IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/68-18.html
   My bibliography  Save this paper

Distribution regression with sample selection, with an application to wage decompositions in the UK

Author

Listed:
  • Victor Chernozhukov

    (Institute for Fiscal Studies and MIT)

  • Ivan Fernandez-Val

    (Institute for Fiscal Studies and Boston University)

  • Siyi Luo

    (Institute for Fiscal Studies)

Abstract

We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much rich patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identi fication of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the fi rst step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation. We construct estimators of functionals of interest such as actual and counterfactual distributions of latent and observed outcomes via plug-in rule. We derive functional central limit theorems for all the estimators and show the validity of multiplier bootstrap to carry out functional inference. We apply the methods to wage decompositions in the UK using new data. Here we decompose the difference between the male and female wage distributions into four effects: composition, wage structure, selection structure and selection sorting. We uncover positive sorting for single men and negative sorting for married women that accounts for a substantial fraction of the gender wage gap at the top of the distribution. These fi ndings can be interpreted as evidence of assortative matching in the marriage market and glass-ceiling in the labor market.

Suggested Citation

  • 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.
    • Handle: RePEc:ifs:cemmap:68/18
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP681818.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Richard Blundell & Howard Reed & Thomas M. Stoker, 2003. "Interpreting Aggregate Wage Growth: The Role of Labor Market Participation," American Economic Review, American Economic Association, vol. 93(4), pages 1114-1131, September.
    2. Maddala,G. S., 1986. "Limited-Dependent and Qualitative Variables in Econometrics," Cambridge Books, Cambridge University Press, number 9780521338257.
    3. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    4. 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.
    5. Murray D. Smith, 2003. "Modelling sample selection using Archimedean copulas," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 99-123, June.
    6. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    7. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    8. Oaxaca, Ronald, 1973. "Male-Female Wage Differentials in Urban Labor Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 693-709, October.
    9. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    10. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    11. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    12. 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.
    13. Alan S. Blinder, 1973. "Wage Discrimination: Reduced Form and Structural Estimates," Journal of Human Resources, University of Wisconsin Press, vol. 8(4), pages 436-455.
    14. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    15. Derek Neal, 2004. "The Measured Black-White Wage Gap among Women Is Too Small," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 1-28, February.
    16. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    17. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    18. Van de Ven, Wynand P. M. M. & Van Praag, Bernard M. S., 1981. "The demand for deductibles in private health insurance : A probit model with sample selection," Journal of Econometrics, Elsevier, vol. 17(2), pages 229-252, November.
    19. 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.
    20. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    21. 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.
    22. James Albrecht & Anders Bjorklund & Susan Vroman, 2003. "Is There a Glass Ceiling in Sweden?," Journal of Labor Economics, University of Chicago Press, vol. 21(1), pages 145-177, January.
    23. 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.
    24. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    25. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 355-372.
    26. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    27. Newey, Whitney K., 1999. "Consistency of two-step sample selection estimators despite misspecification of distribution," Economics Letters, Elsevier, vol. 63(2), pages 129-132, May.
    28. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    29. R. F. Engle & D. McFadden (ed.), 1986. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 4, number 4.
    30. Poirier, Dale J., 1980. "Partial observability in bivariate probit models," Journal of Econometrics, Elsevier, vol. 12(2), pages 209-217, February.
    31. Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
    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. Miguel A Delgado & Andrés García-Suaza & Pedro H C Sant’Anna, 2022. "Distribution regression in duration analysis: an application to unemployment spells [Lecture notes in statistics: Proceedings]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 675-698.
    2. Strittmatter, Anthony & Wunsch, Conny, 2021. "The Gender Pay Gap Revisited with Big Data: Do Methodological Choices Matter?," Working papers 2021/05, Faculty of Business and Economics - University of Basel.
    3. Dominik Wied, 2022. "Semiparametric Distribution Regression with Instruments and Monotonicity," Papers 2212.03704, arXiv.org.
    4. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

    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. 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.
    2. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    3. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    4. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    5. Claudia Olivetti & Barbara Petrongolo, 2008. "Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps," Journal of Labor Economics, University of Chicago Press, vol. 26(4), pages 621-654, October.
    6. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    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. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2018_1702, CEMFI.
    9. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2017_1702, CEMFI.
    10. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
    11. Valentina Corradi & Daniel Gutknecht, 2019. "Testing for Quantile Sample Selection," Papers 1907.07412, arXiv.org, revised Jan 2021.
    12. Seneviratne, Prathi, 2020. "Gender wage inequality during Sri Lanka’s post-reform growth: A distributional analysis," World Development, Elsevier, vol. 129(C).
    13. James J. Heckman, 2005. "Micro Data, Heterogeneity and the Evaluation of Public Policy Part 2," The American Economist, Sage Publications, vol. 49(1), pages 16-44, March.
    14. Claudia PIGINI, 2012. "Of Butterflies and Caterpillars: Bivariate Normality in the Sample Selection Model," Working Papers 377, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    15. Denis Y. Orlov & Evgeniy M. Ozhegov, 2016. "Do sequel movies really earn more than non-sequels? Evidence from the US box office," ACEI Working Paper Series AWP-03-2016, Association for Cultural Economics International, revised Apr 2016.
    16. Denis Y. Orlov & Evgeniy M. Ozhegov, 2015. "Estimating the Efficiency of Sequels in the Film Industry," HSE Working papers WP BRP 96/EC/2015, National Research University Higher School of Economics.
    17. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    18. Casey B. Mulligan & Yona Rubinstein, 2004. "The Closing of the Gender Gap as a Roy Model Illusion," NBER Working Papers 10892, National Bureau of Economic Research, Inc.
    19. Ahrsjö, Ulrika & Niknami, Susan & Palme, Mårten, 2021. "Wage Inequality, Selection and the Evolution of the Gender Earnings Gap in Sweden," Research Papers in Economics 2021:3, Stockholm University, Department of Economics.
    20. Francine D. Blau & Lawrence Kahn & Nikolai Boboshko & Matthew Comey, 2021. "Th Impact of Selection into the Labor Force on the Gender Wage Gap," CESifo Working Paper Series 9103, CESifo.

    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:ifs:cemmap:68/18. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.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.