A simple distributional difference-in-differences estimator for univariate and bivariate outcomes

TL;DR

This paper introduces a simple distribution regression estimator for treatment effects in difference-in-differences designs, capable of handling distributional heterogeneity and multiple outcomes, under a key parallel trend assumption.

Contribution

It proposes a novel, easy-to-implement distributional DiD estimator that extends to multivariate outcomes and incorporates covariates, linking to the changes-in-changes framework.

Findings

The estimator effectively captures distributional treatment effects.

Application to minimum wage study demonstrates practical utility.

The approach generalizes existing DiD methods to joint outcome distributions.

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.