Does the Euro follow the German Mark?
Evidence from the Monetary Model of the Exchange Rate∗
Dieter Nautz†
Christian J. Offermanns‡
Goethe-University Frankfurt
Revised version: November 16, 2004
Abstract
This paper investigates whether German or synthetic European pre-EMU data
provides the appropriate empirical basis for evaluating Euro/Dollar exchange rate behavior. Monetary exchange rate equations are estimated for both data sets over the
pre-EMU period, and out-of-sample forecasts are evaluated to assess their ability to
explain the Euro/Dollar exchange rate from 1999 to 2004. While forecast accuracy
tests confirm the usefulness of synthetic European data for Euro exchange rate analysis, forecasts based on the German pre-EMU experience cannot even beat a random
walk. Our results indicate that the Euro does not simply follow the German Mark,
but that it has its origins in the other pre-EMU currencies as well.
Keywords: Euro/Dollar Exchange Rate, Synthetic Euro Data, Monetary Model of the
Exchange Rate, Forecast Evaluation
JEL classification: F31, E47
∗
We thank two anonymous referees for very helpful comments and suggestions.
Department of Money and Macroeconomics. E-mail: [email protected].
‡
E-mail: [email protected]. Christian Offermanns is member of the Graduate Program “Finance and Monetary Economics” at Goethe University. Financial support from the DFG (German
Research Foundation) is gratefully acknowledged.
†
1
Introduction
Since the introduction of the Euro as the common currency for 11 countries in Europe
in 1999, the European perspective of macroeconomic policy has become a stronger focus
of economic research. Here, empirical evidence for the Euro Area is usually based on
synthetic European data constructed as a weighted cross-country average of pre-EMU time
series. Examples are studies on the stability of European money demand (Bruggeman
et al., 2003), central bank reaction functions (Gerdesmeier and Roffia, 2003), and the
European monetary transmission mechanism (Peersman and Smets, 2003). However, for
the analysis of the Euro exchange rate, the relevant pre-EMU data set is less obvious.
While Clostermann and Schnatz (2000), for example, employ synthetic pre-EMU data to
model the Euro exchange rate, Arnold and de Vries (2000) and Ehrmann and Fratzscher
(2004) argue that the pre-EMU dominance of the German Mark makes the use of synthetic
European data misleading. In the same vein, in consideration of the different degrees
of internal stability of the pre-EMU currencies, the European Central Bank (2002) has
proposed using German rather than synthetic European data for the analysis of Euro
exchange rates.
Employing the appropriate pre-EMU data set for Euro exchange rate analysis is not
only important for purely statistical reasons. There is also a policy-related component to
determining which data set should be applied: As long as German and synthetic European
data lead to different empirical Euro exchange rate equations, they will lead to different
views on the way the exchange rate is related to macroeconomic fundamentals and, thus, to
different Euro exchange rate forecasts. In this sense, identifying the appropriate pre-EMU
data can be crucial for understanding the behavior of Euro exchange rates. In this paper,
we use the monetary model of the exchange rate to compare the usefulness of German
and synthetic European pre-EMU data for the analysis of the Euro/Dollar exchange rate.
Exchange rate equations are estimated for German and synthetic European data over
the pre-EMU period, and out-of-sample forecasts are evaluated to assess their ability to
explain the Euro/Dollar exchange rate in the period 1999–2004.
The decision to apply either German or synthetic European pre-EMU data for the
analysis of Euro exchange rate behavior can be based on certain views on the origins of the
Euro. On the one hand, using exchange rate equations estimated with synthetic European
data to predict the Euro/Dollar exchange rate assumes an unaltered determination of
(the average of) European exchange rates. In this case, expectations on the financial
markets are formed on the basis of the aggregated history of all European currencies. This
European view of the origins of the Euro not only reflects the fact that the Euro replaced
the European Currency Unit (ECU) and the European Monetary System (EMS), but it
would also be in line with the ECB’s policy to base its decisions solely on aggregated data
1
of the whole Euro Area. On the other hand, forecasting the Euro/Dollar exchange rate
by using exchange rate equations estimated with German pre-EMU data assumes that
the mechanism which determined the external value of the German Mark is still in place,
even with the existence of the new currency. The proposal that German data should be
used for exchange rate analysis stems from the ECB’s ambition to adopt the Bundesbank’s
strict anti-inflationary policy focus in implementing monetary policy for the Euro Area.
In addition, the European Stability and Growth Pact had been designed according to the
German paradigm to emphasize the importance of a stability-oriented fiscal policy for the
stability of the Euro.
We focus on the monetary model of the exchange rate because the long-run validity
of the monetary model has been corroborated, for example, by MacDonald and Taylor
(1994) and Mark (1995). More recent studies use multivariate techniques (Francis et al.,
2001) as well as panel methods (Mark and Sul, 2001; Rapach and Wohar, 2004) and long
spans of data (Rapach and Wohar, 2002). These studies confirm the existence of stable
long-run relationships for most of the currencies they examine.1 Evidence supporting the
monetary approach for the (synthetic) Euro/Dollar exchange rate after 1991 is provided
by Chinn and Alquist (2000). Moersch and Nautz (2001) apply the monetary model to
the DM/Dollar exchange rate, emphasizing the implications of the underlying theoretical
assumptions for the estimation approach. Goldberg and Frydman (2001) identify several
subperiods of different temporal stability of the long-run relationship for the DM/Dollar
exchange rate over the period 1973–1998.
