Using Long-Run Restrictions to Investigate the Sources of Exchange Rate Fluctuations *

Transcription

1 Using Long-Run Restrictions to Investigate the Sources of Exchange Rate Fluctuations * Pao-Lin Tien Wesleyan University Abstract This paper makes use of long-run restrictions to identify macroeconomic shocks and evaluate their relative importance for exchange rate fluctuations. Unlike previous studies that employ a similar approach, I consider a large eight variable vector autoregressive system that includes short term interest rates rather than money stocks in order to help identify monetary policy shocks. Results for the U.S. and the U.K. show that monetary policy shocks and other macroeconomic shocks behave according to theory. However, monetary shocks account for only a small fraction of the variance of the real exchange rate. Instead, taste shocks that can be associated with the degree of trade openness, terms of trade, and current account appear to be the key factor driving the U.S. U.K. real exchange rate. Results for other countries under consideration (Canada, Germany, and Japan) are similar. JEL Classification: F31 Key words: Real exchange rate, long-run identifying restrictions, vector autoregression, monetary shocks, real shocks * I would like to thank Gaetano Antinolfi, Ryan Compton, Yunjong Eo, Steve Fazzari, Jeremy Jackson, James Morley, John Rogers, and Tara Sinclair for their helpful comments and continued support. Funding for this research was provided by the Center for Research in Economics and Strategy (CRES) in the Olin School of Business at Washington University in St. Louis.

2 I. INTRODUCTION The volatile nature of exchange rate movements since the collapse of the Bretton Woods system of fixed exchange rates has led economists to consider these important questions: What are the sources of exchange rate fluctuations? Are monetary policy shocks the main factor? Do other macroeconomic shocks matter more? In this paper, I present a large vector autoregressive (VAR) model with long-run restrictions to address the long-standing issue of whether nominal/monetary shocks matter for exchange rates. I find that nominal shocks are not important for the bilateral exchange rates between the U.S. and four other G7 countries (U.K., Canada, Germany, and Japan). Instead, exchange rate fluctuations appear to arise from taste shocks that can be related to the international trade sector of the economies under investigation. The nature of the shocks that lead to exchange rate fluctuations has been a source of contention for economists for a long time. In one of the most influential papers in the area, Mussa (1986) argues that sluggish price adjustment must be the key factor in explaining the short-run movements in real and nominal exchange rates. This of course implies that the interaction of sticky prices and monetary shocks could have been the source of volatile exchange rates in the post-bretton Woods era. On the other hand, Stockman (1987) disputes the idea that monetary shocks are to blame for the behavior of real exchange rates after the collapse of Bretton Woods. He argues that real shocks with large permanent components are the main culprits. With competing theories explaining exchange rate fluctuations, the debate must be brought to the data. Indeed, there exists a large body of empirical work in the area. However, even empirical studies on exchange rates have failed to reach consensus on whether monetary shocks matter for exchange rate variability. Some papers suggest little or no role for monetary shocks while other papers have found that monetary shocks are the most important in driving exchange rate movements. For example, Grilli and Roubini (1995) report the share of the dollar-pound exchange rate variance accounted for by monetary shocks to be as low as 2 percent while Rogers (1999) reports a share as high as 41 percent. This large discrepancy primarily reflects the major difficulty in empirical work on exchange rates: how to correctly identify monetary policy shocks to judge their relative importance. The most common approach to identification of economic shocks, including monetary policy shocks, involves the imposition of short-run restrictions within a VAR model. In particular, some of the contemporaneous effects of shocks on the variables in the VAR are restricted to zero. These restrictions can be either recursive or non-recursive, though under both categories the assumptions made can be rather implausible. For example, Eichenbaum and Evans (1995) assume that foreign interest rates do not respond to Federal Reserve policy shocks until a month after policy is changed, which is inconsistent with large movements in foreign rates immediately after the Federal Open Market Committee s (FOMC) policy announcements. In work that employs this kind of identification procedure, the estimated range of the share of monetary shocks in the total 1

