Exchange Rates and International Macroeconomics 9780226262536

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Exchange Rates and International Macroeconomics

A Conference Report National Bureau of Economic Research

Exchange Rates and International Macroeconomics

Edited by

Jacob A. Frenkel

The University of Chicago Press

Chicago and London

The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 1983 by The National Bureau of Economic Research All rights reserved. Published 1983 Paperback edition 1986 Printed in the United States of America 95 94 93 92 91 90 89 88 87 86 6 5 4 3 2

Library of Congress Cataloging in Publication Data Main entry under title: Exchange rates and international macroeconomics. (A conference report / National Bureau of Economic Research) Papers and comments presented at a conference held in Cambridge, Mass., Nov. 20-21,1981; sponsored by the National Bureau of Economic Research. Includes indexes. 1. Foreign exchange-Congresses. 2. International finance-Congresses. I. Frenkel Jacob A. II. National Bureau of Economic Research. III. Series: Conference report (National Bureau of Economic Research) HG205 1981c 332.4'56 83-14524 ISBN 0-226-26249-9 (cloth) ISBN 0-226-26250-2 (paper)

National Bureau of Economic Research Officers Walter W. Heller, chairman Franklin A. Lindsay, vice-chairman Eli Shapiro, president David G. Hartman, executive director and corporate secretary

Charles A. Walworth, treasurer Sam Parker, director of finance and administration

Directors at Large Moses Abramovitz George T. Conklin, Jr. Jean A. Crockett Morton Ehrlich Edward L. Ginzton David L. Grove Walter W. Heller Saul B. Klaman

Franklin A. Lindsay Roy E. Moor Geoffrey H. Moore Michael H. Moskow James J. 0 'Leary Peter G. Peterson Robert V. Roosa Richard N. Rosett

Bert Seidman Eli Shapiro Stephen Stamas Lazare Teper Donald S. Wasserman Marina v. N. Whitman

Directors by University Appointment Charles H. Berry, Princeton Otto Eckstein, Harvard Walter D. Fisher, Northwestern Ann F. Friedlaender, Massachusetts Institute of Technology J. C. LaForce, California, Los Angeles Paul McCracken, Michigan Almarin Phillips, Pennsylvania

James L. Pierce, California, Berkeley Nathan Rosenberg, Stanford James Simler, Minnesota James Tobin, Yale William S. Vickrey, Columbia Dudley Wallace, Duke Burton A. Weisbrod, Wisconsin Arnold Zellner, Chicago

Directors by Appointment of Other Organizations Carl F. Christ, American Economic Association Gilbert Heebner, National Association of Business Economists Robert C. Holland, Committee for Economic Development Stephan F. Kaliski, Canadian Economics Association Douglass C. North, Economic History Association

Rudolph A. Oswald, American Federation of Labor and Congress of Industrial Organizations Joel Popkin, American Statistical Association G. Edward Schuh, American Agricultural Economics Association Albert Sommers, The Conference Board Charles A. Walworth, American Institute of Certified Public Accountants

Directors Emeriti Arthur Burns Emilio G. Collado Solomon Fabricant Frank Fetter

Thomas D. Flynn Gottfried Haberler Albert J. Hettinger, Jr. George B. Roberts

Murray Shields Boris Shishkin Willard L. Thorp Theodore O. Yntema

Since this volume is a record of conference proceedings, it has been exempted from the rules governing critical review of manuscripts by the Board of Directors of the National Bureau of Economic Research (resolution adopted 8 June 1948, as revised 21 November 1949 and 20 April 1968).

Contents

Preface

1.

2.

3.

4.

5.

vii

An Introduction to Exchange Rates and International Macroeconomics Jacob A. Frenkel An Accounting Framework and Some Issues for Modeling How Exchange Rates Respond to the News Peter Isard Comment: Sebastian Edwards Comment: Jeffrey A. Frankel The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspe~ification? Richard Meese and Kenneth Rogoff Comment: Nasser Saldi Comment: Michael K. Salemi Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis of Linear Models Lars Peter Hansen and Robert J. Hodrick Comment: Craig S. Hakkio Comment: Kenneth J. Singleton Rational Expectations and the Foreign Exchange Market Peter R. Hartley Comment: Debra Glassman Comment: Maurice Obstfeld

ix 1

19

67

113

153

viii

6.

Contents

The Use of Monetary Policy for Internal and External Balance in Ten Industrial Countries Stanley W. Black Comment: Leonardo Leiderman Comment: Alan C. Stockman

189

7.

Staggered Contracts and Exchange Rate Policy Guillermo A. Calvo Comment: John B. Taylor Comment: Michael Mussa

235

8.

Oil Shocks and Exchange Rate Dynamics Paul Krugman Comment: Pentti J. K. Kouri Comment: Charles A. Wilson

259

9.

Real Adjustment and Exchange Rate Dynamics J. Peter Neary and Douglas D. Purvis Comment: Kent P. Kimbrough Comment: Jeffrey Sachs

285

10.

Real Exchange Rate Overshooting and the Output Cost of Bringing Down Inflation: Some Further Results Willem H. Buiter and Marcus Miller Comment: RobertP. Flood Comment: Jiirg Niehans

317

List of Contributors

369

Author Index

373

Subject Index

376

Preface

This volume contains papers and comments presented at a conference on Exchange Rates and International Macroeconomics, held in Cambridge, Massachusetts, on 20-21 November 1981 and sponsored by the National Bureau of Economic Research. When invited to organize the conference, I was asked to prepare the text for a "call for papers" announcement specifying the range of topics that would be considered. In contemplating the proper scope of such a conference I decided to consider a broad range of topics. Accordingly, the announcement stated that: The conference will be broad enough to accommodate a wide variety of issues relating in one way or another to international macroeconomics. Appropriate for the conference are papers dealing with the following topics: exchange rate determination, interactions between commodity prices and exchange rates, efficiency of the foreign exchange market, the role of information, labor-market institutions and indexation, structural adjustment and international competitiveness, the economics of managed floating, rules for crawling pegs, stabilization policy and balance-of-payments adjustment, international capital markets, international reserves and world inflation, aspects of international monetary reform such as: design of an optimal reserve investment and international consistency of national pegging arrangements, and the role of policy coordination. Other possible topics that can be interpreted as related to international macroeconomics will be considered. Priority will be given to empirically oriented research, but submission of theoretical papers on these topics is welcome also. Papers will be selected on the basis of abstracts of about 500 words or, when possible, complete papers, with preference being given to papers by younger members of the profession. Any research that will not have been published at the time of the conference may be submitted. ix

x

Preface

The response to this call for papers was overwhelming. Within a few weeks several hundred papers and abstracts were submitted for consideration of possible inclusion in the conference program. The quality of the submissions was exceedingly high and without doubt sufficient papers could have been selected to fill up the programs of three or four highquality conferences. As always in such circumstances, the final selection had to be somewhat arbitrary even though one must admit that personal taste always plays an important role in "arbitrary" selection processes. In making the selection, I attempted to have some blend of empirical and theoretical research even though this volume gives a somewhat larger share to empirical contributions. Each paper was assigned to formal discussants whose comments are also included in this volume.

1

An Introduction to Exchange Rates and International Macroeconomics Jacob A. Frenkel

This introduction begins with a reader's guide to the book, containing a summary of each chapter and an outline of the discussants' comments. It concludes with a brief discussion of some open questions in the analysis of exchange rates and international macroeconomics, represented by four examples of suggested research issues. 1.1

A Reader's Guide

In chapter 2, Peter Isard develops a useful framework for discussing the limitations of existing empirical models of exchange rate determination. He starts by manipulating the interest parity condition to develop some accounting identities that relate observable exchange rates to three unobservable expectational terms: an expected future real exchange rate, an expected inflation differential, and an expected premium for bearing exchange risk. He then focuses attention on issues relevant for modeling how news is transmitted to exchange rates through revisions in the three expectational terms. Given the presumption that exchange rate movements are predominantly unexpected-or, equivalently, that they predominantly reflect revisions in expectations in response to news-Isard argues that the poor performance of the empirical exchange rate models of the 1970s is not surprising. To model exchange rate expectations, Isard represents the expected future real exchange rate by a model of the expected long-run real exchange rate or purchasing power parity (PPP) level. The question "How long is it expected to take for the real exchange rate to converge to Jacob A. Frenkel is the David Rockefeller Professor of Economics at the University of Chicago, a research associate of the National Bureau of Economic Research, and an editor for the Journal of Political Economy.

1

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Jacob A. Frenkel

its PPP level?" is viewed to be roughly equivalent (as would be the case under risk neutrality) to the question "How long is it expected to take for real interest differentials to vanish?" The latter question is addressed through several comparisons of nominal interest rate term structures and measures of inflation expectations. Isard presents data which suggest that the adjustment lasts between two and five years. Based on this evidence, he recommends using the five-year forward rate and the long-term (five years) interest differentials as the relevant variables in exchange rate equations. Isard argues that his modeling strategy avoids reliance on arbitrary assumptions about the expected dynamics of adjustment to long-run PPP, which are explicit or implicit in traditional attempts to explain the "response" of exchange rates to changes in short-term interest differentials. The paper devotes considerable attention to assessing the types of news that contributed to the major swings in the German mark/U.S. dollar (spot and five-year forward) exchange rates during 1980-81. Major swings in the exchange value of the dollar during 1981 coincided strikingly with major shifts in the outlook for U.S. fiscal policy. Isard argues that available survey data on long-term U.S. inflation expectations support the view that revisions in inflation expectations "explained" the major share of the exchange rate response to fiscal policy news. In addition, the arithmetic of the accounting identities suggests that part of the exchange rate response to fiscal policy news may have reflected changes in the risk premium in response to substantial revisions in expectations about the cumulative size of U.S. budget deficits over a five-year horizon. An important message from the 1980-81 experience is that attempts to quantify the news on the basis of autoregressions may be largely inadequate. In particular, the fiscal policy news during 1981 was not accompanied by contemporaneous jumps in prices, activity levels, money supplies, or budget deficits, so its influence on exchange rates-whether transmitted through revisions in inflation expectations or changes in the risk premium-cannot be captured with autoregressions.Moreover, it is also apparent that long-term nominal dollar interest rates were not a good proxy for long-term U.S. inflation expectations during 1980-81; long-term real dollar interest rates changed considerably. Thus, the quantification of expectations poses a major hurdle for empirical attempts to explain the behavior of exchange rates. In their comments on Isard's paper Sebastian Edwards and Jeffrey Frankel discuss several conceptual and empirical issues. Edwards demonstrates the numerous channels through which news affects the exchange rate and proposes alternative ways for testing the key empirical relation. Frankel's discussion focuses on the relative qualities of short- and long-

3

Introduction

term rates of interest as the relevant variables in exchange rate equations. He argues that since both rates are related to each other, they should both, in principle, be equally acceptable indicators of monetary conditions. Frankel concludes his discussion by pointing out some puzzles in the pattern of the relations among the short-term interest rate, expected inflation, the exchange rate, and the long-term interest rate in the United States during 1981. In the third chapter, Richard Meese and Kenneth Rogoff analyze the reasons for the poor performance of a variety of exchange rate models. This chapter complements their earlier work in which they have compared the out-of-sample fit of various structural and time series exchange rate models, and have found that the random walk model performs as well as any estimated model at one- to twelve-month horizons for 1970s dollar Imark, dollar Ipound, dollar Iyen, and trade-weighted dollar exchange rates. The structural models included the flexible-price and the sticky-price monetary models, as well as a sticky-price asset model which incorporates the trade balance. The various models performed poorly, even though their forecasts were purged of all uncertainty concerning the future paths of their explanatory variables by using actual realized values. Meese and Rogoff present evidence that the poor performance of the structural models may not be attributed to inconsistent or inefficient parameter estimates. They rule out such a possibility on the grounds that these models fail to yield any improvement over the random walk model in mean absolute or root-mean-squared error over one to twelve months out of sample for a broad range of theoretically plausible coeficient values, even when autoregressive error terms are introduced. They argue therefore that it is unlikely that more efficient estimation techniques, such as imposing all the cross-equation rational expectations restrictions, would yield parameter estimates which would perform much better. While the various models do not outperform the random walk model over periods of one to twelve months out of sample, they perform better over longer forecast horizons. The three models considered by Meese and Rogoff share the same asset market specfication, which is based on uncovered interest parity and a conventional real money demand equation with income and short-term interest rates. The models differ in their assumptions about purchasing power parities. Since all three models perform poorly, their joint failure is likely a result of the asset market specification. While, in principle, the breakdown of empirical exchange rate models may be the result of volatile time-varying risk premiums, volatile long-run real exchange rates, or poor measurement of inflationary expectations, the authors argue that the main problems seem to lie in the specifications of the demand for money. They conclude by noting that if this is indeed the

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Jacob A. Frenkel

case, then the same improvements which resuscitate domestic empirical money demand equations should also lead to similar improvements in empirical exchange rate equations. In his comments on the Meese and Rogoff paper, Nasser Saldi notes that since the residual errors for various exchange rates are likely to be correlated, a joint estimation of the various exchange rate equations could improve the forecast accuracy of the structural models. He also notes that since forecasts for horizons longer than one period follow a moving average process, tests for evaluating the forecasts of alternative models are more meaningful when based on one-period ahead forecasts rather than on multiperiod forecast horizons. As for the source of the failure of the structural models, Saldi highlights the inadequate modeling of expectations formation. In particular, he believes that the distinction between anticipated and unanticipated movements in the exogenous driving variables has not been given sufficient attention in existing structural models. Commenting on the same paper, Michael K. Salemi analyzes Meese and Rogoff's findings by pointing out that in contrast with the results for short-term horizons (up to twelve months), long-term forecasts based on the three structural models are more successful than the forecasts based on the random walk model. Salemi suggests the possibility that in the short run the exchange rate behaves like a speculative asset, but over longer runs the exchange rate is related systematically to a range of economic variables that is broader than the one assumed by the typical asset models. Salemi concludes his comments by noting that the results reported by Meese and Rogoff do not reject the conceptual framework underlying the asset-market approach to exchange rate determination. Rather, they shed doubt on some specific formulations of that approach. In the fourth chapter, Lars P. Hansen and Robert J. Hodrick study three alternative statistical models of the relationship between expected return and risk in the forward foreign exchange market. If the forward exchange rate deviates from the expected future spot rate, there is expected profit on contracting in the forward market. The risk one bears in writing such contracts is caused by covariance of the nominal profit on the contract in terms of its currency of denomination with the intertemporal marginal rate of substitution of that money which is the nominal counterpart of the intertemporal marginal rate of substitution of consumption. This latter concept is the key ingredient used in defining risk that emerges from real intertemporal asset-pricing models. Each of Hansen and Hodrick's statistical models of the risk-return relationship in the forward foreign exchange market can be viewed as a restriction on linear time series representations, and each is interpreted by examining the first order conditions of the intertemporal optimization problems of international investors under the assumption of rational expectations. Hansen

5

Introduction

and Hodrick estimate these models from a semiweekly sample of spot and one-month forward exchange rates for the period from February 1976 to December 1980. Their first statistical model relies on the auxiliary assumption that exchange rates and the intertemporal marginal rate of substitution of money are jointly lognormally distributed. Under this assumption the expected deviations between the logarithms of future spot rates and current forward rates should be constant. They report empirical results that shed doubts on the adequacy of this model. These results suggest that time variation in risk premiums in the forward·market should be taken seriously. The second statistical model examined by Hansen and Hodrick relies on the assumption that the conditional covariance between the profit on the forward contract and the intertemporalmarginal rate of substitution of money is constant. In this case, time variation in the risk-free nominal return should capture the time variation in the risk premiums. Statistical analysis of this model indicates that little, if any, of these movements is explained by movements in the risk-free nominal return. The authors then examine a final statistical model which is patterned after the single beta capital asset-pricing model that has played an important role in the empirical finance literature. In this model risk premiums are linked to the covariance of the return on an asset with the return on a benchmark asset that is on the mean variance frontier. From the intertemporal asset-pricing models it is known that the return on the aggregate wealth portfolio will not, in general, be an appropriate benchmark. From theory it is known that appropriate candidates for benchmark returns are explicitly linked to the intertemporal marginal rate of substitution of money. Such returns, however, are difficult, if not impossible, to observe. Consequently, in their statistical model Hansen and Hodrick postulate that the "betas" on the forward contracts are constant through time, while they allow the conditional expected return on the unobservable benchmark return to vary over time. Under these assumptions they estimate a time series version of a latent variable model in which severe cross-equation restrictions apply to the parameter estimates. In estimating the statistical model, they are unable to reject these restrictions, and they find evidence for nontrivial risk premiums in at least two and possibly three of the five forward markets considered. Although the statistical analysis cannot be construed as providing tests for intertemporal equilibrium models of forward foreign exchange markets, because they have placed assumptions directly on endogenous variables, the results are sufficiently encouraging to promote the important endeavor of integrating the theory of intertemporal asset pricing with international monetary theory. In their discussion of the Hansen-Hodrick paper, Craig S. Hakkio and

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Jacob A. Frenkel

Kenneth J. Singleton make econometric and methodological comments. Hakkio notes that Hansen and Hodrick's analysis builds on an intertemporal arbitrage condition derived from a nonmonetary model of a representative individual. He suggests that the application of this framework to a monetary model of the aggregate economy may be sensitive to the way in which money is introduced into the model as well as to the conditions which make aggregation valid. In interpreting the results, Hakkio recommends a more detailed analysis of the specific causes which underlie a rejection of various models. He concludes his discussion by noting that Hansen and Hodrick's findings should be interpreted as evidence against the constant risk premium hypothesis rather than against the efficient market hypothesis. Singleton elaborates on some theoretical properties of the models investigated by Hansen and Hodrick and discusses ways of testing nonlinear, intertemporal models of exchange rate determination that do not impose the restrictive assumptions underlying their linear relations. Singleton argues that in the absence of more information about the underlying assumptions which lead to the linear exchange rate representations, there are various possible ways of interpreting Hansen and Hodrick's findings. Specifically, Hansen and Hodrick present the nominal risk-free relation and the latent variable representation as if they represent very different theoretical models of exchange rate determination. While admitting this possibility, Singleton notes that since so little structure is imposed on the empirical representations of the theoretical models, one representation could also be interpreted as a special case of the other. In the fifth chapter, Peter R. Hartley analyzes the hypothesis that expectations of exchange rate movements are formed rationally. He argues that this hypothesis implies that forecasts of future exchange rates are based on any publicly available information which is known to be useful for predicting exchange rate movements, and he tests the hypothesis within the context of the simple monetary model of exchange rate determination. The simple monetary model predicts that movements in the rate of exchange between two currencies will be determined by current and anticipated future movements in the supplies of, and demands for, the two currencies. Hartley supposes that changes in money supplies and incomes follow stable autoregressive processes, and therefore, if agents use this fact, anticipated future movements in money supplies and incomes depend on past movements in the same variables. Anticipated movements in exchange rates then depend on past movements in money supplies and incomes. If expectations are rational, there are crossequation restrictions on the autoregressive parameters describing the money supply and income growth processes and on the parameters in the exchange rate equation.

