Data Science and Statistics Seminar: "Regression Under Endogeneity: Bernstein-von Mises Theory and Bayes Factors Testing"

Abstract: We develop a semiparametric Bayesian analysis of linear regression with possibly endogenous regressors. To avoid the risk of distributional misspecification, the prior-posterior analysis is based solely on moment restrictions, and the associated exponentially tilted empirical likelihood. We study the consequences of neglected endogeneity and derive a Berstenin-von Mises (BvM) theorem for the posterior distribution of a (default) base model that assumes that the treatment variables are exogenous when that assumption, in fact, is false. Due to the negative consequences of neglected endogeneity, we develop a Bayes factor test for endogeneity that compares the base model with an extended model that is immune from the problem of neglected endogeneity. We prove that this test is a consistent selection procedure: as the sample becomes large, it almost surely selects the base model if the treatments are exogenous, and the extended model if the treatments are endogenous. The theory is illustrated with simulated data, and problems concerning the causal effect of education on wages, financial asset pricing with potentially endogenous risk factors, and the causal effect of (potentially endogenous) airplane ticket prices on passenger volume.

Host: Debashis Mondal