Regression Discontinuity Design with Distribution-Valued Outcomes
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915229488644096 |
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| author | Van Dijcke, David |
| author_facet | Van Dijcke, David |
| contents | 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 Fréchet 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regression Discontinuity Design with Distribution-Valued Outcomes Van Dijcke, David Econometrics Machine Learning Statistics Theory Applications Methodology 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 Fréchet 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. |
| title | Regression Discontinuity Design with Distribution-Valued Outcomes |
| topic | Econometrics Machine Learning Statistics Theory Applications Methodology |
| url | https://arxiv.org/abs/2504.03992 |