7

Introduction

Hartley's equation relating the change in exchange rates to present and past changes in money supplies and incomes has an error term which is an amalgam of the error terms in the money demand functions for two countries and deviations from purchasing power parity, and there is no reason to expect this error term to be white noise. If the error term follows a stable autoregressive process, then unanticipated changes in the exchange rate depend on unanticipated money and income growth rates and an error term which is serially uncorrelated (so long as the forecast horizon and observation interval coincide). Rationality of expectations again implies a set of cross-equation restrictions on the parameters of the forecasting equations for money and income growth rates and. on the parameters in the unanticipated change in the exchange rate equation. Hartley argues that tests of rationality can be strengthened by simultaneously estimating equations explaining unanticipated changes in exchange rates between several overlapping pairs of currencies. If expectations are rational, then the forecast of, for example, U.S. money growth rates that agents use when attempting to predict changes in the dollar / pound exchange rate should be the same forecast they use when attempting to predict changes in the dollar/mark exchange rate. Rationality implies restrictions across the parameters of the forecasting equations and both exchange rate equations. He argues further that the term structure of the forward exchange rate can also be used in exchange rate equations for different forecasting horizons and that the rationality implies another set of cross-equation restrictions. Hartley applies these tests to data from the 1970s. Although the cross-equation restrictions implied by the model are not rejected, the estimated coefficients have large standard errors, and thus many alternative hypotheses are also consistent with the data. He then estimates joint forecasting equations relating Eurocurrency interest rates to money and income growth, and unanticipated exchange rate movements to unanticipated movements in interest rates. Rationality again implies crossequation restrictions on the estimated parameters which are not rejected. In commenting on Hartley's paper, Debra Glassman notes specific aspects of data from the foreign exchange market. She argues that each day of the week has its own characteristics which might be relevant in a detailed empirical study of exchange rates. For example, on Monday there might be substantial catching up with· the news of the weekend, while on Friday the weekly U.S. money supply figures are released. In addition, since there are subperiods with differing characteristics of the foreign exchange market, Glassman suggests that a further pursuit of the heteroscedasticity correction is warranted. She concludes her comments by noting that Hartley's procedure tests the joint hypothesis of rational expectations along with a specific specification of the model. To separate the two, she suggests that the expectations hypothesis can be fruitfully

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Jacob A. Frenkel

tested by using other data on exchange rate forecasts, like those supplied by professional services and those implicit in futures, options, and stock markets. Maurice Obstfeld's comments on Hartley's paper focus on alternative strategies {or estimating exchange rate equations. Specifically, Obstfeld discusses the trade-off between asymptotic efficiency, on the one hand, and robustness and tractability, on the other, by comparing Hartley's maximum likelihood approach to an alternative, instrumental variables approach. Obstfeld notes that in Hartley's framework consistency of maximum likelihood estimates requires some strong exogeneity assumptions that may not be valid. He argues that under such circumstances it is desirable to have an estimator that is consistent under a broader set of assumptions, even if that estimator is inefficient relative to the maximum likelihood estimate. Obstfeld describes an instrumental variables estimator which permits the weakening of Hartley's assumptions while easing the computational difficulties. In addition, the instrumental variables approach has the attractive feature of taking into account the possible conditional heteroscedasticity of the disturbances. In the sixth chapter, Stanley W. Black studies the use of monetary policy for internal and external balance in ten industrial countries. Black assumes that the monetary authorities behave as if they maximize an intertemporal welfare function depending on internal and external target variables, such as inflation, unemployment, and the level of reserves, subject to an implicit, perceived econometric model of the private economy. Policy reaction functions then relate the policy instruments directly under the authorities' control to the target variables. The appropriate instruments in each country include discount rates, reserve ratios, open market operations, discount quotas, and credit controls. Black allows for information lags as well as lags in the adjustment of instruments that are adjusted only discretely, such as discount rates and credit controls. These lags are allowed for by using threshold and logit regression models. Black's results show that the instruments of monetary policy respond significantly in predictable ways to customary measures of internal and external balance. Cross-country comparisons in the context of the discount rate equations, which are reasonably homogeneous across countries, show that inflation receives a relatively high weight in the policy reaction functions of Belgium, Germany, Italy, France, and the United States, while it receives lower weights in Britain, Canada, the Netherlands, Japan, and Sweden. A cross-sectional regression equation shows that, after taking account of orientation of monetary policy toward external targets and differing vulnerability to oil price increases, the observed average inflation rate is negatively correlated with the policy weight that the reaction function assigns to the inflation target. In addition, Black shows that: (i) the importance attached to inflation and

9

Introduction

unemployment objectives varies inversely across countries; (ii) there appears to be little relationship across countries between the importance of unemployment objectives and observed rates of unemployment; (iii) there is an inverse correlation across countries between the importance of internal and external objectives for monetary policy; (iv) there is an inverse correlation between the flexibility of the exchange rate and the relative importance of external compared to internal objectives; and (v) conservative election victories have often led to tighter monetary policies. In commenting on Black's paper, Leonardo Leiderman discusses the robustness of the empirical findings as well as the methodology. His methodological comments raise issues concerning the derivation and the specification of Black's postulated reaction functions. Leiderman points out some difficulties of interpreting the estimated coefficients of the reaction function. These difficulties stem from the fact that each estimated coefficient represents the joint influence of the effect of the policy instrument on a target variable and the weight of the target in the objective function. As a result the estimated coefficients are generally functions of the structural parameters and of the parameters reflecting policy preferences, and disentangling the two may not always be possible. Alan Stockman's comments on Black's paper also focus on methodological and empirical issues. He argues that the view of policy as an isolated action undertaken in response to a particular set of circumstances may be inappropriate. Instead, policy should be analyzed within a more general framework which views a specific policy action as part of a broader policy rule. On the empirical side, Stockman questions the robustness of the estimates, as well as whether they reflect structural or reduced-form coefficients. He suggests that some of these questions could be resolved by following a procedure that imposes and tests the cross-equation restrictions that are imposed by the model. The seventh chapter by Guillermo A. Calvo provides an analytical framework for the analysis of exchange rate policies for an economy with staggered contracts. An important methodological innovation in this paper is the development of a continuous time formulation of the staggered contracts model. The model is that of a small open economy that is governed by rational expectations and in which the prices of home goods are set intermittently in a dissynchronized manner. This formulation enables Calvo to analyze in detail the dynamic evolution of an economy with slow price adjustment. The central concern of the paper is the characterization of circumstances in which unanticipated devaluations exert contractive influences on the economy. As a general rule, circumstances like those must be associated with situations in which there is a multiplicity of rational expectations equilibria. Calvo shows that this characteristic is robust: it

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Jacob A. Frenkel

does not depend on the degree of capital mobility, nor on whether the exchange rate is freely flexible or preannounced. Having established the conditions that give rise to the fundamental indeterminacy, Calvo examines the case for which equilibrium is unique and analyzes the shortand long-run effects of an announced future change in policies. The paper concludes with an application of the staggered contracts model to the analysis of monetary policies under a fixed exchange rate regime. In discussing Calvo's paper, John B. Taylor deals with the specification of the price and contract equations as well as with the nonuniqueness property. He observes that the randomness of contract length in Calvo's specification is exogenous, and thus, even though the length of contracts is not fixed, it is not responsive to endogenous events. Taylor proposes another way of interpreting Calvo's equations in which each individual contract has a given nonrandom length, but there is, because of heterogeneity of markets and products, a distribution of contracts by length across firms. He also suggests an extension of Calvo's price-setting formulation by which foreign prices also influence the aggregate price level. Taylor concludes his comments by noting that the nonuniqueness that arises in Calvo's model is consistent with the general principles underlying nonuniqueness in rational expectations models and does not stem from the existence of contracts. In discussing Calvo's paper, Michael Mussa deals with the situations in which Calvo finds that a devaluation is contractionary with respect to aggregate demand. Mussa notes that such a situation need not only arise if the equilibrium is "unstable" in the Walrasian sense. A devaluation may be contractionary because it reduces the real value of cash balances. Mussa notes further that in cases of multiple paths of which only one converges to a stable equilibrium, none of the paths converging to the Walrasian-unstable equilibrium represents an economically sensible solution to the relevant system. Mussa suggests focusing attention on the equilibria that are stable in the usual Walrasian sense. The eighth chapter by Paul Krugman analyzes the influence of oil stocks on exchange rate dynamics. Krugman argues that the effects of oil price increases on exchange rates cannot be studied in a "small country" context. If all oil importing countries were alike, the rates at which their currencies exchange would be unaffected by the price of oil; thus any effects must depend on asymmetries between oil importers. This paper attempts to identify the crucial asymmetries by developing a series of models of a world consisting of three countries: two oil importers, America and Germany, and one oil exporter, OPEC. The first model is a pure "trade balance" model which puts on one side the issue of recycling: OPEC is assumed to spend all its income, while the exchange rate between America and Germany adjusts to preserve balanced trade. The exchange rate effect of an oil price increase depends on

11

Introduction

two offsetting forces. On the one side, higher oil prices place a direct burden on a country's balance of payments, with the magnitude depending on how large the initial oil bill was and on the elasticity of oil demand. On the other side, there is an indirect benefit as OPEC spends its increased income on imports. Whether the dollar appreciates or depreciates depends, first, on whether America's share of world oil imports is more or less than its share of world exports to OPEC and, second, on how its elasticity of demand for oil imports compares with Germany's. The second model adds the complications introduced by OPEC surpluses and capital flows. OPEC is allowed to hold two assets, dollars and marks, and the two oil importers are also allowed to hold each other's currencies. OPEC's spending is assumed to lag behind its income, so that after an oil price increase there is a temporary surplus which must be invested abroad. The result is that in the short run financial factors playa crucial role: whether the dollar appreciates depends on whether America's share in OPEC asset holdings is more or less than its share in the increase in the world oil bill. In the long run, on the- other hand, real factors dominate: whether the dollar ultimately comes to rest at a higher or lower level depends on the variables analyzed in the pure trade balance model. Interestingly, the short-run and long-run effects can run in opposite directions. Loosely speaking, if OPEC likes American investments but prefers German products, an oil shock will cause the dollar to rise now but decline even more later. The third model adds speculation to the story. If the dollar must eventually decline, won't the expectation of this affect its current value? The model shows that it will. For simplicity, it is assumed that dollars are the only traded asset, so that OPEC surpluses naturally tend to strengthen the dollar; but it is assumed that the long-run real factors favor the mark, and that asset demands depend on the rationally expected rate of change of the exchange rate. The result is that even though the short-run financial considerations tend to cause dollar appreciation, expectations of a future decline can cause the dollar to depreciate at the start. In his lengthy comment on Krugman's paper, Pentti J. K. Kouri discusses the balance of payments and exchange rate effects of oil price increases from the point of view of the theory of international transfers. Kouri shows that in the context of a general equilibrium model, "oil transfers" can be effected without any changes in international relative prices and interest rates. Thus, he argues, it is basically an empirical question whether oil shocks have important international relative price, interest rate, and exchange rate effects. There is, however, a strong theoretical presumption as far as domestic relative prices and real wages are concerned: the countries paying the "oil transfer" will experience a decline in real wages and an increase in the relative price of traded goods.

12

Jacob A. Frenkel

Charles Wilson's comments on Krugman's paper examine the implications of the model for exchange rate movements during the course of a worldwide recession. Wilson demonstrates that the impact of decreased business activity in the industrialized countries on exchange rate movements depends critically on how sensitive the level of OPEC expenditure is to its level of wealth. If expenditure merely adjusts to OPEC revenue with a lag, then one should expect the value of the German mark first to rise and then to fall during the course of a recession. If, however, the decline in OPEC wealth induces a significant decrease in its expenditure, then the opposite pattern would emerge. The ninth chapter by J. Peter Neary and Douglas D. Purvis deals with the interaction between real adjustment and exchange rate dynamics. The authors develop a model that is designed to clarify the nature of macroeconomic responses to sectoral shocks and to provide a basis for investigation of the interaction between resource allocation and exchange rate variability. They first develop the implications for the dynamics of the real exchange rate of a Marshallian distinction between shortand long-run supply responses to an endogenous disturbance. Marshall's partial-equilibrium analysis stressed the overshooting of a relative price because of short-run factor fixity; Neary and Purvis's analysis derives this result in a general equilibrium context, although in a general equilibrium model it is possible that the long-run price response is perverse so that, rather than overshooting, the short-run relative price response would actually be in the "wrong direction." They then extend the framework to incorporate the behavior of money prices in the face of these changing relative prices. The model focuses on monetary equilibrium combined with rational speculation; the dynamic behavior of the nominal exchange rate exhibits a straightforward dependence on that of the real exchange rate. But the latter is independent of monetary equilibrium and, in particular, of any speculative behavior; any influence of speculators on the nominal exchange rate gives rise to identical movements in the equilibrium nominal price of services. This complete, short-run neutrality of nominal changes vanishes in an extended specification of the Neary-Purvis model which allows for nominal short-term rigidities. In his comments on the Neary and Purvis paper, Kent P. Kimbrough suggests that a useful extension of the model would allow for discrepancies between income and spending. Such an extension would demonstrate the dynamic link between exchange rate movement, deviations from purchasing power parity, and the current account. Kimbrough indicates that this dynamic link is a consequence of transfer problem criteria applied to goods and assets markets. He concludes his comments by discussing alternative ways by which the model could be modified to allow for exchange rate variability to influence resource allocation. In this

13

Introduction

context he outlines a stochastic framework that is €haracterized by shortrun confusion about the sources of shocks. Jeffrey Sachs's comments on the Neary and Purvis paper focus on possible extensions of the dynamic analysis. He argues forcefully that one of the central channels through which dynamic adjustment is effected is the channel of international borrowing. Thus, the discovery of a natural resource base generates incentives for current account imbalances, and the allocational effects of the shock depend on how much foreign borrowing is encouraged or restricted by the authorities. The tenth chapter by William H. Buiter and Marcus Miller concludes the volume. This chapter focuses on the interaction between the dynamics of the real exchange rate and the output cost of reducing inflation. In dealing with this issue, Buiter and Miller analyze the proposition that under a floating exchange rate regime restrictive monetary policy results in substantial overshooting of the real exchange rate-a loss of competitiveness. By considering alternative specifications of the wage-price process, the paper brings out the crucial role in the overshooting phenomenon of nominal stickiness or inertia in domestic money wages and prices combined with a freely floating exchange rate. A further "sensitivity analysis" of the overshooting proposition is performed by generalizing the basic open economy IS-LM model in terms of which earlier analyses have been conducted in a number of directions. First, the long-run real interest rate rather than the short rate is included as an argument in the IS function, and dynamic and static Pigou effects are included as determinants of effective demand. Second, external wealth adjustment via current account deficits and surpluses is incorporated, and general wealth effects on money demand and output demand are added. Finally, gradual rather than instantaneous adjustment of the level of output is considered. The real exchange rate overshooting proposition survives all these model generalizations, although a strong wealth effect on the demand for money reduces its magnitude. One of the virtues claimed for the sharp initial appreciation of the currency (i.e., the fall in the real and nominal exchange rates in response to an unanticipated tightening of the stance of monetary policy) is its immediate effect on the domestic price level, through a reduction in the domestic currency price of internationally traded goods. The model analyzed in this paper does indeed have the property that tight money reduces on impact both the general price level and the underlying or "core" rate of inflation. Buiter and Miller show, however, that while exchange rate "jumps" induced by restrictive monetary policy do speed up the process of disinflation, they do not reduce the cost, in terms of lost output, of bringing down the rate of inflation. The effect of such exchange rate jumps is merely to redistribute the cost of reducing inflation over

14

Jacob A. Frenkel

time. Early gains have to be "handed back" later as the equilibrium level of competitiveness is restored. The authors conclude the paper by discussing more efficient ways of bringing down the rate of inflation. In commenting on this paper, Robert P. Flood notes that Buiter and Miller's formulation presumes that governments may sharply reduce the rate of monetary expansion without significant political opposition. This supposition enables Buiter and Miller to solve their model conditional on the assumption that individuals believe that the current policy regime will last indefinitely. Flood proposes to examine the situation under which this assumption is relaxed. He develops a formal model which allows for the possibility of a stochastic model switching which is used to illustrate the importance of these considerations. Jiirg Niehans's comments on the Buiter and Miller paper deals with its policy implications and with the correspondence between the model and the British experience. As for the policy, Niehans takes issue with Buiter and Miller's recommendation to lower inflation by combining a reduction in the monetary growth rate with an actual one-time rise in the money stock. As for modeling, he suggests that the Buiter-Miller model be extended to take into account the requirement that any trade imbalances arising, for example, from changes in competitiveness, must be consistent with the desired accumulation or reduction of foreign assets.