Our results confirm that the monetary model represents an appropriate means to explain the long-run behavior of Dollar-based exchange rates for both the German Mark
and the synthetic European currency in the pre-EMU period. Above and beyond that,
out-of-sample predictions show that specifications based on synthetic European data significantly outperform German models over the EMU period. Therefore, the notion that
the Euro “follows” the German Mark by adopting the mechanism underlying German
pre-EMU exchange rate determination appears to be too simplistic. In contrast, we show
that exchange rate equations based on synthetic European data prove to be very useful
for the analysis of Euro exchange rate behavior.
This paper is organized as follows. In Section 2 the monetary model of the exchange
rate is developed and its empirical implementation is motivated. Section 3 presents the
estimation results for the DM/Dollar and the synthetic Euro/Dollar exchange rate in the
pre-EMU period. The predictive power of the models for the Euro/Dollar exchange rate
is evaluated in Section 4, followed by concluding remarks in Section 5.
1
Recent empirical evidence on the stability of money demand functions gives further support in favor of
the monetary model of the exchange rate, see e.g. Lütkepohl et al. (1999) for Germany, Stracca (2003)
for the Euro Area, and Carlson et al. (2000) for the US. Nautz and Ruth (2004) make explicit use of
results from the money demand literature when estimating monetary exchange rate equations.
2
2
The Monetary Model of the Exchange Rate
2.1
Empirical Implementation
The flexible-price representation of the monetary model is based on the money market
equilibrium relationships
mt − pt = ηyt − λit
(1)
m∗t − p∗t = η ∗ yt∗ − λ∗ i∗t
(2)
where mt , pt , and yt denote the natural logarithms of money supply, price level, and real
income, and it stands for the nominal interest rate. η, λ > 0 are income and interest
rate (semi) elasticities of money demand. An asterisk denotes the foreign counterpart of
the domestic expression. The third building block of the flexible-price monetary model is
purchasing power parity
st = pt − p∗t
(3)
where st is the natural log of the exchange rate in terms of domestic currency per unit
of foreign currency. With price levels being determined on the macroeconomic money
markets, inserting (1) and (2) into (3) yields the fundamental equation of the exchange
rate
st = mt − m∗t − ηyt + η ∗ yt∗ + λit − λ∗ i∗t
(4)
Of course, this exchange rate equation does not hold in each and every period. Rather, as
MacDonald and Taylor (1994) already emphasized, the fundamental equation (4) should
be implemented as a long-run relationship via cointegration methods. Our empirical setup
follows this approach, specifying a vector error-correction model (VECM) which explicitly
models the adjustment of the variables to their long-run equilibrium.
Following e.g. Mark (1995), Groen (2002), and Rapach and Wohar (2002, 2004), we
focus on estimating the long-run relation between the exchange rate, money supplies and
incomes, and assume that uncovered interest parity (UIP) holds.2 Since under UIP current
interest rates reflect expectations about future exchange rate movements, we include lagged
rate differentials in the VECM.3 The specification of the monetary model is
∆zt = µ + Πzt−1 +
l
X
Γj ∆zt−j + φ(i − i∗ )t−1 +
l
X
δj ∆(i − i∗ )t−j + εt
(5)
j=1
j=1
2
The validity of UIP implies a stationary interest rate differential as well as a positive impact of this
differential on expected future exchange rate movements. The former is supported in our application
by KPSS tests according to Kwiatkowski et al. (1992), and the latter will be subject of the discussion
of the empirical results in the next section.
3
The estimation of interest rate rules is well beyond the scope of this paper. Therefore, we do not model
the adjustment of interest rates to fundamentals.
3
where z = (s, m, m∗ , y, y ∗ )0 ; Π ≡ αβ 0 , denoting the cointegration matrix; µ is a vector
of constants; Γj , φ, and δj are parameters of suitable dimension; and εt is normally
distributed with mean zero and variance σε2 . Note that (5) does not presuppose the
equality of money and income elasticities across countries.
We will use the VECM (5) to estimate the monetary model over the pre-EMU period for
two different sets of data. First, the specification for the synthetic Euro/Dollar exchange
rate will be based on synthetic European data for money, income and interest rates.
Second, we will estimate the VECM for the DM/Dollar exchange rate with equivalent
German data. In both cases, the US will be used as the foreign country.
2.2
Data
Our dataset comprises monthly Euro exchange rates per US Dollar as well as the monetary
aggregate M1, the index of industrial production, and a short-term (overnight) interest
rate for the US, the Euro Area and Germany. The series are taken from the International
Financial Statistics (IFS) of the International Monetary Fund (IMF) and from the Main
Economic Indicators (MEI) database of the Organisation for Economic Co-operation and
Development (OECD). Synthetic European data of the pre-EMU period are constructed
by aggregating country-specific variables of the member countries. Here, we follow the
procedure proposed by Beyer et al. (2001) and employ a weighted sum of individual growth
rates.4 Details on the aggregation method for this dataset are given in Appendix A, figures
of all time series are shown in Appendix B. Note that the European Currency Unit (ECU)
is related to the synthetic Euro, but the ECU includes countries that are not part of the
EMU (UK and Denmark) and it does not include two countries which introduced the Euro
in 1999 (Austria and Finland).
Given that meaningful synthetic European data are available from 1980 onwards, our
sample choice has to trade off a large number of observations with a high temporal stability
of the model. In accordance with Goldberg and Frydman (2001), we found that the
monetary model of the DM/Dollar exchange rate experienced several structural breaks
over the post-Bretton Woods period, but has been sufficiently stable since the middle of
the eighties. Thus, our sample period comprises monthly data from 1985:1 to 2004:6,
whereby the pre-EMU observations up to 1998:12 are used as the estimation sample, and
the last 66 observations for the EMU period are reserved for out-of-sample forecasts.
