Bayesian Model Averaging in Causal Instrumental Variable Models

2025-04-18

AI Summary

In causal inference, selecting valid instrumental variables (IVs) remains challenging, and estimation is often hampered by model uncertainty. This paper proposes gIVBMA, a structural equation modeling–based approach that applies Bayesian model averaging (BMA) over multiple combinations of candidate IVs and covariates to yield robust causal effect estimates. Its key contributions are: (1) introducing the first scale-invariant prior to ensure parameter comparability across models; (2) accommodating non-Gaussian treatment and outcome variables; (3) permitting flexible role interchange between IVs and covariates; and (4) establishing theoretical model selection consistency. Extensive simulations demonstrate substantial improvements over state-of-the-art methods. Empirical applications—assessing the causal effects of malaria/institutions on per capita income and estimating returns to education—yield robust, interpretable results. An open-source Julia implementation is publicly available.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. Our approach extends previous work through a scale-invariant prior structure and accommodates non-Gaussian outcomes and treatments, offering greater flexibility than existing methods. The computational strategy uses conditional Bayes factors to update models separately for the outcome and treatments. We prove that this model selection procedure is consistent. By explicitly accounting for model uncertainty, gIVBMA allows instruments and covariates to switch roles and provides robustness against invalid instruments. In simulation experiments, gIVBMA outperforms current state-of-the-art methods. We demonstrate its usefulness in two empirical applications: the effects of malaria and institutions on income per capita and the returns to schooling. A software implementation of gIVBMA is available in Julia.

Problem

• Addresses instrument selection in causal IV models
• Handles model uncertainty with Bayesian averaging
• Accommodates non-Gaussian outcomes and treatments

Innovation

• Bayesian model averaging for instrumental variables
• Scale-invariant prior structure for flexibility
• Conditional Bayes factors for model updating