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GMM Estimation of Spatial Autoregressive Models with Cluster Dependent Errors

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  • Takaki Sato

Abstract

This study considers the generalized method of moment (GMM) estimation of spatial autoregressive (SAR) models with unknown cluster correlations among error terms. In the presence of cluster correlations within errors, nonlinear moment conditions suitable for independent errors lose their validity and GMM estimators obtained from the moment condition are inconsistent. In this paper, we propose the GMM estimator obtained from another nonlinear moment condition suitable for cluster dependent error terms and show its asymptotic properties. Because the asymptotic variance of the GMM estimator depends on the choice of the weight matrix for GMM estimation, we also discuss the optimal weight which minimizes the asymptotic variance, and introduce the feasible optimal GMM estimator based on the consistent estimator of the weight. Monte Carlo experiments indicate that the proposed GMM estimator has a small bias and root mean squared errors when error terms in SAR models have cluster correlation compared to two stage least squares estimators and GMM estimators for independent errors.

Suggested Citation

  • Takaki Sato, 2022. "GMM Estimation of Spatial Autoregressive Models with Cluster Dependent Errors," DSSR Discussion Papers 131, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:dssraa:131
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    File URL: http://hdl.handle.net/10097/00135983
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