Estimating unconditional QTT under Conditional Copula Invariance

Develop an estimator for the unconditional quantile treatment effect on the treated (QTT) in staggered difference-in-differences settings when identification relies on Conditional Copula Invariance, so that the parameter can be estimated in practice without restricting attention to special covariate cases.

Background

The paper generalizes distributional difference-in-differences methods to settings with multiple periods and staggered treatment adoption, identifying counterfactual distributions using a Distributional Parallel Trends assumption and a Copula Invariance assumption. While the author provides estimators in several scenarios, a practical gap is noted when Conditional Copula Invariance is the basis for identification of the QTT.

In discussing concurrent work by Li and Lin (2024), the author points out that although identification may hold under Conditional Copula Invariance, the absence of an explicit estimator and unclear treatment of covariates leave open how to estimate the unconditional QTT in practice.