Academic journal article Journal of Money, Credit & Banking

The Long-Run U.S./U.K. Real Exchange Rate

Academic journal article Journal of Money, Credit & Banking

The Long-Run U.S./U.K. Real Exchange Rate

Article excerpt

RECENT STUDIES of purchasing power parity using long data series have found a tendency for real exchange rates among the major industrialized countries to converge in the long run.(1) This literature, which typically examines time series with over one hundred years of data, rejects the null hypothesis of a unit root in real exchange rates using standard unit root tests, such as the Dickey-Fuller test.

Should we conclude, therefore, that there is no permanent component to these real exchange rates? There are at least two reasons to doubt this conclusion. First, it is likely there have been shifts in the data-generating process for the real exchange rate over this period. For example, as Mussa (1986) and Grilli and Kaminsky (1991) have noted, the stochastic process for real exchange rates appears to be different under regimes of fixed and floating nominal exchange rates. The literature has not established how robust unit root tests are to changes in regimes. Indeed, Kim, Nelson, and Startz (1998) have presented evidence in variance ratio tests for mean reversion in U.S. stock prices that the tests are sensitive to the pattern of heteroskedasticity in the data. Frankel and Rose (1996) test for purchasing power parity using panels of real exchange rates beginning only in 1973, because "of concerns about the use of long time series, since they include potentially serious structural shifts." (p. 210).

The second reason why we should not rule out the presence of a permanent component based on the conclusion of the unit root tests is that the tests have a large size bias when a series contains both a permanent and a transitory component. In this case, the first difference of the real exchange rate has a moving average component in its ARMA representation. Schwert (1989) and others have shown that unit root tests tend to reject the null far too frequently in the presence of moving average components. Engel (2000) calibrates some unit root tests to real exchange rate data, and argues that tests with a nominal size of 5 percent may have a true size of about 80 percent. That is, the tests reject the null 80 percent of the time, even when a large fraction of the variance of real exchange rate movements in the sample are generated from the permanent component.

We investigate the behavior of the U.S./U.K. real exchange rate, using monthly data from January 1885 to November 1995.(2) The data is plotted in Figure 1. Inspection of the graph suggests that the real exchange rate process has not been homoskedastic over the entire 111-year period. It is impossible to conclude visually whether there is a permanent or a transitory component to the real exchange rate. We note that, using an Augmented Dickey-Fuller test, we reject a unit root in this real exchange rate at the 5 percent level. But we do not accept this as conclusive evidence that there is no permanent component in this real exchange rate. Instead, we explore models in which there are unobservable permanent and transitory components. We allow both the transitory and the permanent component to switch among three states characterized by low, medium, and high variance. Our model, therefore, allows for the structural shifts that were the concern of, for example, Frankel and Rose (1996)(3); and, it investigates the possibility that both transitory and permanent components exist, as Engel (1996) advocates.

We initially examine a generously parameterized model that allows three variance states for both the permanent and transitory components. However, we shall demonstrate in section 3 that the permanent component is overparameterized in this case. In fact, a homoskedastic permanent component, along with a three-state model for the transitory component, best describes the data. Hence, we can conclude that the pattern of shifting variances clearly visible in the data reflects heteroskedasticity in the transitory component.

Interestingly, as section 4 shows, the transitory component appears to shift among states at points where significant nominal events occur. …

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