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

James Heckman and Edward Vytlacil

No 259, NBER Technical Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C50 H43 (search for similar items in EconPapers)
Date: 2000-08
Note: TWP
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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