Partial identification of distributional and quantile treatment effects in difference-in-differences models

In this paper, we supplement the identification results for the mean treatment effect for the treated in the difference-in-differences framework studied by Abadie (2005) by establishing partial identification results for the distribution and quantile of the counterfactual outcome and of the treatment effect for the treated. Unlike the mean treatment effect which is identifiable from either the panel or the repeated cross sectional data, we show that the distribution/quantile of either the counterfactual outcome or of the treatment effect is only partially identified and in general the identified interval is tighter with panel than with the repeated cross sectional data. We further illustrate this gain from the panel via a numerical example.