3 variance in real or nominal exchange rate is quite large, from around 2 percent (Grilli and Roubini 1995, U.S. U.K. nominal exchange rate on impact) to 34 percent (Kim and Roubini 2000, U.S. U.K. 7 variable model, six-month horizon for nominal exchange rate). Identification of VAR models can also be achieved with long-run restrictions, as originally advocated by Blanchard and Quah (1989). With this method, some shocks (most likely nominal/monetary shocks) are assumed to have no long-run effect on real economic activity. These restrictions often make intuitive economic sense. They also often allow for easy structural interpretation of all of the shocks in the VAR system. Most other popular techniques of identification, such as recursive and non-recursive short-run restrictions or sign/shape restrictions, 1 typically only allow for partial identification of the shock of interest without giving an interpretation to all the other shocks in the system. Clarida and Gali (1994) provide the seminal investigation of the effects of real and nominal shocks on real exchange rate by using long-run identification restrictions. I use the same identification approach in this paper. However, unlike Clarida and Gali (1994) or other previous papers that employ a similar identification strategy, I estimate a much larger VAR system that includes many potentially relevant variables. (Clarida and Gali s model has only 3 variables, while I include 8 variables.) In addition, I use shortterm interest rates rather than the usual money stocks to identify monetary policy shocks (see arguments in Bernanke and Blinder 1992). As in the studies using short-run identification restriction, past results on the importance of monetary policy shocks for real exchange rates using long-run restrictions are often at odds with each other. Clarida and Gali (1994) suggest monetary shocks are unimportant (their highest estimated share of variance due to monetary shocks is 2.2 percent for U.S. U.K. real exchange rate), while Rogers (1999) finds that the contribution of monetary shocks can be as high as 40.6 percent for U.S. U.K. real exchange rate. I find results that correspond well with the findings in Clarida and Gali (1994) in spite of the differences in the included variables in our models. In particular, I find that monetary policy shocks only account for about 2 percent of the total variance of the dollar-pound real exchange rate on impact. I also find that the other macroeconomic shocks identified in the VAR, such as supply or commodity price shocks, have little influence on the real exchange rate. The 1 Sign and shape restrictions are fairly recent developments in the area of VAR identification. In Canova and De Nicoló (2002), Faust (1998), and Uhlig (2005), the general idea is to systematically examine a variety of identification schemes, and then, through elimination by penalty functions or sign/shape restrictions on the impulse-response functions, find a unique solution. This approach is well suited to assessing the robustness of certain claims from identified VAR work. However, the formal restrictions imposed to arrive at the final choice, such as sign restrictions, are still subjective and some would argue even more restrictive than the short-run or long-run restriction approaches. Also, Faust (1998) and Uhlig (2005) only partially identify the structural model. Hence, besides the shock of interest, one cannot examine what other shock in the system may have important effect on the real exchange. Farrant and Peersman (2006) modified the Uhlig (2005) method to allow the full set of shocks to be identified by imposing a larger collection of sign restrictions. However, this is only feasible in relatively small VAR systems (the largest system in Farrant and Peersman (2006) has just four variables) as it becomes increasingly difficult to impose credible sign restrictions as the number of variables in the model gets larger. 2

4 only shock that consistently produces large fluctuations in the real exchange rate is what I label as a taste shock, following the terminology used in Rogers (1999). Based on the VAR analysis, this taste shock does not appear to be associated with traditional demandtype shocks that would have only a short-term impact on output and interest rates. Instead, using regression analysis, I find that changes in relative trade openness, relative terms of trade, and relative current account between the countries could be important factors driving the taste shock, implying that real shocks originating from the international trade sector of the economy are the main sources of exchange rate fluctuations. The remainder of the paper will proceed as follows: Section II details the VAR model under consideration, the data, and the shock identification strategy. Section III shows the results of the VAR estimation. Section IV investigates the properties and the sources of the taste shock. Finally, Section V offers concluding remarks. II. VAR MODEL SPECIFICATION AND IDENTIFICATION SCHEME Data Besides the United States, four other countries from the G7 (United Kingdom, Canada, Germany, and Japan) are studied in this paper, with the U.S. U.K. VAR model used as the benchmark case for easy comparison with other papers in the literature. The currencies of these countries are among the most heavily traded in the world. This may in part reflect their status as major trading partners with the United States. 2 The countries are also selected to facilitate comparisons with Clarida and Gali (1994) and Rogers (1999), and to represent distinctly different trading areas (Non-continental Europe, North America, Continental Europe, and East Asia). The sample period is 1970Q2 to 2006Q1 for all countries except Canada (1970Q2 to 2006Q2) and Germany (1970Q2 to 2005Q4). Eight variables are used in the estimation of each U.S. foreign country VAR. All the variables used are transformed to natural logs (except for the interest rate variables) and demeaned. Please refer to Table I for details of the variables and their corresponding data sources. Here I will give a brief overview. Note that a variable with an asterisk indicates that it is non-u.s. (1) y y* : Relative output, U.S. less foreign country. (2) y : U.S. output. 2 In terms of total trade, using the most recent data (January 2007) from the BLS, Canada is the U.S. s number 1 trading partner, Japan is number 4, Germany is number 5, and the U.K. is number 6. These rankings have not changed much for the last twenty or so years. All countries considered here have been top ten trading partners of the U.S. over the past decades, though the ranking for Japan and the U.K. have dropped back somewhat in recent years due to the increase in U.S. trade with China and Mexico. 3

