MONEY, PRICES AND THE EXCHANGE RATE: EVIDENCE FROM FOUR OECD COUNTRIES

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1 money 15/10/98 MONEY, PRICES AND THE EXCHANGE RATE: EVIDENCE FROM FOUR OECD COUNTRIES Mehdi S. Monadjemi School of Economics University of New South Wales Sydney 2052 Australia December 1997 Abstract This study examines the short-run and the long-run responses of price and exchange rate to changes in monetary conditions. The empirical results of the study, based on monthly data from Britain, Canada, Germany and Japan, provide support for overshooting exchange rate in the short-run. Furthermore, the hypothesis of a proportional relationship between price ratio and the exchange rate as indicated by purchasing power parity is not empirically supported. However, the results of the study show that domestic price, foreign price and the exchange rate are cointegrated.

2 1 1. Introduction In an open economy with a flexible exchange rate system the effects of monetary policy are transmitted to the economy through changes in interest rates and the exchange rate in the short-run, and through changes in the price level in the long-run. The effects of monetary policy in an open economy were initially discussed in Mundell (1963) and Fleming (1962). The Mundell-Fleming model is basically a short-run model since it assumes a fixed price level. Sometimes this model is also called an open economy Keynesian model. With the advents of the 1970s, a fixed price model had very little applicability. Dornbusch (1976) developed a model of an open economy with fixed and flexible price levels. Dornbusch assumed that the price level is flexible in the long-run and rigid in the short-run. With the help of this and some other behavioural assumptions, Dornbusch was able to explain the responses of the price level and the exchange rate to a monetary shock. In Dornbusch s model the exchange rate overshoots its long-run equilibrium in the short-run but retrieves to a new equilibrium in the long-run. The price level remains constant in the short-run and changes in the long-run proportional to the exchange rate and money. Dornbusch s theoretical proposition was subject to several empirical investigations. In particular, recently Eichenhaum and Evans (1995) (EE) provided no support for the overshooting proposal and showed that the exchange rate appreciates persistently after introduction of a contractionary monetary shock. The authors also provided evidence against the uncovered interest parity condition. The purpose of this paper is to examine the effects of a change in interest rates on the exchange rate using an error correction model (ECM). The theoretical discussions of the paper are given in Section 2. The econometric methodology is discussed in Section 3. Data description and empirical results are presented in Sections 4 and 5 respectively. Summary and concluding remarks are offered in Section 6.

3 2 2. Theoretical Discussion A model of exchange rate determination may be developed using Dornbusch (1976) as a starting point. In Dornbusch s model an LM type of equation representing the monetary equilibrium, the uncovered interest parity condition and an exchange rate adjustment mechanism constitute the main theoretical framework of the model. These basic relationships are presented in equations 1, 2 and 3. * it it = Et 1 et (1) ( M / P) = α βr + γ y (2) t t t ( ) E 1 e = f e e t t t (3) * where i t, i t, Et-1, (M/P) t, y t, e t and e respectively are the domestic rate of interest, the foreign rate of interest, the expectations formed at time t-1, the real value of money stock, the level of output, the nominal exchange rate defined as the domestic price of foreign currency and the equilibrium exchange rate respectively. All variables except the exchange rate are in logarithms. By combining equations 1, 2 and 3 one is able to derive a single equation with six variables including it it *, e t, e t, y t, M t and P t. Data on these variables are available readily with the exception of the long-run equilibrium exchange rate. In Dornbusch s model the deviation of the exchange rate from its long-run equilibrium is proportional to the deviation of price level from its long-run equilibrium. Again, the long-run price level remains as a variable which needs to be quantified. In this paper it is assumed that the long-run equilibrium value of the exchange rate is determined by the current account. This assumption is based on models developed in Kouri (1976), Branson (1979) and Dornbusch and Fischer (1980) in which the path of the exchange rate is determined by the current account. The model used here is similar to EE s, with the

