IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v53y2019i2d10.1007_s00355-019-01183-9.html
   My bibliography  Save this article

A note on the decomposability of inequality measures

Author

Listed:
  • Frédéric Chantreuil

    (University of New Caledonia, LARJE, Ateliers DEG
    TEPP-CNRS)

  • Sébastien Courtin

    (Normandie Univ., Unicaen, CREM, UMR CNRS 6211
    TEPP-CNRS)

  • Kevin Fourrey

    (Normandie Univ., Unicaen, CREM, UMR CNRS 6211
    TEPP-CNRS)

  • Isabelle Lebon

    (Normandie Univ., Unicaen, CREM, UMR CNRS 6211
    TEPP-CNRS)

Abstract

We propose a decomposition of inequality measures. By taking the example of the decomposition of income inequality by components, we show that this decomposition fits the definition of two elements: the sum of pure marginal contributions of income components and the sum of the pairwise interactions of all income components. This decomposition relies on the Shapley function and remains valid for a decomposition by subgroups and by components.

Suggested Citation

  • Frédéric Chantreuil & Sébastien Courtin & Kevin Fourrey & Isabelle Lebon, 2019. "A note on the decomposability of inequality measures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 283-298, August.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:2:d:10.1007_s00355-019-01183-9
    DOI: 10.1007/s00355-019-01183-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-019-01183-9
    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/s00355-019-01183-9?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chantreuil, Frédéric & Lebon, Isabelle, 2015. "Gender contribution to income inequality," Economics Letters, Elsevier, vol. 133(C), pages 27-30.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Frank Cowell & Carlo Fiorio, 2011. "Inequality decompositions—a reconciliation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 509-528, December.
    4. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    5. Frédéric Chantreuil & Alain Trannoy, 2011. "Inequality Decomposition Values," Annals of Economics and Statistics, GENES, issue 101-102, pages 13-36.
    6. Frédéric Chantreuil & Alain Trannoy, 2013. "Inequality decomposition values: the trade-off between marginality and efficiency," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 83-98, March.
    7. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    8. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    9. St鰨ane Mussard & Luc Savard, 2012. "The Gini multi-decomposition and the role of Gini's transvariation: application to partial trade liberalization in the Philippines," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1235-1249, April.
    10. Kojadinovic, Ivan, 2004. "Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals," European Journal of Operational Research, Elsevier, vol. 155(3), pages 741-751, June.
    11. repec:adr:anecst:y:2011:i:101-102:p:02 is not listed on IDEAS
    12. 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.
    13. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    14. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Iryna Kyzyma & Alessio Fusco & Philippe Van Kerm, 2022. "Distributional Change: Assessing the Contribution of Household Income Sources," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(1), pages 158-184, February.
    3. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebiere, Therese, 2020. "Decomposing US Income Inequality à La Shapley: Race Matters, but Gender Too," IZA Discussion Papers 12950, Institute of Labor Economics (IZA).
    4. Rodrigue Tido Takeng & Arnold Cedrick Soh Voutsa & Kévin Fourrey, 2023. "Decompositions of inequality measures from the perspective of the Shapley–Owen value," Theory and Decision, Springer, vol. 94(2), pages 299-331, February.
    5. Sébastien Courtin & Rodrigue Tido Takeng & Frédéric Chantreuil, 2024. "Decomposition of interaction indices: alternative interpretations of cardinal–probabilistic interaction indices," Theory and Decision, Springer, vol. 97(1), pages 139-165, August.
    6. Hu'e Sullivan & Hurlin Christophe & P'erignon Christophe & Saurin S'ebastien, 2022. "Measuring the Driving Forces of Predictive Performance: Application to Credit Scoring," Papers 2212.05866, arXiv.org, revised Jun 2023.
    7. Sébastien Courtin & Rodrigue Tido Takeng & Frédéric Chantreuil, 2020. "Decomposition of interaction indices: alternative interpretations of cardinal-probabilistic interaction indices ," Working Papers hal-02952516, HAL.
    8. Ollier, Maxime & Jayet, Pierre-Alain & Humblot, Pierre, 2024. "An assessment of the distributional impacts of autonomous adaptation to climate change from European agriculture," Ecological Economics, Elsevier, vol. 222(C).

