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Lorenz Curves and Generalised Entropy Inequality Measures

In: Modeling Income Distributions and Lorenz Curves

Author

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  • Nicholas Rohde

    (The University of Queensland)

Abstract

Lorenz curves and Generalised Entropy (GE) measures are popular tools for analyzing income inequality. This paper seeks to connect these techniques by demonstrating that GE inequality measures may be derived directly from the Lorenz curve. The paper provides analytical expressions for Theil’s T and L inequality measures, half the square of the coefficient of variation and Atkinson’s utility based measure in terms of the Lorenz curve. Mathematical expressions for common GE measures are derived for three simple parametric specifications. The results are empirically illustrated and shown to be consistent with Lorenz dominance.

Suggested Citation

  • Nicholas Rohde, 2008. "Lorenz Curves and Generalised Entropy Inequality Measures," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 15, pages 271-283, Springer.
    • Handle: RePEc:spr:esichp:978-0-387-72796-7_15
    DOI: 10.1007/978-0-387-72796-7_15
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    Cited by:

    1. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    2. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Working Papers halshs-02320110, HAL.
    3. Muszyńska Joanna & Oczki Jarosław & Wędrowska Ewa, 2018. "Income Inequality in Poland and the United Kingdom. Decomposition of the Theil Index," Folia Oeconomica Stetinensia, Sciendo, vol. 18(1), pages 108-122, June.
    4. Vogel, Sebastian & Meyr, Herbert, 2015. "Decentral allocation planning in multi-stage customer hierarchies," European Journal of Operational Research, Elsevier, vol. 246(2), pages 462-470.
    5. Muszyńska Joanna & Wędrowska Ewa, 2018. "Income Inequality of Households in Poland: A Subgroup Decomposition of Generalized Entropy Measures," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 22(4), pages 43-64, December.

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