arXiv 4 Apr 2025 · Econometrics
arXiv:2504.03992 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| frandsen2012quantile | unmatched citation key frandsen2012quantile | 1.000 | 11 | 7 | 100% |
| hahn2001identification | unmatched citation key hahn2001identification | 1.000 | 6 | 5 | 100% |
| qu2019uniform | unmatched citation key qu2019uniform | 0.956 | 8 | 5 | 88% |
| qu2024inference | unmatched citation key qu2024inference | 0.928 | 5 | 3 | 80% |
| calonico2014robust | unmatched citation key calonico2014robust | 0.855 | 8 | 7 | 62% |
| chernozhukov2010quantile | unmatched citation key chernozhukov2010quantile | 0.843 | 3 | 3 | 100% |
| chiang2019causal | unmatched citation key chiang2019causal | 0.843 | 3 | 3 | 100% |
| petersen2019frechet | unmatched citation key petersen2019frechet | 0.822 | 9 | 5 | 56% |
| chiang2019robust | unmatched citation key chiang2019robust | 0.737 | 20 | 6 | 40% |
| fan1996local | unmatched citation key fan1996local | 0.737 | 4 | 3 | 50% |
Showing the top 10 of 94 scored citations. 10 of these could not be matched to a bibliography entry, so only the citation key is shown.