, for the monetary-approach partial equilibrium models Frenkel (1976), Mussa (1976), and Bilson (1978) discuss the ﬂexible-price model, while Dornbusch (1976), Frankel (1979), Mussa (1979), and Buiter and Miller (1982) consider the stickyprice model. The general equilibrium asset-pricing models are studied by Stockman (1980), Lucas (1982), Svensson (1985a, b), and Hodrick (1989), and extended into the continuous-time stochastic framework by Bakshi and Chen (1997) and Basak and Gallmeyer (1998). 3. Among the empirical studies are those by Frenkel (1976), Bilson (1978), Hodrick (1978, 1989), Meese and Rogoff (1983, 1988), Backus (1984), Meese (1990), MacDonald and Taylor (1994), Chinn and Meese (1995), Mark (1995), and Flood and Rose (1995, 1999). 4. Mathematical applications are partially adopted from Cuthbertson (1999). 5. This equation is derived from the uncovered interest parity (UIP) and from an assumption corresponding to the monetary models that the interest rate differential depends on the fundamentals f~t : it i ¼ af~: t

t

6. For a summary, see Meese (1990). 7. See Campbell, Lo, and MacKinlay (1997, ch. 7). 8. This solution is derived by applying to equation (1) the law of iterated expectations, that is Et ½Etþ1 ½X ¼ Et ½X. Suppose that the discount rate is lower than one, that it is governed by an interest semi-elasticity to money demand smaller than one. The expectation would be assigned a lower exponential weight (to the power i) as looking forward (to time t þ i). From the limit theorem, at inﬁnity T ! y the bubble term (with a weight to the power T þ 1) vanishes (See also Blanchard and Fischer 1993, ch. 5). 9. For instance, MacDonald and Taylor (1994) ﬁnd cointegration between exchange rates and monetary variables in the fundamental exchange rate models. Chinn and Meese (1995), as well as Mark (1995), ﬁnd evidence that for long horizons the monetary-based exchange rate model overcomes the random walk model in predicting exchange rates. Groen (1999) shows that at a pooled time series level, there is cointegration between exchange rates and macroeconomic variables in the monetary model. 10. The exceptions include the studies by Cragg (1982), Engle (1982, 1983), Obstfeld (1987), Hodrick (1989), Arnold (1996), and Bekaert (1996). 11. In appendix B, I provide the derivation (in detail) of the reduced-form solutions of the ﬂexible-price and sluggish-price models. It should be noted that for the sluggish-price model one actually works with a more complex assumption of price inertia. As a result the solution can be tedious (but similar), compared to equation (4). Importantly, it facilitates our closed-form derivation shown next. 12. The argument and derivation are in appendix D. 13. The nonlinearity in the model seems to coincide with the idea of nonlinear bubbles. For example, in Froot and Obstfeld (1991) the bubble is a nonlinear function of stock’s dividend. 14. A GARCHð1; 1Þ model (with a Student’s t distribution, if necessary) is used to capture fundamental uncertainty. The model, originated by Bollerslev (1986), suggests a form of heteroskedasticity in which the conditional variance changes over time as a function of past errors and past conditional variances. Therefore a turbulent (tranquil) period

