<P>This paper considers a spatial panel data regression model with serial correlation on each spatial<BR>unit over time as well as spatial dependence between the spatial units at each point in time. In<BR>addition, the model allows for heterogeneity across the spatial units using random effects. The paper<BR>then derives several Lagrange multiplier tests for this panel data regression model including a joint<BR>test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two<BR>strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in<BR>Anselin and Bera [1998. Spatial dependence in linear regression models with an introduction to<BR>spatial econometrics. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics.<BR>Marcel Dekker, New York] and in the panel data context by Baltagi et al. [2003. Testing panel data<BR>regression models with spatial error correlation. Journal of Econometrics 117, 123–150]. The second<BR>is the LM tests for the error component panel data model with serial correlation derived by Baltagi<BR>and Li [1995. Testing AR(1) against MA(1) disturbances in an error component model. Journal of<BR>Econometrics 68, 133–151]. Hence, the joint LM test derived in this paper encompasses those derived<BR>in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests<BR>become marginal LM tests that ignore either serial correlation over time or spatial error correlation.<BR>The paper then derives conditional LM and LR tests that do not ignore these correlations and<BR>contrast them with their marginal LM and LR counterparts. The small sample performance of thesetests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is<BR>significant can lead to misleading inference.</P><BR>