Size distortions of tests of the null hypothesis of stationarity: evidenceand implications for the PPP debate

Tests of the null hypothesis of stationarity against the unit root alternat ive play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asympto tic critical values for stationarity tests may cause extreme size distortio ns, if the model under the null hypothesis is highly persistent. This fact calls into question the use of these tests in empirical work. We illustrate the practical importance of this point for tests of long-ran purchasing po wer parity (PPP) under the recent float. We show that the common practice o f viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions and in spurious rejections of lo ng-run PPP. While the size distortions may be overcome by the use of finite -sample critical values, the resulting tests tend to have low power under e conomically plausible assumptions about the half-life of deviations from PP P. Thus, the fact that stationarity is not rejected cannot be interpreted a s convincing evidence in favor of mean reversion. Only in the rare case tha t stationarity is rejected, do size-corrected tests shed light on the quest ion of long-run PPP. (C) 2001 Elsevier Science Ltd. All rights reserved.