-19-

4. The Poor Performances of the Structural Models: Possible Causes

The constrained-coefficient experiments of section 3 reinforce the
results of our earlier study. The selected structural models (with
autoregressive error terms) fail to forecast or even explain out of sample as
well as the random walk model at horizons of up to twelve months. The models
do sometimes produce better forecasts than the random walk model at longer
horizons, but in an unstable fashion. As noted in section 2, the limited
floating rate data set necessarily contains more information about short than
about lang forecast horizons.

In this section we try to trace the instability or misspecification of
these empirical exchange rate equations to their building blocks, such as
uncovered interest parity, the particular money demand specification,
the proxies for inflationary expectations, and the goods markets
specifications. These building blocks are not, of course, strictly
indepencient.

The assumption of uncovered interest parity has been strongly
challenged by recent work on exchanye rate risk prenia.2e/ However,
while some authors find evidence of risk premia, the weight of the evidence
is that the maynitudes involved are not larye. Nevertheless, volatile
time-varying risk prenia remain a possible explanation of the results.

The goods market specifications of the three representative structural
models are relatively simple. The flexible-price Frenkel-Bilson monetary
model imposes purchasing power parity, even in the short run. The
sticky-price Dornbusch-Frankel monetary model allows for short-run deviations

from PPP. The Hooper-Horton model is similar except that it attempts to


-40-

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 Supplies

Data 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: O.E.C.D., Main Economic Indicators.

Series: Trade Balance (f.0.b. - c.i.f.) in billions of yen.
Description: Monthly data.
United Kingdom
Bond Yields
Data Source: Financial Times
Series: “British funds, Undated, War loans 3s" in percent per
annum.
Description: Daily data.
Consumer Prices
Data Source: Department of Employment, Employment Gazette, Table 6.4.
Series: General index of retail prices, all items.

Description: Monthly index.


Data Appendix

The data set consists of seasonally unadjusted monthly observations
over the period March 1973 to June 1981. All the raw data are seasonally
adjusted using dummy variables (the results reported in the text are

described in Meese-Rogoff (1981)).
insensitive to the use of more sophisticated seasonal adjustment procedures/\
In the U.K. data set, the spot and forward exchange rates, short-term
interest rate, and long-term bond rate are always drawn from the same date.
Because daily bond series are not readily available for Japan and Germany,
only the exchange and interest rates correspond in these data sets. All
other series are monthly data, 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. dollars

per local currency unit.

Description: Daily data based on 12:00 noon New York market rates.


Forecast error
variance in

k

m-m

TB

-45-

Table 2

Unconstrained U.S.-Japan VAR, March 1973-June 1981,
regular variable order

Proportions of forecast error variance k months
ahead attributable to each innovation

943
-866
2551
2424

+044
+038
lll
+120

+142
+183
-110
115

-128
+252
+219
+224

-O11
+010
011
+012

-011
-010
015
-019

.011
016
-016
-026

*
y-y

+003
+045
«298
+319

+929
915
+637
-531

.076
+092
-058
054

-014
+039
+046
-071

-016
.022
+032
-036
od
~036
+945
051
041

.007
004
+004
+006

Innovation in:
r=
ss
+001
+004
021
-070

+009
-009
-086
.111

+770
+581
«284
~238

+294
.207
-108
.104

-032
+059
.078
079

+031
+023
+935
+039

-007
+004
-003
+003

002
+010
~009
-013

.001
-008
+019
+019

-006
-022
+058
-076

-520
+342
-184
.172

~000
-O11
.017
2024

-064
-095
-105
+093

020
-014
+057
-060

TB

-012
+024
+045
048

-009
+005
+042
-048

.002
+030
-069
.120

-000
+024
.079
-186

-904

-858
+726

671

-030
040
+103
+130

071
+139
+285
313

+024
-021
.039
2045

-000
+020
-090
+072

-001
+058
348
+320

-003
+022
-092
+085

.005
-008
+097
-11l

+823
- 780
-626
+523

.055
-080
+127
.138

-014
+029
-038
-080

-008
+004
-014
+099

-003
+034
-073
-076

+041
-113
-172
+157

.031
+031
-040
-068

005
-007
+066
2154

-828
+741
-507
+455


-13-

income elasticity of money demand to be .19 in the short run, and .68 in the
long run; his short-run and long-run interest elasticities are -.064 and
-.23. Since the present study takes the approach of modeling the serial
correlation properties of the error term rather than specifying an ad-hoc
lagged adjustment mechanism, it follows that the higher long-run elasticities
are more relevant for our purposes.

We are now ready to specify a complete grid of constraints for the
Frenkel-Bilson model. The income elasticity constraints considered are .5,
-65, .75, .85, and 1. This grid excludes the lowest ranges of income
elasticities obtained in the theoretical models; we implicitly assume that
income yrowth is accompanied by some yrowth in the size of transactions. The
interest rate semi-elasticity constraints include -3, -4.5, -6, -7.5, and
-10. The latter grid encompasses interest rate elasticity priors ranging
from somewhere between -.18 and -.21 to -.60 and -.70, depending on the
bilateral exchange rate. The sewi-elasticity priors are obtained by dividing
the interest elasticity priors by tie average prevailing level of short-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 and interest-rate
semi-elasticity constraints as the Frenkel-Bilson model yrid. 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 a ranye of
constraints for 6 using the fact that it also represents the speed at which

deviations from the long-run real exchanye rate are damped. The grid for 6


-53-
Table 10
‘Comparing the random walk model, a VAR model estimated by roliing

regressions, and the best representative Dornbusch-Frankel model when

predicted values of the explanatory variables are used.

Model
$/DM $/E $/Yen
Horizon MAE RMSE MAE RMSE MAE RMSE
Random Walk
model 1 2.2 3.0 2.0 2.6 2.3 3.2
3 4.0 5.2 4.1 5.2 4.7 6.2
12 10.1 11.7 10.1 11.5 13.2 16.1
36 24.2 26.2 18.8 21.2 24.8 28.1
(a), a3» ay» ) (-5, -1, 4, 1.0) (-.5, -1, 4, 0) (-5., -3, ll,
Dornbusch-Frankel 1 2.4 3.2 14.0 17.3 2.9 4.2
model 3 4.6 5.7 14.7 18.0 6.6 8.6
(with best 12 7.3 10.9 17.5 20.1 12.4 16.0
parameter con- 36 12.4 19.1 9.0 10.8 17.0 18.7
figuration)
Unconstrained
VAR model 1 5.2 6.3 5.4 6.3 4.9 6.4
3 7.9 9.5 8.0 9.6 7.4 9.5
12 11.1 13.2 17.3 19.3 15.9 19.6
36 16.9 18.5 39.5 44.8 37.5 40.6

MAE (mean absolute error) and RMSE (root mean squared error) are approximately in
percentage terms, since forecasts are for the logarithm of the exchange rate.

Forecasts are compared over the period June 1975-June 1981.


-51-

Table 8

Comparing the random walk model and the structural models

(with their best representative parameter configurations)

when realized values of the explanatory variables are used,

Model

(with best
parameter
configurations)

Random Walk
model

(ays ag» p)

Frenkel-Bilson

(ay> a3» a,» P)

Dornbusch-Frankel
model

(ays Ag+ ay» ass 6)

Hooper-Morton
model

1

3
12
36

$/DM

Horizon MAE RMSE
1 2.4 3.2
3 4.8 6.2
12 9.4 10.9
36 18.1 21.0
(-.5, 4.5, .4)

1 9.1 11.4
3 11.5 14.2
12 12.2 15.2
36 12.6 17.0
(-.85, -l, 6,

1 5.5 6.9
3 8.1 9.7
12 8.8 10.8
36 8.2 10.5

(-.5, -1, 7, .005, 0)

10.4
11.0
11.6
11.6

00MM
WN Ow

S/E
RMSE

NB
UPuN
PUBL

Pee
WAH D
ODE

+4) (-.5, -1, 4, 0)

10.0
10.5
12.3
10.0

0 OMe
Whar

(-.5, -1, 4, .005, 0)

ind

=

$/Yen

MAE RMSE
2.1 3.0.
4.2 5.7
0.6 13.8
9.4 23.3
(-.5, 4.5, .8)
4.5 6.4
7.9 11.5
9.7 13.3
0.2 14.5
(-.5, -1, 9, .8)
4.4 8.4
7.4 9.4
7.0 8.5
8.8 10.2
(-1, -1, 9, .003, 8)

wwmor
Wowo
bee

NEOO
NNoON

MAE (mean absolute: error) and RMSE (root mean squared error) are approximately

in percentage terms, since "forecasts" are for the logarithm of the exchange

rate.

