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Investigating equality: The Rényi spectrum

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  • Eliazar, Iddo

Abstract

An equality index is a score quantifying the socioeconomic egalitarianism of the distribution of wealth in human societies; the score takes values in the unit interval, with the unit upper bound characterizing purely communist societies. In this paper we explore the Rényi spectrum, a continuum of equality indices that: (i) is based on the moments of the societies’ distributions of wealth; (ii) unifies various measures of socioeconomic inequality, including the Theil and Atkinson indices; (iii) displays a collection of amicable analytic properties; (iv) admits multiple Rényi-divergence representations; and (v) provides a high-resolution gauging of egalitarianism that is way beyond what can be offered by the common-practice measures of socioeconomic inequality, the Gini and Pietra indices. At large, the Rényi spectrum is applicable in the context of any distribution of non-negative sizes with a positive mean—yielding a high-resolution gauging of the distribution’s inherent statistical heterogeneity.

Suggested Citation

  • Eliazar, Iddo, 2017. "Investigating equality: The Rényi spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 90-118.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:90-118
    DOI: 10.1016/j.physa.2017.04.003
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    References listed on IDEAS

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    1. François Bourguignon, 2015. "The Globalization of Inequality," Economics Books, Princeton University Press, edition 1, number 10433.
    2. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    3. Milanovic Branko & Roemer John E., 2016. "Interaction of Global and National Income Inequalities," Journal of Globalization and Development, De Gruyter, vol. 7(1), pages 109-115, June.
    4. Atkinson, Anthony B., 2015. "Inequality: what can be done?," LSE Research Online Documents on Economics 101810, London School of Economics and Political Science, LSE Library.
    5. repec:cup:cbooks:9781107013445 is not listed on IDEAS
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