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Measuring Segregation

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  • Frankel, David M.
  • Volij, Oscar

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

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

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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Keywords: Segregation; measurement; schools; education; indices; peer effects; equal opportunity;

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References

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  1. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
  2. Cutler, David & Vigdor, Jacob & Glaeser, Edward, 1999. "The Rise and Decline of the American Ghetto," Scholarly Articles 2770033, Harvard University Department of Economics.
  3. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
  4. 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.
  5. 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.
  6. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
  7. Michael A. Boozer & Alan B. Krueger & Shari Wolkon, 1992. "Race and School Quality Since Brown vs. Board of Education," NBER Working Papers 4109, National Bureau of Economic Research, Inc.
  8. David M. Cutler & Edward L. Glaeser, 1995. "Are Ghettos Good or Bad?," NBER Working Papers 5163, National Bureau of Economic Research, Inc.
  9. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
  10. 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.
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  12. Ricardo Mora & Javier Ruiz-Castillo, 2003. "Gender Segregation By Occupation In The Public And The Private Sector. The Case Of Spain," Economics Working Papers we031604, Universidad Carlos III, Departamento de Economía.
  13. 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.
  14. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
  15. 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.
  16. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  17. 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.
  18. 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.
  19. Card, David & Rothstein, Jesse, 2007. "Racial segregation and the black-white test score gap," Journal of Public Economics, Elsevier, vol. 91(11-12), pages 2158-2184, December.
  20. 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.
  21. 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.
  22. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  23. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  24. 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.
  25. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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Citations

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Cited by:
  1. Coral del Río & Olga Alonso-Villar, 2009. "Gender segregation in the Spanish labor market: An alternative approach," Working Papers 0904, Universidade de Vigo, Departamento de Economía Aplicada.
  2. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
  3. David M. Frankel & Oscar Volij, 2008. "Scale-Invariant Measures of Segregation," Working Papers 0814, Ben-Gurion University of the Negev, Department of Economics.
  4. Federico Echenique & Roland G. Fryer, Jr., 2005. "On the Measurement of Segregation," NBER Working Papers 11258, National Bureau of Economic Research, Inc.
  5. Coral del Río & Olga Alonso-Villar, 2011. "Occupational Segregation Measures: A Role for Status," Working Papers 1103, Universidade de Vigo, Departamento de Economía Aplicada.
  6. 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.
  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. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
  9. 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.
  10. 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.
  11. 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.
  12. 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.

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