The response of real exchange rates to various economic shocks.

I. Introduction

Substantial fluctuations in real exchange rates, i.e., deviations from purchasing power parity (PPP), which closely mirror movements in nominal rates, have been one of the most notable international economic events since the breakdown of the Bretton Woods system. Dornbusch's disequilibrium theory [9], which presumes different speeds of adjustment in assets and goods markets, offers an explanation for temporary deviations from PPP only. Models assuming PPP as a long-run relationship have not been successful in interpreting the movements of the real exchange rates. Although, studies conducted for countries experiencing high or hyper-inflation provide evidence favoring PPP [42; 30; 29], the empirical evidence on PPP for industrialized, low inflation countries is not generally favorable.(1) This is consistent with the view that PPP may hold better in high-inflation countries where the disturbances to their economies are mostly monetary in origin [31,123-24], but PPP may not hold well when the real disturbances, which change equilibrium relative prices, dominate. Statistical evidence indicates that the real exchange rates of many countries are likely to be nonstationary or have long memory. That is, changes in the real values of many currencies tend to persist for very long period of time. This persistence implies that fluctuations in the real exchange rates are largely due to long-lasting effect of real disturbances. After revealing that "PPP does not hold as a long-run concept" for several exchange rates, Flynn and Boucher [12, 121] suggest that "One possible explanation . . . is that there are time-varying real factors that are omitted from the PPP relationship."

There are several well-established reasons why the real exchange rates may change in response to real disturbances. In the first place, permanent exogenous shocks to the tradable sector of the economy call for changes in competitiveness. For instance, a rise in the real price of oil will worsen the balance of trade position of a net oil-importing country and, therefore, call for a real depreciation of the currency of the country in order to improve its competitive position [32]. Second, when countries are growing at different rates, "productivity bias" will typically result in an appreciation of the faster-growing country's currency in real terms [4]. It is also argued that fiscal variables might be important in explaining the fluctuations in real exchange rates [23].

Although we expect that the real factors listed above may have influences on the real exchange rates, the questions of how significant the influences are and whether the influences are persistent in the long run have not been well addressed. In the theoretical literature, the determination of the nominal and real exchange rates has been extensively studied, but there have been only a limited number of efforts at empirically studying the sources of fluctuations in the real exchange rates [15; 2; 34; 43].

The present paper offers an investigation of the sources of movements of the real exchange rates. The study focuses on the stochastic trend movements of the real exchange rates. Since most of the relevant variables are nonstationary, which we will verify later, it seems appropriate to employ some recent advances in time series analysis, including the cointegration tests and the common stochastic trend approach. These new econometric techniques are applied to deal with the problem of nonstationarity in the data series and to test how real exchange rates react to changes in real variables, such as the world real price of oil, the productivity differentials, and the domestic and foreign fiscal variables, as well as to changes in nominal variables, such as the differentials of monetary bases. By including a monetary variable in the model, we may empirically test the hypothesis of the long-run neutrality of money, rather than assuming it holds. If the results verify that money is neutral in the long run, it may suggest limited effectiveness of the monetary policy designed to affect real economic activities.

The model developed in the study is applied to the real yen-dollar rate ([RER.sub.[yen]/$]) and the real markka-dollar rate ([RER.sub.FM/$]). The former is the relative real value of the two major currencies, while the latter is the real value of the currency of a small open economy, Finland, relative to the U.S. dollar. Discussions about the possible differences and similarities of the two rates in their response to various shocks will be given in the next section. Choosing these two rates may allow us to show the general applicability of the method employed in this study under different circumstances and provide more insights to our understanding of the real exchange rate movements.

The issue of what cause fluctuations in the yen-dollar rate has drawn much attention. Ohno [34] studied the mechanism of long-run mean reversion of the real yen-dollar rate by using the vector autoregressive model, but he did not take care of the possible problem of nonstationarity in the variables in his study. Lastrapes [26] offered an investigation of the sources of fluctuations in real and nominal exchange rates using only information contained in the exchange rates and price indices. His study led to the conclusion that "fluctuations over the current flexible rate period in real and nominal exchange rates are due primarily to real shocks" [26, 538] but did not explain what kind of real shocks are important. Yoshikawa [43] carefully examined the relative importance of different real factors in affecting the long-run trend of the nominal yen-dollar rate. Our study is different from Yoshikawa's by (a) focusing on the real yen-dollar rate, (b) applying some new methods in time series analysis to the investigation and (c) including the fiscal variables in the real factors, which may influence the movement of the real exchange rate, in the study. In contrast to the relatively rich literature of the yen-dollar rate, the study of the Finnish exchange rate is rather scarce. Our study may help to fill this gap in the literature.

The remaining part of the paper is organized as follows. Section II discusses some theoretical issues of the study. Section III lays out the methodology employed. In section IV, we apply the empirical model to the two real exchange rates. The results are reported and analyzed in the same section. The last section gives conclusions of this study.

