Addressing endogeneity issues in a spatial autoregressive model using copulas

This paper develops a novel, instrument-free semiparametric copula framework for a spatial autoregressive (SAR) model to address endogeneity arising from an endogenous spatial weights matrix, endogenous regressors, or both. Moving beyond conventional Gaussian copulas, we develop a flexible estimator based on the Student’s copula with an unknown degrees-of freedom (df) parameter, which nests the Gaussian case and allows the data to determine the presence of tail dependence. We propose a sieve maximum likelihood estimator (SMLE) that jointly estimates all structural, copula, and nonparametric marginal parameters, and establish that this joint estimator is consistent, asymptotically normal, and – unlike prevailing multi-stage copula-correction methods – semiparametrically efficient. Monte Carlo simulations highlight the flexibility of our approach, showing that copula misspecification inflates bias and variance, whereas joint estimation improves efficiency. In an empirical application to regional<br/>productivity spillovers, we find evidence of tail dependence and demonstrate that our method offers a credible alternative to approaches that rely on hard-to-verify excluded instruments.