# Quantile Treatment Effects in Difference in Differences Models under Dependence Restrictions and with only Two Time Periods

## TL;DR

This paper develops a method to identify and estimate quantile treatment effects in difference-in-differences models with only two periods under dependence restrictions, using bootstrap inference, and applies it to minimum wage effects.

## Contribution

It introduces a novel identification strategy for quantile treatment effects under dependence assumptions with two periods and discrete covariates, along with a bootstrap inference procedure.

## Key findings

- Successfully estimates the impact of minimum wage changes on earnings distribution.
- Validates the bootstrap inference method through theoretical proofs.
- Provides new tools for quantile treatment effect analysis in limited data settings.

## Abstract

This paper shows that the Conditional Quantile Treatment Effect on the Treated can be identified using a combination of (i) a conditional Distributional Difference in Differences assumption and (ii) an assumption on the conditional dependence between the change in untreated potential outcomes and the initial level of untreated potential outcomes for the treated group. The second assumption recovers the unknown dependence from the observed dependence for the untreated group. We also consider estimation and inference in the case where all of the covariates are discrete. We propose a uniform inference procedure based on the exchangeable bootstrap and show its validity. We conclude the paper by estimating the effect of state-level changes in the minimum wage on the distribution of earnings for subgroups defined by race, gender, and education.