Causal Inference with the Instrumental Variable Approach and Bayesian Nonparametric Machine Learning

TL;DR

This paper introduces a flexible Bayesian nonparametric framework for causal inference using instrumental variables, leveraging machine learning techniques like BART and Dirichlet Process mixtures to handle nonlinearities effectively.

Contribution

It proposes a novel Bayesian nonparametric approach for instrumental variable analysis that accommodates nonlinear effects without manual tuning.

Findings

Performs well with linear effects, with minimal loss.

Significantly improves inference in nonlinear settings.

Demonstrates effectiveness on simulated and real data.

Abstract

We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine learning via Bayesian Additive Regression Trees (BART). Error terms and their distribution are inferred using Dirichlet Process mixtures. Simulated and real examples show that when the true functions are linear, little is lost. But when nonlinearities are present, dramatic improvements are obtained with virtually no manual tuning.