Forecasts are compared over the period March 1973-June 1981.


-23-
Footnotes

Vthe authors have benefited from the comments and suggestions of

Jeffrey Frankel, Robert Flood, Robert Hodrick, Peter Hooper, Peter Isard, and
Julio Rotemberg. We are indebted to Julie Withers and Tamara McKann for
excellent research assistance. This paper represents the views of the
authors and snould not be interpreted as reflectiny the views of the Board of

Governors of the Federal Reserve Systeia or other members of its staff.

2 the structural models are described here in section 3 below. It

should be noted that all the models considered are derivatives of the
Monetary or asset approach in that they specify real money demand at home and
abruad as a function of real income, short-term interest rates and possibly
wealth. The random walk iwodel predicts that today's exchange rate will

obtain at all future dates.

in a study of the dollar/pound rate, Hacche and Townend (1981) use
different methods to arrive at a similar conclusion; that the models do a
very poor job of explaining the dollar/pound rate. The present study

exaitines the three bilateral dollar rates and also cross-rates.

the assuuption that U.S. and foreign variables enter exchange rate

equation systems with equal but opposite signs is relaxed later in a limited
number of experiments on tne structural models. Economizing on variables in
the otherwise highly paraneterized VAR systeus is quite important, so we only

estimate the VAR models with the relative variables.


-41-

Industrial Production

Data Source: 0.E.C.D., 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 Supplies

Tata 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 millions of
pounds. The reserve-adjusted monetary base is calculated
in millions of pounds as total currency in circulation
plus bankers' deposits.

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

Trade Balance

Data Source: 0O.E.C.D., Main Economic Indicators.

Series: Trade balance (f.o.b. - c.i.f.) in millions of pounds.

Description: Monthly data.

United States

With the exception of the trade balance statistics, all data are taken

from the Federal Reserve Board data base. Many of these series are published

in the Federal Reserve Bulletin, and all are available to the public.


n across all (seven) equations is estimated using Parzen's (1975) lag length
selection criterion!
We estimate the VAR model for the dollar/imark, dollar/pound, and

dollar/yen exchange rates over the floating rate period; the data consist of
monthly observations for March 1973 through June 1981 (our seasonal adjustment
procedures are described in the data appendix). Once having obtained the
coefficient estimates, the dynamic interactions among the variables 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 terms of the disturbances or innovations [:the
Wit in (1) for example]. Studying the MA representation is complicated

by the fact that the disturbance tems in the MA (or AR) representation are in
general contemporaneously correlated; see Sims (1980) or Fischer (1981). So
in order to simulate a "typical" shock to a given variable it is necessary to
recognize that the expectation of other disturbances in the system,
conditional on the particular shock of interest, are usually nonzero.
Unfortunately, for two correlated disturbances z(t) and Zo(t), if the
ELzy(t)| Zo(t) = 1] =a, a an arbitrary constant, it is not in general

true that ELz9(t)| z1(t) = aj] = 1. Because of this fact, there is no

unique way to simulate "typical" shocks to these systems of endogenous
variables when contemporaneous variable interactions are present. (In cther
words, when the covariance matrix of the disturbance terms is nondiagonal.)

In order to identify a typical shock to the VAR system with a particular
variable, we will follow the Sims’ (1980) procedure of specifying a variable
ordering a priori. The variable ordering essentially specifies that the first

variable is predetermined with respect to all other variables, that the second


-34-

Technical Appendix

In this appendix we describe the triangularization of the VAR system
used in section 2 to analyze the dynamic effects of an innovation to a
particular variable. First suppose the t-th observation of the VAR is

represented by

(Al) Ely = ACL) ye = Ups

where LIy - A(L)J is a inatrix polynomial in the lag operator L, Ye is
the N x 1 vector of variables in the system, E(uy) = 0, and Var(ut) ad,
positive definite. Using the Cholesky factorization V = WW' » Where W is
lower triangular, we can transfor (Al) to the system

1

-1 aoe _
(A2) WwW {ly - A(L) Jy, =W Ub = ep>

where E(e,) = 9 and VAR(e,) = Iy, the order N identity matrix. Since
wl is also lower triangular, the system (AZ) is recursive as described

in the text. The moving average representation of (A2) is

(93) yy = Ly - ALT Weg,
aid in this expression the contemporaneous value of the first component: of
@ enters all N equations, the contemporaneous value of the second component
of e enters the last N-1 equations, etc. Because the decomposition of V is

not unique, studying the effect of the uncorrelated innovations ey, ON ve

will depend on the variable ordering unless V is diagonal, i.e. unless the


-20-

incorporate movements in the long-run PPP level of the exchange rate by
assuming that these movements take place in response to unanticipated trade
balance (current account) deficits or surpluses. While short-run PPP does
not provide an accurate characterization of the 1970's ,2V/ there is no
strong evidence that the long-run PPP level of the exchange rate changed
significantly. The results in Meese and Rogoff (1982) suggest also that
although the deviations from PPP damp quite slowly, the rate at which they
damp is relatively stable.

The performance of the Dornbusch-Frankel and Hooper-Morton models are
potentially quite sensitive to the use of a variable other than the long-term
interest differential as a proxy for the long-run expected inflation

- differential. Although we did not find a proxy which yielded better results
[see footnote (15)], this issue merits further attention.

However, the major problem with the structural models considered here
may be the instability of the underlying money demand specifications. The
recent breakdown of U.S. money demand relationships was first noted by
Goldfeld (1976) and is documented extensively by Simpson and Porter (1980).
Conventional empirical money demand specifications such as equations (4) of
section 3 have consistently underpredicted U.S. Ml velocity since mid-1974.
For this reason, the present study uses MI-B, for which the systematic bias
over the sample period is much smaller, and the new definition of M2, for
which the bias is negligible. But equations (4) still fail to predict these
aggregates or the reserve-adjusted base with any notable deyree of precision.
As reported above, our exchanye rate experiment results are not sensitive to
which of these aggregates (together with their respective foreign _

counterparts) we employ.


~26-

though, given the endogeneity of the explanatory variables indicated by the
VAR's in section 2. In fact, if the variance of the error term is larye and
its (unknown) covariance with the relevant linear combination of the
explanatory variables (the "fundaiientals") negative, our ex-post forecaster
need not dominate optimal ex-ante forecasters. In this perverse case,
knowing that the realized fundamentals suyyest a higner exchange rate means

that you should guess a lower excnanye rate.

1/the results for the Dornbusch-Frankel and Hooper-Morton models

reported in Tables 7-10 are obtained using long-term interest differentials
as a proxy for expected long-run inflation differentials. It is important to
recognize that these models are potentially quite sensitive to this variable.
However, using instead current-period inflation differentials, a moving
averaye of past inflation differentials, or future inflation differentials,
yields qualitatively similar results in the ex-post forecasting experi uwents
(Tables 7 and 8). We did not try these other proxies in the expensive

ex-ante experiments (Tables 9 and 10).

IH ot k = 1, «++, 36 denote tie forecast step, Ny the total number
of forecasts in the projection period for which the actual value A(t) is
known, F(t) denote the forecast value, and let forecasting beyin in period
(t+]). Define

Nv -1

Mean absolute error = *z [F(t +s +k) - A(t +s +k) | 7,
s=0

Nol 2) 1/2
Root wean square error “¢ zLF(t +s +k) - A(t +s +k)] ini}
s=0


5. Conclusions

The unimpressive out-of-sample performance of the Frenkel-Bilson,
Dornbusch-Frankel and Hooper-Morton empirical exchange rate models cannot be
attributed to inconsistent or inefficient parameter estimates. These models
fail to yield any improvement over the random walk model in mean absclute or
root mean squared error one to twelve months out of sample for a broed range
of theoretically plausible coefficient values even when autoregressive error
terms are introduced. Thus it is unlikely that sore efficient estimation
techniques, such as imposing all the cross-equation rational expectations
restrictions, will yield parameter estimates which do vetter.23/ The
coefficient-constrained models do prevail at longer horizons but in an
unstable fashion; the best coefficient values bounce around depending on the
forecast horizon.24/

Wnile the breakdown of empirical exchange rate models may be due to
volatile time-varying risk premia, volatile long-run real exchange rates, or
poor measurement of inflationary expectations, the main problems appear to
lie in their ioney demand specifications. If this is the case, then the same
improvements which resuscitate domestic empirical woney demand equations

should lead to great improvements in empirical exciiange rate equations as

well.


