Bayesian Inference for Joint Estimation Models Using Copulas to Handle Endogenous Regressors

ABSTRACT This study proposes a Bayesian approach for finite‐sample inference of the Gaussian copula endogeneity correction. Extant studies use frequentist inference, build on a priori computed estimates of marginal distributions of explanatory variables, and use bootstrapping to obtain standard errors. The proposed Bayesian approach facilitates precise statistical inference through Markov chain Monte Carlo simulation techniques and requires neither asymptotics nor tuning. It is one‐step, where regression coefficients, error variance, copula correlations, and probability masses of marginals are treated as random and sampled jointly, rather than fixed or pre‐estimated. Simulation experiments illustrate finite‐sample performance, complemented by an empirical application.