On Quantile Treatment Effects, Rank Similarity, and Multiple IVs

Abstract
This paper investigates how certain relationship between observed and counterfactual distributions plays a role in the identification of distributional treatment effects under endogeneity, and shows that this relationship holds in a range of nonparametric models for treatment effects and can be tested with the data. To motivate the new identifying assumption, we first provide a novel way of characterizing popular assumptions restricting treatment heterogeneity in the literature, specifically rank similarity assumptions. We show the stringency of this type of assumptions and propose to relax them in economically meaningful ways. This relaxation will justify certain parameters (e.g., treatment effects on the treated) against others (e.g., treatment effects for the entire population). It will also justify the quest of richer exogenous variation in the data (e.g., the use of multiple instrumental variables). The prime goal of this investigation is to provide empirical researchers with tools for identifying and estimating treatment effects that are flexible enough to allow for treatment heterogeneity, but that still yield tight policy evaluation and are easy to implement.