Advertisement

The Journal of Economic Inequality

, Volume 13, Issue 2, pp 275–297 | Cite as

Polarization measurement for ordinal data

  • Martyna Kobus
Article

Abstract

Atkinson’s Theorem (Atkinson J. Econ. Theory 2, 244–263, 1970) is a classic result in inequality measurement. It establishes Lorenz dominance as a useful criterion for comparative judgements of inequality between distributions. If distribution A Lorenz 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 Res. Econ. Inequal. 16, 177–188, 2008), such as self-reported health status or educational attainment. A new theory in development (Abul Naga and Yalcin J. Health Econ. 27(6), 1614–1625, 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 (J. Health Econ. 23(3), 505–524, 2004). We characterize classes of polarization measures equivalent to the AF relation analogously to Atkinson’s original approach.

Keywords

Polarization Inequality measurement Ordinal data Atkinson’s Theorem Dominance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allison, R.A., Foster, J.E.: Measuring health inequality using qualitative data. J. Health Econ. 23 (3), 505–524 (2004)CrossRefGoogle Scholar
  2. 2.
    Abul Naga, R.H., Yalcin, T.: Inequality measurement for ordered response health data. J. Health Econ. 27 (6), 1614–1625 (2008)CrossRefGoogle Scholar
  3. 3.
    Abul Naga, R.H., Yalcin, T.: Median Independent Inequality Orderings, University of Aberdeen Business School working paper series Vol 3, pp. 1–25 (2010)Google Scholar
  4. 4.
    Apouey, B.: Measuring health polarization with self-assessed health data. Health Econ. 16 (9), 875–894 (2007)CrossRefGoogle Scholar
  5. 5.
    Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory 2, 244–263 (1970)CrossRefGoogle Scholar
  6. 6.
    Berry, K.J., Mielke, P.W.: Indices of ordinal variation. Percept. Mot. Skills 74, 576–578 (1992)CrossRefGoogle Scholar
  7. 7.
    Blair, J., Lacy, M.G.: Statistics of ordinal variation. Sociol. Methods Res. 28 (251), 251–280 (2000)CrossRefGoogle Scholar
  8. 8.
    Blackburn, M., Bloom, D.: What is happening to the middle class. Am. Demogr. 7 (1), 19–25 (1985)Google Scholar
  9. 9.
    Dasgupta, P., Sen, A.K., Starret, D.: Notes on the measurement of inequality. J. Econ. Theory 6, 180–187 (1973)CrossRefGoogle Scholar
  10. 10.
    Diener, E., Lucas, R.E.: Personality and subjective well-being. In: Kahneman, D., Diener, E., chwarz, N. (eds.) (1999)Google Scholar
  11. 11.
    Esteban, J., Ray, D.: On the measurement of polarization. Econometrica 62, 819–852 (1994)CrossRefGoogle Scholar
  12. 12.
    Di Tella, R., McCulloch, R.: Some uses of happiness data in economics. J. Econ. Perspect. 20 (1), 25–46 (2006)CrossRefGoogle Scholar
  13. 13.
    Esteban, J., Ray, D.: Comparing polarization measures. In: Garfinkel, M.R., Skaperdas, S. (eds.) The Oxford Handbook of the Economics of Peace and Conflict, Chapter 7. Oxford University Press, New York (2012)Google Scholar
  14. 14.
    Foster, J., Wolfson, M.: Polarization and the decline of the middle class: Canada and the US. J. Econ. Inequal. 8(2), 247–273 (2010)Google Scholar
  15. 15.
    Frey, B.S., Stutzer, A.: Happiness and Economics. Princeton University Press, Princeton, NJ (2002)Google Scholar
  16. 16.
    Hemming, R., Keen, M.J.: Single-crossing conditions in comparisons of tax progressivity. J. Publ. Econ. 20, 373–380 (1983)CrossRefGoogle Scholar
  17. 17.
    Kahneman, D., Krueger, A.B.: Developments in the measurement of subjective wellbeing. J. Econ. Perspect. 22, 3–24 (2006)CrossRefGoogle Scholar
  18. 18.
    Kobus, M., Miłoś, P.: Inequality decomposition by population subgroups for ordinal data. J. Health Econ. 31, 15–21 (2012)CrossRefGoogle Scholar
  19. 19.
    Layard, R.: Happiness. Lessons from a New Science, London: Allen Lane (2005)Google Scholar
  20. 20.
    Leik, R.K.: A measure of ordinal consensus. Pac. Sociol. Rev. 9, 85–90 (1966)CrossRefGoogle Scholar
  21. 21.
    Levy, F., Murnane, R.J.: U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations. J. Econ. Lit. 30 (3), 1333–1381 (1992)Google Scholar
  22. 22.
    Oswald, A.J.: Happiness and economic performance. Econ. J. 107, 1815–1831 (1997)CrossRefGoogle Scholar
  23. 23.
    Parker, D.S., Ram, P.: Greed and majorization, Tech. Report. Department of Computer Science, University of California, Los Angeles (1997)Google Scholar
  24. 24.
    Shorrocks, A.F.: Inequality decomposition by population subgroups. Econometrica 52 (6), 1369–85 (1984)CrossRefGoogle Scholar
  25. 25.
    Tsui, K.Y.: Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation. Soc. Choice Welf. 16 (1), 145–157 (1999)CrossRefGoogle Scholar
  26. 26.
    Wang, Y.Q., Tsui, K.Y.: Polarization orderings and new classes of polarization indices. J. Publ. Econ. Theory 2, 349–363 (2000)CrossRefGoogle Scholar
  27. 27.
    Wolfson, M.C.: When inequalities diverge. Am. Econ. Rev. P&P 94, 353–358 (1994)Google Scholar
  28. 28.
    Wolfson, M.C.: Divergent inequalities: theory and empirical results. Rev. Income Wealth 43, 401–421 (1997)CrossRefGoogle Scholar
  29. 29.
    Zheng, B.: A new approach to measure socioeconomic inequality in health. J. Econ. Inequal. 9, 555–577 (2011)CrossRefGoogle Scholar
  30. 30.
    Zheng, B.: Measuring inequality with ordinal data: a note. Res. Econ. Inequal. 16, 177–188 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of EconomicsPolish Academy of SciencesWarsawPoland

Personalised recommendations