1.2 Further Issues One of the major advances of the past decade's research in open economy macroeconomics has been the modeling of the foreign sector. By now it is well understood that a proper modeling of the open economy should not attach a foreign sector as an appendix to the otherwise closed economy model. Rather, it is now clear that the entire economic system operates in a different way once allowance is made for the openness of the economy, and, therefore, open economy considerations should be incorporated in a consistent manner through the various layers of the open economy macro model. The papers and comments that are included in this volume deal with the frontiers of research in the area of exchange rates and international macroeconomics. It is pertinent to note that there are still numerous conceptual and technical issues that deserve further research. This section outlines four examples of such issues. 1

1. The following remarks draw on Jacob Frenkel, "Comments on Research Issues on Exchange Rate Economics" in Annales de L'INSEE, July-December 1982, forthcoming, and on Jacob Frenkel, "Comments on the Theory of Exchange Rate Determination" in Exchange Rate Theory and Policy, ed. J. F. O. Bilson and R. Marston (Chicago: University of Chicago Press, forthcoming).

15

Introduction

1.2.1 The Peso Problem One issue relevant for empirical research in the area of exchange rate determination may be referred to as the "peso problem." The original peso problem is characterized by the situation of the Mexican peso which was eventually devalued during the third quarter of 1976. Since this devaluation was expected for several years, the peso was traded at a forward discount in the market for foreign exchange. Obviously, as long as the devaluation did not take place, the forward exchange rate proved (ex post) to have been a biased forecast of the realized future spot exchange rate. But once the devaluation took place it exceeded the prediction that was implied by the forward discount on the peso. Generally, the peso problem is a situation in which there are many observations but many fewer events. For example, in Mexico's case there were many days (observations) during which the forward discount prevailed, and yet there was only one event-the devaluation itself. These circumstances affect the properties of the statistical distribution of rates of return and raise conceptual and practical difficulties for studies which attempt to examine the efficiency of foreign exchange markets and the biasedness of forecasts of future spot rates based on lagged forward rates. Likewise, in such circumstances it is not clear whether a rise in the number of observations in any sample, brought about by a greater frequency of measurements, should be treated as a corresponding increase in the number of effective degrees of freedom. In a way, the peso problem could be cast in terms of a small samples problem. As such it has much wider applications. However, since the foreign exchange market is strongly influenced by expectations of future events and policies, and since current expectations of future changes in policies (like a devaluation or a specific change in intervention policies) are based on probabilistic evaluations, it is evident that the peso problem is especially relevant in the foreign exchange market. Another example that falls under the heading of the peso problem relates to the current price of gold. Studies of optimal portfolios have found that gold has a small role in the optimal portfolio of assets. A possible rationale for the observed large holdings of gold can be provided by noting that current holdings and pricing of gold reflect the probability of a sharp rise in its price in the event of a fundamental change in the role of gold in the international monetary system. Again we have a situation where there are many observations but only one (or even no) event. 1.2.2 The Role of Innovations A second issue relates to the role of innovations. One of the central implications of the rational expectations hypothesis is that unanticipated events, news, playa predominant role in affecting real variables and asset

16

Jacob A. Frenkel

yields. This implication has been embodied in the modern theory of exchange rate determination. Accordingly, exchange rates are presumed to reflect current as well as expected future values of the relevant economic variables. The anticipatory role of exchange rates suggests that empirical research of exchange rate determination should relate changes in exchange rates to the innovations in the relevant regressors. While this methodology has a strong theoretical justification, its empirical application is extremely complicated. Since the innovations are intrinsically unobservable, any empirical analysis involves the joint examination of the model as well as the measurement of the innovation (i.e., the measurement of the expected values which are used in the construction of the innovations). Since there is no practical way to avoid completely the joint hypotheses problem, it seems that inference from empirical estimates should be made with great care. A similar difficulty, also relating to the anticipatory nature of exchange rates and the prompt response of asset prices to new information, concerns the implications of different frequencies of data collections for various time series. For example, data on exchange rates and interest rates are available much more frequently than data on national income or on the current account. These different frequencies of data availability are reflected in different patterns of revisions of expectations and may affect systematically the time series characteristics of the innovations of the various data. 1.2.3

Structural Models

Recent examinations of the various structural models of exchange rate determination, including the monetary models, the portfolio balance models, the current account models, and others, have shown that they have not performed well in explaining movements in nominal exchange rates. With the benefit of hindsight, it seems that the key reason for the poor performance of the various models is the intrinsic characteristics of exchange rates as asset prices. As indicated above, exchange rates are very sensitive to expectations concerning future events and policies. Periods that are dominated by rumors, announcements, and news which alter expectations are likely to induce a relatively large degree of exchange rate volatility. Since by definition news cannot be predicted on the basis of past information, it follows that by and large the resulting fluctuations of exchange rates are unpredictable. In a way, this asset market perspective suggests that we should not expect to be able to forecast accurately exchange rate changes with the aid of the simple structural models. The role of the simple structural models is to account for the systematic component of the evolution of exchange rates. In cases where the systematic, predictable component is relatively small, we may expect to account for only a small fraction of the variability of exchange

17

Introduction

rates. A potentially productive line of research would examine the implications of the different structural models for the relation among the variance of exchange rates and the variance of the various fundamentals. 1.2.4 Lucas Critique One of the central insights that has affected economic research during the past decade has been the "Lucas critique." The key point of that critique is the observation that the behavior of economic agents reflects the prevailing pattern of policies as well as agents' expectations concerning the future path of policies. As a result, policy actions which attempt to exploit a correlation between two endogenous variables (e.g., the correlation between inflation and unemployment or the correlation between exchange rates and interest rates) may fail since the policy actions themselves might alter the structure of the relation between the two variables in a way that could not have been predicted from the historical correlations. Such an outcome is likely to occur when policies are based on reduced-form relations rather than structural relations. This critique is of course fundamental for the evaluation of the results of simulations based on parameter estimates that are obtained from historical data. It is pertinent to note, however, that as a practical matter the quantitative importance of. the Lucas critique depends on the circumstances: it may be significant for some experiments while negligible for others. It certainly should not discourage further empirical research. Rather, it should encourage the use of an improved research methodology that takes into account the endogeneity of the structural parameters. The foregoing examples illustrate the type ofissues relevant for empirical research. There are of course many more issues that should be fruitfully addressed as part of a research agenda in the area of exchange rates and international macroeconomics. It is hoped that the essays and comments collected in this volume will stimulate further research in that direction.

2

An Accounting Framework and Some Issues for Modeling How Exchange Rates Respond to the News Peter Isard

2.1 Introduction This paper develops a framework of approximate accounting identities that is used to discuss the limitations of existing empirical models of exchange rate determination. The poor explanatory power of the empirical models of the seventies has now been well documented by Meese and Rogoff (1983 and in this volume) and Backus (1981). In this paper the limitations are first addressed by using the accounting framework to demonstrate that some commonly adopted behavioral assumptions cannot jointly explain a major portion of exchange rate movements. The middle sections of the paper address some issues in modeling how news leads to revisions in the expectational terms that enter the exchange rate accounting framework. The final sections illustrate the issues by drawing inferences and conjectures about. the types of news that contributed to the major swings in mark/dollar exchange rates (spot and forward) during 1980-81. The paper stops short of using the accounting framework as a building block for conducting regression tests of specific behavioral assumptions about the expectational terms. Most empirical models of exchange rate determination seem deficient in "anchoring" the level of the expected path of the (real) exchange rate. Peter Isard is a senior economist on the staff of the Board of Governors of the Federal Reserve System. The author is especially indebted to Michael P. Dooley and Ralph W. Smith for many helpful discussions of issues addressed in this paper and is also grateful for constructive criticism received from William A. Allen, Bruce Brittain, Peter B. Clark, Sebastian Edwards, Robert P. Flood, Jeffrey A. Frankel, Dale W. Henderson, Peter Hooper, Kengo Inoue, Alexandre Lamfalussy, Jeffrey Marquardt, Warren D. McClam, Richard A. Meese, John Morton, Kenneth S. Rogoff, Jeffrey R. Shafer, Edwin M. Truman, and John R. Wilson. The analysis and opinions of this paper do not necessarily represent the views of the Federal Reserve Board or the individuals acknowledged above.

19

20

Peter Isard

The observed level of an exchange rate can be explained in terms of expectations about the level of the exchange rate that will prevail at any future date, but the exchange rate level expected at some future date must be anchored independently to explain the general level of the expected exchange rate path. This point is clear from interest rate parity conditions under the assumption of risk neutrality, and the argument extends to finite-horizon portfolio balance analysis under the assumption of risk aversion, as emphasized by Dooley and Isard (1981).1 One feature of the accounting framework is to provide a building block for using the notion of long-run goods market or balance of payments equilibrium to construct a behavioral model that anchors expectations about the longrun real exchange rate. The accounting framework also describes the general (nonbehavioral) form of the "rope" that links the observed spot and forward exchange rates to the anchored but unobservable level of the expected long-run real exchange rate. Under risk neutrality, the long-term real interest differential is the link between the observed level of the (price-adjusted) spot rate and the expected long-run real spot rate. Equivalently, the expected long-term inflation differential is the link between the observed level of the (price-adjusted) long-term forward rate and the expected long-run real spot rate. For the risk averse case, a long-term exchange risk premium is added to the rope. The general form of the accounting framework can accommodate survey data, macromodel forecasts, autoregressive forecasts, or analytic structural models of inflation expectations. Similarly, it can accommodate either structural models or alternative representations of the risk premium. By characterizing the rope, moreover, the accounting framework suggests that quantitative discussions of exchange rate volatility can benefit from focusing on the length of the rope. In particular, if it is expected to take T years for the real exchange rate to converge to its long-run level, then the percentage change in the spot exchange rate that should be associated with a ceteris paribus shift in the term structure of nominal interest differentials (and hence real interest differentials) is the percentage point change in the compound T-year interest differential, or roughly T times the change in the T-year interest differential as commonly measured in percentage points per annum. 1. By contrast, Rodriguez (1980) develops a reduced-form exchange rate equation for a rational expectations portfolio balance framework in which the coefficient on the exchange rate currently expected to prevail at horizon T converges to zero as T approaches infinity. The speed of convergence can be interpreted to depend inversely on the degree of substitutability between assets denominated in domestic and foreign currencies, and the assumption of imperfect substitutability or risk aversion is a necessary condition for the rational expectations assumption to "eliminate" the expected future exchange rate from the model by pushing the future to infinity (see Dooley and Isard 1982a).

21

How Exchange Rates Respond to the News

The accounting framework is developed in section 2.2 by manipulating the covered interest rate parity condition and some definitional identities. Attention is focused on one resulting form of the exchange rate equation in which the observable long-term forward rate, deflated (or priceadjusted) by the observable ratio of current domestic and foreign price levels, is approximately identical (in logarithmic form) to the sum of three unobservable terms: the expected long-run real exchange rate, the expected long-term inflation differential, and the expected long-term premium for bearing exchange risk. The framework emphasizes the different channels through which news can lead to changes in observed exchange rates (and/or interest rates and/or price levels) by generating revisions in the unobservable expectations terms. Section 2.3 applies the accounting framework, using a time series of OECD (Organization for Economic Cooperation and Development) inflation expectations (forecasts) for seven industrial countries, to construct measures of the extent that observed changes in exchange rates (between six foreign currencies and the,U.S. dollar) can be "explained" under the commonly adopted assumptions of time invariant expectations about the long-term real exchange rate (or purchasing power parity level, PPP) and the risk premium. Under these assumptions the substantial observed variability of spot exchange rates can only be explained by substantial variability in long-term real interest differentials. To the extent that real interest differentials are expected to vanish beyond the long-run horizon, this in turn suggests that exchange rate variability has been associated with variability in the shape of the term structure of nominal interest differentials'(relative to the shape of the term structure of expected inflation differentials), and that the traditional use of shortterm interest differentials in exchange rate equations may be a poor substitute for a focus on long-term interest differentials. Section 2.4 provides some empirical evidence on the length of the horizon over which real interest differentials are expected to persist, which is assumed to be roughly the same as the length of time that is expected to elapse before the real exchange rate converges to its long-run value. The evidence compares survey data on long-term inflation expectations, collected several times between early October 1980 and early September 1981, with data on the two- to five-year and five- to ten-year forward nominal interest rates that are implicit in the term structures of yields on dollar- and mark-denominated Eurodeposits and Treasury issues. The evidence supports the assumption that it is expected to take longer than two years, but perhaps less than five years, for the real exchange rate to converge to its long-run value. Empirical work on exchange rate determination has made only limited progress in modeling the news (see Dornbusch 1980; Frenkel 1981; Isard 1980; Longworth 1980), despite the strong presumption that changes in

22

Peter Isard

exchange rates predominantly reflect revisions in expectations in response to the news (see Mussa 1979). Sections 2.5-2.7 focus on some issues in modeling expectations of the long-run real exchange rate, the long-term inflation differential, and the premium for bearing exchange risk. Sections 2.8 and 2.9 illustrate the issues by focusing on the major swings in mark/dollar exchange rates (spot and five-year forward) during 1980-81 and by drawing inferences or conjectures about the extent to which the swings were "explained" by revisions in each of the three expectational terms. Section 2.10 summarizes the main points that emerge from sections 2.5-2.9. An appendix discusses how the accounting framework can be used as a basis for forecasting. 2.2

An Accounting Framework

The framework developed in this section can be divided into two parts: an anchor and a rope. The anchor is a theory about the expected long-run real exchange rate based on notions of balance of payments equilibrium and consistent with the conditional expectation of long-run purchasing power parity (PPP). The rope that links observed exchange rates to the expected long-run real exchange rate is provided by the interest rate parity framework, as modified to allow for risk premiums. The rope can be characterized by combining the covered interest rate parity condition, (1)

with definitions of the risk premium, (2)

and the real exchange rate, (3)

sreal

==

s + PB - PA,

where s,!, and se denote the logarithms of the nominal values of the spot, forward, and expected long-run spot rates, in units of currency A per unit currency B; R A and R B denote nominal own rates of interest on assets denominated in currencies A and B, as compounded over horizons that extend until the long run is reached; PA and PB denote the logarithms of the price levels in countries A and B; and a superscript e labels the variable as an expectation. Together conditions (1)-(3) imply (4)

It is convenient to express the expected future logarithmic price levels in terms of expected rates of inflation (PA, PB) using the approximations

23

How Exchange Rates Respond to the News

(5)

PA == PA + PA,

(6)

PR==PB+P R .

It is also convenient to introduce traditional definitions for real interest rates:

PA,

(7)

rA == R A

(8)

rR == R B - P R .

-

Substitution then converts (4) into (9)

s == (PA - PB) + (rR - rA) + sreal e

-

risk e .

Equivalently, when all observable variables are transposed to the left side, (10) where the manipulation uses condition (1) and defines a price-adjusted forward rate, (11) Condition (11) is analogous to condition (3). It is important to emphasize that the nominal forward rate is adjusted by current price levels rather than forward price levels; in a risk neutral world it would not be an unbiased estimator of the expected future real exchange rate unless the future relative price level was expected to equal the current relative price level. Much of the discussion below will focus on equation (9), but (10) is more attractive for applying the model empirically since it imposes prior coefficient values on observable price and nominal interest rate levels. Models in which interest rates or money supplies are treated as "causing" the exchange rate, rather than as jointly endogenous variables, have been shown to involve specification bias by Glaessner (1979), Caves and Feige (1980), and Meese and Rogoff (1983), among others. Equations (9) and (10) apply to any horizon for expectations. In this paper they are discussed in terms of a long-term horizon, based on the view that the most plausible behavioral hypotheses for anchoring an expected future exchange rate are hypotheses about the real exchange rate that is consistent with long-run goods market or balance of payments equilibrium. In empirical analysis based on condition (10), fadj is represented by a price-adjusted five-year forward rate after section 2.4 presents evidence suggesting that investors expect it to take longer than two years for the real exchange rate to converge to its long-run equilibrium value.

