On the Robust Estimation of Spatial Autoregressive Models

Abstract

The spatial autoregressive (SAR) model is commonly used for cross-sectional data with spatial dependence in the response variable. A robust M-estimator for the SAR model with independent normal random errors is proposed, which is resistant to extreme contamination or outliers in the data. The proposed estimator is defined by a set of robust estimating functions derived by modifying the estimating functions for the standard maximum likelihood (ML) estimator using the Huber function. An iterative algorithm based on iteratively reweighted least squares and a fixed point method is provided to compute the robust M-estimator. The proposed estimator is shown to be Fisher-consistent under the core model, has a bounded influence function, and is asymptotically normally distributed. A closed-form expression for the asymptotic covariance matrix estimator under the core model is derived, and used to study the asymptotic relative efficiency of the proposed estimator. Simulation studies demonstrate that the proposed robust M-estimator greatly outperforms the ML estimator as well as several other non-robust estimators of the SAR model, in terms of both estimation and inference under different contamination scenarios. Additionally, the proposed estimator offers comparable performance to some robust estimators of the SAR model under contamination. Applying the robust M-estimator for the SAR model to the U.S. federal grants and U.S. Nielsen Local Television View datasets reveals strong positive spatial dependence in the grant value among counties, insignificant positive effect of news watching on grant distribution, and evidence of outliers in the data. This results in different conclusions from those obtained using the ML estimator.