Euro to Dollar Exchange Rate

An eclectic view on the euro/dollar exchange rate Dieter Nautz and Jan Scheithauer∗ April 15, 2005 Abstract Empirical exchange rate analysis is usually based on a specific exchange rate theory emphasizing the impact of a few key fundamentals. This paper investigates the usefulness of an eclectic view on the exchange rate covering different theories. Automatic econometric model selection is employed to obtain a parsimonious exchange rate equation suited for forecasting purposes. Our results obtained for the euro/dollar exchange rate indicate that incorporating more fundamentals in the empirical analysis does not necessarily improve the forecasting performance of exchange rate equations. The evaluation of out-of-sample forecasts shows that the eclectic exchange rate equation is outperformed by an equation that restricts the attention to monetary fundamentals. JEL codes: F31; E47 Keywords: Euro/Dollar exchange rate, behavioral equilibrium exchange rate model, monetary exchange rate model, automatic econometric model selection ∗ Department of Money and Macro, Goethe University Frankfurt. E-mail: nautz@wiwi.uni- frankfurt.de; scheitha@wiwi.uni-frankfurt.de 1 2 1 Introduction Since Meese and Rogoff (1983) documented the discouraging forecasting performance of exchange rate models, a large part of exchange rate economics has aimed at finding empirical support for numerous exchange rate conceptions including the monetary exchange rate model, the portfolio balance approach or, more recently, the behavioral equilibrium exchange rate (BEER) models. Yet empirical evidence supporting these models has remained elusive, see e.g. Cheung et al. (2002). Different exchange rate theories usually emphasize the importance of different economic fundamentals. According to Dornbusch (1980) these models can thus be regarded as partial views on the exchange rate. So far, few attempts have been made to integrate the various models in empirical analysis to get a more complete picture of exchange rate determination. The current paper investigates the benefits and drawbacks of a more eclectic view on exchange rates. In particular, we try to account for the information contained in a broad set of fundamentals related to various exchange rate theories. On the one hand, this approach will certainly improve the in-sample fit of empirical exchange rate models. On the other hand, however, an eclectic model does not correspond to a well-defined exchange rate theory and could, thus, be less helpful for understanding exchange rate dynamics. In our empirical application, cointegration analysis is applied to pre-EMU data to determine the long-run relationships between the synthetic euro/dollar exchange rate and economic fundamentals. For obtaining a parsimonious exchange rate equation suited for forecasting purposes, we employ automatic econometric model selection procedures developed by Hendry and Krolzig (2001). Following the empirical literature, we assess the performance of exchange rate models by evaluating out-of-sample forecasts of the exchange rate. The closest references to this paper are Nautz and Offermanns (2005) and Cheung et al. (2002). Nautz and Offermanns (2005) examine the euro/dollar exchange rate with similar estimation and forecasting periods. However, they restrict the attention to the monetary exchange rate model ignoring the possible impact of non-monetary fundamentals. Updating the seminal work by Meese and Rogoff (1983), Cheung et al. (2002) compare the forecasting performance of various exchange rate models for different pairs of currencies. However, in contrast to the current paper, they do not integrate the competing exchange rate models into a general model that incorporates all relevant variables simultaneously. Using information from a broad set of economic fundamentals, we obtain a statistically 3 well-behaved forecast equation for the euro/dollar exchange rate. Yet, in spite of its strong performance in-sample, the eclectic exchange rate equation completely fails in the out-of-sample forecasting exercise. In particular, the equation build on several exchange rate theories cannot beat the random walk and is clearly outperformed by an equation exclusively based on the monetary model of the exchange rate. The remainder of this paper is organized as follows. Section 2 introduces the economic fundamentals under consideration and the corresponding exchange rate theories. Section 3 contains the cointegration analysis, describes the automatic model selection procedure, specifies the forecast equation for the euro/dollar exchange rate, and assesses its out-of-sample forecasting performance. Section 4 offers some conclusions. 