    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. 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.
    2. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebiere, Therese, 2020. "Decomposing US Income Inequality à La Shapley: Race Matters, but Gender Too," IZA Discussion Papers 12950, Institute of Labor Economics (IZA).
    3. Carlos Gradín, 2020. "Quantifying the contribution of a subpopulation to inequality an application to Mozambique," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(3), pages 391-419, September.
    4. Teixidó Figueras, Jordi & Duro Moreno, Juan Antonio, 2012. "Ecological Footprint Inequality: A methodological review and some results," Working Papers 2072/203168, Universitat Rovira i Virgili, Department of Economics.
    5. Mussard, Stéphane & Pi Alperin, Maria Noel, 2011. "Poverty growth in Scandinavian countries: A Sen multi-decomposition," Economic Modelling, Elsevier, vol. 28(6), pages 2842-2853.
    6. SOLOGON Denisa & ALMEIDA Vanda & VAN KERM Philippe, 2019. "Accounting for the distributional effects of the 2007-2008 crisis and the Economic Adjustment Program in Portugal," LISER Working Paper Series 2019-05, Luxembourg Institute of Socio-Economic Research (LISER).
    7. Rodrigue Tido Takeng & Arnold Cedrick Soh Voutsa & Kévin Fourrey, 2023. "Decompositions of inequality measures from the perspective of the Shapley–Owen value," Theory and Decision, Springer, vol. 94(2), pages 299-331, February.
    8. Guido Erreygers & Roselinde Kessels, 2013. "Regression-Based Decompositions of Rank-Dependent Indicators of Socioeconomic Inequality of Health," Research on Economic Inequality, in: Health and Inequality, volume 21, pages 227-259, Emerald Group Publishing Limited.
    9. Carlos Gradín, 2018. "Quantifying the contribution of a subpopulation to inequality: An application to Mozambique," WIDER Working Paper Series 60, World Institute for Development Economic Research (UNU-WIDER).
    10. Sebastian Leitner, 2015. "Drivers of wealth inequality in euro area countries," Working Paper Reihe der AK Wien - Materialien zu Wirtschaft und Gesellschaft 137, Kammer für Arbeiter und Angestellte für Wien, Abteilung Wirtschaftswissenschaft und Statistik.
    11. Lwin Lwin Aung & Peter Warr, 2021. "Decomposing changes in inequality: Evidence from Myanmar," Review of Development Economics, Wiley Blackwell, vol. 25(3), pages 1172-1196, August.
    12. SOLOGON Denisa & VAN KERM Philippe & LI Jinjing & O'DONOGHUE Cathal, 2018. "Accounting for Differences in Income Inequality across Countries: Ireland and the United Kingdom," LISER Working Paper Series 2018-01, Luxembourg Institute of Socio-Economic Research (LISER).
    13. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.
    14. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    15. Hu'e Sullivan & Hurlin Christophe & P'erignon Christophe & Saurin S'ebastien, 2022. "Measuring the Driving Forces of Predictive Performance: Application to Credit Scoring," Papers 2212.05866, arXiv.org, revised Jun 2023.
    16. Yawo Agbényég Noglo, 2014. "Monetary Inequality Among Households in Togo: An Illustration Based on the Decomposition of the Gini Coefficient Using the Shapley Value Approach," WIDER Working Paper Series wp-2014-151, World Institute for Development Economic Research (UNU-WIDER).
    17. Arthur Charpentier & Stéphane Mussard, 2011. "Income inequality games," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 529-554, December.
    18. Marco Ranaldi, 2016. "On the Measurement of Functional Income Distribution," Documents de travail du Centre d'Economie de la Sorbonne 16051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. F. Chantreuil & A. Trannoy, 1999. "Inequality decomposition values : the trade-off between marginality and consistency," THEMA Working Papers 99-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    20. Omoniyi B Alimi & David C Maré & Jacques Poot, 2020. "The effects of immigration and skills on urban income inequality in New Zealand: two decomposition approaches," RF Berlin - CReAM Discussion Paper Series 2023, Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM).

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:sochwe:v:53:y:2019:i:2:d:10.1007_s00355-019-01183-9. 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.