Distributional Discontinuity Design

Thomas M. Menino Convention & Exhibition Center 

We introduce distributional discontinuity design, a framework for studying distributional causal effects for a scalar outcome at the boundary of a discontinuity in treatment assignment (a generalization of the regression discontinuity design). Our causal estimand is the Wasserstein distance between limiting conditional outcome distributions above and below the treatment discontinuity; 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. Moreover, we show that the Wasserstein distance can be decomposed into squared differences in L-moments, thereby quantifying the contribution from location, scale, skewness, etc. to the overall distributional distance. This decomposition provides a novel way of encoding the heterogeneity in the treatment effect. Next, we extend this framework to distributional kink designs by evaluating the Wasserstein derivative at a deterministic policy kink; this describes the flow of probability mass through the kink. In both settings, we allow the treatment assignment to be either sharp or fuzzy. Notably, we derive

Regression Discontinuity Design

Regression Kink Design

Optimal Transport



Wasserstein Distance

Quantile Treatment Effects 

IMS