=35-

system (2) has no contemporaneous interactions among variables.

Expression (A3) is also used to construct the variance decompositions
of tables 1-6. Since all components of et have unit variance, the variance
of Yit (the i-th element of the vector Yt) is tne sun of squares of
the elements in the i-th row of [Ty - A(L) Tw. The percentage of the
forecast error variance of Yit explained by the j-th innovation eit

(the j-th element in the vector et) is calculated as the ratio of the sum

of squares of the (i, j) element of []y- AL) Iw to the variance of

Vit


-17-

horizons of twelve months or more--longer than we could exatine in our study
based on estimated coefficients--the RMSE and MAE of the models do sometimes
improve on the random walk model. This result is tempered by the fact that
the minimum RMSE or MAE coefficient configurations bounce around at different
forecasting horizons. Still the percentage of the parameter grids which
improve on the random walk model does increase with forecast horizon.

Overall these essentially in-sample results--in-sample, because not all
coefficient configurations improve on the random walk model--must be
interpreted with caution.

Table 8 presents best representative parameter values for each of the
models, toyether with their corresponding RMSE and nae Ll/ These two
statistics are also given for the random walk model. At 36 months, the best
representative coefficient values for the Dornbusch-Frankel and Hooper-Morton
models clo about 50% better than the random walk model in RMSE and MAE; the
Frenkel-Bilson model only does about 30% better.

Since the models do not forecast well at short horizons in the ex-post
experiment, it is not surprising that the one model considered in the ex-ante
experiment does poorly at short horizons as wel) 28/ Tables 9 and 10
present results for ex-ante forecasting experiment with the Dornbusch-Frankel
model. No parameterization of that model ever improves on the random walk
model in MAE for horizons under 12 months; the threshold horizon is even
longer when RMSE is the metric. Furthemnore, for the dollar/pound and
dollar/ven exchange rates, over 90% of the parameter grids fail to beat the
random walk model in MAE or RMSE at any horizon. It is true, however, that

at 36 months the best representative Dornbusch-Frankel model performs almost


3a. The representative structural models

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

specification below:

2 _ + * \ * * e *e
(2) S = a ay(m- m) + an(y - y) + ag(ry - re) + ag(m -1

*

+ a5(TB - TB) + u,

where (r® = x) is the expected lony-tenn inflation differential, TB
and i are the cumulated U.S. and foreign trade balances, u is a disturbance
term, and the other variables are as defined in section 2 above. In (2) we
have imposed the usual constraint that domestic and foreign variables affect
the exchanje rate with coefficients of equal but opposite sign; this constraint
is relaxed in a limited number of experiments both here and in our earlier

study 3

We choose not to specify an ad-hoc lagged adjustient mechanisi
in (2), preferring to model the dynamics using an autoregressive error term as
described below.

All three models hypothesize first-deyree homogeneity of the exchange
rate with respect to relative imoney supplies, or a; = 1. The Frenkel-Bilson,
or flexible-price monetary model, formed by differencing two identical money
demand specificatiuns while imposing purchasing power parity (PPP), posits tne

additional coefficient restrictions ay < 0, a3 > 0, ag = a5 = 0.


~32-

Haynes, Stephen E. and Stone, Joe A. 1981. On the mark: Comment.

American Economic Review 71: 1060-67.

Hooper, Peter and Morton, John E. 1982. Fluctuations in the dollar: Pp

model of nominal and real exchange rate determination. Forthconing in

the Journal of International Money and Finance.

Isard, Peter. 1977. How far can we push the law of one price? American

Economic Review 67: 942-48,

Meese, Richard A. and Sinyleton, Kenneth J. 1980. Rational expectations,
risk premia, and the market for spot and forward exchange.

International Finance Discussion Papers no. 165. Board of Governors

of the Federal Reserve System.
Meese, Richard A. and Rogoff, Kenneth S. 198]. Empirical exchange rate
models of the seventies: Are any fit to survive? International _

Finance Discussion Papers no. 184. Board of Governors of the Federal

Reserve Systen.

- 1982. The sources of terns of trade instability: An

empirical analysis. Mimeograph. Board of Governors of the Federal

Reserve Systen.

Miller, Merton and Orr, Daniel. 1966. A model of the demand for money by

firms. Quarterly Journal of Economics 80: 413-35.

Parzen, Emanuel. 1975. Multiple time series: Determining the order of
approximating autoregressive schemes. Technical Report no. 23. State

University of New York at Buffalo.


-29-

References

Barro, Robert J. 1976. Integral constraints and aggregation in an inventory

model of money demand. Journal of Finance 31: 77-88.

Baumol, William. 1952. The transactions demand for cash--an

inventory-theoretic approach. Quarterly Journal of Economics 66:

545-56.

Bilson, John F.0. 1978. Rational expectations and the exchange rate. In”

J. Frenkel and H. Johnson, eds., The economics of exchange rates.

Reading: Addison-Wesley Press.

. 1979. Tne deutsche mark/dollar rate -- A monetary analysis.

In K. Brunner and A. Meltzer, eds., Policies for employment, prices and

exchange rates. Carnegie-Rochester conference volume 11. Amsterdam:

North Holland Publishing Company.

- 1981. The "speculative efficiency" hypothesis. Journal of

business 54: 435-51.

Chow, Gregory C. 1960. Tests of equality between sets of coefficients in

two linear reyressions. Econometrica 28: 591-605.

Cumby, Robert and Obstfeld, Maurice. 1981. A note on exchange-rate
expectations and nominal interest differentials. The Journal of

Finance 36: 697-703.

Dornbusch, Rudiyer. 1976a. The tieory of flexible exchange rate regimes and

macroeconomic policy. Scandinavian Journal of Economics 78: 255-75.

- 1976b. Expectations and exchange rate dynamics.

vJourna! of Political Economy 84: 1161-76.



observations apply to the U.S.-U.K. and U.S.-Japanese VAR systems.

A second important observation to be made from tables 1-6 is that no
variable appears to be exogenous to the VAR system. Abstracting froin
coefficient uncertainty, an exogenous variable would manifest itself as
follows: at all horizons a variable's own innovations would account for all
of its forecast error variance, so there would be a one in the column
corresponding to a variable's own innovation and zeros elsewhere. (Block
exogeneity is the odvious smultivariate generalization. )o/ In the
U.S.-German VAR the exchange rate, relative incomes, the long-term interest
differential, and tie German and U.S. trade balances all appear to have large
exogenous components, since for both variable orderings and all horizons
(1-36 months) own innovations in these variables explain at least 48%, 55%,
50%, 59%, and 65% of their respective forecast error variances. For the
U.S.-U.K. VAR, own innovations in the exchange rate, the U.K. and U.S. trade
balances, and the long-term interest differential account for most of he
forecast error variance of these variables. In the U.S.-Japanese system, it
is the exchange rate, the Japanese and U.S. trade balances, and relative
incomes that have this property.

The last feature of tables 1-6 that we wish to emphasize concerns the
difference between those factors which appear to explain the forecast error
variance of the three bilateral exchanye rates at snort horizons (1-3 1ionths)
as opposed to longer horizons (1-3 years). Based on the numbers reported in
these tables it is clear that own innovations in exchange rates explain a
large fraction of the exchanye rate forecast error variance at one and three

month forecast horizons, while innovations in the other variables become


variable is predetermined with respect to all but the first, etc. The
identification of the VAR systems is pursued in greater detail in the
technical appendix.