II. Theoretical Issues

In this study, five variables are considered to have influence on the bilateral real exchange rates. They are the world real price of oil, the domestic and U.S. government consumption spending/ GDP ratios, the productivity differential and monetary differential between the two countries. We now briefly demonstrate how these variables may affect the movement of the real exchange rate.

The real exchange rate (RER) between two currencies is measured in terms of overall price levels,

RER = [e.sub.d/f] + [p.sup.f] - [p.sup.d] (1)

where [e.sub.d/f] is the log of nominal exchange rate (domestic currency price of foreign exchange). [p.sup.d] and [p.sup.f] are the logs of price indices of the two countries that encompass both tradable and non-tradable sectors. We then express the exchange-rate-adjusted relative price of foreign and domestic tradable goods as

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the logs of domestic and foreign prices of tradable goods respectively. We assume

[Mathematical Expression Omitted],

[Mathematical Expression Omitted],

where [Phi]'s are the share parameters of tradable goods. [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the logs of domestic and foreign prices of non-tradable goods respectively. Substituting (2), (3a), and (3b) into (1), we get

[Mathematical Expression Omitted].

Therefore, if [[Phi].sup.d] is similar to [[Phi].sup.f], a rise in the relative price of domestic tradable, [Mathematical Expression Omitted], by a bigger proportion than the change in the relative price of foreign tradable [Mathematical Expression Omitted], would cause a rise in the real exchange rate measured by (1). Moreover, home and foreign traded goods are likely imperfect substitutes. If an exogenous shock results in higher exchange-rate-adjusted prices of foreign tradable products relative to the prices of domestic tradable goods (i.e., a higher [Mathematical Expression Omitted]), a real depreciation of the home currency (i.e., a rise in RER) would occur.

Differential of Productivity Growth

Balassa [4] first noted the systematic tendency for productivity to grow more rapidly in tradable than non-tradable sectors, and for this differential to be greater in faster-growing countries. The relative price of non-traded commodity in terms of traded goods will thus be higher in the faster-growing country than in the others. Therefore, if one measures the real exchange rate by multiplying the nominal exchange rate by the ratio of the two countries' price indices that encompass both tradable and non-tradable sectors, the currency of the faster-growing country will appear to have appreciated even if the prices of tradable goods would be equalized in the two countries through international exchanges. That is, a country having a faster productivity growth would experience a lower [Mathematical Expression Omitted]. This may lead to a real appreciation of the home currency, a lower RER.

World Real Price of Oil

The link between the price of oil or energy and exchange rate dynamics has been noted by Krugman [24], McGuirk [32], Yoshikawa [43], and a number of other researchers. The influence of the oil price on the bilateral real exchange rate relies on the difference of the two relevant countries in their dependence on imported oil. Japan and Finland are more heavily dependent on imported oil than the U.S. is. A real oil price hike may increase the prices of tradables relative to non-tradables, [Mathematical Expression Omitted], in Japan and Finland by a bigger proportion than that in the U.S., [Mathematical Expression Omitted], and thus cause a real depreciation of their currencies against the dollar. In addition, in order to improve their competitiveness when the oil price shock worsens their balance of trade positions, Japan and Finland tend to raise the nominal exchange rates, [e.sub.d/f], by a greater proportion than the changes in the prices of domestic tradable products relative to foreign tradables, thus a higher [Mathematical Expression Omitted] in equations (2) and (4). This may prompt a further real depreciation of their currencies.

Domestic and Foreign Government Spendings(2)

Ahmed [2] and Koray and Chan [23] show that changes in government spending may affect the real exchange rate or the terms of trade. The sign of the effect depends on whether the rise is in the spending on tradables or non-tradables. High domestic government spending on non-traded goods and services may raise the relative price of non-traded commodity and thus has the same effect of a rise in tradable goods productivity, i.e., an appreciation of the real exchange rate. Besides, if home and foreign traded goods are imperfect substitutes, an increase in domestic government spending may put upward pressure on the prices of home-traded goods relative to those of foreign-traded goods. A lower [Mathematical Expression Omitted], and consequently a real appreciation of the home currency, is likely a result. The effects of a higher foreign government spending should be just the opposite.

Monetary Differentials

The theoretical ground of monetary influence on real exchange rates is based on the well-known overshooting model of Dornbusch [9]. According to this model, when the domestic money supply grows faster than the foreign money supply, the nominal exchange rate may deviate from the position corresponding to PPP because of sluggish response of the price variables. The slow adjustment of the price variables increases the real money balance and therefore causes interest rates to fall below their equilibrium levels to raise the demand for money. As a consequence, the interest rate parity condition requires an overshooting exchange rate. An overshooting [e.sub.d/f] together with a slow adjustment of price levels generates a change in [Mathematical Expression Omitted], and thus a change in the real exchange rate. The theory suggests that money could have only a temporary influence rather than long-term impact on the real exchange rate. When prices catch up after the disturbance occurs, the real exchange rate will move back to the original position. We would like to empirically confirm this hypothesis of the long-run neutrality of money.

