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

Abstract

This study proposes a Bayesian approach for exact finite-sample inference of an instrument-free estimation method that builds upon joint estimation using copulas to deal with endogenous covariates. Although copula approaches with applications to handle regressor-endogeneity have been frequently used, extant studies base inference on a frequentist basis, build on a-priori computed estimates of marginal distributions of explanatory variables, and use bootstrapping to obtain standard errors. Furthermore, empirical identification checks are hardly possible so far. Unlike frequentist models, the proposed Bayesian approach facilitates exact statistical inference (e.g., credible intervals) through computationally efficient Markov chain Monte Carlo simulation techniques and does neither require asymptotics nor tuning. The approach is one-step, in which neither marginal distributions nor between-regressor correlations are considered fixed, nor do they have to be estimated a-priori; regression coefficients, variance of structural errors, copula correlation matrix, and probability masses formalising marginal distributions of explanatory variables are considered random and sampled simultaneously. Simulation experiments assess the finite sample performance of the proposed estimator and demonstrate exactness of Bayesian inference. As a particular merit, we show that model (non)identification can be checked by assessing convergence of Markov chains and testing based on posterior draws, which offers valuable diagnostic tools in empirical applications. Practical applicability is demonstrated via an empirical example.

Keywords: Bayesian inference, Markov chain Monte Carlo, endogeneity, copula function

JEL Classification: C11, C14, C21, C51, C61, M31