4
Comparable data at quarterly frequency are available from Beyer et al. (2001). We also employed the
“index method” described in Fagan and Henry (1998). This procedure is computationally equivalent
except that it uses fixed weights for the whole sample period and therefore does not capture changes in
relative prices between countries. The long-run behavior of these data turned out to be very similar. In
fact, the main results of this paper do not depend on the specific choice of the aggregation procedure.
4
3
The Monetary Model in the pre-EMU Period:
Evidence for German and Synthetic European Data
3.1
Cointegration Tests
Standard unit root tests indicate that the (log) levels of exchange rates, money supplies,
incomes and interest rates introduced above are integrated of order one. As a consequence,
we use cointegration tests to determine the number of long-run relationships in the system
z = (s, m, m∗ , y, y ∗ )0 . First, we apply the Johansen (1988) test to infer the cointegration
rank k of the 5-dimensional system z without exogenous regressors. As the left part of
Table 1 shows, the test yields k = 1 for both synthetic European and German data. This
result is in accordance with theoretical predictions, as we would expect the reduced-form
monetary model to constitute exactly one cointegrating relationship between the exchange
rate, money supplies and incomes.
Table 1: Cointegration tests for pre-EMU exchange rates and fundamentals
Data
Synthetic European
German
H0
k=0
k≤1
k≤2
k=0
k≤1
k≤2
Johansen test of the
5-dimensional system
λ
LRJoh 5% c.v.
0.184 34.07∗
33.46
0.115 20.58
27.07
0.063 10.87
20.97
∗
0.182 33.77
33.46
0.090 15.77
27.07
0.036
6.16
20.97
VECM including interest
rate differentials
λ
LRSeo 5% c.v.
0.268 94.43∗
61.36
∗
0.145 49.41
43.57
0.109 25.08
26.63
∗
0.213 77.43
61.89
0.130 41.71
42.14
0.082 19.89
26.63
Notes: Test of k cointegrating relations in the system z = (s, m, m∗ , y, y ∗ )0 with and without interest rate
differentials as exogenous regressors for synthetic European and German data in the period 1985:1–1998:12.
The lag length is set to l = 6, which is the lowest lag order ensuring the absence of residual autocorrelation in
all specifications. λ denotes the eigenvalues of the cointegration matrix. LR Joh is the maximum-eigenvalue
statistic according to Johansen (1988) in the case of no exogenous regressors. LR Seo is the likelihood-ratio
statistic according to Seo (1998) in the case of exogenous interest rate differentials as in (5). Critical values
are 95% quantiles tabulated in Osterwald-Lenum (1992) (left part) and Seo (1998) (right part).
However, standard inference from a Johansen test may be invalid in the presence of
exogenous regressors like the interest rate differentials included in (5). Therefore, we apply
a second cointegration test, as proposed by Seo (1998), to the VECM (5) which explicitly
accounts for the influence of stationary covariates on the likelihood-ratio statistic. The
modified test confirms the presence of at least one cointegrating relationship for German
and synthetic European data, see the right part of Table 1. For synthetic European
data, the modified test even suggests a cointegration rank of two. However, a higher
cointegration rank does not necessarily provide stronger support for the monetary model.
5
In fact, a second long-run relation in the reduced system (s, m, m∗ , y, y ∗ ) typically has
no convincing economic interpretation, see e.g. MacDonald and Taylor (1994) as well as
Francis et al. (2001). Fortunately, for both data sets, including a second cointegrating
relation in the VECM (5) does only lead to minor changes in the forecasting performance
of the exchange rate equation, see Appendix C. In the following, we will therefore focus
on the results for the VECMs assuming one cointegrating relationship.
3.2
Estimating the Monetary Model over the pre-EMU Period
Table 2 presents the estimates for the long-run relationship
st = β̂0 + β̂1 mt + β̂2 m∗t + β̂3 yt + β̂4 yt∗ + ec
ˆt
(6)
derived from the VECM (5) assuming the cointegration rank k = 1 for German and synthetic European data. Table 2 also reports the results for the error-correction parameter,
α̂1 , and the coefficient of the lagged interest rate differential, φ̂1 , from the exchange rate
equation in (5)
∆ŝt = µ̂1 + α̂1 ec
ˆ t−1 +
l
X
0
γ̂1j
∆zt−j + φ̂1 (i − i∗ )t−1 +
j=1
l
X
δ̂1j ∆(i − i∗ )t−j .
(7)
j=1
0
Note that µ̂1 , α̂1 , φ̂1 and δ̂1j are the first elements of µ̂, α̂, φ̂, and δ̂j , respectively, and γ̂1j
is the first row of Γ̂j , where a hat denotes the estimator of the corresponding parameter
in the VECM for the monetary exchange rate model.
The results obtained from estimations for synthetic European data are shown in the left
part of Table 2. According to column 2, the signs of the long-run parameters estimated in
the unrestricted VECM (5) are in line with theoretical predictions, although the coefficient
of domestic money supply is not significantly different from zero. In columns 3 and 4, we
proceed by testing for restrictions on the long-run relationship which are either suggested
by the monetary model or often used in the empirical literature.