In sum, we may describe the real exchange rate as a function of the world real price of oil (Poil), the domestic and foreign government spending (G and USG respectively), the productivity differential (Y), and the monetary differential (M). That is,

RER = F(Poil, G, USG, Y, M). (5)

Expression (5) is somewhat ad hoc, but it incorporates most of the arguments in the literature regarding the sources of movements of the real exchange rates. One may argue the possibility of missing some other important variables in this expression. However, the purpose of this study is to explore a long-term relationship between the real exchange rate and the relevant explanatory variables and then to study the relative importance of different variables in their contributions to the fluctuations of the real exchange rate based on that explored long-term relationship. If we can find the existence of a stable long-run relationship among the variables in our model, that could be viewed as an indication that there is no serious problem of missing important variables.

The influences of the variables on the right hand side of equation (5) could be different or similar on the two real exchange rates in the study. The reasons are listed as follows.

(1) Finland is a small open economy. If we define an openness index as the ratio of tradable goods (the sum of exports and imports) to GDP, the average index of Finland over the last twenty years is about 0.5, which is much greater than the indices of Japan and the U.S., 0.21 and 0.17 respectively. Therefore, for Finland, its [[Phi].sup.d] in equation (4), the share parameters of traded goods, is largely greater than [[Phi].sup.f]. Accordingly, a change [Mathematical Expression Omitted] caused by changes in the domestic government spending or in the differential of productivity growth would have less impact on the real markka-dollar rate than on the real yen-dollar rate, while the influence of the U.S. government spending is expected to be more important on the real markka-dollar rate than on the real yen-dollar rate.

(2) With no crude oil of their own, Finland and Japan have a heavier dependence on imported oil than the U.S. has. Both real exchange rates in the study are expected to be significantly affected by the changes in the world real price of oil. However, since Finland's imported oil mainly came from the former Soviet Union under processing the trade agreement between the two countries, Soviet oil partly insulated Finland from the oil price rises of the 1970s. The effect of the real oil price might be smaller on the real markka-dollar rate than on the real yen-dollar rate.(3)

(3) The exchange rate systems chosen by Finland and Japan were different until 1992. According to the International Financial Statistics of the International Monetary Fund (IMF), the Finnish markka was characterized as the currency pegged to a basket of currencies, whereas the Japanese yen and the U.S. dollar have been freely float. It is known that a pegged exchange rate system, different than a strictly fixed rate system, allows for changes in exchange rates when economic circumstances warrant such changes, but it requests more government interventions, mostly monetary interventions, in the foreign exchange market. Through a study of the real markka-dollar rate and the real yen-dollar rate, we would be able to see whether the two real rates under two different nominal exchange rate regimes behave differently in response to various economic shocks and whether the hypothesis of the long-run neutrality of money still holds even if the central bank of a country frequently intervenes the foreign exchange market to keep the nominal exchange rate within some boundaries.

III. Econometric Methodology

Significant developments in time series analysis have strongly influenced research in applied economics over the last decade. Vector autoregression (VAR) methodology has been widely applied to address the questions of elasticity or responsiveness by means of variance decomposition or impulse response analysis. However, as shown by Stock [39], Phillips [36], and Engle and Granger [11], simple VARs based on differenced data fail to provide an adequate explanation for the behavior of a group of integrated variables when those variables are cointegrated. Here cointegration means that among a group of integrated variables, certain linear combinations can be stationary. The variables being cointegrated do not drift too far apart from one another and there is a long-term equilibrium relationship among them. Stock and Watson [40] demonstrate that cointegrated variables are driven by common trends. That is, for a set of n integrated variables, if they share r cointegrating relationships, there must exist k = n - r stochastic trends driving the co-movements of the cointegrated variables. Recently, King, Plosser, Stock, and Watson [22], hereafter referred to as KPSW, provided a method to measure the response of time series variables to disturbances to the common trends that are thought to be underlying important economic variables.

If there is only one cointegrating relationship among the n variables in the study and therefore there are k = n - 1 common trends, applying the approach suggested by KPSW [22], the structural model studied in this paper could be written as:

[Mathematical Expression Omitted]

where [X.sub.t] is a vector of k variables that might explain the movement of the real exchange rate. [1 [[Beta].sub.x]] represents the coefficients of the normalized cointegrating vector which indicates a stable long-run relationship between [RER.sub.t] and [X.sub.t]. 0 is a (k x 1) vector of zeros. [I.sub.k] is an identity matrix with k dimensions. [[Pi].sub.t] is a (k x k) lower triangular matrix with ones on the diagonal. [[Tau].sub.t] is a k-dimensional vector of random walks that serve as common trends driving the co-movements of the real exchange rate and [X.sub.t]. They are the stochastic trends in the permanent components of the corresponding variables. [Mu] is a vector of the coefficients of the deterministic trend, t, and [[Epsilon].sub.t] is a vector of the usual error terms. The reduced form of common trend representation that corresponds to equation (6) is:

[Mathematical Expression Omitted].