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is likely to be followed by turbulent (tranquil) periods. Alternatively, regative news has persistent effect in some periods. 15. For empirical results, see, for example, MacDonald and Taylor (1994) and Groen (1999). 16. Hodrick (1989) applies the ARCH-LR test and models fundamental volatility by using an ARCH(1) model with a normal distribution. In contrast, we specify the conditional variance model by using a GARCHð1; 1Þ-t model, suggested in Bollerslev (1987). First, this is because the GARCHð1; 1Þ model is considered to be a parsimonious model of conditional variance that adequately ﬁts many economic time series. See, for example, Bollerslev (1986) for the merit of the GARCHð1; 1Þ model in allowing long memory. Second, heteroskedasticity may be a reason for a heavy-tailed distribution, see, for example, de Haan, Resnick, Rootzen, and de Vries (1989) and Embrechts, Kluppelberg, and Mikosch (1999); Bollerslev (1987) shows the adequacy of the GARCHð1; 1Þ-t model for fat-tail distributed economic series. Additionally my empirical results show highly signiﬁcant GARCH coefﬁcients and signiﬁcantly reject the null hypothesis of normally distributed error terms. 17. For more detail, the reader is referred to appendix A. I also studied Austria, Germany, and the Netherlands. There is no evidence of a cointegration relationship in the Netherlands. However, there are ambiguous cointegration test results between the Johansen (1988) test and the augmented Engle and Granger (1987) test in the case of Austria and Germany. 18. This deﬁnition is given in Krugman and Obstfeld (1997). The US dollar is broadly accepted and held as a ﬁnancial asset. 19. There are many studies investigating ARCH properties in the logarithmic changes in exchange rates. At short horizons, strong ﬁndings in weekly and daily intervals respectively have been reported by Engle and Bollerslev (1986) and Baillie and Bollerslev (1987), but due to temporal aggregation (see Drost and Nijman 1993) rather weak evidence for monthly data has been reported by Baillie and Bollerslev (1989) and Hodrick (1989). Within our sample, we ﬁnd rather strong evidence of ARCH in monthly exchange rate returns and fundamental growth rates. The results of the ARCH(1)-LM test, the ARMAGARCH modeling method and the estimated coefﬁcients of GARCH models are available upon request. 20. These reduced-form equations are the unrestricted monetary models of equations (5) and (6). This follows from the discussion in Meese (1990) and MacDonald and Taylor (1994) regarding the failure of the monetary models due to imposing inappropriate coefﬁcient restrictions. Meese (1990) states that although most models are formulated in relative terms to simplify exposition, in estimation there is no need to impose the constraints on structural parameters. Furthermore MacDonald and Taylor (1994) show that their unrestricted ﬂexible-price monetary model is valid in explaining the long-run exchange rate. 21. If the theoretical speciﬁcations are correct, one would expect the coefﬁcients of domestic and foreign variables to be equal (in absolute term but with opposite signs). In practice, the coefﬁcient restrictions are rejected by the data in three out of ﬁve countries. Only in the case of Canada and the United Kingdom, at the 5 percent signiﬁcance level, the Wald test cannot reject the restriction that the coefﬁcients of the domestic and foreign (US) variables are equal in money supply and real income. 22. For more detail, the reader is referred to Hamilton (1994) and Greene (2000).

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333

23. Based on the method of Engle and Granger (1987), the long-run equilibrium relationship is ﬁrst estimated. The estimated parameters of the cointegration vector are, subsequently, used in the error correction equation. See, for example, Engle and Granger (1987), Phillips and Loretan (1991), and MacDonald and Taylor (1994). The estimated coefﬁcients of the long-run and short-run relationships are presented in tables 10.4 and 10.5, respectively. 24. However, if the explanatory variables and the disturbance term are not independent but they are contemporaneously uncorrelated, the OLS retains its desirable properties; see Dougherty (1992). 25. According to Hamilton (1994), the similar method has been suggested by Saikkonen (1991) and Phillips and Loretan (1991). 26. It should also be stressed that this approach is not exposed to the simultaneity bias. To avoid the simultaneity bias (or other violation of the fourth Gauss-Markov condition, e.g., from stochastic regressors or measurement errors), we use instrumental variables that are highly correlated with the regressors but not correlated to the error terms. In this chapter, rather than using the true conditional variances, whose random components may be correlated with error terms in the exchange rate equation, I use the predicted values of the endogenous explanatory variables, namely the GARCH forecast of volatility. By using the forecasts that are functions of the squared lagged residual and the estimated variances from the previous period, one can eliminate the random components in the fundamentals’ conditional variances. 27. The regression result for Canada is ~ t 0:304~ yt þ 149:477 ^h m; t þ 1739:14 ^h m ; t et ¼ 0:889 þ 0:343 m ^ þ 141:418 h y; t 440:945 hy ; t þ xt : The regression result for the United Kingdom is ~ t 0:566 y~ 1500:33 h^ m; t 5263:13 ^h m ; t et ¼ 0:320 þ 0:119m t

315:254 ^ h y; t 341:454hy ; t þ xt : 28. An increase in risk is not always a bad thing if society at large receives (nonmarketable) gains from the higher risk, as noted in Cumperayot et al. (2000). 29. For example, see Levy and Sarnat (1970) and Solnik (1974). 30. The ambiguous result for the impact of volatile money growth on the exchange rate is an interesting topic for further research. 31. The estimation is based on the two-step method of Engle and Granger (1987). Thus the estimated parameters of the cointegration vector in table 10.4 are used in this errorcorrection model. See, for instance, Engle and Granger (1987) and MacDonald and Taylor (1994). 32. For example, in our data set only Canada and the United Kingdom show weak evidence of this feature.

