GMM estimation of a spatial autoregressive model with autoregressive disturbances and endogenous regressors
研究了带空间自回归扰动和内生回归量的空间自回归模型的广义矩估计方法，允许异方差，证明了估计量的一致性和渐近正态性，并推导了最优矩条件。
This paper considers the generalized method of moments (GMM) estimation of a spatial autoregressive (SAR) model with SAR disturbances, where we allow for endogenous regressors in addition to a spatial lag of the dependent variable. We do not assume any reduced form of the endogenous regressors, thus we allow for spatial dependence and heterogeneity in endogenous regressors, and allow for nonlinear relations between endogenous regressors and their instruments. Innovations in the model can be homoscedastic or heteroskedastic with unknown forms. We prove that GMM estimators with linear and quadratic moments are consistent and asymptotically normal. In the homoscedastic case, we derive the best linear and quadratic moments that can generate an optimal GMM estimator with the minimum asymptotic variance.