Modified QML Estimation of Spatial Autoregressive Models with Unknown Heteroskedasticity and Nonnormality

In the presence of heteroskedasticity, Lin and Lee (2010) show that the quasi maximum likelihood (QML) estimators of spatial autoregressive models (SAR) can be inconsistent as a ‘necessary’ condition for consistency can be violated, and thus propose robust GMM estimators for the model. In this paper, we first show that this condition may hold in many practical situations and when it does the regular QML estimators can be consistent. In cases where this condition is violated, we propose a modified QML estimation method robust against heteroskedasticity of unknown form. In both cases, asymptotic distributions of the estimators are derived, and methods for estimating robust variances are given, leading to robust inferences for the model. Extensive Monte Carlo results show that the modified QML estimator outperforms the GMM estimators, and the regular QML estimator even when it is consistent. The proposed robust inference methods can also be easily applied.