The matrix [Mathematical Expression Omitted] is called the factor loading matrix which could be used to identify the common trends of the cointegrated system. The structure defined by equation (7) satisfies the necessary and sufficient conditions for the identification of a unique vector in the cointegration space. When there is only one common trend, the only identifying assumption needed to analyze the dynamics of the system is that the permanent shock is uncorrelated with the transitory shocks.

However, when there are more than one common trend, i.e., k [greater than] 1, the second assumption that the permanent shocks are mutually uncorrelated and the third assumption that the factor loading matrix is lower triangular are required to achieve identification [22].

We begin our investigation by examining the order of integration for the variables in the study. Once the variables are confirmed to be integrated of order one, or I(1) for short, the cointegration tests developed by Johansen [18] and Johansen and Juselius [20] are employed to determine the number of cointegrating vectors among the variables. Since the number of common trends, k, equals the number of integrated variables in the system minus the number of cointegrating vectors, r, k could be inferred once r is determined.

Define a vector [W.sub.t] = [[RER.sub.t] [X.sub.t]][prime] which contains n variables. If all of n variables are I(1) processes, then a vector error correction model (VECM) can be written as

[Delta][W.sub.t] = [summation of] [[Phi].sub.i][Delta][W.sub.t-i] + [Phi] [W.sub.t-1] + [v.sub.t] (8)

where [v.sub.t] is a vector white noise process and the matrix [Phi] conveys the long-run information contained in the data. If the rank of [Phi] is r, where r [less than or equal to] n - 1, [Phi] can be decomposed into two n x r matrices, [Alpha] and [Beta], such that [Phi] = [Alpha][Beta][prime]. The matrix [Beta] consists of r linear, cointegrating vectors while [Alpha] can be interpreted as a matrix of vector error-correction parameters.

The Johansen approach involves the likelihood ratio tests for the number of cointegrating relationships, r, and maximum likelihood estimates of cointegrating vectors, [Beta]. If the evidence indicates only one cointegrating vector, it implies that [RER.sub.t] and [X.sub.t] share a long-term equilibrium relationship and there are k(= n - 1) common trends driving the co-movements of [RER.sub.t] and [X.sub.t], as it is in equation (6). The estimated cointegrating vector, [Beta], could tell us what the long-run relationship between [RER.sub.t] and [X.sub.t] is like. By testing the significance of the [Beta]-coefficients, we would know whether the variables enter the cointegrating relationship significantly. The vector of the error-correction coefficients, [Alpha], shows the short-run adjustment of the variables to the past errors. We have [Alpha] = [[[Alpha].sub.rer] [[Alpha].sub.x]][prime] where [[Alpha].sub.x] has a dimension of 1 x (n - 1) and the subscript of each coefficient denotes the variable that adjusts to deviations from the long-term relationship. The significance of the [Alpha]-coefficients provides information of the weak exogeneity of the variables in the system.(4) An insignificant [[Alpha].sub.h] suggests that the variable h is weakly exogenous. It drives the co-movements of the variables in the cointegrated system. On the other hand, a significant [[Alpha].sub.j] implies that the variable j endogenously reacts to the past errors (deviations from the cointegrating relationship) and adjusts to restore the long-term relationship.

We then use the multivariate approach of KPSW [22] to get a decomposition of the variables in the system into a permanent/trend and a stationary/cyclical component. Briefly, KPSW define the permanent component of the vector [W.sub.t] as

[Mathematical Expression Omitted]

where the elements of [W.sub.0] are the values of the variables in [Mathematical Expression Omitted] at period 0, which are proxied by the initial observations of the actual [Mathematical Expression Omitted] represents the common trends of the system, where [Mathematical Expression Omitted] are the innovations in the permanent component of the variables. In order to satisfy the assumption that the permanent shocks are mutually uncorrelated, which implies the exogeneity of the common trends in the model, the innovations in the permanent components are orthogonalized and the corresponding factor loadings are rotated [14]. The matrix A equals the factor loading matrix in equation (7) after rotation (see Appendix m KPSW [22], and Hoffman and Rasche [14] for a sophisticated derivation of [Mathematical Expression Omitted] and steps how to estimate [[Mu].sup.*], A, and [Mathematical Expression Omitted] based on the estimated cointegration relation and VECM). Once we obtain estimated [[Mu].sup.*], A, and [[Tau].sub.t], following the steps similar to the standard procedure of the impulse response analysis and variance decomposition, we may shock [[Tau].sub.t] to study the dynamic responses of the variables to the shocks to different common trends. Then we decompose the forecast-error variance attributed to the different permanent shocks.(5) Finally, we define an equilibrium real exchange rate as the permanent/trend component of the actual rate. Through equation (9) we may also obtain the estimates of the unobservable equilibrium rates.