The multi-horizon forecast error variance decompositions listed in
tables 1-3 are based on a variable ordering with the logarithm of U.S. to
foreign relative money supplies min first, followed by the logarithm of
relative outputs y-y, the short-term interest differential
ro te the long-term interest differential ro re the
U.S. and foreign trade balances T8 and Tb, and the loyarithn of the
dollar price of foreign currency s. In tables 4-6 the variable ordering is
reversed. In the U.S.-German system, the laryest estimated contemporaneous
correlation is 44% between the short and long-term interest differential
equations. The other estimated contemporaneous correlations range from 5 to
20%. These results suggest that the variable ordering is potentially
important in the U.S.-Gennan VAR system. And indeed there are some
differences between the U.S.-Gernian VAR systems, regular versus reverse
order, at both short and long forecast horizons. Note that in the regular
(reverse) order system, exchange rate and long-term interest rate innovations
account for 78.6% (93.7%) and 12.8% (4.9%) of the one-month-ahead forecast
error variance of the exchanye rate, and 48.1% (60.1%) and 15.4% (10.5%) of
the 36-month-ahead forecast error variance of the exchange rate. However,
the significance of these differences cannot be ascertained from tables 1 and
4. We have not yet performed the requisite (expensive) stochastic
simulations to obtain estimates of the dispersion of these forecast error
variance decoipositions. Of course, the data necessarily contain less

information about long-run variable interactions than short-run. Similar


-18-

as well in the ex-ante experiient as the best representative
Dornbusch-Frankel model in the ex-post experiment; compare tables 8 and 10.
Ayain, we should emphasize that the evidence presented here on the possible
forecasting superiority of the structural models is essentially in-sample,
since not all confiyurations of the parameter constraints improve on the
random walk model.

Also reported in Table 10 are the forecasting properties of the
seven-variable VAR system of section 2. This model, estimated by rolling
regressions, is a true ex-ante forecaster. The VAR outforecasts the random
walk model at three-year horizons for the dollar/DM rate. It does worse at
one-year horizons for that exchange rate, though, and worse at all horizons
for the dollar/pound and dollar/yen exchange rates. It is possible that
these results can improved by imposing probabilistic priors on the VAR; see
Litterman (1979). (An identified structural inodel such as the
Dornbusch-Frankel model can be thought of as a VAR with a priori

restrictions.)


3. Predicting and Explaining the Exchange Rate Out of Sample Using _
Structural Models with Constrained Coefficients

Elsewhere [Meese-Rogoff (1981)] we employ rolling regressions to
construct out-of-sample forecasts of the exchange rate using three structural
models: a flexible-price monetary model (Frenkel-Bilson), a sticky*pvice
monetary model (Dornbusch-Frankel), and a sticky-price asset model which
incorporates the trade balance (Hooper-Morton) _/ The fact that these
structural models do not outperfonn the random walk model at horizons of one
to twelve months cannot be attributed to the inherent unpredictability of the
explanatory variables; this uncertainty is purged from the forecasts by using
realized explanatory variable values. Still, there remains the possibility
that our small-sauple results can be attributed to poor parameter estimates
rather than specification error. This possibility is especially worrisome in
light of the estimated VAR models presented in the previous section. They
indicate that it is difficult to find legitimate exogenous variables in the
three structural exchange rate models. If this is the case, then consistent
coefficient estimation becomes problematic and requires a priori knowledge of
the serial correlation process of the error terms. These possible estimation
problems may explain why the instrumental variables techniques implemented in
our other study do not yield better results than ordinary least squares.

Here we explore a range of constrained-coefficient models and present
evidence that our other results concerning one to twelve month forecast
horizons cannot be explained by coefficient uncertainty. In addition, since
the coefficient-constrained models do not require a significant portion of
the limited floating-rate data set for estimation, we are able to look at

longer forecast horizons.


-24-

parzen's (1975) criterion selects an order 2* which ininimizes

cAT(2) = trace(# v5 - vi). 2=1,2, 04,

Mp4 zo

J
where N is the number of variables in the VAR, T is sample size, L is the
waximal order considered, and Vy is an estimate (adjusted for deyrees of
freedom) of the covariance matrix of disturbances for the imodel with 2 lags
of each variable. Asymptotically, the order selected is never less than the

true order, assuming the true order is finite.

Vin Meese-Rogoff (1981), the block exogeneity assumptions of the

Dornbusch-Frankel sodel are formally tested.

see Bilson (1978, 1979), Frenkel (1976), Dornbusch (1976b), Frankel

(1979, 1981), and Hooper and Morton (1982). The identification of particular
empirical models with authors who contributed significantly to their
development follows one conventional nomenclature. It is relevant to note,
however, that several of these sate authors have analyzed more than one of
the three models. For example, Frenkel (1981b) discusses a sticky-price
model, and emphasizes that the flexible-price model is a limiting
approximation which is applicable in a highly inflationary environment.
Dornbusch (1976a) exainines a flexible-price monetary model with traded and

nontraded goods.

8/aynes and Stone (1981) suggest .that a problem with the
representative structural models we consider is the restriction of equal but
opposite coefficients on domestic and fureiyn variables. In Meese-Rogoff

(1981), relaxing this restriction by lettiny certain domestic and foreign


International Finance Discussion Papers
Number 204

March 1982

TEE OUT-OF-SAMPLE FAILURE OF EMPIRICAL EXCHANGE RATE MODELS:
SAMPLING ERROR OR MISSPECIFICATION?

by

Richard Meese and Kenneth Rogoff

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished material)
should be cleared with the author or authors.


Forecast error
variance in

*
m-m

TB

-47-

Table 4

Unconstrained U.S.-German VAR, March 1973-June 1981,
reverse variable order

Proportions of forecast error variance k months
ahead attributable to each innovation

k m-m
1 +703
3 +522
12 281
36 2243
1 011
3 -009
12 014
36 015
1 -011
3 -008
12 +014
36 -015
1 +000
+013

12 +080
36 +081
1 011
3 -014
12 +017
36 .018
1 +001
3 003
12 .003
36 -008
1 001
3 +013
12 +056

36 -073

y-y

-017
011
024
022

-868
2779
-580
+558

+016
+013
.018
-018

.000
-068
2145
-140

+036
-053
+070
+069

-014
+025
+050
+047

+005
-007
+013
-013

Innovation in:
®
ri-r
ss

«111
-138
081
-067

-007
-014
+049
-050

522
+343
+232
+222

-002
023
-014
-015

-000
-008
+024
2025

-001
+009
+034
+035

-001
+001
+001
.002

ry-Ty TB

+047 +042
.191 025
-298 -020
-287 026
+018 -068
-068 +057
+048 +075
+146 +076
+350 +013
-333 -083
+279 085
272 -084
+963 -008
-848 -014
-663 048
+647 -051
+006 +918
006 -873
-032 +757
-036 -733
+019 028
016 +023
+023 +024
+028 +024
+049 +004
-068 +045
-060 024
+105 116

+017
-058
~264
~264

020
+059
094
-095

+085
+115
+353
+343

.002
.017
-023
.028

005
022
+032
-036

+932
-906
+750
721

+003
-007
+054
091

-062
+054
+032
+089

+009
-013
-096
-059

-002
+004
.019
047

024
.026
-027
-038

-023
+023
-068
-083

004
-017
.117
+137

.937
.859
-690
+601


-l1-

Frankel demonstrates that augnented regressive expectations are

rational 2

- *
(6) styy > Sp = 80S = 8), + (wo - we)

e
tt]

based on period t information. Substituting (3) into (6) for §, and also

where s is the exchange rate expected to prevail at time tt]
imposing uncovered interest parity by substituting r, - t, for
seal - St, one arrives at the quasi-reduced form of the

Dornbusch-Frankel sodel:

(1) se a4 (m= tt) = Oy =H) -P (rg = Fe) + EH adn ~ 8) AY

So in the Vornbusch-Frankel model a3, the coefficient on the short-tera
interest differential r. - Ts does not depend on the nominal

interest rate semi-elasticity of the demand for real balances 4. Rather it
depends on the negative of the inverse of 9, tne coefficient on excess demand
in the price adjustment equation. The coefficient on the expected long-run
inflation differential, ag, is the sum of 1/6 and d.

