Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View
AbstractA 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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Length: 14 pages
Date of creation: 25 Jul 2002
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More information through EDIRC
Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
- 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.
- Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
- Amiel,Yoram & Cowell,Frank, 1999. "Thinking about Inequality," Cambridge Books, Cambridge University Press, number 9780521466967, October.
- 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.
- Nygard, Fredrik & Sandstrom, Arne, 1989. "Income inequality measures based on sample surveys," Journal of Econometrics, Elsevier, vol. 42(1), pages 81-95, September.
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