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.

翻译：回归不连续性与拐点设计通常通过均值效应进行分析，即使处理改变了整个结果分布的形状。为解决此问题，我们提出了分布不连续性设计框架，用于在处置分配不连续的边界处估计标量结果的因果效应。我们的估计量是极限条件结果分布之间的Wasserstein距离——一种具有单一尺度可解释性的分布偏移度量。我们证明该距离弱约束了平均处理效应，当且仅当处理效应为纯可加性时等式成立；因此，对等式的偏离程度可度量效应异质性。为进一步刻画效应异质性，我们证明Wasserstein距离可正交分解为$L$-矩的平方差，从而量化位置、尺度、偏度及高阶形状分量对总体分布距离的贡献。随后，我们通过计算政策拐点处的Wasserstein导数将此框架扩展至分布拐点设计，这描述了概率质量通过拐点的流动特性。针对模糊拐点设计，我们推导出新的识别结果。最后，我们通过重新分析两项自然实验将所提方法应用于实际数据，以比较分布效应与传统因果估计量。