Nonparametric Point Identification of Treatment Effect Distributions via Rank Stickiness

2026-04-23

AI Summary

This study addresses the challenge of estimating the full distribution of treatment effects, which is generally unidentifiable due to the non-observability of the joint distribution of potential outcomes. Existing approaches rely on strong assumptions or yield only wide partial identification bounds. The authors propose a novel scalar parameter, “rank stickiness,” that enables nonparametric point identification even in the presence of rank violations. By maximizing average rank correlation under a relative entropy constraint, they construct a unique Bregman–Sinkhorn copula that fully determines the joint distribution, subsuming comonotonic and Gaussian copulas as special cases and permitting closed-form expressions for conditional moments and the probability of rank violations. Integrating exponential tilting via Bregman divergences, entropy-regularized optimal transport, and nonparametric inference, this framework delivers the first point estimator for the entire treatment effect distribution. The resulting estimator of the average treatment effect achieves a variance strictly smaller than the Fréchet–Hoeffding and Neyman bounds, and the empirical copula attains a √n convergence rate in an infinite-dimensional function space.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Treatment effect distributions are not identified without restrictions on the joint distribution of potential outcomes. Existing approaches either impose rank preservation -- a strong assumption -- or derive partial identification bounds that are often wide. We show that a single scalar parameter, rank stickiness, suffices for nonparametric point identification while permitting rank violations. The identified joint distribution -- the coupling that maximizes average rank correlation subject to a relative entropy constraint, which we call the Bregman-Sinkhorn copula -- is uniquely determined by the marginals and rank stickiness. Its conditional distribution is an exponential tilt of the marginal with a Bregman divergence as the exponent, yielding closed-form conditional moments and rank violation probabilities; the copula nests the comonotonic and Gaussian copulas as special cases. The empirical Bregman-Sinkhorn copula converges at the parametric $\sqrt{n}$-rate with a Gaussian process limit, despite the infinite-dimensional parameter space. We apply the framework to estimate the full treatment effect distribution, derive a variance estimator for the average treatment effect tighter than the Fréchet--Hoeffding and Neyman bounds, and extend to observational studies under unconfoundedness.

Problem

• treatment effect distribution
• nonparametric identification
• rank stickiness
• copula
• potential outcomes

Innovation

• rank stickiness
• Bregman-Sinkhorn copula
• nonparametric point identification
• treatment effect distribution
• relative entropy constraint