5 (3) q : Bilateral real exchange rate defined as amount of U.S. dollars per unit of foreign currency. (4) p c : U.S. intermediate material price. (5) p p* : Relative prices, U.S. less foreign country, with structural breaks accounted for. (6) p : U.S. prices with structural breaks accounted for. (7) i i* : Relative short-term interest rate, U.S. less foreign country, with structural breaks accounted for. (8a) i tbr : U.S. 3-month treasury bill rate with structural break accounted for. (8b) i ffr : U.S. federal funds rate with structural break accounted for. (The choice of using either 8a or 8b depends on the type of foreign interest rate used to calculate i i*). An important aspect of the VAR model is the inclusion of relative terms. First, as will be discussed in more detail later, these variables are essential for the long-run identification scheme. Second, they allow relevant information from foreign variables to be incorporated without over-expanding the dimensions of the VAR and generating a tremendous loss of degrees of freedom that would undermine the quality of the estimates. Unit Root Tests and Structural Breaks Estimation of the VAR model requires that each of the variables entering the VAR is stationary. Series that are non-stationary should be transformed appropriately prior to estimation, otherwise finite-sample inferences may suffer serious distortions. I follow the general testing strategy suggested by Campbell and Perron (1991). Tables IIa and IIb report two types of unit root tests. One is the standard Augmented Dickey Fuller (ADF) test, which tests the presence of unit root as the null hypothesis. The other is the test developed by Kwiatkowski, Phillips, Schmidt, and Shin (1992), usually called the KPSS test. This test has the null hypothesis of stationarity. The two different tests are performed in order to make sure that the presence or absence of unit roots in the series is robust to alternative testing procedures. The results in Table II show that some of the series under consideration could be stationary or non-stationary depending on the unit root test used, but in general variables (1) through (6) listed above are integrated of order one in levels, hence they enter into the VAR in first differences. Looking at the results in Tables IIa in more detail, it is not surprising to see that the relative outputs are non-stationary. What is perhaps more surprising is that U.S. output (y) appears to be stationary in levels. 3 However, this result seems to be particular to the relatively short sample period being examined here. If unit root tests are carried out on a longer sample of U.S. output (quarterly data from 1947 to current), the result is unambiguously non-stationary for both ADF and KPSS unit root tests. Due to data availability issues for other series in the VAR, and my particular interest in the floating 3 Murray and Nelson (2000), among many others, have shown that post World War II U.S. GDP data is dominated by permanent shocks, implying that the U.S. GDP series is not trend stationary. 4

6 exchange rate period post Bretton Woods, I cannot allow the longer sample of U.S. output into the estimation, although I will treat y as non-stationary in levels for my sample period. An important assumption in my model is that there are permanent shocks to the real exchange rate. This is only possible if the real exchange rate series are non-stationary in levels. It is common knowledge that testing for the presence of unit roots in exchange rates is extremely difficult. Research in this area has presented evidence on both sides of the argument. Rogoff (1996) provides an excellent summary of the debate. The general consensus is that in the short-run, real exchange rate fluctuations are too persistent to be justifiably monetary in nature. Hence the fluctuations can be treated as effectively permanent, implying the presence of unit root in real exchange rates. But over the very long-run (over one hundred years of data) one can find more evidence that the exchange rate conforms to some version of the purchasing power parity (PPP) condition (see Edison 1987). The results in Table IIa provide some support for my claim that real exchange rates are non-stationary. The KPSS test reports all four bilateral real exchange rates to be non-stationary, and for the U.S. Canadian exchange rate even the ADF test shows the presence of a unit root. Since the purpose of this paper is not to determine if PPP holds over very long-run periods, but to determine what factors are important over the relatively shorter horizons (i.e. 20 to 30 years), I will proceed as if real exchange rates are non-stationary. Conventional wisdom is that prices are non-stationary in levels but inflation rates might be stationary. Table IIa shows that for all the price variables (p p*, p c, and p), the presence of unit roots are supported as expected. However, results presented in Table IIb show more inconsistency for the inflation variables (first difference of the price variables, which are in logs), some are stationary but most are still non-stationary. A possible explanation for these mixed results is that there are structural breaks in the mean of the level of U.S. inflation during the sample period considered in this paper. Failure to take into account such breaks could yield spuriously high degree of persistence in the inflation series that may affect the VAR estimates. A wide range of potential break dates have been suggested for the U.S. inflation rate. Levin and Piger (2003) found a break in mean in 1991Q1 or 1991Q2 using four different measures of inflation, while Rapach and Wohar (2005) located three break dates (1967Q3, 1973Q1, and 1982Q1). Instead of adopting break dates reported in earlier studies, I test for structural break dates using a procedure based on Bai and Perron (1998). The results are presented in Table III along with some details of the procedure. 4 I have uncovered only one break for the U.S. inflation rate over my sample period. The break date 1981Q2 is in agreement with findings in the literature that inflation persistence was exceptionally high during the period from 1965 to the early 1980s, though whether persistence continued to be high since then, or has declined, is more hotly contested. Since a break in U.S. inflation could 4 In Table III the results for Δydef (first difference of U.S. GDP deflator) is presented because GDP deflator is used as the price data for Germany, hence to construct relative prices I have to use U.S. GDP deflator as well. Due to this complication, the structural breaks for the Δp and Δ(p p*) variables in the U.S. German case differs somewhat from the other country pairs as Δp equals U.S. GDP deflator and Δ(p p*) is the inflation differential between U.S. and German GDP deflator. 5

