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Inequality Measurement and the Rich: Why inequality increased more than we thought

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  • Frank A Cowell
  • Emmanuel Flachaire

Abstract

Many standard inequality measures can be written as ratios with the mean in the denominator. When one income moves away from equality, both the numerator and the denominator may vary in the same direction and such indices may decrease. This anomalous behaviour is not shared by median-normalised inequality measures developed in this paper, where the mean at the denominator is replaced by the median. However, median-normalised inequality measures do not respect the principle of transfers. We show that the absolute Gini and the mean logarithmic deviation, or second Theil index, are the only measures that both avoid anomalous behaviour when one income is varied and also satisfy the principle of transfers. An application shows that the increase in inequality in the United States over recent decades is understated by the Gini index and that the mean logarithmic deviation index should be preferred in practice.

Suggested Citation

  • Frank A Cowell & Emmanuel Flachaire, 2018. "Inequality Measurement and the Rich: Why inequality increased more than we thought," STICERD - Public Economics Programme Discussion Papers 36, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stippp:36
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    References listed on IDEAS

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Richard Burkhauser & Shuaizhang Feng & Stephen Jenkins & Jeff Larrimore, 2009. "Recent Trends in Top Income Shares in the USA: Reconciling Estimates from March CPS and IRS Tax Return Data," Working Papers 09-26, Center for Economic Studies, U.S. Census Bureau.
    3. Frank A. Cowell & Emmanuel Flachaire, 2017. "Inequality with Ordinal Data," Economica, London School of Economics and Political Science, vol. 84(334), pages 290-321, April.
    4. Anthony Atkinson & Thomas Piketty, 2010. "Top Incomes : A Global Perspective," PSE-Ecole d'économie de Paris (Postprint) halshs-00754875, HAL.
    5. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    6. Atkinson, A. B. & Piketty, Thomas (ed.), 2010. "Top Incomes: A Global Perspective," OUP Catalogue, Oxford University Press, number 9780199286898.
    7. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins & Jeff Larrimore, 2012. "Recent Trends in Top Income Shares in the United States: Reconciling Estimates from March CPS and IRS Tax Return Data," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 371-388, May.
    8. Frank Cowell & Emmanuel Flachaire, 2021. "Inequality Measurement: Methods and Data," Post-Print hal-03589066, HAL.
    9. 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.
    10. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
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    Cited by:

    1. Satya R. Chakravarty & Palash Sarkar, 2023. "New perspectives on the Gini and Bonferroni indices of inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 47-64, January.
    2. Juan C Palomino & Gustavo A Marrero & Brian Nolan & Juan G Rodríguez, 2022. "Wealth inequality, intergenerational transfers, and family background [Intergenerational wealth mobility and the role of inheritance: Evidence from multiple generations]," Oxford Economic Papers, Oxford University Press, vol. 74(3), pages 643-670.
    3. Martin Ravallion, 2018. "What might explain today's conflicting narratives on global inequality?," WIDER Working Paper Series wp-2018-141, World Institute for Development Economic Research (UNU-WIDER).
    4. Arthur Charpentier & Emmanuel Flachaire, 2024. "Oaxaca-Blinder decomposition of changes in means and inequality: A simultaneous approach," Economics Bulletin, AccessEcon, vol. 44(1), pages 308-320.
    5. Marrero,Gustavo Alberto & Rodríguez,Juan Gabriel & Van Der Weide,Roy, 2021. "Does Race and Gender Inequality Impact Income Growth ?," Policy Research Working Paper Series 9865, The World Bank.
    6. Martin Ravallion & Shaohua Chen, 2022. "Is that really a Kuznets curve? Turning points for income inequality in China," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 749-776, December.
    7. Pablo Gutiérrez Cubillos, 2022. "Gini and undercoverage at the upper tail: a simple approximation," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 29(2), pages 443-471, April.
    8. Juan C. Palomino & Gustavo A. Marrero & Brian Nolan & Juan G. Rodriguez, 2020. "Wealth inequality, intergenerational transfers and socioeconomic background," Working Papers 537, ECINEQ, Society for the Study of Economic Inequality.
    9. Martin Ravallion, 2018. "What might explain today’s conflicting narratives on global inequality?," WIDER Working Paper Series 141, World Institute for Development Economic Research (UNU-WIDER).
    10. Leventi, Chrysa & Katsimi, Margarita & Tsakloglou, Panos, 2022. "Going regional: distributional effect of taxes and transfers in six EU countries and the UK," Centre for Microsimulation and Policy Analysis Working Paper Series CEMPA4/22, Centre for Microsimulation and Policy Analysis at the Institute for Social and Economic Research.
    11. Satya R. Chakravarty & Palash Sarkar, 2023. "Notes on the postulate of the monotonicity in distance in inequality," Bulletin of Economic Research, Wiley Blackwell, vol. 75(2), pages 312-322, April.

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    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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