Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect

22 Pages Posted: 25 Aug 2000 Last revised: 18 Sep 2010

See all articles by James J. Heckman

James J. Heckman

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER); American Bar Foundation; Institute for the Study of Labor (IZA); CESifo (Center for Economic Studies and Ifo Institute)

Edward Vytlacil

Yale University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: August 2000

Abstract

This paper exposits and relates two distinct approaches to bounding the average treatment effect. One approach, based on instrumental variables, is due to Manski (1990, 1994), who derives tight bounds on the average treatment effect under a mean independence form of the instrumental variables (IV) condition. The second approach, based on latent index models, is due to Heckman and Vytlacil (1999, 2000a), who derive bounds on the average treatment effect that exploit the assumption of a nonparametric selection model with an exclusion restriction. Their conditions imply the instrumental variable condition studied by Manski, so that their conditions are stronger than the Manski conditions. In this paper, we study the relationship between the two sets of bounds implied by these alternative conditions. We show that: (1) the Heckman and Vytlacil bounds are tight given their assumption of a nonparametric selection model; (2) the Manski bounds simplify to the Heckman and Vytlacil bounds under the nonparametric selection model assumption.

Suggested Citation

Heckman, James J. and Vytlacil, Edward J., Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect (August 2000). NBER Working Paper No. t0259. Available at SSRN: https://ssrn.com/abstract=240088

James J. Heckman (Contact Author)

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Edward J. Vytlacil

Yale University - Department of Economics ( email )

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