Is there an empirical link between the dollar price of the euro and the monetary fundamentals?

by

Costas Karfakis[1]

ABSTRACT

This paper examines the empirical link between the dollar exchange rate of the euro and the monetary fundamentals. The exchange rate is found to be cointegrated with money and income differentials, while the homogeneity restrictions are supported by the data. The weak form restrictions of the present-value model of the foreign exchange market are not rejected by the data, but the most stringent restrictions are strongly rejected. An estimated error-correction model explains a substantial part of the short-run exchange rate volatility and outperforms the random walk forecasts.

Keywords: dollar price of euro, monetary fundamentals, present-value model, cointegration, VAR, error-correction model

JEL classification: F31

Is there an empirical link between the dollar price of the euro and the monetary fundamentals?

1. Introduction

Since euro began its life in January 1999, it was trading at 1,167 dollars. By September 2000 the euro had fallen below 0,90 dollars and by early November 2000 had reached its nadir of 0,83 dollars. Thereafter, the euro fluctuated significantly with an upward trend. By the end of 2002, the euro was trading at par with the dollar. The appreciation of the euro continued and in the beginning of the first week of 2004 it hit a lifetime high, rising to 1,27 dollars. In turn, it slipped back to 1,20 dollars per euro, and then started to rise again.

Market commentators and currency analysts have attributed the swings of the dollar price of the euro to the combination of a number of factors, such as differences in the rates of growth and productivity between the euro area and the USA, differences in the interest rates between the two areas, the alarming increase in the US current account deficit and the cross border capital movements.

The empirical literature has investigated the determinants of the “synthetic” nominal and real exchange rates of the euro against the dollar. Sartore et al (2002) constructed an econometric model of the euro-dollar real exchange rate, which estimated from January 1990 to December 1999. The real exchange rate equation depended on the real long-term interest rate differential, the ratio of traded to non-traded goods prices, a measure of fiscal policy, the real price of oil and the terms of trade. The cointegration analysis showed a well-established real exchange rate equation, while the forecasting performance of the short-run model was satisfactory compared with random walk forecasts. Jamaleh (2002), on the other hand, constructed an econometric model of the euro-dollar nominal exchange rate, which estimated from January 1992 to August 2000. The exchange rate equation depended on short-term interest rate differential, income differential and inflation differential. The empirical analysis showed that the model performed well, while the introduction of nonlinear effects improved the forecasting performance of the model. Ehrmann and Fratzscher (2004) examined whether the real-time news of fundamentals in USA and in the euro area affected the euro-dollar exchange rate using daily data from 1 January 1993 to 14 February 2003. The empirical findings confirmed that the new component of macroeconomic announcements had a significant impact on the exchange rate. Brooks et al (2004) examined the role of capital flows in determining the dollar price of the euro, using quarterly data from 1988 to 2000. The analysis showed that net portfolio flows tracked movements in the exchange rate of the euro against the dollar.[2]

The purpose of this paper is to contribute to the existing literature by analyzing the behaviour of the dollar price of the euro since its inception in the context of the analytically attractive present-value monetary model.[3] The following issues are addressed:

1. Is there an empirical link between the dollar price of the euro and the monetary fundamentals?

2. Does the difference between the current exchange rate and the current monetary fundamentals determine the future changes in the monetary fundamentals, as implied by the present-value monetary model?

3. To what extent the changes in the dollar price of the euro are predictable and how they are related to random walk forecasts?

2. The Present-Value Monetary Model

The present-value monetary model of the exchange rate determination is given by the following equation:

(1)

where et, ft denote is the logarithms of the exchange rate, defined as dollars per euro, and the monetary fundamentals, defined as (y-y*)-(mt-mt*), where y, y* are the logarithms of the domestic and foreign income, and mt, mt* are the logarithms of the domestic and foreign money stocks, σ is the interest rate elasticity of money demand and Ht is the information set.

Subtracting ft from both sides yields, after a little manipulation:

(2)

where Dt=et-ft.

Bringing (2) one period backward and taking expectations at t-1, yields:

(3)

Multiplying (3) by 1+σ/σ and subtracting the resultant expression from (2), yields, after little manipulation:

(4)

The left-hand side of expression (4) is the unforecastable revision from t-1 to t in the expected change in the monetary fundamentals.

