Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch Pagan statistic has become a standard tool to infer on unobserved heterogeneity over the cross section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the Breusch Pagan statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions which could be overcome by the robust bootstrap procedure.