Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects

We derive analytically the local asymptotic power of two pooled t-ratio tests for the presence of a unit root in a panel with fixed effects. We consider two statistics which differ according to the method used to remove the bias of the pooled OLS estimator. We show that when we bias-correct the numerator only, the resulting test has significant local power in n^-1/4 T^-1 neighbourhoods of the null of a panel unit root, while when the entire estimator is corrected for bias, the resulting statistic has local asymptotic power in neighbourhoods shrinking at the faster rate of n^-1/2 T^-1. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1-24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153-74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416-51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework.