The Out-of-Sample Failure of Empirical Exchange Rate Models

This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: Exchange Rates and International Macroeconomics

Volume Author/Editor: Jacob A. Frenkel, ed.

Volume Publisher: University of Chicago Press

Volume ISBN: 0-226-26250-2

Volume URL: http://www.nber.org/books/fren83-1

Publication Date: 1983

Chapter Title: The Out-of-Sample Failure of Empirical Exchange RateModels: Sampling Error or Misspecification?

Chapter Author: Richard Meese, Kenneth Rogoff

Chapter URL: http://www.nber.org/chapters/c11377

Chapter pages in book: (p. 67 - 112)

The Out-of-Sample Failureof Empirical ExchangeRate Models: SamplingError or Misspecification?Richard Meese and Kenneth Rogoff

3.1 Introduction

A companion study (Meese and Rogoff 1983) compared the out-of-sample fit of various structural and time-series exchange rate models andfinds that the random walk model1 performs as well as any estimatedmodel at one- to twelve-month horizons for 1970s dollar/mark, dol-lar/pound, dollar /yen, and trade-weighted dollar exchange rates.2 Thestructural models perform poorly even though their forecasts are purgedof all uncertainty concerning the future paths of their explanatory vari-ables by using actual realized values.

The present study demonstrates that the dismal short- to medium-runforecasting performance of the structural models is not attributable to thesample distribution of the coefficient estimates. We rule out that explana-

Richard Meese is a faculty member at the Berkeley School of Business. Kenneth Rogoffis an economist at the International Finance Division of the Board of Governors of theFederal Reserve System in Washington, D.C. Meese was also an economist at the FederalReserve Board at the time this paper was written.

The authors have benefited from the comments and suggestions of Jeffrey Frankel,Robert Flood, Robert Hodrick, Peter Hooper, Peter Isard, and Julio Rotemberg. We areindebted to Julie Withers and Tamara McKann for excellent research assistance. This paperrepresents the views of the authors and should not be interpreted as reflecting the views ofthe Board of Governors of the Federal Reserve System or other members of its staff.

1. The structural models are described here in section 3.3 below. It should be noted thatall the models considered are derivatives of the monetary or asset approach in that theyspecify real money demand at home and abroad as a function of real income, short-terminterest rates, and possibly wealth. The random walk model predicts that today's exchangerate will obtain at all future dates.

2. In a study of the dollar/pound rate, Hacche and Townend (1981) use differentmethods to arrive at a similar conclusion; that the models do a very poor job of explainingthe dollar/pound rate. The present study examines the three bilateral dollar rates and alsocross-rates.

67

68 Richard Meese/ Kenneth Rogoff

tion by showing that the models (with autoregressive error terms) per-form poorly at one- to twelve-month forecast horizons over a wide rangeof coefficient values. These values are based on the theoretical andempirical literature on money demand and purchasing power parity.However, since the coefficient-constrained models only require estima-tion of the intercept terms, it is possible to look at longer forecasthorizons here than in our other study. There the relative superiority ofthe random walk model over the structural models diminishes as theforecast horizon approaches twelve months. The present study exploresthe possibility that the structural models may improve on the randomwalk model forecasts at horizons of twelve to thirty-six months.

The main part of the paper is contained in section 3.3, which discussesthe coefficient-constrained experiments. In section 3.2, vector autore-gressions (VAR) are used to identify the factors that influence the ex-change rate over short versus long horizons. The results from the VARexperiments also highlight the difficulties of finding legitimate instru-ments with which to estimate the structural models, thus motivating theconstrained-coefficient approach of section 3.3. Section 3.4 asks which ofthe common building blocks of the structural models is most likely tohave failed. We cite other studies and /or present evidence of our own oneach of the factors which may have gone awry. But we are unable toclearly identify a single dominant cause of the breakdown of empiricalexchange rate equations.

3.2 Decomposing the Forecast Error Variance ofthe Exchange Rate at Long and Short Horizons

Before proceeding to tests of the representative structural exchangerate models, we first examine a vector autoregression (VAR) consistingof the exchange rate and the explanatory variables of these models:relative money supplies, relative outputs,3 relative short-term and long-term interest rates, and trade balances. The VAR is a tool for analyzingthe relative importance of the explanatory variables in exchange ratemodel forecasts at both short and long horizons. As a by-product, theVAR also provides limited information on whether the conventionalexogeneity assumptions used in estimation of the structural models areappropriate.

A convenient normalization for estimation of the VAR is one in whichthe contemporaneous value of each variable is regressed against laggedvalues of all the variables; for example, the exchange rate equation isgiven by

3. The assumption that U.S. and foreign variables enter exchange rate equation systemswith equal but opposite signs is relaxed later in a limited number of experiments on thestructural models. Economizing on variables in the otherwise highly parameterized VARsystems is quite important, so we only estimate the VAR models with the relative variables.

69 Failure of Empirical Exchange Rate Models

(1) St = fl/i5r_i

+ B'ilXt_l + B'i2Xt_2

+ . . . B'inXt_n + uit,

where st is the (logarithm of the) exchange rate at time t and Xt_j isa vector of lagged values of the other included variables (listed above).Expressing the VAR system in the form of equation (1) facilitates es-timation, as ordinary least squares equation by equation is an efficientestimation strategy. This normalization does not, however, precludecontemporaneous interactions between the variables, as these effects arecaptured in the covariance matrix of the disturbance terms uit. Theuniform lag length n across all (seven) equations is estimated usingParzen's (1975) lag length selection criterion.4

We estimate the VAR model for the dollar/mark, dollar /pound, anddollar/yen exchange rates over the floating rate period; the data consistof monthly observations for March 1973 through June 1981 (our seasonaladjustment procedures are described in appendix B). Once havingobtained the coefficient estimates, the dynamic interactions among thevariables are most easily studied with the use of the moving average(MA) representation, which is derived by inverting the autoregressive(AR) representation to express each of the endogenous variables in termsof the disturbances or innovations (the uit in [1], for example). Studyingthe MA representation is complicated by the fact that the disturbanceterms in the MA (or AR) representation are in general contempora-neously correlated (see Sims 1980 or Fischer 1982). So to simulate a"typical" shock to a given variable it is necessary to recognize thatthe expectation of other disturbances in the system, conditional on theparticular shock of interest, is usually nonzero. Unfortunately, fortwo correlated disturbances Zi(t) and z2(t), if E[zi{t)\z2{t) = 1] = a,with a as an arbitrary constant, it is not in general true thatE[z2{t)\zl{t) — a] = 1. Because of this fact, there is no unique way tosimulate "typical" shocks to these systems of endogenous variables whencontemporaneous variable interactions are present. (In other words,when the covariance matrix of the disturbance terms is nondiagonal.) Toidentify a typical shock to the VAR system with a particular variable, wewill follow the Sims (1980) procedure of specifying a variable ordering apriori. The variable ordering essentially specifies that the first variable is

4. Parzen's (1975) criterion selects an order €* which minimizes

CAT(€) = trace!— 1 V~x - Vf\ € = 1, 2, . . . L ,

where N is the number of variables in the VAR, T is sample size, L is the maximal orderconsidered, and Vj is an estimate (adjusted for degrees of freedom) of the covariance matrixof disturbances for the model with € lags of each variable. Asymptotically, the orderselected is never less than the true order, assuming the true order is finite.

70 Richard Meese Kenneth Rogoff

predetermined with respect to all other variables, that the second vari-able is predetermined with respect to all but the first, etc. The identifica-tion of the VAR systems is pursued in greater detail in appendix A.

The multihorizon, forecast error variance decompositions listed intables 3.1-3.3 are based on a variable ordering with the logarithm of U. S.to foreign relative money supplies, m — m*, first, followed by the loga-rithm of relative outputs, y—y*, the short-term interest differential,rs ~ r*s7the long-term interest differential, rL - r*L, the U.S. and foreigntrade balances, TB and TB*, and the logarithm of the dollar price offoreign currency, s. In tables 3.4-3.6 the variable ordering is reversed. Inthe U.S.-German system, the largest estimated contemporaneous cor-relation is 44 percent between the short- and long-term interest differen-tial equations. The other estimated contemporaneous correlations rangefrom 5-20 percent. These results suggest that the variable ordering ispotentially important in the U.S.-German VAR system. And indeedthere are some differences between the U.S.-German VAR systems,regular versus reverse order, at both short- and long-forecast horizons.Note that in the regular (reverse) order system, exchange rate andlong-term interest rate innovations account for 78.6 percent (93.7) and12.8 percent (4.9) of the one-month-ahead forecast error variance of theexchange rate, and 48.1 percent (60.1) and 15.4 percent (10.5) of thethirty-six-month-ahead forecast error variance of the exchange rate.However, the statistical significance of these differences cannot be ascer-tained from tables 3.1 and 3.4. We have not yet performed the requisite(expensive) stochastic simulations to obtain estimates of the dispersion ofthe forecast error variance decompositions. Of course, the data neces-sarily contain less information about long-run variable interactions thanshort-run. Similar observations apply to the U.S.-U.K. and U.S.-Japanese VAR systems.

A second important observation to be made from tables 3.1-3.6 is thatno variable appears to be exogenous to the VAR system. Abstractingfrom coefficient uncertainty, an exogenous variable would manifest itselfas follows: at all horizons a variable's own innovations would account forall of its forecast error variance, so there would be a one in the columncorresponding to a variable's own innovation and zeros elsewhere.(Block exogeneity is the obvious multivariate generalization.)5 In theU.S.-German VAR, the exchange rate, relative incomes, the long-terminterest differential, and the German and U.S. trade balances all appearto have large exogenous components, since for both variable orderingsand all horizons (one to thirty-six months) own innovations in thesevariables explain at least 48, 55, 50, 59, and 65 percent of their respective

5. Glaessner (1982) formally tests the block exogeneity assumptions underlying someempirical specifications of the monetary model.


forecast error variances. For the U. S. -U. K. VAR, own innovations in theexchange rate, the U.K. and U.S. trade balances, and the long-terminterest differential account for most of the forecast error variance ofthese variables. In the U.S.-Japanese system, it is the exchange rate, theJapanese and U.S. trade balances, and relative incomes that have thisproperty.

The last feature of tables 3.1-3.6 that we wish to emphasize concernsthe difference between those factors which appear to explain the forecasterror variance of the three bilateral exchange rates at short horizons (oneto three months) as opposed to longer horizons (one to three years).Based on the numbers reported in these tables it is clear that owninnovations in exchange rates explain a large fraction of the exchangerate forecast error variance at one- and three-month forecast horizons,while innovations in the other variables become relatively more impor-tant at horizons of one and three years. This result is not atypical of VARsestimated on macroeconomic data (see Fischer 1982).

All of the features of tables 3.1-3.6 noted above suggest both (1) thedifficulty in specifying the menu of variables to include in a structuralexchange rate equation, and (2) the problems associated with findinglegitimate instruments with which to consistently estimate the parametersof these models. The latter difficulty has led to the constrained-coefficientmethodology of the next section.

3.3 Predicting and Explaining the Exchange Rate Outof Sample Using Structural Models with Constrained Coefficients

Elsewhere (Meese and Rogoff 1983) we employ rolling regressions toconstruct out-of-sample forecasts of the exchange rate using threestructural models: a flexible-price monetary model (Frenkel-Bilson), asticky-price monetary model (Dornbusch-Frankel), and a sticky-priceasset model which incorporates the trade balance (Hooper-Morton).6

The fact that these structural models do not outperform the random walkmodel at horizons of one to twelve months cannot be attributed to theinherent unpredictability of the explanatory variables; this uncertainty ispurged from the forecasts by using realized explanatory variables values.Still, the possibility remains that our small-sample results can be attrib-uted to poor parameter estimates rather than specification error. This

6. See Bilson (1978, 1979), Frenkel (1976), Dornbusch (19766), Frankel (1979, 1981),and Hooper and Morton (1982). The identification of particular empirical models withauthors who contributed significantly to their development follows one conventionalnomenclature. It is relevant to note, however, that several of these same authors haveanalyzed more than one of the three models. For example, Frenkel (19816) discusses asticky-price model and emphasizes that the flexible-price model is a limiting approximationwhich is applicable in a highly inflationary environment. Dornbusch (1976a) examines aflexible-price monetary model with traded and nontraded goods.

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84 Richard Meese/Kenneth Rogoff

possibility is especially worrisome in light of the estimated VAR modelspresented in the previous section. They indicate that it is difficult to findlegitimate exogenous variables in the three structural exchange ratemodels. If this is the case, then consistent coefficient estimation becomesproblematic and requires a priori knowledge of the serial correlationprocess of the error terms. These possible estimation problems mayexplain why the instrumental variables techniques implemented in ourother study do not yield better results than ordinary least squares.

Here we explore a range of constrained coefficient models and presentevidence that our previous results concerning one- to twelve-monthforecast horizons cannot be explained by coefficient uncertainty. In addi-tion, since the constrained coefficient models do not require a significantportion of the limited, floating rate data set for estimation, we are able tolook at longer forecast horizons.

3.3.1 The Representative Structural Models

All three of the structural exchange rate models we consider are basedon a common money demand specification, thereby allowing us to imposecoefficient constraints on a consistent basis across models. The quasi-reduced form specification of each of the models is subsumed in thegeneral specification below:

(2) s = 0O + ax{m - rn) + a2(y - / ) + a3(rs - r*s)

+ 04 (V - **e) + « 5 (TB - TTr) + u,

where (ire - ir*e) is the expected long-term inflation differential, TB andTB* are the cumulated U.S. and foreign trade balances, u is a disturbanceterm, and the other variables are as defined in section 3.2 above. (Recallthat s is the logarithm of the dollar price of foreign currency.) In equation(2) we have imposed the usual constraint that domestic and foreignvariables affect the exchange rate with coefficients of equal but oppositesign; this constraint is relaxed in a limited number of experiments bothhere and in our earlier study.7 We choose not to specify an ad hoc laggedadjustment mechanism in (2), preferring to model the dynamics using anautoregressive error term as described below.

All three models hypothesize first-degree homogeneity of the ex-change rate with respect to relative money supplies, or a1 = 1. TheFrenkel-Bilson or flexible-price monetary model, formed by differencingtwo identical money demand specifications while imposing purchasing

7. Haynes and Stone (1981) suggest that a problem with the representative structuralmodels we consider is the restriction of equal but opposite coefficients on domestic andforeign variables. In Meese and Rogoff (1983), relaxing this restriction by letting certaindomestic and foreign variables—incomes, money supplies, and cumulated trade balances—enter equation (2) separately yielded no forecasting improvement. Here we tried separatingthe incomes and trade balances, but again found no forecasting improvement.


power parity (PPP), posits the additional coefficient restrictions: a2<0,a3>0, and a4 = a5 — 0.

