IDEAS home Printed from https://ideas.repec.org/p/aiz/louvad/2024005.html

A penalised bootstrap estimation procedure for the explained Gini coefficient

Author

Listed:
  • Jacquemain, Alexandre

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Heuchenne, Cédric

    (Université de Liège)

  • Pircalabelu, Eugen

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

The Lorenz regression estimates the explained Gini coefficient, a quantity with a natural application in the measurement of inequality of opportunity. Assuming a single-index model, it corresponds to the Gini coefficient of the conditional expectation of a response given some covariates and it can be estimated without having to estimate the link function. However, it is prone to overestimation when many covariates are included. In this paper, we propose a penalised bootstrap procedure which selects the relevant covariates and produces valid inference for the explained Gini coefficient. The obtained estimator achieves the Oracle property. Numerically, it is computed by the SCAD-FABS algorithm, an adaptation of the FABS algorithm to the SCAD penalty. The performance of the procedure is ensured by theoretical guarantees and assessed via Monte-Carlo simulations. Finally, a real data example is presented.

Suggested Citation

  • Jacquemain, Alexandre & Heuchenne, Cédric & Pircalabelu, Eugen, 2024. "A penalised bootstrap estimation procedure for the explained Gini coefficient," LIDAM Discussion Papers ISBA 2024005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2024005
    as

    Download full text from publisher

    File URL: https://dial.uclouvain.be/pr/boreal/en/object/boreal%3A284897/datastream/PDF_01/view
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. François Bourguignon & Francisco H. G. Ferreira & Marta Menéndez, 2013. "Inequality of Opportunity in Brazil: A Corrigendum," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(3), pages 551-555, September.
    2. Shi, Xingjie & Huang, Yuan & Huang, Jian & Ma, Shuangge, 2018. "A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 235-251.
    3. Heuchenne, Cédric & Jacquemain, Alexandre, 2022. "Inference for monotone single-index conditional means: A Lorenz regression approach," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. Juan Carlos Escanciano & Joel Robert Terschuur, 2022. "Debiased Machine Learning U-statistics," Papers 2206.05235, arXiv.org, revised Jun 2026.
    5. Francisco H.G. Ferreira & Jérémie Gignoux, 2011. "The Measurement of Inequality of Inequality of Opportunity: Theory and an Application to Latin America," Post-Print halshs-00754503, HAL.
    6. Paolo Brunori & Paul Hufe & Daniel Gerszon Mahler, 2017. "The Roots of Inequality: Estimating Inequality of Opportunity from Regression Trees," Working Papers - Economics wp2017_18.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    7. Lin, Huazhen & Peng, Heng, 2013. "Smoothed rank correlation of the linear transformation regression model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 615-630.
    8. 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.
    9. Francisco H. G. Ferreira & Jérémie Gignoux, 2011. "The Measurement Of Inequality Of Opportunity: Theory And An Application To Latin America," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(4), pages 622-657, December.
    10. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    11. repec:dau:papers:123456789/1552 is not listed on IDEAS
    12. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
    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. Zbigniew Mogila & Patricia C. Melo & José M. Gaspar, 2022. "Estimating labour‐income‐based inequality of opportunity for a selection of EU‐SILC countries: National and urban–rural perspectives," Regional Science Policy & Practice, Wiley Blackwell, vol. 14(5), pages 1158-1187, October.
    2. Arnaud Lefranc & Tista Kundu, 2020. "Inequality of Opportunity in Indian Society," Working Papers hal-02539364, HAL.
    3. Pedro Salas-Rojo & Juan Gabriel Rodríguez, 2019. "The distribution of wealth in the U.S. and Spain: the role of socio-economic factors," Working Papers 506, ECINEQ, Society for the Study of Economic Inequality.
    4. 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.
    5. Leonardo Gasparini & Irene Brambilla & Andrés César & Guillermo Falcone & Carlo Lombardo, 2020. "The Risk of Automation in Argentina," CEDLAS, Working Papers 0260, CEDLAS, Universidad Nacional de La Plata.
    6. Shi, Xinjie, 2022. "Inequality of opportunity in earnings in rural China," Journal of Asian Economics, Elsevier, vol. 81(C).
    7. Paolo Brunori & Vito Peragine & Laura Serlenga, 2019. "Upward and downward bias when measuring inequality of opportunity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 635-661, April.
    8. Paul Hufe & Andreas Peichl & Daniel Weishaar, 2022. "Lower and upper bound estimates of inequality of opportunity for emerging economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(3), pages 395-427, April.
    9. Oscar Torrealba Rodriguez, 2024. "The weight of circumstances in the inequality of opportunity in Mexico: an estimation over a wide set based on machine learning," Sobre México. Revista de Economía, Sobre México. Temas en economía, vol. 1(9), pages 160-195.
    10. Ana Suárez Álvarez & Ana Jesús López Menéndez, 2020. "Trends in Inequality of Opportunity for Developing Countries: Does the Economic Indicator Matter?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 503-539, June.
    11. Yuxiang Xie & E. Xie, 2025. "Intergenerational Transmission of Opportunity Inequality in the Context of the Healthy China Initiative," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 178(2), pages 929-960, June.
    12. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    13. Brock, J Michelle, 2018. "Inequality of opportunity, governance and individual beliefs," CEPR Discussion Papers 12636, Centre for Economic Policy Research.
    14. Song, Yang & Zhou, Guangsu, 2019. "Inequality of opportunity and household education expenditures: Evidence from panel data in China," China Economic Review, Elsevier, vol. 55(C), pages 85-98.
    15. Ferreira, Francisco H. G. & Peragine, Vito, 2015. "Equality of Opportunity: Theory and Evidence," IZA Discussion Papers 8994, IZA Network @ LISER.
    16. Michał Brzeziński, 2015. "Inequality of opportunity in Europe before and after the Great Recession," Working Papers 2015-02, Faculty of Economic Sciences, University of Warsaw.
    17. Maurizio Bussolo & Daniele Checchi & Vito Peragine, 2023. "Long-term evolution of inequality of opportunity: Educated parents still matter," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(2), pages 277-323, June.
    18. Vincenzo Carrieri & Apostolos Davillas & Andrew M. Jones, 2023. "Equality of opportunity and the expansion of higher education in the UK," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 69(4), pages 861-885, December.
    19. Dirk Van de gaer & Joost Vandenbossche & José Luis Figueroa, 2014. "Children's Health Opportunities and Project Evaluation: Mexico's Oportunidades Program," The World Bank Economic Review, World Bank, vol. 28(2), pages 282-310.
    20. Marrero,Gustavo Alberto & Rodríguez,Juan Gabriel & Van Der Weide,Roy, 2021. "Does Race and Gender Inequality Impact Income Growth ?," Policy Research Working Paper Series 9865, The World Bank.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aiz:louvad:2024005. 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: Alain Gillis (email available below). General contact details of provider: https://edirc.repec.org/data/isuclbe.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.