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Scale-Invariant Measures of Segregation

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  • David M. Frankel

    ()
    (Iowa State University)

  • Oscar Volij

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

Abstract

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 a¤ect 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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Bibliographic Info

Paper provided by Ben-Gurion University of the Negev, Department of Economics in its series Working Papers with number 0814.

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Length: 47 pages
Date of creation: 2008
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Handle: RePEc:bgu:wpaper:0814

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  1. Yannis M. Ioannides & Linda Datcher Loury, 2004. "Job Information Networks, Neighborhood Effects, and Inequality," Journal of Economic Literature, American Economic Association, vol. 42(4), pages 1056-1093, December.
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  4. David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
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  7. 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..
  8. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
  9. 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.
  10. 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.
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  12. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  13. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  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. 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..
  16. Jonathan Guryan, 2004. "Desegregation and Black Dropout Rates," American Economic Review, American Economic Association, vol. 94(4), pages 919-943, September.
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