This paper proposes a generalized specification for the panel data model with random effects and first-order spatially autocorrelated residuals that encompasses two previously suggested specifications. The first one is described in Anselinís (1988) book and the second by Kapoor, Kelejian, and Prucha (2004). Our encompassing specification
allows us to test these models as restricted specifications. In particular, we derive three LM and LR tests that restrict our generalized model to obtain (i) the Anselin model, (ii) the Kapoor, Kelejian, and Prucha model, and (iii) the simple random effects model that ignores the spatial correlation in the residuals. For two of these three LM tests, we obtain closed form solutions. Our Monte Carlo results show that the suggested tests are powerful in testing for these restricted
specifications even in small and medium sized samples.