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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
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    References listed on IDEAS

    as
    1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    2. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    3. Maddala,G. S., 1986. "Limited-Dependent and Qualitative Variables in Econometrics," Cambridge Books, Cambridge University Press, number 9780521338257, December.
    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. 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.
    6. 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.
    7. R. F. Engle & D. McFadden (ed.), 1986. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 4, number 4.
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    Cited by:

    1. Miguel A. Delgado & Andr'es Garc'ia-Suaza & Pedro H. C. Sant'Anna, 2019. "Distribution Regression in Duration Analysis: an Application to Unemployment Spells," Papers 1904.06185, arXiv.org.

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