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A note on testing the monetary model of theexchange rateMathias Moersch & Dieter NautzPublished online: 07 Oct 2010.

To cite this article: Mathias Moersch & Dieter Nautz (2001) A note on testing the monetary model of the exchangerate, Applied Financial Economics, 11:3, 261-268, DOI: 10.1080/096031001300138654

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A note on testing the monetary model of the

exchange rate

M A T H I A S M O E R S C H and D I E T E R N A U T Z * {

DG Bank, Economics Department, D-60265 Frankfurt /Main, Germany and

Department of Economics, University of Frankfurt, Mertonstr. 17, D-60054

Frankfurt/Main, Germany

In this note an alternative to the widely used reduced± form tests of the monetary

model of the exchange rate is proposed. It is shown that the reduced form approach

rests on implausible parameter restrictions which can be easily avoided by estimating

the long-run money demand functions separately. Moreover, the resulting `struc-

tural’ forecast equation allows an economic interpretation of the various channels

aŒecting the exchange rate in the monetary model. This approach is illustrated with

reference to the DM /Dollar exchange rate where the structural model outperforms

several alternative forecasting strategies out-of-sample.

I . I N T R O D U C T I O N

Renewed interest in the monetary model of exchange rate

determination is due to the fact that recent empirical

research has provided more solid underpinnings for two

of its main assumptions, namely purchasing power parity

(RogoŒ, 1996) and the existence of stable money demand

functions, see e.g. the overview provided in LuÈ tkepohl and

Wolters (1999). M acDonald and Taylor (1991, 1994), using

cointegration techniques, show that the monetary model is

appropriate for modelling exchange rate behaviour in the

long run and demonstrate its usefulness in forecasting

exchange rates. Following MacDonald and Taylor, e.g.

Moosa (1994), Kim and Mo (1995), Diamandis and

Kouretas (1996), and Choudhry and Lawler (1997) provide

further support to the monetary model. In all these papers,

both the cointegration analysis and the exchange rate

forecasts are performed in a reduced system where prices

have been eliminated.

In this note it is shown that this widely used reduced

form approach to the monetary model is not without prob-

lems. The main point is that the reduced form approach

requires implausible restrictions on the parameters of the

exchange rate forecast equation. Moreover, it often leads

to highly implausible estimates of the underlying economic

long-run relations. For example, the number of cointegrat-

ing relations found and the implied estimates of long-run

income and interest elasticities are often at variance with

economic theory. In order to capture these shortcomings of

the reduced form approach, a more `structural’ strategy is

proposed which gives more emphasis on the speci® cation

of the underlying economic long-run relations. This

approach to the monetary model guarantees plausible

long-run relations, and avoids the parameter restrictions

of the reduced form approach. In addition, it leads to a

forecast equation that allows an economic interpretation of

the various channels aŒecting the exchange rate.

The features of the structural approach are illustrated

with reference to the DM /Dollar exchange rate. This

explanatory example shows that this approach gives rise

to a plausible equation for the exchange rate. At the

same time it demonstrates that the forecast equation

implied by the reduced form approach can rest on invalid

parameter restrictions. Finally, out-of-sample forecasts

Applied Financial Economics ISSN 0960± 3107 print/ISSN 1466± 4305 online # 2001 Taylor & Francis Ltd

http:/ /www.tandf.co.uk/journals

Applied Financial Economics, 2001, 11, 261 ± 268

261

*Corresponding author. E-mail: Nautz@ t-online.de

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demonstrate that the structural error correction model out-

performs several alternative forecast strategies, among

them a random walk.

I I . T H E M O N E T A R Y M O D E L :

S T R U C T U R A L V E R S U S R E D U C E D

F O R M

If purchasing power parity (PPP) holds in the long run,

then there is a long-run equilibrium

e ˆ p ¡ p* …1†

where e denotes the log of the exchange rate (expressed as

domestic currency per unit of foreign currency), and p and

p* are the logs of the home and foreign price levels (here

and in the following an asterisk denotes the corresponding

foreign variable). Empirical tests typically involve

cointegration analysis, since the nonstationarity of prices

and exchange rates implies that for PPP to hold Equation 1

is a cointegrating relation, see e.g. Steigerwald (1996).

