2Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for the PPP Debate

Abstract: Tests of the null hypothesis of stationarity against the unit root alternative play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asymptotic critical values for stationarity tests may cause extreme size distortions, 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-run purchasing power parity under the recent float. We show that the common practice of viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions and in spurious rejections of long-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 economically plausible assumptions about the half-life of deviations from PPP. Thus, the fact that stationarity is not rejected cannot be interpreted as convincing evidence in favor of mean reversion. Only in the rare case that stationarity is rejected do size-corrected tests shed light on the question of long-run PPP