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Index

Adjusted cumulative current account, 297 Aggregate consumption externality, 65, 81 Aggregate demand, effective, and domestic bond price, 175–76 Allocations, feasible, and bond market equilibrium, 176–80 Arbitrage and fundamentalists, 132 and law of one price, 87–88, 93–94 ARCH-M model, 329 ARCH model(s), 233, 313, 332n.19 ARIMA model, 47 ARMA model, 47, 98 Asset pricing models, 310, 312, 319, 322 Asset-supply approach, 1 Asset trading theories, 3 Asymmetric payoff information, 3, 4–5 Asymptotic theory, for kernel regressions, 29 Balassa-Samuelson formulation or effect, 240, 241, 242, 279, 281, 288, 290–91 Bank for International Settlements, 243, 270 Bank nationality, and volume-volatility relationship, 44, 55, 57, 59 Bank size and volatility, 41 and volume-volatility relationship, 44, 54–55, 58 Bayesian-Nash equilibrium (BNE), 25 Behavioral equilibrium exchange rate (BEER) approach, 241–42, 247, 257, 272– 73n.7, 278 Bifurcation analysis, 189–201 Black money, 207, 225, 227–29 Bond market equilibrium, and feasible allocations, 176–80

Bond price, domestic, and effective aggregate demand, 175–76 Border effect, 92 Bretton Woods system, collapse of, 239, 307, 322 British sterling, in study of exchange rate models, 245, 247, 261 Business cycles, and expectation formation in model, 171 Canada in nonlinear model for exchange rates, 313, 319, 320, 321, 322, 332n.21 in study of euro, 283, 285, 290, 300 Canadian dollar in nonlinear model for exchange rates, 319 in study of exchange rate models, 245, 247, 264, 269 Capital asset pricing model (CAPM), 310, 312 Capital markets, international, 201 Causality, and price-order ﬂow relationship, 14–15 Central bank (CB), 23, 68. See also European Central Bank Central bank (CB) currency demand, and price, 3 Central bank-demand approach, 1, 1–2 Central bank trades, in micro portfolio balance model, 6–7 Chartists and chartism, 128–32, 160, 160– 61 evolutionary stability of, 159–60 and money markets, 277 and simple nonlinear exchange rate model, 135, 137, 149

340

Classical unemployment, 176, 177 Clustering, volatility, 152–55 Cobb-Douglas utility function, 186 Cointegration and long-run equilibria relationships, 277 in nonlinear model, 312, 314, 316, 317, 318, 320, 322 in real-exchange-rate model, 280–81 in study of euro, 292, 293, 295 in study of exchange rate models, 240, 245, 247, 251, 252, 253, 264, 265 Cointegration analysis, 97–100, 147–48, 230, 232, 278, 279. See also Johansen cointegration analysis method, 278, 281, 291, 299 Competitive international capital markets, 201 Consistency test, 240, 253, 264–65 Constant-coefﬁcient model, 16 Consumers, domestic, in model, 171–73 Croatia, and deutschmark holdings, 227 Currency hypothesis, 208, 233 and deutschmark/euro, 223–29 quantitative assessment of, 229–33 and role of money, 215–23 Currency stocks, 207 Czech Republic, and deutschmark holdings, 227 Demand foreign, 174 government, 174 and imperfect substitutability, 1 Deutschmark (German mark) and euro conversion, 223–29, 233 shift of interest from to dollar, 226 stock and value of, 207 in study of exchange rate models, 243, 245, 247 Deutschmark-dollar exchange rate, 208 Dickey-Fuller test, 314 Diebold-Mariano statistic, 252, 253, 271 Different-currency assets, as imperfect substitutes, 1, 5. See also Imperfect substitutability) Direction-of-change statistic, 239, 252–53, 257–61, 264, 265 loss differential series for, 271–72 Disconnect puzzle, 145, 146–48, 161, 170 Dispersion of beliefs, and volumevolatility relationship, 40, 53 DM/$ spot market, 11