2 Economic fundamentals related to the exchange rate This section presents the economic fundamentals and the data employed in the empirical analysis of the euro/dollar exchange rate. The variables summarized in Table 1 are borrowed from various approaches to exchange rate determination. The upper part of the table consists of economic fundamentals typically related to monetary exchange rate models. Specifically, these are the monetary aggregate M1, short- and long-term interest rates, and industrial production as a proxy for output. According to the monetary approach to the exchange rate, e.g. an increase in domestic money supply (output) leads ceteris paribus to a depreciation (appreciation) of the domestic currency. The empirical support for the monetary exchange rate model is mixed and often depends on the specific currency and the underlying sample period, see Rapach and Wohar (2004). Recently, Nautz and Offermanns (2005) and Nautz and Ruth (2005) showed that monetary exchange rate equations based on synthetic European data can provide an appropriate basis for euro/dollar exchange rate analysis. The current account is included in the empirical analysis as a reference to both portfolio balance models and behavioral equilibrium exchange rate (BEER) models. Both approaches to model exchange rate behavior use cumulated current accounts as a proxy for net foreign assets. According to the portfolio balance channel, investors require a risk premium for the adjustment of portfolio structures which is necessary to finance a domestic current account deficit. At given interest rates, this risk premium implies a depreciation of the domestic currency, see e.g. Taylor (1995) and Clostermann and Schnatz (2000). The variables shown in the lower part of the table are mainly inspired by BEER models which combine various economic arguments. The fiscal indicator (f isc), measured 4 Table 1. List of variables - (synthetic) European and US∗ data st M 1, M 1∗ iip, iip is, is il, il ∗ ∗ ∗ ∗ ∗ log nominal euro/dollar exchange rate (euro per dollar) log nominal M1 index of industrial production (proxy for output) short-term interest rate (Call Money Rate; IFS line 60B) long term interest rate (Government Bond Yield; IFS line 61) current account (as % of gdp) government expenditure (as % of gdp) relative prices in the traded and non-traded goods sector average labor productivity (as gdp per person employed) unemployment rate (ILO definition) log nominal oil price ca, ca f isc,f isc tnt, tnt u, u oil ∗ ∗ ∗ alp, alp Notes: Sample for Estimation: 1987:01 to 1998:12 (T=144 monthly observations). Sources: IFS, OECD, Eurostat, Statistisches Bundesamt. If monthly frequency data has been unavailable, we employ suitable interpolation methods. The construction of the pre-EMU aggregates follows Nautz and Offermanns (2005). Seasonal adjustment has been applied after aggregation, see Rietzler et al. (2000). as government expenditure relative to GDP, reflects the idea that foreign exchange risk premia may be associated with government debt stocks (Cheung et al. 2002) and decreasing confidence in a currency (Clostermann and Schnatz 2000). Relative prices in the traded and non-traded goods sector (tnt) are supposed to capture the BalassaSamuelson effect. A positive shock in average labor productivity alp can be assumed to trigger capital inflows, implying an appreciation of the exchange rate. An extensive discussion on the relevance of tnt, alp and other productivity measures for the synthetic euro/dollar exchange rate is delivered by Schnatz et al. (2003). Unemployment has rarely been considered in exchange rate economics, see MacDonald (2000). We include it into our model because financial markets seem to react sensitively to news in (particularly US-) unemployment, see Ehrmann and Fratzscher (2005). The oil price represents a key exogenous terms-of-trade shock. The presumption made here is that an oil price shock would lead to a depreciation in the currency of the country that depends relatively more on oil imports, i.e. the Euro area in our setup, see Clostermann and Schnatz (2000). In forecasting experiments, BEER models have proved to be at best competitive with conventional models, see e.g. Clostermann and Schnatz (2000) or Cheung et al. (2002). 5 3 3.1 A forecast equation for the euro/dollar exchange rate Cointegration analysis Unit root tests suggest that the log-levels of the variables introduced in Table 1 as well as their cross-country differentials are integrated of order one. 1 Therefore, to account for long-run equilibrium relations between the exchange rate and economic fundamentals, a cointegration analysis is performed in a first step.2 In line with the data-oriented modeling strategy, we do not impose coefficient restrictions on long-run parameters. Yet, to keep the cointegration analysis tractable, we follow e.g. Rapach and Wohar (2004) or Cheung et al. (2002) and assume a symmetric influence of domestic and foreign variables on the long-run equilibrium exchange rate. Consequently, all economic fundamentals (except, of course, the oil price) are included as cross country differentials dx = x∗ − x in the cointegration tests. Table 2 presents the results of the Johansen trace test applied to the synthetic euro/dollar exchange rate and the corresponding fundamentals over the pre-EMU period. The results are based on an unrestricted VAR including the exchange rate, the nine cross country differentials (see Table 1), and the oil price. The lag-length p = 8 was sufficient to obtain a statistically well-behaved specification. The cointegration rank r of the system is 2 at the 5 % significance level but 1 at the 1% level. In the following, we will assume r = 2 but the final assessment of the resulting exchange rate equation will not depend on that choice. Table 2. Cointegration test for exchange rate and fundamentals H0 r=0 r≤1 r≤2 Trace statistic 833.8 664.7 521.9 ∗∗ ∗ 5% critical value 786.8 660.5 546.5 1% critical value 831.4 700.3 580.7 Notes: The underlying system contains the synthetic euro/dollar exhange rate, the oil price and cross country differentials of the fundamentals shown in Table 1. Sample 1987:1 to 1998:12. Critical values of the Johansen trace test with small sample adjustment by Reimers (1992). ∗ (∗∗ ) denotes rejection of the null hypothesis at the 5%(1%) level. As a consequence of the eclectic modeling strategy, we do not attempt to identify structural long-run relations where the sign and magnitude of long-run coefficients 1 2 Results of unit root tests are not presented for sake of brevity but are available on request. A comprehensive survey on recent cointegration methods is provided by Hassler and Wolters (2005). 