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Measuring Segregation

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  • David M. Frankel

    ()
    (Iowa State University)

  • Oscar Volij

    ()
    (Dept. of Economics, Ben-Gurion University of the Negev, Israel ,Iowa State University)

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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Bibliographic Info

Paper provided by Ben-Gurion University of the Negev, Department of Economics in its series Working Papers with number 0703.

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Length: 41 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:bgu:wpaper:0703

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

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References

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  1. 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.
  2. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
  3. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
  4. 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.
  5. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
  6. 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, Cornell University, ILR School, vol. 49(3), pages 472-483, April.
  7. 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.
  8. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  9. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
  10. Ricardo Mora & Javier Ruiz-Castillo & Neus Herranz, 2005. "An algorithm to reduce the occupational space in gender segregation studies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 25-37.
  11. 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.
  12. 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.
  13. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  14. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 1997. "The Rise and Decline of the American Ghetto," NBER Working Papers 5881, National Bureau of Economic Research, Inc.
  15. Ricardo Mora & Javier Ruiz-Castillo, 2003. "Additively Decomposable Segregation Indexes. The Case of Gender Segregation by Occupations and Human Capital Levels in Spain," Journal of Economic Inequality, Springer, vol. 1(2), pages 147-179, August.
  16. 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.
  17. David Card & Jesse Rothstein, 2005. "Racial Segregation and the Black-White Test Score Gap," Working Papers 93, Princeton University, Department of Economics, Center for Economic Policy Studies..
  18. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  19. 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.
  20. 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.
  21. Michael Boozer & Alan 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..
  22. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  23. 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.
  24. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  25. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
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Citations

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Cited by:
  1. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
  2. Coral Río & Olga Alonso-Villar, 2010. "Gender Segregation in the Spanish Labor Market: An Alternative Approach," Social Indicators Research, Springer, vol. 98(2), pages 337-362, September.
  3. Federico Echenique & Roland G. Fryer, Jr., 2005. "On the Measurement of Segregation," NBER Working Papers 11258, National Bureau of Economic Research, Inc.
  4. Olga Alonso-Villar & Coral del Río, 2009. "Geographic Concentration of Economic Activity: An aggregate index," Working Papers 0901, Universidade de Vigo, Departamento de Economía Aplicada.
  5. Coral del Río & Olga Alonso-Villar, 2010. "Occupational segregation measures: A role for status," Working Papers 167, ECINEQ, Society for the Study of Economic Inequality.
  6. Olga Alonso-Villar & Coral del Río & Carlos Gradín, 2010. "The extent of occupational segregation in the US: Differences by race, ethnicity, and gender," Working Papers 180, ECINEQ, Society for the Study of Economic Inequality.
  7. 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.
  8. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
  9. Olga Alonso-Villar & Coral del Río, 2009. "Industrial segregation of female and male workers in Spain," Working Papers 0905, Universidade de Vigo, Departamento de Economía Aplicada.
  10. 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.
  11. 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.
  12. David M. Frankel & Oscar Volij, 2008. "Scale-Invariant Measures of Segregation," Working Papers 0814, Ben-Gurion University of the Negev, Department of Economics.

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