4 3 exception of the choice of monetary variable. In EE s model, the effects of shocks to monetary policy are represented by three measures, including innovations to the federal fund rate, ratio of non-borrowed to total reserves, and a special index for monetary policy contractions suggested by Romer and Romer (1989). Here, it is assumed that the effect of monetary policy on the economy is mainly transmitted through changes in the rate of interest. Hence, the empirical analysis of the model will examine the response of the exchange rate to changes in domestic interest rates relative to the foreign rate. It is argued that the effect of a shock to interest rate differential is similar to the effect of a shock to a monetary variable. Accordingly, by including an interest rate differential in the model, one may capture the effects of a monetary policy shock without explicitly including a proxy. The following vector autoregressive model (VAR) is employed as a framework for analysing the dynamic responses of five bilateral exchange rates. X = A( L) Y + U t t t [ t t t t t t] where X t is a vector of six time series, M, C, y,( i i* ), P, e, ( ) AL is ( p p) polynomial matrix in the lag operator L and V t is a vector of random disturbances with U N( ) t ~, 0 Σ and C t is the balance on the current account. 3. Econometric Methodology Most macroeconomic time series are non-stationary in levels and the use of conventional regression techniques with such data tends to produce spurious results. However, non-stationary time-series data may be cointegrated if some linear combinations of the series become stationary. That is, the series may wander around, but in the long-run there are economic forces that tend to push them to an equilibrium. That

5 4 is, cointegrated series will not move far away from each other and are linked in the longrun. Johansen (1988 and 1991) suggested tests for determining numbers of cointegrating vectors among a group of variables. Consider the following p variable VAR model: k Y = u+ φ Y + ε t i t i t i= 1 (6) where u is the constant term, Y t is (p 1) vector of the variables under study, and the disturbance vector ε t of dimension (p 1) is distributed as an i.i.d. Gaussian process with zero mean and variance Ω. Assuming that the series are cointegrated, equation 2 may be re-parameterised to give the following ECM representation: k 1 t i t i t k t i= 1 Y = u+ Γ Y + ΠY + ε (7) Γ j j = I φ i i= 1 (8) Π= I k φ i i= 1 (9) where I is the identity matrix. [See Johansen (1991) for details.] The long-run relationship between the series is determined by the rank of Π. If time series are non-stationary and cointegrated, then Π is not full rank, but 0 < rank(π) = r < p, where r is the number of cointegrating vectors. Johansen (1991) proposed two likelihood testing procedures in order to estimate the rank of Π. The first tests the hypothesis that the number of cointegrating vectors is, at most, equal to r (Trace test). The second tests the hypothesis that the number of cointegrating vectors is equal to r (Max Eigenvalue test). When the series are found to be cointegrated, Johansen further demonstrates that Π can be factored as:

6 5 Π= αβ (10) where β is the matrix of r cointegrating vectors and α is the matrix of weights attached to each cointegrating vector in equation 3. Both α and β are (p r) matrices. 4. Data Description All of the data in this study are monthly time series on OECD countries collected from the Time Series Data Express, dx v2.1, site licence held by the School of Economics, University of New South Wales, Sydney, Australia. The interest rate series are averages of overnight money market rates during the month. The exchange rate series are end of the month bilateral exchange rate against the U.S. dollar measured by the number of U.S. currency in one unit of domestic currency. The price level is the all items consumer price indices. The money stock is the monthly observation on M1. The level of output is measured by the index of domestic production. The balance on current account is approximated by the difference between exports and imports. 5. Empirical Results The Augmented Dickey-Fuller and Phillips-Perron s test for unit-roots were applied to six time series in each individual country, and the results indicated that all variables are non-stationary in levels but stationary in first differences. The results of the Johansen test for cointegration are reported in Table 1. These results indicate that the hypotheses of two cointegrating vectors for Britain, Canada and Japan and one cointegrating vector for Germany cannot be rejected at the 5 percent significant level. Normalized coefficients of cointegration are also reported in Table 1. These results indicate that there is a long-run equilibrium between variables included in the model. The

