GMM Estimation of Spatial Autoregressive Models with Moving Average Errors

Abstract

In this paper, we introduce the one-step generalized method of moments (GMM) estimation methods considered in Lee (2007a) and Liu, Lee, and Bollinger (2010) to a spatial autoregressive model that has a spatial moving average process in the disturbance term (for short SARMA (1,1)). First, we determine the set of the best linear and quadratic moment functions for the GMM estimation. Second, we show that the GMM estimator (GMME) formulated from this set is the most efficient estimator within the class of GMMEs formulated from the set of linear and quadratic moment functions. Our analytical results show that the GMME can be asymptotically equivalent to the maximum likelihood estimator (MLE), when the disturbance term is i.i.d. Normal. When the disturbance term is simply i.i.d., the one-step GMME can be more efficient than the quasi MLE (QMLE). With an extensive Monte Carlo study, we compare its finite sample properties against the MLE, the QMLE and the estimators suggested in Fingleton (2008).