Orthogonal Integrated Conditional Moment Tests for Treatment Effect Heterogeneity

2026-07-14

AI Summary

This study investigates whether treatment effects exhibit heterogeneity across subpopulations defined by covariates. Under the unconfoundedness assumption, the null hypothesis of no heterogeneity is reformulated as a conditional moment restriction based on Neyman-orthogonal scores. A test statistic expressed as a continuous functional is constructed and inference is carried out via marked empirical processes. By leveraging Neyman orthogonality, the procedure mitigates first-order sensitivity to estimation errors in nuisance parameters, achieving nontrivial power against local alternatives converging at the $n^{-1/2}$ rate. The framework naturally extends to settings with endogenous treatments and instrumental variables. Theoretically, the paper establishes the asymptotic behavior of the test statistic under both the null and various alternative hypotheses. Practically, it proposes an easily implementable inference procedure based on the multiplier bootstrap and demonstrates its utility by examining whether the effect of maternal smoking during pregnancy on infant birth weight varies with mother’s age.

Abstract

We propose a nonparametric integrated conditional moment (ICM) test for treatment effect heterogeneity across subpopulations defined by a given covariate subvector. Under unconfoundedness, the null is recast as a conditional moment restriction based on a Neyman-orthogonal score, which reduces the first-order sensitivity of the empirical process to nuisance parameter estimation. The test statistics are constructed as continuous functionals of a marked empirical process. We establish a uniform feasible-to-oracle approximation and derive the asymptotic properties of these test statistics under the null and fixed alternatives. We further show that the test has nontrivial power against local alternatives converging to the null at the $n^{-1/2}$ rate, and develop an easy-to-implement multiplier bootstrap for feasible inference. We also develop extensions to tests of parametric CATE specifications and to settings with endogenous treatment and a binary instrument. Finally, we apply the proposed testing approach to study whether the effect of maternal smoking during pregnancy on infant birth weight varies with maternal age.

Problem

• treatment effect heterogeneity
• conditional moment test
• nonparametric test
• causal inference
• subpopulation analysis

Innovation

• Neyman-orthogonal score
• integrated conditional moment test
• treatment effect heterogeneity
• multiplier bootstrap
• conditional average treatment effect