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The Bonferroni index and the measurement of distributional change

Author

Listed:
  • Elena Bárcena-Martin

    (Universidad de Málaga)

  • Jacques Silber

    (Bar-Ilan University
    CEPS/INSTEAD)

Abstract

This paper extends previous work that derived a matricial approach to the definition of the Bonferroni index. The present study is devoted to the decomposition of a change over time in the Bonferroni index into two components, one measuring re-ranking and the other the progressivity of income change. An extension is then proposed, based on a generalization of the Bonferroni index. The paper ends with an empirical illustration, based on the EU-SILC database, which analyzes the change in income inequality that was observed in 23 European countries between 2007 and 2010.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-016-0105-8
    DOI: 10.1007/s40300-016-0105-8
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    1. Stephen P. Jenkins & Philippe Van Kerm, 2006. "Trends in income inequality, pro-poor income growth, and income mobility," Oxford Economic Papers, Oxford University Press, vol. 58(3), pages 531-548, July.
    2. 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.
    3. Elena Bárcena-Martin & Jacques Silber, 2013. "On the generalization and decomposition of the Bonferroni index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 763-787, October.
    4. Giovanni Maria Giorgi & Alessio Guandalini, 2013. "A sampling estimator of the Bonferroni inequality index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(3-4), pages 151-158, July-Dece.
    5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    6. Frank A. Cowell, 1985. "Measures of Distributional Change: An Axiomatic Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 135-151.
    7. 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.
    8. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    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. Giovanni Maria Giorgi & Saralees Nadarajah, 2010. "Bonferroni and Gini indices for various parametric families of distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 23-46.
    11. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    12. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    13. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    14. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    15. Berrebi, Z. M. & Silber, Jacques, 1983. "On an absolute measure of distributional change," European Economic Review, Elsevier, vol. 22(2), pages 139-146, July.
    16. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    17. G. M. Giorgi & M. Crescenzi, 2001. "Bayesian estimation of the Bonferroni index from a Pareto-type I population," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 41-48, January.
    18. Oihana Aristondo & José Luis García-Lapres & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2012. "Classical inequality indices, welfare functions, and the dual decomposition," Working Papers 253, ECINEQ, Society for the Study of Economic Inequality.
    19. Giovanni Maria Giorgi & Michele Crescenzi, 2005. "A look at the Bonferroni inequality measure in a reliability framework," Econometrics 0507004, University Library of Munich, Germany.
    20. 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.
    21. 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.
    22. Giovanni Maria Giorgi & Riccardo Mondani, 2005. "Sampling distribution of the Bonferroni inequality index from exponential population," Econometrics 0507008, University Library of Munich, Germany.
    23. Jenkins, Stephen P. & Brandolini, Andrea & Micklewright, John & Nolan, Brian (ed.), 2012. "The Great Recession and the Distribution of Household Income," OUP Catalogue, Oxford University Press, number 9780199671021.
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    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.

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