The Hooper-Horton trade-weighted dollar model imposes the same
constraints as the Dornbusch-Frankel model, except that it allows
unanticipated shocks to the U.S. trade balance tu affect the PPP or long-run
real level of the exchanye rate. In our bilateral version of their model,
incipient trend U.S. trade balance surpluses require an appreciation of the
Jony-run real exchanye rate, while incipient trend foreign surpluses require
a depreciation. Thus, as <0. It should be noted that the random walk

wodel is also subsumed in the general specification (2). That model is given


-10-

The Dornbusch-Frankel, or sticky-price monetary inodel also
hypothesizes that the coefficient on relative incomes ap > 0, but in
contrast to the Frenkel-&ilson model hypothesizes that the coefficient on the
short-term interest differential ag < QO, and that the coefficient on tie
long-term expected inflation differential aq > 0. The derivation of tnese
coefficient restrictions is exposited in Frankel (1979). The principal
theoretical difference between the Frenkel-Bilson :nodel and the
Dornbusch-Frankel model is that the latter allows for short-run deviations
from purchasing power parity due to sticky domestic prices. Prices adjust
only gradually, in response to both excess demand, which depends on the terias
of trade, and to secular inflation differentials [n® - 7° in equation
(2)]. The long-run or flexible price exchanye rate § is derived in the
same tanner as s in the Frenkel-Bilson model except that it depends on
n® - 7°, which is equal to the long-run short-term interest

differential:

(3) Ss -a + (m= ia) - Bly - ¥) + alae - 48),

Using money demand functions of the fona

(4a) a-p

"
Q
'

Are + by

* *

* *
(40) m-pta- Are - By,
and a price adjustment equation of the form

(5) (P= Pagy - (P= Ble = (8 - p+ Pet (x? = 3),


-43-

Adjustment: 1973 statistics are adjusted to a F.A.S. vaiue basis
using the 1974 average ratio of Customs Valuation to
F.A.S. value.
1979-1931 Data:

Data Source: Department of Commerce, Summary of U.S. Export and Import

Merchandise Trade, December 1980 (advance statistics

for Highlights of U.S. Export and Import Trade), Exports

Table 3; Imports Table 5.

Series: Total domestic exports, excluding Department of Defense
grant-aid, in millions of $ on a F.A.S. value basis;
General imports in millions of $ on a F.A.S. value basis.

Description: Monthly data.


-31-

Glaessner, Thomas. 1982. Theoretical and empirical essays on spot and
forward exchange rate determination. Ph.D Diss., University of
Virginia.

Goldfeld, Stephen MN. and Quandt, Richard £. 1965. Some tests for

homoscedasticity. Journal of the American Statistical Association 60:

539-47.

Goldfeld, Stephen 11. 1973. The demand for money revisited. In Artnur Ckun

and Georye Perry, eds., Brookinys papers on economic activity 3.

washington: The Brookings Institution.

. 1976. The case of the missing money. In Arthur Okun and

George Perry, eds., Brookings papers on economic activity 3.

Washington: The Brookings Institution.

Hacche, Graham and Townend, John. 1981. Exchange rates and imonetary
policy: Modeling sterling's effective exchange rate, 1972-80. In

WW. Eltis and P. Sinclair, eds., The money supply and the exchange

vate. Oxford: Oxford University Press.

Hakkio, Craig S. 1981. Expectations and the forward exchange rate.

International Economic Review 22: 663-78.

Hansen, Lars P. and Hodrick, Robert J. 1980a. Forward exchange rates as
optimal predictions of future spot rates: an econometric analysis.

Journal of Political Economy 88: 829-53.

- 1980b. Speculation and forward foreign exchange rates:
Some tests of cross-currency restrictions. Mimeoyraph.

Carneyie-lNellon University.


Forecast error
variance in

*
n-m

TB

-48-

Table 5

Unconstrained U.S.-Japan VAR, March 1973-June 1981
reverse variable order

Proportions of forecast error variance k months
ahead attributable to each innovation

n-m

+749
686
+394
+271

-000
+003
-014
+014

+011
-056
-046
+052

-009
+134
+151
-193

+006
+006
+009
-010

-012
+008
-017
-019

-001
+004
+009
+016

y-y

+106
+178
+396
469

898
+857
693
658

-001
-001
+017
+020

+003
-002
029
-068

+016
-017
.017
+029

008
-013
-035
-038

-000
+000
-001
-002

Innovation in:
.
ro-r
ss

028
+020
+023
+045

-058
+050
-073
+068

+505
+503
+308
+273

+000
+017
+032
-035

+005
041
+072
+075

+000
-008
-058
-053

+002
+004
+024
027

UL
060
-039
045
066

-002
-016
-088
+090

+417
«274
134
117

+826
-599
+304
+283

+007
+006
-010
+012

-001
-003
-006
-012

-020
+014
+017
-016

TB

-013
+034
+064
.051

+015
+014
-016
+028

016
022
-052
-107

+012
-026
+133
+148

842
-800
+672
+622

+033
+046
119
-131

.000
024
+137
2175

-036
2024
049
051

-019
+044
+092
-O71

+049
+124
+320
+302

+122
-118
.105
«097

-009
«010
«114
«131

928
906
«739
.601

001
012
042
088

-010
-019
+024
+045

+009
+015
022
-071

-001
+020
+124
-130

+026
-109
+246
-226

2115
119
+105
-120

-018
+016
+026
-146

+976
-942
+739
-676


-30-

Driskell, Robert A. and Sheffrin, Steven M. 1981. On the mark: Comment.

American Economic Review 71: 1068-74.

Fischer, Stanley. 1981. Relative price variability and inflation in the
United States and Germany. Forthcoming in the European Economic

Review.

Frankel, Jeffrey A. 1979. Un the mark: A theory of floating exchanye

rates based on real interest differentials. American Economic 2eview

69: 610-22.

+ 1981. "On the inark: reply." American Economic Review

71: 1075-82.

Frenkel, Jacob A. 1976. A tonetary approach to the exchange rate:

Doctrinal aspects and empirical evidence. Scandanavian Journal of

Economics 78: 200-24.

+ 198la. The collapse of purchasing power parities during

the 1970's. European Economic Review 16: 145-65.

+ 1981b. Flexible exchange rates, prices, and the role of

news: Lessons from the 1970's. Journal of Political Economy 89:

§65-705.

Genbery, Ilans. 1978. Purchasiny power parity under fixed and flexible

exchange rates. Journal of International Economics 8: 247-76.

Geweke, John and Feige, Edward. 1979. Some joint tests of the efficiency
of markets for forward foreign exchange. Review of Econonlics and_

Statistics 61: 334-41,


-7-

relatively more important at horizons of one and thre years. This result is
not atypical of VARs estimated on macro-economic data; see Fischer (1981).
All of the features of tables 1-6 noted above suggest both (1) the
difficulty in specifying the menu of variables to include in a structural
exchange rate equation, and (2) the problems associated with finding
~ legitimate instruments with which to consistently estimate the parameters of
these mode's. The latter difficulty has led to the constrained-coefficient

methodology of the next section.


-21-

Whether or not money demand instability and/or misspecification is
responsible for the exchange rate results, it is certainly true that the
conventional money demand equation does not work well when expressed in terms
of U.S. minus foreign variables. That equation [(4(a) minus 4(b)] fails Chow
(1960) tests for the stability of the intercept term at four different breaks
in the sample. It also fails Goldfeld-Quandt (1965) tests of homoscedastic
disturbance terms over the same sample breaks.22/

To investigate the possibility that our results are generated solely
by money demand instability in the U.S., we perforined ex-post forecasting
experiments using the Dornbusch-Frankel model on the pound/mark, pound/yen
and yen/mark cross exchange rates. For the case of the yen/nark rate, we
found coefficient values for which the model pulled even with the random walk
model as early as six months. But the subsequent improvement at longer
horizons never exceeded 30%. (The pound/mark and pound/yen cross-rate
results are no better than the results for the various dollar exchange
rates.)

In sum, money demand instability is an important potential explanation
of our results, but further work is needed to demonstrate that time-varying

risk premia, volatile long-run real exchange rates, or poor measurenent of

inflationary expectations are not the dominant problems.


