Efficient GMM Estimation of High Order Spatial Autoregressive Models With Autoregressive Disturbances

In this paper, we extend the GMM framework for the estimation of the mixed-regressive spatial autoregressive model by Lee(2007a) to estimate a high order mixed-regressive spatial autoregressive model with spatial autoregressive disturbances. Identification of such a general model is considered. The GMM approach has computational advantage over the conventional ML method. The proposed GMM estimators are shown to be consistent and asymptotically normal. The best GMM estimator is derived, within the class of GMM estimators based on linear and quadratic moment conditions of the disturbances. The best GMM estimator is asymptotically as efficient as the ML estimator under normality, more efficient than the QML estimator otherwise, and is efficient relative to the G2SLS estimator.