Two-Stage Bayesian Model Averaging in Endogenous Variable Models

TL;DR

This paper introduces a Two-Stage Bayesian Model Averaging method for endogenous variable models, improving model selection, instrument validity testing, and coefficient estimation in economic analyses with endogeneity.

Contribution

It extends the 2SLS estimator with a Bayesian framework, incorporating model uncertainty and providing Bayesian tests for instrument validity.

Findings

2SBMA effectively recovers model structure and improves coefficient estimates.

The Bayesian Sargan test has higher power in detecting exogeneity violations.

Application to development accounting supports multiple determinants after addressing endogeneity.

Abstract

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed.