A simple distributional difference-in-differences estimator for univariate and bivariate outcomes
Abstract
We provide a simple distribution regression estimator for treatment effects in the difference-in-differences (DiD) design. Our procedure is particularly useful when the treatment effect differs across the distribution of the outcome variable. Our proposed estimator easily incorporates covariates and, importantly, can be extended to settings where the treatment potentially affects the joint distribution of multiple outcomes. Our key identifying restriction is that the untreated outcome distribution does not exhibit an interaction effect of group and time. This assumption results in a parallel trend assumption on a transformation of the distribution. We highlight the relationship between our procedure and assumptions with the changes-in-changes approach of Athey and Imbens (2006). We also reexamine the Card and Krueger (1994) study of the impact of minimum wages on employment to illustrate the utility of our approach.
Cite
@article{arxiv.2409.02311,
title = {A simple distributional difference-in-differences estimator for univariate and bivariate outcomes},
author = {Iván Fernández-Val and Jonas Meier and Aico van Vuuren and Francis Vella},
journal= {arXiv preprint arXiv:2409.02311},
year = {2026}
}
Comments
43 pages, 3 figures, 4 tables; new section on asymptotic theory with respect to previous version