Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for Applied Work

It is common in applied econometrics to test a highly persistent process under the null hypothesis against an alternative of a unit root process. We show that the conventional asymptotic critical values for the stationarity tests of Kwiatkowski et al. and Leybourne and McCabe may have substantial size distortions if the model under the null hypothesis is highly persistent. Such size distortions have not been recognized in the literature. The practical importance of these distortions is illustrated when testing for long-run purchasing power parity under current float. Size distortions of tests of the null of a unit root may be overcome by the use of finite sample or bootstrap critical values. We show such corrections are not possible when testing the null of stationarity, and we conclude that tests of this null cannot be recommended for applied work unless the sample size is very large.