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Decomposition of rank-dependent measures of inequality by subgroups

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  • Rolf Aaberge
  • Steinar Bjerve
  • Kjell Doksum

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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File URL: ftp://metron.sta.uniroma1.it/RePEc/articoli/si11.pdf
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Bibliographic Info

Article provided by Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome in its journal Metron.

Volume (Year): LXIII (2005)
Issue (Month): 3 ()
Pages: 493-503

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Handle: RePEc:mtn:ancoec:si11

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References

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  1. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
  2. 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.
  3. 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.
  4. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
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  8. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA.
  9. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-29, September.
  10. 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.
  11. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  12. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
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  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.
  15. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  16. 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.
  17. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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Citations

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Cited by:
  1. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2009. "Inference on counterfactual distributions," CeMMAP working papers CWP09/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Makdissi, Paul & Mussard, Stéphane, 2006. "Decomposition of s-Concentration Curves," IRISS Working Paper Series 2006-09, IRISS at CEPS/INSTEAD.
  3. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  4. 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.
  5. 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.
  6. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Research Department of Statistics Norway.

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