نرخ واقعی ارز و تفاوت نرخ بهره واقعی: تفسیر ارزش فعلی

Although the real exchange rate–real interest rate (RERI) relationship is central to most open economy macroeconomic models, empirical support for the relationship is generally found to be rather weak. In this paper we re-investigate the RERI relationship using bilateral US real exchange rate data spanning the period 1978–2007. Instead of testing one particular model, we build on Campbell and Shiller [1987. Cointegration tests of present-value models. Journal of Political Economy 95, 1062–1088] to propose a metric of the economic significance of the relationship. Our empirical results provide robust evidence that the RERI link is economically significant and that the real interest rate differential is a reasonable approximation of the expected rate of depreciation over longer horizons.

Many well-known exchange rate models highlight the role of the real interest rate differential as a key determinant of real exchange rates. For example, sticky price models (see Dornbusch, 1976; Mussa, 1984) and optimizing models (see, for example, Grilli and Roubini, 1992; Obstfeld and Rogoff, 1996) emphasize the effect of liquidity impulses on real interest rates and consequently the real exchange rate. This relationship is often summarized in the form of the real exchange rate–real interest rate (RERI) relationship. However, despite its centrality to many open economy macro models, the empirical evidence on the RERI relationship is rather mixed. In this paper we revisit the RERI relationship and suggest a new way of testing it, based on the VAR-method of Campbell and Shiller (1987) for testing present-value models. Our results indicate that the real interest rate differential is a reasonable proxy for the expected real depreciation of the US dollar and can be interpreted as the transitory part of the real exchange rate. This empirical finding provides strong support for the results of Baxter (1994) and also of Edison and Pauls (1993) who have emphasized that the link between real exchange rates and real interest differentials is to be found in the business cycle domain, instead of lower frequencies. Our way of casting the RERI relationship into an empirical model rests on the idea that the real interest rate differential is the sum of expected period-to-period changes in real exchange rates. In this context, the real interest rate differential can be interpreted as the spread variable in a present-value model in which the discount factor is known and equal to one.1 This allows us to take the projection for the change in the real exchange rate from a bivariate VAR, consisting of the change in the real exchange rate and the real interest differential, and to correlate this projection with the real interest differential. We argue that this kind of test is much closer in spirit to the RERI relationship than many extant tests and it produces measures of long-run expected changes in the exchange rate which are highly correlated with real interest rate differentials. In our analysis we study bilateral real exchange rates for the US vis-à-vis the other G7 countries: Canada, France, Germany, Italy, Japan and the UK. The sample period is 1978 quarter 2 to 2007 quarter 3. In common with most other applications of the VAR-based present value approach, we find that the cross-equation restrictions of the present-value model are statistically rejected. However, we note that this can be attributed to the time variability of the discount factor, rather than to a rejection of the RERI per se. Indeed, we suggest interpreting the RERI more broadly as a significant and positive relationship between expected real exchange rate changes and the real interest rate differential. We first present graphical evidence which indicates that this broader version of the RERI is strongly supported by the data and economically significant. A key aspect of our broader interpretation is that it does not amount to a test of a particular model but that it provides a taxonomy of the economic significance of the RERI by asking what fraction of the variability in interest rate differentials is explained by changes in the rate of expected depreciation. This fraction is high and significant for all pairs of exchange rates we consider. Our method can be thought of as a formalization of the approach advocated by Campbell (1986) who argued in the context of the permanent income hypothesis that ‘[...]models which are strongly rejected statistically may be good approximations of the behavior of economic variables’ (p. 29). We further illustrate the empirical relevance of the RERI by investigating how various structural shocks affect the relationship. While doing so sheds light on the RERI as a conditional relationship, we also view this as a way to collect a set of stylized facts on the dynamic interaction between real interest rates and real exchange rates that may also be of more general interest: under the null of the RERI, shocks to the real interest rate differential should only have a transitory impact on the real exchange rate, whereas shocks that do not affect the real interest rate differential should be associated with the permanent component. We find that these hypothesized relationships are in fact in the data. Furthermore, we also find that a positive interest rate shock leads to a temporary decline (appreciation) in the real exchange rate that is then gradually offset as relative prices and nominal interest rates adjust. This, again, is very much in line with theoretical predictions. We examine the robustness of this conclusion using an adaptation of the method suggested by King and Watson (1997), which involves examining the robustness of the response of the two variables to the choice of identification scheme. Interestingly, it turns out that our structural conclusions are independent of the particular approach to identification that we choose: the same pattern arises based on long-run identification schemes in the spirit of Blanchard and Quah (1989), more conventional short-run Choleski decompositions and, in fact, based on most other possible identifications. The outline of the remainder of this paper is as follows. In the next section we consider the RERI relationship in some detail and discuss how the VAR-based method of Campbell and Shiller (1987) can be adapted to explore the RERI link. We then go on to outline how the relationship can be identified using the projections from a simple VAR model. In Section 3 we present our empirical results, while in Section 4 we examine the impact of structural shocks on the long-run relationship between real exchange rates and the real interest differential. Section 5 provides a further discussion of our results and concludes.

In this paper we have re-examined the real exchange rate–real interest rate relationship using data for six US dollar bilateral exchange rates, over the period 1978–2007. Many previous tests of this relationship have involved attempting to cointegrate measures of a real exchange rate with a measure of a country's real interest differential. However, following Baxter (1994), the derivation of the RERI relationship suggests that such a method is likely to be flawed since if the real exchange rate is integrated of order one, the real interest differential must be stationary. Building on this insight, we proposed interpreting the RERI by building on the VAR-based approach for present-value models of Campbell and Shiller (1987). This involves taking the projection of the change in the real exchange rate from a bivariate VAR, consisting of the change in the real exchange rate and the real interest differential, and correlating it with the real interest differential. We argued that this kind of test is much closer in spirit to the RERI relationship than many extant tests, and it produces measures of long-run expected changes in the exchange rate which are highly correlated with real interest rate differentials. While the particular set of cross-equation restrictions that arise from a fixed-discount factor model are statistically rejected, our framework allows us to trace this back to the presence of predictable excess returns. We show that this rejection does not invalidate the RERI link as an economically significant relationship: a significant fraction of the variability in real interest rate differentials is explained by time-variation in expected exchange rate changes and real interest rate differentials are highly correlated with measures of the expected rate of depreciation. The upshot of our results is that the RERI is no more elusive than other important relationships in macroeconomics and finance that have been tested in a present value context, such as: the stock price/dividend relationship; the consumption–income relationship; the term structure of interest rates and the New Keynesian Phillips curve. Such models are often statistically rejected in a present value setting, but the statistical rejection is usually associated with a fixed discount-factor assumption. As argued by Campbell (1986), such rejections per se are not informative with respect to the economic significance of a particular theory. Our approach formalizes this philosophy in the sense that, instead of focusing on the cross-equation restrictions implied by a particular incarnation of the theory, we have proposed a metric of the economic significance of the hypothesized theoretical link. Clearly, this approach can be generalized to other theoretical relationships than the RERI. We provide further evidence in support of the RERI by identifying structural shocks to the RERI relationship. We find that shocks to the real interest rate differential, in general, only produce temporary responses in the real exchange rate and these responses have the right sign: on impact, a widening interest rate differential leads to a temporary appreciation that is then offset through a subsequent depreciation as relative price levels start to converge and as the interest rate differential starts to narrow again. This result turns out to be independent of the particular identification scheme imposed on our VAR model. The evidence we have reported in this paper therefore strongly supports the conclusion that the RERI as an economic relationship should be taken seriously: real interest rate differentials constitute a good proxy for the temporary component in real exchange rates!