Analyzing Unit Root Tests in Finite Samples Using Power Profiles.

This study analyzes the size and power of tests of the null of stationarity against the unit root alternative. Existing evidence is limited to processes with roots between 0 and 0.7. In sharp contrast, virtually all applications of economic interest involve null hypotheses much closer to 1. We focus on the Leybourne and McCabe (1994) test because of its superior small-sample properties. We document that conventional asymptotic critical values for this test are inappropriate in small samples, and we provide finite-sample critical values for the economically relevant range of parameter values and sample sizes. Using power profiles, we show that it is very difficult to obtain meaningful results, even with large samples.