Quantile Treatment Effects in Difference-in-Discontinuities Designs
2026-09-05
This paper studies identification and doubly robust (DR) estimation of quantile treatment effects (QTEs) in difference-in-discontinuities (diff-in-disc) designs when a new treatment is introduced in the post period and a confounding discontinuous policy is present in both periods. We show that QTEs are point identified under a conditional stable-distributional-effect assumption for the confounding treatment, a restriction that is analogous to the distributional parallel trends assumption in the recent difference-in-differences literature. We then propose a DR estimator and inference procedure that remain valid when either the outcome regression or the propensity score model is correctly specified, while avoiding high-dimensional nonparametric adjustment for covariates in the local estimation setting. We establish asymptotic normality of the proposed estimator, and Monte Carlo simulations illustrate its double-robustness and good finite-sample performance. In an application to Italian municipal fiscal data (Grembi et al. 2016),, the estimates suggest that relaxing fiscal constraints increases deficits primarily over the lower and central portions of the distribution, shifting municipalities from surplus or near balance into moderate deficits—a distributional pattern not captured by mean effects.