Index

Dollar, Canadian. See Canadian dollar Dollar, US. See also United States and euro area currencies, 290–99 and forecasts from monetary vs. random walk model, 79 in nonlinear model for exchange rates, 313 real exchange rate of, 282–90 shift of interest to from deutschmark, 226 Dollar-deutschmark exchange rate, 208 Dollar-deutschmark (DM/$) spot market, 11 Dollar-euro exchange rate, 279, 282–83, 299–300 Domestic bond price, and effective aggregate demand, 175–76 Domestic consumers, in model, 171–73 Domestic production, in model, 173–74 Dornbusch (Dornbush and Frankel) model, xi, 63, 125, 169, 190, 239, 241, 310, 325 Dynamic closed economy model extended to small open economy, 171, 201 behavioral assumptions of, 171–74 dynamics and expectations formation in, 180–88 numerical analysis on, 188–201 temporary feasible states in, 174–80 Dynamic ﬂex price setting, 171 Dynamic general equilibrium models, 170 Eastern Europeans, 207 and deutschmarks, 227, 233 and Euro, 229, 234 ECB (European Central Bank), 221, 224, 227, 228, 229 Eclectic model, 279, 281–82, 284, 286, 290 restricted, 284 ECM (error correction model), 293, 295 Econometrics techniques, xiv Economic prosperity view, 209–12 theoretical ﬂaw in, 212–15 Effective aggregate demand, and domestic bond price, 175–76 Electronic trading and data on public trades, 1 and testing for imperfect substitutability, 22 EMS collapse of, 223 Soros’s tilting of, 224 Equilibrium trading strategies, 27–28

Index

Error correction model (ECM), 293, 295 ESTAR model, 64, 82n.3, 108, 109–10 Estimation, and forecasting, 250–252 Euro, 207, 208–209, 277 and black money, 227–29 depreciation and recovery of, xiv, 233– 34 and deutschmark, 225–27, 233 and economic prosperity view, 209–12, 213 exchange rate for (analysis), 229–33 factors affecting, 279 stock of, 224–25 Euro, study of, 277–78, 299–300 data sources for, 300–302 empirical results in, 282–99 and modeling of real exchange rates, 279–82 Euro-dollar exchange rate, 279, 282–83, 299–300 European Central Bank (ECB), 221, 224, 226, 227, 228, 229. See also at Central bank European Monetary Union, 278 European Union, 69–70. See also speciﬁc countries Eurosclerosis, 210 Excess kurtosis, in exchange rate distributions, 150–52, 161 Excess volatility puzzle, 148–50, 161 Exchange rate(s). See also Nominal exchange rate; Real exchange rate dollar-deutschmark, 208 dollar-euro, 279, 282–83, 299–300 in dynamical system, 185–87 of euro (analysis), 229–33 failure to explain, 307 ﬁxed and ﬂoating (volatility), 81 ﬂoating, 307 in logarithmic form, 96 microstructure of, 229–30, 233 as price of money vs. interest-bearing assets, 212, 233 recent empirical literature on, 278–79 Exchange rate determination, microstructural approaches to, 63 Exchange rate disconnect puzzle. See Disconnect puzzle Exchange rate economics cycles in, xi divergent paradigms in, xv models vs. data in, 63

