The Error-in-Rejection Probability of Meta-Analytic Panel Tests

Meta-analytic panel unit root tests such as Fisher?s X2 test, which consist of pooling the p-values of time series unit root tests, are widely applied in practice. Recently, several Monte Carlo studies have found these tests? Error-in-Rejection Probabilities (or, synonymously, size distortion) to increase with the number of series in the panel. We investigate this puzzling finding by modelling the finite sample p-value distribution of the time series tests with local deviations from the asymptotic p-value distribution. We find that the size distortions of the panel tests can be explained as the cumulative effect of small size distortions in the time series tests.