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Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints

Author

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  • Stefan Boes

    (Socioeconomic Institute, University of Zurich)

Abstract

This paper explores semi-monotonicity constraints in the distribution of potential outcomes, first, conditional on an instrument, and second, in terms of the response function. The imposed assumptions are strictly weaker than traditional instrumental variables assumptions and can be gainfully employed to bound the counterfactual distributions, even though point identification is only achieved in special cases. The bounds have a simple analytical form and thus have much practical relevance in all instances when strong exogeneity assumptions cannot be credibly invoked. The bounding strategy is illustrated in a simulated data example and applied to the effect of education on smoking.

Suggested Citation

  • Stefan Boes, 2009. "Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints," SOI - Working Papers 0920, Socioeconomic Institute - University of Zurich.
    • Handle: RePEc:soz:wpaper:0920
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    File URL: https://www.econ.uzh.ch/apps/workingpapers/wp/wp0920.pdf
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    References listed on IDEAS

    as
    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(3), pages 669-709, June.
    3. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification And Economic Content Of Ordered Choice Models With Stochastic Thresholds," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1273-1309, November.
    4. Stefan Boes, 2009. "Partial Identification of Discrete Counterfactual Distributions with Sequential Update of Information," SOI - Working Papers 0918, Socioeconomic Institute - University of Zurich.
    5. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    6. Guggenberger, Patrik & Hahn, Jinyong & Kim, Kyooil, 2008. "Specification testing under moment inequalities," Economics Letters, Elsevier, vol. 99(2), pages 375-378, May.
    7. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    8. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    9. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    10. Grimard, Franque & Parent, Daniel, 2007. "Education and smoking: Were Vietnam war draft avoiders also more likely to avoid smoking?," Journal of Health Economics, Elsevier, vol. 26(5), pages 896-926, September.
    11. Machado, Cecilia & Shaikh, Azeem M. & Vytlacil, Edward J., 2019. "Instrumental variables and the sign of the average treatment effect," Journal of Econometrics, Elsevier, vol. 212(2), pages 522-555.
    12. Kenkel, Donald S, 1991. "Health Behavior, Health Knowledge, and Schooling," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 287-305, April.
    13. Janet Currie & Enrico Moretti, 2003. "Mother's Education and the Intergenerational Transmission of Human Capital: Evidence from College Openings," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(4), pages 1495-1532.
    14. Donald Kenkel & Dean Lillard & Alan Mathios, 2006. "The Roles of High School Completion and GED Receipt in Smoking and Obesity," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 635-660, July.
    15. Hsiao,Cheng & Morimune,Kimio & Powell,James L. (ed.), 2001. "Nonlinear Statistical Modeling," Cambridge Books, Cambridge University Press, number 9780521662468.
    16. Brent Kreider & John Pepper, 2008. "Inferring disability status from corrupt data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 329-349.
    17. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    18. Tsunao Okumura & Emiko Usui, 2014. "Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling," Quantitative Economics, Econometric Society, vol. 5, pages 175-194, March.
    19. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    20. 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, September.
    21. Donald W. K. Andrews & Sukjin Han, 2009. "Invalidity of the bootstrap and the m out of n bootstrap for confidence interval endpoints defined by moment inequalities," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 172-199, January.
    22. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    23. 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.
    24. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    25. Brent Kreider & Steven C. Hill, 2009. "Partially Identifying Treatment Effects with an Application to Covering the Uninsured," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    26. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    27. John F. Ermisch & Marco Francesconi, 2001. "Family structure and children's achievements," Journal of Population Economics, Springer;European Society for Population Economics, vol. 14(2), pages 249-270.
    28. Libertad González, 2005. "Nonparametric bounds on the returns to language skills," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 771-795.
    29. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    30. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    31. Victor R. Fuchs, 2018. "Schooling and Health: The Cigarette Connection," World Scientific Book Chapters, in: Health Economics and Policy Selected Writings by Victor Fuchs, chapter 9, pages 99-113, World Scientific Publishing Co. Pte. Ltd..
    32. Jay Bhattacharya & Azeem M. Shaikh & Edward Vytlacil, 2008. "Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization," American Economic Review, American Economic Association, vol. 98(2), pages 351-356, May.
    33. Andrew M Jones & John Wildman, 2005. "Disentangling the relationship between health and income," Health, Econometrics and Data Group (HEDG) Working Papers 05/07, HEDG, c/o Department of Economics, University of York.
    34. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
    35. de Walque, Damien, 2007. "Does education affect smoking behaviors?: Evidence using the Vietnam draft as an instrument for college education," Journal of Health Economics, Elsevier, vol. 26(5), pages 877-895, September.
    36. Rosenzweig, Mark R, 1995. "Why Are There Returns to Schooling?," American Economic Review, American Economic Association, vol. 85(2), pages 153-158, May.
    37. Tenn, Steven & Herman, Douglas A. & Wendling, Brett, 2010. "The role of education in the production of health: An empirical analysis of smoking behavior," Journal of Health Economics, Elsevier, vol. 29(3), pages 404-417, May.
    38. Monique de Haan, 2011. "The Effect of Parents' Schooling on Child's Schooling: A Nonparametric Bounds Analysis," Journal of Labor Economics, University of Chicago Press, vol. 29(4), pages 859-892.
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    More about this item

    Keywords

    nonparametric bounds; treatment effects; causality; endogeneity; instrumental variables; policy evaluation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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