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On the Decomposition of the Esteban and Ray Index by Income Sources
Open AccessArticle

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

1
Department of Statistical Sciences, “Sapienza” University of Rome, Piazzale Aldo Moro 5, Rome 00185, Italy
2
Italian National Institute of Statistics—ISTAT, Via Cesare Balbo 16, Rome 00184, Italy
*
Author to whom correspondence should be addressed.
Econometrics 2018, 6(2), 18; https://doi.org/10.3390/econometrics6020018
Received: 11 December 2017 / Revised: 20 March 2018 / Accepted: 23 March 2018 / Published: 2 April 2018
(This article belongs to the Special Issue Econometrics and Income Inequality)
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. View Full-Text
Keywords: inequality measurement; Bonferroni index; Gini concentration ratio; decomposition methods; Shapley value; balance of inequality; complex survey data inequality measurement; Bonferroni index; Gini concentration ratio; decomposition methods; Shapley value; balance of inequality; complex survey data
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Giorgi, G.M.; Guandalini, A. Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality. Econometrics 2018, 6, 18.

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