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Trimming for Bounds on Treatment Effects with Missing Outcomes

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  • David S. Lee
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    Abstract

    Empirical researchers routinely encounter sample selection bias whereby 1) the regressor of interest is assumed to be exogenous, 2) the dependent variable is missing in a potentially non-random manner, 3) the dependent variable is characterized by an unbounded (or very large) support, and 4) it is unknown which variables directly affect sample selection but not the outcome. This paper proposes a simple and intuitive bounding procedure that can be used in this context. The proposed trimming procedure yields the tightest bounds on average treatment effects consistent with the observed data. The key assumption is a monotonicity restriction on how the assignment to treatment effects selection -- a restriction that is implicitly assumed in standard formulations of the sample selection problem.

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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0277.

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    Date of creation: Jun 2002
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    Handle: RePEc:nbr:nberte:0277

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    1. Horowitz, Joel L. & Manski, Charles F., 1998. "Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations," Journal of Econometrics, Elsevier, Elsevier, vol. 84(1), pages 37-58, May.
    2. repec:att:wimass:8909 is not listed on IDEAS
    3. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, American Economic Association, vol. 80(2), pages 319-23, May.
    4. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    5. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, American Economic Association, vol. 80(2), pages 313-18, May.
    6. Manski, C.F., 1990. "The Selection Problem," Working papers, Wisconsin Madison - Social Systems 90-12, Wisconsin Madison - Social Systems.
    7. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0118, National Bureau of Economic Research, Inc.
    8. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, Elsevier, vol. 58(1-2), pages 3-29, July.
    9. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
    10. James J. Heckman & Edward J. Vytlacil, 2000. "Instrumental Variables, Selection Models, and Tight Bounds on the Average Treatment Effect," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0259, National Bureau of Economic Research, Inc.
    11. Horowitz, Joel & Manski, Charles, 1997. "Nonparametric Analysis of Randomized Experiments With Missing Covariate and Outcome Data," Working Papers, University of Iowa, Department of Economics 97-16, University of Iowa, Department of Economics.
    12. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0252, National Bureau of Economic Research, Inc.
    13. Angrist, J.D., 1996. "Conditional Independance in Sample Selection Models," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 96-27, Massachusetts Institute of Technology (MIT), Department of Economics.
    14. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0136, National Bureau of Economic Research, Inc.
    15. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 331-341, January.
    16. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, Econometric Society, vol. 42(4), pages 679-94, July.
    17. Andrews, Donald W K & Schafgans, Marcia M A, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 497-517, July.
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