Estimation problems in models with spatial weighting matrices which have blocks of equal elements

Spatial models whose weighting matrices have blocks of equal elements might be considered if units are viewed as equally distant within certain neighborhoods, but unrelated between neighborhoods. We give exact small sample results for such models that contain a spatially lagged-dependent variable. We consider cases in which the data relate to one or more panels, for example, villages, schools, etc. Our results are consistent with large sample results given in Kelejian and Prucha (2002) but indicate a variety of issues they did not consider.