A Gini and concentration index decomposition with an application to the APK reranking measure
In this paper, we suggest an alternative way to calculate the concentration index and a new matrix form approach, which can be applied both to the Gini and to the concentration index. For both indices, this approach yields expressions that are decomposable by groups and easily comparable. Our findings are illustrated by applying them to the Atkinson Plotnick Kakwani (APK) reranking measure. It is known that when a population is not homogeneous, the reranking measure can be decomposed following the suggestions of the conventional Gini index decomposition. We show that the reranking between groups and the reranking related with the overlapping term cannot be considered as measures of the tax system unfairness.
|Date of creation:||24 Apr 2010|
|Date of revision:||13 Dec 2010|
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- 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.
- Achille Vernizzi, 2009. "Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1085, Universitá degli Studi di Milano.
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- Maria Giovanna MONTI & Alessandro SANTORO, 2009. "The Gini decomposition: an alternative formulation with an application to tax reform," Departmental Working Papers 2009-30, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- 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.
- Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June. Full references (including those not matched with items on IDEAS)
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