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The Marginal Effects in Subgroup Decomposition of the Gini Index

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  • Ogwang Tomson

    () (Brock University – Economics, 500 Glenridge Avenue St. Catharines Ontario L2S3A1, Canada.)

Abstract

In this article, we derive the elasticity of the Gini index with respect to changes in subgroup incomes for subgroups that are characterized by significant income separation. The resulting elasticity, which is structurally similar to that of the empirically popular Lerman and Yitzhaki’s (1985) elasticity for Gini income-source decomposition, entails easy and transparent computations. Some possible checks for income separation are described and an illustrative example using Canadian data is provided. The advantages of the proposed methodology over the Shapley value approach to Gini subgroup decomposition are stated.

Suggested Citation

  • Ogwang Tomson, 2016. "The Marginal Effects in Subgroup Decomposition of the Gini Index," Journal of Official Statistics, Sciendo, vol. 32(3), pages 733-745, September.
  • Handle: RePEc:vrs:offsta:v:32:y:2016:i:3:p:733-745:n:9
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    References listed on IDEAS

    as
    1. Stéphane Mussard & Patrick Richard, 2012. "Linking Yitzhaki's and Dagum's Gini decompositions," Applied Economics, Taylor & Francis Journals, vol. 44(23), pages 2997-3010, August.
    2. Ogwang Tomson, 2014. "A Convenient Method of Decomposing the Gini Index by Population Subgroups," Journal of Official Statistics, Sciendo, vol. 30(1), pages 91-105, March.
    3. Arthur Charpentier & Stéphane Mussard, 2011. "Income inequality games," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 529-554, December.
    4. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
    5. Mauro Mussini, 2013. "A matrix approach to the Gini index decomposition by subgroup and by income source," Applied Economics, Taylor & Francis Journals, vol. 45(17), pages 2457-2468, June.
    6. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.
    7. Stéphane Mussard & Luc Savard, 2012. "The Gini multi-decomposition and the role of Gini's transvariation: application to partial trade liberalization in the Philippines," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1235-1249, April.
    8. Stephane Mussard, 2004. "The bidimensional decomposition of the Gini ratio. A case study: Italy," Applied Economics Letters, Taylor & Francis Journals, vol. 11(8), pages 503-505.
    9. repec:oup:jafrec:v:9:y:2000:i:1:p:79-99. is not listed on IDEAS
    10. M Leibbrandt & C Woolard & I Woolard, 2000. "The contribution of income components to income inequality in the rural former homelands of South Africa: a decomposable Gini analysis," Journal of African Economies, Centre for the Study of African Economies (CSAE), vol. 9(1), pages 79-99.
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