Skip to main content

An Extension of a Measure of Polarization, with an application to the income distribution of five OECD countries


We introduce an extension of the Esteban and Ray [Econometrica, 62:819–851 1994] measure of polarization that can be applied to density functions. As a by-product we also derive the Wolfson [Am. Econ. Rev., 84:353–358 1994] measure as a special case. This derivation has the virtue of casting both measures in the context of a (statistically) unified framework. We study the polarization of the distribution of household income for five OECD countries (LIS database): US, UK, Canada, Germany and Sweden.

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


  1. Anderson, G.: Toward an empirical analysis of polarization. J. Econ. 122, 1–26 (2004)

    Google Scholar 

  2. Anderson, G.: “Polarization”, mimeo, Department of Economics, University of Toronto (2005)

  3. Aghevli, B.B., Mehran, F.: Optimal grouping of income distribution data. J. Am. Stat. Assoc. 76, 22–26 (1981)

    Article  Google Scholar 

  4. Chakravarty, S., Majumder, A.: Inequality, polarization and welfare: Theory and applications. Aust. Econ. Papers 40, 1–13 (2001)

    Article  Google Scholar 

  5. Chakravarty, S., Majumder, A., Roy, S.: A treatment of absolute indices of polarization. Mimeo, forthcoming in The Japanese Economic Review (2002)

  6. Davies, J.B., Shorrocks, A.F.: Optimal grouping of income and wealth data. J. Econ. 42, 97–108 (1989)

    Google Scholar 

  7. Duclos, J-Y., Esteban, J., Ray, D.: Polarization: Concepts, measurement, estimation. Econometrica 72, 1737–1772 (2004), reprinted in Christopher Barrett (ed.) The Social Economics of Poverty: On Identities, Groups, Communities, and Networks. Routledge, London (2005)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Esteban, J., Gradín, C., Ray, D.: Extensions of a Measure of Polarization, with an Application to the Income Distributions of Five OECD Countries. Working Paper 24, Instituto de Estudios Económicos de Galicia-P. Barrié de la Maza, A Coruña, Spain. Also in: Luxembourg Income Study (LIS) Working Paper Series, 218, Maxwell School of Citizenship and Public Affairs, Syracuse University, Syracuse, New York (1999)

  10. Gradín, C.: Polarization by sub-populations in Spain, 1973–91. Rev. Income Wealth 46(4), 457–474 (2000)

    Article  Google Scholar 

  11. Love, R., Wolfson, M.C.: Income Inequality: Statistical Methodology and Canadian Illustrations, Catalogue 13–559 Occasional. Ottawa, Statistics Canada (1976)

  12. Montalvo, J., Reynal-Querol, M.: Ethnic polarization, potential conflict, and civil wars. Am. Econ. Rev. 95, 796–816 (2005)

    Article  Google Scholar 

  13. Reynal-Querol, M.: Ethnicity, political systems, and civil wars. J. Confl. Resolut. 46, 29–54 (2002)

    Article  Google Scholar 

  14. Salas, R., Rodríguez, J.G.: Extended bi-polarization and inequality measures. Res. Econ. Inequal. 9, 69–83 (2002)

    Google Scholar 

  15. Wang, Y., Tsui, K.: Polarization orderings and new classes of polarization indices. J. Public Econ. Theory 2(3), 349–363 (2000)

    Article  Google Scholar 

  16. Wolfson, M.C.: When inequalities diverge. Am. Econ. Rev. 84, Papers and Proceedings, 353–358 (1994)

  17. Zhang, X., Kanbur, R.: What difference do polarization measures make? An application to China. J. Dev. Stud. 37(3), 85–98 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Joan Esteban.

Additional information

The present paper is essentially based on Esteban, Gradín and Ray [9], published as #218 in the working papers series of the Luxembourg Income Study. Changes have been kept to a minimum. We have provided a brief reference to the literature on polarization measurement that has appeared since then and have updated the data of our application.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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 Inequal 5, 1–19 (2007).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words

JEL classification