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Scale-Invariant Measures of Segregation

  • David Frankel

    (Department of Economics, Iowa State University.)

  • Oscar Volij

    (Department of Economics, Ben-Gurion University.)

We characterize measures of school segregation for any number of ethnic groups using a set of purely ordinal axioms that includes Scale Invariance: a school district's segregation ranking should be invariant to changes that do not affect the distribution of ethnic groups across schools. The symmetric Atkinson index is the unique such measure that treats ethnic groups symmetrically and that ranks a district as weakly more segregated if either (a) one of its schools is subdivided or (b) its students in a subarea are moved around so as to weakly raise segregation in that subarea. If the requirement of symmetry is dropped, one obtains the general Atkinson index. The role of Scale Invariance is illustrated by studying segregation among U.S. public schools from 1987/8 to 2005/6, a period in which ethnic groups became distributed more similarly across schools. While the Atkinson indices declined sharply, most other indices either rose or declined only slightly.

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Paper provided by Oscar Volij in its series Economic theory and game theory with number 018.

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Date of creation: 18 Sep 2005
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Handle: RePEc:nid:ovolij:018
Contact details of provider: Postal: Oscar Volij, Department of Economics, Ben-Gurion University, Beer-Sheva 84105, Israel
Web page: http://volij.co.il/

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  1. David Card & Jesse Rothstein, 2005. "Racial Segregation and the Black-White Test Score Gap," Working Papers 879, Princeton University, Department of Economics, Industrial Relations Section..
  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. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
  4. 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.
  5. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
  6. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  7. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
  8. 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.
  9. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. Jonathan Guryan, 2001. "Desegregation and Black Dropout Rates," NBER Working Papers 8345, National Bureau of Economic Research, Inc.
  12. 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.
  13. Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers 12818, Iowa State University, Department of Economics.
  14. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  15. 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.
  16. Yannis M. Ioannides & Linda Datcher Loury, 2002. "Job Information Networks, Neighborhood Effects and Inequality," Discussion Papers Series, Department of Economics, Tufts University 0217, Department of Economics, Tufts University.
  17. 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.
  18. 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.
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