7 induce a break in the relative inflation variables as well, the same break date found for U.S. inflation is allowed for each of the relative inflation variables. Then a search for additional breaks is carried out. All of the relative inflation measures appear to have multiple structural breaks. Rapach and Wohar (2005) have also found multiple breaks in 13 industrialized countries inflation rates. With the structural break dates at hand, the inflation variables can be modified to take them into account. 5 Table IIb shows unit root test results for the modified variables, which are unambiguously stationary. The structural break for U.S. inflation also has implications for the short-term interest rate variables in the VAR. As can be seen in Table IIa, some of the relative shortterm interest rates may be non-stationary. Also, two different measures of the U.S. rates in levels (i tbr and i ffr ) are found to be non-stationary by both the ADF and KPSS tests. Cochrane (1991) argues in his comment to Campbell and Perron (1991) that intuitively interest rates should be treated as stationary, citing examples that interest rates in ancient Babylon are comparable with current rates, and that the mean reversion property of interest rates are economically important for explaining expected return premia in term structures. It is possible that the near random walk structure of the short-term rates tends to cause unit root tests to detect the presence of unit root even though it does not exist. Furthermore, Caporale and Grier (2000) and Bai and Perron (2003) have both found that multiple structural breaks exist in U.S. real interest rates. Given Cochrane s argument and evidence of structural breaks, we may find short-term rates in levels to be stationary once structural breaks are taken into account. I start by imposing the break date found for U.S. inflation rate (Δp) on the 3-month treasury bill rate (i tbr ) and then use the same procedure as used for inflation rates above to search for additional breaks in the interest rate variables. As shown in Table III, four break dates are found for i tbr. 6 Then, to be consistent, I impose the break dates found for i tbr on the relative short-term rates (i i*) and search for further breaks. The relative interest rates tend to have more breaks than the U.S. domestic rates. This is possibly related to the findings in Rapach and Wohar (2005) of multiple structural breaks in real interest rates using international data. The modified short-term interest rate series with structural breaks in Table IIa are now clearly stationary. Structural VAR Framework For the benchmark model, the vector of variables x [Δ(y y*), Δy, Δq, Δp c, Δ(p p*), Δp, i i*, i tbr ] is assumed to follow a multivariate covariance stationary process. Recall that all the variables in x have been demeaned for convenience, and that the inflation and interest rate variables all have structural breaks imposed. The typical VAR representation assumes that the vector x depends on lags of itself and some vector of structural shocks ε: 5 Each inflation variable is divided into a number of subsamples dictated by their respective break dates, the mean of each subsample is then calculated, and demeaned subsamples created. Finally, I reconstruct the inflation series using the demeaned subsamples. 6 The same four break dates found for i tbr are assumed for the federal funds rate i ffr as well. 6

8 k 0 t = j t j t j= 1 (1) Ax A x + ε, ε t N(0,D). Note that the structural shocks are normally distributed with mean zero and that the variance covariance matrix D is diagonal as the shocks are uncorrelated with each other. Provided that the coefficient matrix A 0 is invertible, equation (1) can be rewritten more compactly as 1 (2) AL ( ) x t = A 0 εt, where k j A( L) = I A A L, and L is the lag operator. j= j The Wold moving average (Wold MA) representation of equation (2) can be written as (3) x = CL ( ) ε, t t 1 1 where CL ( ) = AL ( ) A0. Note here that A(L) would have to be invertible for equation (3) to make sense. With C(L) known, a straightforward transformation allows recovery of expressions for the variables of interest in x in terms of the current and lagged values of the structural disturbances in ε. However, in order to determine what C(L) is, a few more expressions and new notation need to be introduced. First of all, the reduced-form Wold moving average representation of x is given by (4) x = EL ( ), ν t N(0,Σ). t ν t Comparing equation (4) with equation (2) above, one can interpret E(L) to be equal to A(L) -1 1, hence E(0) = I and E(L) is invertible. As a consequence, ν = A ε is the vector of innovations where each element in ν is some linear combination of the structural shocks in x. The (reduced-form) autoregressive representation of the system in equation (4) can be given by (5) AL ( ) x t = ν t. Note that equation (5) above is the same as equation (2) except that the right hand side of (2), A ε, is denoted by ν. A(L) can be consistently estimated using standard ordinary 1 0 least squares (OLS) technique. 7 The residuals from the OLS regression can then be used to calculate Σ. In an attempt to simplify the notation, denote t 0 t 7 This is equivalent to estimating the model using conditional maximum likelihood under normality or using the SUR model with identical regressors in all equations. 7

