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On the Decomposition of the Gini Coefficient: an Exact Approach, with an Illustration Using Cameroonian Data


  • Abdelkrim Araar


Decomposing inequality indices across household groups or income sources is useful in estimating the contribution of each component to total inequality. This can help policy makers draw efficient policies to reduce disparities in the distribution of incomes using targeting tools. Decomposing relative inequality indices, such as the Gini coefficient, is not a simple procedure since, in many cases, the functional form of inequality indices is not additively separable in incomes. More importantly, for some of the indices on which this decomposition can be performed, the interpretation of the decomposition components is often not well founded. In this paper, we use the Shapley value as well as analytical approaches to perform the decomposition of the Gini coefficient and generalize it, in some cases, to the decomposition of other inequality indices. For the analytical approach, our aim is to extend the same interpretation, attributed to the Gini coefficient, to that of the contribution components.

Suggested Citation

  • Abdelkrim Araar, 2006. "On the Decomposition of the Gini Coefficient: an Exact Approach, with an Illustration Using Cameroonian Data," Cahiers de recherche 0602, CIRPEE.
  • Handle: RePEc:lvl:lacicr:0602

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    References listed on IDEAS

    1. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    2. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    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. Podder, Nripesh & Chatterjee, Srikanta, 2002. "Sharing the national cake in post reform New Zealand: income inequality trends in terms of income sources," Journal of Public Economics, Elsevier, vol. 86(1), pages 1-27, October.
    5. 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.
    6. 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.
    7. repec:ebl:ecbull:v:3:y:2003:i:19:p:1-16 is not listed on IDEAS
    8. Lerman, Robert I & Yitzhaki, Shlomo, 1985. "Income Inequality Effects by Income," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 151-156, February.
    9. John D. Hey & Peter J. Lambert, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 95(3), pages 567-573.
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    Cited by:

    1. Abdelkrim Araar & Jean-Yves Duclos, 2007. "Poverty and Inequality Components: a Micro Framework," Cahiers de recherche 0735, CIRPEE.
    2. H. Lehmann & M. G. Silvagni, 2013. "Is There Convergence of Russia’s Regions? Exploring the Empirical Evidence: 1995 – 2010," Working Papers wp901, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Mbu Daniel Tambi & Francis Menjo Baye, 2012. "The change in Inequality in the Distribution of Living Standards," EuroEconomica, Danubius University of Galati, issue 3(31), pages 97-111, August.
    4. Peter Lindner, 2015. "Factor decomposition of the wealth distribution in the euro area," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(2), pages 291-322, May.
    5. Abdelkrim Araar & Awoyemi Taiwo, 2006. "Poverty and Inequality Nexus: Illustrations with Nigerian Data," Economics Bulletin, AccessEcon, vol. 28(15), pages 1.
    6. repec:ebl:ecbull:eb-17-00446 is not listed on IDEAS
    7. Abdelkrim Araar, 2008. "On the Decomposition of Polarization Indices: Illustrations with Chinese and Nigerian Household Surveys," Cahiers de recherche 0806, CIRPEE.
    8. Nnaemeka Chukwuone & Ebele Amaechina & Sunday Emeka Enebeli-Uzor & Evelyn Iyoko & Benjamin Okpukpara, 2012. "Analysis of Impact of Remittance on Poverty in Nigeria," Working Papers PMMA 2012-09, PEP-PMMA.
    9. Jordi Teixidó-Figueras & Juan Duro, 2015. "International Ecological Footprint Inequality: A Methodological Review and Some Results," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(4), pages 607-631, April.
    10. Noglo, Yawo Agbenyegan, 2014. "Monetary inequality among households in Togo: An illustration based on the decomposition of the Gini coefficient using the Shapley value approach," WIDER Working Paper Series 151, World Institute for Development Economic Research (UNU-WIDER).

    More about this item


    Equity; Inequality; Decomposition; Shapley value;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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