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Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis

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  • Azeem Shaikh
  • Edward Vytlacil

Abstract

This paper considers the evaluation of the average treatment effect of a binary endogenous regressor on a binary outcome when one imposes a threshold crossing model on both the endogenous regressor and the outcome variable but without imposing parametric functional form or distributional assumptions. Without parametric restrictions, the average effect of the binary endogenous variable is not generally point identified. This paper constructs sharp bounds on the average effect of the endogenous variable that exploit the structure of the threshold crossing models and any exclusion restrictions. We also develop methods for inference on the resulting bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:nbr:nberte:0307
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    1. N/A, 2004. "Index for 2004," European Union Politics, , vol. 5(4), pages 511-512, December.
    2. Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, August.
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    Cited by:

    1. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, July.
    2. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    3. Stefan Boes, 2013. "Nonparametric analysis of treatment effects in ordered response models," Empirical Economics, Springer, vol. 44(1), pages 81-109, February.
    4. Steven T. Berry & Philip A. Haile, 2009. "Identification of a Heterogeneous Generalized Regression Model with Group Effects," Cowles Foundation Discussion Papers 1732, Cowles Foundation for Research in Economics, Yale University.
    5. Lina Zhang & David T. Frazier & Don S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Monash Econometrics and Business Statistics Working Papers 34/20, Monash University, Department of Econometrics and Business Statistics.
    6. Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, August.
    7. Anders Forslund & Oskar Nordström Stans, 2006. "Swedish Youth Labour Market Policies Revisited," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 75(3), pages 168-185.
    8. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    9. Alfred Galichon & Marc Henry, 2021. "Inference in Incomplete Models," Papers 2102.12257, arXiv.org.
    10. 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.
    11. Stefan Boes, 2009. "Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints," SOI - Working Papers 0920, Socioeconomic Institute - University of Zurich.
    12. Amit Gandhi & Jeremy T. Fox, 2009. "Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures," 2009 Meeting Papers 165, Society for Economic Dynamics.
    13. Flavio Cunha & James Heckman & Salvador Navarro, 2005. "Separating uncertainty from heterogeneity in life cycle earnings," Oxford Economic Papers, Oxford University Press, vol. 57(2), pages 191-261, April.
    14. 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.
    15. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    16. Shaikh, Azeem M. & Vytlacil, Edward, 2008. "Endogenous binary choice models with median restrictions: A comment," Economics Letters, Elsevier, vol. 98(1), pages 23-28, January.
    17. Stefan Boes, 2009. "Partial Identification of Discrete Counterfactual Distributions with Sequential Update of Information," SOI - Working Papers 0918, Socioeconomic Institute - University of Zurich.
    18. Casey Quinn, 2005. "Generalisable regression methods for costeffectiveness using copulas," Health, Econometrics and Data Group (HEDG) Working Papers 05/13, HEDG, c/o Department of Economics, University of York.
    19. Lara Shore-Sheppard & John Ham & Serkan Ozbeklik, 2012. "Estimating Heterogeneous Take-up and Crowd-Out Responses to Current Medicaid Limits and Their Nonmarginal Expansions," Department of Economics Working Papers 2012-05, Department of Economics, Williams College.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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