Purchasing Power Parity (PPP) is one of the most enduring topics in international economics, and the question of whether PPP holds both over long horizons and during the post-Bretton-Woods system of flexible nominal exchange rates has been extensively analyzed. All variants of PPP postulate that the real 1 exchange rate reverts to a constant mean. Evidence ofPPP can be provided by tests of a unit root in the ! real exchange rate. If the unit root null hypothesis can be rejected in favor of a level stationary alternative, then there is mean reversion and, therefore, PPP. Most of the existent work on purchasing power parity focuses on the narrow question of whether or not unit roots in real exchange rates can be rejected. The purpose of this proposal is to go beyond the narrow statistical focus to consider what can be learned about the behavior of real exchange rates from the results of unit root tests. Recent work has begun to appear which reports strong rejections of unit roots in real exchange rates for panels with quarterly data. The first part of the proposal investigates whether these results really provide evidence of purchasing power parity. Using panel methods, unit roots in post-1973 real exchange rates with the U.S. dollar as the numeraire currency can only be consistently rejected if the sample extends to 1997 or beyond. This leads to the question of what, if any, data generating processes for real exchange rates are consistent with both the recent rejections of unit roots with data extending through 1997 and the earlier failures to reject unit roots with shorter spans of data. Preliminary work indicates that the evidence is not consistent with real exchange rates being a stationary autoregressive process with high persistence, a combination of a stationary and a unit root process, or a nonlinear mean reverting process. The evidence is more consistent with a process of reversion to PPP restricted structural change. The second part of the proposal focuses on the speed of mean reversion. The half-lives ofPPP deviations, the expected number of years for a disturbance to the real exchange rate to decay by 50 percent, are generally calculated to be between three and five years with univariate methods. The use of median unbiased estimation methods with long-horizon and post-1973 data, however, shows that these estimates are biased downwards. More strikingly, the confidence intervals of the half-lives, especially with the post-l 973 data, are so wide as to make the point estimates virtually uninformative. This work will be extended in two directions. First, applying median unbiased estimation techniques to panel methods, the half-lives ofPPP deviations from panel unit root tests can be investigated. Preliminary results indicate that, while (as with the univariate tests) the point estimates are biased downwards, the confidence intervals from the median unbiased estimates (in contrast with the univariate case) are tight enough to be informative. Second, median unbiased estimation techniques can be applied to a recently developed univariate unit root test that has more power than the conventional tests. This creates the potential for tighter confidence intervals of the estimated half-lives. The third part of the proposal focuses on the behavior of long-horizon and post- World War II real exchange rates. Using long spans of data and sufficiently powerful techniques, unit roots can be rejected in favor of level stationarity (PPP) for most real exchange rates. An obvious econometric point, however, is that rejection of a null hypothesis in favor of a particular alternative hypothesis does not necessarily mean that the alternative is correct. In this case, there are other alternative hypotheses, including regime- wise level stationarity and regime-wise trend stationarity (both with and without PPP restrictions), that may provide better characterizations of real exchange rates. For long-horizon data, multiple level changes appear to be the most promising hypothesis. For post-World War II data, a combination of level changes (to account for the devaluations and revaluations at the end of the Bretton Woods period) plus slope changes (to account for the appreciation and depreciation of the dollar in the 1980s) appears to be most promising. The proposed research first involves conducting unit root tests with different alternative hypotheses. Depending on the results of these tests, simulation evidence can help uncover which data generating processes are most congruent with the results.
