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On the Generalization and Decomposition of the Bonferroni Index

Listed author(s):
  • Elena Barcena-Martin and Jacques Silber

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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File URL: http://www3.qeh.ox.ac.uk/pdf/ophiwp/OPHIWP051.pdf
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Paper provided by Queen Elizabeth House, University of Oxford in its series OPHI Working Papers with number ophiwp051.

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Date of creation: Jun 2012
Handle: RePEc:qeh:ophiwp:ophiwp051
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  1. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
  2. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 183-196.
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  7. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
  8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  9. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
  10. Rolf Aaberge & Steinar Bjerve & Kjell Doksum, 2005. "Decomposition of rank-dependent measures of inequality by subgroups," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 493-503.
  11. Giovanni Maria Giorgi & Michele Crescenzi, 2001. "A proposal of poverty measures based on the Bonferroni inequality index," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 3-16.
  12. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  13. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  14. Satya Chakravarty, 2007. "A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 339-351, December.
  15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  16. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
  17. Giovanni Maria Giorgi, 2011. "Corrado Gini: the man and the scientist," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-28.
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