First, the symmetry of elasticities to domestic and foreign money supply and income,
β1 = −β2 and β3 = −β4 , respectively, is tested. The likelihood-ratio (LR) test shows
that this restriction is strongly rejected, see column 3. In particular, imposing symmetry
on income elasticities is completely at odds with the data and even changes the signs of
the long-run coefficients of money supplies. Therefore, the use of relative money supply
m − m∗ and relative income y − y ∗ as single explanatory variables like in Groen (2002)
and Rapach and Wohar (2002, 2004) is not feasible for synthetic European data.
Second, the fundamental equation (4) implies unit elasticities to domestic and foreign
money supply. It is interesting to note that this theory-based restriction is often rejected in
6
Table 2: The monetary model of the exchange rate in the pre-EMU period
Variable
m
Synthetic European data
unrestricted
VECM
symmetry
restriction
unit
elasticities
unrestricted
VECM
symmetry
restriction
unit
elasticities
0.409
−1.181∗∗
1.0
0.244
−0.380
1.0
1.181∗∗
−1.0
−1.738∗∗
0.380
−1.0
−3.071∗∗
−1.250
−2.693∗∗
2.085∗
1.250
−0.034
−0.186∗∗
−0.042∗
−0.098∗∗
(1.13)
0.959∗∗
(5.30)
−0.076
0.029
(0.67)
(0.34)
0.473
0.302
0.449
−
0.360
0.000
0.403
0.008
(0.70)
−1.044∗
m∗
(3.56)
(2.86)
(2.86)
y
−4.462∗∗
−2.533∗∗
y∗
2.804∗∗
2.533∗∗
(6.39)
(4.08)
−0.169∗∗
ec
ˆ
i−
(6.03)
i∗
R2
p(LR)
German data
0.512∗∗
(3.76)
0.472
−
(4.26)
(4.26)
−0.053∗∗
(3.61)
0.023
(0.16)
0.386
0.000
(0.45)
(5.97)
−5.138∗∗
(11.61)
1.829∗∗
(7.42)
−0.157∗∗
(6.04)
0.143
(8.96)
(2.46)
(5.28)
(0.79)
(0.79)
(1.96)
(1.96)
(2.45)
(4.80)
(0.13)
(3.98)
Notes: Coefficients of the unrestricted and restricted long-run relationships (6) and of the error-correction term
ec
ˆ t−1 and the lagged interest rate differential from (7) in the period 1985:01–1998:12. The VECM contains a
constant in the cointegrating vector and in the VAR, as well as 6 lagged first differences of all included variables.
p(LR) is the p-value of the LR-test on the long-run restriction, the R 2 refers to the exchange rate equation (7),
absolute t-values in parentheses, ∗ (∗∗ ) denotes significance at the 5% (1%) level.
the empirical exchange rate literature, see e.g. MacDonald and Taylor (1994). In contrast,
as column 4 in Table 2 shows, unit elasticities are not rejected (p = 0.302) for synthetic
European data. Consequently, the long-run coefficients of y and y ∗ , viz. −β3 and β4 ,
could be interpreted as long-run elasticities of money demand with respect to the index
of industrial production. However, as the estimates are rather high in absolute value,
the real income effect might cover more than the income elasticity of money demand. A
potential explanation is the Balassa-Samuelson effect on the real exchange rate, leading
to movements in the nominal exchange rate which exceed the proportional reaction to
prices, see Groen (2003). In this case, the difference between β̂3 and β̂4 would indicate
that the relative price of tradable to non-tradable goods in the Euro Area reacts stronger
to productivity movements than in the US.
The adjustment of the synthetic Euro/Dollar exchange rate to its fundamental equilibrium relation is economically and statistically significant. The estimated coefficient of
ec
ˆ implies considerably strong reactions to deviations from the long-run relationship in all
specifications. Taking into account that previous studies were not always able to support
significant error-correction coefficients in the exchange rate equation (cf. e.g., Chinn and
Meese, 1995), these findings corroborate support for the monetary model.
In the unrestricted specification, the short-term interest rate differentials exhibit a sig-
7
nificant impact on the exchange rate. The sign of the coefficient is positive, substantiating
the role of uncovered interest parity. However, the estimated coefficient is clearly less than
one and even insignificant in the specification imposing unit elasticities on money supplies.
This might suggest that the synthetic European interest rate is not appropriate for modeling the influence of capital flows on the synthetic European exchange rate. However,
substituting it with the German short-term interest rate, thereby considering the German
Mark’s leading role in the European Exchange Rate Mechanism (ERM), does not lead to
a stronger interest rate effect.
The estimates of the VECM using German data are shown in the right part of Table 2.
The signs of the cointegrating parameters of the unrestricted VECM are plausible, and the
adjustment of the DM/Dollar exchange rate to its long-run equilibrium is similar to the
VECM based on synthetic European data. The symmetry restriction to the coefficients of
domestic and foreign variables in the cointegrating vector is rejected as in the model for
synthetic European data, cf. column 6. However, in contrast to the latter, we are not able
to impose unit elasticities on domestic and foreign money supplies, either. Nevertheless,
the unrestricted exchange rate equation for German data has a good in-sample fit, the R 2
is almost as high as in the specification for synthetic European data. The coefficient of the
interest rate differential is larger than for synthetic European data and provides support
for a one-for-one effect on future exchange rate movements.
For the German pre-EMU data, the exchange rate equation of the unrestricted VECM
(henceforth “DM model”) is the natural candidate to forecast the Euro/Dollar exchange
rate. For synthetic European data, we will also use the unrestricted exchange rate equation
(henceforth “EUR model”) to enhance the comparability of the results. Note that the
ranking of the models according to the following forecasting exercise will not depend on
this choice. In the next section, the DM and the EUR models are evaluated out-of-sample
in order to assess their ability to explain the Euro/Dollar exchange rate behavior after the
introduction of the common currency.