9 1 (6) S = A, therefore (7) ν = Sε. 0 1 The structural model, i.e., the coefficients of CL ( ) = AL ( ) Swill be identified to the extent that there are enough restrictions to determine the elements of C(L) uniquely. In the case of long-run restrictions, by making assumptions about the long-run behavior of the variables in the model that will render C(1) to be lower triangular, one can invoke the relationship that the spectral density for x at frequency zero is proportional to the longrun variance-covariance matrix denoted Λ: ' ' (8) Λ= E(1) Σ E(1) = C(1) DC(1), such that Cholesky decomposing Λ provides a unique lower triangular matrix that is 12 equivalent to C(1) D. Given C(1) and A(1), the impact matrix S can be obtained, and the vector of structural shocks ε can then be recovered by inverting equation (7). While long-run identification procedures are popular, there are some issues with their implementation. Faust and Leeper (1997) present two major criticisms. The first one is the problem of inference regarding the estimated C(1) coefficients. As C(1) estimates are inherently imprecise even in large samples, imposing long run restrictions transfers this uncertainty to all the structural parameters including coefficients of the impulseresponse functions. To address this issue, I assume that the true model driving the data is a VAR with a known maximum lag order K, where K is determined by standard model selection procedures and is small relative to the sample size. In addition, I construct confidence intervals for the impulse-responses and variance decompositions with the more reliable bias corrected bootstrap method proposed by Kilian (1998). Kilian and Chang (2000) have shown that these confidence intervals (along with the Sims and Zha 1999 Bayesian Monte Carlo integration confidence intervals) have superior coverage accuracy when compared with the more common ways of constructing confidence intervals for impulse-responses, such as Runkle (1987) and Lütkepohl (1990). Faust and Leeper (1997) were also concerned with the problem posed by multiple shocks. Since the VAR methodology is usually applied in low dimensional models, the identified shocks must be viewed as aggregates of a larger number of underlying shocks. So if one identified structural shock consists of two independent shocks, then the Blanchard and Quah long-run identification method is valid only if the underlying macroeconomic variables respond to the two shocks in the same way. My eight variable benchmark model, rather large for a VAR with long-run restrictions, should allow me to see if this is a valid concern in terms of the various shocks impact on exchange rates. Due to the size of my VAR model, the identified shocks are disaggregated into a larger number of sensible categories: the supply and monetary shocks are decomposed into those that are common to both countries and those that are particular to only one of the 8

10 countries; the monetary shocks are further refined into money supply and money demand shocks. In addition, a commodity price shock is introduced to allow for shocks coming from that particular sector of the economy to be separated from more productivity related supply shocks. Finally, a taste shock is allowed to have permanent effects on the real exchange rate but not on output. Identification of the VAR Model The long run restrictions imposed on the benchmark model can be expressed in the following Wold MA form: (9) x = C(1) ε s Δ( y y*) C11(1) ε Δy C21(1) C22(1) s c ε Δq C31(1) C32(1) C33(1) d ε c cp Δp C41(1) C42(1) C43(1) C44(1) = ε Δ( p p*) C51(1) C52(1) C53(1) C54 (1) C55(1) ms ε ms c Δp C61(1) C62(1) C63(1) C64(1) C65(1) C66(1) 0 0 ε i i* md C71(1) C72(1) C73(1) C74(1) C75(1) C76(1) C77 (1) 0 ε md c itbr C81(1) C82(1) C83(1) C84 (1) C85 (1) C86(1) C87(1) C88(1) ε The lower triangularity of C(1) can be justified in a straightforward manner. Output is supply-driven in the long run, 8 hence shocks unrelated to the supply side of the economy should not have long run effect on output. For relative output, a supply shock that is common to both countries (ε s-c ) should not lead to long run differences between the two countries. Take a technological advancement as an example of a positive common supply shock. There may be short-run variations in the rate at which the countries incorporate this new technology into production of output, but over time there should be no major gaps in the outputs of the two countries that would lead to a shift in the relative output. This assumption should be fairly uncontroversial for the industrialized country pairs that I consider in the paper. Hence only a country specific supply shock (ε s ) would have long-run impact on relative output. For U.S. output, both common and relative supply shocks would have long run effect. This justifies the zeros in the first and second rows of C(1). For the real exchange rate, I only allow the supply shocks and the taste shock to have permanent effects (hence the zero restrictions on the third row of C(1)). Research on exchange rate determination shows that real factors from both the supply and demand 8 Here I follow the arguments in Blanchard and Quah (1989). Demand factors may indeed have long-run impact on output, but the magnitude of the effect would be very small relative to that of supply disturbances. Hence I make the assumption that output is only influenced by supply shocks in the long-run. 9

11 sides of the economy may lead to long run changes in the real exchange rate, whereas nominal shocks such as monetary shocks only have temporary impact. The taste shock is meant to capture a variety of disturbances that would have permanent impact on exchange rates but not on output. For example, it could represent a shift in preferences towards or away from traded goods, changes in trade policy that may alter the relative demand for traded goods, etc. The properties of the taste shock will be analyzed in much more detail later in the paper. One would expect that commodity prices in the long-run are driven by changes in supply and demand of goods and by shocks directly to the commodities market like an oil price shock. However, monetary shocks should have no reason to leave permanent effects on commodity prices. This underlies the zero restrictions on the fourth row of C(1). For the consumer price variables in the VAR, real shocks should play a role in their long-run value, however, not all nominal shocks would. Money supply shocks, defined as adjustments in the nominal interest rate in excess of the Federal Reserve s reaction to changing output and inflation, have long run impact on prices. On the other hand, money demand shocks may not have the same effect. For example, the monetary authority, in an effort to keep prices stable, may adjust monetary policy (i.e. interest rates) when a money demand shock hits, leaving prices unchanged. This implies that these money demand shocks will not have long run impact on prices. Again, relative shocks would affect the relative and non-relative variables but the common shocks would only affect the non-relative variables, hence the zero entries in the fifth and sixth rows of C(1). Finally, note that because interest rates enter the VAR in levels (i.e. it is stationary), none of the structural shocks should lead to permanent changes in them. However, as interest rates respond quickly to any changes in the economy, all structural shocks are allowed to have short-term impacts on the interest rate variables. The only exception is that the common money demand shock (ε md-c ) is assumed to not have permanent impact on an accumulation of the relative interest rates. This justifies the remaining zero restriction. III. ESTIMATION RESULTS FOR STRUCTURAL VAR MODEL Benchmark U.S. U.K. Case This section presents and discusses the estimation results for the U.S.-U.K. benchmark case. The reduced-form benchmark VAR is estimated using 4 lags for quarterly data. Standard lag selection criterions select fewer lags (Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Hannan-Quinn 10

