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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Bibliographic InfoPaper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS366.
Length: 14 pages
Date of creation: 25 Jul 2002
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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
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- Giovanni Maria Giorgi, 2005. "A fresh look at the topical interest of the Gini concentration ratio," Econometrics 0511005, EconWPA.
- Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
- Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA.
- Amiel,Yoram & Cowell,Frank, 1999. "Thinking about Inequality," Cambridge Books, Cambridge University Press, number 9780521466967.
- 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.
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