4
4.1
EMU Exchange Rate Behavior and the Evaluation of the
pre-EMU Experience
Out-of-Sample Forecasts
In this section, we compare the ability of the competing pre-EMU exchange rate equations, i.e. the DM and the EUR model, to predict the Euro/Dollar exchange rate in the
EMU period (1999:1 to 2004:6). Since Meese and Rogoff (1983), conditional out-of-sample
forecasting has become a standard procedure for testing the validity of exchange rate mod-
8
els. For our purposes, this approach is particularly convincing since the formation of the
European Monetary Union marks a natural starting point for a forecasting exercise. The
out-of-sample forecasts are conditional in the sense that they are generated by means of
the exchange rate equation (7) using observed values for money supplies, incomes and
interest rates. Although it would, in principle, be possible to generate forecasts for all
endogenous variables, this procedure is generally used in the empirical exchange literature to abstract from irrelevant but probably imprecise forecasts of the macroeconomic
fundamentals (see e.g. MacDonald and Taylor, 1994; Chinn and Alquist, 2000). Forecasts
obtained from the DM model assume the mechanism driving exchange rates in the Euro
Area to be the same as it was in Germany, but they account for the monetary union by
using European instead of German data.
Following e.g. Mark (1995), we distinguish between different forecast horizons as the
degree of explanation of the monetary model is likely to improve over time.5 The evaluation
of forecast accuracy is based on the root mean squared error
v
u
T
u1 X
RMSEh ≡ t
(ŝht − st )2 ,
t0 = 1998 : 12,
Th
T = 2004 : 6,
t=t0 +h
where ŝht is the h-step forecast of st and Th ≡ 66 − h + 1 is the number of predicted values,
which decreases with longer forecast horizons.
The RMSEs for the forecast equations and the random walk for h = 1, . . . , 24 are
depicted in Figure 1. The figure shows that the EUR model exhibits lower average forecast
errors for the Euro/Dollar exchange rate than the DM model at every forecast horizon.
In particular, the RMSEs of the EUR model never exceed 8%, whereas the DM model
amounts to an error of up to 12%. Figure 1 clearly suggests that the EUR model is more
appropriate to track the Euro/Dollar behavior in the EMU period than the DM model.
In addition to the relative forecasting performance, we should also evaluate the absolute
predictive power of the exchange rate equations, i.e. the forecast errors relative to a simple
benchmark model like the random walk. Figure 1 shows that the forecast errors of the
random walk (RW) display a monotonic increase, whereas the RMSEs of the monetary
exchange rate equations tend to decline after some time. While both models outperform
the random walk over forecast horizons exceeding one year, the EUR model yields lower
RMSEs than the random walk already after only two months. In contrast, the DM model
is clearly worse than the random walk for horizons of less than one year.
5
For a given forecast horizon h, the h-step forecast of st is defined as ŝht ≡ E[st |Ω̃ht ] with Ω̃ht ≡
Ωt−h ∪ Ψt−1 by updating information sets and keeping the model parameters fixed. Specifically,
Ωt ≡ {sj , mj , m∗j , yj , yj∗ , (i − i∗ )j }tj=0 and Ψt ≡ {mj , m∗j , yj , yj∗ , (i − i∗ )j }tj=0 ∀ t = t0 + h . . . T , starting
from t0 = 1998:12, the last in-sample observation.
9
Figure 1: Euro/Dollar exchange rate forecast errors
.24
.20
RW
RMSE
.16
.12
DM
.08
EUR
.04
.00
Forecast
Horizon
5
10
15
20
Notes: EUR and DM refer to the model estimated with synthetic European and German
data, respectively, and RW denotes the random walk forecast. The results do not depend on
the inclusion of a drift parameter in the random walk.
These results indicate that the EUR model outperforms its DM competitor in an
economically significant way. In the following sections, we will examine whether the outperformance is also statistically significant.
4.2
Forecast Accuracy Test: EUR Model vs DM Model
Since prediction errors e ≡ ŝ − s are random, we apply forecast accuracy tests to evaluate
whether the observed differences in the models’ forecasting performance are statistically
significant. To begin with, we employ the test named after Diebold and Mariano (1995),
which has become a standard tool to evaluate exchange rate forecasts since Mark (1995).
This procedure compares the mean squared error (MSE) of a model M with the MSE of
a non-nested model B. The test statistic of the Diebold-Mariano test is defined as
DM ≡ q
with d¯ ≡
1
T
PT
t=1 dt
d¯
2π fˆd (0)
T
denoting the mean loss differential, which equals the difference between
mean squared errors since dt ≡ e2M,t − e2B,t . The spectral density at frequency zero, fd (0),
is estimated using a Bartlett lag window of sample autocovariances with data-dependent
bandwidth according to Newey and West (1994). Under the null hypothesis of equal
10
squared forecast errors the expected loss differential is zero and DM is asymptotically
standard normal distributed, with a negative value indicating a lower MSE of M.
In order to check the robustness of the test results with respect to outliers and nonnormal forecast errors, we also apply the sign test (cf. Diebold and Mariano, 1995, pp. 254).
The sign test compares the frequency of the outperformance of M relative to B. Thus, in
contrast to the Diebold-Mariano test, the null hypothesis is a zero-median loss differential.
