Efficient tests for autoregressive unit roots in panel data

In this paper the class of admissable tests for unit roots in panel data sets of autoregressive, Gaussian time series will be partially characterized. Using this characterization, several recently suggested tests are shown to be inadmissable. Since the sufficient statistic for this testing problem is multidimensional, there is no uniformly most powerful test; however, in light of the inadmissability result, a new test is proposed that appears to do well relative to existing tests. The test is parameterized in a way that allows the choice of different directional deviations from the null hypothesis over which power is to be maximized, giving added flexibility to researchers.