Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect
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.
|Date of creation:||Aug 2000|
|Date of revision:|
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- Manski, C.F., 1989.
"Nonparametric Bounds On Treatment Effects,"
8909, Wisconsin Madison - Social Systems.
- Imbens, Guido W & Angrist, Joshua D, 1994.
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- Charles F. Manski & John V. Pepper, 1998.
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NBER Technical Working Papers
0224, National Bureau of Economic Research, Inc.
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- Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables: With an Application to the Returns to Schooling," Virginia Economics Online Papers 308, University of Virginia, Department of Economics.
- James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
- Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
- Manski, C.F., 1990. "The Selection Problem," Working papers 90-12, Wisconsin Madison - Social Systems.
- Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
- James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 487-535.
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