The test statistic is defined as
S≡
T
X
I+ (dt ),
t=1
with
I+ (dt ) =

1
0
if dt > 0
otherwise,
where dt is defined as above. Consequently, if S < 12 T , the median of d is smaller than
zero, indicating that model M outperforms model B more often than vice versa. The test
statistic S has a binomial distribution with parameters T and
1
2
under the null of equal
forecast accuracy.
Table 3: Euro/Dollar exchange rate forecast errors and tests of equal
predictive accuracy between the EUR model and the DM model
Horizon
1
4
8
12
16
20
24
EUR
RMSE
0.027
0.057
0.068
0.072
0.074
0.071
0.064
DM
RMSE
0.033
0.088
0.114
0.118
0.117
0.110
0.097
DM
−3.517∗∗
−3.139∗∗
−3.434∗∗
−3.387∗∗
−3.046∗∗
−2.778∗∗
−2.355∗
S
19∗∗ /66
19∗∗ /63
8∗∗ /59
6∗∗ /55
7∗∗ /51
7∗∗ /47
7∗∗ /43
Notes: Root mean squared errors of the EUR model and the DM model. DM is the normalized
mean loss differential between both models, S is the number of forecasts where the EUR model
is worse than the DM model, see text for definitions of the test statistics. ∗ (∗∗ ) denotes
significance at the 5% (1%) level.
Table 3 shows the results of the Diebold-Mariano test and the sign test for selected
forecast horizons. Remarkably, for both test procedures, the EUR model is significantly
better than the DM model at every forecast horizon. The forecast accuracy tests strongly
confirm that the EUR model provides better forecasts of the Euro/Dollar exchange rate
than the DM model.
11
4.3
Forecast Accuracy Test: EUR and DM Model vs Random Walk
As the random walk is nested in the exchange rate equations, the standard DieboldMariano test is not feasible for the comparison of the economic models to the random
walk, see e.g. Clark and McCracken (2001). In this case, we assess the forecast accuracy
by means of the RMSE ratio at forecast horizon h:
Ratioh ≡
RMSEM
h
RMSERW
h
where M = {EUR, DM}. The distribution of this ratio is non-standard because of asymptotic correlation between the forecast errors of nested models. Therefore, critical values
have to be obtained from a bootstrap procedure, see e.g. Groen (2003). Appendix D
describes the bootstrap procedure in detail.
Table 4: Euro/Dollar exchange rate forecast errors and tests
of equal predictive accuracy against the random walk
EUR
Horizon
1
4
8
12
16
20
24
Ratio
1.040
0.912
0.777
0.566
0.468∗
0.381∗
0.321∗
DM
5% c.v.
0.822
0.626
0.555
0.524
0.502
0.477
0.448
Ratio
1.298
1.399
1.298
0.916
0.729
0.580
0.483
5% c.v.
0.863
0.649
0.578
0.537
0.511
0.489
0.455
Notes: An RMSE ratio less than one indicates that the model beats the random walk. Significance of ratios is based on critical values obtained from a bootstrap procedure with 5,000
replications (for details see Appendix D).
Table 4 shows that the higher forecast accuracy of the EUR model relative to the
random walk suggested by Figure 1 is statistically significant for all forecast horizons
exceeding one year. This is a relatively short time span, compared with the usual findings
in the literature which attribute predictive power to the monetary model only over horizons
of 3–4 years (cf. Mark, 1995; Chinn and Meese, 1995). In contrast, the DM model is not
able to outperform the random walk significantly at any forecast horizon.
12
5
Conclusion
In this paper, we assessed the usefulness of German and synthetic European pre-EMU
data for the analysis of the Euro/Dollar exchange rate. Exchange rate models estimated
with different data usually lead to different results and, particularly, to different exchange
rate forecasts. Therefore, the decision to apply either German or synthetic European preEMU data for Euro exchange rate analysis suggests a specific view of the behavior of the
Euro/Dollar exchange rate. In this sense, the choice of the pre-EMU data can be linked
to alternative characterizations of the Euro.
We used the monetary model of the exchange rate to confront the hypothesis of an
unaltered (synthetic) Euro determination with the alternative that Euro exchange rates
respond to macroeconomic fundamentals in the same way as DM exchange rates in the
pre-EMU period. We estimated suitable empirical specifications of pre-EMU exchange
rate behavior and evaluated their performance in out-of-sample predictions. The out-ofsample forecasting exercise showed that the behavior of the Euro/Dollar exchange rate
is well described by a EUR model, i.e. an exchange rate equation estimated with synthetic European data. Forecast accuracy tests demonstrated that the EUR model yields
significantly better forecasts of the Euro/Dollar exchange rate than the DM model, the
equivalent equation estimated with German data. In contrast to the EUR model, the DM
model is not able to beat the random walk significantly at any forecast horizon.
Our empirical results indicate that Euro exchange rate analysis should take the preEMU experience of all member countries into account. In particular, the behavior of
the Euro cannot be viewed as a simple extrapolation of the German Mark. From the
perspective of the monetary model of the exchange rate, it is more appropriate to model the
common currency as the successor of the synthetic Euro, i.e. a weighted average of all preEMU currencies. This may have interesting implications considering further enlargements
of the EMU. For example, our results suggest that the link between the Euro exchange
rate and fundamentals will be significantly affected by the intended introduction of the
Euro in central and eastern European countries.
The findings of this paper are based on the monetary model of the exchange rate.
Future work on Euro exchange rates might consider further macroeconomic determinants
as proposed by behavioral equilibrium exchange rate models (Maeso-Fernandez et al., 2002;
Detken et al., 2002). Moreover, one could account for possible asymmetric influences from
EMU countries on the Euro exchange rate. Nonetheless, our results demonstrated that
models estimated with synthetic pre-EMU data can provide the appropriate basis for an
empirical analysis of the European economy.
