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Decomposition of Rank-Dependent Measures of Inequality by Subgroups

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Rolf Aaberge, Steinar Bjerve and Kjell Doksum () (Statistics Norway)

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Abstract

The purpose of additive subgroup decomposition is to study the relationship between overall inequality and inequality within and between population subgroups defined by variables like gender, age, education and region of residence. As opposed to the inequality measures that are additively decomposable, the so-called generalized entropy family of inequality measures, the Gini coefficient does not admit decomposition into within- and between-group components but does also require an interaction (overlapping) term. The purpose of this paper is to introduce an alternative decomposition method that can be considered to be a parallel to Lerman and Yitzhaki’s (1985) elasticity approach for decomposing the Gini coefficient by income sources, which means that the elasticity of the Gini coefficient with respect to various income components is treated as the basic quantities of the decomposition method. Thus, rather than decomposing the Gini coefficient or any other inequality measure into a within-inequality term, a between-inequality term and eventually an interaction term, the basic quantities of the introduced method are the effects of marginal changes in variables that are used to specify the population subgroups

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Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 437.

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Date of creation: Oct 2005
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Handle: RePEc:ssb:dispap:437

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Keywords: The Gini coefficient; the Bonferroni coefficient; rank-dependent measures of inequality; decomposition by subgroups;

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  7. 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 107-15, February. [Downloadable!] (restricted)
  8. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November. [Downloadable!] (restricted)
  9. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April. [Downloadable!] (restricted)
  10. Porath Elchanan Ben & Gilboa Itzhak, 1994. "Linear Measures, the Gini Index, and The Income-Equality Trade-off," Journal of Economic Theory, Elsevier, vol. 64(2), pages 443-467, December. [Downloadable!] (restricted)
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  11. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November. [Downloadable!] (restricted)
  12. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-27, September. [Downloadable!] (restricted)
  13. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, Blackwell Publishing, vol. 37(3), pages 313-29, September.
  14. Lerman, Robert I & Yitzhaki, Shlomo, 1985. "Income Inequality Effects by Income," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 151-56, February. [Downloadable!] (restricted)
  15. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653. [Downloadable!] (restricted)
  16. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March. [Downloadable!] (restricted)
  17. 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. [Downloadable!]
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  18. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November. [Downloadable!] (restricted)
  19. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Mussard, Stéphane, 2007. "Between-Group Pigou-Dalton Transfers," IRISS Working Paper Series 2007-02, IRISS at CEPS/INSTEAD. [Downloadable!]
    Other versions:
  2. D'Angelo, Emanuela & Lilla, Marco, 2007. "Is there more than one linkage between Social Network and Inequality?," IRISS Working Paper Series 2007-12, IRISS at CEPS/INSTEAD. [Downloadable!]
  3. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Research Department of Statistics Norway. [Downloadable!]
  4. Paul Makdissi & Stéphane Mussard, 2006. "Decomposition of s-Concentration Curves," Cahiers de recherche 06-21, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke. [Downloadable!]
    Other versions:
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