Beyond the Average: Distributional Causal Inference under Imperfect Compliance

2025-09-19

AI Summary

This paper addresses the challenge of incomplete compliance in randomized experiments by identifying and estimating the Local Average Distributional Treatment Effect (LATE-D)—the difference in outcome distributions between treatment and control groups among compliers. We propose a regression-adjusted estimator grounded in distributional regression and Neyman-orthogonal moment conditions, using the treatment assignment as an instrumental variable. The method accommodates continuous, discrete, and mixed-type outcomes, exhibits double robustness, adapts to high-dimensional covariates, and applies to stratified block, simple random, and other randomization designs. We establish its semiparametric efficiency, derive its asymptotic normal distribution, and demonstrate strong finite-sample performance in simulations. Empirical validation using the Oregon Health Insurance Experiment confirms its practical efficacy.

Technology Category

• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We study the estimation of distributional treatment effects in randomized experiments with imperfect compliance. When participants do not adhere to their assigned treatments, we leverage treatment assignment as an instrumental variable to identify the local distributional treatment effect-the difference in outcome distributions between treatment and control groups for the subpopulation of compliers. We propose a regression-adjusted estimator based on a distribution regression framework with Neyman-orthogonal moment conditions, enabling robustness and flexibility with high-dimensional covariates. Our approach accommodates continuous, discrete, and mixed discrete-continuous outcomes, and applies under a broad class of covariate-adaptive randomization schemes, including stratified block designs and simple random sampling. We derive the estimator's asymptotic distribution and show that it achieves the semiparametric efficiency bound. Simulation results demonstrate favorable finite-sample performance, and we demonstrate the method's practical relevance in an application to the Oregon Health Insurance Experiment.

Problem

• Estimating distributional treatment effects under imperfect compliance
• Leveraging instrumental variables for local distributional effects
• Developing robust estimators for various outcome types

Innovation

• Instrumental variable for distributional treatment effects
• Neyman-orthogonal regression-adjusted estimator
• Semiparametric efficient under covariate-adaptive randomization