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 the endogenous regressor and the outcome. The bounds proposed by Shaikh and Vytlacil (2011,SV) on the ATE 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 this setting, I provide a methodology that allows the construction of sharp bounds on the ATE by efficiently using the variation of covariates without imposing support restrictions.