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.
Highlights
Carlo Emilio Bonferroni (1930) proposed the inequality index B as an alternative to the Gini indexR, referred to as the concentration ratio (Gini 1914)
For about half a century, B remained almost forgotten because it was ostracized by Corrado Gini and his followers, who tried to prevent any measures of inequality from overshadowing the concentration ratio R (Giorgi 1998)
We extend the balance of inequality” (BOI) to provide a decomposition of B
Summary
Carlo Emilio Bonferroni (1930) proposed the inequality index B as an alternative to the Gini index. In this field, two main lines of research can be distinguished: decomposition by income sources and by population subgroups. The reason lies in the difficulties we face when trying to additively decompose (as in the analysis of variance) inequality indices, including R and B. To overcome such a drawback when R is entailed, Deutsch and Silber (2007) used the so-called “Shapley value”, while. The paper is organized as follows: in Section 2, the main properties of Gini and Bonferroni indices are discussed. A brief overview on the inequality indices’ decomposition is given, while the so-called “Shapley method” and “balance of inequality” (BOI) are detailed in Sections 4 and 5, respectively.
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