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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 Archive 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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  1. 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.
  2. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  3. Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers 12818, Iowa State University, Department of Economics.
  4. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  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. 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.
  8. 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.
  9. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  10. 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.
  11. 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.
  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. 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.
  14. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, 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. 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.
  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. 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.
  19. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
  20. 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.
  21. 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.
  22. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
  23. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  24. 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.
  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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