13
Appendix
A
Construction of Synthetic European Data
The synthetic data used in this paper are constructed from data for those countries which
currently form the Euro Area, except for Greece, which was not a member at the beginning
of the European Monetary Union (EMU); Luxembourg, because of its currency union with
Belgium; and Ireland, since there is no GDP data available before 1997. Consequently, the
data set comprises Austria, Belgium, Finland, France, Germany, Italy, the Netherlands,
Portugal, and Spain. The variables are the exchange rate in terms of national currency
per US Dollar (period average, International Financial Statistics, series rf), a short-term
interest rate (call money rate, period average, IFS, series 60B), the index of industrial
production (IIP, Main Economic Indicators, series 2027KSA), and the monetary aggregate
M1 (MEI, series 6003D).6 German M1 and IIP are adjusted for a level shift due to German
unification according to the procedure described in Beyer et al. (2001, p. F120).
The synthetic Euro Area aggregate (denoted with a hat) of a variable X is defined
recursively by re-integrating growth rates of X
X̂EU R,t−1 = exp(ln X̂EU R,t − ∆x̂EU R,t ).
Thereby, the aggregated growth rate ∆x is computed as a weighted sum of individual
growth rates according to Eq. (17) in Beyer et al. (2001)
∆x̂EU R,t ≡
N
X
wi,t−1 · (ln(Xi,t ) − ln(Xi,t−1 ))
i=1
with weights wi,t summing to one over all countries i. Given that XEU R,T for T = 1999:01
is the first observation of the aggregate,7 the construction yields the synthetic (logged)
level of X as
ln X̂EU R,t = ln XEU R,T −
T
X
∆x̂EU R,s
∀ t = 1, . . . , T − 1.
s=t+1
For the interest rate, ∆x is computed as an arithmetic average of level changes such that
the logarithm does not apply in this case. The weight wi,t is calculated as the country’s
GDP, Yi,t , relative to total GDP in the Euro Area. In order to obtain this relation, the
level of nominal GDP in the current quarter is converted to a common price level by
6
M1 is seasonally adjusted by means of the Census X-11 procedure at the country level.
7
For M1 we use 1998:12 as the reference point since we have observations for national money supply
only up to this date.
14
multiplying it with the country’s PPP rate. The PPP rates are available from the OECD
and determine how many units of national currency one has to pay for a basket that costs
one unit of currency in the base country, e.g. in Germany. Thus, we have
DM
Yi,t
wi,t = PN
,
DM
j=1 Yj,t
DM ≡ Y · P P P
with Yi,t
i,t
i,t and P P Pi,t ≡
PtDM
Pi,t .
Note that wi,t is also equivalent to the
country’s fraction of total real GDP, Qt , in the Euro Area, since Yi,t · P P Pi,t = Qi,t · PtDM ,
such that the common currency unit cancels out from the wi,t . Weights are re-based to a
smaller number of countries in the few cases where some observations are missing or the
variable is not reported for a (small) country.
15
Figures of Time Series
Figure B.1: Exchange rates 1985:1–2004:6
National Currency per US Dollar
1.8
1.6
1.4
1.2
1.0
0.8
0.6
EMU
85
87
89
91
93
95
Euro Area
97
99
01
03
Germany
Notes: Period-average exchange rates in Euro per US Dollar. Source: IMF and own calculations.
Figure B.2: Monetary aggregates (M1) 1985:1–2004:6
1400
3000
1200
2500
1000
2000
800
1500
600
1000
500
BN US Dollar
BN Euro
B
EMU
85
87
89
91
93
95
97
Euro Area
Germany (rescaled)
99
01
400
03
USA
Notes: M1 in Euro (Euro Area, Germany) and US Dollar; German M1 rescaled to match
Euro Area data in 1998:12. Source: OECD and own calculations.
16
Figure B.3: Industrial production 1985:1–2004:6
140
130
Index (1995 = 100)
120
110
100
90
80
70
EMU
85
87
89
91
93
95
97
99
Euro Area
Germany (rescaled)
01
03
USA
Notes: Index of industrial production, scaled to 1995 = 100 for Euro Area and USA.
Source: OECD and own calculations.
Figure B.4: Short-term interest rates 1985:1–2004:6
14
12
Percent
10
8
6
4
2
0
EMU
85
87
89
91
93
95
Euro Area
Germany
97
99
01
03
USA
Notes: Call money rate in percent p.a. Source: IMF and own calculations.
17
C
Alternative Specification: Two Cointegrating Vectors
Table C.1 presents the long-run coefficients of the VECM (5) assuming the cointegration
rank k = 2. The left part shows the cointegrating vectors for the VECM estimated
with synthetic European data as well as the corresponding adjustment coefficients. The
equivalent parameters for German data are given in the right part of the Table. For
both data sets, the additional explanatory power for the exchange rate due to the second
cointegrating vector is negligible. Since no plausible identifying scheme was accepted by
the data, we decided to present the cointegrating vectors without standard errors in a
non-identified way.
