Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for applied work

It is common in applied econometrics to test the null hypothesis of a level-stationary process against the alternative of a unit root process. We show that the use of conventional asymptotic critical values for the stationarity tests of Kwiatkowski et al. (1992) and Leybourne and McCabe (1994) may cause extreme size distortions, if the model under the null hypothesis is highly persistent. The existence of such size distortions has not been recognized in the previous literature. We illustrate the practical importance of these distortions for the problem of testing for long-run purchasing power parity under the recent float. Size distortions of tests of the unit root null hypothesis may be overcome by the use of finite-sample or bootstrap critical values. We show that such corrections are not possible for tests of the null hypothesis of stationarity. Our results suggest that the common practice of viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions or in spurious acceptances of the unit root hypothesis. We conclude that tests of the null hypothesis of stationarity cannot be recommended for applied work unless the sample size is very large.