Panel Unit Root Tests Under Cross Sectional Dependence

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 against a sequence of local alternatives is compared. To adjust for short-run serial correlation of the errors, a pre-whitening procedure is suggested 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. From our Monte Carlo simulations it turns out that the robust OLS t-statistic performs well with respect to size and power, whereas the the GLS t-statistic may suffer from severe size distortions in small and moderate sample sizes. To improve the small sample properties of the GLS test procedure, a bootstrap version of the test is available. ∗The research for this paper was carried out within research project “Unit roots and cointegration in panel data” financed by the German Research Association (DFG). We like to thank Uwe Hassler, Adina Tarcolea, the participants of the Workshop on Nonstationary Panel Data Analysis (May 2003, University of Bonn) and the Econometric Seminar at the KU Leuven (September 2003) for their comments and suggestions.