Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing

TL;DR

This paper introduces a new method to estimate and test for distributional treatment effects conditioned on covariates, capturing impacts beyond average effects, with robust estimation and valid testing guarantees.

Contribution

It proposes a novel estimand for conditional distributional effects, a doubly robust estimator, and a valid, efficient test for distributional homogeneity in treatment effects.

Findings

Estimator is minimax optimal in local asymptotics.

Developed a valid, consistent test for distributional differences.

Provided closed-form expressions and an efficient algorithm for the test.

Abstract

Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives -- the first test, to our knowledge, with such guarantees in this setting. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.