GMM estimation of SAR models with endogenous regressors

• We consider the GMM estimation of SAR models with endogenous regressors.
• We propose a new set of quadratic moment conditions for the GMM estimator.
• We establish the consistency and asymptotic normality of the GMM estimator.
• The GMM estimator can be asymptotically as efficient as the ML estimator.
• The GMM estimator is easy to implement and performs well infinite samples.

In this paper, we extend the GMM estimator in Lee (2007) to estimate SAR models with endogenous regressors. We propose a new set of quadratic moment conditions exploiting 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 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 ML estimator under normality. Monte Carlo experiments show that the proposed GMM estimator performs well in finite samples.