IDEAS home Printed from https://ideas.repec.org/a/spr/joecin/v21y2023i3d10.1007_s10888-023-09565-x.html
   My bibliography  Save this article

Gender wage inequality: new evidence from penalized expectile regression

Author

Listed:
  • Marina Bonaccolto-Töpfer

    (University of Genova)

  • Giovanni Bonaccolto

    (Kore University of Enna, Cittadella Universitaria)

Abstract

The Machado-Mata decomposition building on quantile regression has been extensively analyzed in the literature focusing on gender wage inequality. In this study, we generalize the Machado-Mata decomposition to the expectile regression framework, which, to the best of our knowledge, has never been applied in this strand of the literature. In contrast, in recent years, expectiles have gained increasing attention in other contexts as an alternative to traditional quantiles, providing useful statistical and computational properties. We flexibly deal with high-dimensional problems by employing the Least Absolute Shrinkage and Selection Operator. The empirical analysis focuses on the gender pay gap in Germany and Italy. We find that depending on the estimation approach (i.e. expectile or quantile regression) the results substantially differ along some regions of the wage distribution, whereas they are similar for others. From a policy perspective, this finding is important as it affects conclusions about glass ceiling and sticky floors.

Suggested Citation

  • Marina Bonaccolto-Töpfer & Giovanni Bonaccolto, 2023. "Gender wage inequality: new evidence from penalized expectile regression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(3), pages 511-535, September.
  • Handle: RePEc:spr:joecin:v:21:y:2023:i:3:d:10.1007_s10888-023-09565-x
    DOI: 10.1007/s10888-023-09565-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10888-023-09565-x
    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/s10888-023-09565-x?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. Strittmatter, Anthony & Wunsch, Conny, 2021. "The Gender Pay Gap Revisited with Big Data: Do Methodological Choices Matter?," IZA Discussion Papers 14128, Institute of Labor Economics (IZA).
    2. 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.
    3. Paolo Brunori & Guido Neidhöfer, 2021. "The Evolution of Inequality of Opportunity in Germany: A Machine Learning Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(4), pages 900-927, December.
    4. Francine D. Blau & Lawrence M. Kahn, 2006. "The U.S. Gender Pay Gap in the 1990S: Slowing Convergence," ILR Review, Cornell University, ILR School, vol. 60(1), pages 45-66, October.
    5. Stahlschmidt, Stephan & Eckardt, Matthias & Härdle, Wolfgang Karl, 2014. "Expectile treatment effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers 2014-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Bonaccolto, Giovanni & Caporin, Massimiliano & Maillet, Bertrand B., 2022. "Dynamic large financial networks via conditional expected shortfalls," European Journal of Operational Research, Elsevier, vol. 298(1), pages 322-336.
    7. Claudia Goldin, 2014. "A Grand Gender Convergence: Its Last Chapter," American Economic Review, American Economic Association, vol. 104(4), pages 1091-1119, April.
    8. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    9. Bellini, Fabio & Cesarone, Francesco & Colombo, Christian & Tardella, Fabio, 2021. "Risk parity with expectiles," European Journal of Operational Research, Elsevier, vol. 291(3), pages 1149-1163.
    10. 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.
    11. C. Davino & R. Romano & D. Vistocco, 2022. "Handling multicollinearity in quantile regression through the use of principal component regression," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 153-174, August.
    12. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, May.
    13. Domenico Depalo & Raffaela Giordano & Evangelia Papapetrou, 2015. "Public–private wage differentials in euro-area countries: evidence from quantile decomposition analysis," Empirical Economics, Springer, vol. 49(3), pages 985-1015, November.
    14. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
    15. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    16. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    17. Chinhui Juhn & Kristin McCue, 2017. "Specialization Then and Now: Marriage, Children, and the Gender Earnings Gap across Cohorts," Journal of Economic Perspectives, American Economic Association, vol. 31(1), pages 183-204, Winter.
    18. Bonaccolto-Töpfer, Marina & Briel, Stephanie, 2022. "The gender pay gap revisited: Does machine learning offer new insights?," Labour Economics, Elsevier, vol. 78(C).
    19. Wiji Arulampalam & Alison L. Booth & Mark L. Bryan, 2007. "Is There a Glass Ceiling over Europe? Exploring the Gender Pay Gap across the Wage Distribution," ILR Review, Cornell University, ILR School, vol. 60(2), pages 163-186, January.
    20. Bassett, Gilbert W. & Koenker, Roger W., 1986. "Strong Consistency of Regression Quantiles and Related Empirical Processes," Econometric Theory, Cambridge University Press, vol. 2(2), pages 191-201, August.
    21. Gert Wagner & Jan Göbel & Peter Krause & Rainer Pischner & Ingo Sieber, 2008. "Das Sozio-oekonomische Panel (SOEP): Multidisziplinäres Haushaltspanel und Kohortenstudie für Deutschland – Eine Einführung (für neue Datennutzer) mit einem Ausblick (für erfahrene Anwender)," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 2(4), pages 301-328, December.
    22. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    23. Collischon Matthias, 2019. "Is There a Glass Ceiling over Germany?," German Economic Review, De Gruyter, vol. 20(4), pages 329-359, December.
    24. R. Giacometti & G. Torri & S. Paterlini, 2021. "Tail risks in large portfolio selection: penalized quantile and expectile minimum deviation models," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 243-261, February.