341

Exchange rate modeling, xi–xiii turnaround in, xii Exchange rate models, 125, 239. See also Dynamic closed economy model extended to small open economy; Micro portfolio balance model; Neoclassical explanation of nominal exchange rate volatility; Nonlinear model for exchange rates; Simple nonlinear exchange rate model eclectic, 279, 281–82, 284, 286, 290 ESTAR, 64, 82n.3, 108, 109–10 evaluation of (Meese and Rogoff), xi, xii, 125 ﬂexible-price, 239, 307, 310–11 (see also Flexible-price model) interest differential, 239 interest rate parity, 257, 261, 265 (see also Interest rate parity speciﬁcation or model) macroeconomic, xiii monetary-based, 125, 308 new approaches to, 125–26 ‘‘News,’’ 125, 148 Obstfeld-Rogoff, 126 portfolio balance, 22, 125, 208 (see also Portfolio balance model or approach) productivity-based, 245, 247, 269 random walk, xi–xii, 63, 78, 97 (see also random walk model) rational expectations efﬁcient market model(s), 125 smooth transition autoregressive (STAR), 107–109 sticky (sluggish)-price, 239, 241, 245, 261, 264, 307 (see also Dornbusch model; Sticky-price monetary models) threshold autoregressive (TAR), 94, 107 UIP, 244, 250, 273n.8 Exchange rate models, study of, 239–42, 265, 269–70 data in, 242–43, 270–71 empirical results of, 245–50 forecast comparison in, 250–69, 271–72 full-sample estimation of, 243–44 Exchange rate predictability, 240 Exchange rate variability, xiii Exchange rate volatility. See Volatility Expectation(s). See also at Rational expectations exchange rates’ reliance on, 308–10 and fundamentals, 311, 328–29

342

Expectation(s) (cont.) inﬂuence of, 321–22 law of iterated expectations, 324, 327 long-run unitary elasticity of, 265 in simple nonlinear exchange rate model, 127 Expectations feedback, in dynamic model, 201 Expectations formation, in dynamic model, 183–85 Expected rate of inﬂation, 185–87 Expected volume, 47 Fat tails, in exchange rate distributions, 150–52, 161 Feasible allocations, and bond market equilibrium, 176–80 Fiscal policy, 282 Fixed-point attractors, and simple nonlinear exchange rate model, 133, 135, 137, 160 Flexible-price model, 239, 307, 310–11 and British sterling-dollar rate estimate, 245 modiﬁed, 312, 317, 320 and nonlinear model for exchange rates, 310–11, 312 reduced form solution of, 323–25, 331n.11 Flight money, 224–25 black money as, 227–29 Floating exchange rate, 81, 307 Forecasting of exchange rates, 78–81 chartists’ rules of, 128–30 in study of euro, 297 in study of exchange-rate models, 250– 69, 271–72 Foreign demand, in model, 174 Forward market and exchange rate, 40 and volatility, 43 Forward swaps, 51 Franc, in study of exchange rate models, 245 France in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 300 Fundamental equilibrium exchange rate (FEER), 278 Fundamentalists, economic, 106, 128, 132, 160

Index

and simple nonlinear exchange rate model, 135, 137 and transactions costs, 132 Fundamental levels, exchange rates’ reliance on, 308–10 ‘‘Fundamentals’’ (future payoff information), 4 Fundamental variables and disconnect puzzle, 146–47, 161, 170 and exchange rate movements, 146 and expectations, 311, 328–29 in nonlinear model for exchange rates, 328, 329 in rational expectations efﬁcient market model, 125 GARCH, 152, 161, 312, 314 GARCH forecast of volatility, 333n.26 GARCH(1,1)-M, 48 GARCH(1,1) model, 47, 152, 312, 317, 330, 331–32n.14 German reuniﬁcation, 245 Germany, in study of euro, 283, 285, 300 Global Financial Data, 270 Global stability of adjustment process, 164n.7 Government demand, in model, 174 Habit model, in model of nominal exchange rate volatility, 65, 72, 73, 78, 79, 81, 83n.15 Habit persistence externality, 64, 65, 67–68 Hausman test, 286, 288, 290 Heterogeneity and aggregate analyses, 291 of beliefs (simple nonlinear model), 127 in panel analyses of euro exchange rate, 299 and volatility, 40, 41 Heterogeneous agents, 106 and exchange rate model, 126 Heterogeneous expectations, xiii ‘‘Hot potato’’ trading, 21 Hungary, and deutschmark holdings, 227 ‘‘Iceberg’’ transport costs, 93 Imperfect substitutability, xii–xiii, 1–2 as intervention condition, 21 and micro portfolio balance model, 5–30 and relation of value of currency to stock of currency, 222–23 trading-theoretic approach to, 3–5