-38-

Monetary Base (Reserve-Adjusted)

Data Source:

Series:

Description:

Money Supplies

Data Source:

Series:

Description:

Deutsche Bundesbank, Monthly Report of the Deutsche

Bundesbank, Table II-1 (components of the unadjusted
monetary base) and Table IV (average reserve ratio).
The unadjusted base is’.calculated in millions of DM as
total Bundesbank assets less the reserve adjustment
balancing asset, foreign and domestic public authority
deposits, SDR allocations, EMCF gold contributions,
liquidity paper liabilities, and "other" liabilities.
The reserve adjustment is made by multiplying the
unadjusted base statistic by [.631 + 3.2/total average
reserve ratio] where .631 = the currency percentage
of the unadjusted base in the base period (January 1980)
and 3.2 = [1-.631] [the total average reserve ratio in
the base period].

Monthly data. Data for components of the unadjusted
base refer to the last banking day of the month. The

average reserve ratio is a monthly average statistic.

Deutsche Bundesbank, Monthly Report of the Deustche

Bundesbank, Table I-2.
Money stock Ml and money stock M2 in millions of DM.
Monthly data. Data refer to the last banking day of

the month.


Adjustment:

Trade Balance
Data Source:
Series:
Description:

Japan

Bond Yields

Data Source:

Series:

Description:

Consumer Prices
Data Source:
Series:

Description:

ere

~39-

¢ he oges Sock Fo 9ve
A break in the series, caused by the introduction of
eh ataeres of
a new method of computation, occurs in December 1973.
The 1973 statistics are adjusted using the ratio of

the new to the old statistic for December 1973.

0.E.C.D., Main Economic Indicators.

Trade balance (f.o.b. - c.i.f.) in billions of DM.

Monthly data.

Data prior to 1981 are taken from Bank of Japan, Economic
Statistics Monthly, Table 71(2). 1981 data are taken
from Planning and Research Department, Tokyo Stock Exchange,

Monthly Statistics Report, Table 8-1.

Yields in percent per annum on listed government bonds
(Tokyo Stock Exchange).
Monthly data. Data refer to the last banking day of the

month.

Bank of Japan, Economic Statistics Monthly, Table 119(1).

General consumer price index for all Japan.

Monthly index.

Industrial Production

Data Source:
Series:

Description:

0.E.C.D., Main Economic Indicators.
Total industrial production.

Monthly index.


-27-

Our use of mean absolute error covers problems that might arise if, as
sugyested by Westerfield (1977), exchange rate changes are drawn fro a
stable Paretian distribution with infinite variance. The mean errors of the
models (not reported) are small relative to mean absolute errors in almost
all cases where p > .2, indicating that the structural models are not siinply

systematically over or underpredicting.

UW The "best" representative set of parameter constraints for each

model in Table 8 is chosen in an ad hoc fashion as the one which comes in
first (also ahead of the random walk model) at the yreatest number of
horizons. The maximuii improvements over the random walk model in MAE or RMSE
at 36 month horizons exhibited by these representative models are as larye as
those exhibited by any other parameter configurations.

Linite only one model is considered in the ex-ante experiment, note

that all three models yield qualitatively equivalent results for the ex-post
experiuient. Also, since the Vornbusch-Frankel model predicts that tie
exchange rate will return in the lony run tu its flexible-price or
Frenkel-Bilson model value, we should a priori expect the performance of both

wwodels at long forecast horizons to be quite similar.

6
Win later versions of the Huoper-Morton inodel this assumption is

relaxed.

20/ See for example Hansen and Hodrick (1980a,b), Cumby and Ubstfeld
(1981), Hakkio (1981), Tryon (1979), Bilson (1981), Meese and Singleton
(1980), or Geweke and Feige (1979). Hansen and Hodrick study this issue in

tiieir paper contained in this volume.


2. Decomposiny the Forecast Error Variance of the Exchange Rate at Long
and Short Horizons

Before proceeding to tests of the representative structural exchange
rate models, we first examine a vector autoregression consisting of the
exchange rate and the explanatory variables of these models: relative money

supplies, relative outputs ,4/

relative short-term and long-tem interest
rates, and trade balances. The VAR is a tool for analyzing the relative
importance of the explanatory variables in exchange rate model forecasts at
both short and long horizons. As a by-product, the VAR also provides
information on whether the conventional exogeneity assumptions used in
estimation of the structural models are appropriate.

A convenient normalization for estimation of the VAR is one in which

the contemporaneous value of each variable is regressed against lagged values

of all the variables; e.g., the exchanye rate equation is given by

(1) Sg * 5p Spy t 8y2Spg tei nSten * BG heed * Bi2%e2 + oe Binkton

+ Uige

where sy is the (logarithm of the) exchange rate at time t and Xj
is a vector of lagged values of the other included variables (listed above).
Expressing the VAR system in the fonn of equation (1) facilitates estimation,
as ordinary least squares equation by equation is an efficient estimation
strategy. This normalization does not, however, preclude contemporaneous
interactions between the variables, as these effects are captured in the

covariance matrix of the disturbance terms Yee The uniform lag length


Forecast error
variance in

*
n-m

TB

-46-
Table 3

Unconstrained U.S.-U.K. VAR, March 1973-June 1981,
regular variable order

Proportions of forecast error variance k months
ahead attributable to each innovation

Innovation in:

k * * * * *
n-m y-y rot, Oty TB TB
1 +911 -023 +059 -001 +006 -001
3 +789 +041 142 -004 +004 +019
12 +398 +058 +292 +052 -004 -140
36 +270 +032 +200 -076 -028 +148
1 009 +820 +039 +012 +026 .027
3 +034 -600 +029 +087 +059 -073
12 +058 +431 019 +138 +066 +183
36 +058 +407 -021 +145 +068 177
1 +047 -018 -880 +034 -001 +019
3 +034 +012 -830 +031 +001 +089
12 +136 -018 +641 +050 -000 +144
36 +159 +017 +600 -060 +002 139
1 +027 -007 +209 +725 +003 -018
3 -026 +032 +190 -637 005 +066
12 -018 -091 149 -528 +025 +050
36 +022 086 -160 496 -036 051
1 +013 +041 +113 +016 +755 -018
3 +014 -050 +126 +069 +634 +057
12 -018 052 117 078 511 082
36 -036 047 105 074 -420 -115
1 -028 -069 052 002 -008 -830
3 +054 +106 +049 +038 +034 +710
12 +118 +128 «044 +068 +030 +596
36 -119 -116 +052 +079 033 555
1 -000 021 +014 +026 +007 +005
3 +001 +018 -008 +038 +008 +035
12 012 -006 -002 .088 048 168

36 +066 +007 058 -099 +059 -150

.000

-000

+011

+138
-148

-044
+049
+143
«203

-010
-008
-015
+045

-926
891
+675
-560


-44-
Table 1

Unconstrained U.S.-German VAR, March 1973-June 1981,
regular variable order

Proportions of forecast error variance k months
ahead attributable to each innovation—

Innovation in:
Forecast error

i i k n ; r z TB H
variance in mn-m y-y Foot, TOT T s
om 1.843 005 132 004 .001 904.011
3.629 .003 +259 029 .019 -.940- .020
12.293 .007 +295 -100 1035 «249.016
360.252 007 -268 122 .037 6.254.061
x
y-y 1.006 942 000 035 -011 = .905. 001
3.006 856 002 010 .008 = .927..001
12.014 646 004 +223 .029-.970— 014
36.015 622 004 1224 .031 = .972, .032
*
rr 1.007 024 .838 .073 .030 -.907-.021
ss 3.011 017 641 080 10974124 .929
12.008 016 491 081 :091 © .282- .030
360.011 017 469 088 .088 = -.276 S051
*
Ty 1.024 .000 -161 +781 :002. 002.030
3.056 054 126 683 .007 128.044
12.152 099 .101 +524 .036 = -.048-— 040
36 0.147 096 -108 -510 -039 = -.052.048
TB 1.080, See 009 005 .769° 01.025
3.078 +144 011 005 -721 014.026
12.068 .167 -010 063 .617 24.050
36.068 .163 010 | 071 596 = -.028-— 063
1B 1.021 034 063% .008 .042 .832- 001
3.024 061 047 012 .036  .813 = .006
12.023 101 037 061 .032. 4676 = .069
36.028 096 040 069 .030 649.086
8 1.041 011 022 .128 .005 006.786
3.077 .008 022 .163 .032 010.687
12.155 034 018 +125 1064 = -.050 553,
360.155 .033 .030 154 .058 = -.090 481
al

Notes for Columns of the table correspond to innovations in a particular variable
tables 1-6: for the specified forecast horizon k = 1, 3, 12, and 36. ‘The rows add

to one because the total forecast error variance attributable to each
variable on the left of the table is allocated across the seven innovations.
Abstracting from coefficient uncertainty, an exogenous variable would
manifest itself as follows: At all horizons a variable's own innovations
would account for all of its forecast error variance, so there would be

a one in the column corresponding to a variable's own innovation and

zeros elsewhere.


