Optimal Instrument Selection using Bayesian Model Averaging for Model Implied Instrumental Variable Two Stage Least Squares Estimators

TL;DR

This paper introduces MIIV-2SBMA, a Bayesian model averaging extension for MIIV-2SLS, enhancing detection of problematic and weak instruments with improved specificity and comparable estimation performance.

Contribution

The paper proposes MIIV-2SBMA, a novel Bayesian extension that improves instrument-specific tests for model misspecification and weak instruments in latent variable models.

Findings

MIIV-2SBMA performs comparably to MIIV-2SLS in parameter estimation.

Instrument-specific tests within MIIV-2SBMA have increased power to detect problematic instruments.

Empirical example demonstrates practical application of MIIV-2SBMA.

Abstract

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, non-iterative estimator for latent variable models. Associated with this estimator are equation specific tests of model misspecification. One issue with equation specific tests is that they lack specificity, in that they indicate that some instruments are problematic without revealing which specific ones. Instruments that are poor predictors of their target variables (weak instruments) is a second potential problem. We propose a novel extension to detect instrument specific tests of misspecification and weak instruments. We term this the Model-Implied Instrumental Variable Two-Stage Bayesian Model Averaging (MIIV-2SBMA) estimator. We evaluate the performance of MIIV-2SBMA against MIIV-2SLS in a simulation study and show that it has comparable performance in terms of parameter estimation. Additionally, our instrument specific overidentification tests developed within the MIIV-2SBMA framework show increased power to detect specific problematic and weak instruments. Finally, we demonstrate MIIV-2SBMA using an empirical example.