The Dornbusch-Frankel or sticky-price monetary model also hypothe-sizes that the coefficient on relative incomes a2 < 0, but, in contrast to theFrenkel-Bilson model, hypothesizes that the coefficient on the short-terminterest differential a3<0, and that the coefficient on the long-termexpected inflation differential a4>0. The derivation of these coefficientrestrictions is explained in Frankel (1979). The principal theoreticaldifference between the Frenkel-Bilson model and the Dornbusch-Frankel model is that the latter allows for short-run deviations from PPPcaused by sticky domestic prices. Prices adjust only gradually in responseboth to excess demand, which depends on the terms of trade, and tosecular inflation differentials (TT6 - Tr*e in equation [2]). The long-run orflexible price exchange rate s is derived in the same manner as s in theFrenkel-Bilson model, except that it depends on ire - TT*6, which is equalto the long-run, short-term interest differential:

(3) I = - a + ( m - m )

Using money demand functions of the form

(4a) m - p - a - Xrs + 0y

and

(4b) m -p* = a - \r*s-0*y,

and a price adjustment equation of the form

(5) (p -p*) ,+ i - (p ~p)t = %{s -p +p')t + (ire - Tf'\,

Frankel demonstrates that augmented regressive expectations arerational:8

(6) Set+1 - St = 0 ( ^ - 5 ) , + (iTe - TT*e)t,

where set+1 is the exchange rate expected to prevail at time t -f-1 based on

period t information. Substituting (3) into (6) for 5, and also imposinguncovered interest parity by substituting rs — r* for se

t+\— st, one arrives atthe quasi-reduced form of the Dornbusch-Frankel model:

(7) s= -OL + (m - m) - 0{y - y*) -\{rs- r*s)0

8. It is also straightforward to show that deviations from PPP caused by monetary shocksare expected to damp at rate 0.

9. Frankel uses both long-term interest differentials and past inflation differentials asproxies for IT* - ir'e, the flexible-price or long-run expected inflation differential.


So in the Dornbusch-Frankel model, a3, the coefficient on the short-terminterest differential rs - r*s, does not depend on the nominal interest ratesemielasticity of the demand for real balances \ . Rather it depends on thenegative of the inverse of 0, the coefficient on excess demand in the priceadjustment equation. The coefficient on the expected long-run inflationdifferential, a4, is the sum of 1/0 and \ .

The Hooper-Morton trade-weighted dollar model imposes the sameconstraints as the Dornbusch-Frankel model, except that it allows unan-ticipated shocks to the U.S. trade balance to affect the PPP or long-runreal level of the exchange rate. In our bilateral version of their model,incipient trend U.S. trade balance surpluses require an appreciation ofthe long-run real exchange rate, while incipient trend foreign surplusesrequire a depreciation. Thus, a5 < 0. It should be noted that the randomwalk model is also subsumed in the general specification (2). That modelis given by ax = a2 = a3 = a4 = a5 = 0, and ut = ut_\ + et, where et is awhite noise process.

3.3.2 A Description of the Coefficient Constraints

The least controversial constraint we impose is that ax, the coefficienton the logarithm of relative money supplies, is unity. While we shall notconsider other values for al5 we do experiment with different definitionsof the money supply; the reserve adjusted base, Ml-B, and M2 (inconjunction with their respective foreign counterparts).10

Widespread agreement is lacking on the values of the other param-eters. For example, there is a range of theoretical and empirical estimatesof the interest and income elasticities of money demand. The quantitytheory puts the income elasticity at one, and the interest elasticity at zero.Alternatively, the Baumol (1952) and Tobin (1956) inventory theoreticapproach, in its simplest form, can be used to derive an income elasticityof .5 and an interest elasticity of —.5. Taking into account integerconstraints raises the income elasticity toward one and the interest elas-ticity toward zero (see Barro 1976). The Miller and Orr (1966) model of afirm's optimal cash-management procedures yields an interest elasticityof —.33. The income elasticity suggested by that model ranges from . 33 to.67, depending on whether a rise in income brings a rise in the number oftransactions or in the average size of transactions. The Whalen (1966)model of the precautionary demand for money also suggests an interestelasticity of - .33. In addition it yields an income elasticity which dependson how the size versus frequency of transactions changes as income rises,ranging from .33 to 1. Finally, we consider empirical estimates of thedemand for money, for which Goldfeld's (1973) paper is a standard

10. For the dollar/pound rate we use M3's, since there are no data on M2 for the U.K.The results presented later in this section are based on Ml (Ml -B) data. However, weobtain very similar results with the different monetary aggregates.


reference. He estimates the income elasticity of money demand to be .19in the short run and .68 in the long run; his short-run and long-run interestelasticities are —.064 and —.23. Since the present study takes theapproach of modeling the serial correlation properties of the error termrather than specifying an ad hoc lagged adjustment mechanism, it followsthat the higher long-run elasticities are more relevant for our purposes.

We are now ready to specify a complete grid of constraints for theFrenkel-Bilson model. The income elasticity constraints considered are.5, .65, .75, .85, and 1. This grid excludes the lowest ranges of incomeelasticities obtained in the theoretical models; we implicitly assume thatincome growth is accompanied by some growth in the size of transactions.The interest rate sem/elasticity constraints include —3, -4.5, —6, -7.5,and —10. The latter grid encompasses interest rate elasticity priors rang-ing from somewhere between -.18and —.21 to —.60and —.70, depend-ing on the bilateral exchange rate. The semielasticity priors are obtainedby dividing the interest elasticity priors by the average prevailing level ofshort-term interest rates during the sample.

The grids of constraints for the Dornbusch-Frankel and Hooper-Morton models incorporate the same range of income elasticity andinterest rate semielasticity constraints as the Frenkel-Bilson model grid.The two sticky-price models also require the specification of a grid for 0,the speed of adjustment parameter in the goods market. We choose arange of constraints for 0 using the fact that it also represents the speed atwhich short-run deviations of the real exchange rate from its long-runequilibrium are damped. The grid for 0 is based on the assumption thatbetween 33 percent and 100 percent of today's deviation from PPP isexpected to be eliminated one year hence. This range encompassesGenberg's (1978) estimates as well as those of Frankel (1979), both ofwhich are based on data for Germany. Since in the Dornbusch-Frankelmodel the coefficient on relative short-term interest rates, a3, is equal to— 1/0, our grid of priors for a3 in that model includes —1, —2, and - 3 .(The values for 0 and therefore -1/0 are conceived on an annual basis,since the short-term interest differentials and expected long-term infla-tion differentials in the data set are annualized.) The coefficient on theexpected long-run inflation differential, a4, is equal to X. + 1/0, where —Xis the interest semielasticity of money demand. The grid of constraints fora4 is 4, 7, 9, 11, and 13, which includes the minimum and maximumpossible values of X + 1/0, given the individual grids of constraints for Xand 1/0. For consistency, we exclude from our overall grid for theDornbusch-Frankel model combinations of a4 and a3 such that a4 - a3 isless than 3 or greater than 10, the bounds on the grid for X.

The coefficients on the cumulative monthly trade balances (taken asdeviations from trend) in the Hooper-Morton model are based primarilyon Hooper and Morton's work. We assume that a billion dollar U.S.


trade balance surplus above trend level leads, ceteris paribus, to anoffsetting .3 to .5 percent appreciation of the dollar; that is, a5, is .003 or.005. The results reported below are robust to using values of a5 of .01 or.02. For simplicity, and to limit the size of the large grid of coefficientconstraints for the Hooper-Morton model, we assume that a foreign tradebalance surplus has an effect on the exchange rate of equal magnitude butopposite sign.

