Skip to main content

Constructing indices of multivariate polarization

Abstract

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-economic inequality. For the latter, we employ the special inequality indices of Maasoumi (Econometrica 54:991–997, 1986), Tsui (J Econ Theory 67:251–265, 1995; Soc Choice Welf 16:145–157, 1999) and Koshevoy and Mosler (J Multivar Anal 60:252–276, 1997). Then, postulates for multidimensional polarization measurement are stated and discussed. The approach is illustrated by an empirical application to the population of the East and West Germany with polarization defined on income and education.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Atkinson, A., Bourguignon, F.: The comparison of multidimensional distributions of economic status. Rev. Econ. Stud. 49, 183–201 (1982)

    Article  Google Scholar 

  2. 2.

    Bhattacharya, N., Mahalanobis, B: Regional disparities in household consumption in India. J. Am. Stat. Assoc. 62, 143–161 (1967)

    Article  Google Scholar 

  3. 3.

    Blackorby, C., Donaldson, D., Auersperg, M.: A new procedure for the measurement of inequality within and among population subgroups. Can. J. Econ. 14, 665–685 (1981)

    Article  Google Scholar 

  4. 4.

    Bourguignon, F., Chakravarty, S.R.: The measurement of multidimensional poverty. J. Econ. Inequality 1, 25–49 (2003)

    Article  Google Scholar 

  5. 5.

    Chakravarty, S.R., Majumder, A.: Inequality, polarization and welfare: theory and applications. Aust. Econ. Pap. 40, 1–13 (2001)

    Article  Google Scholar 

  6. 6.

    Chakravarty, S.R., Weymark, J.A.: Axiomatizations of the entropy numbers equivalent index of industrial concentration. In: Eichhorn, W. (ed.) Measurement in economics, pp. 437–484. Kluwer, London (1988)

    Google Scholar 

  7. 7.

    D´Ambrosio, C.: Household characteristics and the distribution of income in Italy: an application of a social distance measures. Rev. Income Wealth 47, 43–64 (2001)

    Article  Google Scholar 

  8. 8.

    Davis, J., Huston, J.: The shrinking middle-income class: a multivariate analysis. East. Econ. J. 18, 277–285 (1992)

    Google Scholar 

  9. 9.

    Donaldson, D., Weymark, J.: A single-parameter generalization of the Gini indices of inequality. J. Econ. Theory 22, 67–86 (1980)

    Article  Google Scholar 

  10. 10.

    Duclos, J., Esteban, J., Ray, D.: Polarization: concepts, measurement, estimation. Econometrica 72, 1737–1772 (2004)

    Article  Google Scholar 

  11. 11.

    Esteban, J., Gradín, C., Ray, D.: An extension of a measure of polarization, with an application to the income distribution of five OECD countries. J. Econ. Inequality 5, 1–19 (2007)

    Article  Google Scholar 

  12. 12.

    Esteban, J., Ray, D.: On the measurement of polarization. Econometrica 62, 819–851 (1994)

    Article  Google Scholar 

  13. 13.

    Gradín, C.: Polarization by sub-populations in Spain, 1973–91. Rev. Income Wealth 46, 457–474 (2000)

    Article  Google Scholar 

  14. 14.

    Kolm, S.: Multidimensional egalitarianisms. Q. J. Econ. 91, 1–13 (1977)

    Article  Google Scholar 

  15. 15.

    Koshevoy, G., Mosler, K.: Multivariate Gini indices. J. Multivar. Anal. 60, 252–276 (1997)

    Article  Google Scholar 

  16. 16.

    Lasso de la Vega, M.C., Urrutia, A.M.: A new factorial decomposition for the Atkinson measure. Econ. Bull. 4, 1–12 (2003)

    Google Scholar 

  17. 17.

    Maasoumi, E.: The measurement and decomposition of multidimensional inequality. Econometrica 54, 991–997 (1986)

    Article  Google Scholar 

  18. 18.

    Maasoumi, E., Nickelsburg, G.: Multivariate measures of well-being and an analysis of inequality in the Michigan data. J. Bus. Econ. Stat. 6, 327–334 (1988)

    Article  Google Scholar 

  19. 19.

    Marshall, A., Olkin, I.: Inequalities: Theory of Majorization and its Applications. Academic, New York (1979)

    Google Scholar 

  20. 20.

    Milanovic, B.: A New Polarization Measure and Some Applications. Mimeo, Development Research Group, World Bank (2000)

  21. 21.

    Mosler, K.: Majorization in economic disparity measures. Linear Algebra Appl. 199, 91–114 (1994)

    Article  Google Scholar 

  22. 22.

    Rodríguez, J.G., Salas, R.: Extended bi-polarization and inequality measures. Res. Econ. Inequal. 9, 69–83 (2003)

    Article  Google Scholar 

  23. 23.

    Tsui, K.: Multidimensional generalizations of the relative and absolute inequality indices: the Atkinson-Kolm-Sen approach. J. Econ. Theory 67, 251–265 (1995)

    Article  Google Scholar 

  24. 24.

    Tsui, K.: Multidimensional inequality and multidimensional generalized entropy measures: an axiomatic derivation. Soc. Choice Welf. 16, 145–157 (1999)

    Article  Google Scholar 

  25. 25.

    Wang, Y., Tsui, K.: Polarization orderings and new classes of polarization indices. J. Public Econ. Theory 2, 349–363 (2000)

    Article  Google Scholar 

  26. 26.

    Wolfson, M.C.: When inequalities diverge. Am. Econ. Rev. 48, 353–358 (1994)

    Google Scholar 

  27. 27.

    Wolfson, M.C.: Divergent inequalities: theory and empirical results. Rev. Income Wealth 43, 401–421 (1997)

    Article  Google Scholar 

  28. 28.

    Zhang, X., Kanbur, R.: What difference do polarisation measures make? An application to China. J. Dev. Stud. 37, 85–98 (2001)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chiara Gigliarano.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gigliarano, C., Mosler, K. Constructing indices of multivariate polarization. J Econ Inequal 7, 435 (2009). https://doi.org/10.1007/s10888-008-9096-x

Download citation

Keywords

  • Polarization index
  • Decomposable inequality indices
  • Multidimensional inequality
  • Multivariate social evaluation

JEL Classifications

  • C43
  • D63