IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01802703.html
   My bibliography  Save this paper

Income inequality measurement: a fresh look at two old issues

Author

Listed:
  • Brice Magdalou

    (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

The literature on income inequality measurement is split into (1) the ethical approach, from which the Atkinson–Kolm–Sen and Kolm–Pollak classes of indices are derived, and (2) the axiomatic approach, which mainly leads to the generalised entropies. This paper shows how to rationalise, under utilitarianism, the generalised entropies as ethical indices. In this framework a generalised entropy index is consistent with the principle of transfers if and only if the underlying utility function is increasing. This unconventional interpretation explains the strange behaviour of the generalised entropies for some values of the inequality aversion parameter, as identified by Shorrocks (Econometrica 48:613–625, 1980). In that case, the underlying utility function is convex. Then, it provides a solution to escape the so-called Hansson–Sen paradox (Hansson in Foundational problems in the special sciences. Reidel Publishing Company, Dordrecht, 1977; Sen in Personal income distribution. North-Holland, Amsterdam, pp 81–94, 1978) that affects the standard ethical indices and which corresponds to a counterintuitive increase in inequality as a result of a concave transformation of the utility function. A normalised version of the generalised entropies behaves appropriately after such a transformation.

Suggested Citation

  • Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Post-Print hal-01802703, HAL.
    • Handle: RePEc:hal:journl:hal-01802703
    DOI: 10.1007/s00355-018-1121-9
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    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. Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.
    3. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    4. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    5. Bosmans, Kristof & Cowell, Frank A., 2010. "The class of absolute decomposable inequality measures," Economics Letters, Elsevier, vol. 109(3), pages 154-156, December.
    6. Lambert, Peter J. & Millimet, Daniel L. & Slottje, Daniel, 2003. "Inequality aversion and the natural rate of subjective inequality," Journal of Public Economics, Elsevier, vol. 87(5-6), pages 1061-1090, May.
    7. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    9. Anthony B. Atkinson & Andrea Brandolini, 2015. "Unveiling the Ethics behind Inequality Measurement: Dalton's Contribution to Economics," Economic Journal, Royal Economic Society, vol. 0(583), pages 209-234, March.
    10. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    11. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    12. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    13. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    14. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    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. 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.

    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. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
    2. Rodolfo Hoffmann & Diego Camargo Botassio, 2020. "Sensitivity of inequality measures considering regressive transfers with fixed relative income distance," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 279-296, December.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. Frank Cowell, 2005. "Theil, Inequality Indices and Decomposition," Working Papers 01, ECINEQ, Society for the Study of Economic Inequality.
    9. 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.
    10. 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.
    11. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    12. 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.
    13. Lasso de la Vega, Casilda & Aristondo, Oihana, 2012. "Proposing indicators to measure achievement and shortfall inequality consistently," Journal of Health Economics, Elsevier, vol. 31(4), pages 578-583.
    14. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    15. Stephen P. Jenkins & John Micklewright, 2007. "New Directions in the Analysis of Inequality and Poverty," Discussion Papers of DIW Berlin 700, DIW Berlin, German Institute for Economic Research.
    16. repec:wsr:wpaper:y:2010:i:062 is not listed on IDEAS
    17. Casilda Lasso de la Vega & Ana Urrutia, 2008. "The ‘Extended’ Atkinson family: The class of multiplicatively decomposable inequality measures, and some new graphical procedures for analysts," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 211-225, June.
    18. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    19. Satya R. Chakravarty & Amita Majumder & Sonali Roy, 2007. "A Treatment Of Absolute Indices Of Polarization," The Japanese Economic Review, Japanese Economic Association, vol. 58(2), pages 273-293, June.
    20. 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.
    21. Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.

    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:hal:journl:hal-01802703. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.