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Generalised Income Inequality Index

Author

Listed:
  • Ziqing Dong
  • Yves Tille
  • Giovanni Maria Giorgi
  • Alessio Guandalini

Abstract

This paper proposes a deep generalisation for income inequality indices. A generalised income inequality index that depends on two parameters and that involves a large set of income inequality indices in the same framework is proposed. The two parameters control the sensitivity of the generalised index to different levels of the income distribution. A thorough investigation of the generalised index paves the way for understanding the influence of the low, middle and high incomes on various income inequality indices and thereby facilitates the choice of multiple indices simultaneously for a better analysis of inequality as advocated by several recent studies. Moreover, two methods for estimating the generalised index in the case of finite populations are shown. A new method for estimating the inequality indices is proposed.

Suggested Citation

  • Ziqing Dong & Yves Tille & Giovanni Maria Giorgi & Alessio Guandalini, 2024. "Generalised Income Inequality Index," International Statistical Review, International Statistical Institute, vol. 92(1), pages 87-105, April.
  • Handle: RePEc:bla:istatr:v:92:y:2024:i:1:p:87-105
    DOI: 10.1111/insr.12551
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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. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    3. Lars Osberg, 2017. "On the Limitations of Some Current Usages of the Gini Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(3), pages 574-584, September.
    4. Matti Langel & Yves Tillé, 2012. "Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1093-1110, November.
    5. Pundir, Sudesh & Arora, Sangeeta & Jain, Kanchan, 2005. "Bonferroni Curve and the related statistical inference," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 140-150, November.
    6. Thomas Piketty, 2015. "About Capital in the Twenty-First Century," American Economic Review, American Economic Association, vol. 105(5), pages 48-53, May.
    7. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    8. Giovanni Maria Giorgi & Alessio Guandalini, 2013. "A sampling estimator of the Bonferroni inequality index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(3-4), pages 151-158, July-Dece.
    9. Sandstrom, Arne & Wretman, Jan H & Walden, Bertil, 1988. "Variance Estimators of the Gini Coefficient--Probability Sampling," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 113-119, January.
    10. Koen Decancq & María Ana Lugo, 2012. "Inequality of Wellbeing: A Multidimensional Approach," Economica, London School of Economics and Political Science, vol. 79(316), pages 721-746, October.
    11. Shyamal K. De & Bhargab Chattopadhyay, 2017. "Minimum Risk Point Estimation of Gini Index," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 247-277, November.
    12. Giovanni Maria Giorgi & Chiara Gigliarano, 2017. "The Gini Concentration Index: A Review Of The Inference Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 31(4), pages 1130-1148, September.
    13. Matti Langel & Yves Tillé, 2013. "Variance estimation of the Gini index: revisiting a result several times published," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 521-540, February.
    14. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
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