3. Methodological Issues

Assuming that the monetary fundamentals are I(1) processes, the right-hand side of (2) is stationary, implying that the left-hand side must also be stationary. Alternatively, et and ft are cointegrated with a cointegrating vector [1 –1]. Thus, we can model the data generation process for Δft and Dt as a bivariate VAR system, in the context of which the restrictions of the present-value monetary model can be examined.

Consider the following bivariate VAR model

(5)

where z=[Δf D]’ is a 2x1 vector of endogenous variables; Ψ=[Ψ1 Ψ2]’ is a fixed intercept vector; A(L)=[AΔf(L) AD(L)] is a 2x2 polynomial matrix in the lag operator, with AΔf(L)=[a(L) c(L)]’ and AD(L)=[b(L) d(L)]’; Σt=[v1t, v2t]’ is a 2x1 vector of white noise errors with properties: E(vt)=0, E(vt, vt-s)=Σ when t=s and zero otherwise, with Σ denoting the variance-covariance matrix of residuals. The polynomials in the lag operators a(L), b(L), c(L) and d(L) are all of order p.

An implication of the present-value model of exchange rate determination for the VAR system (5) is that Dt will Granger-cause the future path of Δft if agents have information beyond the history of Δft. This constitutes the weak form restrictions of the present-value model. If we assume that a second-order VAR captures the time-series properties, the VAR model (5) can be written as:

= (6)

or, in compact notation, as Xt=ΓXt-1+wt, where E(Xt+j½Ωt)=ΓjXt for all j, where Ωt is the information set containing current and lagged values of Δft and Dt. Using (6), the restrictions on Dt in (2) can be expressed as:

(7)

where and .

These restrictions insure that for any Xt, Dt equals the expected present value of Δft. Post-multiplying both sides of (7) by (I-(σ/1+σ))Γ yields the following set of restrictions:

(8)

By writing out the restrictions on the individual coefficients of matrix Γ, we get –c1=a1, -c2=a2, d1+b1=1+σ/σ, -d2=b2. To interpret these restrictions, add the Δft equation of the VAR to the Dt equation to get:

(9)

or, (10)

where

The left-hand side of (10) is unpredictable given lagged values of Δf and D, which follows from equation (4). Hence a test of this set of restrictions can be obtained using a Wald test of the orthogonality of ξt on the information set consisting of lagged values of Δf and D. This constitutes the strong form restrictions of the present-value model.

4. Empirical Analysis

Data. We use monthly US and euro area observations on the exchange rate, defined as dollars per euro, money supplies and industrial production indices from the International Statistical Yearbook CD-ROM from January 1999 to March 2004. All the data were transformed in logarithms.

Unit roots. Estimation of the VAR system (5) requires investigation of the time-series properties of the variables involved. Chart 1 plots the variable Dt, which is the difference between the current exchange rate and the current monetary fundamentals - called the error correction (EC) term. A feature of this graph is the marked decrease for Dt up to the end of 2001 and a substantial increase thereafter, implying that the series exhibits a change in the slope around the end of 2001. Thus, the unit root test proposed by Perron (1988), and Zivot and Andrews (1992) is used to test the univariate time-series properties of Dt. This test is more robust than the traditional ADF test, when the time series has a structural break.

Consider the null hypothesis that the series Dt is integrated without an exogenous structural break, that is:

(11)

where m is the constant and ωt is a stationary error term. The alternative hypothesis stipulates that the EC term Dt can be represented by a trend-stationary process with a one-time break in the slope of the trend function, occurring at an unknown point in time, that is

(12) where DTt (l)=t-Tl if t>Tl and 0 otherwise, l=TB/T and TB is the breakpoint.[4] The goal is to estimate the breakpoint that gives the most weight to the trend-stationary alternative. Equation (12) was estimated with the breakpoint TB, ranging from t=2 to t=T-1, and the breakpoint is the month corresponding to the minimum t-statistic over all regressions.

Table 1 reports the results for those months where the breakpoint gives most weight to the trend-stationary alternative. The estimated break date occurs at December 2001 and the unit root hypothesis is rejected at the 1 percent significance level. This result states that the EC term Dt can be characterized as a trend-stationary process with on-time shift in the slope of the trend function.

