Panel unit root tests under cross‐sectional dependence

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Abstract
In this paper alternative approaches for testing the unit root hypothesis in panel data are considered. First, a robust version of the Dickey‐Fuller t‐statistic under contemporaneous correlated errors is suggested. Second, the GLS t‐statistic is considered, which is based on the t‐statistic of the transformed model. The asymptotic power of both tests is compared against a sequence of local alternatives. To adjust for short‐run serial correlation of the errors, we propose a pre‐whitening procedure that yields a test statistic with a standard normal limiting distribution as N and T tends to infinity. The test procedure is further generalized to accommodate individual specific intercepts or linear time trends. From our Monte Carlo simulations it turns out that the robust OLS t‐statistic performs well with respect to size and power, whereas the GLS t‐statistic may suffer from severe size distortions in small and moderate sample sizes. The tests are applied to test for a unit root in real exchange rates.