Following the Engle± Granger representation theorem for

cointegrated time series, long-run PPP implies that the

short run dynamics of the exchange rate are characterized

by an error correction equation where the exchange rate

should adjust to the stationary deviations from PPP. In the

trivariate system …e; p; p*†, this equation can be stated as

¢et ˆ ® ‰e ¡ …p ¡ p*†Št¡1 ‡ lags…¢e; ¢p; ¢p*† ‡ "t …2†

where ‰e ¡ …p ¡ p*†Št¡1 ˆ: ecppp

t¡1 is the error correction term

indicating the observed deviation from long-run PPP.

According to Equation 2, deviations from PPP are the

only economic disequilibria the exchange rate responds

to. Not surprisingly, this adjustment process is too

simplistic to account for the complexity of exchange rate

dynamics, and exchange rate forecasts based on Equation 2

alone typically lead to disappointing results.

The monetary model of exchange rate determination

considers a richer set of economic long-run equilibria.

Assuming stable long-run money demand functions for

the domestic and foreign economy that are linked by

PPP, the basic monetary model relies on three cointegrat-

ing relationships:

m ¡ p ˆ ¬y ‡ ¯i ‡ ecm …3†

m* ¡ p* ˆ ¬*y* ‡ ¯*i* ‡ ecm* …4†

e ˆ p ¡ p* ‡ ecppp …5†

where m ; y, are the logs of money supply and income,

respectively, i is an interest rate measuring the opportunity

cost of holding money, and the ec0s are the stationary

deviations from the corresponding long-run equilibria.

Therefore, it is a distinguishing feature of the monetary

model that the error correction equation for the exchange

rate may involve not only one but three error correction

terms related to the long-run relations stated above:

¢et ˆ ®pppecppp

t¡1 ‡ ®mecmt¡1 ‡ ®m¤ec

m*t¡1

‡ lagged differences ‡ "t …6†

In the spirit of Konishi et al. (1993), the monetary model of

exchange rate determination thus generalizes the usual

partial cointegration framework to a more general

equilibrium setting. It gives further insight into the process

of exchange rate determination if and only if monetary

disequilibria have an impact on the exchange rate, i.e. if

®m 6ˆ 0 or ®m¤ 6ˆ 0. In this case, Equation 2, which ignores

the in¯ uence of money markets, could be misspeci® ed due

to omitted variables and resulting forecasts may be

misleading. Plausible values of the adjustment parameters

are ®ppp < 0; ®m 5 0, and ®m¤ 4 0. For example, if ecm¤

> 0

then there is an excess supply for foreign currency which

should lead to a depreciation and, thus, to a decrease of e.

It is worth emphasizing that the monetary model implies

no additional restrictions on the adjustment parameters in

Equation 6. In particular, there is no reason why the

strength of adjustment towards the three diŒerent mone-

tary long-run relations should be equal, i.e. the absolute

values of ®m , ®m¤ and ®ppp may well diŒer.

