A note on tests of sphericity and cross-sectional dependence for fixed effects panel model

This paper theoretically explains why bias correction appears in two statistics recently developed by Baltagi et al. (2011, 2012), which are designed to test the sphericity and cross-sectional dependence of the errors in the fixed effects panel model respectively. Our explanation shows that the bias correction is in fact avoidable, which is demonstrated by two corresponding statistics that are newly constructed in this paper. Simulation suggests that our statistics perform as well as the two in Baltagi et al. (2011, 2012). In addition, according to the theories underlying our explanation, we extend a new sphericity test proposed by Fisher et al. (2010) to the fixed effects model. Simulation finds that the test behaves well only if both the cross-sectional and the time series dimension are large.