7 6 results are supportive of Dornbusch s theoretical proposal that suggested the existence of a long-run equilibrium in the model of exchange rate determination. However, Dornbusch showed that the purchasing power parity (ppp) holds in the long-run but not in the shortrun. This issue will be discussed after the dynamic responses of variables to a monetary shock are examined. The dynamic interactions among various variables can be examined by impulse response functions (IRF) and variance decompositions (VDC). To this end, as suggested by Engle and Granger (1987), the estimated coefficients of ECM are converted into levels and are inverted to vector moving average form. However, since coefficients of ECM are reduced form, they can provide little information about the structural coefficients of the model. In order to draw useful structural information, some form of identifying restrictions that are consistent with economic theory should be imposed on the ECM. Orden and Fisher (1993) used a standard Choleski-type of contemporaneous identifying restriction. This type of restriction is less restrictive than the long-run zero identifying restrictions used in King et al. (1991). In this study a Choleski-type of identifying restriction is imposed on the ECM. When this type of restriction is used, the ordering of variables imposes a particular recursive structure on the model, so that variables appearing earlier contemporaneously influence the latter variables, but not vice versa. The recursive order of variables chosen here is M t, y t, C t, P t, r * r and e t. This type of recursive ordering allows the contemporaneous values of M t to affect all of the other variables. t t

8 Table 1 RESULTS OF COINTEGRATION TEST Hypothesis Trace 95%CV Alternative λ Max 95%CV Britain r r = r r = r r = r r = r * r = * r * r = * Normalized Coefficients of Cointegrating Vectors m t y t * it it P t C t e t (0.013) (0.18) (0.13) (0.29) (0.002) (0.02) (0.02) (0.04) Canada r r = r r = r r = r r = r * r = * r * r = * Normalized Coefficients of Cointegrating Vectors m t y t * it it P t C t e t (0.018) (0.15) (0.92) (0.32) (0.00) (0.05) (0.31) (0.11) Germany r r = r r = r r = r r = r r = r * r = * Normalized Coefficients of Cointegrating Vectors m t y t * it it P t C t e t (0.31) (0.006) (0.15) (0.07) (0.11) Japan r r = r r = r r = r r = r * r = * r * r = * Normalized Coefficients of Cointegrating Vectors m t y t * it it P t C t e t (0.01) (0.16) (0.13) (0.29) (0.00) (0.02) (0.018) (0.04) Sample periods are Number of lags are 4. *indicates significant cases. 7

9 8 In Table 2 the results of VDC for 1, 5, 10, 15 and 20 quarters ahead are reported. These results show the relative importance of various shocks in forecast error variance of exchange rate. With the exception of Japan, and to some extent Germany, in the other two cases, the interest rate differentials are important variables in explaining forecast error variance of nominal exchange rates. The results of IRF derived from the ECM are presented in Figure 1 1. These functions show the dynamic responses of nominal exchange rate to one standard deviation shock of the interest rate differentials between the U.S. rate and the rates in each particular country. The U.S. rate is treated as the foreign rate. The exchange rate is measured by the number of U.S. currency per unit of domestic currency, so the downwards movement of the exchange rate means appreciation of the domestic currency. The confidence intervals are not produced here. However, a particular response is considered significant if it is located further away from the zero line. Accordingly the IRF results show that the responses of nominal exchange rates to shocks of interest rate differentials were significant in all cases except Japan. Moreover, in the cases of Britain and Canada the exchange rate appreciated and remained high over the long-run. The Deutschmark did not follow this pattern as the exchange rate returned to its initial level over a long period of time. However, in Germany, like the other two countries, the sharpest depreciation occurred during the initial periods. Accordingly, the results of this study show overshooting of the nominal exchange rate in the short-run. These results are in contrast with EE results, in which the sharpest appreciation of the nominal and real exchange rates to a negative innovation in monetary policy instrument occurred roughly about months after the shock was introduced.

10 9 Table 2 VARIANCE DECOMPOSITION OF NOMINAL EXCHANGE RATE Britain Months Ahead m t y t c t p t i * t i t e t Canada Germany Japan Sample periods are Variables are in log levels as specified in the ECM. Lag length of variables is six for Japan and four for the other three countries. 1 In Figure 1, ED, EC, EG, EJ, and ID are the exchange rates in Britain, Canada, Germany, Japan and the interest rate differential respectively.

11 10

12 11 Testing for Purchasing Power Parity (ppp) One of the important implications of Dornbusch s model is the existence of ppp in the long-run. That is, in the long-run the exchange rate and the price level move proportionally, leaving the real exchange rate constant. Kim (1990) examined this hypothesis in the context of cointegration of the exchange rate and the price ratio. Using this approach assumes that the exchange rate and the price ratio are related through the following equation. st = a0 + a1 pt + ut (11) where p t is the log of the ratio of domestic and foreign prices. Kim (1990) argued that the hypothesis of long-run ppp is accepted if a 1 = 1 and u t is a stationary autoregressive process. The empirical results of this study showed that in a group of five OECD countries, ppp was accepted for France, Italy, Japan and U.K. but not for Canada. He argued that the Canadian data against the U.S. showed very little fluctuation and, hence, the resulting regressions failed to produce significant coefficients. A similar approach is followed here using monthly data on four OECD countries. The hypothesis of ppp is accepted if the coefficient of price ratio in an equation similar to equation 11 is equal to 1, and the residual of the regression is a stationary process. These results are presented in Table 3. The price ratio is the log of the ratio of domestic CPI to the U.S. CPI, and the exchange rate is the logarithm of the number of U.S. dollars in a unit of domestic currency. The sign of the coefficient of the price ratio is expected to be negative. This means that as the price ratio rises, the domestic currency weakens against the U.S. dollar.

13 12 Table 3 TESTS FOR PURCHASING POWER PARITY Coefficient of price ratio ADF T Test ADF T Test for real exchange rate Britain (-13.7) Canada (-15.00) Germany (-11.5) Japan (-25.3) MacKinnon critical values for rejection of hypothesis of unit root at 1% and 5% significant levels are and respectively. The values in brackets are t ratios. The results presented in Table 3 indicate that the coefficients of price ratio are significantly different from zero, but the values of coefficients are not close to 1. Furthermore, Augmented Dickey-Fuller (ADF) statistics tend to accept the hypothesis of unit-root in residuals. The last column in Table 3 shows ADF test results for stationarity of real exchange rate. In the long-run the hypothesis of ppp is valid if the real exchange rate is a stationary process. Kim (1990) and Frenkel (1986) accepted the stationarity of the real exchange rate, whereas Adler and Lehman (1983) rejected it. The results in Table 3 provide further evidence for the rejection of ppp. All of the ADF statistics indicate that the real exchange rates are non-stationary. A further test of ppp was conducted by applying Johansen s procedure to the Trivariate case of (p, p* and e), where p* is the foreign price. Evidence of cointegration may indicate that there is a long-run equilibrium between domestic price, foreign price

14 13 and the exchange rate. This evidence also suggests stationarity of the real exchange rate. The results of the Johansen test are reported in Table 4. Table 1 RESULTS OF COINTEGRATION TEST FOR PPP Hypothesis Trace 95%CV Alternative λ Max 95%CV Britain r r = r r = r * r = Canada r r = r r = r * r = Germany r r = r r = r * r = Japan r r = r r = r * r = Sample periods are Number of lags are 4. * indicates significant cases. The results of the Johansen test indicate that in all four cases domestic price, foreign price and the exchange rate are cointegrated. These results provide some support for ppp, however, they are in conflict with the results of the ADF test. Similar conflicting results were reported by Cheung and Lai (1993). The authors argued that the conflict is due to the low power of the ADF test. Furthermore, they also showed that the hypothesis of cointegration is more likely to be rejected when the number of variables tested is

