IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v88y2020i3p1007-1029.html
   My bibliography  Save this article

Selection Without Exclusion

Author

Listed:
  • Bo E. Honoré
  • 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. The additional structure 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 practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. 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. Honoré & Luojia Hu, 2020. "Selection Without Exclusion," Econometrica, Econometric Society, vol. 88(3), pages 1007-1029, May.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:3:p:1007-1029
    DOI: 10.3982/ECTA16481
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA16481
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA16481?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    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. 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.
    3. 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.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    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. 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.
    7. 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.
    8. 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.
    9. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781316510520.
    10. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    11. 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.
    12. 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.
    13. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400022.
    14. 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.
    15. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    16. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400008.
    17. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    18. 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.
    19. 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.
    20. 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.
    21. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108414982.
    22. 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.
    23. 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.
    24. Powell, James L., 1987. "Semiparametric Estimation Of Bivariate Latent Variable Models," SSRI Workshop Series 292689, University of Wisconsin-Madison, Social Systems Research Institute.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lixiong Li & D'esir'e K'edagni & Ismael Mourifi'e, 2020. "Discordant Relaxations of Misspecified Models," Papers 2012.11679, arXiv.org, revised Dec 2022.
    2. Chu, Yongqiang & Li, Zeguang, 2022. "Banking relationship, information reusability, and acquisition loans," Journal of Banking & Finance, Elsevier, vol. 138(C).
    3. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2021. "Intercept Estimation in Nonlinear Selection Models," IZA Discussion Papers 14364, Institute of Labor Economics (IZA).
    4. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    5. Shosei Sakaguchi, 2021. "Partial Identification and Inference in Duration Models with Endogenous Censoring," Papers 2107.00928, arXiv.org.
    6. Zhewen Pan & Zhengxin Wang & Junsen Zhang & Yahong Zhou, 2024. "Marginal treatment effects in the absence of instrumental variables," Papers 2401.17595, arXiv.org.
    7. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    8. 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).
    9. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.
    10. Irene Botosaru & Chris Muris, 2022. "Identification of time-varying counterfactual parameters in nonlinear panel models," Papers 2212.09193, arXiv.org, revised Nov 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    5. Gayle, George-Levi & Viauroux, Christelle, 2007. "Root-N consistent semiparametric estimators of a dynamic panel-sample-selection model," Journal of Econometrics, Elsevier, vol. 141(1), pages 179-212, November.
    6. Martin Huber & Giovanni Mellace, 2014. "Testing exclusion restrictions and additive separability in sample selection models," Empirical Economics, Springer, vol. 47(1), pages 75-92, August.
    7. Victor Chernozhukov & Ivan Fernandez-Val & Siyi Luo, 2018. "Distribution regression with sample selection, with an application to wage decompositions in the UK," CeMMAP working papers CWP68/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    9. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    10. McGovern, Mark E. & Canning, David & Bärnighausen, Till, 2018. "Accounting for non-response bias using participation incentives and survey design: An application using gift vouchers," Economics Letters, Elsevier, vol. 171(C), pages 239-244.
    11. Victor Chernozhukov & Ivan Fernandez-Val & Siyi Luo, 2023. "Distribution regression with sample selection and UK wage decomposition," CeMMAP working papers 09/23, Institute for Fiscal Studies.
    12. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Michael Lechner & Blaise Melly, 2010. "Partial Idendification of Wage Effects of Training Programs," Working Papers 2010-8, Brown University, Department of Economics.
    14. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2018_1702, CEMFI.
    15. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
    16. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2017_1702, CEMFI.
    17. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    18. Mark McGovern & David Canning & Till Bärnighausen, 2018. "Accounting for Non-Response Bias using Participation Incentives and Survey Design," CHaRMS Working Papers 18-02, Centre for HeAlth Research at the Management School (CHaRMS).
    19. David S. Lee, 2002. "Trimming for Bounds on Treatment Effects with Missing Outcomes," NBER Technical Working Papers 0277, National Bureau of Economic Research, Inc.
    20. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:88:y:2020:i:3:p:1007-1029. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.