IDEAS home Printed from https://ideas.repec.org/a/spr/empeco/v64y2023i6d10.1007_s00181-023-02406-w.html
   My bibliography  Save this article

DS-HECK: double-lasso estimation of Heckman selection model

Author

Listed:
  • Masayuki Hirukawa

    (Ryukoku University)

  • Di Liu

    (Stata Corp)

  • Irina Murtazashvili

    (Drexel University)

  • Artem Prokhorov

    (University of Sydney Business School
    St.Petersburg State University
    University of Montreal)

Abstract

We extend the Heckman (1979) sample selection model by allowing for a large number of controls that are selected using lasso under a sparsity scenario. The standard lasso estimation is known to under-select causing an omitted variable bias in addition to the sample selection bias. We outline the required adjustments needed to restore consistency of lasso-based estimation and inference for vector-valued parameters of interest in such models. The adjustments include double lasso for both the selection equation and main equation and a correction of the variance matrix. We also connect the estimator with results on redundancy of moment conditions. We demonstrate the effect of the adjustments using simulations and we investigate the determinants of female labor market participation and earnings in the US using the new approach. The paper comes with dsheckman, a dedicated Stata command for estimating double-selection Heckman models.

Suggested Citation

  • Masayuki Hirukawa & Di Liu & Irina Murtazashvili & Artem Prokhorov, 2023. "DS-HECK: double-lasso estimation of Heckman selection model," Empirical Economics, Springer, vol. 64(6), pages 3167-3195, June.
    • Handle: RePEc:spr:empeco:v:64:y:2023:i:6:d:10.1007_s00181-023-02406-w
    DOI: 10.1007/s00181-023-02406-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00181-023-02406-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00181-023-02406-w?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Francine D. Blau & Lawrence M. Kahn, 2007. "Changes in the Labor Supply Behavior of Married Women: 1980–2000," Journal of Labor Economics, University of Chicago Press, vol. 25(3), pages 393-438.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "High-Dimensional Methods and Inference on Structural and Treatment Effects," Journal of Economic Perspectives, American Economic Association, vol. 28(2), pages 29-50, Spring.
    5. David Neumark & Sanders Korenman, 1994. "Sources of Bias in Women's Wage Equations: Results Using Sibling Data," Journal of Human Resources, University of Wisconsin Press, vol. 29(2), pages 379-405.
    6. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    7. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    8. Tiago V. de V. Cavalcanti & José Tavares, 2008. "Assessing the "Engines of Liberation": Home Appliances and Female Labor Force Participation," The Review of Economics and Statistics, MIT Press, vol. 90(1), pages 81-88, February.
    9. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    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. Paul J. Devereux, 2004. "Changes in Relative Wages and Family Labor Supply," Journal of Human Resources, University of Wisconsin Press, vol. 39(3).
    13. 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.
    14. Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
    15. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    16. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    17. 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.
    18. Kaspar Wuthrich & Ying Zhu, 2019. "Omitted variable bias of Lasso-based inference methods: A finite sample analysis," Papers 1903.08704, arXiv.org, revised Sep 2021.
    19. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    20. 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.
    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. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    23. David M. Drukker & Di Liu, 2022. "Finite-sample results for lasso and stepwise Neyman-orthogonal Poisson estimators," Econometric Reviews, Taylor & Francis Journals, vol. 41(9), pages 1047-1076, September.
    24. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    25. Michael Bar & Seik Kim & Oksana Leukhina, 2015. "Gender Wage Gap Accounting: The Role of Selection Bias," Demography, Springer;Population Association of America (PAA), vol. 52(5), pages 1729-1750, October.
    26. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Fan Wu & Yi Xin, 2024. "Estimating Nonseparable Selection Models: A Functional Contraction Approach," Papers 2411.01799, arXiv.org.
    3. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    4. 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.
    5. Michael Bar & Seik Kim & Oksana Leukhina, 2015. "Gender Wage Gap Accounting: The Role of Selection Bias," Demography, Springer;Population Association of America (PAA), vol. 52(5), pages 1729-1750, October.
    6. Paul Ellickson & Sanjog Misra, 2012. "Enriching interactions: Incorporating outcome data into static discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 1-26, March.
    7. Matthias Westphal & Daniel A Kamhöfer & Hendrik Schmitz, 2022. "Marginal College Wage Premiums Under Selection Into Employment," The Economic Journal, Royal Economic Society, vol. 132(646), pages 2231-2272.
    8. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    9. Seonho Shin, 2022. "To work or not? Wages or subsidies?: Copula-based evidence of subsidized refugees’ negative selection into employment," Empirical Economics, Springer, vol. 63(4), pages 2209-2252, October.
    10. Mustafizur Rahman & Md. Al-Hasan, 2022. "The Reverse Gender Wage Gap in Bangladesh: Demystifying the Counterintuitive," The Indian Journal of Labour Economics, Springer;The Indian Society of Labour Economics (ISLE), vol. 65(4), pages 929-950, December.
    11. Ledic, Marko, 2012. "Estimating Labor Supply at the Extensive Margin in the presence of Sample Selection Bias," MPRA Paper 55745, University Library of Munich, Germany.
    12. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    13. 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.
    14. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," Econometrica, Econometric Society, vol. 70(6), pages 2367-2420, November.
    15. J. B. Engberg & T. Kim, "undated". "Person or Place? Parametric and semiparametric estimates of intrametropolitan earnings variation," Institute for Research on Poverty Discussion Papers 1089-96, University of Wisconsin Institute for Research on Poverty.
    16. 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.
    17. 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.
    18. Angrist, Joshua D., 1997. "Conditional independence in sample selection models," Economics Letters, Elsevier, vol. 54(2), pages 103-112, February.
    19. Seonho Shin, 2021. "Were they a shock or an opportunity?: The heterogeneous impacts of the 9/11 attacks on refugees as job seekers—a nonlinear multi-level approach," Empirical Economics, Springer, vol. 61(5), pages 2827-2864, November.
    20. 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.

    More about this item

    Keywords

    Heckman; Probit; Double lasso; Post selection inference;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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:spr:empeco:v:64:y:2023:i:6:d:10.1007_s00181-023-02406-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.