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−1/4T−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−1/2T−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.