ARTICLES

EFFICIENT GMM ESTIMATION OF HIGH ORDER SPATIAL AUTOREGRESSIVE MODELS WITH AUTOREGRESSIVE DISTURBANCES

Lung-fei Lee^a1 c1 and Xiaodong Liu^a2

^a1 Ohio State University

^a2 University of Colorado at Boulder

Abstract

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.

Correspondence:

^c1 Address correspondence to Lung-fei Lee, Department of Economics, Ohio State University, Columbus, OH 43210, USA; e-mail: lflee@econ.ohio-state.edu.

Footnotes

This version is an extension that generalizes and unifies two previous working papers with the titles “Efficient GMM Estimation of High Order Spatial Autoregressive Models” and “Efficient GMM Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances.” We gratefully acknowledge financial support from the National Science Foundation Grant No. SES-0519204 and research assistantship support from the Department of Economics at the Ohio State University. We appreciate having received valuable comments and suggestions from three anonymous referees, an associate editor, and the editor to improve the presentation of our paper. Any remaining errors are solely ours.