A straightforward test of the monetary model therefore

involves testing the signi® cance and sign of the monetary

adjustment parameters ®®m and ®®m¤ in an equation such as

Equation 6. Obviously, the validity of such an exercise

requires a careful estimation of the underlying money

demand functions. However, to date the issue of sensibly

specifying the underlying long-run relations has not

received the attention it deserves in the empirical literature

on the monetary model. In fact, it is usually circumvented

by estimating a so-called reduced form equation of the

monetary model

et ˆ ­ 0 ‡ ­ 1m t ‡ ­ 2m*t ‡ ­ 3yt ‡ ­ 4y*t

‡ ­ 5 it ‡ ­ 6i*t ‡ ut …7†

where both price levels are eliminated by substituting

Equation 5 in (3) ¡ (4). It follows that ­ 1 ˆ ¡­ 2 ˆ 1,

­ 3 ˆ ¬, ­ 4 ˆ ¡¬*, ­ 5 ˆ ¯, and ­ 6 ˆ ¡¯*. Since

ut ˆ ecppp ¡ …ec

m ¡ ecm¤†, it is also implied that Equation

7 is a cointegrating relation if the three basic long-run

relations of the monetary model Equations 3± 5 hold. As

a preliminary test of the monetary model, the presence of

cointegration in the reduced system …e; m ; m*; y; y*; i; i*†has been established for many countries using the cointe-

gration test introduced by Johansen (1988), see e.g.

MacDonald and Taylor (1991, 1994), Moosa (1994), Kim

and Mo (1995), Diamandis and Kouretas (1996), and

Choudhry and Lawler (1997). In these papers, exchange

rate forecasts are made by use of an error correction

262 M. Moersch and D. Nautz

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equation which entails the estimated uut¡1 as single error

correction term.1

Several issues remain unresolved in this type of analysis.

First, even though the cointegration rank of the reduced

system is one, often more than one cointegrating vector is

found. This problem, presumably due to the shortcomings

of the Johansen test in small samples, forces the researcher

to somewhat arbitrarily identify the `relevant’ cointegrating

vector.2

Second, in the reduced form approach, long-run in-

come and interest rate elasticities of two separate money

demand functions are estimated simultaneously in a high-

dimensional system. As a result, the Johansen estimator

may become less reliable in ® nite samples since its exact

distribution does not have ® nite moments, see Phillips

(1994). Therefore, the identi® cation of long-run money

demands has not much chance of success, and long-run

income and interest rate elasticities implied by the

estimated cointegrating relation Equation 7 are usually

highly implausible.

For example, having found three cointegrating vectors

MacDonald and Taylor (1994, p. 283) base their exchange

rate forecasts on the vector which corresponds to the

second largest eigenvalue. They argue that the resulting

equation would not do `great violence’ to the monetary

model, but the implied long-run income elasticity close to

zero for the UK and the incorrectly signed interest rate

eŒect on money demand for the US indicate the problems

of the reduced form approach.

Third, the reduced form approach leads to restrictions

on the adjustment parameters in the error correction

equation of the exchange rate which are not implied by

the monetary model. Since Equation 7 is the only

cointegrating relation in the reduced system, error

correction equations used in the reduced form approach

only include utut as error correction term. Thus, exchange

rate forecasts are based on an equation of the following

form (ignoring lagged diŒerences):

¢et ˆ ®r…ut¡1† ‡ "t ˆ ®r…ecppp ¡ ec

m ‡ ecm* † ‡ "t …8†

Comparing Equation 8 with its structural counterpart

Equation 6 reveals that the adjustment of the exchange

rate is restricted to ®ppp ˆ ¡®m ˆ ®m¤. Thus, the reduced

form approach assumes that the adjustment is of equal

strength for each underlying long-run relation.3

In view of these problems of the reduced form approach,

our more structural approach to the monetary model

emphasizes the sensible speci® cation of the underlying

economic long-run relations. In the following empirical ex-

ample, long-run money demands are therefore estimated

referring to the relevant subsystems …m ; p; y; i† and

…m*; p*; y*; i*†. Moreover, there is an analysis of whether

there are additional, i.e. more than three, long-run relations

in the system. In this example, the expectations hypothesis

of the term structure and uncovered interest parity are

natural candidates. Having established the relevant eco-

nomic long-run relations, the estimated disequilibria are

used to estimate an error correction equation for the

exchange rate such as Equation 6. This approach not

only assures more reliable income and interest rate elasti-

cities, but also aŒords tests of the relative size and import-

ance of the adjustment parameters, thereby addressing

another possible source of misspeci® cation in the exchange

rate forecast equation. Finally, the observed error correc-

tion terms can be explicitly linked to exchange rate move-

ments, thus allowing a clearer economic interpretation.

I I I . A N E M P I R I C A L I L L U S T R A T I O N

Data

Data is quarterly and runs from 83 : 1 until 96 : 3. 96 : 4 to

97 : 3 is set aside for out-of-sample prediction exercises. The

starting date is chosen in order to avoid structural breaks

in the long-run relations due to the monetarist experiment

in the United States and increased capital mobility in

Germany. M oreover, as Nautz (1998) recently emphasized,

there is evidence for marked changes of the German money

supply process since the beginning of the 1980s. Germany

is the home country and e, the exchange rate, is de® ned as

DM /US$. m , the money supply measure for both

countries, is M 1, y, the activity measure is real GDP.

Money, real GDP and the consumer price index p are

seasonally adjusted. For estimating money demand func-

tions, the proper measurement of the opportunity cost for

holding money is critical to obtaining sensible results. In

particular, short- and long-term interest rates may aŒect

Monetary model of the exchange rate 263

1Thus, although the above contributors emphasize the merits of the multivariate Johansen procedure, they basically follow the tradi-

tional two step procedure introduced by Engle and Granger (1987).2

Reinsel and Ahn (1992) therefore suggest a ® nite sample correction of the Johansen test statistic.3

As a referee pointed out, stationarity of ecPPP

, ecm

, ecm* is su� cient for the stationarity of u ˆ ec

PPP ¡ …ecm ¡ ec

m* † but not necessary.

In particular, if ecPPP ¹ I …0† and …ec

m ¡ ecm* † ¹ I …0†, then u ¹ I …0† even if ec

m ¹ I …1† and ecm* ¹ I …1†. Notice however that in this case

the monetary model is still based on two independent cointegrating relations. Therefore, technically speaking, the problems of thereduced form approach where the exchange rate adjusts to only one disequilibrium term remain. Moreover, nonstationarity of ec

m

and ecm*

implies that there are no stable long run money demand functions. Hence the stationarity of ecm ¡ ec

m*would require currency

substitution on a large scale. Yet recent empirical evidence not only suggests that e.g. German money demand is stable (see e.g. Wolters

et al. (1998) or LuÈ tkepohl et al. (1999)) but also that currency substitution is not a crucial factor for money demand in Europe, seeDeutsche Bundesbank (1995).

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the rate of return on alternatives to money. We therefore

consider not only the in¯ uence of the German money

market rate (r) and the US federal funds rate (r*) but

also the in¯ uence of the corresponding 10-year bond

rates, denoted by R and R*. All variables except for the

interest rates are entered in logs. All data is from the FERI

Database.

Money demand functions

The money demand functions for the two countries are

estimated using the single-equation conditional error cor-

rection framework introduced by Stock (1987). This

approach has the advantage that it directly includes the

short run dynamics by incorporating lagged diŒerences

and lagged levels in one equation. We regress ¢…m ¡ p†t

on …m ¡ p†t¡1, yt¡1 ; rt¡1 , R t¡1 , all diŒerences of these vari-

ables up to lag order four and an intercept term. Following

Wolters et al. (1998), the shifts in the levels of the German

money and income series due to German uni® cation are

captured by a step-dummy D t which equals one for uni® ed

Germany and zero before. In Germany, income velocities

for broad and narrow money supply show a signi® cant

downward trend. W e therefore included the linear time

trend t as an additional variable.4

Applying a general-to-speci® c procedure, we develop the

following parsimonious dynamic speci® cation for German

money demand:

¢…m ¡ p†t ˆ ¡0:22…2:97†

‰…m ¡ p ¡ y†t¡1 ‡ 2:54R t¡1

¡ 0:00866 …t ¡ 1† ‡ 0:075D t¡1Š

¡ 1:38…2:95†

¢rt¡1 ‡ 0:16…9:16†

¢D t ¡ 1:07…2:92†

‡ ""t …9†

Sample: 83 : 1-96 : 3 ·RR2 ˆ 0:71 LM …1† ˆ 0:09‰0:76Š

Q…12† ˆ 15 :35‰0:22Š HW ˆ 0:99‰0:46Š

Notes: t-values are given in parentheses and p-values in

brackets. LM …1† gives the F -value of the Lagrange

multiplier test against ® rst order serial correlation, Q…12†denotes the Ljung± Box statistic against serial correlation

up to 12th order, and HW belongs to the White± test

against heteroscedasticity.

The diagnostic statistics computed from the residuals

indicate that Equation 9 adequately accounts for serial

correlation and heteroscedasticity. The estimated deviation

from long-run money demand, ececm

, appears in the square

brackets. Equation 9 leads to the following long-run money

demand:

…m ¡ p†t ˆ yt ¡ 2:54R t ¡ 0:075Dt ‡ 0:00866 t ‡ ececm …10†

The estimated coe� cients show plausible signs. Estimating

an unrestricted version of Equation 10, the null hypothesis

that the long-run income elasticity equals one could not be

rejected. In line with BruÈ ggemann and Wolters (1998), we

® nd that it is the bond rate (R) which in¯ uences the

demand for narrow money in the long run. The short-

term rate (r), however, plays an important role in the

money demand’ s short run dynamics. W hen the

Bundesbank determines its yearly money growth targets

for M3, it adds one percentage point to account for the

velocity trend. Similarly, Equation 10 implies a yearly

decrease in M1-velocity of about 3% .

For the United States, using again the general± to ± speci-

® c procedure, we obtain:

¢…m ¡ p†*t ˆ ¡0:79…4:37†

¢R*t¡1 ‡ 0:52…6:21†

¢…m ¡ p†*t¡1

‡ 0:32…3:48†

¢…m ¡ p†*t¡3 ¡ 0:61…4:00†

¡ 0:11…4:00†

‰…m ¡ p ¡ y†*t¡1 ‡ 1:57r*t¡1 Š …11†

Sample: 83 : 1-96 : 3 ·RR2 ˆ 0:77 LM …1† ˆ 0:05‰0:83Š

Q…12† ˆ 14:42‰0:27Š HW ˆ 1:33‰0:25Š

Notes: For further explanation see Equation 9.

where the estimated equilibrium error ececm¤

appears again in

the square brackets. Accordingly, the US long-run money

demand is given by

…m ¡ p†*t ˆ y*t ¡ 1:57r*t ‡ ececm* …12†

In accordance with the results obtained by HoŒman and

Rasche (1996), evidence for a long-run income elasticity of

one was found. Again, the interest rate eŒect is plausibly

signed. However, the role of the interest rates has changed:

in the US equation it is the short-term interest rate which

appears in the long-run relation while the bond rate has

only a short run eŒect.

Purchasing power parity and interest rate diVerentials

As RogoΠ(1996) already emphasized, there is some

evidence for PPP over fairly long time intervals but not

over shorter time spans. According to Fritsche and

Wallace (1997) estimating PPP may thus introduce incor-

rect coe� cient estimates because of an insu� ciently long

sample period. In order to avoid these problems, we tested

the cointegration implications of PPP for an extended

sample starting already in 1975, immediately after the

breakdown of the Bretton± Woods system of ® xed exchange

rates.

264 M. Moersch and D. Nautz

4Wolters et al. (1998) captive the velocity-trend of German M3 by adding the in¯ ation rate in the long-run equation. In this sample,

however, the in¯ ation rate is not signi® cant.

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The results of the cointegration test procedure intro-

duced by Johansen (1988) are summarized in Table 1. In

line with long run PPP the trace statistic indicates that the

cointegration rank of the trivariate system (e; p*; p) equals

one.

