GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations

This dissertation proposes a generalized method of moments (GMM) estimation framework for the spatial autorregressive (SAR) model in a system of simultaneous equations with homoskedastic and heteroskedastic disturbances. It includes two chapters based on joint work with Prof. Xiaodong Liu.\nThe first chapter extends the GMM estimator in Lee (2007) to estimate SAR models with endogenous regressors and homoskedastic disturbances. We propose a new set of quadratic moment equations exploring the correlation of the spatially lagged dependent variable with the disturbance term of the main regression equation and with the endogenous regressor. The proposed GMM estimator is more efficient than the IV-based linear estimators in the literature, and computationally simpler than the ML estimator. With carefully constructed quadratic moment equations, the GMM estimator can be asymptotically as efficient as the full information ML estimator. Monte Carlo experiment shows that the proposed GMM estimator performs well in finite samples.\nThe second chapter proposes a GMM estimator for the SAR model in a system of simultaneous equations with heteroskedastic disturbances. Besides linear moment conditions, the GMM estimator also utilizes quadratic moment conditions based on the covariance structure of model disturbances within and across equations. Compared with the QML approach considered in Yang and Lee (2014), the GMM estimator is easier to implement and robust under heteroskedasticity of an unknown form. We also derive a heteroskedasticity-robust estimator for the asymptotic covariance of the GMM estimator. Monte Carlo experiments show that the proposed GMM estimator performs well in finite samples.