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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 practical toolkit to recover the whole counterfactual 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.
Andrea Ciaccio (Fri,) studied this question.