GMM estimation of spatial autoregressive models with moving average disturbances

• We introduce one-step GMM estimation methods to SARMA models.
• We determine the set of the best linear and quadratic moment functions.
• The optimal GMME formulated from this set is the most efficient estimator.
• The optimal GMME can be more efficient than the quasi MLE (QMLE).

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 spatial models that impose a spatial moving average process for the disturbance term. First, we determine the set of best linear and quadratic moment functions for GMM estimation. Second, we show that the optimal 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 one-step GMME can be more efficient than the quasi maximum likelihood (QMLE), when the disturbance term is simply i.i.d. With an extensive Monte Carlo study, we compare its finite sample properties against the MLE, the QMLE and the estimators suggested in Fingleton (2008a).