IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.07773.html
   My bibliography  Save this paper

Axiomatic characterization of pointwise Shapley decompositions

Author

Listed:
  • Marcus C Christiansen

Abstract

A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the decomposition of functions with real arguments, a popular method is the pointwise application of the Shapley value on the domain. However, this pointwise application largely ignores the overall structure of functions. In this paper, axioms are developed which fully preserve functional structures and lead to unique decompositions for all Borel measurable functions.

Suggested Citation

  • Marcus C Christiansen, 2023. "Axiomatic characterization of pointwise Shapley decompositions," Papers 2303.07773, arXiv.org.
  • Handle: RePEc:arx:papers:2303.07773
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.07773
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Profit and loss decomposition in continuous time and approximations," Papers 2212.06733, arXiv.org, revised Dec 2024.
    3. Nicholas Moehle & Stephen Boyd & Andrew Ang, 2021. "Portfolio Performance Attribution via Shapley Value," Papers 2102.05799, arXiv.org.
    4. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
    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. 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.
    2. 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.
    3. Elbers, Benjamin, 2018. "A Method for Studying Differences in Segregation Across Time and Space," SocArXiv ya7zs, Center for Open Science.
    4. Alessandra Brito & Miguel Foguel & Celia Kerstenetzky, 2017. "The contribution of minimum wage valorization policy to the decline in household income inequality in Brazil: A decomposition approach," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 40(4), pages 540-575, October.
    5. Florent Dubois, 2017. "The Sources of Segregation," AMSE Working Papers 1720, Aix-Marseille School of Economics, France.
    6. Daniela Piazzalunga & Maria Laura Di Tommaso, 2019. "The increase of the gender wage gap in Italy during the 2008-2012 economic crisis," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(2), pages 171-193, June.
    7. Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Profit and loss decomposition in continuous time and approximations," Papers 2212.06733, arXiv.org, revised Dec 2024.
    8. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebière, Thérèse, 2021. "Magnitude and evolution of gender and race contributions to earnings inequality across US regions," Research in Economics, Elsevier, vol. 75(1), pages 45-59.
    9. Giang Nguyen, 2020. "Changes in the distribution of household consumption in Southeast Asia," Economic Change and Restructuring, Springer, vol. 53(1), pages 39-60, February.
    10. Tomoki Fujii, 2015. "Poverty decomposition by regression: An application to Tanzania," WIDER Working Paper Series wp-2015-102, World Institute for Development Economic Research (UNU-WIDER).
    11. Florent Bresson & Jean-Yves Duclos & Flaviana Palmisano, 2019. "Intertemporal pro-poorness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(1), pages 65-96, January.
    12. Paul Allanson, 2022. "Ordinal health disparities between population subgroups: measurement and multivariate analysis with an application to the North-South divide in England," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 841-860, December.
    13. Carlos Gradín, 2021. "Inequality by Population Groups and Income Sources: Accounting for Inequality Changes in Spain During the Recession," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(2), pages 481-508, June.
    14. Fujii Tomoki, 2015. "Poverty decomposition by regression," WIDER Working Paper Series 102, World Institute for Development Economic Research (UNU-WIDER).
    15. Julian Jetses & Marcus C. Christiansen, 2021. "A General Surplus Decomposition Principle in Life Insurance," Papers 2111.12967, arXiv.org.
    16. Ali Enami & Nora Lustig & Rodrigo Aranda, 2016. "Analytic Foundations: Measuring the Redistributive Impact of Taxes and Transfers," Commitment to Equity (CEQ) Working Paper Series 1325, Tulane University, Department of Economics.
    17. Peter Lindner, 2015. "Factor decomposition of the wealth distribution in the euro area," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(2), pages 291-322, May.
    18. Zhao, Guangchuan & Cao, Xinbang & Ma, Chao, 2020. "Accounting for horizontal inequity in the delivery of health care: A framework for measurement and decomposition," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 13-24.
    19. Becker, Gideon, 2015. "Econometric analysis of the wealth gap between East and West Germany," University of Tübingen Working Papers in Business and Economics 87, University of Tuebingen, Faculty of Economics and Social Sciences, School of Business and Economics.
    20. Kobus, Martyna & Kapera, Marek & Maasoumi, Esfandiar, 2024. "Gap in many dimensions: Application to gender," Labour Economics, Elsevier, vol. 89(C).

    More about this item

    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:arx:papers:2303.07773. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.