Copula joint estimation for spatial dynamic panel data models with endogeneity issues

Abstract

Spatial dynamic panel data (SDPD) models often encounter endogeneity issues, especially when spatial weights depend on socioeconomic characteristics or when regressors – beyond the spatial lag, dynamic spatial lag, and dynamic time lag terms – are correlated with the error term. This study introduces a semiparametric copula-based endogeneity correction technique that avoids the need for excluded instruments or control-function-type model specifications. We develop a three-stage estimator that includes a nonparametric first stage, an OLS-based second stage, and a final stage using the generalized method of moments (GMM) estimation. The consistency and asymptotic normality of the third-stage GMM estimator are rigorously established through asymptotic inference under spatial-time near-epoch dependence (NED). Additionally, we propose a bias-corrected expression for the variance of this multi-stage estimator and a bootstrap procedure for a practical calculation. To assess the finite-sample performance of our approach, we conduct Monte Carlo simulations in different scenarios. In an empirical application, our endogeneity correction alters the estimated magnitude of spatial dependence and reveals that state-level cigarette consumption is influenced by neighbouring states’ behaviour, which underscores the economic relevance of our method in recovering credible effects.