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The necessary requirement of median independence for relative bipolarisation measurement

Listed author(s):
  • Gaston Yalonetzky

    ()

    (University of Leeds, U.K.)

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    The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster-Wolfson index. This note shows that the use of the median in the design and computation of relative bipolarisation indices is both unnecessary and problematic. It is unnecessary because we can rely on existing well-behaved, median-independent indices. It is problematic because, as the note shows, median-dependent indices violate the basic transfer axioms of bipolarisation (defining spread and clustering properties), except when the median is unaffected by the transfers. The convenience of discarding the median from index computations is further illustrated with the proposal of a corrected, median-independent version of the Foster-Wolfson index which always fulfills the basic transfer axioms.

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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2016-420.pdf
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    Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 420.

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    Length: 11 pages
    Date of creation: Nov 2016
    Handle: RePEc:inq:inqwps:ecineq2016-420
    Contact details of provider: Web page: http://www.ecineq.org
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    1. 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.
    2. repec:ebl:ecbull:v:4:y:2007:i:36:p:1-6 is not listed on IDEAS
    3. Walter Bossert & William Schworm, 2008. "A Class of Two-Group Polarization Measures," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1169-1187, December.
    4. 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.
    5. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    6. 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.
    7. Satya R. Chakravarty & Conchita D'Ambrosio, 2010. "Polarization Orderings Of Income Distributions," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 47-64, 03.
    8. James Foster & Michael Wolfson, 2010. "Polarization and the decline of the middle class: Canada and the U.S," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 247-273, June.
    9. M-super-a 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, 03.
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