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Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View

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  • Ricardas Zitikis

    ()
    (Department of Statistical and Actuarial Sciences, The University of Western Ontario, AND Laboratory for Research in Statistics and Probability, Carleton University,)

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    Abstract

    A number of indices of economic inequality have been proposed in the literature. Their constructions are based on various econometric motives and justifications such as axioms of fairness. In this paper we analize the indices stepping slightly aside from their econometric meanings and adopting a mathematical approach that treats the indices as distances – in some functional spaces – between the egalitarian and actual Lorenz curves. More specifically, starting with, and being guided by, the econometric definitions of various indices, we modify the indices in such a way that the resulting ones become natural from the mathematical point of view. It turns out that some of the new “mathematical” indices coincide with the corresponding well known “econometric” ones, some appear to be only asymptotically equivalent, and some turn out to have different asymptotic behaviour when the sample size indefinitely increases.

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    File URL: http://www.repad.org/ca/on/lrsp/TRS366.pdf
    File Function: First version, 2002
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    Bibliographic Info

    Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS366.

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    Length: 14 pages
    Date of creation: 25 Jul 2002
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    Handle: RePEc:pqs:wpaper:0092005

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    Keywords: Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.;

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    1. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-28, October.
    2. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA.
    3. 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.
    4. Nygard, Fredrik & Sandstrom, Arne, 1989. "Income inequality measures based on sample surveys," Journal of Econometrics, Elsevier, vol. 42(1), pages 81-95, September.
    5. Amiel,Yoram & Cowell,Frank, 1999. "Thinking about Inequality," Cambridge Books, Cambridge University Press, number 9780521466967, April.
    6. Giovanni Maria Giorgi, 2005. "A fresh look at the topical interest of the Gini concentration ratio," Econometrics 0511005, EconWPA.
    7. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
    8. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
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