6 could be interpreted. Yet, in order to shed more light on the empirical relevance of specific fundamentals on the long-run equilibrium value of the exchange rate, we employed likelihood ratio tests to examine whether a variable could be excluded from both cointegrating relations. Table 3. Excluding fundamentals from the cointegrating relations H0 : exclude variable st dM 1 diip dis dil dca df isc dtnt dalp du oil χ2 statistic 12.05 19.19 8.72 3.18 21.91 1.03 20.61 19.70 0.19 16.49 ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗ marginal significance level 0.24% 0.01% 1.27% 20.41% 0.00% 0.00% 59.79% 0.00% 0.00% 90.91% 0.02% 28.13∗∗ Notes: Likelihood ratio tests for the exclusion of a variable from both cointegrating relations. ∗ (∗∗ ) denotes significance at the 5% [critical value: 5.99] (1% [critical value: 9.21]) level. According to Table 3, most of the economic fundamentals are important for the longrun exchange rate. Only unemployment, the fiscal variable and the short-term interest rate differential seem to be of less significance for exchange rate determination. These results support the common disregard of unemployment by the exchange rate literature. However, the low long-run impact of the fiscal indicator is at variance with the evidence provided by Clostermann and Schnatz (2000). In the following, we proceed without imposing zero restrictions on the cointegrating vectors. Excluding these fundamentals from the system would not affect the forecasting properties of the resulting exchange rate equation and our main conclusions. In line with the results presented in Table 3, we normalize the two cointegrating vectors with respect to the exchange rate and the money differential. This identifies the 7 following error correction terms (t-statistics in brackets): ec1,t = st − 0.95 diipt + 0.034dist − 0.104 dilt + 2.21 dcat (−1.36) (2.53) (−8.22) (1.48) + 3.30 df isct − 1.88 dtntt + 3.49 dalpt − 0.02 dut + 0.015 oilt (0.63) (−0.83) (4.67) (−0.58) (0.115) (1) ec2,t = dM 1t + 3.05 diipt − 0.006 dist + 0.03 dilt + 10.5 dcat (6.85) (−0.81) (3.55) (11.02) + 3.76 df isct + 10.73dtntt + 1.14 dalpt + 0.005dut + 0.45 oilt (1.13) (7.47) (2.39) (0.25) (5.45) (2) The cointegration analysis implies that the exchange rate adjusts to two separate longrun relations. The short-run dynamics of the corresponding error-correction equation are specified in the following subsection. 3.2 Short-run dynamics: automatic econometric model selection In empirical exchange rate economics, forecasting contests are an important measure of evaluation for theory-based models, as the link between in-sample criteria and forecasting performance is far from obvious. If, however, researchers are tempted to optimize their specifications with respect to forecasting performance, the models are in danger of becoming less suited for the goal of gaining insight into the mechanisms governing foreign exchange markets. Therefore, computer-automated model selection appears to be particularly attractive in the field of exchange rate economics, as it guarantees that the criteria used for model determination are distinct from to the criteria used for model evaluation. Apart from the issue of transparency of model determination, automatic model selection serves to separate the variables containing useful information from the nuisance variables, and those variables that contain some, but very little information. While increasing the number of explanatory variables can only increase the in-sample fit of an equation, parsimonious models have the advantage of more precise parameter estimates. The large number of variables considered in the exchange rate literature illustrates the need to concentrate on some of them. Which of the variables shown in Table 1 to retain and which to drop, and whether to use predominantly theory or statistics to that end, is an open issue. In the following, we use the PcGets software by Hendry and Krolzig (2001) to determine the short-run dynamics of the error-correction equation of the euro/dollar exchange rate. Starting point of the procedure is the estimation of a general unrestricted model, which contains the full information set. In our application, the information set used to determine the short-run dynamics comprises five lagged differences of the explanatory 8 variables shown in Table 1 and the error correction terms (1) and (2). The features of the automatic econometric model selection procedure of the PcGets software can be sketched as follows. Moving from general-to-specific, irrelevant variables are subsequently eliminated from the model, as