Alternative GMM estimators for spatial regression models

Jörg Breitung () and Christoph Wigger

Spatial Economic Analysis, 2018, vol. 13, issue 2, 148-170

Abstract: Using approximations of the score of the log-likelihood function, we derive moment conditions for estimating spatial regression models, starting with the spatial error model. Our approach results in computationally simple and robust estimators, such as a new moment estimator derived from the first-order approximation obtained by solving a quadratic moment equation, and performs similarly to existing generalized method of moments (GMM) estimators. Our estimator based on the second-order approximation resembles the GMM estimator proposed by Kelejian and Prucha in 1999. Hence, we provide an intuitive interpretation of their estimator. Additionally, we provide a convenient framework for computing the weighting matrix of the optimal GMM estimator. Heteroskedasticity robust versions of our estimators are also proposed. Furthermore, a first-order approximation for the spatial autoregressive model is considered, resulting in a computationally simple method of moment estimator. The performance of the considered estimators is compared in a Monte Carlo study.

Date: 2018
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Working Paper: Alternative GMM estimators for spatial regression models (2017)
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DOI: 10.1080/17421772.2018.1403644

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