Testing for heteroskedasticity and spatial correlation in a random effects panel data model

A panel data regression model with heteroskedastic as well as spatially correlated disturbances is considered, and a joint LM test for homoskedasticity and no spatial correlation is derived. In addition, a conditional LM test for no spatial correlation given heteroskedasticity, as well as a conditional LM test for homoskedasticity given spatial correlation, are also derived. These LM tests are compared with marginal LM tests that ignore heteroskedasticity in testing for spatial correlation, or spatial correlation in testing for homoskedasticity. Monte Carlo results show that these LM tests, as well as their LR counterparts, perform well, even for small NN and TT. However, misleading inferences can occur when using marginal, rather than joint or conditional LM tests when spatial correlation or heteroskedasticity is present.