24

Peter Isard

The right-side terms in condition (10) represent unobservable expectations. The spirit of condition (10) is that news about the factors on which expectations are based leads to unobservable revisions in expectations and observable changes in exchange rates (and/or interest rates and/or price levels). The usefulness of condition (10) is for testing behavior hypotheses about the expectational variables. Insofar as the expectational variables are unobservable, the behavioral tests must be implicit or indirect, and, given that three expectational variables enter the exchange rate equations, the tests are joint or simultaneous tests of three behavioral hypotheses. This paper is oriented toward addressing the inadequacies of commonly adopted behavioral hypotheses and stops short of subjecting alternative hypotheses to regression tests. 2.3

The Inadequacy of Some Common Behavioral Assumptions

In principle, all of the expectational terms on the right side of condition (10) should be treated as variables. Sections 2.5-2.7 will address the issues of modeling the expectational terms. This section uses the accounting framework in conjunction with OECD inflation expectations (forecasts) to argue that under the common assumptions of time invariant expectations about the long-run real exchange rate (PPP level) and the risk premium, only a minor portion of observed changes in exchange rates can be explained by focusing on the relationship between exchange rates and short-term interest differentials-as is commonly done-without explicitly taking account of changes in nominal interest differentials that can be earned on investments beyond a twelve-month horizon. 2 The empirical exercise is to construct a time series of "residual" changes in the spot exchange rate that cannot be "explained" by observed changes in price levels or twelve-month nominal interest differentials, or by revisions in the twelve-month OECD inflation forecasts. The construction is based on a formula derived by first differencing condition (9), assuming time invariant values of sreal e and risk e . Reflecting the limited horizon of the OECD inflation forecasts, the real interest differential is truncated beyond the twelve-month horizon. This leads to

(12)

resid t == St - St-l + (PA - PB)t - (PA - PB)t-l + (RA - RB)t, t+2 - (RA - R B)t-1, t+1 - (PA - PB)~, t+2 + (PA - PB)~-l, t+1,

2. The tradition of focusing on the relationship between exchange rates and short-term interest differentialspartly reflects (and has contributed to) the fact that data on short-term interest rates that are comparable across currencies are more readily available than data on comparable long-term interest rates. The tradition also reflects an infatuation, prior to the development of Eurocurrency markets, with examining the relative behavior of spot and short-term forward exchange rates without providing a theory of the absolute level of either.

25

How Exchange Rates Respond to the News

where t runs through semiannual observations, corresponding to the semiannual dates of the GECD forecasts. Given the assumptions underlying the derivation of condition (12), the proper interpretation is that "resid" measures the sum of the changes in the expected long-run real exchange rate, the expected return for bearing exchange risk, and the real interest differential beyond a twelve-month (i.e., two-period) horizon. The GECD forecasts are published for seven countries (Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States) and thus provide time series of "residual" changes in the exchange rates between the U.S. dollar and six other currencies. Table 2.1 shows the observed, explained, and residual changes in the logrithms of exchange rates, which correspond to percentage changes in the levels of exchange rates. (The explained changes are computed last as the differences between the observed and residual changes.) For thirtynine of the forty-eight entries the residual changes are larger than the explained changes. As noted above, the residual changes can be viewed as the error terms that arise from the joint assumptions that the expected long-run real. exchange rate and exchange risk premium are time invariant, and that real interest differentials are not expected to persist for longer than twelve months. The residuals are generally too large to attribute to differences between GECD inflation forecasts and "true" measures of inflation expectations. Accordingly, the evidence suggests that at least one of the following propositions must be true. Either (1) expectations about the long-run real exchange rate (or PPP level) vary widely over time, or (2) the exchange risk premium is large and variable, or (3) substantial real interest differentials are frequently expected to persist for longer than twelve months. Thus, to the extent that there is some long-run horizon beyond which real interest differentials are expected to vanish, the assumptions of time invariant expectations of the long-run real exchange rate and the risk premium would suggest that exchange rate variability has been associated with variability in the shape of the term structure of nominal interest differentials (relative to the term structure of expected inflation differentials), which in turn suggests that the traditional use of short-term interest differentials in exchange rate analysis may be a poor substitute for a focus on long-term interest differentials. 2.4 The Persistence of Real Interest Differentials: How Distant Is the Long Run? Condition (10) provides a useful analytic framework only to the extent that the right-side expectational terms can be modeled, and among these terms, the expected future real exchange rate.cannot be easily modeled (or convincingly assumed to be constant) without appealing to the notion

0.69 2.50

1.55 -1.21 2.76

French franc observed explained residual

---.1J2.

10.85 -0.55 11.40

1977H1

1.41 -0.44 1.85

5.39 -0.52 5.91

11.36 -2.05 13.41

1977H2

5.54 -3.34 8.88

6.34 2.24 4.10

1.58 8.00

~

1978H1

4.07 -3.99 8.06

8.51 -0.11 8.62

12.73 -0.45 13.18

1978H2

-.13 3.12 -3.25

0.68 8.46 -9.14

-10.95 9.26 -20.21

1979H1

Explained and Residual Percentage Changes in U.S. Dollar Price of Foreign Currencies a

German mark observed explained residual

Japanese yen observed explained residual

Table 2.1

6.52 -3.67 10.19

7.90 -0.15 8.05

-12.38 2.14 -14.52

1979H2

0.07 1.84 -1.77

-0.89 6.07 -6.96

12.60 9.31 3.29

1980H1

-8.02 -4.68 -3.34

-8.63 -0.44 -8.19

3.96 -0.57 4.53

1980H2

-2.47 -0.98 -1.49

3.36 -7.85 11.21

Canadian dollar observed explained residual

British pound observed explained residual

5.60 -7.22 12.82

-4.24 -0.40 -3.84

0.88 -5.50 6.38

0.99 5.52 -4.53

-1.03 0.89 -1.92

1.97 -2.43 4.40

6.06 -1.99 8.05

-4.58 -1.23 -3.35

-2.83 3.86

---.LQl

6.14 -3.68 9.82

-0.07 1.06 -1.13

-0.28 -6.41 6.13

4.63 -7.06 11.69

-0.15 -1.68 1.53

3.75 -2.57 6.32

7.19 -3.14 10.33

1.71 0.39 1.32

-1.45 -0.01 -1.44

3.11 -6.16 9.27

-2.75 -1.40 -1.35

-8.73 9.59 -0.86

aThe half-year periods correspond to intervals between the published cutoff dates for material included in the semiannual issues of the DECO Economic Outlook. These cutoff dates are 1 December 1976,29 June 1977,28 November 1977,12 June 1978,23 November 1978,11 June 1979,23 November 1979,4 June 1980, and 17 November 1980. Exchange rates and interest differentials (measured as forward premiums) are represented by Federal Reserve data for the cutoff dates. Observed and forecast inflation rates are taken from the DECO Economic Outlook and represent percentage changes in GNP or GOP deflators over corresponding half-year periods.

-2.19 -10.61 8.42

Italian lira observed explained residual

28

Peter Isard

of a long-run steady state. For purposes of empirical analysis it is important to focus on forward exchange rate observations for a maturity that exceeds the expected length of the convergence interval over which the real exchange rate moves to its long-run steady-state value (following an isolated, ceteris paribus shock that disrupts an initial steady-state equilibrium). For many currencies, adequate historical data on forward exchange rates against the U.S. dollar are not available for maturities longer than one year. For a few currencies, including the mark, two-year and fiveyear forward rates against the dollar are available (or can be constructed from Eurocurrency deposit rates) on a daily basis. This section argues for using the five-year forward rate in condition (10), based on evidence suggesting that it is expected to take longer than two years, but perhaps less than five years, for the real exchange rate to converge to its long-run level. The evidence is presented in table 2.2 The first two rows of table 2.2 present time series of survey data on the average annual rates of U.S. inflation expected over the first and second halves of a ten-year horizon. The two series are assumed to provide upper and lower bounds on the U.S. inflation rates that were expected from the end of the second year through the end of the fifth year. The expected two- to five-year U.S. inflation rate declined from early October 1980 through early September 1981, and there is a strong presumption that any revisions in expected long-term German inflation rates were upward,3 thus implying an even greater decline in the expected inflation differential. By contrast, there were increases over the same period in the differentials between the implicit two- to five-year nominal yields on dollar- and mark-denominated assets, as shown for both Eurocurrency deposits and Treasury issues. 4 Such evidence indicates that real interest differentials beyond a twoyear horizon were not time invariant, which rejects the assumption that real interest differentials were expected to vanish within a two-year horizon. Unless the substantial changes in two- to five-year real interest differentials were offset by equal and opposite changes in the implicit two- to five-year risk premium, the evidence also rejects the assumption that the real exchange rate was expected to converge to its long-run level within a two-year horizon. 3. Forecasts of German inflation, typically extending out over one-to-two-year horizons, were generally revised upward as the mark depreciated against the dollar from October 1980 through mid-August 1981. 4. The trends in the two- to five-year nominal interest differentials, computed for the samples of daily Eurocurrency observations and the twelve observations of Treasury differentials, pass the test of being significantly greater than zero with a high degree of confidence.

29

How Exchange Rates Respond to the News

Table 2.2

Long-Term Inflation Expectations and Nominal Interest Rates a Early October 1980

Early January 1981

9.4 8.3 8.3-9.4

8.9 7.8 7.8-8.9

Eurodollar rates C 2 years 5 years 2-5 years

12.5-13.1 12.5-13.0 12.5-13.0

14-14.5 13.9-14 13.5-13.9

Euromark rates C 2 years 5 years 2-5 years

8.3-8.6 8.3-8.5 8.3-8.5

9-9.3 9-9.3 9-9.3

Eurodifferential 2-5 years

4.2-4.6 Sept.IOet. 3.7/3.7

Expected U.S. inflation b 0-5 years 5-10 years 2-5 years

Treasury differential d 2-5 years 5-10 years

3.3/3.1

Early September 1981

Early November 1981

8.4 7.3 7.3-8.4

7.8 7.4 7.4-7.8

7.9 7.5 7.5-7.9

16.4-16.8 15.9-16.5 15.5-16.3

17.5 16.8-17.0 16.3-16.7

14.6-14.8 14.9-15.3 15.0-15.6

11.1-12 10.4-11 9.9-10.3

12.5 11.9 11.5

11 10.6 10.4

4.5-5.8

5.7-6.1

4.9-5.1

4.7-5.2

Jan.

Apr. IMay 4.2/3.7 3.2/3.0

Aug.lSept. 4.9/5.6 3.1/3.4

Nov.

3.6 3.3

Early May 1981

4.6 3.4

aIn percent per annum. bBased on survey data on five- and ten-year U.S. inflation expectations collected abqut once each quarter since mid-1980 by Richard B. Hoey, vice-president and chief economist at Warburg Paribas/A. G. Becker, 55 Water Street, New York, N.Y. 10041. Data represent simple averages of the expectations of several hundred institutional investment decision makers. 1, that is, if the forecast interval is greater than the sampling interval, the forecast errors will be serially correlated. Condition (22) merely reiterates that the conditional forecast errors are orthogonal to all information contained in the information set r which includes Xt. Since X t is unobservable to the econometrician, we substitute into (20) the best linear prediction of X t based on an observable subset of the information in r. We choose this parsimonious subset based on the fact that in our previous study and in section 4.2 past forward rate forecast errors' of currencies were useful in predicting Yt+ k, but we also need to keep the information set small for computational purposes. Consequently, let (23) where Et is the prediction error which has mean zero and is orthogonal to Substituting (23) into (20) gives:

Yt.

(24) which is a constrained vector regression ofYt+k on a constant andYt where vt,k == Ut,k + ~*Et, which implies that vt,k is orthogonal to Yt also. The specification of the model does not imply that v t , k is orthogonal to Yt- i for i"?l. Our goal is to estimate ~ * and a *' == (ad, a{ '). Estimation of the k-step-ahead forecasting equation for Yt+k, given Yt subject to the nonlinear cross-equation restrictions embedded in (24), allows us to recover consistent estimators of ~ * and a * once one of the elements of ~ * is normalized to one which is necessary because of the lack of identification of h discussed above. For the discussion of estimation, take this normalized ~ to be ~1. Once again, the ~* parameters provide us with information about the relative importance of risk across currencies, and the knowledge of a{ indicates the nature of time variation in the risk premiums. Several strategies are available for estimating 8 * == (~*2, ... ~ *P, a *') in (24). We now discuss the relative merits of alternative possibilities and in the process describe our estimation procedures. One strategy is to impose the additional requirement: (25)

and to estimate the parameters via maximum likelihood, that is, employ a Gaussian density function but not necessarily assume that Yt is Gaussian. It is customary to employ some time or frequency domain approximation to the likelihood function to ease the computational burden. Even with these approximations, maximum likelihood estimation can be difficult for values of k and p that substantially exceed one. The reason for this is that

132

Lars Peter Hansen/Robert J. Hodrick

all the parameters of the vector moving average error process must be estimated simultaneously with the structural parameters of interest. Furthermore, if (25) is false, the technique ismisspecified. A second strategy is to estimate the parameters of (24) using generalized method of moments (GMM) estimators. The procedure which we employ is a generalization of nonlinear three-stage least squares and is included in the class of GMM estimators studied by Hansen (1982) who derived their large sample properties. This procedure allows us to impose the cross-equation restrictions implied by our latent variable model either with or without imposition of the auxiliary assumption (25). As in maximum likelihood, it requires a numerical search algorithm to compute estimates, but the search is undertaken over a much smaller parameter space. On the other hand, in circumstances in which (25) holds, maximum likelihood is asymptotically more efficient. We now develop the GMM estimator for 8*. A GMM estimator can be thought of as arising from the minimization of a criterion function that exploits the orthogonality conditions of the model. To see this, we construct a family of criterion functions that employ the same set of orthogonality conditions. Let z; == (Yt, 1) and define the matrix of reduced form parameters:

where 8 is the m == 2p dimensional parameter vector. Construct the vector function, f(Yt+k' Zt, 8), of the data and the parameters that summarize the r == (p + l)p orthogonality conditions of the model,

(26) where ® is the Kronecker product. Since Zt is in t, we are assured that the expectation of f evaluated at the true parameters 8* is zero:

(27)

E[f(Yt+k' Zt, 8*)]

==

E(Vt,k® Zt)

==

o.

The r orthogonality restrictions in (27) are used to estimate the parameters 8 *. Let (28) where T is the sample size of the data set. Let aT be an r-dimensional symmetric matrix which is allowed to be dependent on the sample data.

133

Speculation in Foreign Exchange

We can estimate 8* by choosing 8 function:

= 8T

where 8 T minimizes the criterion

(29) Under regularity conditions specified in Hansen (1982), it is demonstrated that if a random sequence of matrices {aT: T?:.1} converges almost surely to a constant r-dimensional nonsingular symmetric matrix a*, the estimator proposed above is strongly consistent. Furthermore, Vf(8 T - 8*) converges in distribution to a normally distributed random vector with mean zero and covariance matrix ~(a*). Details on how to compute and estimate ~ (a*) are provided in appendix A. We followed Hansen (1982) in choosing a* optimally to produce the smallest asymptotic covariance matrix among the class of estimators that exploit the orthogonality conditions defined by (27). To motivate a test of the model, recognize that 8 T is the parameter vector that sets a linear combination of the sample orthogonality conditions gT(8) to zero via the first-order conditions for the minimization of (29). More precisely, the first-order conditions require that 8 T sets m linear combinations of the r orthogonality restrictions equal to zero. Thus there are r - m linearly independent combinations of gT(8) that are not necessarily equated to zero but which should be close to zero if the restrictions are true. Under an alternative hypothesis, the elements in the reduced form parameter matrix 8 are unrestricted and can be estimated using equation-by-equation ordinary least squares. These estimates are provided in table 4.4. Relaxing the restrictions in this manner is equivalent to setting the r sample orthogonality conditions equal to zero. Therefore a test of the restrictions can be conducted by examining the minimized value of the criterion function when the restrictions are imposed relative to zero, which is its unrestricted value. 17 Hansen demonstrates that T gT(8 T)'aTgT(8 T) is asymptotically chisquare distributed with r - m degrees of freedom, where 0T is a minimizer of (29) and aTis an estimator of an optimal choice of a*. We use this as a test of our model restrictions. An additional set of tests that we performed amounts to examination of whether subsets of the reduced form parameters in the matrix 8* = 8(8*) equal zero. First we examined the unrestricted reduced forms and tested whether the coefficients other than the constants were zero. Consistent with our earlier results, we found substantial evidence against the hypothesis of no time variation in the risk premiums. These same tests were repeated with the restrictions imposed. The results for the latent variable model are presented in table 4.5. The 17. Gallant and Jorgensen (1979) propose tests similar to this for the case in which disturbances are serially uncorrelated.

lJ

h;Sf-9

(S{-F{-99) .' +

NOTE:

See table 4.1.

Deutsche mark

0.328 (0.341) 0.664

-0.055 (0.097) 0.430

0.014 (0.199) 0.056

0.568 (0.371 ) 0.874

U.K.

0.067 (0.161) 0.323

-0.102 (0.292) 0.272

0.328 (0.414) 0.572

-0.281 (0.167) 0.907

-0.051 (0.123) 0.320

0.204 (0.148) 0.832

Swiss franc

-0.287 (0.162) 0.932

0.428 (0.420) 0.691

-0.003 (0.116) 0.018

(Std. Err.) Confidence

hi2

Japanese yen

(Std. Err.) Confidence

(Std. Err.) Confidence

-0.165 (0.142) 0.754

hit

iii

0.297 (0.320) 0.646

pound

'

u;. 9

0.417 (0.162) 0.990

0.214 (0.112) 0.944

0.626 (0.161) 0.999

0.463 (0.162) 0.996

0.252 (0.151) 0.904

(Std. Err.) Confidence

hi3

-0.034 (0.108) 0.245

0.190 (0.132) 0.849

-0.113 (0.155) 0.533

0.090 (0.126) 0.528

-0.122 (0.088) 0.835

(Std. Err.) Confidence

hi4

9.462 0.908

8.390 0.864

-0.406 (0.182) 0.974 -0.323 (0.194) 0.904

16.100 0.993

20.303 0.999

6.738 0.759

X2 (5) All hi/s j?:.l = 0 Confidence

-0.853 (0.325) 0.991

-0.596 (0.272) 0.972

-0.173 (0.225) 0.557

(Std. Err.) Confidence

hiS

0.124

0.072

0.178

0.165

0.068

R2

Exchange Rates: US$/Foreign Currency; Sample: 5 February 1976 to 29 December 1980; Number of Observations: 512

j=l

. ' =a; + f

S;

S:+9- F /9

French franc

Currency

Table 4.4

6.394

6.943

10.939

9.626

5.698

Resid. Var.

