Difference-in-differences Estimator of Quantile Treatment Effect on the Treated

Abstract

We propose a new difference-in-differences (DID) estimator of the quantile treatment effect on the treated (QTT). The model assumes a common time effect on the cumulative distribution functions of untreated potential outcomes, allowing for covariates. This condition holds if and only if the net change in the untreated outcome densities is common across treated and control groups. Unlike the Changes-in-Changes model proposed by Athey and Imbens (2006), our model is compatible with the usual DID assumption for means, and it provides a computationally simple and straightforward way to control for covariates. We establish uniform consistency and weak convergence of the proposed estimator of QTT and the related functions. The estimators and the simultaneous confidence bands remain valid even for discrete outcome variables. As an empirical application, the distributional impact of the earned income tax credit on birth weight is investigated. We provide a STATA ado file package.