The final variable for which it is necessary to specify a grid of con-straints is one which we logically know nothing about—the error term ut.We assume that ut follows a first-order autoregressive process:

(8) ut = [>ut-l + et = etl{\-pL),

where et is white noise and L is the lag operator. The grid for theautoregressive parameter p is 0,.2, .4, .6, .8, and 1.0, so both the no serialcorrelation case and the first-difference case are covered.11 The decisionto analyze only a first-order autoregressive process is made in part to limitthe size of the parameter grids, but it is also in part because of the resultsof our previous study. There, optimal linear combinations of structuralmodels and very general autoregressive time series models are analyzed.A wide variety of optimal lag length selection criteria are used in develop-ing the time series components of the forecasts; these criteria generallyselect a lag length of one for the univariate models.

Given the range of constraints we have selected, the grid for theFrenkel-Bilson model contains 150 different combinations of param-eters; the grid for the Dornbusch-Frankel model has 330 elements; andthe Hooper-Morton model grid has 660 elements.12

3.3.3 Results

The grid of parameter values developed above is now used to performtwo basic experiments, designed to compare the structural models to therandom walk model at forecast horizons of one, three, six, twelve,eighteen, twenty-four, thirty, and thirty-six months. The ex post and exante forecasting experiments differ mainly in whether forecasts aregenerated using realized values of the explanatory variables (ex post), orusing predictions of the explanatory variables based on informationavailable at the time of the forecast (ex ante). ° The other difference is

11. For the Dornbusch-Frankel model we also experimented with a range of constraintson p concentrated between .8 and 1. The lowest end of this range produced the best results.

12. Recall that the Dornbusch-Frankel and Hooper-Morton model grids exclude com-binations of a3 and a4 incompatible with the range of constraints specified for the interestrate semielasticity of real money demand \ .

13. In the absence of greater knowledge about the true underlying structure than isinherent in equation (2), it is not possible to take advantage of any correlation between theerror term and the explanatory variables in generating the ex post forecasts. Such correla-tion is likely, though, given the endogeneity of the explanatory variables indicated by theVARs in section 3.2. In fact, if the variance of the error term is large and its (unknown)


that ex ante forecasting begins in June 1975 while ex post forecastingcovers the entire sample period. The ex ante experiment requires enoughobservations for first-round estimation of the VAR that generates predic-tions of the explanatory variables. (Because the ex ante experiment isquite expensive to conduct, it is performed only for the Dornbusch-Frankel model.) Otherwise, the experiments are conducted in identicalfashion. Constant terms corresponding to each constellation of param-eter values are estimated using rolling regressions. The autoregressivecomponent of forecasts made at time t are based on the period t errorterm.

The results of the ex post forecasting experiment are broadly character-ized in table 3.7, where the structural model "forecasts" are comparedwith the random walk model forecasts on the basis of RMSE and MAE.14

For each model and exchange rate, table 3.7 reports the shortest forecasthorizon, in months, at which 0.1,10, 25, and 50 percent of each model'sparameter grid outpredicts the random walk model when realized valuesof the explanatory variables are used. Table 3.7 demonstrates that theresults of Meese and Rogoff (1983) cannot be explained by parameteruncertainty. For the entire parameter grid and for all three exchangerates, the structural models never improve at all, much less significantly,on the random walk model in MAE or RMSE at forecast horizons lessthan twelve months. However, at horizons of twelve months or more—longer than we could examine in our study based on estimated coef-ficients—the RMSE and MAE of the models do sometimes improve on

covariance with the relevant linear combination of the explanatory variables (the "fun-damentals") is negative, our ex post forecaster need not dominate optimal ex ante forecast-ers. In this perverse case, knowing that the realized fundamentals suggest a higher exchangerate means that you should guess a lower exchange rate.

14. The results for the Dornbusch-Frankel and Hooper-Morton models reported intables 3.7-3.10 are obtained using long-term interest differentials as a proxy for expectedlong-run inflation differentials. It is important to recognize that these models are potentiallyquite sensitive to this variable. However, using instead current-period inflation differen-tials, a moving average of past inflation differentials, or future inflation differentials, yieldsqualitatively similar results in the ex post forecasting experiments (tables 3.7 and 3.8). Wedid not try these other proxies in the expensive ex ante experiments (tables 3.9 and 3.10).

Let k = 1, . . . , 36 denote the forecast step, Nk the total number of forecasts in theprojection period for which the actual value A(t) is known, F(t) the forecast value, and letforecasting begin in period {t + 1). Define:

Nk-l

mean absolute error = X \ F(t + s + k) - A {t + s + k) \ INk.

\root-mean-square error = { 2 \F(t + s + k) - A(t + s + k)]2/Nk

I * = oOur use of mean absolute error covers problems that might arise if, as suggested byWesterfield (1977), exchange rate changes are drawn from a stable Paretian distributionwith infinite variance. The mean errors of the models (not reported) are small relative tomean absolute errors in almost all cases where p> .2, indicating that the structural modelsare not simply systematically over or underpredicting.

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the random walk model. This result is tempered by the fact that theminimum RMSE or MAE coefficient configurations bounce around atdifferent forecasting horizons. Still, the percentage of the parametergrids which improve on the random walk model does increase withforecast horizon. Overall these essentially in-sample results—in-samplebecause not all coefficient configurations improve on the random walkmodel—must be interpreted with caution.

Table 3.8 presents best representative parameter values for each of themodels, together with their corresponding RMSE and MAE.15 These twostatistics are also given for the random walk model. At thirty-six months,the best representative coefficient values for the Dornbusch-Frankel andHooper-Morton models do about 50 percent better than the random walkmodel in RMSE and MAE; the Frenkel-Bilson model only does about 30percent better.

Since the models do not forecast well at short horizons in the ex postexperiment, it is not surprising that the one model considered in the exante experiment does poorly at short horizons as well.16 Tables 3.9 and3.10 present results for the ex ante forecasting experiment with theDornbusch-Frankel model. No parameterization of that model ever im-proves on the random walk model in MAE for horizons under twelvemonths; the threshold horizon is even longer when RMSE is the metric.Furthermore, for the dollar/pound and dollar/yen exchange rates, over90 percent of the parameter grids fail to beat the random walk model inMAE or RMSE at any horizon. It is true, however, that at thirty-sixmonths the best representative Dornbusch-Frankel model performsalmost as well in the ex ante experiment as the best representativeDornbusch-Frankel model in the ex post experiment (compare tables 3.8and 3.10). Again, we should emphasize that the evidence presented hereon the possible forecasting superiority of the structural models is essen-tially in-sample, since not all configurations of the parameter constraintsimprove on the ramdom walk model.

Also reported in table 3.10 are the forecasting properties of the seven-variable VAR system of section 3.2. This model, estimated by rollingregressions, is a true ex ante forecaster. The VAR outforecasts therandom walk model at three-year horizons for the dollar/mark rate. Itdoes worse at one-year horizons for that exchange rate, though, and

15. The "best" representative set of parameter constraints for each model in table 3.8 ischosen in an ad hoc fashion as the one which comes in first (also ahead of the random walkmodel) at the greatest number of horizons. The maximum improvements over the randomwalk model in MAE or RMSE at thirty-six-month horizons exhibited by these representa-tive models are as large as those exhibited by any other parameter configurations.

16. While only one model is considered in the ex ante experiment, note that all threemodels yield qualitatively equivalent results for the ex post experiment. Also, since theDornbusch-Frankel model predicts that the exchange rate will return in the long run to itsflexible-price or Frenkel-Bilson model value, we should a priori expect the performance ofboth models at long forecast horizons to be quite similar.

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worse at all horizons for the dollar/pound and dollar/yen exchange rates.It is possible that these results can be improved by imposing probabilisticpriors on the VAR (see Litterman 1979). (An identified structural modelsuch as the Dornbusch-Frankel model can be thought of as a VAR witha priori restrictions.)