Index

Inﬂation expected rate of, 185–87 and PPP-relationship, 158 repressed, 176, 177 Information. See Private information; Public information Interest differential model, 239 Interest parity, uncovered (UIP), in dynamic model, 183–85, 201 Interest rate expected, 185–87 national, 220–22 Interest rate differential, real, 279, 291 Interest rate parity speciﬁcation or model, 240, 242, 257, 261, 265, 269, 270 International capital markets, competitive, 201 International Comparison Programme (ICP) data set, 90 International Monetary Fund (IMF), 70 International Financial Statistics (IFS), 243, 270, 300, 322 on transportation costs, 92 International risk sharing, 68–69 International Sectoral Database (OECD), 300 International substitutability of assets, 223 Intervention and micro portfolio balance model, 21– 22 trading-theoretic approach to, 23 Intervention policy, 2 Inventory effects, 4 Italy in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 300 Iterated expectations, law of, 324, 327 Japan in nonlinear model for exchange rates, 313, 321, 322 in study of euro, 283, 285, 290, 300 Johansen cointegration analysis method, 278, 281, 291, 299 Johansen test, 98, 230, 314, 316 Kernel estimation, 18–19 Kernel regression, 29–30 Keynesian unemployment, 176, 177 Kurtosis, in exchange rate distributions, 150–52

343

Law of iterated expectations, 324, 327 Law of one price (LOP), 87–93 absolute version of, 87–88 nonlinearities in deviations from, 88, 93– 95 and purchasing power parity, 89–90 relative version of, 88 Linear exchange rate determination models, 69 MacDonald’s hamburgers, product differentiation of across countries, 112n.1 Macroeconomic models, xiii Macroeconomics, open economy, xiii Macroeconomic uncertainty, xv Mean squared error (MSE) criterion, 78, 239, 240, 252, 253–57, 265, 269 Micro portfolio balance model, 2, 5–11, 22–23. See also Portfolio balance model or approach empirical analysis of, 11–15 and kernel regression, 29–30 and log price changes, 30 model solution in, 23–28 results and implications of, 15–22 Microstructure of exchange rate, 229–30, 233 Misalignment problem, 146 Misspeciﬁcation tests, 293 Mixture of distribution hypothesis, 40 Models of exchange rates. See Exchange rate models Monetary-based exchange rate models, 125, 308 Money, in exchange rate determination, 215–23. See also Currency hypothesis; Deutschmark; Dollar, US; Swedish krona (SEK) market; Yen; other currencies MSE (mean squared error) criterion, 78, 239, 240, 252, 253–57, 265 , 269 M3, redeﬁnition of, 226 Mundell-Fleming model or approach, 282, 284 ‘‘Mystery of the multiplying marks,’’ 230 National interest rates, 220–22 Nationality of banks, and volumevolatility relationship, 44, 55, 57, 59 Negative feedback rule, 128, 160

344

Neoclassical explanation of nominal exchange rate volatility, 64 data for, 69–70 model for, 64–69 model calibration in, 70–73 results in, 73–81 ‘‘New open economy macroeconomics,’’ xiii, 63, 170, 170–71 ‘‘News’’ models, 125, 148 Noise traders, 129 Nominal exchange rate. See also Neoclassical explanation of nominal exchange rate volatility and Dornbusch model, 169 and real exchange rate, 87 Nominal exchange rate volatility, neoclassical explanation of. See Neoclassica explanation of nominal exchange rate volatility Nonlinear exchange rate model, simple. See Simple nonlinear exchange rate model Nonlinearity(ies) and deviations from law of one price, 88, 93–95 in real exchange rate movements, 87, 105–11 of transactions costs, 132 Nonlinear model for exchange rates, 307– 308, 321–22 and closed-form solutions, 329–30 data sources for, 322–23 and expectations of future fundamentals, 311 and ﬂexible-price model, 310–11, 312 motivation for, 308–10 speciﬁcation and estimation in, 312–21 and sticky-price model, 311, 312 stochastic volatility added to fundamental expectations in, 328–29 Obstfeld-Rogoff framework of dynamic utility optimization, 125 Obstfeld-Rogoff new open economy macro model, 126 Open economy macroeconomics. See ‘‘New open economy macroeconomics’’ Options, and volatility, 43, 51 Option volume, 49 Order ﬂow and micro portfolio balance model, 2, 5 and price, 15, 21, 22

