Hoderlein, Stefan, and Yuya Sasaki. “Outcome Conditioned Treatment Effects”. Boston College Working Papers in Economics 840, 2013.
This paper introduces average treatment effects conditional on the outcome variable in an endogenous setup where outcome Y, treatment X and instrument Z are continuous. These objects allow to refine well studied treatment effects like ATE and ATT in the case of continuous treatment (see Florens et al (2008)), by breaking them up according to the rank of the outcome distribution. For instance, in the returns to schooling case, the outcome conditioned average treatment effect on the treated (ATTO), gives the average effect of a small increase in schooling on the subpopulation characterized by a certain treatment intensity, say 16 years of schooling, and a certain rank in the wage distribution. We show that IV type approaches are better suited to identify overall averages across the population like the average partial effect, or outcome conditioned versions thereof, while selection type methods are better suited to identify ATT or ATTO. Importantly, none of the identification relies on rectangular support of the errors in the identification equation. Finally, we apply all concepts to analyze the nonlinear heterogeneous effects of smoking during pregnancy on infant birth weight.