    25. Carolina Castagnetti & Luisa Rosti & Marina Töpfer, 2020. "Discriminate me — If you can! The disappearance of the gender pay gap among public‐contest selected employees in Italy," Gender, Work and Organization, Wiley Blackwell, vol. 27(6), pages 1040-1076, November.
    26. 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.
    27. Fabio Bellini & Elena Di Bernardino, 2017. "Risk management with expectiles," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 487-506, May.
    28. 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.
    29. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    30. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    31. repec:hum:wpaper:sfb649dp2014-059 is not listed on IDEAS
    32. Bonaccolto-Töpfer, Marina & Castagnetti, Carolina & Prümer, Stephanie, 2022. "Understanding the public-private sector wage gap in Germany: New evidence from a Fixed Effects quantile Approach∗," Economic Modelling, Elsevier, vol. 116(C).
    33. Lina Liao & Cheolwoo Park & Hosik Choi, 2019. "Penalized expectile regression: an alternative to penalized quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 409-438, April.
    34. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    35. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    36. repec:pri:indrel:dsp01gb19f581g is not listed on IDEAS
    37. Blaise Melly, 2005. "Public-private sector wage differentials in Germany: Evidence from quantile regression," Empirical Economics, Springer, vol. 30(2), pages 505-520, September.
    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. Bonaccolto-Töpfer, Marina & Briel, Stephanie, 2022. "The gender pay gap revisited: Does machine learning offer new insights?," Labour Economics, Elsevier, vol. 78(C).
    2. Bonaccolto, Giovanni & Caporin, Massimiliano & Maillet, Bertrand B., 2022. "Dynamic large financial networks via conditional expected shortfalls," European Journal of Operational Research, Elsevier, vol. 298(1), pages 322-336.
    3. Bonaccolto-Töpfer, Marina & Castagnetti, Carolina & Rosti, Luisa, 2023. "Changes in the gender pay gap over time: the case of West Germany," Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 57, pages 1-11.
    4. Bonaccolto-Töpfer, Marina & Satlukal, Sascha, 2024. "Gender differences in reservation wages: New evidence for Germany," Labour Economics, Elsevier, vol. 91(C).
    5. Stahlschmidt, Stephan & Eckardt, Matthias & Härdle, Wolfgang Karl, 2014. "Expectile treatment effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers 2014-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. repec:hum:wpaper:sfb649dp2014-059 is not listed on IDEAS
    7. Sonja C. Kassenboehmer & Mathias G. Sinning, 2014. "Distributional Changes in the Gender Wage Gap," ILR Review, Cornell University, ILR School, vol. 67(2), pages 335-361, April.
    8. Kaya Ezgi, 2021. "Gender wage gap across the distribution: What is the role of within- and between-firm effects?," IZA Journal of Development and Migration, Sciendo & Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 12(1), pages 1-49, January.
    9. Bonaccolto-Töpfer, Marina & Castagnetti, Carolina & Prümer, Stephanie, 2022. "Understanding the public-private sector wage gap in Germany: New evidence from a Fixed Effects quantile Approach∗," Economic Modelling, Elsevier, vol. 116(C).
    10. Jacqueline Mosomi, 2019. "Distributional changes in the gender wage gap in the post-apartheid South African labour market," WIDER Working Paper Series wp-2019-17, World Institute for Development Economic Research (UNU-WIDER).
    11. 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.
    12. C. Adam & I. Gijbels, 2022. "Local polynomial expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 341-378, April.
    13. Thomas Grandner & Dieter Gstach, 2015. "Decomposing wage discrimination in Germany and Austria with counterfactual densities," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(1), pages 49-76, February.
    14. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    15. Biewen, Martin & Fitzenberger, Bernd & Seckler, Matthias, 2020. "Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap," Labour Economics, Elsevier, vol. 67(C).
    16. Garbay, Sergio & Barrera, Raquel, 2021. "¿Mujeres en suelos pegajosos? Un análisis de la evolución de las distribuciones de ingresos laborales en Bolivia en el periodo 2011-2019," Revista Latinoamericana de Desarrollo Economico, Carrera de Economía de la Universidad Católica Boliviana (UCB) "San Pablo", issue 36, pages 123-168, Noviembre.
    17. Männasoo, Kadri, 2022. "Working hours and gender wage differentials: Evidence from the American Working Conditions Survey," Labour Economics, Elsevier, vol. 76(C).
    18. Wang, Wen & Lien, Donald, 2018. "Union membership, union coverage and wage dispersion of rural migrants: Evidence from Suzhou industrial sector," China Economic Review, Elsevier, vol. 49(C), pages 96-113.
    19. Collischon Matthias, 2019. "Is There a Glass Ceiling over Germany?," German Economic Review, De Gruyter, vol. 20(4), pages 329-359, December.
    20. Deshpande, Ashwini & Goel, Deepti & Khanna, Shantanu, 2018. "Bad Karma or Discrimination? Male–Female Wage Gaps Among Salaried Workers in India," World Development, Elsevier, vol. 102(C), pages 331-344.
    21. Domenico Depalo & Raffaela Giordano & Evangelia Papapetrou, 2015. "Public–private wage differentials in euro-area countries: evidence from quantile decomposition analysis," Empirical Economics, Springer, vol. 49(3), pages 985-1015, November.

    More about this item

    Keywords

    Expectile regression; Gender pay gap; Quantile regression; Penalized estimation;
    All these keywords.

    JEL classification:

    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J16 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Gender; Non-labor Discrimination
    • J45 - Labor and Demographic Economics - - Particular Labor Markets - - - Public Sector Labor Markets
    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects

    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:joecin:v:21:y:2023:i:3:d:10.1007_s10888-023-09565-x. 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.