IV. Data and Empirical Results

Data

Quarterly data are collected for Finland, Japan, and the U.S. The data are obtained from the International Financial Statistics (IFS) of the IMF, the OECD Main Economic Indicators, and Annual Statistical Bulletin published by the Organization of Petroleum Exporting Countries. The sample period runs from the first quarter of 1973 to the second quarter of 1993. The real exchange rate is measured by [e.sub.d/f] + [p.sup.f] - [p.sup.d], as defined in the previous section. [e.sub.d/f] is the log of the nominal exchange rate (the domestic currency price of a dollar). [p.sup.d] and [p.sup.f] are the logs of the domestic and foreign overall price levels, measured by the GDP (or GNP) deflators. Poil is the log of the world real price of oil, proxied by the crude oil price index of the United Arab Emirates deflated by the world non-fuel price index. G and USG are the logs of the ratios of government consumption spending to GDP of the home country and the U.S. respectively. We calculate the productivity differential of the home country and the U.S., Y, by the log of the ratio of the productivity of the two countries, log([Y.sup.d]/[Y.sup.us]), where [Y.sup.d] and [Y.sup.us] are constructed by real GDP divided by the employment index. The differential of the money supplies, M, is measured by the difference between the logs of the monetary variables of the home country and the U. S. We employ a monetary base measure, listed on line 14 of the IFS data tape, to represent the monetary variable. Changes in the monetary bases generally reflect actions taken by the central banks to alter reserves of the banking system in their attempt to change monetary aggregates. Using other monetary measures, such as M1, would be more likely to confuse unforeseen movements in money demand with the policy actions of the central banks.

Tests of Order of Integration

The empirical work starts by examining the order of integration for the variables in the study. A well-known conclusion drawn from the standard unit root tests, such as the augmented Dickey-Fuller (ADF) tests [7; 37], is that many aggregate economic time series contain a unit root. That is, they are nonstationary and integrated of order one, or I(1) for short. However, these tests are based on a null hypothesis of a unit root and seek rejection against a stationary alternative. It [TABULAR DATA FOR TABLE I OMITTED] is important to note that the way in which classical hypothesis testing is implemented ensures the acceptance of the null hypothesis unless there is strong evidence against it. Therefore, the common failure to reject a unit root may be simply due to the standard unit root tests having low power against stable autoregressive alternatives with roots near unity (see DeJong et al. [6] for more details). In order to decide whether economic series are stationary or integrated, a more complete investigation shall be carried out by performing tests of the null hypothesis of integration as well as tests of the null hypothesis of stationarity, and then drawing the conclusions based on the combined results. For this purpose, we apply both the ADF tests, with the null of integration, and the tests of Kwiatkowski, Phillips, Schmidt, and Shin [25] (called KPSS tests thereafter), with the null of stationarity, in our study.(6) The KPSS approach is based on a Lagrange Multiplier score testing principle and assumes the univariate series can be decomposed into a deterministic trend, a random walk and a stationary error. The KPSS test statistic [[Eta].sub.[Mu]] is computed based on residuals from a regression with an intercept but no time trend. When a time trend is included in the initial regression, the test statistic is denoted by [[Eta].sub.[Tau]]. Under the null hypothesis of the series being stationary, KPSS show that both [[Eta].sub.[Mu]] and [[Eta].sub.[Tau]] are asymptotically functions of a Brownian bridge and they provide tables of critical values.

We apply the ADF tests and KPSS tests to the level and the first difference of the variables.(7) The results are reported in Table I. For the level of the variables, we find failure to reject the null by the ADF tests and rejection by the KPSS tests. This appears to be a strong indication of [TABULAR DATA FOR TABLE II OMITTED] integration. For the first difference of the variables, the ADF statistics reject the null of a unit root, while the KPSS statistics fail to reject the null of stationarity.(8) This is viewed as strong evidence that the first differences are stationary and therefore we may conclude that all the variables in the study are nonstationary series and they are integrated of the same order.

Cointegration Tests

Table II presents the results from the Johansen cointegration tests. The trace statistics, which are used to determine the number of cointegrating vectors, are listed in columns 1 to 6. The statistics in line 2 and line 6 suggest that there exists one cointegrating relationship between the variables in equation (5) for both real exchange rates.(9) Columns 7 to 12 report the estimated parameters of the cointegrating vectors. The numbers below the parameters are the asymptotic t-statistics.

The results show that the real oil price, the U.S. government spending, and the productivity differential are significant in the cointegrating relationship with the real markka-dollar rate, but the Finnish government spending and the differential of monetary bases are not. For the real yen-dollar rate, all the variables enter the cointegrating relationship significantly except the monetary variable. The signs of the significant [Beta]-coefficients are as expected. A rise in the real oil price is followed by a real depreciation of the home currency against the dollar. A faster growth in the productivity trend of the home country leads to an appreciation in the real exchange rate against the dollar. High U.S. government spending, assuming mostly on U.S. products especially on U.S. non-traded goods, may have the effects on the two real exchange rates similar to those of a rise in the real oil price, resulting in a real depreciation of the currencies of Finland and Japan against the U.S. dollar. The coefficient of domestic government spending, [[Beta].sub.g], is significant for Japan but not for Finland. This is in line with the argument made in section II. That is, for a small open economy with a big share parameter of traded goods, [[Phi].sup.d], a change in its own government spending may not have much impact on the real value of its currency. In no case, the differential of money supplies is found to be significant.(10) The results imply that the monetary variables do not share a long-term relationship with the real exchange rates no matter whether the country is practicing flexible or pegged exchange rates. Therefore there is no persistent overshooting effect of a monetary shock.