1.164 (0.316)

0.421 (0.242)

0.659 (0.229)

Japanese yen

Swiss franc

U.K. pound

Deutsche mark

0.160 (0.188) 0.603

0.102 (0.129) 0.569

0.282 (0.325) 0.614

0.242 (0.281) 0.611

0.084 (0.108) 0.565

=

0.054 (0.048) 0.742

-0.040 (0.075) 0.406

18.834. See table 4.1.

0.084 (0.063) 0.818

0.149 (0.106) 0.843

-0.111 (0.200) 0.421

-0.063 (0.114) 0.419

0.128 (0.092) 0.836

0.043 (0.049) 0.622 0.068 (0.070) 0.667

0.298 (0.115) 0.991

0.120 (0.121) 0.681

0.190 (0.116) 0.899

0.526 (0.157) 0.999

0.103 (0.104) 0.677

0.452 (0.148) 0.998

=0

2.745 0.261 12.943 0.976 17.205 0.996 2.941 0.291 8.398 0.864

-0.715 (0.232) 0.998 -0.832 (0.245) 0.999 -0.301 (0.183) 0.901 -0.471 (0.182) 0.990

Confidenee

r~l

All ei/s

x2(5)

-0.249 (0.157) 0.888

(Std. Err.) Confidenee

(Std. Err.) Confidence 0.036 (0.041) 0.617

eiS

ei4

0.157 (0.099) 0.889

(Std. Err.) Confidence

(Std. Err.) Confidence 0.045 (0.040) 0.733

ei3

ei2

-0.095 (0.172) 0.421

-0.033 (0.062) 0.406

(Std. Err.) Confidence

(Std. Err.) Confidence

Test of the constrained model X2(20)

1.0

French franc

NOTE:

0.348 (0.178)

Currency

~i

eil

em

Reduced Form Coefficients

Exchange Rates: US$/Foreign Currency; Sample: 5 February 1976 to 29 December 1980; Number of Observations: 512

The Latent Variable Model

(Std. Err.)

Table 4.5

0.066

0.009

0.146

0.152

0.023

R2

136

Lars Peter Hansen/Robert J. Hodrick

value of the test statistic of the model restrictions is 18.834, which is below the mean of a chi-square variable with 20 degrees of freedom. Therefore, there is little evidence in the sample against the restrictions imposed by our model. Using the estimates of the betas as measures of relative risk, we find that the Swiss franc and Japanese yen were the most risky contracts. The French franc and the U.K. pound were least risky, and the Deutsche mark was intermediate between the two sets of currencies. Tests of the reduced form parameters for time variation in the risk premiums are quite consistent with the evidence of table 4.4. The restrictions of our model still capture most of the significant time variation in the risk premiums found in the unrestricted estimates.

4.6

Summary and Conclusions

In this paper we investigated risk premiums in the forward foreign exchange market using linear time series models. We relied on first-order conditions of a rational investor to interpret alternative statistical restrictions about the divergence of forward exchange rates from expected future spot rates. Three basic conclusions emerged from our analysis. First, risk premiums are not adequately characterized by constants as was implied by a time invariant lognormal model. Second, time variation in the risk premiums are not accurately summarized by movements in the nominal interest rate of the currency of denomination of the forward contract. Third, using a single beta latent variable model to measure risk, we found risk premiums to be important in at least two of the five currencies studied. It may be that longer time series or more powerful econometric procedures will alter some of our conclusions. Also from a practical standpoint, in all of our statistical inference we are forced to rely on asymptotic distribution theory in computing significance and confidence levels, and knowledge of the correct small sample distributions of the test statistics we have employed might overturn some of our conclusions. Nonetheless, we believe that we have been successful in providing additional insights into the nature of the forward foreign exchange market. While we used first-order conditions of the intertemporal maximization problems of investors to motivate and interpret alternative restrictions on time series representations, our statistical tests cannot be construed as direct tests of an equilibrium model. An explicit equilibrium analysis would require that we write down specifications of stochastic forcing variables that generate the restrictions on the endogenous time series that are imposed and tested here. An obvious criticism of our approach is that by placing our auxiliary assumptions on endogenous variables, we are in danger of analyzing empirically specifications that may not be either internally consistent nor consistent with plausible

137

Speculation in Foreign Exchange

specifications of the stochastic forcing variables. Even though we take this criticism seriously, we view our analysis as a useful starting point in studying equilibrium models of the forward foreign exchange market. Recent theoretical work of Lucas (1982) has begun to integrate monetary theory and modern general equilibrium financial theory. We interpret our results as demonstrating the potential importance of this integration, although additional work needs to be done in obtaining general equilibrium models with implications that are susceptible to formal statistical inference. Such models would allow us to investigate the ultimate sources of risk premiums and would provide a vehicle for interpretation of movements in spot exchange rates. While a direct and explicit equilibrium econometric study will be of great interest, such an exercise may be overly ambitious at this time, given problems in calculating dynamic, stochastic equilibria. Our research to date has focused on time series representations that do not require measurements of intertemporal marginal rates of substitution of money. Incorporating such measurements could lead to valuable extensions of this paper. Unfortunately, obtaining such measurements is particularly difficult because much of the existing consumption and price data are aggregated over time and across commodities. Although Hansen and Singleton (1982) have described distribution-free procedures for testing intertemporal asset pricing models, their procedures require point-in-time measurements of consumption and purchasing power. Alternatively, distributional assumptions on the point-in-time data coupled with a priori specification of the possibly nonlinear averaging filters might lead to testable implications of the intertemporal asset pricing models using the available data.

Appendix A In this appendix we describe how the asymptotic covariance matrices for the parameter estimators of the various statistical models were estimated.

Lognormal Model The parameters were estimated equation by equation using ordinary least squares. Consider the k-step-ahead regression equation Yt+k ==

z;J3o + Ut,k·

Under the assumptions of the lognormal model, the conditional covariances

138

Lars Peter Hansen/Robert J. Hodrick

are constant. The asymptotic covariance matrices were estimated using the formula in Hansen and Hodrick (1980), pp. 833-35. Nominal Risk-Free Return

Again the parameters were estimated equation by equation using ordinary least squares. We relaxed the assumption that the conditional covariances were constant. Let U[k denote the estimated least-squares residual of t using a sample of size T. The asymptotic covariance matrices were estimated using the formula. 1

2i ST2i

1 ,

where

k-l

ST

2

j= -k+ 1

0_1 RT(J) - -T

T

~

t=J+ 1

RT(j); T

T

,

Ut,k Ut-j,kZtZt-j,

05:j 1 and conditional heteroscedasticity, just as Hansen and Hodrick accounted for these econometric difficulties in their analyses. The exchange rate relation (1) can also be tested without having to specify the values of parameters characterizing the preference function a priori. Suppose Qm,t+k depends on a k x 1 vector of parameters 'Yo, Qm,t+k('YO)' that are unknown to the econometrician. Also, let Zt be an r X 1 vector of variables in It that are observed by the econometrician, with r>k. Then (1) implies that

(9)

E[Qm,t+k('Yo)(S{+k - F{k)Zt]

==

0,

where E[ . ] is the unconditional expectation. Equation (9) represents r nonlinear equations in k unknowns. Hansen and Singleton (1982a) describe how the sample counterparts of these orthogonality conditions can be used to obtain consistent and asymptotically normal estimates of 'Yo under fairly weak regularity conditions. Their procedures turn out to set k linear combinations of the sample orthogonality conditions equal to zero in estimation. Hence, there are r - k independent linear combinations that were not used in estimation, but should be close to zero if the restrictions (9) are valid. These r - k conditions can form the basis of a test of the model (1), using a chi-square statistic with r - k degrees of freedom. References Frenkel, Jacob A., and Assaf Razin. 1980. Stochastic prices and tests of efficiency of foreign exchange markets. Economics Letters 6, no. 2:165-70. Hansen, Lars Peter, and Robert J. Hodrick. 1980. Forward exchange rates as optimal predictors of future spot rates: An econometric analysis. Journal of Political Economy 88, no. 5:829-53. Hansen, Lars Peter, and Kenneth J. Singleton. 1982a. Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica 50, no. 5:1269-86. - - - . 1982b. Stochastic consumption, risk aversion, and the temporal behavior of asset returns. Graduate School of Industrial Administration, Carnegie-Mellon University. Working paper.

5

Rational Expectations and the Foreign Exchange Market Peter R. Hartley

In this paper I test the hypothesis that expectations of exchange rate movements are formed rationally. To do so, I need, in addition to the hypothesis of rational expectations, a theory of the determinants of exchange rate movements. I shall first consider a very simple monetary approach model of exchange rate determination (section 5.1). A serious defect of the model considered in this paper is that it ignores the possibility of a simultaneous determination of the exchange rate along with macroeconomic variables. However, it extends previous models in this genre by attempting to distinguish the effects of changes in expectations on exchange rates from the effects of changes in underlying determining variables apart from expectations. Furthermore, it does this in a context where the· assumption of rationality of expectations can be tested. In section 5.3 I shall present some results for the dollar/mark and dollar /pound exchange rates in the most recent floating rate period. In section 5.4 I examine a model similar to one studied by Frenkel (1981). However, I am able to test for rationality of expectations where Frenkel could not. I have chosen to emphasize the test of rationality in this paper for two reasons. First, the test of rationality, unlike the tests of the restrictions implied by the simple monetary model, does not depend on the validity of the exogeneity assumptions. If we do find a rejection of the crossequation restrictions implied by rationality, this is indeed a rejection Peter R. Hartley is assistant professor in the Department of Economics at Princeton University and is a faculty research fellow of the National Bureau of Economic Research. The author would particularly like to thank Frederic S. Mishkin for his many valuable discussions and suggestions and Jacob A. Frenkel and Robert J. Hodrick for their comments. Financial support from the Lilly Endowment Fund, the University of Chicago, and Princeton University is gratefully acknowledged.

153

154

Peter R. Hartley

either of the assumption that expectations are formed rationally or that the forward premium differs from the rationally expected depreciation or appreciation by no more than a constant term. Second, I have tested two alternative models of exchange rate determination and, while both lead to valid tests of rationality (given our assumption on the forward rate), they do not arise from a single, simple model. 5.1

Simple Monetary Approach Model

Proponents of the monetary approach to exchange rate determination view the exchange rate as the relative price of two monies. They therefore argue that variables affecting the supply of and demand for two monies will affect the rate of exchange between them. Quite a few studies have tested the monetary approach to exchange rate determination and some of the earlier ones are collected in Frenkel and Johnson (1978). Since money is a durable asset, it has been argued that expectations about the values of variables affecting its future supply of demand ("exogenous" variables)! will be important determinants of current demand. Suppose expectations of future movements in exogenous variables are influenced by current movements in the same exogenous variables. 2 Movements in the exogenous variables would then affect money supply and demand directly, but they would also affect expectations and hence money demand. More significantly, it is most probable that anticipated and unanticipated movements in the exogenous variables will have quite different effects on exchange rates. Frenkel (1981) has suggested that short-run movements in exchange rates are dominated by the effect of unanticipated movements in the exogenous variables. Many previous tests of simple monetary models have included lagged exogenous variables among the explanatory variables. Insofar as the justification for including these variables is that they are useful for proxying expectations, an important source of restrictions on the distributed lags has been ignored. The present study focuses on explaining errors in forecasting exchange rate movements rather than the exchange rate movements themselves. This is one way (also used in Frenkel (1981» to separate out the effects of anticipated and unanticipated movements in the exogenous variables. Only unanticipated movements in the exogenous variables should lead to unanticipated movements in the exchange rate. Rationality of expecta1. I shall use the term "exogenous" for these determining variables for ease of exposition. Some of them might, in fact, be simultaneously determined with money supply and/ or demand. This shall be discussed further below. 2. This will be true, for example, if the evolution of these exogenous variables can be explained by a stable, low-order autoregression and if agents are aware of this fact and form expectations rationally.

155

Rational Expectations

tions implies a set of cross-equation restrictions on distributed lags. The conformity of these restrictions with the data provides a test of rationality which I shall implement in this paper. The statistical theory I shall use derives from a paper by Abel and Mishkin (1979) and has been applied to a study of bond yields by Mishkin (1981). Let S denote the T x 1 vector of observations in the one-period percentage change in the exchange rate, and let ~ denote the T x 1 vector of observations on the errors in the forecast of one-period exchange rate changes. Hence, (1)

where O. This is illustrated in figure 7.4 under the same assumptions as in figure 7.1. The phase diagram corresponds to the situation before the jump in E, and the dashed curve is the new saddle path after the jump. Thus, the system first jumps from a to b and then smoothly travels from b to c; it reaches c at t == to, and then abruptly starts moving toward d (in a smooth fashion). In

245

Staggered Contracts

v

p=o

r

.

a·

. I

"-

.J

"

v=o p Fig 7.4

p

Effect of dE at t = to> O.

other words, suppose the system was at a rest point under the expectation that E would be constant forever, and then it is announced that E will have a once-and-for-all increase at t == to> O. Then our analysis has shown that the real exchange rate will start appreciating (p rises) until the change in E actually occurs; then p will start to go down until eventually the real exchange rate returns to its initial level. Notice that unlike the one-step depreciation experiment considered before, here p always stays above p. Furthermore, an anticipated future change in E sharply contrasts with the case where E suffers a once-and-forall change at t == 0 (the "present"), because the latter results in no change in p (assuming, as usual, that Po == p). It is interesting to note in this connection that the Dornbusch-type model discussed in section 7.1 will exhibit no impact on the real exchange rate whether or not the change in the rate of devaluation is anticipated.

7.4

Crawling Peg and Controls on Capital Mobility

In this section we briefly examine the significance of a familiar crawling peg system and of capital mobility controls for eliminating the nonuniqueness problem that was discovered in section 7.3.

246

Guillermo A. Calvo

Let us first consider the case where E t is chosen according to a rule that sets it as a function of some average ofpast rates of inflation (this appears to be the rule followed for a considerable amount of time by several countries, like Colombia and Brazil, and has apparently, and very recently, been adopted by Argentina). Specifically, we assume,15 •

(30)

E t ==

t

Et

•

== 'Y JPse-,,/(t-s) ds, -

00

implying (31)

and, hence, (32) where EO is given by history at t == O. Now substituting the expression for Et given by (32) in equations (27)-(28) we obtain a differential equation system in v and p, and we are thus able to check the uniqueness condition as we did in section 7.3. However, as is readily verifiable, uniqueness is also insured in this case if /p < 0 at steady state. Thus the crawling peg system does not eliminate the nonuniqueness problem. Let us now study the implications of imposing controls on capital mobility. For the sake of simplicity, let us consider the case of total capital immobility, where the money market equilibrium is given by (33)

where the right-hand side is the money demand function, M denotes (the log of) money supply, and k is a positive parameter. Assuming that both the money supply and the exchange rate are constant (and equal to M and E, respectively), we get (34)

rt ==

. It -

• Pt

Pt-M

== - - k

• Pt·

Thus by (9), (10), and (34), (35a) (35b) Applying the procedure of section 7.3, the condition for uniqueness now becomes 15. More precisely (30) should have P- (the left-hand derivative of P) in the integrand, but this would not affect our implications.

247

(36)

Staggered Contracts

Nt)

(- -

Nt)

P1 - - p - - - +f,P-E--- O. Solving the implicit function f for p results in p == g(p), where g' < 0 iff /p > O. As is now well known in rational expectations modeling, nonuniqueness occurs in a simple first-order differential equation system if any initial "price" p leads to convergence. Clearly this is the situation if g' < 0, and it arises whether or not contracts are in the system. Whether /p > 0 is an econometric issue related to the relative importance of income and substitution effects. As in other examples of nonuniqueness in rational expectations models/ the conditions for nonuniqueness arise when the demand or supply curves slope the "wrong way." In Calvo's open economy model, the aggregate demand curve must be upward sloping in the relevant price because substitution effects are dominated by wealth or income effects.

Comment

Michael Mussa

Guillermo Calvo has presented us with a paper that is both ingenious in its formal analysis and interesting in its substantive economic content. I am especially impressed by Calvo's modeling of the mechanism of price adjustment in a situation where the prices of individual commodities are fixed by long-term contracts. The differential equation system (equations [9] and [10]) that describes the dynamic behavior of the general price level and the individual commodity price for a newly negotiated contract is simple and intuitively appealing. As Calvo demonstrates, this model of price adjustment is easily applied to interesting issues in open-economy macroeconomics. I believe it will find many other interesting applications. My concerns with Calvo's paper arise primarily in connection with his discussion of, and his emphasis upon, situations in which a devalutaion of a country's currency is contractionary with respect to aggregate demand. In Calvo's model of macroeconomic behavior (as distinct from his model 2. In J. B. Taylor, "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica 45 (September 1977):1377-85; for example, it is shown that the IS-LM curves must cross in an unusual way to get nonuniqueness. Michael Mussa is the William H. Abbott Professor of International Business at the University of Chicago and a research associate of the National Bureau of Economic Research.