3.4 The Poor Performances of the Structural Models:Possible Causes

The constrained coefficient experiments of section 3.3 reinforce theresults of our earlier study. The selected structural models (with autore-gressive error terms) fail to forecast or even explain out of sample as wellas the random walk model at horizons of up to twelve months. Themodels do sometimes produce better forecasts than the random walkmodel at longer horizons, but in an unstable fashion. As noted in section3.2, the limited floating rate data set necessarily contains more informa-tion about short than about long forecast horizons.

In this section we try to trace the instability or misspecification of theseempirical exchange rate equations to their building blocks, such as un-covered interest parity,17 the particular money demand specification, theproxies for inflationary expectations, and the goods market specifi-cations. These building blocks are not, of course, strictly independent.

The assumption of uncovered parity has been strongly challenged byrecent work on exchange rate risk premiums.18 However, while someauthors find evidence of risk premiums, the weight of the evidence is thatthe magnitudes involved are not large. Nevertheless, volatile time-varying risk premiums remain a possible explanation of the results.

The goods market specifications of the three representative structuralmodels are relatively simple. The Frenkel-Bilson flexible-price monetarymodel imposes PPP, even in the short run. The Dornbusch-Frankelsticky-price monetary model allows for short-run deviations from PPP.The Hooper-Morton model is similar except that it attempts to incorpo-rate movements in the long-run PPP level of the exchange rate byassuming that these movements take place in response to unanticipatedtrade balance (current account) deficits or surpluses. While short-runPPP does not provide an accurate characterization of the 1970s,19 there is

17. In some versions of the Hooper-Morton model this assumption is relaxed.18. See, for example, Hansen and Hodrick (1980a, b), Cumby and Obstfeld (1981),

Hakkio (1981), Tryon (1979), Bilson (1981), Meese and Singleton (1982), or Geweke andFeige (1979). Hansen and Hodrick study this issue in their paper contained in this volume.

19. Isard (1977), Genberg (1978), and Frenkel (1981a, b) provide evidence on this point.In this context, it would be useful to remind the reader that our identification of particularmodels with particular authors oversimplifies the history, development, and application ofthese models (see note 6).


no strong evidence that the long-run PPP level of the exchange ratechanged significantly.

The performance of the Dornbusch-Frankel and Hooper-Mortonmodels are potentially quite sensitive to the use of a variable other thanthe long-term interest differential as a proxy for the long-run expectedinflation differential. Although we did not find a proxy which yieldedbetter results (see note 14), this issue merits further attention.

Perhaps the major problem with the structural models considered hereis the instability of their underlying money demand specifications. Therecent breakdown of U.S. money demand relationships was first noted byGoldfeld (1976) and is documented extensively by Simpson and Porter(1980). Conventional empirical money demand specifications such asequations (4) of section 3.3 have consistently underpredicted U.S. Mlvelocity since mid-1974. For this reason, the present study uses Ml-B, forwhich the systematic bias over the sample period is much smaller, and thenew definition of M2, for which the bias is negligible. But equations (4)still fail to predict these aggregates or the reserve-adjusted base with anynotable degree of precision. As reported above, our exchange rate ex-periment results are not sensitive to which of these monetary aggregates(together with their respective foreign counterparts) we employ.

Whether or not money demand instability and/or misspecification isresponsible for the exchange rate results, it is certainly true that theconventional money demand equation does not work well when ex-pressed in terms of U.S. minus foreign variables. Equation (4a) minus(4b) fails Chow (1960) tests for the stability of the intercept term at fourdifferent breaks in the sample. It also fails Goldfeld and Quandt (1965)tests of homoscedastic disturbance terms over the sample breaks.20

To investigate the possibility that our results are generated solely bymoney demand instability in the United States, we performed ex postforecasting experiments using the Dornbusch-Frankel model on thepound/mark, pound/yen, and yen/mark cross-exchange rates. For thecase of the yen/mark, we found coefficient values for which the modelpulled even with the random walk model as early as six months. But thesubsequent improvement at longer horizons never exceeded 30 percent.(The pound/mark and pound/yen cross-rate results are no better thanthe results for the various dollar exchange rates.)

In sum, money demand instability is an important potential explana-tion for our results, but further work is needed to demonstrate thattime-varying risk premiums, volatile long-run real exchange rates, or

20. The breaks in the sample at which these stability tests are conducted are chosenarbitrarily and correspond to (1) June 1974—the start of the mature float; (2) November1976—the approximate sample midpoint; (3) November 1978—the dollar support program;and (4) October 1979—the change in Federal Reserve operating procedures. The tests wereconducted using all parameter configurations with the grids for (A., 0) reported in section3.3.2.


poor measurement of inflationary expectations are not the dominantproblems.

3.5 Conclusions

The unimpressive out-of-sample performance of the Frenkel-Bilson,Dornbusch-Frankel, and Hooper-Morton empirical exchange ratemodels cannot be attributed to inconsistent or inefficient parameterestimates. These models fail to yield any improvement over the randomwalk model in mean absolute or root-mean-squared error one to twelvemonths out of sample for a broad range of theoretically plausible coef-ficient values, even when autoregressive error terms are introduced. Thusit is unlikely that more efficient estimation techniques, such as imposingall the cross-equation rational expectations restrictions, will yield param-eter estimates which do better.21 The constrained coefficient models doprevail at longer horizons but in an unstable fashion; the best coefficientvalues bounce around depending on the forecast horizon.22

The breakdown of empirical exchange rate models may be the result ofvolatile time-varying risk premiums, volatile long-run real exchangerates, or poor measurement of inflationary expectations. Alternatively,the main problem may lie in their money demand specifications. At thispoint, we are reluctant to draw any firm conclusions.

Appendix A

In this appendix we describe the triangularization of the VAR systemused in section 3.2 to analyze the dynamic effects of an innovation to aparticular variable. First suppose the tth observation of the VAR isrepresented by

(Al) [IN-A(L)]yt = u,,

where [IN — A(L)] is a matrix polynomial in the lag operator L, yt is theN x 1 vector of variables in the system, E{ut) = 0, and var(wf) = V, posi-tive definite. Using the Cholesky factorization V = WW', where W islower triangular, we can transform (Al) to the system

(A2) W-l[IN - A{L)]yt = W~lut = et,

21. See Driskill and Sheffrin (1981) or Glaessner (1982). These more sophisticatedstatistical techniques may provide superior expectations proxies, however.

22. If the true structural model were known and combined with an accurate representa-tion of the serial correlation process of the error term, then such a model would produceminimum MSE forecasts at all horizons.

98 Richard Meese Kenneth Rogoff

where E(et) = 0 and var(ef) = IN, the order N identity matrix. Since W 1

is lower triangular, the system (A2) is recursive, as described in the text.The moving average representation of (A2) is

(A3) yt=[lN-A{L)]-'Wet,

and in this expression the contemporaneous value of the first componentof e enters all N equations, the contemporaneous value of the secondcomponent of e enters the last N — 1 equations, etc. Because the decom-position of V is not unique, studying the effect of the uncorrelatedinnovations et on yt will depend on the variable ordering unless V isdiagonal, that is, unless the system (A2) has no contemporaneous in-teractions among variables.

Expression (A3) is also used to construct the variance decompositionsof tables 3.1-3.6. Since all components of et have unit variance, thevariance ofyit (the ith element of the vector j f) is the sum of squares of theelements in the ith row of [IN - A(L)] ~1W. The percentage of the fore-cast error variance of yit explained by the yth innovation ejt (the ythelement in the vector et) is calculated as the ratio of the sum of squares ofthe (/, /) element of [IN - A(L)]~1W to the variance of yit.

