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On the Generalization and Decomposition of the Bonferroni Index

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  • Elena Barcena-Martin and Jacques Silber

Abstract

A simple algorithm is proposed which defines the Bonferroni index as the product of a row vector of individual population shares, a linear mathematical operator called the Bonferroni matrix and a column vector of income shares. This algorithm greatly simplifies the decomposition of the Bonferroni index by income sources or classes and population subgroups. The proposed algorithm also links the Bonferroni index to the concepts of relative deprivation and social welfare and leads to a generalization where the traditional Bonferroni and Gini indices are special cases. The paper ends with an empirical illustration based on EU-SILC data for the year 2008.

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  • Elena Barcena-Martin and Jacques Silber, 2012. "On the Generalization and Decomposition of the Bonferroni Index," OPHI Working Papers ophiwp051, Queen Elizabeth House, University of Oxford.
  • Handle: RePEc:qeh:ophiwp:ophiwp051
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    Cited by:

    1. Giovanni Maria Giorgi & Alessio Guandalini, 2013. "A sampling estimator of the Bonferroni inequality index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(3-4), pages 151-158, July-Dece.
    2. Giovanni Maria Giorgi & Alessio Guandalini, 2016. "Bonferroni Index Decomposition And The Shapley Method," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 70(4), pages 67-78, October-D.
    3. Elena Bárcena-Martin & Jacques Silber, 2017. "The Bonferroni index and the measurement of distributional change," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 1-16, April.

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