12 Criterion (HQC) suggest 3, 1, and 1 lags respectively). 9 However, using just one lag suggested by the BIC and HQC leads to non-white-noise like residuals. It is possible that in large size VARs such as the one in this paper, the lag selection criteria penalize additional lags to a greater degree than for smaller dimension VARs. Four lags were found to fully capture the serial correlation in the data, hence they are used for the benchmark case and for all other cases considered in this paper. Figure I shows the estimated dynamic response of the variable of interest to a onestandard deviation realization of a particular structural shock. The estimates have been suitably transformed to reflect the effect of shocks on the levels of the variables rather than their growth rates. I have omitted the results on relative variables in the VAR for brevity. The impulse-response functions shown in Figure I correspond to predictions of macroeconomic theory in general, although the point estimates (solid lines in Figure I) are not always statistically significant. For example, consider the exchange rate and monetary policy shock. Looking at the fifth row in Figure I, the relative money supply shock ε ms, which can best be interpreted as a monetary policy shock, is associated with a drop in the 3-month treasury bill rate i tbr. This indicates an expansionary monetary policy shock, 10 which should and does lead to an immediate depreciation of the real exchange rate, and an increase in output and price level. Focusing on the impact of shocks on the real exchange rate, the most striking feature in Figure I is the impulse-response of q to the taste shock ε d. The taste shock displays a large and statistically significant effect on the real exchange rate on impact and beyond. This shock, however, does not appear to be picking up demand-side factors that are related to output; it has essentially zero influence on output both in the short and long-run. Hence I would argue that it is appropriate to label the shock as a taste shock rather than a demand shock. A related way to examine the impact of individual shocks on the real exchange rate is to consider the variance decomposition presented in Table IV, which reports the share of the variance of the forecasting error made due any structural shock at any given time horizon. Looking at the first row of Table IV, one can easily see that the most important shock which explains about 70 percent of the variance in the real exchange rate on impact is the taste shock ε d. No other shock even comes close. The relative monetary policy shock (ε ms ) accounts for a mere 2 percent. However, if we consider monetary shocks more generally as the combination of money supply and demand shocks, then their importance grow, accounting for about 28 percent of the variance in the real exchange rate on impact. As the forecast horizon expands, the taste shock becomes even more dominant while the monetary shocks combined effect declines quickly. After four quarters, the total effect of the monetary shocks is less than half of that on impact. As for the other shocks in the system, neither the supply shocks nor the commodity price shocks have much influence over the real exchange rate at the short or long horizons (the 9 Ivanov and Kilian (2005), a recent paper on lag order selection for VAR impulse-response analysis, indicated that for quarterly VAR models the HQC tends to produce the most accurate structural and semistructural impulse-response estimates for sample sizes greater than It is possible that an expansionary monetary policy shock may not lead to a drop in interest rates if a liquidity effect does not dominate. Bernanke and Mihov (1998) have shown that there is no reason to reject the liquidity effect under their VAR framework, and as the sign of the monetary policy shock cannot be identified in any other fashion in this context, I will stick to the conventional assumption. 11