Index

and swap transaction, 49 vs. trading volume, 33n.4 Orderly market, and intervention, 21–22 Organization for Economic Cooperation and Development (OECD), 70 Panel analysis, 283–290, 299 Partial autocorrelation function (PACF), 113n.20 Payoff information, asymmetric, 3, 4–5 ‘‘Payoffs,’’ 33n.8 Perfect substitutability, and law of one price, 88 Persistent portfolio balance channel, 4, 16 Pooled mean group (PMG), estimator, 277–78, 285–86 Portfolio balance effect, 4 Portfolio balance model or approach, xi, xii, 2, 3, 22, 125, 207–208, 233. See also Micro portfolio balance model and currency hypothesis, 208, 215–23, 229 currency stocks in, 207 theoretical ﬂaw in, 212–15 Positive feedback rule, 128, 160 PPP. See Purchasing power parity Predictability, exchange rate, 240 Price(s) adjustment of (dynamic model), 180–82 and central bank (CB) currency demand, 3 and order ﬂow, 15, 21, 22 Price differentials, and law of one price, 91–92 Price index problems, 89–90 Price stickiness. See Sticky (sluggish)-price monetary models; Sticky prices Pricing-to-market (PTM) theory, 94–95, 112n.3 Pricing puzzles, 170 Private information, xii and weekends, 48 Product differentiation across countries, of MacDonald’s hamburgers, 112 Production, domestic, in model, 173–74 Production economy, and nominal exchange rate volatility, 81–82 Productivity advances, and real exchange rate, 281 Productivity-based model, 245, 247, 269 PTM (pricing-to-market) theory, 94–95, 112n.3

Index

Public demand, and imperfect substitutability, 1 Public information and micro portfolio balance model, 14– 15, 26 and weekends, 48 Purchasing power parity (PPP), xi, 95–96, 278 absolute, 95 and Balassa-Samuelson models, 241 and cointegration and unit root tests, 96– 100, 109 (see also Unit root test) deviations from, 89, 97, 106, 279, 325, 326 and Dornbusch model, 169 and ﬂexible-price model, 323 and law of one price, 87, 89–90 long-span studies of, 101 and nontraded goods, 281 OECD, US, and German, 209 panel data studies of, 102–103 puzzle of, 104–105, 110, 170 and real exchange rate, 87 relative, 95 and sluggish-price model, 325, 326 stochastic assumption of, 323 in study of exchange rate models, 239 Quantity theory of money, xi Quoting strategies, optimal, 25 Random walk model, xi–xii, 63, 78, 97 and closed-form solutions, 329 and cointegration, 98 and euro-area model, 297 and expectations, 311, 321 naı¨ve, 271 and study of exchange rate models, 239, 240, 241, 252, 257, 261, 269 Rate of return adjustments, 220 Rational expectations, and effect of public information, 15 Rational expectations efﬁcient market model, 125 Rational expectations fully informed agent paradigm, xiv Real exchange rate, 87 under ﬁxed vs. ﬂoating regime, 169 modeling of, 279–82 nonlinearities in, 87, 105–11 nonstationarity of, 96, 97, 98, 102 and purchasing power parity puzzle, 104–105

345

testing for stability of, 99–100, 101 Real exchange rate adjustment, nonlinearity in, 87 Real interest rate differential, 279, 291 Redundancy problem, 212–13 Relative proﬁtability of chartism, 130 Reporters, and volatility, 53 Representative behavioral equilibrium exchange rate model, 240 Reservation prices, and volume-volatility relationship, 40 Reverse causality hypothesis, 14–15 Risk and imperfect substitutability, 3–4 in nonlinear model, 307, 312, 320, 328 Risk sharing, international, 68–69 Rolling regressions, 250–51 Sensitivity analysis, for simple nonlinear exchange rate model, 135–40 Short swaps, 60n.1 and volatility, 43, 49, 51 Simple nonlinear exchange rate model, 126–32, 160–61 empirical relevance of, 145–55, 161 and evolutionary stability of chartism, 159–60 and permanent shocks, 141–45 sensitivity analysis of, 135–40 solution of, 133–34 stochastic version of, 140–41 with transactions costs, 132–33 and variance of shocks, 155–58 Simultaneity bias, 333n.26 Slovakia, and deutschmark holdings, 227 Slovenia, and deutschmark holdings, 227 Sluggish-price models. See Dornbusch (Dornbusch and Frankel) model; Sticky (sluggish)-price monetary models Smooth transition autoregressive (STAR) model, 107–109 Soros, George, 224 SPA (superior predictive ability), test of, 80 Spain, in study of euro, 283, 285, 300 Speculators, and volatility, 41 Spot market DM/$, 11 and exchange rate, 40, 49 interdealer transactions in, 34n.17 and volatility, 43 Spot volatility, 49 Spot volumes, and volatility, 51