Appendix B Data Sources

The data set consists of seasonally unadjusted monthly observations overthe period of March 1973 to June 1981. All the raw data are seasonallyadjusted using dummy variables (the results reported in the text areinsensitive to the use of more sophisticated seasonal adjustment proce-dures described in Meese and Rogoff 1983). In the U.K. data set, the spotand forward exchange rates, short-term interest rate, and long-term bondrate are always drawn from the same date. Because daily bond series arenot readily available for Japan and Germany, only the exchange andinterest rates correspond in these data sets. All other series are monthlydata, and all data are taken from publicly available sources.

The bilateral data sets draw exchange rate data from identical sources,as follows:One-, Six-, and Twelve-Month Forward Exchange Rates

Data Source: Data Resources, Inc. data base.Series: One-, six-, and twelve-month forward bid rates in U.S.

dollars per local currency unit.Description: Daily data based on 10:00 A.M. opening New York

market rates.Three-Month Forward and Spot Exchange Rates

Data Source: Federal Reserve Board data base.


Series: Three-month forward and spot bid rates in U.S. dollarsper local currency unit.

Description: Daily data based on 12:00 noon New York market rates.Sources of the other data series are discussed below by country.

GermanyBond Yields

Data Source: Deutsche Bundesbank, Statistical Supplement to theMonthly Reports of the Deutsche Bundesbank, series 2,Securities Statistics, table 7b.

Series: Yields in percent per annum on fully taxed outstandingbonds of the Federal Republic of Germany.

Description: Monthly data. Data are calculated as averages of fourbank-week return dates including the end-of-monthyield of the preceding month.

Consumer PricesData Source: Deutsche Bundesbank, Monthly Report of the Deutsche

Bundesbank, table VIII-7.Series: Total cost-of-living index for all households.Description: Monthly index.

Industrial ProductionData Source: Organization for Economic Cooperation and Develop-

ment (OECD), Main Economic Indicators.Series: Total industrial production.Description: Monthly index.

Interest Rates (three-month)Data Source: Frankfurter Allegemeine Zeitung.Series: "Geldmarkt Vierteljahresgeld" in percent per annum

(three-month interbank rate).Description: Daily data.

Monetary Base (reserve-adjusted)Data Source: Deutsche Bundesbank, Monthly Report of the Deutsche

Bundesbank, table II-l (components of the unadjustedmonetary base) and table IV (average reserve ratio).

Series: The unadjusted base is calculated in millions of deut-sche marks as total Bundesbank assets less the reserveadjustment balancing asset, foreign and domestic publicauthority deposits, SDR allocations, EMCF gold con-tributions, liquidity paper liabilities, and "other" liabili-ties. The reserve adjustment is made by multiplying theunadjusted base statistic by (.631 + 3.2/total averagereserve ratio), where .631 = the currency percentage ofthe unadjusted base in the base period (January 1980),and 3.2 = (1 — .631) (the total average reserve ratio inthe base period).


Description: Monthly data. Data for components of the unadjustedbase refer to the last banking day of the month. Theaverage reserve ratio is a monthly statistic.

Money SuppliesData Source: Deutsche Bundesbank, Monthly Report of the Deutsche

Bundesbank, table 1-2.Series: Money stock Ml and money stock M2 in millions of

deutsche marks.Description: Monthly data. Data refer to the last banking day of the

month.Adjustment: A break in the series, caused by the introduction of a

new method of computation, occurs in December 1973.The 1973 statistics are adjusted using the ratio of thenew to the old statistic for December 1973.

Trade BalanceData Source:Series:

Description:JapanBond Yields

Data Source:

OECD, Main Economic Indicators.Trade balance (FOB - CIF) in billions of deutschemarks.Monthly data.

Data prior to 1981 are taken from Bank of Japan, Eco-nomic Statistics Monthly, table 71(2). 1981 data aretaken from Planning and Research Department, TokyoStock Exchange, Monthly Statistics Report, table 8-1.

Series: Yields in percent per annum on listed governmentbonds (Tokyo Stock Exchange).

Description: Monthly data. Data refer to the last banking day of themonth.

Consumer PricesData Source: Bank of Japan, Economic Statistics Monthly, table

119(1).Series: General consumer price index for all Japan.Description: Monthly index.

Industrial ProductionData Source: OECD, Main Economic Indicators.Series: Total industrial production.Description: Monthly index.

Interest Rates (three-month)Data Source: Federal Reserve Board data base.Series: "Over two-month ends" bill discount rate (Tokyo Stock

Exchange) in percent per annum.Description: Daily data based on Reuters quotes.

Money SuppliesData Source: Bank of Japan, Economic Statistics Monthly, table 4.


Series: Ml and M2 + CD in 100 million yen.Description: Monthly data. Data refer to the last banking day of the

month.Trade Balance

Data Source: OECD, Main Economic Indicators.Series: Trade balance (FOB - CIF) in billions of yen.Description: Monthly data.

United KingdomBond Yields

Data Source: Financial Times.Series: "British funds, undated, war loans 3V2" in percent per

annum.Description: Daily data.

Consumer PricesData Source: Department of Employment, Employment Gazette,

table 6.4.Series: General index of retail prices, all items.Description: Monthly index.

Industrial ProductionData Source: OECD, Main Economic Indicators.Series: Total industrial production.Description: Monthly data.

Interest Rates (three-month)Data Source: Financial Times.Series: Three-month local authority deposits (London money

rates) in percent per annum.Description: Daily data.

Monetary Base (reserve-adjusted) and Money SuppliesData Source: Bank of England, Quarterly Bulletin, table 1 (monetary

base components) and table II (money supplies).Series: Money stock Ml and money stock sterling M3 in mil-

lions of pounds. The reserve-adjusted monetary base iscalculated in millions of pounds as total currency incirculation plus bankers' deposits.

Description: Monthly data. Data refer to the third Wednesday of themonth (second in December).

Trade balanceData Source: OECD, Main Economic Indicators.Series: Trade balance (FOB - CIF) in millions of pounds.Description: Monthly data.

United StatesWith the exception of the trade balance statistics, all data are taken

from the Federal Reserve Board data base. Many of these series arepublished in the Federal Reserve Bulletin, and all are available to thepublic.


Bond YieldsSeries: Government bonds with at least ten years to maturity.Description: Daily data.

Consumer PricesSeries: Consumer Price Index.Description: Monthly index.

Industrial ProductionSeries: Total industrial production.Description: Monthly index.

Interest Rates (three-month)Series: Treasury bill rates.Description: Daily data.

Monetary Base (reserve-adjusted) and Money SuppliesSeries: Reserve-adjusted monetary base, Ml — B, M2, and M3.Description: Weekly Wednesday data.

Trade Balance (data through 1978)Data Source: Department of Commerce, Highlights of U.S. Export

and Import Trade, Exports table E-l; Imports table 1-1.Series: Domestic and foreign exports, excluding Department of

Defense shipments, in millions of dollars on a FASvalue basis; general imports in millions of dollars on acustoms valuation basis changing to a FAS basis in 1974.

Description: Monthly data.Adjustment: 1973 statistics are adjusted to a FAS value basis using

the 1974 average ratio of customs valuation to FASvalue.

Trade Balance (1979-81 data)Data Source: Department of Commerce, Summary of U.S. Export

and Import Merchandise Trade, December 1980 (ad-vance statistics for Highlights of U. S. Export and ImportTrade), Exports table 3; Imports table 5.

Series: Total domestic exports, excluding Department of De-fense grant-aid, in millions of dollars on a FAS valuebasis; general imports in millions of dollars on a FASvalue basis.

