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Measuring Segregation

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Author Info
Oscar Volij
David Frankel

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Abstract

We define a segregation ordering as a ranking of cities from most segregated to least segregated. \ We propose a set of basic properties that any reasonable segregation ordering should have. \ We then fully characterize the class of segregation orderings that satisfy these basic properties. \ We prove that every such ordering is representable by a segregation index that has a particular simple form. \ Finally, we show that with one rarely used exception, each index defined in the literature violates one or more of our basic properties.

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 210.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:210

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Related research
Keywords: segregation; evenness; isolation; dissimilarity; axiomatic method;

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Find related papers by JEL classification:
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Microeconomic Data
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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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!]
  11. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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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!]
    Other versions:
  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.
    Other versions:
  17. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society. [Downloadable!]
    Other versions:
  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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