Nonparametric Point Identification of Treatment Effect Distributions via Rank Stickiness

Tengyuan Liang

Papers from arXiv.org

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 Fr\'{e}chet--Hoeffding and Neyman bounds, and extend to observational studies under unconfoundedness.

Date: 2026-04
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2604.21548 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2604.21548

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().