What question did this study set out to answer?

The focus is on developing robust estimation methods for spatial autoregressive models to handle various disturbances effectively.

February 14, 2026Open Access

Robust Estimation for the Spatial Autoregressive Model

TLTuo LiuXiamen University XXXingbai XuXiamen University LLLung‐fei LeeShanghai University of Finance and Economics

Key Points

The focus is on developing robust estimation methods for spatial autoregressive models to handle various disturbances effectively.
Proposed Huber IV and GMM estimation approaches.
Established consistency and asymptotic distributions of estimators.
Conducted simulation studies comparing robustness to traditional estimators.
Applied methods to assess the urban heat island effect on housing prices.
Huber estimators show increased robustness against long-tailed disturbances.
Minor efficiency loss observed for short-tailed disturbances.
Huber GMM estimator outperforms existing robust estimators in literature.
Provided a GitHub package for practical application.

Abstract

This article proposes and studies two Huber-type estimation approaches, namely, the Huber instrumental variable (IV) estimation and the Huber generalized method of moments (GMM) estimation, for a spatial autoregressive model. We establish the consistency, asymptotic distributions, finite sample breakdown points, and influence functions of these estimators. Simulation studies show that compared to the corresponding traditional estimators (the two-stage least squares estimator, the best IV estimator, and the GMM estimator), our estimators are more robust when the unknown disturbances are long-tailed, and our estimators only lose a little efficiency when the disturbances are short-tailed. Moreover, the Huber GMM estimator also outperforms several robust estimators in the literature. Finally, we apply our estimation method to investigate the impact of the urban heat island effect on housing prices. A package is published on GitHub for practitioners to use in their empirical studies.

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