Regression Discontinuity Design with Distribution-Valued Outcomes

• URL: http://arxiv.org/abs/2504.03992v1
• Date: Fri, 04 Apr 2025 23:12:35 GMT
• Title: Regression Discontinuity Design with Distribution-Valued Outcomes
• Authors: David Van Dijcke,
• Abstract summary: This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D)<n>It extends the standard RDD framework to settings where the outcome is a distribution rather than a scalar.<n>I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

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