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Measuring Segregation

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  • Oscar Volij
  • David Frankel

Abstract

We define a segregation ordering as a ranking of cities from most segregated to least segregated. \ We propose a set of basic properties that any reasonable segregation ordering should have. \ We then fully characterize the class of segregation orderings that satisfy these basic properties. \ We prove that every such ordering is representable by a segregation index that has a particular simple form. \ Finally, we show that with one rarely used exception, each index defined in the literature violates one or more of our basic properties.

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File URL: http://repec.org/esNASM04/up.24268.1075231745.pdf
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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 210.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:210

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Keywords: segregation; evenness; isolation; dissimilarity; axiomatic method;

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References

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  1. 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.
  2. David M. Cutler & Edward L. Glaeser, 1995. "Are Ghettos Good or Bad?," NBER Working Papers 5163, National Bureau of Economic Research, Inc.
  3. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  4. Clotfelter, Charles T., 1998. "Public School Segregation in Metropolitan Areas," Working Papers 98-12, Duke University, Department of Economics.
  5. David Frankel & Oscar Volij, 2005. "Measuring Segregation," Economic theory and game theory 017, Oscar Volij.
  6. 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..
  7. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
  8. 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.
  9. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  10. 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.
  11. 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.
  12. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
  19. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
  20. 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.
  21. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  22. 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.
  23. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
  24. 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.
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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. 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.
  3. 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.
  4. David Frankel & Oscar Volij, 2005. "Measuring Segregation," Economic theory and game theory 017, Oscar Volij.
  5. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
  6. 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.
  7. 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.
  8. Coral del Río & Olga Alonso-Villar, 2010. "Occupational segregation measures: A role for status," Working Papers 167, ECINEQ, Society for the Study of Economic Inequality.
  9. Federico Echenique & Roland G. Fryer Jr., 2005. "On the Measurement of Segregation," Labor and Demography 0503006, EconWPA.
  10. David Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij.
  11. 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.
  12. 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.

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