On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors

In this paper, we consider a spatial-autoregressive model with autoregressive disturbances, where we allow for endogenous regressors in addition to a spatial lag of the dependent variable. We suggest a two-step generalized method of moments (GMM) and instrumental variable (IV) estimation approach extending earlier work by, e.g., Kelejian and Prucha (1998, 1999). In contrast to those papers, we not only prove consistency for our GMM estimator for the spatial-autoregressive parameter in the disturbance process, but we also derive the joint limiting distribution for our GMM estimator and the IV estimator for the regression parameters. Thus the theory allows for a joint test of zero spatial interactions in the dependent variable, the exogenous variables and the disturbances. The paper also provides a Monte Carlo study to illustrate the performance of the estimator in small samples.