Sharp Bounds on Treatment Effects in a Binary Triangular System

20 Pages Posted: 6 Jan 2013 Last revised: 23 Oct 2014

See all articles by Ismael Mourifie

Ismael Mourifie

University of Toronto - Department of Economics

Date Written: October 21, 2014


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.

Keywords: partial identification, threshold crossing model, triangular system, average treatment effect, endogeneity, program social evaluation

JEL Classification: C14, C31, C35

Suggested Citation

Mourifie, Ismael, Sharp Bounds on Treatment Effects in a Binary Triangular System (October 21, 2014). Available at SSRN: or

Ismael Mourifie (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7

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