Alternative GMM estimators for spatial regression models

Using approximations of the score of the log-likelihood function we derive optimal moment conditions for estimating spatial regression models. Our approach results in computationally simple and robust estimators. The moment conditions resemble those proposed by Kelejian & Prucha (1999), hence we provide an intuitive interpretation of their estimator as a second order approximation to the log-likelihood function. Furthermore we propose simplified and efficient GMM estimators based on a convenient modification of the moment conditions. Heteroskedasticity robust versions of our estimators are also provided. Finally, a first order approximation for the spatial lag model is also considered. Monte Carlo results suggest that a simple just-identified estimator based on a quadratic moment derived from a first order approximation of the score of the log-likelihood function performs similar to the GMM estimator proposed by Kelejian & Prucha (2010).