Testing for random effects in panel data under cross sectional error correlation—A bootstrap approach to the Breusch Pagan test

Abstract

When testing the pooled regression via the Breusch Pagan test model disturbances are often assumed to be i.i.d. over both the time and the cross section dimension. A bootstrap approach to generate critical values for the Breusch Pagan statistic is provided which is valid under heteroskedasticity and cross sectional correlation as typically formalized in the framework of seemingly unrelated regressions. Moreover, asymptotic results are derived for a finite cross section and infinite time dimension. Finite sample simulations show that ignoring cross sectional correlation may lead to large size distortions in practice. Conditional versions of the test statistic designed to cope with random time effects or spatial error correlation show empirical size distortions in case the source of contemporaneous error correlation is misspecified. Moreover, the bootstrap is robust if contemporaneous error correlation is induced by random time effects or in case of spatial error correlation.