SHARP BOUNDS ON TREATMENT EFFECTS IN A BINARY TRIANGULAR SYSTEM

This paper considers the evaluation of the average treatment effect (ATE) in a triangular system with binary dependent variables. I impose a threshold crossing model on both endogenous regressor and the outcome. No parametric functional form or distributional assumptions are imposed. Shaikh and Vytlacil (2011, SV) proposed bounds on ATE which are sharp only under a restrictive condition on the support of the covariates and the instruments, which rules out a wide range of models and many relevant applications. In some cases, when SV's support condition fails, their bounds retrieve the same empirical content as the model with unrestricted endogenous regressor. In this setting, I provide a methodology which allows to construct sharp bounds on the ATE by efficiently using variation on covariates without imposing support restrictions.