Learning control variables and instruments for causal analysis in observational data

TL;DR

This paper presents a machine learning-based method to identify control variables and instruments for causal inference in observational data, ensuring valid causal effect estimation.

Contribution

It introduces a data-driven approach to detect and partition instruments and control variables, with proven consistency and demonstrated effectiveness.

Findings

Method successfully detects valid instruments and controls in simulations.

Empirical application to Oregon Health Insurance data illustrates practical utility.

Finite sample performance aligns with theoretical consistency results.

Abstract

This study introduces a data-driven, machine learning-based method to detect suitable control variables and instruments for assessing the causal effect of a treatment on an outcome in observational data. Our approach tests the joint existence of instruments, which are associated with the treatment but not directly with the outcome (at least conditional on observables), and suitable control variables, conditional on which the treatment is exogenous, and learns the partition of instruments and control variables from the observed data. The detection of sets of instruments and control variables relies on the condition that proper instruments are conditionally independent of the outcome given the treatment and suitable control variables. We establish the consistency of our method for detecting control variables and instruments under certain regularity conditions, investigate the finite sample performance through a simulation study, and provide an empirical application to health data from the Oregon Health Insurance Experiment.