Causal Machine Learning for Moderation Effects

TL;DR

This paper introduces the balanced group average treatment effect (BGATE) to better interpret treatment heterogeneity by accounting for covariate distributions, using advanced machine learning estimation techniques.

Contribution

It proposes a new parameter, BGATE, and develops estimation methods based on double/debiased machine learning for causal analysis of subgroup effects.

Findings

BGATE effectively separates treatment effect differences from covariate distribution differences.

The proposed estimators are $\\sqrt{N}$-consistent and asymptotically normal.

Simulation and empirical results demonstrate the usefulness of BGATE in practice.

Abstract

It is valuable for any decision maker to know the impact of decisions (treatments) on average and for subgroups. The causal machine learning literature has recently provided tools for estimating group average treatment effects (GATE) to better describe treatment heterogeneity. This paper addresses the challenge of interpreting such differences in treatment effects between groups while accounting for variations in other covariates. We propose a new parameter, the balanced group average treatment effect (BGATE), which measures a GATE with a specific distribution of a priori-determined covariates. By taking the difference between two BGATEs, we can analyze heterogeneity more meaningfully than by comparing two GATEs, as we can separate the difference due to the different distributions of other variables and the difference due to the variable of interest. The main estimation strategy for this parameter is based on double/debiased machine learning for discrete treatments in an unconfoundedness setting, and the estimator is shown to be $\sqrt{N}$-consistent and asymptotically normal under standard conditions. We propose two additional estimation strategies: automatic debiased machine learning and a specific reweighting procedure. Last, we demonstrate the usefulness of these parameters in a small-scale simulation study and in an empirical example.