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An Axiomatization of the Multigroup Atkinson Segregation Indices

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  • Frankel, David M.
  • Volij, Oscar

Abstract

This paper gives an axiomatic characterization of the multigroup Atkinson indices of segregation relying entirely on ordinal axioms. We show that the Symmetric Atkinson index represents the unique ordering that treats ethnic groups symmetrically, that is invariant to population growth rates that differ among ethnic groups, that regards school districts as more segregated when schools in them are subdivided (unless the new schools have the exact same ethnic distribution), and that satisfy an independence property. If symmetry among ethnic groups is dropped, one obtains the family of orderings that are represented by the Asymmetric Atkinson indices. The latter result requires the addition of a continuity axiom.

Suggested Citation

  • Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers Archive 12902, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:12902
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    File URL: http://www2.econ.iastate.edu/papers/p3879-2008-04-14.pdf
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    References listed on IDEAS

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    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Eric A. Hanushek & John F. Kain & Steven G. Rivkin, 2009. "New Evidence about Brown v. Board of Education: The Complex Effects of School Racial Composition on Achievement," Journal of Labor Economics, University of Chicago Press, vol. 27(3), pages 349-383, July.
    4. Federico Echenique & Roland G. Fryer Jr., 2005. "On the Measurement of Segregation," Labor and Demography 0503006, EconWPA.
    5. Macpherson, David A & Hirsch, Barry T, 1995. "Wages and Gender Composition: Why Do Women's Jobs Pay Less?," Journal of Labor Economics, University of Chicago Press, vol. 13(3), pages 426-471, July.
    6. Michael A. Boozer & Alan B. Krueger & Shari Wolkon, 1992. "Race and School Quality Since Brown vs. Board of Education," Working Papers 681, Princeton University, Department of Economics, Industrial Relations Section..
    7. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 1999. "The Rise and Decline of the American Ghetto," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 455-506, June.
    8. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
    9. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
    10. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
    11. David M. Cutler & Edward L. Glaeser, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, Oxford University Press, vol. 112(3), pages 827-872.
    12. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    13. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
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    Cited by:

    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.

    More about this item

    Keywords

    education; Segregation; schools; diversity;

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General

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