Addressing Endogeneity Issues in a Spatial Autoregressive Model using Copulas

This paper develops a new, instrument-free semi-parametric copula framework for a spatial autoregressive (SAR) model to address endogeneity stemming 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 t copula with an unknown degrees-of-freedom (df) parameter, which nests the Gaussian case and allows the data to reveal the presence of tail dependence. We propose a sieve maximum likelihood estimator (MLE) that jointly estimates all structural, copula, and non-parametric 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 underscore the flexibility of our approach, showing that copula misspecification inflates bias and variance, whereas joint estimation improves efficiency. In an empirical application to regional 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