We would like to point out that the results indicate there is no long-lasting monetary impact on the trend movement of the real exchange rate, and thus verities the hypothesis of the long-run neutrality of money. Yet they do not preclude the possibility of an overshooting effect on the real exchange rate in the short run. Rather they imply that the monetary shocks have only short-lived effects.

Since our study focuses on the trend movements of the real exchange rates, the variables that are found to be insignificant in the long-term relationships are dropped from the further analysis. Hence, the relevant vectors and matrices in the reduced forms of common trend representations of the models for the two real exchange rates, corresponding to equation (7), become:

[X.sub.t] = ([Poil.sub.t], [USG.sub.t], [Y.sub.t])[prime]; [[Tau].sub.t] = ([[Tau].sub.poil,t], [[Tau].sub.usg,t], [[Tau].sub.y,t])[prime]; A = 4 x 3 matrix (10)

for the real markka-dollar rate, and

[X.sub.t] = ([Poil.sub.t], [USG.sub.t], [G.sub.t], [Y.sub.t])[prime]; [[Tau].sub.t] = ([[Tau].sub.poil,t], [[Tau].sub.usg,t], [[Tau].sub.g,t], [[Tau].sub.y,t])[prime]; A = 5 x 4 matrix (110)

for the real yen-dollar rate.

We then conduct the cointegration tests only for the variables included in (10) and (11). The results are given in lines 4 and 8 of Table II. The test statistics again show the existence of a cointegrating vector between the real exchange rate and the relevant variables in both cases, and all the remaining variables enter the cointegrating relationships significantly.

Having obtained the cointegrating vectors, we test the weak exogeneity of the variables in the cointegrated system. The estimated error-correction coefficients for the model of the real markka-dollar rate are ([[Alpha].sub.rer], [[Alpha].sub.poil], [[Alpha].sub.usg], [[Alpha].sub.y]) = (-0.13, 0.20, 0. 11, 0.01) with the t-statistics equal to -2.84, 1.76, 1.01, and 0.32, respectively. These results suggest that Poil, USG, and Y are weakly exogenous in the cointegrated system with the real markka-dollar rate to be endogenous. For the model of the real yen-dollar rate, the estimated error-correction coefficients are ([[Alpha].sub.rer], [[Alpha].sub.poil], [[Alpha].sub.g], [[Alpha].sub.usg], [[Alpha].sub.y]) = (-0.25, 0.36, 0.01, -0.01, -0.02) with the t-statistics equal to -2.91, 1.56, 0.51, -0.40, and -1.12, respectively. The results support the weak exogeneity of Poil, G, USG, and Y, while the real yen-dollar rate is relatively endogenous.

Impulse Responses and Variance Decompositions

As there are more than one common trend in the models, different ordering of the trends may affect the results of variance decompositions and impulse responses if the common trends are not absolutely uncorrelated. Following the practice of Sims [38] and KPSW [22], the presumably exogenous trend is ordered first followed by relatively endogenous trends. Therefore, the trends are ordered as [[Tau].sub.poil], [[Tau].sub.usg], [[Tau].sub.y] for the real markka-dollar rate, and [[Tau].sub.poil], [[Tau].sub.usg], [[Tau].sub.g], [[Tau].sub.y] for the real yen-dollar rate. We then change the ordering of [[Tau].sub.poil] and [[Tau].sub.usg] to test the sensitivity of the results. The impulse responses of the real markka-dollar rate to various shocks are plotted in Figure 1 and those of the real yen-dollar rate are plotted in Figure 2. The results show the long-lasting effects of the real shocks on the real exchange rates. The variance decompositions are presented in Panel A of Tables III and IV which could be used to analyze the relative importance of the different real factors in the models in influencing the trend movements of the real exchange rates. It is found that changes in the real oil price trend explain a substantial portion of the forecast error variance in the real exchange rates, 29 percent of the variance in the real markka-dollar rate and 32 percent of variance in the real yen-dollar rate in the first quarter after the shock occurs. The proportions increase to 51 percent and 52 percent respectively in one year horizon. Shocks to the trends of productivity differential explain about 15 percent and 20 percent of the variances in the forecast errors of [RER.sub.FM/$] and [RER.sub.[yen]/$] respectively in the first quarter, but the proportions decline over time. The proportions of the forecast error variances resulting from a shock to the U.S. government spending are 8 percent and 2 percent for [RER.sub.FM/$ and [RER.sub.[yen]/$] respectively in the first quarter. The proportions rise to 18 percent and 7 percent respectively in a two year horizon. The influence of the Japanese government spending on the forecast error variance of the real yen-dollar rate is 4 percent in the first quarter and rises to 12 percent in a two year horizon. Together, the real factors explain about 51 percent and 60 percent of the error variances in the real markka-dollar rate and the real yen-dollar rate respectively in the first quarter and 85 percent and 93 percent respectively in a three year horizon.