-14-

is based on the assumption that between 33% and 100% of today's deviation
from PPP is expected to be eliminated one year hence. This range encompasses
Genberg's (1978) estimates as well as those of Frankel (1979), both of whicn
are based on data for Germany. Since in the Dornbusch-Frankel model the
coefficient on relative short-term interest rates, a3, is equal to -1/6,

our grid of priors for a3 in that model includes -1, -2, and -3 . (The
values for 6 and therefore -1/6 are conceived on an annual basis, since the
short-term interest differentials and expected long-term inflation
differentials in the data set are annualized.) The coefficient on the
expected long-run inflation differential aq is equal to A + 1/6, where -A

is the interest semi-elasticity of ioney demand. The grid of constraints for
aq is 4,7, 9, ll, 13, which includes the minimum and maximum possible
values of + 1/6 given the individual grids of constraints for A and 1/6.
For consistency, we exclude from our overall grid for the Dornbusch-Frankel
fodel combinations of aq and a3 such that aq - a3 is less than 3 or

greater than 10, the bounds on the yrid for i.

The coefficients on the cumulative monthly trade balances (taken as
deviations from trend) in the Hooper-Morton model are based primarily on
Hooper and itorton's work. We assume that a billion dollar U.S. trade
balance surplus above trend level leads, ceterus paribus, to an offsetting
+3 to .5 percent appreciation of the dollar; that is, as is -003 or -.005.

The results reported below are robust to using values of ag of -O1 or .02.
For simplicity, and in order to limit the size of the large grid of
coefficient constraints for the Hooper-Morton model, we assume that a foreiyn
trade balance surplus has an effect on the exchange rate of equal magnitude

but opposite siyn.


-16-

forecasting experiments differ mainly in whether forecasts are generated
using realized values of the explanatory variables (ex-post), or using
predictions of the explanatory variables based on information available at
the time of the forecast (ex-ante) 4/ The other difference is that

ex-ante forecasting begins in June 1975 while ex-post forecasting covers the
entire sample period. The ex-ante experiment requires enough observations
for first-round estimation of the VAR that generates predictions of the
explanatory variables. (Because the ex-ante experiment is quite expensive to
conduct, it is performed only for the Dornbusch-Frankel model.) Otherwise,
the experiments are conducted in identical fashion. Constant terms
corresponding to each constellation of parameter values are estimated using
rolling regressions. The autoregressive component of forecasts made at time
t are based on the period t error term.

The results of the ex-post forecastiny experiment are broadly
characterized in table 7, where the structural model "forecasts" are compared
with the random walk wodel forecasts on the basis of RMSE and
mane 19/16/ For each model and exchanye rate, table 7 reports the
shortest forecast horizon, in months, at which 0.1%, 10%, 25% and 50% of each
model's parameter grid outpredicts the random walk model when realized values
of the explanatory variables are used. Table 7 demonstrates that the results
of Meese-Rogoff (1981) cannot be explained by parameter uncertainty. For the
entire parameter yrid and for all ttiree exchange rates, the structural models
never improve at all, much less significantly, on the random walk model in

MAE or RMSE at forecast horizons less than twelve months. llowever, at


-2-

with which to estimate the structural models, thus motivating the
constrained-coefficient approach of section 3. Section 4 asks which of the
common building blocks of the structural models is most likely to have
failed. It appears that the breakdown of empirical exchange rate equations

is the international counterpart of the breakdown of money demand

specifications.


-37-

Sources of the other data series are discussed below by country.

Germany
Bond Yields

Data Source: Deutsche Bundesbank, Statistical Supplement to the

Monthly Reports of the Deutsche Bundesbank, Series 2,

Securities Statistics, Table 7b.

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

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

Consumer Prices

Data Source: Deutsche Bundesbank, Monthly Report of the Deustche

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

Data Source: O.E.C.D., 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.
(3-month interbank rate).

Description: Daily data.


~25-

variables--incomes, money supplies and cumulated trade balances--enter
equation (2) separately yielded no forecasting improvement. Here we tried
separating the incomes and trade balances, but again found no forecasting

improvement.

Ve is also straightforward to show that deviations from purchasing

power parity caused by monetary shocks are expected to damp at rate 6.

10/Frankel uses both long-term interest differentials and past
inflation differentials as proxies for n® - re, the flexible price or

long-run expected inflation differential.

Ur op the dollar/pound rate we use i3's, since there is no data on M2
for the U.K. The results presented later in this section are based on Ml
(M1-B) data. However, we obtain very similar results with the different

monetary aggregates.

12/ go the Dornbusch-Frankel model, we also experimented with a range
of constraints on p concentrated between .8 and 1. The lowest end of this

range produced the best results.

13/ Recall that the Dornbusch-Frankel and Hooper-Morton imodel grids
exclude combinations of ay and ay incompatible with the range of
constraints specified for the interest rate sewi-elasticity of real money

deinand 2.

Win the absence of greater knowledge about the true underlying
structure than is inherent in equation (2), it is not possible to take
advantaye of any currelation between the error term and the explanatory

variables in generating the ex-post forecasts. Such correlation is likely,


I. Introduction!

A companion study [Meese-Rogoff (1981)] compares the out-of-sample fit
of various structural and time series exchange rate models, and finds that
the random walk node 12! performs as well as any estimated model at one
to twelve month horizons for 1970's dollar/mark, dollar/pound, dollar/yen and
trade-weighted dollar exchange rates .2/ The structural models perform
poorly ever though their forecasts are purged of all uncertainty concerning
the future paths of their explanatory variables by using actual realized
values.

The present study demonstrates that the dismal performance of the
structural models is not attributable to the sample distribution of the
coefficient. estimates. We rule out that explanation by showing that the
models (with autoregressive error terms) perform poorly at one to twelve
month forecast horizons over a wide range of coefficient values. These
values are based on the theoretical and empirical literature on money demand
and purchasing power parity. Since the coefficent-constrained models only
require est:imation of the intercept terms, it is possible to look at longer
forecast horizons here than in our other study. There the relative
superiority of the random walk model over the structural models diminishes as
the forecast horizon approaches twelve months. The present study explores
the possibility that the structural models may improve on the random walk
model forecasts at horizons of twelve to thirty-six months.

