Addressing Endogeneity Issues in a Spatial Autoregressive Model using Copulas

Yanli Lin, Yichun Song   Published : October 2025   JEL Code: C31, C51   URL to this Article: https://doi.org/10.1016/j.jeconom.2025.106106

Abstract

This paper develops a novel, instrument-free semiparametric copula framework for a spatiaautoregressive (SAR) model to address endogeneity arising from an endogenous spatial weightsmatrix, endogenous regressors, or both, Moving beyond conventional Gaussian copulas, wedevelop a flexible estimator based on the Student's t copula with an unknown degrees-offreedom (df) parameter, which nests the Gaussian case and allows the data to determinethe presence of tail dependence. We propose a sieve maximum likelihood estimator (SMLE)that jointly estimates all structural, copula, and nonparametric marginal parameters, andestablish that this joint estimator is consistent, asymptotically normal, and - unlike prevailingmulti-stage copula-correction methods - semiparametrically efficient, Monte Carlo simulationshighlight the flexibility of our approach, showing that copula misspecification inflates bias andvariance, whereas joint estimation improves efficiency, In an empirical application to regionaproductivity spillovers, we find evidence of tail dependence and demonstrate that our methocoffers a credible alternative to approaches that rely on hard-to-verify excluded instruments.

Keywords

Spatial autoregressive model; Endogenous spatial weights matrix; Endogenous regressors; Copula method; Sieve maximum likelihood estimation