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The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement

In: Research on Economic Inequality

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  • Gaston Yalonetzky
Abstract
The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster–Wolfson index. This study 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 study 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 a numerical example in which median-independent indices rank distributions according to the basic transfer axioms while median-dependent indices do not.

Suggested Citation

  • 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.
    • Handle: RePEc:eme:reinzz:s1049-258520170000025002
    DOI: 10.1108/S1049-258520170000025002
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    References listed on IDEAS

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    1. repec:ebl:ecbull:v:4:y:2007:i:36:p:1-6 is not listed on IDEAS
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. repec:bla:jpbect:v:2:y:2000:i:3:p:349-63 is not listed on IDEAS
    8. 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.
    9. 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.
    10. 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, March.
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    Cited by:

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    More about this item

    Keywords

    Relative bipolarisation; median; D30; D31;
    All these keywords.

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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