Distributional Discontinuity Design

2026-02-22

AI Summary

This study addresses a key limitation of traditional regression discontinuity and kink designs, which focus solely on average treatment effects while ignoring how policies reshape the entire outcome distribution. The authors propose a novel distributional framework that introduces the Wasserstein distance into causal inference to quantify discrepancies between conditional distributions at the treatment threshold. By leveraging an L-moments-based orthogonal decomposition, the method disentangles changes in distributional features—such as location, scale, and skewness—to uncover sources of treatment effect heterogeneity. In the fuzzy kink setting, this approach yields new identification results. Empirical applications to two real-world natural experiments demonstrate that distributional effects can differ markedly from conventional average effects, underscoring the method’s explanatory power and practical relevance.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Regression discontinuity and kink designs are typically analyzed through mean effects, even when treatment changes the shape of the entire outcome distribution. To address this, we introduce distributional discontinuity designs, a framework for estimating causal effects for a scalar outcome at the boundary of a discontinuity in treatment assignment. Our estimand is the Wasserstein distance between limiting conditional outcome distributions; a single scale-interpretable measure of distribution shift. We show that this weakly bounds the average treatment effect, where equality holds if and only if the treatment effect is purely additive; thus, departure from equality measures effect heterogeneity. To further encode effect heterogeneity we show that the Wasserstein distance admits an orthogonal decomposition into squared differences in $L$-moments, thereby quantifying the contribution from location, scale, skewness, and higher-order shape components to the overall distributional distance. Next, we extend this framework to distributional kink designs by evaluating the Wasserstein derivative at a policy kink; this describes the flow of probability mass through the kink. In the case of fuzzy kink designs, we derive new identification results. Finally, we apply our methods on real data by re-analyzing two natural experiments to compare our distributional effects to traditional causal estimands.

Problem

• regression discontinuity design
• distributional effects
• Wasserstein distance
• treatment effect heterogeneity
• kink design

Innovation

• distributional discontinuity design
• Wasserstein distance
• L-moments
• effect heterogeneity
• distributional kink design