Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors

TL;DR

This paper introduces a Bayesian model averaging approach for two-stage regression with endogeneity, using conditional Bayes factors within a Gibbs sampler to handle model uncertainty efficiently.

Contribution

It extends existing Gibbs sampling methods to incorporate model uncertainty in instrumental variable regression using conditional Bayes factors.

Findings

Efficient Gibbs sampler with model averaging for endogeneity problems

Application to macroeconomic growth determinants

Estimation of demand functions with instrumental variables

Abstract

We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct evaluation of model probabilities is intractable in this setting. We show that by nesting model moves inside the Gibbs sampler, model comparison can be performed via conditional Bayes factors, leading to straightforward calculations. This new Gibbs sampler is only slightly more involved than the original algorithm and exhibits no evidence of mixing difficulties. We conclude with a study of two different modeling challenges: incorporating uncertainty into the determinants of macroeconomic growth, and estimating a demand function by instrumenting wholesale on retail prices.