In a second step, the parameter restrictions implied by

the long run relation et ˆ pt ¡ p*t are tested. The resulting

likelihood ratio statistic is 6:42 which does not exceed the

5% critical value of the relevant À2

distribution. Thus long

run PPP cannot be rejected and the empirical example pro-

ceeds letting ecpppt ˆ et ‡ p*t ¡ pt.

So far, three independent cointegrating relations have

been found in the system of eleven variables including the

exchange rate, and, for both countries, money supplies,

prices, incomes, and short- and long-term interest rates.

In order to get a well speci® ed error correction equation

for the exchange rate one has to assure that no long-run

relation of the system is omitted. In particular, long- and

short-term interest rates should be cointegrated according

to the expectations hypothesis of the term structure, see

Campbell and Shiller (1987). Speci® cally, if the expecta-

tions hypothesis holds, the interest rate spreads …R ¡ r†and …R* ¡ r*† should be stationary. In this case, the

spreads have to be included in the error correction equa-

tion for the exchange rate in order to avoid a misspeci® ca-

tion bias. However, the connection between (very) short-

and (very) long-term interest rates is usually not at all as

close as the expectations theory predicts. In fact, con® rm-

ing the results from e.g. Engsted and Tanggaard (1994) for

the USA and Hassler and Nautz (1998) for Germany, unit

root and cointegration tests indicate that there is no stable

relationship between short- and long-term interest rates in

the two countries.5

The second source of additional long-run relations is

uncovered interest rate parity (UIP) which implies cointe-

gration of home and foreign interest rates of the same

maturity. In particular, interest rate diŒerentials should

be stationary if UIP holds. The degree of synchronization

of German and US interest rate movements declines as

maturities become shorter. In fact, cointegration tests

suggest that there is no long-run relation between the

mainly policy determined short-term interest rates in the

United States and Germany, see e.g. Deutsche Bundesbank

(1997). By contrast, the increasing international integration

of the German bond market has reinforced the link

between German and US long-term interest rates,

especially since the beginning of the 1990s. Since then,

the spread between the German and the US bond rate

can be viewed as stationary. Therefore, the lagged bond

rate diŒerential has to be included as an additional error

correction term in the exchange rate equation.

Overall, four independent economic long-run relations

are found in the whole system which all may aŒect the

exchange rate. These are related to the two long-run

money demands, PPP and the UIP relation for the bond

rates. The monetary model should thus be tested on a

structural error correction equation for the exchange rate

of the following form:

¢et ˆ ®pppecppp

t¡1 ‡ ®m ececmt¡1 ‡ ®m¤ ecec

m¤t¡1 ‡ ®uipec

uip

t¡1

‡ lagged differences ‡ "t …13†

where ecppp ˆ e ¡ p ‡ p* and ec

uip ˆ …R ¡ R*† are the

deviations from PPP and UIP and ececm

and ececm¤

are the

estimated deviations from the long-run money demands

de® ned in Equations 9 and 11.

The monetary model

Based on a testing down strategy, the four error correction

terms were combined with lagged diŒerences to arrive at

the following speci® cation for the exchange rate error

correction equation.

¢et ˆ ¡0:23…3:46†

ecppp

t¡1 ‡ 0:77…5:04†

ececmt¡1 ¡ 0:35

…2:04†ecec

m*t¡1

¡ 2:67…3:74†

ecuip

t¡1 ¡ 4:19…2:99†

¢R t¡1 ‡ 0:06…1:40†

‡ 0:06…1:40†

¢D t …14†

Sample: 83 : 1 ¡ 96 : 3 ·RR2 ˆ 0:47 LM …1† ˆ 0:05‰0:83Š

Q…12† ˆ 16:06‰0:19Š HW ˆ 1:10‰0:38Š

Notes: For further explanation see Equations 9 and 13.

This equation allows a number of interesting observa-

tions concerning the adjustment mechanisms of the

exchange rate and the working of the monetary model.

