The local power of fixed-T panel unit root tests allowing for serially correlated errors

The asymptotic power properties of fixed-T panel unit root tests allowing for serially correlated error terms are examined by deriving their asymptotic local power functions. This is done for dynamic panel data models allowing for individual effects or individual effects and incidental trends. For the first model, the paper shows that an instrumental variables (IV) based test statistic, which exploits orthogonal moment conditions of the demeaned by their initial observations individual series of the panel, performs better than least squares (LS) tests based on the "within group" transformation of the series. Allowing for serial correlation reduces the power of the IV based test. This reduction however is unimportant in the case of positive serial correlation of the error terms. For the panel data model with incidental trends, the paper shows that LS based test statistics relying on "within group" or forward deviations transformations of the data have non-trivial power in the natural root-N neighbourhood of unity, if the errors terms are negatively correlated. This power is retained even in panels with small N. For the IV based test statistic, the asymptotic local power function constitutes a poor approximation of its true power, even in large N panels.