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Measuring Segregation

  • Frankel, David M.
  • Volij, Oscar

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 32130.

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Date of creation: 16 Nov 2010
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Publication status: Forthcoming in Journal of Economic Theory
Handle: RePEc:isu:genres:32130
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Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070

Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
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  1. Ruiz-Castillo, Javier & Mora, Ricardo, 2005. "The axiomatic properties of an entropy based index of segregation," UC3M Working papers. Economics we056231, Universidad Carlos III de Madrid. Departamento de Economía.
  2. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
  3. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  4. 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.
  5. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
  6. 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.
  7. 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.
  8. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
  9. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  10. Gregory B. Lewis, 1996. "Gender Integration of Occupations in the Federal Civil Service: Extent and Effects on Male-Female Earnings," ILR Review, Cornell University, ILR School, vol. 49(3), pages 472-483, April.
  11. 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.
  12. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
  13. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
  14. Ruiz-Castillo, Javier & Mora, Ricardo & Herranz, Neus, 2003. "An algorithm to reduce the occupational space in gender segregation studies," UC3M Working papers. Economics we031402, Universidad Carlos III de Madrid. Departamento de Economía.
  15. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 441-485.
  16. 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, 07.
  17. 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.
  18. 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.
  19. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  20. 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.
  21. Ruiz-Castillo, Javier & Mora, Ricardo, 2003. "An evaluation of an entropy based index of segregation," UC3M Working papers. Economics we034014, Universidad Carlos III de Madrid. Departamento de Economía.
  22. 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.
  23. Charles T. Clotfelter, 1998. "Public School Segregation in Metropolitan Areas," NBER Working Papers 6779, National Bureau of Economic Research, Inc.
  24. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  25. 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.
  26. 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.
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