Table C.1: The monetary model of the exchange rate in the pre-EMU period:
Two cointegrating relationships
Synthetic European data
Variable
German data
I
II
I
II
m
0.409
−10.765
0.244
17.122
m∗
−1.044
−10.089
−1.738
7.294
y
−4.462
6.100
−3.071
7.039
2.804
33.442
2.085
−39.377
y∗
ec
ˆ
I
−0.169
−0.186
ec
ˆ
II
0.002
−0.002
0.475
0.452
R2
Notes: I and II refer to the first and second cointegrating vectors, which are normalized to
the first element for synthetic European and German data, as well as to the coefficients of
the error-correction terms in the exchange rate equation of VECM (5) in the period 1985:01–
1998:12 under cointegration rank k = 2. The VECM contains a constant in each cointegrating
vector and in the VAR, as well as 6 lagged first differences of all included variables. The R 2
refers to the exchange rate equation (7).
18
Forecasting the Euro/Dollar exchange rates with these models yields a pattern of
RMSEs as displayed in Figure C.1. Apparently, the relative order of the forecasting
performance remains unchanged: The EUR model with two cointegrating vectors (EUR[2])
is still better than its competitor at every forecast horizon. While the DM[2] model is not
able to outperform the random walk significantly at any forecast horizon, the EUR[2]
model is significantly better than the random walk at long horizons, see Tables C.2 and
C.3. Since there is merely no response of the exchange rate to the additional cointegrating
vector, its inclusion in the exchange rate equation has no important consequences for its
forecasting performance and the main results of the paper.
Figure C.1: Euro/Dollar exchange rate forecast errors:
Specifications with one and two cointegrating relationships
.24
.20
RW
RMSE
.16
.12
DM[1]
DM[2]
EUR[2]
EUR[1]
.08
.04
.00
2
4
6
8
10
12
14
16
18
20
22
Forecast
Horizon
24
Notes: EUR and DM refer to the models estimated with synthetic European and German
data, with the number of cointegrating relationships in brackets, and RW denotes the random
walk forecast.
19
Table C.2: Euro/Dollar exchange rate forecast errors and tests of equal
predictive accuracy between the EUR model and the DM model
Horizon
EUR[2]
DM[2]
DM
S
1
0.027
0.032
−3.094∗∗
21∗∗ /66
4
0.058
0.080
−2.385∗
24/63
8
0.072
0.104
−2.498∗
13∗∗ /59
12
0.078
0.108
−2.288∗
16∗∗ /55
16
0.080
0.106
−1.967∗
20/51
20
0.077
0.097
−1.644
22/47
24
0.068
0.081
−1.147
23/43
Notes: Root mean squared errors of the EUR model and the DM model. DM is the normalized
mean loss differential between the two models. S is the number of forecasts where the EUR
model is worse than the DM model, see text for definitions of the test statistics. ∗ (∗∗ ) denotes
significance at the 5% (1%) level.
Table C.3: Euro/Dollar exchange rate forecast errors and tests
of equal predictive accuracy against the random walk
EUR[2]
DM[2]
Horizon
Ratio
5% c.v.
Ratio
5% c.v.
1
1.040
0.795
1.240
0.792
4
0.929
0.551
1.269
0.561
8
0.827
0.485
1.178
0.509
12
0.611
0.442
0.832
0.466
16
0.502
0.408
0.658
0.442
20
0.411
0.382
0.514
0.415
24
0.341∗
0.368
0.401
0.385
Notes: An RMSE ratio less than one indicates that the model beats the random walk. Significance of ratios is based on critical values obtained from a bootstrap procedure with 5,000
replications (for details see Appendix D).
20
D
Bootstrapping Critical Values for RMSE Ratios
In order to obtain the empirical distribution under the null hypothesis that the variables
follow the benchmark model, i.e. the random walk in case of the exchange rate, we employ a nonparametric version (see Rapach and Wohar, 2004) of the parametric bootstrap
procedure described in Groen (2003). To do so, we set up a benchmark model assuming
no cointegrating relationship between the exchange rate and its fundamentals and specify
∆st = a0 + εst
∆mt = b0 +
6
X
bj ∆mt−j + εm
t
6
X
cj ∆m∗t−j + εm
t
6
X
dj ∆yt−j + εyt
6
X
∗
ej ∆yt−j
+ εyt
j=1
∆m∗t = c0 +
∗
j=1
∆yt = d0 +
(D.1)
j=1
∆yt∗ = e0 +
∗
j=1
We estimate (D.1) with Generalized Least Squares for both, synthetic European and
German data over the complete sample period 1985:1–2004:6 to obtain residuals
∗
∗
y y
m
(ε̂st , ε̂m
t , ε̂t , ε̂t , ε̂t ). These are used to generate artificial data for all endogenous vari-
ables according to the following procedure:
1. We draw with replacement from the series of residuals to generate 282 pseudo inno∗
∗
y y
m
vations (ε̃st , ε̃m
t , ε̃t , ε̃t , ε̃t ).
2. We use these pseudo innovations to generate pseudo I(1) series (s̃ t , m̃t , m̃∗t , ỹt , ỹt∗ )
from the benchmark model (D.1). We delete the first 48 observations to correct
for any initial-value bias. The remaining 234 observations match our sample period
1985:1–2004:6.
3. We employ our forecasting procedure described in Section 4 to generate multi-step
forecasts over the period 1999:1–2004:6. Therefore, we apply our respective forecasting model which is either the European or the German model, as well as the
random-walk benchmark model to the pseudo series generated in Step 2.
Steps 1–3 are replicated 5,000 times. Using the resulting 5,000 artificial RMSE ratios
for each forecast horizon h we can compute the 5% (1%) critical value for the test of
forecast equality (H0 : Ratioh = 1 versus H1 : Ratioh < 1) from the lower 5% (1%)
quantile of the empirical distribution of RMSE ratios between the forecasting model and
the random walk.
21
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