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A note on the decomposability of inequality measures

Author

Listed:
  • Frederic Chantreuil

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Sebastien Courtin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Kévin Fourrey

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Isabelle Lebon

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

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

  • Frederic Chantreuil & Sebastien Courtin & Kévin Fourrey & Isabelle Lebon, 2019. "A note on the decomposability of inequality measures," Post-Print halshs-02294331, HAL.
    • Handle: RePEc:hal:journl:halshs-02294331
    DOI: 10.1007/s00355-019-01183-9
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02294331
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    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. Frédéric Chantreuil & Alain Trannoy, 2011. "Inequality Decomposition Values," Annals of Economics and Statistics, GENES, issue 101-102, pages 13-36.
    4. 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.
    5. 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.
    6. 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.
    7. repec:adr:anecst:y:2011:i:101-102:p:02 is not listed on IDEAS
    8. 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.
    9. 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.
    10. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    11. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    12. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    13. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    14. 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.
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    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).

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    More about this item

    Keywords

    Interactions; Inequality decomposition; Shapley JEL Codes: C71; D63;
    All these keywords.

    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

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