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Guillermo A. Calvo

of price adjustment) this situation arises only when a country is at an "unstable" equilibrium in the Walrasian sense that an increase in the relative price of that country's output in terms of the output of the rest of the world (which is the impact effect of devaluation in Calvo's model) creates an excess supply of that country's output. My first concern is that operation of an economy in the neighborhood of such an equilibrium is not the only possible or reasonable explanation for observing that devaluations are frequently associated with contractions of national outputs of the devaluing countries. Another possible explanation for such a relationship is that a devaluation has contractionary effects because it reduces the real value of the domestic money supply. In Calvo's model, this effect is not present because it is implicitly assumed that only the prices of domestic goods (which do not respond immediately to a devaluation) are relevant in determining the real value of the domestic money supply. However, in a model that allowed import prices to enter the price index relevant for measuring real money balances, or that allowed some domestic prices to respond essentially immediately to a devaluation, there would be an immediate contractionary effect of devaluation from the reduction in the real value of domestic money balances. In addition, the impact effect of a devaluation in raising the prices of imported inputs and perhaps in raising the costs of some domestic inputs (possibly including wage rates that respond to the actual and anticipated price level effects of a devaluation) would shift the aggregate supply curve upward and have a contractionary effect on national output for any given position of the aggregate demand curve. Further, if a devaluation is combined, as it frequently is, with more restrictive monetary and fiscal policies designed to remove the basic cause for the devaluation and the need for further devaluations, then these more restrictive policies are likely to induce an observed relationship between devaluations and contractions of the outputs of devaluing countries. My second concern is that if there is an equilibrium that is unstable in the Walrasian sense, it should be bracketed by two equilibria that are stable in the Walrasian sense, and the issue arises of which is the relevant equilibrium for comparative static and dynamic analysis. Existence of an odd number of alternating stable and unstable equilibria is implied by continuity of the excess demand function !(p, r) with respect to p, for r equal to the world real interest rate r*, and by the usual boundary conditions that !(p, r*) must be negative for all sufficiently high values of p and must be positive for all sufficiently low values of p. For the case of three equilibria, under the assumptions of Calvo's model (with a fixed exchange rate), the dynamic system governing the behavior of the general price level, Pr, and the price for a newly negotiated contract, V;, must have three steady-state points in the phase space

257

Staggered Contracts

of the state variables Pt and ~. At the two outer steady-state points, which correspond to the two Walrasian-stable equilibria where afl ap < 0, the dynamic system governing Pt and Yr has one positive and one negative characteristic root. There is a unique stable branch of this dynamic system that converges to each of these steady-state points. This is consistent with the normal saddle-point stability property that one expects in a rational expectations model that has both a forward-looking dynamic process and a backward-looking dynamic process. Paths that start outside the region between these two stable branches eventually diverge at an explosive rate from these steady-state points. These paths may be excluded from consideration by assuming that the economically sensible choice for the initial value of the price of a newly negotiated contract should not produce such explosively divergent behavior. The paths that start in the region between the stable branches leading to the two outer steady state points also do not converge to either of these steady state points. This is not peculiar in a model in which we should normally expect saddle-point stability. What is peculiar is that all these paths that start at points between the two stable branches ultimately converge to the middle steady-state point, which is the steady-state point that is associated with the Walrasian-unstable equilibrium. Calvo refers to this result of a continuum of paths converging to an equilibrium where afl ap > 0 as "an embarrassment of riches." I find it simply an embarrassment that a whole continuum of paths should converge to this equilibrium which is unstable in the Walrasian sense, while only a single path converges to each of the equilibria that are stable in the Walrasian sense. In my view the way to avoid this embarrassment is to recognize that none of the paths converging to the Walrasian-unstable equilibrium represents an economically sensible solution for the dynamic system governing Pr and ~. To develop this point, it is important to note that the economic specification of Calvo's model requires that the solutions for Pr and ~ should have forward-looking components; that is, there should be a part of the solutions for Pr and ~ that depends on a discounted sum of expected future economic conditions relevant for determining the behavior of prices. The need for these forward-looking components arises because ~ is defined to depend on a weighted average of expected future values of Ps + J3 . f(Ps, r s ) and because the domestic interest rate depends on the forward-looking expected inflation rate. In the neighborhood of a Walrasian-stable equilibrium, it is easy to construct the forward-looking components of the solutions for Pr and ~ for the linearized form of the dynamic system governing these two variables. In these solutions, the positive characteristic root of the dynamic system at the steady-state point is used as the discount rate applied to expected future economic conditions in constructing the forward-looking components of these solu-

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Guillermo A. Calvo

tions. In the neighborhood of a Walrasian-unstable equilibrium, however, there is no way to construct solutions for the linearized form of the dynamic system governing ~ and ~ that have forward-looking components because both of the characteristic roots of the dynamic system at such an equilibrium have negative real parts. In the neighborhood of a Walrasian-unstable equilibrium, it is possible to construct solutions for Pr and Yr that are wholly backward-looking, but these wholly backwardlooking solutions do not meet the requirements for an economically sensible solution for Calvo's model. Since the continuum of solutions that converge to a Walrasian-unstable equilibrium all ultimately come within a small neighborhood of this equilibrium, it may be concluded that none of these solutions meets the requirements of economic sensibility. Unfortunately, this conclusion requires that we sacrifice some of the more interesting parts of Calvo's paper that deal explicitly with equilibria where afl ap is positive and focus instead on equilibria that are stable in the usual Walrasian sense. In my view this sacrifice is preferable to accepting the proposition that Calvo's ingeniously constructed and intuitively appealing model of price adjustment leads to the obviously unsatisfactory conclusion that a Walrasian-unstable equilibrium is "superstable" in the sense that there is a whole continuum of economically sensible paths of ~ and Yr that converge to such an equilibrium and that there is literally no escape from the neighborhood of such an equilibrium. Moreover, even without the discussion of the case where afl ap is positive, a great deal that is of interest and value remains in Calvo's excellent paper.

8

Oil Shocks and Exchange Rate Dynamics Paul Krugman

8.1

Introduction

In studying the determination of exchange rates, theorists have traditionally relied on models of a two-country world, often further simplified by the assumption that one of the countries is Hsmall" relative to the other. The two oil shocks of the 1970s, however, confronted the international financial system with disturbances of an essentially multilateral nature. When we speak of the effect of the price of oil on the exchange rate, it is not the dollar rate but the dollar-mark or dollar-yen rate that we have in mind. That is, we are concerned with the effects on a bilateral rate of the actions of a third party, 0 PEC. The Hsmall-country" approach is particularly misleading when applied to an oil shock. At first sight it might seem obvious that for an oil importing country a rise in the price of oil leads to currency depreciation; after all, its direct effect is to worsen the balance of payments. But suppose the world consisted of several Hsymmetric" oil importers and OPEC-that is, the oil importers accounted for equal shares of world oil demand, equal shares of OPEC spending, etc. Then surely an oil price increase would leave exchange rates among the oil importing countries unchanged. How can this be? The reason is that while an oil price increase directly worsens an oil importer's balance of payments, it indirectly improves it as OPEC spends its increased income on purchases of goods or assets. It is not enough to know that a country imports oil and that its import demand is inelastic; we must know that it has relatively high import dependence, or relatively inelastic demand, or receives a

Paul Krugman is a professor in the Departnlent of Economics at Massachusetts Institute of Technology and a research associate of the National Bureau of Economic Research.

259

260

Paul Krugman

relatively small share of OPEC spending, before we can be sure that its currency depreciates when the price of oil goes up. 1 To model the exchange rate effects of an oil shock, then, it is necessary to work with a world containing at least two oil importing countries and OPEC, and to systematically allow for asymmetries between the oil importers. In this paper I make an effort in this direction. Three related three-region models are developed. The first is a trade balance model, in which it is assumed that OPEC immediately spends all of its income. This model develops the basic theme that asymmetries determine the direction of exchange rate movement. The second model sacrifices some detail on trade balance determination, but opens the world to capital flows, allowing OPEC to adjust its spending only gradually after the oil price rises. The main point here is the interplay between "real" and "financial" asymmetries, which may push the exchange rate in different directions. Finally, the third model simplifies the asset markets but introduces "rational" speculation.

8.2

A Trade Balance Model

Consider a world containing three countries: America, Germany, and OPEC. America and ,Germany export manufactured goods to OPEC and to each other; OPEC exports oil and imports manufactures. The bilateral trade balance between America and Germany, measured in dollars, depends on the mark price of the dollar: T== T(V).

(1)

In both America and Germany, oil imports depend on the domestic currency price of oil: (2) (3)

0A 0G

== °A(Po )

,

== 0G(V· Po),

where Po is the dollar price of oil. We assume elasticities of demand EA' < 1. Also, it will be useful to use the notation == 0A + 0G for world oil imports, and (J == 0G / for the German share of world oil imports. OPEC will be assumed to fix the price of oil in dollars and to spend all of its income, dividing this expenditure between American and German products. Letting X G , X A be the exports to OPEC, we have

EG

°

°

(4)

X G == -y(V)Po 0,

(5)

X A == [1 - -y(V)]PoO,

where -y is the share of OPEC expenditure falling on German exports. 1. Papers on the exchange rate implications of an oil shock in a small-country framework include Findlay and Rodriguez (1977). Buiter (1978). and Obstfeld (1980). A three-country simulation model is developed by Sachs (1982).

261

Oil Shocks

Notice that there is a difference in the treatment of the industrial countries and OPEC. The trade flows of the industrial countries are determined by partial equilibrium, "elasticity" equations, while OPEC's imports depend explicitly on income. The main reason for this difference in treatment is simplicity-income effects in OPEC play a clear and crucial role in our story; income effects in the industrial countries, while readily introduced, add complication without changing much. It may also be defended as an empirical approximation that OPEC's marginal propensity to import manufactures is much higher than its customers' marginal propensity to spend on oil; so income effects on the OPEC side will be much more noticeable. Given this simple structure, then, we can solve for the exchange rate. Germany's balance of trade is (6) and we assume aBolaV>O, which is the Marshall-Lerner condition for this model. If there are no capital movements, the exchange rate is determined by the condition (7) Consider now the effect of an increase in the price of oil. After some manipulation, this can be shown to be (8) dVldPo = - (aB G I aV)-1 ·0· [-va(1 - EG) - 0"(1 - EO)]'

+ )'(1 - a) (1 - EA)

The sign of this depends on whether if?< 'Y, where (9)

0"(1 - EO) + (1 - 0") (1 -

O"==-------:....---~---

0"(1 -

EO)

EA)

Now if contains three sorts of parameters. The parameter 0" is Germany's share of world oil imports; EO, EA are elasticities of demand for oil; 'Y is Germany's share of world exports to OPEC. It can be interpreted as Germany's share of the increase in world spending on oil when its price increases. If Germany's share of OPEC imports is more than its share of the marginal oil payments burden, the mark will appreciate; if it is less, the mark will depreciate. If elasticities of demand were the same, the expression would reduce to a simple comparison of shares: 'Y?< 0". Countries which are relatively oil-dependent will tend to have depreciation after an oil shock; countries which are relatively successful at selling to OPEC tend to have appreciation. But it is important to note that success at reducing oil imports will also matter. The elasticity of import demand exerts a first-order effect on the exchange rate response. This simple model already reveals several determinants of the exchange rate effects of an oil shock. It does, however, miss a crucial aspect

262

Paul Krugman

of the actual experience of the 1970s, the enormous recycling of oil revenues through international financial markets. OPEC did not immediately increase its imports to match its increased export revenue, so that it is necessary to introduce this lag, and the corresponding capital flows, into the model. 8.3

8.3.1

Capital Flows and Dynamics

Structure of the Model

Let us retain the basic structure of the last model, but introduce the possibility of capital movements. These will be assumed to be two internationally traded assets, marks and dollars, that is, the currencies of the oil importers. Also, OPEC will adjust its spending to its income with a lag. This will give rise to some dynamic complications, because the burden of oil payments may not fall where OPEC wants to invest, nor will investment and import spending be divided in the same proportion between the oil importers. We begin with the goods markets. The determination of the AmericaGermany trade balance is the same as before. OPEC, however, is now assumed to adjust its spending to its income only with a lag, assumed to take the simple form (10) where X is OPEC dollar expenditure. 2 As before, OPEC allocates this expenditure between American and German products: (11)

X G == -y(V)X,

(12)

X A == [1 - -y(V)]X.

Turning now to the asset markets, each country allocates its wealth between dollars and marks. We will treat these markets in the same way as we treated trade flows: that is, partial equilibrium equations for the oil importers; explicit consideration of wealth effects for OPEC. The justifications are also the same. First, this simplification brings out the main points with a minimum of complication. Second, in reality OPEC has a much higher marginal propensity to hold wealth in foreign assets than the oil importing countries, so that the theoretical simplification can also be defended as an empirically valid approximation. We assume, then, following Kouri (1982), that America holds in its portfolio a fixed dollar value of marks, and that Germany holds a fixed mark value of dollars: 2. It would be more reasonable to assume that it is OPEC's real expenditure which lags behind income; but this complicates the exposition without changing the results.

263

Oil Shocks

(13)

DG == HG/V,

(14)

M A == H A · V.

OPEC allocates its dollar wealth Wo in fixed proportions between dollars and marks: (15) (16)

Our next step is to consider balance of payments. First, the current accounts of the three countries may be written as follows: (17)

BG == T(V) + X G - PoGG ,

(18)

B A == - T(V) + X A - PoGA ,

(19)

B o == PoG - X.

A crucial variable is the rate of wealth accumulation by OPEC. This is not simply the OPEC current account, because it also includes capital gains and losses from changes in the exchange rate: (20) The second step is to consider capital accounts. The German capital account is sales of marks to America and OPEC, less German purchase of dollars:

.

.

.

KG == Mo/V + MA/V - D G ,

(21)

or, substituting, (22)

KG == aBo + [MA/V + DG + 0.(1 - a)Wo]V/V.

A similar expression may be derived for the American capital account. 8.3.2

The Dynamic System

We can now derive the equation of change for the exchange rate. The balance of payments must balance; thus we must have BG + KG == 0, or, from (22), BG + aBo MA/V +DG + 0.(1- a)Wo This expression has a natural interpretation. The numerator is what we might call an ex ante balance of payments, that is, it is what Germany's balance of payments would be if the exchange rate did not change. The ex ante balance of payments includes not only the German current account, but also that part of OPEC's current account which is recycled into (23)

v/V == _

264

Paul Krugman

marks. A surplus or deficit in the ex ante balance requires that the exchange rate change to induce offsetting capital flows as investors reallocate their portfolios. The denominator determines the extent of exchange rate change needed; it may be read as an index of the size of the international investment pool. The dynamics of the exchange rate may now be determined. For a given price of oil, the state of the world may be summarized by the exchange rate and the level of OPEC spending, whose laws of motion are determined by (10) and (23). The resulting dynamic system is illustrated in figure 8.1. The schedule X == 0 represents points where OPEC income and expenditure are equal. For simplicity, we will assume that demand elasticities for oil are zero. This means that world oil imports, and hence OPEC income, are independent of the exchange rate; thus X == 0 is a vertical line. To the right, expenditure exceeds income and is falling; to the left, expenditure falls short of income and is rising. The schedule VIV == 0 represents points where Germany's (and America's) ex ante balance of payments is zero. For reference we also show the loci where America's and Germany's current accounts are zero. The slopes of these lines are~ dV

(24)

==

-

dX

(1 - "I) BBGIBV'

B A == 0 dV dX

(25)

-"I

BBGlaV BG == 0

The line VIV == 0 may slope either upward or downward, but it must lie between these lines: (26)

dV dX

BG

+ aBo == 0

The implication is that, in general, neither country's current account determines the direction of exchange rate change. Thus at point R America runs a current account surplus, yet the dollar is falling; at S America runs a current account deficit, yet the dollar is rising. The only s!tuation in which a country's current account is related one-to-one with VIV is when OPEC does not hold that ~ountry's currency. Thus when OPEC holds no marks, a == 0, the line VIV == 0 coincides with BG == 0; when OPEC holds no dollars, a == 1; it coincides with B A == O. 3. We use here the fact that, when oil demand is inelastic,

aBG I av =

-

aB AI avo

265

Oil Shocks

v

.

s·

V/V=o

x Fig. 8.1

8.3.3

The dynamic system.

Effects of an Oil P.rice Increase

Suppose now that the price of oil goes up. In the short run this will create ex ante payment imbalances, forcing gradual appreciation or depreciation of the dollar which generates offsetting capital flows. In the long run the exchange rate must be such as to produce current account balance. The short-run effect is easily computed from (23):

(27)

dey/V) d Po

=

(a-a)O MA/V + DG + a(l - a)Wo

Thus the mark will initially depreciate or appreciate depending on whether Germany's share of world oil imports is more or less than the share of marks in OPEC's portfolio. This makes obvious sense. The effect of an oil price increase in the short run is directly to worsen Germany's ex ante balance of payments via increased spending on oil, but indirectly to improve it via recycled oil revenues (since OPEC expenditure is fixed in the short run, there is no impact effect on Germany's exports). The long-run effect-after OPEC's spending has risen to match its

266

Paul Krugman

income, so that B o == (}-may be determined by the condition of current account balance:

== (IT--y)O aBGlaV

(28) BG == 0

Again, this makes intuitive sense. In the long run, recycling has ended. The direct burden of higher oil prices is now offset by the indirect benefit of increased exports to OPEC; whether the mark depreciates or appreciates in the long run depends on whether Germany's share of world oil imports is more or less than its share of exports to OPEC. Interestingly, the short-run and the long-run effects can run in opposite directions. Suppose that -y > IT > a-loosely speaking, OPEC prefers American investments and German products. Then initially the dollar

v

x=o

V/V =0

x Fig. 8.2

The effect of a rise in the price of oil.

