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Selection Without Exclusion

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  • Bo E. Honore
  • Luojia Hu

Abstract

It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. We find that the additional structure in the classical sample selection model can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one-dimensional line-segment in the parameter space, and we demonstrate that this line segment can be short in principle as well as in practice. We show that the identified set is sharp when the model is correct and empty when model is not correct. We also provide non-sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.

Suggested Citation

  • Bo E. Honore & Luojia Hu, 2018. "Selection Without Exclusion," Working Paper Series WP-2018-10, Federal Reserve Bank of Chicago.
    • Handle: RePEc:fip:fedhwp:wp-2018-10
    DOI: 10.21033/wp-2018-10
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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. 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.
    3. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    4. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    5. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    6. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    7. Krueger, Alan B & Whitmore, Diane M, 2001. "The Effect of Attending a Small Class in the Early Grades on College-Test Taking and Middle School Test Results: Evidence from Project STAR," Economic Journal, Royal Economic Society, vol. 111(468), pages 1-28, January.
    8. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 497-517.
    9. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    10. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    11. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    12. Bo E. Honoré & Adriana Lleras-Muney, 2006. "Bounds in Competing Risks Models and the War on Cancer," Econometrica, Econometric Society, vol. 74(6), pages 1675-1698, November.
    13. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    14. 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.
    15. Juan Carlos Escanciano & David Jacho‐Chávez & Arthur Lewbel, 2016. "Identification and estimation of semiparametric two‐step models," Quantitative Economics, Econometric Society, vol. 7(2), pages 561-589, July.
    16. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781316510520, January.
    17. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    18. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    19. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400022, January.
    20. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400008, January.
    21. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    22. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108414982, January.
    23. Ricardo Mora, 2008. "A nonparametric decomposition of the Mexican American average wage gap," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 463-485.
    24. Powell, James L., 1987. "Semiparametric Estimation Of Bivariate Latent Variable Models," SSRI Workshop Series 292689, University of Wisconsin-Madison, Social Systems Research Institute.
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    Cited by:

    1. Ying-Ying Lee & Chu-An Liu, 2024. "Lee Bounds with a Continuous Treatment in Sample Selection," Papers 2411.04312, arXiv.org.
    2. Shosei Sakaguchi, 2021. "Partial Identification and Inference in Duration Models with Endogenous Censoring," Papers 2107.00928, arXiv.org.
    3. Nicolas Ameye & Jacques Bughin & Nicolas van Zeebroeck, 2024. "From experimentation to scaling: what shapes the funnel of AI adoption?," ULB Institutional Repository 2013/378623, ULB -- Universite Libre de Bruxelles.
    4. Khan, Shakeeb & Nekipelov, Denis, 2024. "On uniform inference in nonlinear models with endogeneity," Journal of Econometrics, Elsevier, vol. 240(2).
    5. Lixiong Li & Désiré Kédagni & Ismaël Mourifié, 2024. "Discordant relaxations of misspecified models," Quantitative Economics, Econometric Society, vol. 15(2), pages 331-379, May.
    6. Zhewen Pan & Zhengxin Wang & Junsen Zhang & Yahong Zhou, 2024. "Marginal treatment effects in the absence of instrumental variables," Papers 2401.17595, arXiv.org, revised Aug 2024.
    7. Chu, Yongqiang & Li, Zeguang, 2022. "Banking relationship, information reusability, and acquisition loans," Journal of Banking & Finance, Elsevier, vol. 138(C).
    8. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    9. Khan, S. & Ponomareva, M. & Tamer, E., 2023. "Identification of dynamic binary response models," Journal of Econometrics, Elsevier, vol. 237(1).
    10. Lin, Zhongjian & Vella, Francis, 2021. "Selection and Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem," IZA Discussion Papers 14167, Institute of Labor Economics (IZA).
    11. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2021. "Intercept Estimation in Nonlinear Selection Models," IZA Discussion Papers 14364, Institute of Labor Economics (IZA).
    12. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.
    13. Irene Botosaru & Chris Muris, 2022. "Identification of time-varying counterfactual parameters in nonlinear panel models," Papers 2212.09193, arXiv.org, revised Nov 2023.
    14. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

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    More about this item

    Keywords

    Sample Selection; exclusion Restrictions; bounds; Partial Identification;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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