These results partly, but not very strongly, support the arguments made in section II. Changes in the differential of productivity growth may have less impact on the real markka-dollar rate than on the real yen-dollar rate, while the influence of the U.S. government spending seems to be stronger on the real markka-dollar rate than on the real yen-dollar rate. The effect of the real oil price shock on the real markka-dollar rate is only slightly smaller than that on the real yen-dollar rate. This may show that importing oil from the former Soviet Union did not much isolate the real markka-dollar rate from the world oil price shocks.

The sensitivity of the results is tested by changing the ordering of the shocks to the trends of the real oil price and the U.S. government spending. The results reported in Panel B of Table III and Table IV indicate no substantial difference between the variance decompositions before and after changing the ordering. The evidence suggests that changes in the real oil price trend seem to have an important and robust effect on the trend movements of the real exchange rates, and the government spending shocks also have a notable long-term impact on the variations of the real exchange rates.

Table III. Forecast-Error Variance Decompositions for the Real
Markka-Dollar Rate

Panel A. Ordering of the trends: [[Tau].sub.poil], [[Tau].sub.usg],
[[Tau].sub.y]

                  Fraction of the Forecast-Error Variance of the
                      Real Markka-Dollar Rate Attributed to:

               World Real Oil      U.S. Government      Productivity
Horizon          Price Shock        Spending Shock          Shock

1                   28.89                7.50               14.64
4                   50.33               10.18                8.04
8                   56.52               18.16                4.14
12                  59.14               23.84                2.08
16                  58.38               27.13                2.32
20                  58.02               28.97                2.47
24                  58.41               29.93                2.56
[infinity]          64.34               32.85                2.80

Panel B. Ordering of the trends: [[Tau].sub.usg], [[Tau].sub.poil],
[[Tau].sub.y]

                   Fraction of the Forecast-Error Variance of the
                       Real Markka-Dollar Rate Attributed to:

               U.S. Government     World Real Oil       Productivity
Horizon         Spending Shock       Price Shock            Shock

1                    9.48               26.91               14.64
4                   12.17               48.34                8.04
8                   21.02               53.96                4.14
12                  26.24               56.74                2.08
16                  29.85               55.66                2.32
20                  31.89               55.11                2.47
24                  32.78               55.55                2.56
[infinity]          37.88               59.32                2.80

Finally, we define an equilibrium real exchange rate as the permanent/trend component of the actual real exchange rate, expressed by equation (9). Following the KPSW method briefly described in section III, the equilibrium real markka-dollar rate and real yen-dollar rate are estimated. Table V reports the estimated factor loading matrices, i.e., the two A matrices in (10) and (11), which have been rotated after the innovations in [[Tau].sub.t] are orthogonalized. The estimated equilibrium rates are plotted in Figure 3 along with the corresponding actual rates (indexed by dividing both rates by the average actual real rates of 1985). It can be seen that, although the actual rates deviate from the estimated equilibrium values frequently, the fluctuations of the actual real exchange rates broadly coincide with the movements of the estimated equilibrium rates. The equilibrium rates estimated by our models seem to well explain the changes in the real exchange rates in the 1970s and the 1980s, but not sufficient to capture the variations of the actual real rates in the 1990s. This could be interpreted either to indicate the limited usefulness of the approach employed here to estimate the equilibrium rates for a long period when the coefficients in the factor loading matrix are assumed constant for the entire period, or to imply the possible existence [TABULAR DATA FOR TABLE IV OMITTED] of some factors other than the variables in our model influencing the trend movements of the real exchange rates in the 1990s.

Table V. Estimated Factor Loading Matrices after Orthogonalization
and Rotation

Corresponding to Equation (7): [[RER.sub.t] [X.sub.t]][prime] =
A[[Tau].sub.t] + [[Mu].sub.*]t + [Mathematical Expression Omitted]

1. For the Real Markka-Dollar Rate: [X.sub.t] = ([Poil.sub.t],
[USG.sub.t], [Y.sub.t])[prime]; [[Tau].sub.t] = ([[Tau].sub.poil,t],
[[Tau].sub.usg,t], [[Tau].sub.y,t])[prime]

                        0.32          2.59         -0.89
                        1.00         -0.01         -0.03
Estimated A =
                        0.01          0.93         -0.30
                       -0.01          0.24          1.11

2. For the Real Yen-Dollar Rate: [X.sub.t] = ([Poil.sub.t],
[USG.sub.t], [G.sub.t], [Y.sub.t])[prime]; [[Tau].sub.t] =
[[Tau].sub.poil,t], [[Tau].sub.usg,t], [[Tau].sub.g,t],
[[Tau].sub.y,t])[prime]