267

Oil Shocks

must appreciate, but in the long run it must be below its original level. The dynamics of this process are illustrated in figure-S.2. Point A represents the initial equilibrium, point B, the new long-run equilibrium. The dollar at first appreciates; then, as OPEC's spending rises and exports of goods become more important relative to exports of assets, the dollar declines past its original level. This is a simply, plausible story. But there is a major question which immediately arises. If the dollar is going to depreciate in the long run, won't this be expected? And won't this expectation tend to make the dollar depreciate in the short run as well? Clearly the next step must be to introduce speculation into the model. 8.4

Speculation: A Perfect Foresight Model

Speculation can fundamentally alter the results of the last model. If asset demands are affected by the expected rate of change of the exchange rate, and these expectations take long-run factors into account, long-run "real" factors may dominate short-run "financial" ones, even at the outset. To study the effect of expectations, we will consider a model which makes further simplifications on both the goods and asset markets. First, we replace the gradual adjustment of OPEC expenditure in (10) with a step function. Suppose the price of oil is increased at time to. We assume that OPEC expenditure remains constant until time to + T, t~en rises immediately to equal income. Letting X o be the original level ofexpenditure, and Xl the new level, we have (29)

t (1, it shifts past its original position, so that the equilibrium involves a lower V than

v

---o+------...-.....__-----,..ro..-------

DG

V/V=Q

Fig. 8.3

Dynamics in the perfect foresight model.

=Q

269

Oil Shocks

v

V/V = 0

---------....l!lir------------- 0G =0

s

F

Fig. 8.4

Examples of possible paths toward the saddle path.

the initial one. We will impose the "no speculative bubbles" assumption that the system does eventually converge to the long-run equilibrium; this closes the system. Figure 8.4 illustrates two possible paths. Poi!'!t A is the initial equilibrium position. After an oil shock, the schedule Do == 0 first shifts up, for T periods, then moves down to below A, so that the new long-run equilibrium is at F. The unique stable path of the long-run dynamic system is indicated by SF. If the world is to converge to F at time to + T, it must have reached a point on SF. Until time to + T, the system follows the laws of motion implied by the initial level of OPEC expenditure. Two ways in which these laws can put the world onto SF are illustrated by BD and CEo The dollar may either appreciate or depreciate when the price of oil increases. The subsequent paths are illustrated against time in figure 8.5. The economic intuition behind these cases is as follows. In one case the financial asymmetry between the countries-the fact that OPEC recycles its surplus into

270

Paul Krugman

v

Fig. 8.5

Two possible patterns.

dollars-leads to an initially rising dollar. But the expected gradual rise makes dollars more attractive, so that there is a step jump. Eventually, however, the long-run factors lead to an expectation of a depreciating dollar, pulling the dollar down even before the end of OPEC recycling. In the other case, these long-run factors dominate from the start. Although OPEC recycles into dollars, the expectation of future dollar depreciation is enough to produce a step drop in the exchange rate. Which path will the exchange rate follow? The crucial point is that the system must arrive at the stable path at just the right time. In figure 8.4, BD takes a longer time than CE, because the required fall in German dollar holdings is larger, yet the German current account deficit is smaller (because V is larger). For each initial jump in V there is a corresponding length of time needed to reach SF; the right initial V is that value for which the time to SF is exactly T periods. It is also immediately obvious that the direction of the initial exchange rate movement depends on T, that is, the more quickly OPEC adjusts its spending, the more likely it is that the dollar's long-run real disadvantage will outweigh its short-run financial advantage.

271

Oil Shocks

8.5 Summary In this paper I have set out three closely related models of the effect of an oil shock on exchange rates. The first model emphasized real factors: the shares of countries in imports from and exports to OPEC and the elasticity of demand for oil. The second model emphasized financial factors: in the short run, when OPEC runs a surplus, it matters where they invest it. The third model emphasized the dependence of the financial side on the real side through expectations. These models represent highly oversimplified representations of the factors at work. They do, however, give some suggestive guidance. And they make clear a point which is too easily overlooked in models which at first sight may seem more realistic and sophisticated: namely, that an oil shock affects all countries, and its exchange rate effects must arise from asymmetries between countries. They cannot be determined by considering each country in isolation.

References Buiter, W. 1978. Short-run and long-run effects of external disturbances under a floating exchange rate. Economica 45:251-72. Findlay, R., and C. Rodriguez. 1977. Intermediate imports and macroeconomic policy under flexible exchange rates. Canadian Journal of Economics 10:208-17. Kouri, P. 1982. Balance of payments and the foreign exchange market: A dynamic partial equilibrium model. In The international transmission ofeconomic disturbances, ed. J. Bhandari and B. Putnam. Cambridge: MIT Press. Krugman, P. 1982. Oil and the dollar. In The international transmission ofeconomic disturbances, ed. J. Bhandari and B. Putnam. Cambridge: MIT Press. Obstfeld, M. 1980. Intermediate imports, the terms of trade, and the dynamics of the exchange rate and current account . Journal ofInternational Economics 10:461-80. Sachs, J. 1982. Energy and growth under flexible exchange rates: A simulation study. In The international transmission of economic disturbances, ed. J. Bhandari and B. Putnam. Cambridge: MIT Press.

272

Paul Krugman

Comment

Pentti J. K. Kouri

Paul Krugman's excellent paper is concerned with the short-run and long-run effects of oil shocks in a three-country (U.S., Germany, and OPEC) partial equilibrium balance of payment model. My comments will be mainly concerned with issues and problems that he does not discuss or assumes away for reasons of convenience. The thrust of my comment is that Krugman's partial equilibrium, "elasticities" approach to the oil transfer problem leaves out effects that may be of first-order importance. I do think, however, that what Krugman does is extremely useful as a step toward a more comprehensive analysis of global adjustment to oil price disturbances. Oil Price and the Exchange Rate Section 8.2 develops a familiar partial equilibrium trade balance model to study the effect of an exogenous increase in the dollar price of oil on the dollar-mark exchange rate, ceteris paribus. In this analysis, Krugman assumes that macroeconomic policies in the United States and Germany keep U.S. and German prices and output levels unchanged despite the oil shock. He also assumes that OPEC supply of oil adjusts to the demand for oil at the exogenously given dollar price. Given these assumptions, the dollar-mark exchange rate has to adjust following an oil shock in~ such a way as to keep the German, or equally the U. S. trade balance equal to zero. The effect of an increase in the dollar price of oil on the German trade balance consists of two parts. First, there is an increase in oil import payments, assuming realistically that the price elasticity of oil demand is less than one. This effect is equal to - 0G Po (1 - EG )po, where 0G is the quantity of German oil imports, Po the dollar price of oil, and EG is the price elasticity of German oil demand and the caret denotes proportional change. The second effect of an oil price increase on the German trade balance is an increase in OPEC demand for German exports. This effect is equal to ')'OPo [(1 - EG)cr + (1 - EA) (1 - cr)]Po, where cr is Germany's share of world oil imports, and E~ is price elasticity of American oil demand. The net effect on the German balance of trade is accordingly [')'(1 - cr) (1 - E) - (1 - ')')cr(1 - EG)] PoD Po. If the demand elasticities are the same in the two countries, this expression simplifies into (')' - cr) (1 - E) PoOPo, so that an increase in the price of oil improves the ex ante German trade balance if Germany's share of world oil imports is less. than its share of OPEC's imports from industrial countries. An increase in the German oil demand elasticity relative to the American oil demand elasPentti J. K. Kouri is a professor in the Department of Economics at New York University and a research associate of the National Bureau of Economic Research.

273

Oil Shocks

ticity has the same effect as a reduction in German "oil dependence" as measured by O, a==A L 8L'YB

b 2 == (A L - AK1l8V) ~O.

A resource boom leads in the long run to a fall in the manufacturing capital stock, as both the spending effect (the leftward shift of L'L' to LL) and the resource movement effect (the leftward shift of K' K' to KK) operate in this direction. However, the long-run effect on the real exchange rate is ambiguous. The spending effect tends to cause a real appreciation by stimulating the demand for services and hence raising their negative price; the resource-movement effect tends to cause a real depreciation by pushing labor out of manufacturing into services, thus stimulating the supply of services and lowering their relative price. In figure 9.5 the new long-run equilibrium at Z depicts what we consider to be the more plausible case-that the resource boom causes a long-run real appreciation. Note that the condition for 71" to fall (b 2 < 0) is identical to the condition that k fall in equation (15).12 If the manufacturing sector is small in its use of capital so that the expulsion of labor to the services sector is small, real appreciation will ensue. Manufacturing output also falls unambiguously in model 2. The capital stock in that sector falls, but there is the possibility, associated with real depreciation, that labor input per unit of capital rises. That rise, however, 12. It also is easily shown that if b 2 is negative so that the long-run effect is a fall in the real exchange rate, that fall is less than the short-run effect given by (8).

J. Peter Neary/Douglas D. Purvis

298

1T

1TO

*

7T

1T,

.__--£-i--------1~~ k

------O Fig. 9.5

k:

k~

M

Equilibrium effects of a resource boom.

cannot be large enough to lead to a net increase in manufacturing output. Using the labor demand condition (5) and the labor market equilibrium condition (8), the logarithm of manufacturing output can be written as: XM = E-1 [(E - ALeLM~M )k M - (l1evALM~M)v].

Using the definition of E, the coefficient of k M is seen to be positive. Hence the level of manufacturing output falls by more the greater the outflow of capital into the benzine sector: the direct output-reducing effect of this outflow is more than sufficient to offset any reduction in costs brought about by a real depreciation. 9.2.4

Short-Run Dynamics

Using the long-run solutions (19), the dynamic adjustment equation (17) can be rewritten as (17') The dynamics can now be illustrated in figure 9.5 where on impact, with k M fixed, the economy moves from the initial equilibrium Eo to E 1 .

299

Real Adjustment

Since the labor market clears continually, and by (17') k M declines steadily to k M *, the economy follows the path E1Z' marked by the arrows along L' L'. In the short run the real exchange rate overshoots its longrun value. 13 This overshooting is the result of Marshallian dynamics: it is worth repeating that it is overshooting the real exchange rate, in response to real shocks, and caused by real inertia.

9.3

Real Shocks and the.Nominal Exchange Rate

In this section we combine the real model of resource allocation and output of the previous sections with a simple monetary model of nominal exchange rate determination in order to examine the effect of a resource boom on the nominal exchange rate. The nominal money stock is treated as exogenously determined; we continue to assume that relative prices adjust instantaneously to clear markets so that there is no role for monetary policy. As before, the dynamics of the model arise from the adjustment of sectoral capital stocks in response to perceived changes in returns. International financial markets are treated as being closely integrated. Domestic and foreign interest-bearing assets are assumed to be perfect substitutes, so domestic and foreign nominal interest rates are linked by the uncovered interest rate parity (IRP) condition, i == if + x, where x is the expected rate of change of the nominal exchange rate. We restrict our attention to equilibrium dynamic paths so we impose long-run perfect foresight on the model. With x equal to the actual change in the exchange rate, we write the IRP condition as: (20) According to equation (20), the domestic interest rate can exceed the foreign interest rate only if there is a (fully anticipated) depreciation of the domestic currency to offset the nominal yield differential. Alternatively, depreciation of the domestic currency is only consistent with asset-market equilibrium if holders of domestic assets are compensated by a yield premium. The demand for domestic money balances in real terms depends on real income and the nominal interest rate, (21) The domestic price index, p, is given by (22) where

p

==

Bps + (1 - B)e,

B is the expenditure share of nontraded goods.

13. If 11" rises in the long run, then, rather than overshooting, the short-run response is in the wrong direction.

300

J. Peter Neary/Douglas D. Purvis

9.3.1

Monetary Equilibrium

Using the definition of the real exchange rate (3), the price index can be rewritten as p = e - ~'IT; using the definition of real income (2) the money market equilibrium condition becomes (23)

m - e = aevv - 5- 1i - ~'IT.

This is depicted in figure 9.6 as the positively sloped locus MM drawn for given values of 'IT, v, and m; its upward slope reflects the fact that an increase in e creates an excess demand for money by reducing the supply of real balances, while an increase in i creates an excess supply by reducing demand. Above and to the left of MM there is excess supply of money balances; below and to the right there is excess demand. A resource boom shifts the MM curve left for given 1T; but since 'IT itself adjusts in response to a resource boom, a full analysis of the effects on e is deferred. For simplicity, we abstract from domestic or foreign inflation so in long-run equilibrium the exchange rate must be constant. Imposing = 0

e

M

·f I

~--------------------------~

Fig. 9.6

Monetary equilibrium and the nominal exchange rate.

e

301

Real Adjustment

in (20) and substituting into (23), we can solve for the long-run nominal exchange rate: (24) where we also have set the real exchange rate at its long-run value. Note that for a given real exchange rate there is an additional force, - a8 v (which we term the liquidity effect), working toward nominal appreciation in response to a resource boom: the effect of the resource boom on real income increases the demand for money and hence tends to cause e to fall. Thus a long-run real appreciation in response to a resource boom is sufficient (but not necessary) to also ensure a nominal appreciation. The determination of the long-run nominal exchange rate is illustrated in figure 9.6. Given the determination of the real exchange rate as described in the previous sections, monetary equilibrium determines the nominal prices of traded goods, e, and of nontraded goods, Ps == e - 1T. Money is neutral, as can be seen by the unitary coefficient of m in equation (24). Further, that neutrality obtains even in the short run; an increase in the money supply causes no change in the real exchange rate and so leads to an immediate equiproportionate change in e and Ps' This, of course, is because the only dynamics in the system result from the need to reallocate capital, and monetary policy creates no incentives to do so even in the short run. 14

9.3.2

Real Shocks and Monetary Dynamics

Real shocks such as a resource boom will give rise to dynamics in e - i space which reflect those in k M - 1T space illustrated in figure 9.5. Using equation (23) to eliminate i from equation (20), the evolution of the exchange rate can be written as follows: (25)

e== 8(e + a8 v v -

m - f31T) - if.

Using the long-run solutions in (19) and (24) this can be written as

e== 8(e -

e*)

+ 8f3( 1T*

- 1T).

Using the fact that 1T* == - (b 1 /b 2 )kM *, we rewrite this in what will prove to be· the more convenient form (26) The complete dynamic system is therefore obtained by writing equations (17') and (26) in matrix form:

(27)

14. In Neary and Purvis (1982) we explore the dynamics which arise when both the capital stock and the price of services adjust sluggishly.

J. Peter Neary/Douglas D. Purvis

302

Denote the transition matrix as A ; since the determinant of A (equal to - 8 0, the earlier analysis is not affected qualitatively. We redefine our state variables as follows: (lOa)

e=

(lOb)

c=e-w.

m - w.

As before, e is predetermined (except when m jumps), and c is a jump variable. The state-space representation of the model given in equations (1), (2), (8), (9), (4), and (5) is:

De

1 a')'(A - k) - A

Dc

a')'

a[A8 - ')'(1 - a)]

e

1

a8(A-k)+a-1

c

a')'A

- A')'(l - a)

(11) 1 + a')'(A - k) - A

A+ ')'(k - A)

Dm -1

-A

r* + T

e

It is easily seen that (7) is the special case of (11) with a = 1. A necessary and sufficient condition for the existence of a unique saddlepoint equilibrium is (12)

a')'(A - k) - A 0, a given percentage appreciation of e will be associated with a smaller percentage reduction in p. The special case a = 0 represents the "law of one price" for all goods or instantaneous purchasing power parity (PPP). Although fewpropositions in economics have been rejected more convincingly by the data than PPP (Kravis and Lipsey 1978; Frenkel 1981; Isard 1977), it is mentioned here briefly for completeness. With the domestic price level moving perfectly in line with the exchange rate, the wage equation (9), which still incorporates stickiness in the level of the money wage, ceases to be relevant to the rest of the model. The relative price of domestic and foreign goods is constant. Real output is a function of the exogenous real interest rate. Unless we impose the requirement that steady-state real wages are constant, output need not be at its full employment level. Alternatively, we could add an equation making output a (decreasing) function of the real wage. As this model has little to recommend it, we shall not pursue it any further here. 10.3.2

Money Wage Flexibility and Real Wage Flexibility

We now consider the case where both the money wage and the real wage are perfectly flexible, and output is always at its equilibrium or capacity value, o. We can view this as the case where the core rate of wage inflation, 'IT, equals the expected (and actual) rate of wage inflation, i.e., (4')

'IT

== Dw.

