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Measuring Segregation

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Author Info
Frankel, David M.
Volij, Oscar

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Abstract

We propose a set of axioms for the measurement of school-based segregation with any number of ethnic groups. These axioms are motivated by two criteria. The first is evenness: how much do ethnic groups’ distributions across schools differ? The second is representativeness: how different are schools’ ethnic distributions from one another? We prove that a unique ordering satisfies our axioms. It is represented by an index that was originally proposed by Henri Theil (1971). This “Mutual Information Index” is related to Theil’s better known Entropy Index, which violates two of our axioms.

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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 12818.

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Length: 40 pages
Date of creation: 24 May 2007
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Handle: RePEc:isu:genres:12818

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Related research
Keywords: Segregation; indices; measurement; peer effects; schools; education; equal opportunity.;

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Find related papers by JEL classification:
R0 - Urban, Rural, and Regional Economics - - General

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ricardo Mora & Javier Ruiz-Castillo, 2004. "Gender segregation by occupations in the public and the private sector.The case of Spain," Investigaciones Economicas, Fundación SEPI, vol. 28(3), pages 399-428, September. [Downloadable!]
    Other versions:
  2. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July. [Downloadable!] (restricted)
  4. Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers 12902, Iowa State University, Department of Economics. [Downloadable!]
  5. Ricardo Mora & Javier Ruiz-Castillo, 2005. "The Axiomatic Properties Of An Entropy Based Index Of Segregation," Economics Working Papers we056231, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  6. Neus Herranza & Ricardo Mora & Javier Ruiz-Castillo, 2003. "An Algorithm To Reduce The Occupational Space In Gender Segregation Studies," Economics Working Papers we031402, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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  7. Eric A. Hanushek & John F. Kain & Steven G. Rivkin, 2002. "New Evidence about Brown v. Board of Education: The Complex Effects of School Racial Composition on Achievement," NBER Working Papers 8741, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. David Card & Jesse Rothstein, 2006. "Racial Segregation and the Black-White Test Score Gap," NBER Working Papers 12078, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. Ricardo Mora & Javier Ruiz-Castillo, 2003. "An Evaluation Of An Entropy Based Index Of Segregation," Economics Working Papers we034014, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  10. Victor R. Fuchs, 1975. "A Note on Sex Segregation in Professional Occupations," NBER Chapters, in: Explorations in Economic Research, Volume 2, number 1, pages 105-111 National Bureau of Economic Research, Inc. [Downloadable!]
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  13. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504. [Downloadable!] (restricted)
  14. Ricardo Mora & Javier Ruiz-Castillo, 2003. "Additively Decomposable Segregation Indexes. The Case Of Gender Segregation By Occupations And Human Capital Levels In Spain," Economics Working Papers we031503, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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  15. 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 426-71, July. [Downloadable!] (restricted)
  16. Cutler, David M & Glaeser, Edward L, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, MIT Press, vol. 112(3), pages 827-72, August.
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  17. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society. [Downloadable!]
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  18. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October. [Downloadable!] (restricted)
  19. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August. [Downloadable!] (restricted)
  20. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
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  21. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September. [Downloadable!] (restricted)
  22. Gregory B. Lewis, 1996. "Gender integration of occupations in the federal civil service: Extent and effects on male-female earnings," Industrial and Labor Relations Review, ILR Review, ILR School, Cornell University, vol. 49(3), pages 472-483, April.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. David Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij. [Downloadable!]
  2. Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers 12818, Iowa State University, Department of Economics. [Downloadable!]
    Other versions:
  3. Ricardo Mora & Javier Ruiz-Castillo, 2007. "The invariance properties of the Mutual Information index of multigroup segregation," Economics Working Papers we077544, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  4. David M. Frankel, 2004. "Was the Late 19th Century a Golden Age of Racial Integration?," Econometric Society 2004 North American Summer Meetings 167, Econometric Society. [Downloadable!]
  5. Federico Echenique & Roland G. Fryer, Jr., 2005. "On the Measurement of Segregation," NBER Working Papers 11258, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers 12902, Iowa State University, Department of Economics. [Downloadable!]
  7. Ricardo Mora & Javier Ruiz-Castillo, 2007. "The statistical properties of the Mutual Information index of multigroup segregation," Economics Working Papers we077443, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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