Distributional Difference-in-Differences Models with Multiple Time Periods

TL;DR

This paper introduces a new method to estimate the entire distribution of untreated outcomes in policy impact studies with multiple time periods, extending existing quantile treatment effect techniques and analyzing their finite-sample properties.

Contribution

It generalizes the QTT estimator for distributional impact analysis in staggered adoption settings and explores alternative distribution summaries without rank invariance assumptions.

Findings

Estimator performs better with larger samples.

Slight bias observed in small samples.

Method effectively recovers distributional impacts.

Abstract

Researchers are often interested in evaluating the impact of a policy on the entire (or specific parts of the) distribution of the outcome of interest. In this paper, I provide a method to recover the whole distribution of the untreated potential outcome for the treated group in non-experimental settings with staggered treatment adoption by generalizing the existing quantile treatment effects on the treated (QTT) estimator proposed by Callaway and Li (2019). Besides the QTT, I consider different approaches that anonymously summarize the quantiles of the distribution of the outcome of interest (such as tests for stochastic dominance rankings) without relying on rank invariance assumptions. The finite-sample properties of the estimator proposed are analyzed via different Monte Carlo simulations. Despite being slightly biased for relatively small sample sizes, the proposed method's performance increases substantially when the sample size increases.