15 14 reduced to one, which simply means testing for cointegration of real exchange rate. The authors state that rejection of ppp may still be supportive of ppp with measurement error. The regression results reported in Table 3, together with the results of the Johansen test, may indicate the existence of a long-run relationship between prices and the exchange rate. The empirical results of this study are in agreement with Cheung and Lai (1993) and are in conflict with Kim (1990). The conflict may be explained in terms of the use of high-frequency data. Most studies in this area agree that ppp should be tested in the long-run rather than short-run. However, there is not a firm agreement on whether high (monthly) or low (annual) frequency data should be used. For example, Glen (1992) employed both monthly and annual data and rejected the hypothesis of random walk in real exchange rate in the long-run. Pippenger (1993) used monthly data over the period and showed that ppp is a valid proposition for four out of seven OECD countries. Furthermore, Cheung and Lai (1993) found evidence in favour of ppp using monthly data during the post-bretton Woods period. Therefore, there is evidence in the literature indicating that ppp may be accepted using low-frequency as well as highfrequency data. The results of this study, based on four countries, show that when price ratio changes, the exchange rate moves according to the direction predicted by ppp. However, the empirical results fail to provide support for the proportional movements of price ratio and the nominal exchange rate. 6. Summary and Concluding Remarks An attempt was made in this paper to examine the response of nominal exchange rate to change in monetary conditions using monthly data on four OECD countries. In particular, the analysis of the study concentrated on the topic of overshooting exchange rate as advocated by Dornbusch (1976). In contrast to Eichenbaum and Evans (1994), the

16 15 empirical results of this study support the overshooting hypothesis for three of the four countries under study. The empirical analysis of the study examined the dynamic responses of nominal exchange rate to changes in interest rate differentials between the domestic and foreign rates of interest. The use of interest rates rather than money was justified on the grounds that the effect of changes in monetary conditions is transmitted to the exchange rate via variations in interest rates. In contrast to Dornbusch s proposition, the hypothesis of proportional relationship between price ratios and the exchange rate was not supported by data. However, the empirical results showed a significant, but not proportional, relationship between price ratios and the nominal exchange rates. Moreover, the results of the Johansen test showed that domestic price, foreign price and the exchange rate are cointegrated.

17 16 References Adler, M. and Leham, B. (1983), Deviations from Purchasing Power Parity in the Long Run, Journal of Finance 83, Branson, W.H. (1977), Asset Markets and Relative Prices in Exchange Rate Determination, Sozialwissenschaftliche Annalen 1, Cheung, Y.W. and Lai, K.S. (1993), Long-Run Purchasing Power Parity during the Recent Float, Journal of International Money and Finance 34, Dornbusch, R. (1976), Expectations and Exchange Rate Dynamics, Journal of Political Economy 8, Dornbusch, R. and Fisher, S. (1980), Exchange Rate and the Current Account, American Economic Review, December, pp Driskill, R.A. (1981), Exchange Rate Overshooting, The Trade Balance, and Rational Expectations, Journal of International Economics 11, Eichenbaum, M. and Evans, C. (1994), Some Empirical Evidence on the Effect of Shocks to Monetary Policy on Exchange Rates, Quarterly Journal of Economics CX, 4, Fleming, J.M. (1962), Domestic Financial Policies under Fixed and Floating Exchange Rates, IMF Staff Papers 9, Frankel, J.A. (1986), International Capital Mobility and Crowding-out in the U.S. Economy: Imperfect Integration of Financial Markets or of Good Markets? in How Open Is The U.S. Economy?, edited by Ruth W. Hafer, 33-67, Lexington Mass. Fuller, W.A. (1976), Introduction to Statistical Time Series, New York, Wiley and Sons.

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