GMM inference in spatial autoregressive models

In this study, we investigate the finite sample properties of the optimal generalized method of moments estimator (OGMME) for a spatial econometric model with a first-order spatial autoregressive process in the dependent variable and the disturbance term (for short SARAR(1, 1)). We show that the estimated asymptotic standard errors for spatial autoregressive parameters can be substantially smaller than their empirical counterparts. Hence, we extend the finite sample variance correction methodology of Windmeijer (2005 Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics 126(1):25–51.Crossref], Web of Science ®] , Google Scholar]) to the OGMME for the SARAR(1, 1) model. Results from simulation studies indicate that the correction method improves the variance estimates in small samples and leads to more accurate inference for the spatial autoregressive parameters. For the same model, we compare the finite sample properties of various test statistics for linear restrictions on autoregressive parameters. These tests include the standard asymptotic Wald test based on various GMMEs, a bootstrapped version of the Wald test, two versions of the C(α) test, the standard Lagrange multiplier (LM) test, the minimum chi-square test (MC), and two versions of the generalized method of moments (GMM) criterion test. Finally, we study the finite sample properties of effects estimators that show how changes in explanatory variables impact the dependent variable.