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On the Link Between the Concepts of Kurtosis and Bipolarization

Author

Listed:
  • Jacques SILBER

    (Bar-Ilan University)

  • Meital Hanoka

    (Bar-Ilan University (Ph.D. student))

  • Joseph Deutsch

    (Bar-Ilan University)

Abstract

In a paper on the measurement of the flatness of an income distribution Berrebi and Silber (1989) showed how it was possible to derive from the Gini index a measure of the degree of Kurtosis of a distribution whose definition made it quite similar to the more famous Pearson measure of Kurtosis. This note shows that it is possible to derive from the index of flatness proposed by Berrebi and Silber (1989) a measure of bipolarization that has all the important properties one would like a bipolarization index to have.

Suggested Citation

  • Jacques SILBER & Meital Hanoka & Joseph Deutsch, 2007. "On the Link Between the Concepts of Kurtosis and Bipolarization," Economics Bulletin, AccessEcon, vol. 4(36), pages 1-6.
    • Handle: RePEc:ebl:ecbull:eb-07d30002
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    References listed on IDEAS

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    1. Berrebi, Z. M. & Silber, Jacques, 1989. "Deprivation, the Gini index of inequality and the flatness of an income distribution," Mathematical Social Sciences, Elsevier, vol. 18(3), pages 229-237, December.
    2. Wang, You-Qiang & Tsui, Kai-Yuen, 2000. "Polarization Orderings and New Classes of Polarization Indices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(3), pages 349-363.
    3. Michael C. Wolfson, 1997. "Divergent Inequalities: Theory And Empirical Results," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 43(4), pages 401-421, December.
    4. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-358, May.
    5. Wolfson, Michael C, 1997. "Divergent Inequalities: Theory and Empirical Results," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 43(4), pages 401-421, December.
    6. Satya R. Chakravarty & Amita Majumder, 2001. "Inequality, Polarisation and Welfare: Theory and Applications," Australian Economic Papers, Wiley Blackwell, vol. 40(1), pages 1-13, March.
    7. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    8. You‐Qiang Wang & Kai‐Yuen Tsui, 2000. "Polarization Orderings and New Classes of Polarization Indices," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(3), pages 349-363, July.
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    Cited by:

    1. Ambra Poggi & Jacques Silber, 2010. "On Polarization And Mobility: A Look At Polarization In The Wage–Career Profile In Italy," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 123-140, March.
    2. Deutsch, Joseph & Fusco, Alessio & Silber, Jacques, 2013. "The BIP Trilogy (bipolarization, inequality and polarization): One saga but three different stories," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-33.
    3. Gaston Yalonetzky, 2017. "The Benchmark of Maximum Relative Bipolarisation," Research on Economic Inequality, in: Research on Economic Inequality, volume 25, pages 39-50, Emerald Group Publishing Limited.
    4. Bénédicte H. Apouey, 2010. "On Measuring And Explaining Socioeconomic Polarization In Health With An Application To French Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 141-170, March.
    5. Fabio Clementi & Francesco Schettino, 2013. "Income polarization in Brazil, 2001-2011: A distributional analysis using PNAD data," Economics Bulletin, AccessEcon, vol. 33(3), pages 1796-1815.
    6. F. Clementi & A. L. Dabalen & V. Molini & F. Schettino, 2017. "When the Centre Cannot Hold: Patterns of Polarization in Nigeria," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 608-632, December.
    7. Paul Makdissi & Stéphane Mussard, 2009. "Rank-Dependent Measures of Bi-Polarization and Marginal Tax Reforms," Working Papers 09-29, LAMETA, Universtiy of Montpellier, revised Dec 2009.
    8. Ma Casilda Lasso de la Vega & Ana Urrutia & Henar Díez, 2010. "Unit Consistency And Bipolarization Of Income Distributions," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 65-83, March.
    9. García-Fernández, Rosa María & Gottlieb, Daniel & Palacios-González, Frederico, 2013. "Polarization, growth and social policy in the case of Israel, 1997-2008," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-40.
    10. Masato Okamoto, 2022. "Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 548-574, November.
    11. Marek Kosny & Gaston Yalonetzky, 2016. "Relative p-bipolarisation measurement with generalised means and hybrid Lorenz curves," Working Papers 404, ECINEQ, Society for the Study of Economic Inequality.
    12. Schettino, Francesco & Gabriele, Alberto & Khan, Haider A., 2021. "Polarization and the middle class in China: A non-parametric evaluation using CHNS and CHIP data," Structural Change and Economic Dynamics, Elsevier, vol. 57(C), pages 251-264.
    13. Gaston Yalonetzky, 2013. "Relative bipolarization quasi-ordering based on Between-Group Gini (BGG) curves," Working Papers 318, ECINEQ, Society for the Study of Economic Inequality.
    14. Chiara Gigliarano & Daniel Nowak & Karl Mosler, 2019. "A Polarization Index for Overlapping Groups," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(4), pages 712-735, December.
    15. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    16. Gaston Yalonetzky, 2014. "Relative bipolarization Lorenz curve," Economics Bulletin, AccessEcon, vol. 34(2), pages 1103-1113.
    17. Gaston Yalonetzky, 2017. "The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement," Research on Economic Inequality, in: Research on Economic Inequality, volume 25, pages 51-62, Emerald Group Publishing Limited.
    18. Joseph Deutsch & Jacques Silber, 2010. "Income Polarization: Measurement, Determinants, And Implications," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 1-6, March.
    19. Tomson Ogwang, 2022. "The Foster–Greer–Thorbecke Poverty Measures Reveal More," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(3), pages 1481-1503, December.
    20. Satya Chakravarty & Bhargav Maharaj, 2012. "Ethnic polarization orderings and indices," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 99-123, May.

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