Description: Monthly data.

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Comment Nasser Saidi

The Meese and Rogoff paper is an assessment and adds up to an indict-ment of the large body of empirical models elaborated to interpret thetime series behavior of exchange rates in the 1970s. This is an introspec-tive, examining-one's-own-belly-button, piece of work. Not havingplaced any bets on the horses running in the Meese-Rogoff races, I admitto being in basic agreement with their dim assessment of existing empiri-cal models.

I discuss, first, the contributions and substantiated conclusions of thepaper. This is followed by some comments on the methodology, includingdiscussion of some technical issues. Finally, I expand on the reasonsadvanced by Meese and Rogoff (hereafter, M-R) for the relative failureof the structural models to accurately forecast exchange rates.

Contributions and Conclusions

The main contributions of this paper are:a. It evaluates the forecast accuracy of a number of competing models

on common ground. Estimates and forecasts are generated for identicalsample periods, using common, point-in-time data and common estima-tion methods. The models are evaluated on common ground by avoidingnoncomparability problems caused by sampling differences betweenmodels.

b. A more stringent criterion is used for evaluating the models' post-sample forecast accuracy. This is important since there is no guaranteethat a model with "good" in-sample operating charcteristics will performwell out of sample.

c. The estimation period covers the major portion of the 1970s experi-ence with floating rates, and the sampled exchange rates display substan-tial variance. The data should be informative and should discriminatebetween alternative models.

Nasser Saidi is a professor of economics at the Graduate Institute of InternationalStudies in Geneva, Switzerland.

This paper addresses both the Meese and Rogoff paper in this volume and Meese andRogoff (1981).


What conclusions can be drawn from M-R's work, and what are theimplications?

1. For all exchange rates, for nearly all forecast horizons, and foralternative measures (RMSE, MAE) of out-of-sample forecast accuracy,a simple random walk (SRW) model is a more accurate forecaster of thelevel of the (log) exchange rate than any structural model or uncon-strained VAR.

2. Although a SRW model ranks best, it is not a good predictor ofexchange rates. The correlations between actual and predicted outcomesare low. The SRW forecast is of poor quality.

3. Structural models fail, rather miserably, at both predicting andexplaining the postsample behavior of exchange rates. They fail to ex-plain in that, provided with the actual realizations of the "exogenous"variables (which in principle introduce a bias in favor of the structuralmodels), their predictions of realized exchange rates are worse than thatof a SRW model.

4. A tentative conclusion is that the structural models fail becausetheir parameter estimates are unstable over time. If coefficient estimatesthat provide good in-sample fits are combined with the postsample valuesof the exogenous variables, the structural models do not explain ex-change rates.

5. However, even if one partially resolves the issue of coefficientuncertainty by generating forecasts using a range of values consistent withtheory—which amounts to giving a weight of unity to prior information—and the postsample realizations of exogenous variables, the structuralmodels still fail to predict exchange rates.

6. Consider the relative performance of nonstrict time series models(i.e., exclude the SRW and univariate AR which only use the past historyof the exchange rate). It turns out that an unrestricted VAR does bet-ter—in terms of average rank for each specific measure and forecasthorizon—than any of the structural models. Since the various structuralmodels are restricted versions of the VAR, the sample evidence rejectsthe joint exogeneity and distributed lag restrictions implicit in the struc-tural models.

Most of these results should come as no surprise. The work of Nelson(1972) and Fair (1979) reaches similar conclusions with respect to theforecast accuracy of large-scale macroeconometric models as comparedto time series models. M-R demonstrate that the poor performance ofmacroeconometric exchange rate models cannot be accounted for byuncertainty due to exogenous variable forecasts or coefficient estimates.

Methodology and Evaluation

I have a number of technical quibbles with the M-R methodology andevaluation criteria. First, it is highly likely that the residual errors for


different exchange rates are contemporaneously correlated. Hence, ajoint estimation strategy that utilizes the information available in thecovariance matrix would provide more efficient coefficient estimates andpotentially improve the forecast accuracy of the structural models. Inaddition, to the extent that the forecast errors for different exchangerates are correlated, the relative failure of the structural models for eachexchange rate does not provide additional, independent evidence.Second, when estimated in the levels, the structural models typically yieldserially correlated residuals. Fair's (1979) results indicate that appropri-ate modeling of the time series error structure can vastly improve theforecast accuracy and performance of structural models. M-R's handlingof this problem is rather cavalier. The modeling of the residual is re-stricted on an a priori basis to a first-order AR, with no use made ofsample information. Appropriate modeling of the residuals using thesample evidence may improve the relative performance of the structuralmodels. Third, as M-R note, forecasts for more than one period aheadfollow a moving average process. Hence, the only statistically meaningfultests for evaluating forecasts obtained from different models are those forthe one period ahead forecasts. The summary measures for multiperiodforecast horizons are not very informative. For the purposes of compar-ing models, it would be as informative to consider the population correla-tion coefficients between actual and predicted exchange rates and pro-vide a ranking.

Despite these reservations, I doubt that the major M-R conclusionswould be reversed by using more sophisticated estimation procedures.We are left with the somewhat disquieting result that existing structuralmodels that seek to interpret exchange rate time series by appealing tothe behavior of observable macroeconomic variables fail to explain andforecast. However, the observation that a SRW model provides betterforecasts does not provide an interpretation of exchange rate movementsin the 1970s.

Reasons for Failure

It seems clear that the structural models fail to explain and forecastexchange rates because they are misspecified. M-R suggest—but provideno evidence in their paper to substantiate—that the major problem lies inthe instability of the money demand specification. The suggestion doesnot seem unreasonable, given the recent accumulating evidence on thetemporal instability of estimated money demand functions or, moregenerally, of behavioral relations in the monetary sector. However, thesuggestion is moot unless the potential factors leading to misspecificationand for instability of estimated reduced forms are identified. One, in myview, crucial source of misspecification is the inadequate modeling ofexpectations formation in existing structural models. In particular, the


role of the distinction between anticipated and unanticipated movementsin the exogenous driving variables is vastly underplayed. Asset pricingmodels of exchange rate determination incorporating rational expecta-tions typically lead to a specification such as:

(1) St=ioAjEl+j_1Zt+J + B(Zt-El_lZl) + ut,

where S is the spot exchange rate, Z stands for a vector of exogenousvariables, E is the expectations operator, and ut is interpreted as beinggenerated by differences in the information available to economic agentspricing foreign exchange and the econometrician (see Sargent 1981). Theforecast error is given by:

St - E,_ i St = B(Zt - E,_! Z,) + (M, - E,_! ut),

proportional to the unanticipated movements in Z, and in ut (althoughsome specifications of ut might lead to the restriction Et _ x u, = 0). As anexample, equation (1) would say that fully anticipated, permanent move-ments in the money stock (a component of Z) would lead to one-to-onechanges in the exchange rate (neutrality), but unexpected changes wouldhave an effect that depends on the magnitude and temporal characteris-tics of the process generating the money stock.

It is clear from equation (1) that if the distinction between anticipatedand unanticipated movements in Z is important, then models of the formSt = CZt + V, are unlikely to provide good out-of-sample forecasts andwill not adequately explain exchange rate movements. If (1) is anappropriate model, then it is not surprising that the structural models failto explain and forecast even when provided with the actual, realizedvalues of the exogenous variables.