First, all four error correction terms are statistically

Monetary model of the exchange rate 265

Table 1. Cointegration tests of long run PPP

Null hypothesis r ˆ 0 r 4 1 r 4 2

1% crit. value 35.65 20.04 6.655% crit. value 29.68 15.41 3.76

Sample 1975.01± 1997.02

Trace ± statistic 31.10 11.43 1.47

Notes: The system under consideration is …e; p; p*†. r denotes the

cointegration rank. Critical values are provided by Johansen(1995). The presented results are based on a VECM including

four lags.

5The cointegration properties of German and US short- and long-term interest rates are already established in the empirical literature.

For sake of brevity, results of cointegration tests are therefore not presented, but are available from the authors on request.

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signi® cant, thus con® rming the economic relevance of the

various adjustment mechanisms. In particular, the null

hypothesis ®m ˆ ®m¤ ˆ 0 stating that the monetary model

provides no additional insight into the determination of the

DM /Dollar exchange rate is easily rejected. Second, the

error correction terms from the money demand functions

have the theoretically expected opposite signs. Note that

the error correction terms for PPP and the interest rate

condition are correctly signed as well. Particularly, devi-

ations from PPP caused by an increase in the US price

level lead to an appreciation of the DM. Third, there is

no indication that the adjustment parameters for PPP

and the money demand functions are the same.

Adjustment to PPP (®®ppp ˆ ¡0:23) is slower than adjust-

ment to the monetary disequilibria (®®m ˆ 0:77,

®®m¤ ˆ ¡0:35). In fact, the coe� cient restriction

®ppp ˆ ¡®m ˆ ®m¤ implied by the reduced form approach

is rejected at the one per cent signi® cance level: The cor-

responding F -statistic (5.33) leads to a p-value of 0.008.

Estimating the single adjustment parameter of the

reduced form error correction Equation 8 gives

®®r ˆ ¡0:32 which is rather close to the estimated adjust-

ment parameters ®®ppp and ®®m¤ corresponding to deviations

from PPP and the US long run money demand,

respectively.6

However, since j®®m j ˆ 0:77 clearly exceeds

0:32, the reduced form equation strongly underestimates

the response of the exchange rate due to a monetary dis-

equilibrium in Germany. Therefore the diŒerence between

forecasts derived from the structural and the reduced form

approach increases in jececm j. Figure 1 shows that only small

deviations from the German long-run money demand

occur in the forecast period (1996 : 4± 1997 : 3). Thus it

can be expected that both forecast equations will lead to

similar results.

Forecast evaluation

Meese and RogoŒ(1983) demonstrated that a signi® cant

impact of monetary disequilibria in-sample does not necess-

arily imply a good forecasting ability out-of-sample. In

order to assess the predictive performance of the structural

error correction Equation 14, its out-of-sample forecasts

denoted by efstruc

are compared with the results from sev-

eral alternative forecast strategies. First, the error correc-

tion equation is reestimated for the exchange rate

restricting the adjustment parameters according to the

reduced form approach, i.e. ®ppp ˆ ¡®m ˆ ®m¤. The corre-

sponding reduced form forecasts are denoted by efred

.

Second, forecasts are based on an equation where the

impact of both monetary disequilibria is neglected (but

not the impact of UIP), i.e. ®m ˆ ®m¤ ˆ 0, which leads to

the forecasts efuip

. Third, an error correction equation is

estimated where the exchange rate only adjusts to devi-

ations from PPP, i.e. ®uip ˆ ®m ˆ ®m¤ ˆ 0, and the resulting

forecasts denoted by efppp

. And ® nally, as a point of refer-

ence these forecasts are compared with a simple random

walk model (efrw

). Following the empirical literature on

the monetary model, forecasts are dynamic in the sense

that forecasts greater than one period ahead use previously

forecasted values of the exchange rate as inputs. However,

for all other variables actual values are used.

