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Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality

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  • Giovanni M. Giorgi

    (Department of Statistical Sciences, “Sapienza” University of Rome, Piazzale Aldo Moro 5, Rome 00185, Italy)

  • Alessio Guandalini

    (Italian National Institute of Statistics—ISTAT, Via Cesare Balbo 16, Rome 00184, Italy)

Abstract

Additive decomposability is an interesting feature of inequality indices which, however, is not always fulfilled; solutions to overcome such an issue have been given by Deutsch and Silber (2007) and by Di Maio and Landoni (2017). In this paper, we apply these methods, based on the “Shapley value” and the “balance of inequality” respectively, to the Bonferroni inequality index. We also discuss a comparison with the Gini concentration index and highlight interesting properties of the Bonferroni index.

Suggested Citation

  • Giovanni M. Giorgi & Alessio Guandalini, 2018. "Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality," Econometrics, MDPI, vol. 6(2), pages 1-16, April.
    • Handle: RePEc:gam:jecnmx:v:6:y:2018:i:2:p:18-:d:139284
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    Cited by:

    1. Hu, Xingwei, 2018. "A Dichotomous Analysis Of Unemployment Welfare," MPRA Paper 88662, University Library of Munich, Germany.
    2. 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.
    3. Alessio Guandalini & Claudio Ceccarelli, 2022. "Impact measurement and dimension reduction of auxiliary variables in calibration estimator using the Shapley decomposition," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 759-784, October.
    4. Xingwei Hu, 2018. "A Dichotomous Analysis of Unemployment Benefits," Papers 1808.08563, arXiv.org, revised Nov 2024.

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