IDEAS home Printed from https://ideas.repec.org/p/inq/inqwps/ecineq2017-445.html
   My bibliography  Save this paper

Some axiomatics of inequality measurement, with specific reference to intermediate indices

Author

Listed:
  • Manfred Krtscha

    (Karlsruher Institute of Technology, Germany)

Abstract

In this paper we consider properties for inequality measurement. A property that should be demanded for every inequality measure we call “axiom” otherwise we call it only “desideratum”. The most important new axiom (A6) and the desideratum “Cowell's Feature (CF)” are motivated carefully. (A6) is more restrictive than Zheng's (2007a) “unit consistency axiom” for partial inequality orderings, but it is not as restrictive as the overwhelmingly favoured “scale invariance” property. We will show that the combination of these two properties characterizes a type of differentiable inequality measure that the author had already introduced and characterized in 1994, but then with a stronger requirement. Since then, this measure has been widely employed in applied work because it has been perceived to possess some attractive properties. However, the aim of this paper is not only a better characterization of a single type of inequality measure, but also a numerical comparison of different “good” inequality measures that qualify under (A6). Our focus lies on the so-called intermediate measures, being a compromise between the scale invariant “relative inequality measures” and the translation invariant “absolute inequality measures”, where equal absolute changes in all incomes do not affect the inequality value. We present three methods to construct strictly intermediate or centrist inequality measures, which are explained with the help of three examples. Then we undertake a comparison of how these illustrative measures satisfy our axioms. Finally we give a complete summary table showing all the properties of these inequality measures. A last relevant example has been taken from true life.

Suggested Citation

  • Manfred Krtscha, 2017. "Some axiomatics of inequality measurement, with specific reference to intermediate indices," Working Papers 445, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2017-445
    as

    Download full text from publisher

    File URL: http://www.ecineq.org/milano/WP/ECINEQ2017-445.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    3. Subramanian, Subbu, 2011. "Inequality measurement with subgroup decomposability and level-sensitivity," Economics Discussion Papers 2011-7, Kiel Institute for the World Economy (IfW Kiel).
    4. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    5. S. Subramanian & D. Jayaraj, 2014. "Money-metric poverty, welfare, growth, and inequality in India: 1983 – 2011/12," Global Development Institute Working Paper Series 21114, GDI, The University of Manchester.
    6. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    7. Tateo Yoshida, 2005. "Social welfare rankings of income distributions A new parametric concept of intermediate inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 557-574, June.
    8. Subramanian, Subbu, 2011. "Inequality measurement with subgroup decomposability and level-sensitivity," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-18.
    9. Coral del RÎo & Javier Ruiz-Castillo, 2000. "Intermediate inequality and welfare," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 223-239.
    10. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 9(1), pages 119-161, December.
    11. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    12. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
    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. Subramanian S., 2017. "On Comprehensively Intermediate Measures of Inequality and Poverty, with an Illustrative Application to Global Data," Journal of Globalization and Development, De Gruyter, vol. 8(2), pages 1-18, December.
    2. D. Jayaraj & S. Subramanian, 2018. "The Distribution of Household Assets in India: 1991–1992 to 2012–2013," Indian Journal of Human Development, , vol. 12(2), pages 181-203, August.

    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. Coral Río & Olga Alonso-Villar, 2010. "New unit-consistent intermediate inequality indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 505-521, March.
    2. Francisco Azpitarte & Olga Alonso-Villar, 2012. "A Dominance Criterion for Measuring Income Inequality from a Centrist View: The Case of Australia," Melbourne Institute Working Paper Series wp2012n03, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    3. Claudio Zoli, 2018. "A Note on Progressive Taxation and Inequality Equivalence," Research on Economic Inequality, in: Inequality, Taxation and Intergenerational Transmission, volume 26, pages 15-33, Emerald Group Publishing Limited.
    4. D. Jayaraj & S. Sreenivasan, 2015. "Growth and inequality in the distribution of India's consumption expenditure: 1983 to 2009-10," WIDER Working Paper Series 025, World Institute for Development Economic Research (UNU-WIDER).
    5. Coral del Río & Olga Alonso-Villar, 2008. "Rankings of income distributions: a note on intermediate inequality indices," Research on Economic Inequality, in: Inequality and Opportunity: Papers from the Second ECINEQ Society Meeting, pages 213-229, Emerald Group Publishing Limited.
    6. Marko Ledić & Ivica Rubil & Ivica Urban, 2023. "Tax progressivity and social welfare with a continuum of inequality views," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 30(5), pages 1266-1296, October.
    7. 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.
    8. Ivica Urban, 2017. "Measuring income redistribution: beyond the proportionality standard," Working Papers 427, ECINEQ, Society for the Study of Economic Inequality.
    9. Francisco Azpitarte & Olga Alonso-Villar, 2011. "Ray-invariant intermediate inequality measures: A Lorenz dominance criterion," Working Papers 226, ECINEQ, Society for the Study of Economic Inequality.
    10. Anthony B. Atkinson & Andrea Brandolini, 2010. "On Analyzing the World Distribution of Income," The World Bank Economic Review, World Bank, vol. 24(1), pages 1-37, January.
    11. Subbu Subramanian, 2014. "Dividing a cake (or) Distributional values in the measurement of economic inequality: an expository note," The Journal of Philosophical Economics, Bucharest Academy of Economic Studies, The Journal of Philosophical Economics, vol. 7(2), May.
    12. Gustav Kjellsson & Ulf-G. Gerdtham, 2013. "Lost in Translation: Rethinking the Inequality Equivalence Criteria for Bounded Health Variables," Research on Economic Inequality, in: Health and Inequality, volume 21, pages 3-32, Emerald Group Publishing Limited.
    13. Paul Allanson & Dennis Petrie, 2014. "Understanding The Vertical Equity Judgements Underpinning Health Inequality Measures," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1390-1396, November.
    14. Casilda Lasso de la Vega & Christian Seidl, 2007. "The Impossibility of a Just Pigouvian," Working Papers 69, ECINEQ, Society for the Study of Economic Inequality.
    15. Satya Chakravarty & Swami Tyagarupananda, 2009. "The subgroup decomposable intermediate indices of inequality," Spanish Economic Review, Springer;Spanish Economic Association, vol. 11(2), pages 83-97, June.
    16. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    17. 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.
    18. Mornet, Pauline, 2016. "On the axiomatization of the weakly decomposable inequality indices," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 71-78.
    19. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(3), pages 253-277, December.
    20. 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.

    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:inq:inqwps:ecineq2017-445. 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: Maria Ana Lugo (email available below). General contact details of provider: https://edirc.repec.org/data/ecineea.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.