Does the Euro follow the German Mark?

Transcription

1 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 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. nautz@wiwi.uni-frankfurt.de. offerman@wiwi.uni-frankfurt.de. 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.

2 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 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

3 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 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

4 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 m t p t = ηy t λi t (1) m t p t = η y t λ i t (2) where m t, p t, and y t denote the natural logarithms of money supply, price level, and real income, and i t 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 s t = p t p t (3) where s t 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 s t = m t m t ηy t + η y t + λi t 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 z t = µ + Πz t 1 + l Γ j z t j + φ(i i ) t 1 + j=1 l δ j (i i ) t j + ε t (5) 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. j=1 3

5 where z = (s, m, m, y, y ) ; Π αβ, denoting the cointegration matrix; µ is a vector of constants; Γ j, φ, and δ j are parameters of suitable dimension; and ε t is normally distributed with mean zero and variance σε. 2 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

6 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 ). 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 Johansen test of the VECM including interest 5-dimensional system rate differentials Data H 0 λ LR Joh 5% c.v. λ LR Seo 5% c.v. Synthetic European k = k k German k = k k Notes: Test of k cointegrating relations in the system z = (s, m, m, y, y ) 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

7 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 s t = ˆβ 0 + ˆβ 1 m t + ˆβ 2 m t + ˆβ 3 y t + ˆβ 4 yt + êc t (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, ˆα 1, and the coefficient of the lagged interest rate differential, ˆφ 1, from the exchange rate equation in (5) l ŝ t = ˆµ 1 + ˆα 1 êc t 1 + ˆγ 1j z t j + ˆφ l 1 (i i ) t 1 + ˆδ 1j (i i ) t j. (7) j=1 j=1 Note that ˆµ 1, ˆα 1, ˆφ 1 and ˆδ 1j are the first elements of ˆµ, ˆα, ˆφ, and ˆδ j, respectively, and ˆγ 1j is the first row of ˆΓ j, 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, β 1 = β 2 and β 3 = β 4, 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

8 Table 2: The monetary model of the exchange rate in the pre-emu period Variable Synthetic European data German data unrestricted VECM symmetry restriction unit elasticities unrestricted VECM symmetry restriction unit elasticities m (0.70) (2.86) (0.45) (0.79) m (3.56) (2.86) (5.97) (0.79) y (6.39) (4.26) (11.61) (8.96) (1.96) (4.80) y (4.08) (4.26) (7.42) (2.46) (1.96) (0.13) êc (6.03) (3.61) (6.04) (5.28) (2.45) (3.98) i i (3.76) (0.16) (1.13) (5.30) (0.67) (0.34) R p(lr) Notes: Coefficients of the unrestricted and restricted long-run relationships (6) and of the error-correction term êc t 1 and the lagged interest rate differential from (7) in the period 1985: :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. β 3 and β 4, 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 ˆβ 3 and ˆβ 4 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 êc 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

9 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 EMU Exchange Rate Behavior and the Evaluation of the pre-emu Experience 4.1 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

10 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 RMSE h 1 T (ŝ h t T s t) 2, t 0 = 1998 : 12, T = 2004 : 6, h t=t 0 +h where ŝ h t is the h-step forecast of s t and T h 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 s t is defined as ŝ h t E[s t Ω h t ] with Ω h t Ω t h Ψ t 1 by updating information sets and keeping the model parameters fixed. Specifically, Ω t {s j, m j, m j, y j, y j, (i i ) j} t j=0 and Ψ t {m j, m j, y j, y j, (i i ) j} t j=0 t = t 0 +h... T, starting from t 0 = 1998:12, the last in-sample observation. 9

11 Figure 1: Euro/Dollar exchange rate forecast errors RW.16 RMSE DM EUR Forecast Horizon 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 d 2π ˆf d (0) T with d 1 T T t=1 d t denoting the mean loss differential, which equals the difference between mean squared errors since d t e 2 M,t e2 B,t. The spectral density at frequency zero, f d(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

12 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 with S T I + (d t ), t=1 1 if d t > 0 I + (d t ) = 0 otherwise, where d t is defined as above. Consequently, if S < 1 2T, 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 forecast accuracy. under the null of equal Table 3: Euro/Dollar exchange rate forecast errors and tests of equal predictive accuracy between the EUR model and the DM model EUR DM Horizon RMSE RMSE DM S / / / / / / /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

13 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 Diebold- Mariano 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: Ratio h RMSEM h RMSE RW 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). describes the bootstrap procedure in detail. Appendix D Table 4: Euro/Dollar exchange rate forecast errors and tests of equal predictive accuracy against the random walk EUR DM Horizon Ratio 5% c.v. Ratio 5% c.v 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

14 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 pre- EMU 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 pre- EMU 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 pre- EMU 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

15 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 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 ˆX EUR,t 1 = exp(ln ˆX EUR,t ˆx EUR,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) ˆx EUR,t N w i,t 1 (ln(x i,t ) ln(x i,t 1 )) i=1 with weights w i,t summing to one over all countries i. Given that X EUR,T for T = 1999:01 is the first observation of the aggregate, 7 the construction yields the synthetic (logged) level of X as ln ˆX T EUR,t = ln X EUR,T ˆx EUR,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 w i,t is calculated as the country s GDP, Y i,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

16 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 with Y DM i,t w i,t = Yi,t DM N j=1 Y, j,t DM Y i,t P P P i,t and P P P i,t P t DM P i,t. Note that w i,t is also equivalent to the country s fraction of total real GDP, Q t, in the Euro Area, since Y i,t P P P i,t = Q i,t P DM t, such that the common currency unit cancels out from the w i,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

17 B Figures of Time Series Figure B.1: Exchange rates 1985:1 2004:6 1.8 National Currency per US Dollar EMU Euro Area 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: BN Euro BN US Dollar EMU Euro Area Germany (rescaled) 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

18 Figure B.3: Industrial production 1985:1 2004: Index (1995 = 100) EMU Euro Area Germany (rescaled) 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: Percent EMU Euro Area Germany USA Notes: Call money rate in percent p.a. Source: IMF and own calculations. 17

19 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 German data Variable I II I II m m y y êc I êc II R 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: :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

20 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 RW.16 RMSE DM[1] DM[2] EUR[2] EUR[1] Forecast Horizon 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

21 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 / / / / / / /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 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

22 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 s t = a0 + ε s t 6 m t = b0 + b j m t j + ε m t m t = c0 + y t = d0 + y t = e0 + j=1 6 j=1 c j m t j + ε m t 6 d j y t j + ε y t j=1 6 j=1 e j y t j + ε y t (D.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 (ˆε s t, ˆε m t, ˆε m t, ˆε y t, ˆεy t ). These are used to generate artificial data for all endogenous variables according to the following procedure: 1. We draw with replacement from the series of residuals to generate 282 pseudo innovations ( ε s t, ε m t, ε m t, ε y t, εy t ). 2. We use these pseudo innovations to generate pseudo I(1) series ( s t, m t, m t, ỹ t, ỹ t ) 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 (H 0 : Ratio h = 1 versus H 1 : Ratio h < 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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