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On the Link between Silber and Dagum Decomposition of the Gini Index

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  • Mauro Mussini

Abstract

In this paper, we combine two alternative procedures for decomposing the Gini index: the Silber matrix approach and the Dagum technique based on Gini mean difference. This combined decomposition can be used for overlapping as well as no overlapping population subgroups. The presented decomposition procedure derives the within-group, the between-group, and the overlapping inequalities by exploiting all of the information on income distribution contained in one matrix accounting for pair wise disparities between per capita income shares. Moreover, this matrix approach can serve the scope of counting the frequency of overlapping, providing new insights for a more complete analysis of overlapping. The suggested methodology is applied to survey data on Italian employee incomes in 2000 and 2008.

Suggested Citation

  • Mauro Mussini, 2010. "On the Link between Silber and Dagum Decomposition of the Gini Index," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 11(3), pages 597-614, December.
    • Handle: RePEc:csb:stintr:v:11:y:2010:i:3:p:597-614
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    References listed on IDEAS

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    1. Achille VERNIZZI, 2009. "Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes," Departmental Working Papers 2009-50, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Achille VERNIZZI & Maria Giovanna MONTI & Mauro MUSSINI, 2010. "A Gini and concentration index decomposition with an application to the APK reranking measure," Departmental Working Papers 2010-10, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano, revised 13 Dec 2010.
    3. Berrebi, Z. M. & Silber, Jacques, 1987. "Regional differences and the components of growth and inequality change," Economics Letters, Elsevier, vol. 25(3), pages 295-298.
    4. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
    5. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    6. Frick, Joachim R. & Goebel, Jan & Schechtman, Edna & Wagner, Gert G. & Yitzhaki, Shlomo, 2006. "Using Analysis of Gini (ANOGI) for Detecting Whether Two Subsamples Represent the Same Universe: The German Socio-Economic Panel Study (SOEP) Experience," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 34(4), pages 427-468.
    7. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    8. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    9. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    10. Joachim R. Frick & Jan Goebel & Edna Schechtman & Gert G. Wagner & Shlomo Yitzhaki, 2006. "Using Analysis of Gini (ANOGI) for Detecting Whether Two Subsamples Represent the Same Universe," Sociological Methods & Research, , vol. 34(4), pages 427-468, May.
    11. repec:zbw:hohpro:325 is not listed on IDEAS
    12. Stephane Mussard, 2004. "The bidimensional decomposition of the Gini ratio. A case study: Italy," Applied Economics Letters, Taylor & Francis Journals, vol. 11(8), pages 503-505.
    13. Maria Monti & Alessandro Santoro, 2009. "A Note on Between-Group Inequality with an Application to Households," Journal of Income Distribution, Ad libros publications inc., vol. 18(3-4), pages 49-62, September.
    14. 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.
    15. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    16. Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
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