The root mean square errors (RMSE) for out-of-sample

forecasts for one to four quarters ahead are presented in

Table 2. As expected, the misspeci® cation of the reduced

form approach is not revealed in the forecasts because

German money demand is too close to equilibrium during

the forecast period. In fact, the structural and the (mis-

speci® ed) reduced form forecasts are broadly similar,

compare Fig. 2. Yet predictions of the monetary model

in its structural form compare most favourably to those

based on more restricted equations. Forecasts exclusively

based on deviations from PPP strongly underestimate the

depreciation of the DM in 1997, while this is captured well

by the monetary approach. Taking into account the

observed monetary disequilibria obviously improves

exchange rate forecasts of the DM /Dollar for longer

horizons. In particular, the monetary model clearly beats

the random walk.

An important feature of the structural forecast strategy

is that it allows more insights into the working of the

monetary model. In particular, the estimated deviations

266 M. Moersch and D. Nautz

6Re-estimating the error correction equation under the restriction implied by the reduced form approach leads to:

¢et ˆ ¡0:32…5:26†

uut¡1 ¡ 3:29…4:83†

ecuip

t¡1 ¡ 4:18…2:78†

¢R t¡1 ‡ 0:10…4:50†

‡ 0:04…0:86†

¢D t …15†

Notes: ececm

and ececm

¤

are the mean adjusted deviations from the

estimated long-run money demands, see Equation 9± 12. Theshaded areas indicate the German monetary union, and the out-

of-sample period.Fig. 1. The estimated monetary disequilibria.

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from the various long-run equilibria oŒer an economic

explanation for the exchange rate movements. For

example, Fig. 1 indicates that there is a remarkable excess

demand for US currency during the forecast period.

According to the structural forecast Equation 14, this

already explains a major part of the recent Dollar upturn.

In contrast, the reduced form approach does not reveal

much information about the economic causes of the

predicted exchange rate behaviour.

I V . C O N C L U D I N G R E M A R K S

In this note an alternative to the reduced± form tests of the

monetary model of the exchange rate which has been

applied in the empirical literature on the monetary model

so far are suggested. It was demonstrated that the reduced

form approach rests on implausible parameter restrictions

which can be easily avoided by estimating the long-run

money demand functions separately. Moreover, the result-

ing `structural’ forecast equation allows an economic

interpretation of the various channels aŒecting the

exchange rate in the monetary model. And ® nally, this

approach was illustrated with reference to the DM /Dollar

exchange rate where the structural model outperforms

several alternative forecasting strategies out-of-sample.

It is worth emphasizing that there are several other fac-

tors which have been identi® ed as causing the poor per-

formance and the empirical failure of the monetary model

of the exchange rate. As Lane (1991) has already pointed

out, these include the presence of bubbles and the question-

able assumption of the exogeneity of the money supply.

A C K N O W L E D G E M E N T S

We thank Keith Cuthbertson, Uwe Hassler, Michael Heise,

JuÈ rgen Wolters, and an anonymous referee for providing

very helpful comments and suggestions. Research support

by the Deutsche Forschungsgemeinschaft (DFG),

Sonderforschungsbereich 373, `Quanti® kation und

Simulation OÈ konomischer Prozesse’ , at the Humboldt-

University at Berlin, is gratefully acknowledged.

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Monetary model of the exchange rate 267

Fig. 2. Out-of-sample forecast performance

Table 2. Out-of-sample forecast performance

efstruc

efred

efuip

efppp

efrw

RMSE (1) 0.039 0.059 0.008 0.029 0.033RMSE (2) 0.033 0.051 0.071 0.099 0.116

RMSE (3) 0.054 0.066 0.092 0.134 0.157RMSE (4) 0.052 0.062 0.133 0.186 0.206

Notes: The out-of-sample forecasts start in 96 : 4 and end in 97 : 3.

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268 M. Moersch and D. Nautz

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