A Generalized Spatial Panel Data Model with Random Effects

This paper proposes a generalized panel data model with random effects and first-order spatially autocorrelated residuals that encompasses two previously suggested specifications. The first one is described in Anselin's (1988) book and the second one by Kapoor et al. (2007). Our encompassing specification allows us to test for these models as restricted specifications. In particular, we derive three Lagrange multiplier (LM) and likelihood ration (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 tests, we obtain closed form solutions and we derive their large sample distributions. Our Monte Carlo results show that the suggested tests are powerful in testing for these restricted specifications even in small and medium sized samples.