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On the measurement of polarization for ordinal data

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  • Martyna Kobus

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    (Institute of Economics, Polish Academy of Sciences)

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    Abstract

    Atkinson’s Theorem (Atkinson, 1970) is a classic result in inequality measurement. It establishes Lorenz dominance as a useful criterion for comparative judgements of inequality between distributions. If a Lorenz distribution A dominates distribution B, then all indices in a broad class of measures must confirm A as less unequal than B. Recent research, however, shows that standard inequality theory cannot be applied to ordinal data (Zheng, 2008), such as self-reported health status or educational attainment. A new theory in development (Apouey, 2007; Abul Naga and Yalcin, 2008) measures disparity of ordinal data as polarization. Typically a criterion used to compare distributions is the polarization relation as proposed by Allison and Foster (AF) (2004). We characterize classes of polarization measures equivalent to the AF relation analogously to Atkinson’s original approach.

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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2014-325.pdf
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    Bibliographic Info

    Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 325.

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    Length: 29 pages
    Date of creation: Mar 2014
    Date of revision:
    Handle: RePEc:inq:inqwps:ecineq2014-325

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    Keywords: Polarization; Inequality measurement; Ordinal data; Atkinson’s Theorem; Dominance.;

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    1. Oswald, A.J., 1997. "Happiness and Economic Performance," Papers 18, Centre for Economic Performance & Institute of Economics.
    2. Abul Naga, Ramses H. & Yalcin, Tarik, 2008. "Inequality measurement for ordered response health data," Journal of Health Economics, Elsevier, vol. 27(6), pages 1614-1625, December.
    3. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    4. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
    5. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," Journal of Economic Inequality, Springer, vol. 9(4), pages 555-577, December.
    6. Daniel Kahneman & Alan B. Krueger, 2006. "Developments in the Measurement of Subjective Well-Being," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 3-24, Winter.
    7. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    8. Esteban, J. & Ray, D., 1993. "On the Measurement of Polarization," UFAE and IAE Working Papers 221.93, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    9. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    10. Hemming, R. & Keen, M. J., 1983. "Single-crossing conditions in comparisons of tax progressivity," Journal of Public Economics, Elsevier, vol. 20(3), pages 373-380, April.
    11. 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 401-21, December.
    12. Levy, Frank & Murnane, Richard J, 1992. "U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations," Journal of Economic Literature, American Economic Association, vol. 30(3), pages 1333-81, September.
    13. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
    14. Martyna Kobus & Piotr Miłoś, 2011. "Inequality decomposition by population subgroups for ordinal data," Working Papers 2011-24, Faculty of Economic Sciences, University of Warsaw.
    15. 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 349-63.
    16. Rafael Di Tella & Robert MacCulloch, 2006. "Some Uses of Happiness Data in Economics," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 25-46, Winter.
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