Equation (1) suggests some further reasons for the potentially poorperformance of the structural models and the unconstrained VAR. Thefirst reason is the Lucas critique argument: Perceived changes in theprocesses or policies generating the Z's will lead to changes in the A's andB's of equation (1). The second is a timing or dating of variables problem,which is intimately linked to the information set available to economicagents. If one uses, as M-R do, point-in-time exchange rate data, then (1)suggests that the Z variables should be appropriately dated. For example,end-of-month exchange rates may well appear unrelated to end-of-monthmoney supplies if information on the latter is known only with a two-week lag. This is a case in which information subsequently available tothe econometrician was not contemporaneously observable to agents.The question of the availability and timing of information, includingannouncement-type effects (see Schwert 1981), is neglected in the M-Rpaper as well as in the empirical literature they assess. Finally, and


related to the Lucas critique, there is the "peso problem" and the"finance minister problem." The peso problem is one in which an event(say a change in monetary policy such as the formation of the EuropeanMonetary System (EMS)) is expected to occur at some future date. Thisalters the exchange rate path in anticipation of the event. Both a struc-tural model that inadequately models expectations and a SRW model willfail to explain and forecast exchange rates. This problem is amenable tocorrection to the extent that anticipations can be conditioned on the pastand contemporaneous movement in observable exogenous variables (fora good example of how to proceed, see LaHaye's 1981 analysis of antic-ipations of currency reforms). On the other hand, the finance ministerproblem is one in which an event is expected to occur, exchange ratesrespond, but the event does not happen (the particular finance minister isnot appointed). In this case, exchange rate expectations will appearunrelated to the past, contemporaneous, or subsequent evolution of theincluded exogenous variables. While the finance minister problem leadsto a theory of the error term ut in equation (1), it is not clear how theestimation or modeling should proceed.

To conclude, Meese and Rogoff have provided a useful and sorelyneeded assessment of existing empirical exchange rate models. The esti-mated VARs suggest that the exogeneity restrictions and lag distributionsof the structural models are not credible and are rejected by the sampleevidence. One direction for research would be to take account of theinformation contained in the VARs in modeling exchange rates. Moreimportant, the inappropriate modeling of expectations appears to be themain reason for the failure of the structural models to explain andforecast exchange rates in the 1970s.

References

Fair, Ray. 1979. An analysis of the accuracy of four macroeconometricmodels. Journal of Political Economy 87:701-18.

LaHaye, Laura. 1981. Inflation and currency reform. University of Illi-nois at Chicago Circle. Mimeo.

Meese, Richard, and Kenneth Rogoff. 1981. Empirical exchange ratemodels of the seventies: Are any fit to survive? Federal Reserve Board,International Finance Discussion Paper no. 184.

Nelson, Charles. 1972. The prediction performance of the FRN-MIT-PENN model of the U.S. economy. American Economic Review62:902-17.

Sargent, Thomas. 1981. Interpreting economic time series. Journal ofPolitical Economy 89:213-48.

Schwert, William. 1981. The adjustment of stock prices to informationabout inflation. Journal of Finance 36:15-29.


C o m m e n t Michael K. Salemi

The present contribution of Meese and Rogoff (hereafter, MR) andMeese and Rogoff (1981) constitute a comprehensive appraisal of theempirical validity of several asset approach models of the spot price offoreign exchange. MR test spot rate equations implied by three models:the flexible-price monetary model of Frenkel and Bilson, the sticky-pricemonetary model of Dornbusch and Frankel, and Hooper and Morton'ssticky-price asset model which incorporates the current account. Theauthors find that these models are not correctly specified structuralequations. They present abundant and compelling evidence to supportthis view.

MR test the so-called structural models in three different ways. InMeese and Rogoff (1981), they perform a battery of tests that comparethe out-of-sample predictions of the models with those of a naive alterna-tive, a random walk model for the spot rate. They estimate restrictedversions of their equation (2) using monthly data beginning at March1973 and generate out-of-sample predictions at one-, three-, six-, andtwelve-month horizons for two periods: December 1976 through Novem-ber 1980, and December 1978 through November 1980. The predictionsof each model use actual realized values of the appropriate explanatoryvariables. MR find that the predictions of the random walk model areconsistently more accurate than those of any of the structural models.Their result apears robust across foreign currencies, the test periodchosen, the statistic used to measure the size of prediction errors, and theprediction horizon.

Although MR refer to their work as a forecasting experiment, theirresults are solid evidence to reject the models themselves. The param-eters of a correctly specified structural equation are invariant with respectto regimes. By their procedure, MR confront equation (2) and themodels it characterizes with a regime shift—a set of realizations for theexplanatory variables different than that used to estimate the parameters.The failure of these models to explain the spot rate as well as the randomwalk model is evidence that the parameters of equation (2) are notinvariant to the regime shift.

In the present paper, MR subject the asset models to additional tests.They first estimate a system of vector autoregressions (VAR) for theseven variables that appear in the Hooper-Morton model, the leastrestrictive of the models they study. Two findings are particularly note-worthy. First, none of the variables in the system is exogenous in thesense of Granger and Sims. The econometric implication of this result is

Michael K. Salemi is associate professor in the Department of Economics at the Uni-versity of North Carolina at Chapel Hill.

Ill Failure of Empirical Exchange Rate Models

that, for the period under study, the parameters of the asset models arenot consistently estimated by ordinary least squares. Of course, thisfinding also challenges model builders to explain the mutual endogeneityof these variables.

MR reach their second interesting finding by inverting the estimatedVAR to obtain a moving average representation for the variables in thesystem. After a necessary preordering of contemporaneous influences,MR compute a variance decomposition for each variable in the system.At short horizons (especially one and three months) they find that most ofthe variation in the spot rate prediction error is attributable to theinnovation in the spot rate itself rather than to the innovations of theother variables in the system. At longer horizons, however, innovationsin the other variables account for as much as 54 percent of the predictionerror variance in the spot rate. Unfortunately, no consistent ranking ofthe importance of the other variables emerges. Relative output levels andshort-term interest rates appear relatively unimportant. Innovations inthe trade balance seem important for the yen, while relative moneystocks and the long-term interest rate differential appear more importantfor the mark.

Finally, MR demonstrate that the results of their first paper (1981) arenot likely to be merely the result of imprecise estimation of the assetmodel coefficients. On the basis of the money demand and monetarytrade literatures, they define a grid of probable values for the parametersof the asset models. For each point on the grid they generate spot ratepredictions for the entire period between March 1973 and June 1981. Forhorizons less than or equal to twelve months, virtually no parameteriza-tion of the asset approach models predicts as well as the random walkmodel. But for longer horizons, the best parameter configuration of eachof the three models predicts the spot rate substantially more accuratelythan the random walk model.

There are two ways to view this result. Because the grid search is anin-sample procedure, one might by reasonably reluctant to conclude thatthe spot rate models studied have long-run validity. On the other hand, Ifind it an interesting possibility that, in the short run, the spot ratebehaves like the price of a speculative asset but that over longer horizonsits equilibrium value is systematically related to other economic vari-ables, as the asset models predict.

In conclusion, Meese and Rogoff have, with exceptional skill andconcern for detail, cast serious doubt on the validity of the Frenkel-Bilson, Dornbusch-Frankel, and Hooper-Morton models. The sharpcontrast between the in-sample and out-of-sample performance of thesemodels cautions us to exercise more care in testing the models we esti-mate. Finally, it bears pointing out that the results of Meese and Rogoffare not evidence to reject the asset approach itself. That approach, in its


most general form, says simply that the spot rate adjusts to guarantee thatportfolio owners are satisfied with the foreign asset component of theirportfolios.

References

Meese, Richard, and Kenneth Rogoff. 1981. Empirical exchange ratemodels of the seventies: Are any fit to survive? Federal Reserve Board,International Finance Discussion Paper no. 184.

The Out-of-Sample Failure of Empirical Exchange Rate Models

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