346

Standard model, in model of nominal exchange rate volatility, 65 STAR (Smooth transition autoregressive) model, 107–109 Stationary states, in dynamical system, 187–88 Sterling (British), in study of exchange rate models, 245, 247, 261 Sticky (sluggish)-price monetary models, 239, 241, 245, 261, 264, 307. See also Dornbusch (Dornbusch and Frankel) model and British sterling-dollar rate estimate, 245 closed-form solution of, 311, 312 modiﬁed, 317, 320 reduced-form solution of, 325–27, 331n.11 Sticky prices, 63, 64, 82, 169, 170, 170–71 Stochastic PPP assumption, 323 Stochastic version of simple nonlinear exchange rate model, 140–41 Stockholm, conference on ﬂexible exchange rates in, xi Stock shares, and portfolio interpretation, 208 Study of exchange rate models. See Exchange rate models, study of Substitutability of assets, imperfect. See Imperfect substitutability Substitutability of assets, international, 223 Superior predictive ability (SPA), test of, 80 Swaps (standard) and exchange rate, 49 and volatility, 43 Swedish krona (SEK) market, and volumevolatility relationship, 39, 40, 58. See also Volume-volatility relationship Swiss franc, in study of exchange rate models, 247, 250 TAR (threshold autoregressive) model, 94, 107 Taylor, Mark, 64 Taylor’s theorem, 328, 329 Temporary ﬁxed-price situations, 171 Temporary portfolio balance channel, 4, 16 Threshold autoregressive (TAR) model, 94, 107

Index

Trading ﬂows, xiii. See also Order ﬂow Trading rounds, in micro portfolio balance model, 7–10 Trading strategies, equilibrium, 27–28 Trading-theoretic approach to imperfect substitutability, 3–5 to intervention, 23 Trading volume, vs. order ﬂow, 33n.4 Transactions costs, xiv, 94, 107, 132–33. See also Arbitrage UIP model, 244, 250, 273n.8 Uncertainty, macroeconomic, xv Uncovered interest parity (UIP), 242. See also UIP model and Dornbusch model, 310 in dynamic model, 171, 183–85, 190, 201 and ﬂexible-price model, 323 and risk premium, 328 Unemployment, classical, 176, 177 Unemployment, Keynesian, 176, 177 United Kingdom in nonlinear model for exchange rates, 313, 319, 321, 322, 332n.21 in study of euro, 283, 285, 290, 300 United States. See also Dollar, US capital ﬂow into (and decline of euro), 209–12 intervention by, 2 in neoclassical explanation, 69 in nonlinear model for exchange rates, 313, 322 savings rate decline in, 211 Unit root test, 97, 100, 101, 102, 103, 104, 107, 109, 110, 111 Variability, exchange rate, xiii VECM, 297, 299 Vector autoregressive (VAR) model, 291, 312 Volatility attempts to explain, 63–64 (see also Neoclassical explanation of nominal exchange rate volatility) in bifurcation analysis, 193–201 and domestic currency prices, 319–20 and risk premium, 308 spot, 49 Volatility clustering, 152–55 Volume-volatility relationship, 39–41, 57– 59 data in study of, 41–48

Index

and expected vs. unexpected volume, 45, 47 results in study of, 48–57 Wages, adjustment of (dynamic model), 180–82 Wholesale price index (WPI), 92, 99 Williamson, John, 146 Yen, in study of exchange rate models, 243, 245, 247, 261, 264, 269

347

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