indicated by their significance levels. Where alternatives in the elimination process arise, the software follows the different paths, and continues the simplification with union models of the pursued alternatives. If finally, more than one candidate model remains, the winner model is chosen on the basis of a standard information criterion. PcGets includes two predefined model selection strategies which according to Hendry and Krolzig (2001) have proved to yield satisfactory results in many applications. The l iberal strategy implies that more parameters remain in the model, whereas the significance levels of the conservative setting are stricter implying more parsimonious models. In the following, we use the conservative strategy but the results remain virtually unchanged for the richer model obtained by the liberal strategy. A number of specification tests (tests for autocorrelation, heteroscedasticity, normality, and structural breaks) ensure that at the starting point and each step of simplification, all models are statistically well behaved. Eventually, we obtain the following forecast equation for the euro/dollar exchange rate: ∗ ∆st = − 0.091 ec1,t−1 − 0.044 ec2,t−1 + 0.33 ∆st−1 − 0.02 ∆ilt−3 (−3.78) (−2.36) (4.47) (−2.75) + 0.69 ∆alp∗ t−4 (3.01) + 1.75 ∆ca∗ t−2 (2.68) + 2.47 ∆ca∗ t−5 (3.72) (3) The R2 of equation (3) is 0.34, which is remarkably high given the parsimonious specification. Interestingly, only US variables appear in the short-run dynamics of the exchange rate equation, which matches the finding of Ehrmann and Fratzscher (2005) that US macroeconomic news are more important for euro/dollar exchange rate movements than euro area news. Note that the short-run dynamics are all plausibly signed. In particular, the significance of productivity and the current account supports the relevance of fundamentals emphasized by behavioral equilibrium exchange rate models. 3.3 Exchange rate forecast evaluation Following the empirical literature, let us now evaluate out-of-sample forecasts of the estimated exchange rate equation to assess its ability to explain the euro/dollar exchange rate from 1999–2003. The forecasting experiments are conducted as rolling dynamic out-of-sample forecasts, starting from the perspective of the end of December 1998, with the coefficients of the models kept fix. Forecasts are conditional in the sense that 9 each forecast uses preceding exchange rate forecasts, while future values of the remaining explanatory variables are treated as known. Root mean square errors (RMSE) for various predictive horizons of the selected exchange rate equation and two benchmark models are presented in Figure 1. Figure 1. Euro/Dollar exchange rate forecast errors Notes: RMSEs of dynamic out-of-sample forecasts from the exchange rate equation (3), the random walk, and the monetary model, see Nautz and Offermanns (2005). The forecasting period is 1999:01 to 2003:12 implying 60 forecasts for h = 1, and 25 forecasts for h = 36. Apparently, the eclectic exchange rate equation (3) fails if evaluated out-of-sample. In spite of its promising in-sample properties, forecast errors are larger than those obtained from a random walk virtually at each horizon. Figure 1 also contains the RMSEs of a standard monetary exchange rate equation for the euro/dollar exchange rate suggested by Nautz and Offermanns (2005). This shows that the failure of the eclectic exchange rate equation cannot be explained by specific data problems or the uncertainty related to a new currency. Note that the eclectic exchange rate equation is outperformed by an equation that restricts the attention a priori to a subset of economic fundamentals. 3 Interestingly, automatic model selection did not further improve the forecasting performance of the monetary model. While in-sample criteria improved substantially, the forecasting performance of the automatically augmented monetary exchange rate equation incurred a complete breakdown. 3 10 4 Conclusions The empirical analysis of exchange rates is usually based on a particular exchange rate model. As a result, the focus is on a few model-specific factors while other determinants of the exchange rate, maybe suggested by competing exchange rate models, are neglected. This paper investigated the usefulness of an eclectic view on the euro/dollar exchange rate. We considered a broad set of economic fundamentals suggested to be influential for the exchange rate by various theoretical approaches including the monetary model of the exchange rate, the portfolio balance approach or behavioral equilibrium exchange rate models (BEER). Cointegration analysis combined with automatic model selection procedures lead to an exchange rate equation with promising in-sample properties. However, evaluating outof-sample forecasts revealed that its predictive ability is extremely poor. In particular, in contrast to an equation based on a standard monetary exchange rate model, forecasts of the eclectic exchange rate equation could not even beat a random walk. Our results indicate that small, structural exchange rate models can be more useful than eclectic approaches which may cover more fundamentals but are less related to a sharplyarticulated economic theory. References Cheung, Yin-Wong, Menzie D. Chinn, and Antonio G. 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