The main part of the paper is contained in section 3, which discusses
the coefficient-constrained experiments. In section 2, vector
autoregressions (VAR) are used to identify the factors that influence the

exchange rate over short versus long horizons. The results from the VAR

experiments also highlight the difficulties in finding legitimate instruments


-49-
Table 6

Unconstrained U.S.-U.K. VAR, March 1973-June 1981,
reverse variable order

Proportions of forecast error variance k months
ahead attributable to each innovation

Innovation in:

Forecast error * * * * *
variance in k n-D y-y rots TOT TB TB s
*
nn 1 749 .106 .028 -060 013 -036 .010
3 -686 -178 -020 -039 +034 +024 -019
12 2394 -396 023 049 -064 049 024
36 .271 470 -045 -066 -051 051 045
*
y-y 1 -000 898 -058 -002 015 -019 -009
3 003 857 -050 016 014 044 015
12 014 “693 -073 088 016 092 +022
36 014 -658 068 090 -028 -071 +072
*
ro. 1 011 001 -505 +417 +016 049 -001
3 056 001 -503 2274 +022 024 020
12 +046 -017 -308 134 +052 -320 124
36 2052 -020 2273 117 .107 -302 -130
x. + 1 -009 -003 -000 826 012 122 -026
LL 3 +134 -002 -017 .594 1026 «118 = .109
12 151 -029 -032 «304 .133 105 +246
36 «143 068 +035 .283 148 -097 -226
TB 1 006 -016 005 -007 ~842 -009 115
3 006 017 041 006 -800 -010 119
12 -009 -014 -072 -010 672 114 -105
36 -010 -029 075 012 +622 131 +120
1B 1 012 008 .000 001 033 -928 018
3 -008 013 008 .003 -046 906 -016
12 017 -035 058 +006 119 +739 026
36 -019 038 053 012 -131 -601 -146
s 1 001 .000 -002 -020 -000 .001 976
3 004 -001 -004 014 024 012 +942
12 -009 -001 024 -017 137 -072 739

36 +016 +002 027 -016 +175 -088 .676


-33-

Simpson, Thomas D. and Porter, Richard D. 1980. Some issues involving the
definition and interpretation of the monetary aggregates. In

Controlling monetary aggregates III. Federal Reserve Bank of Boston

conference series no. 23.

Sims, Christopher A. 1980. Macroeconomics and reality. Econometrica 48:

1-48.

Tobin, James. 1956. The interest-elasticity of transactions demand for

cash, Review of Economics and Statistics 38: 241-47.

Tryon, Ralph. 1979. Testing for rational expectations in foreign exchange

markets. International Finance Discussion Papers no. 139. Board of

Governors of the Federal Reserve Syste.

Westerfield, Janice M. 1977. An examination of foreign exchange risk

under fixed and floating rate regimes. Journal of International

Economics 7: 181-200.

Whalen, Edward L. 1966. A rationalization of the precautionary demand for

cash. Quarterly Journal of Economics 80: 314-24.



-42-

Bond Yields
Series: Government bonds with at least 10 years to maturity.
Description: Daily data.

Consumer Prices
Series: Consumer Price Index.
Description: Monthly index.

Industrial Production
Series: Total industrial production.
Description: Monthly index.

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

Monetary Base (Reserve-Adjusted) and Money Supplies
Series: Reserve-adjusted monetary base, M1-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-1; Imports Table I-1.
Series: Domestic and foreign exports, excluding Department of
Defense shipments, in millions of $ on a F.A.S. value
basis; General imports in millions of $ on a Customs
Valuation basis changing to a F.A.S. basis in 1.974.

Description: Monthly data.


-28-

21/tcard (1976), Genberg (1978), and Frenkel (1981a,b) provide

evidence on this point. In this context, it would be useful to reiind the
reader that our identification of particular models with particular authors
oversimplifies the history, development, and application of these models.

[See footnote (7)].

22/ the breaks in the sample at which these stability tests are

conducted are chosen arbitrarily and correspond to (1) June 1974 - the start

of the mature float, (2) November 1976 - the approximate sample midpoint, (3)
November 1978 - the dollar support program, and (4) October 1979 - the change
in Federal Reserve operating procedures. The tests were conducted using all

parameter configurations with the grids for (A, ®) reported in section 3b.

23/ Soe Driskell and Sheffrin (1981) or Glaessner (1982). These more
sophisticated statistical techiques may provide superior expectations

proxies, however.

24/1¢ the true structural model were known, and combined with an
accurate representation of the serial correlation process of the error term,

then such a model would produce minimum MSE forecasts at all horizons.


-12-

Dy a] = a) = a3 = aq = ag = 0, and up = Up] + e,, where

e; is a white noise process.

3b. A description of the coefficient constraints

The least controversial constraint we impose is that aj, the
coefficient on the logarithm of relative money supplies, is unity. While we
shall not consider other values for a;, we do experiment with different
definitions of the money supply; the reserve adjusted base, MI-B, and Mz (in
conjunction with their respective foreign counterparts) /

Widespread agreement is lacking on the values of the other parameters.
For example, there are a range of theoretical and empirical estimates of the
interest and income elasticities of money demand. The quantity theory puts
the income elasticity at one, and the interest elasticity at zero.
Alternatively, the Baumol (1952) - Tobin (1956) inventory theoretic approach,
in its simplest form, can be used to derive an income elasticity of .5 and an
interest elasticity of -.5. Taking into account integer constraints raises
the income elasticity towards one and the interest elasticity towards zero;
see Barro (1976). The Miller-Orr (1966) model of a firm's optimal
cash-management procedures yields an interest elasticity of -.33. Tne “ncome
elasticity suggested by that model ranges from .33 to .67, depending on
whether a rise in income brings a rise in the number of transactions or in
the average size of transactions. The Whalen (1966) model of the
precautionary demand for money also suggests an interest elasticity of -.33.
In addition it yields an income elasticity which depends on how the size
versus frequency of transactions changes as income rises, ranging from .33 to
1. Finally, we consider empirical estimates of the demand for money, for

which Goldfeld's (1973) paper is a standard reference. He estimates the


-50-

Table 7

Shortest forecast horizon (in months) for which at least x% of each

model's parameter grid improves on the random walk model in MAE/RMSE

when realized values of the explanatory variables are used.

Model

Frenkel-Bilson

(Grid size = 150)

Dornbusch-Frankel model

(Grid size = 330)

Hooper-Morton model

(Grid size = 660)

MAE is mean absolute error, RMSE is root mean square error.

Exchange rate:
Metric:

Threshold

a description of the parameter grids.

second row, first column (30).

To read table 7:

$/DM $/E
MAE RMSE MAE RMSE

Months ahead

24 30 18 24
30 30 18 24
30 30 24 30
36 36 30 36
12 18 18 18
18 18 24 24
30 30 30 36
12 18 18 18
18 18 24 24
30 30 30 36

$/Yen
MAE RMSE
12 12
18 18
24 24
36 30
12 12
12 12
12 12
24 18
12 12
12 12
12 18
24 18

The text contains

Consider the entry in the

The earliest forecast horizon at which at least

10% of the monetary model parameter grid can improve on the random walk model in

MAE for the $/DM rate is 30 months out.


-52-

Table 9

Shortest forecast horizon (in months) for which at least x% of the
Dornbusch-Frankel model's parameter grid improves on the random walk model

dn MAE/RMSE when predicted values of the explanatory variables are usea.2/

$/DM $/E $/Yen
MAE RMSE MAE RMSE MAE RMSE
Threshold Months ahead
0-1% 12 24 30 36 12 18
Dornbusch-Frankel
model 10% 12 24 - - - -
(Grid size = 330) 25% 36 36 - - - -

a! the description of table 9 is essentially the same as given for Table 8.
However, in contrast to the experiment of Table 8, in‘which realized values
of the explanatory variables are used to generate forecasts of the exchange
rate, table 9 is based on an experiment in which the explanatory variables

are forecast with a VAR.


-15-

“he final variable for which it is necessary to specify a yrid of
constraints is one which we logically know nothing about-- the error tena

Up. We assume that ut follows a first order autoregressive process:

(8) Up = OUp_y + ey = e/ (0 - pl),

where e, is white noise and L is the lag operator. The yrid for the
autoregressive parameter p is 0, .2, “4, -6, .8, and 1.0 , so both the no
serial correlation case and the first-difference case are covered 2/
The decision to analyze only a first-order autoregressive process is made in
part to limit the size of the parameter grids, but it is also in part
because of the results of our other study. There, optimal linear
combinations of structural models and very general autoregressive time series
models are analyzed. A wide variety of optimal lag length selection criteria
are used in developing the time series components of the forecasts; these
criteria generally select a lay lenyth of one for the univariate models.
Given the ranye of constraints we have Selected, the grid for the
Frenke!-Bilson model contains 150 different combinations of parameters, the
grid for the Dornbusch-Frankel model has 330 elements, and the Hooper-tlorton

model grid has 660 elements ..2/

3c. Results

The yrid of parameter values developed above is now used to perfornn
two basic experiments, designed to compare the structural models to the
random walk todel at forecast horizons of one, three, six, twelve, eighteen,

twenty-four, thirty, and thiry-six months. The "ex-post" and “ex-ante”