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Inequality Measures: The Kolkata index in comparison with other measures

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  • Suchismita Banerjee
  • Bikas K. Chakrabarti
  • Manipushpak Mitra
  • Suresh Mutuswami

Abstract

We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.

Suggested Citation

  • Suchismita Banerjee & Bikas K. Chakrabarti & Manipushpak Mitra & Suresh Mutuswami, 2020. "Inequality Measures: The Kolkata index in comparison with other measures," Papers 2005.08762, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:2005.08762
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    References listed on IDEAS

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    3. Chatterjee, Arnab & Ghosh, Asim & Chakrabarti, Bikas K., 2017. "Socio-economic inequality: Relationship between Gini and Kolkata indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 583-595.
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    1. Ghosh, Asim & Chakrabarti, Bikas K., 2021. "Limiting value of the Kolkata index for social inequality and a possible social constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    2. Manna, S.S. & Biswas, Soumyajyoti & Chakrabarti, Bikas K., 2022. "Near universal values of social inequality indices in self-organized critical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    3. Christopher W. Kulp & Michael Kurtz & Charles Hunt & Matthew Velardi, 2023. "The distribution of wealth: an agent-based approach to examine the effect of estate taxation, skill inheritance, and the Carnegie Effect," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(2), pages 397-415, April.
    4. Joseph, Bijin & Chakrabarti, Bikas K., 2022. "Variation of Gini and Kolkata indices with saving propensity in the Kinetic Exchange model of wealth distribution: An analytical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    5. Masato Okamoto, 2022. "Level-adjusted S-Gini index and its complementary index as a pair of sensitivity-adjustable inequality measures," Economics Bulletin, AccessEcon, vol. 42(1), pages 1-16.

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