IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v83y2016icp71-78.html
   My bibliography  Save this article

On the axiomatization of the weakly decomposable inequality indices

Author

Listed:
  • Mornet, Pauline

Abstract

In this paper, we focus on a decomposition property recently introduced in the inequality literature and known as the weak decomposition. Such a property provides interesting analyses by allowing one to separate the within-group contribution to total inequality from the between-group contribution. A limitation of the current method of decomposition is that, depending on the structure–absolute, relative, compromise–of the inequality index, specific weights have to be used. To avoid such a problem, we propose a unique decomposition property where the weighting functions depend on the size of the population and the mean income. This allows us to characterize a large family of weakly decomposable inequality indices without any recourse to implicit invariance value judgments.

Suggested Citation

  • Mornet, Pauline, 2016. "On the axiomatization of the weakly decomposable inequality indices," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 71-78.
  • Handle: RePEc:eee:matsoc:v:83:y:2016:i:c:p:71-78
    DOI: 10.1016/j.mathsocsci.2016.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489616300555
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.mathsocsci.2016.07.004?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. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    2. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    3. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    4. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    5. repec:zbw:hohpro:325 is not listed on IDEAS
    6. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    7. Kristof Bosmans & Z. Emel Öztürk, 2018. "An axiomatic approach to the measurement of envy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 247-264, February.
    8. James E. Foster & Efe A. Ok, 1999. "Lorenz Dominance and the Variance of Logarithms," Econometrica, Econometric Society, vol. 67(4), pages 901-908, July.
    9. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    10. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    11. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    12. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-136, February.
    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. Christian Ahlin & Hyeok Jeong, 2021. "A conditional Gini: measure, estimation, and application," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(2), pages 363-384, June.
    2. Stéphane Mussard & Pauline Mornet, 2019. "A Note on α‐Gini Measures," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(3), pages 675-682, September.
    3. Arsen Palestini & Giuseppe Pignataro, 2023. "Inequality assessment in a dynamic framework with heterogenous agents," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 40(2), pages 469-494, July.

    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. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    2. Stéphane Mussard & Michel Terraza, 2009. "Décompositions des mesures d'inégalité : le cas des coefficients de Gini et d'entropie," Recherches économiques de Louvain, De Boeck Université, vol. 75(2), pages 151-181.
    3. Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    4. Mornet, Pauline & Zoli, Claudio & Mussard, Stéphane & Sadefo-Kamdem, Jules & Seyte, Françoise & Terraza, Michel, 2013. "The (α, β)-multi-level α-Gini decomposition with an illustration to income inequality in France in 2005," Economic Modelling, Elsevier, vol. 35(C), pages 944-963.
    5. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    6. Frank A Cowell, 2003. "Theil, Inequality and the Structure of Income Distribution," STICERD - Distributional Analysis Research Programme Papers 67, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Ebert U., 1996. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 57-58, February.
    8. Ebert, Udo, 1997. "Linear inequality concepts and social welfare," LSE Research Online Documents on Economics 6596, London School of Economics and Political Science, LSE Library.
    9. Satya R. Chakravarty & Nachiketa Chattopadhyay & Conchita D'Ambrosio, 2016. "On a Family of Achievement and Shortfall Inequality Indices," Health Economics, John Wiley & Sons, Ltd., vol. 25(12), pages 1503-1513, December.
    10. Berliant, Marcus & Strauss, Robert P., 2008. "Distributional analysis of prospective 2009 US individual income taxes: current law and the candidates’ tax plans," MPRA Paper 11221, University Library of Munich, Germany.
    11. 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.
    12. Frank Cowell, 2005. "Theil, Inequality Indices and Decomposition," Working Papers 01, ECINEQ, Society for the Study of Economic Inequality.
    13. Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    14. 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.
    15. Satya Chakravarty, 2001. "The Variance as a subgroup decomposable measure of inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 53(1), pages 79-95, January.
    16. Francesca Battisti & Francesco Porro, 2023. "A multi-decomposition of Zenga-84 inequality index: an application to the disparity in CO $$_2$$ 2 emissions in European countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 957-981, September.
    17. Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 415-435, October.
    18. Ballano, Carlos, 1992. "Searching by questionaire for the meaning of income inequality," UC3M Working papers. Economics 2889, Universidad Carlos III de Madrid. Departamento de Economía.
    19. Jordi Teixidó-Figueras & Juan Duro, 2015. "International Ecological Footprint Inequality: A Methodological Review and Some Results," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(4), pages 607-631, April.
    20. Buhong Zheng, 2007. "Unit-Consistent Poverty Indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 113-142, April.

    More about this item

    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:eee:matsoc:v:83:y:2016:i:c:p:71-78. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.