Quantile Difference in Differences with Staggered Intervention:

This presentation examines Quantile Difference-in-Differences (QDiD) estimators under staggered treatment adoption. While mean DiD estimators are known to be biased due to “forbidden comparisons,” we show that similar contamination arises in quantile settings. Using simulations and theoretical results, we demonstrate how pooled TWFE quantile regressions mix treated cohorts and distort distributional effects. We propose a cohort-wise QDiD estimator that excludes already-treated units as controls, ensuring unbiased aggregation across cohorts. The estimator is consistent and asymptotically normal, providing a transparent and reliable framework for studying heterogeneous treatment effects across quantiles.