Differences-in-Differences on Distribution Functions for Program Evaluations

Development Economics X Paper Model Ten


We propose a novel method for estimating causal effects on distribution functions in modern difference-in-differences (DiD) settings with multiple time periods. In so doing, we extend the inverse probability weighting (IPW) and augmented inverse probability weighting (AIPW) estimators developed by Lin et al. (2023) to account for the time dimension and the staggered treatment adoption. We use propensity scores to weight the units by their inverse probability of receiving the treatment they actually received at each time point, and then compare the distribution functions of their outcomes before and after the treatment using the Wasserstein distance. We derive the asymptotic properties of our estimators under some additional assumptions, such as no interference between units over time, no anticipation effects, and no time-varying confounders. We also provide a method for constructing confidence intervals based on bootstrapping. Our method offers a flexible and robust way to quantify the causal effects on distribution functions in DiD settings with multiple time periods.

Opoku-Agyemang, Kweku (2023). "Differences-in-Differences on Distribution Functions." Development Economics Paper Model Ten. 

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