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On a new class of continuous indices of inequality

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  • Chan, Terence

Abstract

The Gini index is a well-known and long-established measure of inequality for distributions of income and other quantities. However, it has a number of mathematical disadvantages. Firstly, it is discontinuous with respect to all the main modes of convergence of probability measures. Secondly, it relies critically on the finiteness of the mean of the underlying distribution. Finally, even when the underlying distribution has a finite mean, estimation of the Gini index from data can be problematic if the variance of the underlying distribution is infinite. In this paper, we propose a class of inequality indices which are continuous with respect to setwise convergence of probability measures (and hence also with respect to convergence in total variation) and which do not require the underlying distribution to possess any finite moments whatsoever. Moreover, our class of inequality indices can be easily estimated from data and the standard methods of statistical inference can be applied to the estimators.

Suggested Citation

  • Chan, Terence, 2022. "On a new class of continuous indices of inequality," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 8-23.
    • Handle: RePEc:eee:matsoc:v:120:y:2022:i:c:p:8-23
    DOI: 10.1016/j.mathsocsci.2022.08.003
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    References listed on IDEAS

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    1. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    2. Fields, Gary S, 1993. "Inequality in Dual Economy Models," Economic Journal, Royal Economic Society, vol. 103(420), pages 1228-1235, September.
    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. repec:zbw:hohpro:325 is not listed on IDEAS
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    7. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    8. Jacka, S. D. & Roberts, G. O., 1997. "On strong forms of weak convergence," Stochastic Processes and their Applications, Elsevier, vol. 67(1), pages 41-53, April.
    9. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    10. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-156, February.
    11. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    12. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 89-111.
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    Keywords

    Gini index; Measures of inequality;

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