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

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  • James J. Heckman
  • Edward J. Vytlacil

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

  • James J. Heckman & Edward J. Vytlacil, 2000. "Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect," NBER Technical Working Papers 0259, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0259
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    References listed on IDEAS

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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. 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.
    3. Manski, C.F., 1990. "The Selection Problem," Working papers 90-12, Wisconsin Madison - Social Systems.
    4. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    5. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    6. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    7. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
    8. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
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    Cited by:

    1. Michael Gerfin & Martin Schellhorn, 2006. "Nonparametric bounds on the effect of deductibles in health care insurance on doctor visits - Swiss evidence," Health Economics, John Wiley & Sons, Ltd., vol. 15(9), pages 1011-1020.
    2. David S. Lee, 2002. "Trimming for Bounds on Treatment Effects with Missing Outcomes," NBER Technical Working Papers 0277, National Bureau of Economic Research, Inc.
    3. Hujer, Reinhard & Thomsen, Stephan L., 2006. "Wirksamkeit von Arbeitsbeschaffungsmaßnahmen in Deutschland: Empirische Befunde mikroökonometrischer Analysen," ZEW Discussion Papers 06-054, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    4. Stefanie Hof, 2014. "Does private tutoring work? The effectiveness of private tutoring: a nonparametric bounds analysis," Education Economics, Taylor & Francis Journals, vol. 22(4), pages 347-366, August.
    5. Bhattacharya, Jay & Shaikh, Azeem M. & Vytlacil, Edward, 2012. "Treatment effect bounds: An application to Swan–Ganz catheterization," Journal of Econometrics, Elsevier, vol. 168(2), pages 223-243.
    6. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute for the Study of Labor (IZA).
    7. Michael Gebel & Friedhelm Pfeiffer, 2010. "Educational Expansion and Its Heterogeneous Returns for Wage Workers," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 130(1), pages 19-42.

    More about this item

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • H43 - Public Economics - - Publicly Provided Goods - - - Project Evaluation; Social Discount Rate

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