13 supply shocks are allowed to have permanent effect on the real exchange rate, but empirically they do not appear to be important). Despite the differences in modeling assumptions and data, the results here bear many similarities to those in Clarida and Gali (1994) and Rogers (1999), both of which use the long-run identification schemes to investigate the effect of monetary policy shocks on the U.S. U.K. real exchange rate. Demand-type shocks, i.e. if we consider the taste shock as a demand side shock because it is assumed to have no long-run impact on output, are always very important (accounting for over 95 percent of real exchange rate variance over any horizon in Clarida and Gali, and over 45 percent in Rogers). Whereas supply shocks do not play much of a role (proportions of variance that can be attributed to supply are lower than 10 percent for all papers regardless of the time horizon). The main differences in our results arise from monetary shocks. Using a simple three variable VAR model, Clarida and Gali find that the maximum impact of monetary shock on the real exchange rate is only about 2 percent. In contrast, Rogers five-variable VAR model shows that at a maximum, monetary policy shocks (shocks to the monetary base) account for around 15 percent of the variance in the real exchange rate, and this number almost triples if one also considers the other monetary shock that he identifies (shocks to the money multiplier). The difference in the data employed could account for some of the discrepancies in the results. Clarida and Gali and I both use quarterly data around the post-bretton Woods era, while Rogers utilizes annual data spanning over a hundred years. Also, I make use of short-term interest rates instead of money stocks (used by both Clarida and Gali and Rogers) to identify monetary policy. But as Rogers shows in an encompassing style test, model specification seems to matter a lot more than the differences in data. Comparing results from the Clarida and Gali model on Clarida and Gali sample period with the Clarida and Gali model on Rogers long-term sample show only modest increase in the contribution of the monetary shock. However, comparing estimates of the Clarida and Gali model on Clarida and Gali sample period with the Rogers model on Clarida and Gali sample period, an increase in the contribution of monetary shocks from nearly zero to over 50 percent in some cases is observed. Overall, it is a robust finding under longrun identification schemes that monetary policy and supply shocks are not major sources of exchange rate fluctuations. Hence, one should focus on the demand shocks as the main source for fluctuations in the real exchange rate. This will be the topic of the next section of the paper. How do these results compare to other papers in the literature that implement different identification strategies? For papers that use short-run identification schemes (both recursive and non-recursive restrictions) on the U.S. U.K. bilateral exchange rate, the proportion of variance in exchange rate explained by monetary policy shock varies significantly as well. On the high end, Kim and Roubini (2000) report 34.2 percent (6 months horizon, nominal exchange rate) and Eichenbaum and Evans (1995) report a maximum of 26 percent (average over month horizon for real exchange rate, benchmark specification). On the low end, Grilli and Roubini (1995) found only 2 percent of variance in nominal exchange rate is explained by monetary policy shocks. In 12

14 papers that make use of identification strategies focusing on shape/sign restrictions, the mixed results continue. Faust and Rogers (2003), using sign restrictions, find very strong monetary policy effects for the U.S. U.K. exchange rate, accounting for upwards of around 52 percent of the variance of exchange rate movements in their 7 variable model, though in their 14 variable model the effect of monetary policy decreases dramatically where the upper bound is less than 30 percent. 11 Scholl and Uhlig (2005) implement a similar type of sign restriction approach, and using Bayesian procedures, they find a range between 2 and 10 percent of the exchange rate fluctuations at the median estimate that is attributable to U.S. monetary policy shock. Even considering their upper 86 percent quantile estimates, the proportion of exchange rate variance that can be accounted for by U.S. monetary policy shock remains well below 40 percent for all horizons with very few exceptions. Farrant and Peersman (2006), using an extended approach of Uhlig (2005) that impose enough sign restrictions to identify the full set of structural shocks (as opposed to just one shock of interested in Scholl and Uhlig 2005), find much higher proportion of the variance in real exchange rate can be accounted for by nominal shocks, with a median estimate of 50 percent for their 3 variable Clarida-Gali model on impact. It is interesting to see, however, that in their 4 variable model, Farrant and Peersman (2006) find that the monetary policy shock only accounts for about 4 percent of the variance in the real exchange rate on impact at the median, but an exchange rate shock accounts for as much as 40 percent on impact. This exchange rate shock is identified as a shock which has the same sign on the real exchange rate with respect to relative output, relative prices, and interest rate differential. This means that if the shock does not lead to appreciation of the real exchange rate, then there can be no decrease in relative output, relative prices, or interest rate differential. It is possible that this exchange rate shock they have identified is related to what I identify as a taste shock. Both shocks could capture movements in the exchange rate that are not caused by macroeconomic fundamentals. In general, the results for the effects of monetary shocks on real exchange rate that I reported in Figure I and Table IV are well within the estimated range found in the literature using non-longrun identification schemes. Before moving on to results for other country pairs, one particular feature of monetary policy shock that is worth mentioning is the timing of its maximal impact on the real exchange rate. Looking back at Figure I again, one can see that the impulse of the real exchange rate q in response to the monetary policy shock ε ms does not reach its peak effect until about six quarters after impact. According to the classic Dornbusch (1976) overshooting model, an increase in domestic interest rates relative to foreign interest rates (contractionary U.S. monetary policy shock) should lead to an immediate appreciation 11 This identification procedure involves searching through all possible identification of the model then narrowing the large set of candidate results through mild sign restrictions on the way impulse-responses should be behave in response to a monetary policy shock. Due to the nature of this procedure, there are no specific point estimates for variance decomposition. Instead, Faust and Rogers (2003) provides a range of estimates, where the proportion of variance in exchange rate movements explained by U.S. monetary policy shock ranges from 8 to 52 percent for the 7 variable model, and from 2 to 6 percent for the 14 variable model. However, in the paper, the authors prefer to report the upper bound of the simulated coverage intervals for the variance decomposition at the 90 th percentile of the distribution, which is over 55 percent for the 7 variable model and less than 30 percent for the 14 variable model. Following the authors lead, these are the numbers I report above as well. 13