ARDL Cointegration. The hypothesis that the EC term Dt is stationary can also be investigated in a multivariate context by testing whether or not et, (yt-y*t) and (mt-m*t) are cointegrated with a cointegrating vector [1 1 –1]. The proportionality postulate between exchange rate, income differential and money differential is explained by means of the Autoregressive Distributed Lag (ARDL) procedure advanced by Pesaran, Shin and Smith (2001). The main advantage of this strategy is that it can be applied irrespective of whether the series are I(0) or I(1) processes. The maximum lag length is set at 6 and the optimum lag structure is selected by using the Schwarz Bayesian Criterion (SBC). The underlying ARDL(2,1,0) exchange rate equation, which is reported in the first panel of Table 2, satisfies all econometric criteria namely absence of serial correlation, absence of functional misspecification, existence of normality and homoscedasticity. CUSUM stability tests showed that the equation remained stable over the sample period. The estimated long-run monetary model using the ARDL approach is presented in the second panel of Table 2. The Wald test statistics of the homogeneity restrictions do not reject the hull hypothesis in all cases.

We have also tested for the proportionality postulate between et and ft by means of the ARDL approach. The underlying ARDL(2,0) exchange rate equation, which is also reported in the first panel of Table 2, is well specified. The Wald test statistic of the unit restriction does not reject the hull hypothesis. This evidence, which is consistent with the stationarity of Dt, suggests that the monetary model is validated as a long-run equilibrium relationship, in the sense that a cointegrating relationship exists among the exchange rate and the monetary fundamentals, which appears to satisfy the homogeneity restrictions.

VAR model. The data generation mechanism of Δft and Dt is modeled as a bivariate VAR system in the context of which the present-value monetary model can be examined. The strategy adopted in specifying the optimum lag length of the VAR model was based on the SBC along with LM tests for serial correlation, functional form, normality and heteroscedasticity. In applying these criteria, the maximum lag length of the model was set at 6. The system also included three exogenous regressors: an intercept, a time trend and the dummy variable DT with the breakpoint set at December 2001. The results showed that the SBC selected a VAR(2), while the diagnostic tests, which are reported in the first panel of Table 3, rejected any kind of misspecification.

The results of Granger causality F-tests, which are shown in the second panel of Table 3, suggest that the past history of Dt does not have information content to predict future movements in Δft. Since this finding is sensitive to the presence of the exogenous regressors in the equation of Δft,[5] and given that the past history of Δft does not Granger cause Dt, a restricted VAR system was estimated by SURE. The Δft equation included two lagged values of both variables, while the Dt equation included two lagged values of itself together with the three exogenous regressors. The result of the Wald statistic indicates that the past history of Dt has information content to predict future movements in Δft, as suggested by the present-value approach to exchange rate determination.

The most stringent restrictions of the present-value model were examined by regressing the variable ξt, which was calculated for different values of the interest rate elasticity of money demand, on lagged values of Δf and D and tested the hypothesis that the coefficients are jointly zero. The evidence reported in the third panel of Table 3 rejected the restrictions imposed on the data. Despite the rejection of the strong form restrictions, the monetary model is validated as a long-run equilibrium relationship, in the sense that we have found a cointegrating relationship between exchange rate and the monetary fundamentals which appears to satisfy the homogeneity restrictions.

EC model. Estimated exchange rate models, by and large, perform poorly when predicting out-of sample, compared to random walk forecasts. Given the strong link between the dollar exchange rate of the euro and the monetary fundamentals, it is interesting to see how an estimated EC model predicts post-sample. The results of the EC model, which is estimated by the method of Instrumental Variables (IV) in order to correct for the possibility of simultaneous equations bias, is presented in Table 4. All diagnostics show that the model is well specified. The Wald test statistic, which is equal to 0,096 (with a p-value of 0,76), shows that the growth rate of the monetary fundamentals has a proportional impact on the growth rate of the exchange rate. The EC term is negative and statistically significant. The size of the EC term, which is equal to –0,53, suggests a high speed of adjustment of the exchange rate to equilibrium. In Chart 2, we have plotted the actual and fitted values of the EC model. The value of R2 suggests that 40 percent of the short-run variation in the dollar exchange rate of the euro is explained by the monetary fundamentals.