IDEAS home Printed from https://ideas.repec.org/p/pqs/wpaper/0092005.html
   My bibliography  Save this paper

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

Author

Listed:
  • Ricardas Zitikis

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

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.

Suggested Citation

  • Ricardas Zitikis, 2002. "Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View," RePAd Working Paper Series lrsp-TRS366, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0092005
    as

    Download full text from publisher

    File URL: http://www.repad.org/ca/on/lrsp/TRS366.pdf
    File Function: First version, 2002
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    2. Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
    3. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    4. 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 617-628, October.
    5. Nygard, Fredrik & Sandstrom, Arne, 1989. "Income inequality measures based on sample surveys," Journal of Econometrics, Elsevier, vol. 42(1), pages 81-95, September.
    6. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, University Library of Munich, Germany.
    7. Amiel,Yoram & Cowell,Frank, 1999. "Thinking about Inequality," Cambridge Books, Cambridge University Press, number 9780521466967.
    8. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    9. 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.
    10. Giovanni Maria Giorgi, 2005. "A fresh look at the topical interest of the Gini concentration ratio," Econometrics 0511005, University Library of Munich, Germany.
    11. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-156, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lachióze-Rey, Raphaël & Davydov, Youri, 2011. "Rearrangements of Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2606-2628, November.
    2. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.
    3. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.
    2. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    3. Christopher Bennett & Ričardas Zitikis, 2015. "Ignorance, lotteries, and measures of economic inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 13(2), pages 309-316, June.
    4. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    5. Walter Piesch, 2005. "A look at the structure of some extended Ginis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 263-296.
    6. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    7. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    8. Shlomo Yitzhaki & Edna Schechtman, 2005. "The properties of the extended Gini measures of variability and inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 401-433.
    9. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    10. Erreygers, Guido, 2009. "Can a single indicator measure both attainment and shortfall inequality?," Journal of Health Economics, Elsevier, vol. 28(4), pages 885-893, July.
    11. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    12. Satya R. Chakravarty, 2009. "Equity and efficiency as components of a social welfare function," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(2), pages 181-199, June.
    13. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    14. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    15. Edna Schechtman & Ricardas Zitikis, 2006. "Gini indices as areas and covariances: what is the difference between the two representations?," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 385-397.
    16. Giovanni Maria Giorgi & Paola Palmitesta & Corrado Provasi, 2006. "Asymptotic and bootstrap inference for the generalized Gini indices," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 107-124.
    17. Satya Chakravarty, 2007. "A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 339-351, December.
    18. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    19. Guido Erreygers & Roselinde Kessels, 2017. "Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality," IJERPH, MDPI, vol. 14(7), pages 1-23, June.
    20. Guido Erreygers & Roselinde Kessels & Linkun Chen & Philip Clarke, 2016. "Decomposing Socioeconomic Inequality of Health," EcoMod2016 9574, EcoMod.

    More about this item

    Keywords

    Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pqs:wpaper:0092005. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christian Calmes (email available below). General contact details of provider: https://edirc.repec.org/data/dsuqoca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.