15 followed by a persistent depreciation of the domestic currency. This implies that the maximal effect of the policy shock on the real exchange rate should occur on impact. By contrast, delayed overshooting of the exchange rate, which is evident in my results, is common in the empirical literature. Most studies have found a persistent appreciation of the real exchange rate for up to three years after a contractionary policy shock hits. This finding leads to violation of the uncovered interest parity condition and therefore is also often called the forward discount puzzle. The phenomenon appears to be especially severe in models using recursive short-run identification scheme such as Eichenbaum and Evans (1995). Models that use the sign/shape restriction identification method, which is somewhat designed to resolve this kind of issue (since they can impose the restriction that exchange rate peaks on impact), are able to produce results that fit the Dornbusch model predictions. There is no delayed overshooting in Faust and Rogers (2003); and Scholl and Uhlig (2005), who do not impose very stringent restrictions on exchange rate behavior, find delays of up to one year only for U.S. U.K. pair. Also, despite my findings, other models that implement the long-run identification procedure appear to produce results that correspond to the Dornbusch model as well. Both Rogers (1999) and Clarida and Gali (1994) show no delayed overshooting. The real exchange rate in both studies peaks on impact. If we take the delayed overshooting result at face value and think about the rationalizations for it, one can turn to the literature on possible explanations for the forward discount puzzle. Some have tried to account for the puzzles by modeling risk aversion on the part of market participants, or by departing from the assumption of rational expectations. Small sample phenomena have also been brought up as potential causes of these puzzles, which may arise because of peso problems or learning about regime shifts. In general, as discussed in Eichenbaum and Evans (1995), one can view the delayed overshooting observed here as supporting a broader view of exchange rate overshooting behavior in which exchange rates eventually appreciate after depreciating for a period of time in response to an expansionary monetary policy shock. Results for Other Countries Three other countries from the G7 (Canada, Germany, and Japan) are considered in this paper in additional to the benchmark U.S. U.K. case. In general, results for the non-benchmark countries are qualitatively similar to the benchmark U.K.. Monetary policy shock effects are small and the finding that taste shock is very important in exchange rate fluctuations is robust for all country pairs both in the short-run (except for Japan) and in the long-run. Figure II displays impulse-responses of U.S. output, real exchange rate, U.S. price level, and U.S. interest rate (3-month treasury bill rate for Canada and the federal funds rate for Germany and Japan) to a one standard deviation shock in U.S. monetary policy. These impulse-responses are produced from VAR models with the same specification as the benchmark case using 4 lags. From the analysis in the previous section, we know that 14

16 the long-run restrictions imposed on the U.S. U.K. VAR model appear to have identified an expansionary monetary policy shock that lowers the treasury bill rate i tbr on impact, produces a depreciation of the real exchange rate, and leads to a rise in output and prices over time. Looking at the German and Japanese cases in Figure II, one can see that an increase in the U.S. interest rate (interpreted as expansionary shock to monetary policy) leads to a depreciation of the real exchange rate. However, output and prices both decrease rather than increase as one would expect after a monetary expansion. For Canada, not only do output and prices go in an unexpected direction after a contractionary monetary policy shock, the real exchange rate does as well, depreciating rather than appreciating. The counter-intuitive response of the price level, often called the price puzzle, seems to be a common occurrence when identifying monetary policy shocks using innovations in interest rates (rather than money stocks). Sims (1992) argues that the price puzzle may be due to the fact that positive interest rate innovations partly reflect inflationary pressure that leads to price increases, and vice versa. Hence one possible solution to the problem is to include variables in the VAR that may proxy for inflation expectations. Following the literature, I included intermediate materials prices in the VAR specification. However, while this solved the price puzzle for the U.K. case, it does not do so for these other countries. I have also considered a measure of oil prices instead of the intermediate materials prices in the VAR to proxy for expected inflation/deflation, though the puzzles remain. Even though there are puzzles associated with certain impulse-responses, we can still assess the relative strengths of each structural shock on the real exchange rate for these countries pairs. The variance decompositions presented in Table Va through Table Vc makes it clear that the taste shock is still by far the most important shock that contribute to exchange rate variability. Meanwhile, as I will show in the next section, there is no sense in which this taste shock is capturing the effects from one of the other identified shocks. Specifically, in the U.S. Canada case (Table Va), the effect of the taste shock on impact (87 percent) is even stronger than for the U.S. U.K. pairing, and it remains influential at all horizons, although at very long horizons (40 quarters and more), the proportion of exchange rate variance explained by the taste shock is about 10 percentage points lower in the Canadian case than for the U.K. case, with the supply shocks being more important. The effects of monetary policy shocks are about the same for the U.S. Canadian exchange rate as for the U.S. U.K. exchange rate, although if we consider all four types of monetary shocks, then they matter much less, with a combined total of less than 10 percent on impact. Moving onto the case of Germany, Table Vb shows the first major difference from the benchmark case is a much stronger effect of the monetary policy shock on impact (around 10 percent). However, compared to the benchmark results, the influence of money demand shocks is much smaller in this case, so the combined effect of all monetary shocks is substantially lower than for the U.K. The taste shock remains a major source of variability in the dollar mark exchange rate, accounting for 76 percent of the variance on impact, and continues have a large influence over the exchange rate in the long run. Similar to the Canadian case, the supply shocks play a larger role on the dollar mark exchange rate in the long run. Another distinct difference for Germany is that the 15