Working Paper

Testing for Endogeneity: A Moment-Based Bayesian Approach

Abstract: A standard assumption in the Bayesian estimation of linear regression models is that the regressors are exogenous in the sense that they are uncorrelated with the model error term. In practice, however, this assumption can be invalid. In this paper, under the rubric of the exponentially tilted empirical likelihood, we develop a Bayes factor test for endogeneity that compares a base model that is correctly specified under exogeneity but misspecified under endogeneity against an extended model that is correctly specified in either case. We provide a comprehensive study of the log-marginal exponentially tilted empirical likelihood. We demonstrate that our testing procedure is consistent from a frequentist point of view: as the sample becomes large, it almost surely selects the base model if and only if the regressors are exogenous, and the extended model if and only if the regressors are endogenous. The methods are illustrated with simulated data, and problems concerning the causal effect of automobile prices on automobile demand and the causal effect of potentially endogenous airplane ticket prices on passenger volume

Keywords: Bayesian inference; Causal inference; Exponentially tilted empirical likelihood; Endogeneity; Exogeneity; Instrumental variables; Marginal likelihood; Posterior consistency;

https://doi.org/10.21799/frbp.wp.2024.19

Bibliographic Information

Provider: Federal Reserve Bank of Philadelphia

Part of Series: Working Papers

Publication Date: 2024-11-25

Number: 24-19