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A Gini and concentration index decomposition with an application to the APK reranking measure

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  • Achille VERNIZZI
  • Maria Giovanna MONTI
  • Mauro MUSSINI

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:mil:wpdepa:2010-10
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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. Shujie Yao, 1999. "On the decomposition of Gini coefficients by population class and income source: a spreadsheet approach and application," Applied Economics, Taylor & Francis Journals, vol. 31(10), pages 1249-1264.
    3. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    4. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    5. Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
    6. 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.
    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 107-115, February.
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    Cited by:

    1. 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.
    2. Bin Shao, 2021. "Decomposition of the Gini index by income source for aggregated data and its applications," Computational Statistics, Springer, vol. 36(3), pages 2135-2159, September.
    3. repec:csb:stintr:v:12:y:2010:i:3:p:597-614 is not listed on IDEAS

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    More about this item

    Keywords

    Inequality measure decomposition; reranking; reranking effect decomposition;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies

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