                        0.40          1.29         -1.37       -1.29
                        1.00         -0.03          0.02       -0.08
Estimated A =           0.04          0.88          0.10       -0.36
                        0.08          0.18          0.91        0.34
                       -0.01          0.45         -0.35        1.29

V. Conclusions

This paper offers an investigation of the sources of the trend movements of the real exchange rates. Some recent advances in time series analysis, including the cointegration tests, the vector error correction model, and the common stochastic trend approach with variance decomposition, are employed to investigate the long-run equilibrium relationship regarding the determination of the real exchange rate and the relative importance of different shocks in affecting the changes of the real exchange rate. The empirical model studied in this paper incorporates most of the arguments in the literature concerning the sources of movements of the real exchange rates. The model is applied to the real markka-dollar rate and the real yen-dollar rate. The tests are conducted to show how the two real exchange rates react to changes in the variables such as the world real price of oil, the domestic and foreign fiscal variables, the differentials of productivity growth, and the monetary differentials.

The evidence from the cointegration tests indicates the existence of a stable long-run relationship between the real exchange rates and the real variables, with the expected signs, but not the monetary variables. The results are consistent with the view that changes in real variables have a significant and persistent influence on the variation of the real exchange rate while the monetary disturbances have only short-lived effects. Such a result implies the ineffectiveness of the monetary policy designed to alter the long-term trend of the real exchange rate for the purpose of affecting the real economic activities.

The broad coincidence in the fluctuations of the actual real exchange rates in the 1970s and the 1980s with the movements of the estimated equilibrium rates shows that the trend movements of the two real exchange rates during that period seem to be well explained by the weakly exogenous real factors in our model. However, the model does not seem to be adequate to describe the behavior of the two real exchange rates in the 1990s. Further research should be conducted to study the possible existence of some other factors that may affect the trend movements of the real exchange rates in recent years.

Comparing the influences of the different real factors, the variance decompositions show that changes in the trend of the world real oil price have the most important and robust effects on the trend movements of the two real exchange rates in the study. The government spending of the home country is found to be more influential on the real value of the home currency for a relatively large economy than for a small open economy. The U.S. government spending also has a notable long-term impact on the real dollar value of the other currencies, while the effect of the productivity differential is relatively minor in the long run. These findings suggest that we give considerable attention to oil price shocks in future analyses of the trend movements of real exchange rates for countries having a heavy dependence on imported oil. At the same time, the influence of fiscal variables should not be neglected.

1. For example, studies by Baillie and Selover [3], Taylor [41], Layton and Stark [27], Mark [28], Corbae and Ouliaris [5], and Flynn and Boucher [12] do not favor PPP. On the other hand, Abuaf and Jorion [1], Kim [21], and Diebold, Husted, and Rush [8] provide evidence supporting PPP.

2. Readers may argue that the government budget deficit is probably a more appropriate fiscal variable. There are some existing studies focusing on the effects of budget deficits on exchange rates, for example, Hutchison and Throop [16], and Nakibullah [33]. However, the quarterly data of fiscal deficits of Finland and Japan are not available. Besides, the unit root tests indicate that the U.S. budget deficit is likely a stationary variable. Since a stationary variable would not be able to help explain the nonstationary trend movements of the real exchange rates, we choose a measure of government spending, which is found to be nonstationary, instead of the budget deficit.

3. It would be ideal if we study the real exchange rate of a small open economy like Norway which is less dependent on imported oil. Unfortunately, the study requires the quarterly data for a long period. They are not available for Norway or other similar economies.

4. For the concept of weak exogeneity, see Engle, Hendry, and Richard [10], Hylleberg and Mizon [17], and Johansen [19].

5. The author is grateful to Dennis Hoffman for his generosity of sharing the computer program of the KPSW approach which is employed here.

6. Because the ADF tests are now well known, the descriptions of the tests are omitted here.

7. The lag lengths in the ADF tests are chosen based on the criterion that they are long enough to ensure the residuals to be white noise. The Ljung-Box Q-statistics are computed to test the properties of the residual series and are available from the author upon request. The KPSS test statistics are obtained based on a Newey-West adjustment with four lags and there is no notable change in the test statistics when we lengthen the lags.

8. For the first difference of the variables, the test statistics associated with the model with a time trend are not reported because there is no significant time trend in the first difference of the variables.

9. The lag lengths L in equation (8) are chosen on the basis of the Akaike Information Criterion (AIC). The computed Ljung-Box Q-statistics, available from the author by request, fail to reject the null hypothesis that the residuals from equation (8) are white noise.

10. For the real markka-dollar rate, we have also tried an alternative monetary measure, the differential of international reserves, to capture the effects of central bank interventions in the foreign exchange market. This alternative measure of the monetar} differential is found to be insignificant in the cointegrating relationship. The results are available upon request.

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