The model of equations (1), (2), (8), (9), (4'), and (5) has the following very simple state-space representation: [

~~

] = [

(13)

+

~-1 ~=~~-(1-a)h-1J [~J

[~

-a- 1 (I-a) -a- 1

- x.- 1 o

Dm +T

r*

e

325

Real Exchange Rate Overshooting

With both e and w freely flexible, neither of the two state variables, eand c, is predetermined. A unique convergent solution trajectory exists because there are now two unstable characteristic roots (A -1 and "y -18). The system is also recursive, with Dc independent of e and also of the policy instruments Dm, rt, and 8. Only a real shock (such as a change in the foreign real interest rate r* + T) will affect the dynamics and steadystate behavior of c. The diagrammatic representation of the system is given in figure 10.1. Without loss of generality, we assume that the De = 0 locus is downward sloping. Consider an unexpected, immediately implemented reduction in Dm. The initial equilibrium is at £1, the new equilibrium at £2. Note that these equilibria are completely unstable. Since the cut in the monetary growth rate is immediately implemented, e jumps immediately from £1 to £2 with no change in c. Monetary disinflation is costless. Ifwe consider a previously unanticipated future reduction in Dm, e will jump to an intermediate position like £12 between £1 and £2 at the moment the future policy change is announced. After that it moves gradually in a straight line from £12 to £2, where the system arrives at the moment that Dm is actually reduced. Again, there is no effect on competitiveness in the short run or in the long run. It is instructive to contrast monetary disturbances with a real shock, such as an increase in r* + T, analyzed in figure 10.2. The steady-state effect is to alter the long-run equilibrium from £1 to £2, lowering e and raising c. If the increase in r* + T occurs immediately, both c and e jump c

L E12 E2 - - -__- - -.....----4--~......------Dc

=

0

r DI=O

DI'=O

'--------------------------l Fig. 10.1

Monetary disturbances (with money and real wage flexibility).

326

Willem H. Buiter/Marcus Miller

c

E2

.~

L ............ ....... E12

~

_____________--.~E-l--------Dc = 0

r Dl=O

Fig. 10.2

Real disturbances (with money and real wage flexibility).

to E 2 without delay. If we have a future increase in r* + ,., the system jumps to an intermediate position such as E 12 after which it proceeds gradually to E 2 where it arrives when r* + ,. is actually raised. Note that this adjustment of the real exchange rate is an equilibrium phenomenon, taking place at a constant level of output. 10.3.3

Money Wage Flexibility and Real Wage Rigidity

Some recent work on wage and price behavior can be interpreted as combining the assumption of perfectly flexible money wages with the assumption of sluggish adjustment in the real wage. The latter is treated as predetermined because of (generally unspecified) transactions and adjustment costs. Consider, for example, the following specification for 1T:

(4")

1T==Dp-Tl(w-p),

T) ~ O.

Equation (4"), in combination with (9), yields (14)

Dw

==

O. The response to an unanticipated reduction in Dm is shown in figure 10.3. An unanticipated, immediately implemented reduction in Dm instantaneously moves the system to the new stationary equilibrium E 2 without any change in c, y, or r - Dp. An announced future reduction in Dm instantaneously moves the system to an intermediate position such as E 12 between E 1 and E 2 . From there it moves gradually to E 2 where it arrives at the moment that the reduction in Dm actually occurs. This whole process again takes place without any changes in c, y, or r - Dp. Now consider the effect of an increase in r* + T in this model, which changes the long-run equilibrium in figure 10.4 from E 1 to a point such as E2• With c predetermined, an immediate, unanticipated increase in r* + T causes an equal jump increase in e and w, lowering eto E 12 . From there c and e converge gradually to the new long-run equilibrium E 2 along the

329

Real Exchange Rate Overshooting

c

D1=O

------..1111111..-.----.....- -__-_~-~--

Dc= 0

s L-------------------------1 Fig. 10.3

Money disturbances (with money wage flexibility and real wage rigidity).

unique convergent trajectory S' S'. A previously unanticipated future increase in r* + 'T leads to an immediate jump in e down to a point intermediate between E 1 and E 12 , such as E 12 • From there e declines gradually to E 12 where it arrives when r* + 'T is actually raised. Then c and e increase gradually along S'S' toward E 2 . It is interesting to see what happens to the wage equation (14') when the exchange rate has no effect on the price level, that is, when a = 1. In that case the price equation (8) becomes (20a)

p=W,

while the wage equation reduces to (20b)

y = T)(w - p).

Equations (20a, b) imply that y = 0 at each instant. The model now is in many ways the same as the model with money wage and real wage flexibility discussed in section 10.3.2 and summarized in equation (13). The link between the real wage and the real exchange rate, given by W - P = (a - l)c in the general model, disappears. Even though the real wage is still predetermined (and indeed remains constant throughout at

330

Willem H. Buiter/Marcus Miller

S

c

Dl=O

r - - - - - - -_ _- - - - - o l I

-----CII...---__- - - - Dc = 0

L

L..---------------------------l Fig. 10.4

Real disturbances (with money wage flexibility and real wage rigidity).

0), the real exchange rate again becomes a jump variable. Because w still is a jump variable, ealso stays that way. The state-space representation of this version of the model is given in (21)

(21)

[De] [x.=

Dc

0

1 1'~18][e]+[1 ~

1&

1

0

cOO

-A-

0

Dm +T

r*

e

The response of this system to nominal and real shocks is qualitatively similar to that described in section 10.3.2 and figures 10.1 and 10.2. 10.3.4

Rational Expectations in the Labor Market with Money Wage Stickiness

Without changing the equation for the core rate of inflation (4") or the associated wage equation (14) of the previous section, a single change of assumption concerning the behavior of the money wage destroys the

331

Real Exchange Rate Overshooting

classical policy implications of that model. The crucial change in assumption is to rule out discrete jumps in w, that is, to require w to be a continuous function of time. The exchange rate, however, is still free to make discrete jumps at a point in time. This change in assumption does not rule out a rational expectations interpretation of (14). This is particularly obvious if we assume that 11 == O. The behavior of this rational expectations model of the labor market is, however, very different from the classical behavior of the models of sections 10.3.2 and 10.3.3. Instead it resembles the behavior of the sticky money wage model of sections 10.2 and 10.3.1. Monetary shocks lead to real exchange rate overshooting and departures of actual output from capacity output. Note that this kind of behavior is ruled out when a == 1. This "closed economy" representation means that rational expectations automatically rule out departures of actual output from capacity output. 4 With the assumed assymetry in the behavior of c and w, and with a direct effect of e on p, monetary shocks will alter the real wage and the real exchange rate and cause departures from full employment. With the sticky money wage interpretation of equation (14), e and c again assume the roles of section 10.2, where is predetermined while c (via e) can jump in response to news. The response of the system to an unanticipated reduction in Dm is illustrated in figure 10.5. If the reduction in Dm takes place immediately, c jump-appreciates to E~2' After that it moves gradually to E 2 along S' S' . From equation (16d) we see that this jump-appreciation of c will be associated with a fall in output. An anticipated future reduction in Dm will be associated with a smaller immediate jump-appreciation of c when the news arrives, say to E~2' This jump places c and eon the divergent path, driven by the values of the forcing variables determining E 1 , that will put them on the convergent path through E 2 (S'S') when the cut in Dm is actually implemented. An equal reduction in Dm at a more distant future time will again be associated with a smaller initial jump-appreciation of c (say to E12), after which c and efollow the unstable trajectory (drawn with reference to E 1 ) that will put it on S'S' when Dm is actually cut. There always will be a finite initial jump in c when the news of a future reduction in Dm arrives, except in the limiting case when the announced monetary growth reduction is infinitely far in the future. One implication is that if a monetary deceleration is planned, the loss of output and competitiveness is smaller, the further in advance the proposed policy action is announced. From equation (16c) with 11 == 0, we obtain:

e

(22)

a-I

y == --Dc. 0.

v>O.

The inclusion of the rate of inflation in the money demand function allows for the possibility of substitution between money and commodities as well as between money and bonds. The negative effect of inflation on effective demand represents what Tobin has called the dynamic Pigou effect (Tobin 1975). The long real interest rate R is defined implicitly by (30). This expresses R as a forward-looking, weighted average of future short real interest rates, with exponentially declining weights: R(t)

=

v

J

ev(t-z)

[r(z) - Dp(z)] dz ,

t

where v has the interpretation of the steady-state value of R. Note that R is a forward-looking or jump variable. We consider the solution of the model of equations (28), (29), (30), (8), (9), (4"'), (5), and (lOa, b) for the following parameter values: k = 1, A1 = 2, A2 = 1, ~ = 1, 81 = .5, 82 = .25, v = .05, a = .75, = .5, and ~ = .5. As before, we consider the effect of a previously unanticipated, immediately implemented one-point reduction in the rate of monetary growth, Dm. 8 The steady-state effects are easily obtained. The rate of price inflation, core inflation, wage inflation, and exchange rate depreciation decline by one point, as does the nominal interest rate. Real money balances increase by 2.83 percent, more than in the original model, because both rand Dp have a negative effect on money demand. Real output and the long-run real interest rate remain unchanged, as does the short-run real interest rate r - Dp. The real exchange rate appreciates by .67 percent: lower inflation stimulates demand via the dynamic Pigou 8. The solution is obtained by using the alogrithm "Saddlepoint" of Austin and Buiter (1982).

346

Willem H. Buiter/Marcus Miller

Table 10.3

Generalized IS-LM Model

Long-run change in (%)

e

'IT

2.83

-1

Initial jump in (%)

e

'IT

0

-.60

Eigenvalues

- .2402 ± 2795i; .3022; .0457

c -.67

R

0

-1

y 0

Dp

Dw

De

-1

-1

-1

c R r y Dp Dw De -4.80 .14 - .79 -1.62 -1.256 -1.413 - .79

effect; to clear the goods market in long-run equilibrium a loss of competitiveness is required. The impact effects and dynamics are summarized in table 10.3. There are now four state variables, e, 1T, c, and R: e is predetermined, c and R are pure jump variables, while 'IT, as before, has its initial value determined by equation (24"). There should be two stable and two unstable characteristic roots. This is indeed the case for our choice parameter values, as can be seen from table 10.3. Speaking loosely, the cyclical behavior imparted to the original model by the wage-price block is carried over to the present model, as evidenced by the pair of stable complex conjugate roots. The unstable root "contributed" by the long real interest rate dynamics can be identified with the small positive root .0457. The real exchange rate appreciates on impact by 4.8 percent, which represents real exchange rate overshooting of 4.1 percent. Output declines by 1.6 percent. 10.5.2

Wealth Adjustment through the Current Account

Current account deficits and surpluses alter the stock of net claims on the rest of the world. If nonhuman wealth is an important argument in the output demand function and/or the money demand function, a satisfactory analysis requires the simultaneous analysis of wealth, price, and exchange rate adjustment. Analytical models such as Dornbusch and Fischer (1980) and Branson and Buiter (1983) are restricted to the analysis of the cases of perfect price flexibility (Dornbusch and Fischer, Branson and Buiter) or of a permanently fixed price level (Branson and Buiter) by the need to limit the number of state variables to two. Our numerical algorithm permits us to analyze dynamic models with many more state variables. The "current account" model replaces (28) and (29) by (31), (32), and (33): (31)

m-p-e==kY-~1(r-rd)-~2Dp+~3F,

+ 8l (e - p) - 82Dp + 83(m - p) + 84 F, 83,84 >0. DF== El(e - p) - E2Y + E3 F, El,E2>0;E3~0.

(32) Y == -",R (33)

~32:0.

347

Real Exchange Rate Overshooting

Table 10.4

Current Account Model; No Interest Income from Abroad in the Current Account and No Wealth Effect on Money Demand

e 1T Long-run change in F -3.1 3 -1 (%) e

c 0

R 0

r

-1

y 0

F 0

Eigenvalues

- .2099 ± 2798i; .3102; .0485; - .1099

1T

Dw

De

-1

-1

-1

De Dw y Dp c R r -4.48 .15 -.73 -1.52 -1.17 -1.31 -.73

Initial jump in (%)

0 -.56'

Dp

F denotes the level (not the logarithm) of net private sector claims on the rest of the world. Since F can be negative, a log-linear specification could be awkward. 9 Dornbusch and Fischer (1980) have a wealth effect on output demand (8 3,84 >0) but not on money demand (~3 == 0). Note that our IS equation now includes both the static Pigou effect (8 3[m - p]) and the dynamic Pigou effect (-8 2 Dp). Equation (33) is the current account equation; El(e - p) - ElY is the trade balance surplus; and E3Fis the net interest, property, and dividend income derived from the ownership of foreign assets. With E3 equal to zero, the long-run real exchange rate is invariant under all changes in exogenous variables other than capacity output. In equation (33) the long-run value of c is zero. With a positive value for E3 (which should be identified with r* or r), competitiveness and net claims on the rest of the world are always inversely related across steady states; with E3 > 0 a larger value of F requires a worsening of the trade balance to maintain current account equilibrium. The complete model consists of equations (8), (9), (4"'), (5), (lOa, b), (30), (31), (32), and (33). The following parameter values are used for all current account models: k == 1, ~1 == 2, ~2 == 1, 'Y == 1, 81 == .5, 82 == .25, 83 == .015, 84 == .06, E1 == .9, E2 == .6, a == .75, == .5, ~ == .5, v == .05. The case of no wealth effect on money demand (~3 == 0) and no net interest income from the rest of the world in the current account (E3 == 0) is considered first. The long-run and impact effects of a one percent surprise reduction in monetary growth are given in table 10.4 together with the characteristic roots of the dynamic system. Steady-state claims on the rest of the world decline. There is no long-run change in competitiveness. F and e are predetermined. Competitiveness worsens on impact by about 4.5 percent. Core inflation declines by .56 percent. The short nominal interest rate declines, but the long real interest rate rises. Output falls by 1.5 percent. As in the previous model, the recession and the fall in core inflation contribute to reduce 9. Fis measured in terms of units of the consumption bundle. Capital gains or losses on external assets or liabilities because of exchange rate changes and changes in the general price level are ignored.

348

Willem H. Buiter/Marcus Miller

inflation initially by more than the reduction in monetary growth. This rather implausible feature disappears when output is treated as predetermined. The current account goes into deficit after the monetary contraction, with the loss of competitiveness dominating the effect of a lower level of output. The adjustment process is cyclical, however, and the current account returns temporarily to surplus during the later phases of the adjustment process. When we include net interest income from the rest of the world in the current account (with E3 == .05), the outcome is not very different from that obtained when the current account is equated with the trade balance. Table 10.5 summarizes the results. The percentage long-run reduction in net claims on the rest of the world does not differ noticeably between table 10.5 and table 10.4; the real exchange rate depreciates in the long run in table 10.5. The impact effects are virtually the same. Including wealth as an argument in the money demand function with "-3 == .4 (keeping E3 == .05) yields the results summarized in table 10.6. Having wealth as an argument in the LM equation reduces the long-run increase in real money balances associated with a one~point reduction in the monetary growth rate. The reason is that Fdeclines, thus reducing the demand for real money balances. As a consequence, the magnitude of the initial changes in 'IT, C, R, r, y, Dp, Dw, and De are all smaller than in the versions of the model that did not have wealth in the money demand function. Qualitatively, however, the behavior of this model is the same as that of the earlier ones.

Table 10.5

Current Account Model; Interest Income from Abroad in the Current Account but No Wealth Effect on Money Demand

Long-run change in F e 1T ( %) - 3.1 3.17 - 1 F

e

C

.68

R

o

r

-1

Initial jump in (%)

o

Eigenvalues

- .2128 ± 2759i; .3120; .05; - .0574

Table 10.6

o

1T

-.56

y 0

Dp -1

Dw -1

De -1

cRy Dp Dw De -4.41 .16 -.73 -1.51 -1.16 -1.31 -.73

Current Account Model; Interest Income from Abroad in the Current Account and a Wealth Effect on Money Demand

Long-run change in F e -3.1 .06 (%)

1T

-1

e

1T

0

- .36

c .57

R 0

y

-1

Initial jump in (%)

F 0

Eigenvalues

- .2485 ± .1968i; .3966; .0501; - .0646

c R -2.85 .10

0

Dp -1

Dp y - .47 -.97 - .75

Dw -1

De -1

Dw -.84

De - .47

349

Real Exchange Rate Overshooting Sluggish Output Model; Interest Income from Abroad in the Current Account but no Wealth Effect on Money Demand

Table 10.7

e 1T Long-run change in F -3.1 3.17 -1 (%) e

1T

0

-.57

c .68

R 0

r

y

Dp

Dw

De

-1

0 -1

-1

-1

r

y

Dp

Dw

De

- .31

0 - .51

-.57

-.32

Initial jump in (%)

F 0

Eigenvalues

- .1986 ± .3049i; .3072; .05; - .0572; - 2.0807

10.5.3

R c -4.56 .16

Sluggish Output Adjustment

In all models considered thus far, the level of output adjusts instantaneously. Monetary contraction, for example, brings about an immediate fall in output. This is clearly an undesirable property of these models: the multiplier process takes time. The simplest way of modeling sluggish output adjustment is to treat the level of output as predetermined and make its rate of change an increasing function of "excess demand," as in equation (34): (34)

Dy == a[ -",R

+ 8 1(e -

p) - 82 Dp

+ 83 (m -

p)

+ 84 F - y], a>O. Substituting (34) for (32) in the models of the previous subsection, we now have a model with six state variables: y, F, e, 'IT, C, and R. Variables y, F, and e are predetermined; c and R are jump variables; and 'IT is, as before, a "backward-looking" jump variable whose initial value is determined by equation (24"). The model should have four stable and two unstable characteristic roots. Table 10.7 shows that,for the parameter values k == 1,A1 == 2, A2 == 1, A3 == 0, '" == 1, 8 1 == .5, 82 == .25, 83 == .015, 84 == .06, ex == .75,