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Measuring Segregation

Author

Listed:
  • David Frankel

    (Department of Economics, Iowa State University.)

  • Oscar Volij

    (Department of Economics, Ben-Gurion University.)

Abstract

We propose a set of axioms for the measurement of multigroup school segregation. They are motivated by two criteria: do ethnic groups have similar distributions across schools? And are schools ethnically representative of their district? Our axioms are satisfied by a unique ordering. It is represented by the Mutual Information index. This index, originally proposed by Henri Theil, has a more intuitive decomposition than other indices. As an application, we find that segregation between districts within cities accounts for 33% of school segregation. Segregation across states, driven mainly by the distinct residential patterns of Hispanics, contributes another 32%.

Suggested Citation

  • David Frankel & Oscar Volij, 2005. "Measuring Segregation," Economic theory and game theory 017, Oscar Volij.
    • Handle: RePEc:nid:ovolij:017
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    References listed on IDEAS

    as
    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    2. 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.
    3. Charles T. Clotfelter, 1978. "Alternative Measures of School Desegregation: A Methodological Note," Land Economics, University of Wisconsin Press, vol. 54(3), pages 373-380.
    4. 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, July.
    5. James Sakoda, 1981. "A generalized index of dissimilarity," Demography, Springer;Population Association of America (PAA), vol. 18(2), pages 245-250, May.
    6. Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers Archive 12902, Iowa State University, Department of Economics.
    7. Neus Herranz & Ricardo Mora & Javier Ruiz‐Castillo, 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, January.
    8. 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 426-471, July.
    9. 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.
    10. Ricardo Mora & Javier Ruiz-Castillo, 2003. "Additively Decomposable Segregation Indexes. The Case of Gender Segregation by Occupations and Human Capital Levels in Spain," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(2), pages 147-179, August.
    11. 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.
    12. Michael A. Boozer & Alan B. Kreuger & Shari Wolkon, 1992. "Race and School Quality Since Brown v. Board of Education," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(1992 Micr), pages 269-338.
    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. repec:cte:werepe:we031503 is not listed on IDEAS
    15. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
    16. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
    17. 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.
    18. repec:cte:werepe:we056231 is not listed on IDEAS
    19. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    20. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
    21. 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.
    22. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
    23. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
    24. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    25. David M. Cutler & Edward L. Glaeser, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(3), pages 827-872.
    26. repec:cte:werepe:we034014 is not listed on IDEAS
    27. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    Cited by:

    1. Federico Echenique & Roland G. Fryer Jr., 2005. "On the Measurement of Segregation," Labor and Demography 0503006, University Library of Munich, Germany.
    2. Frankel, David M. & Volij, Oscar, 2008. "An Axiomatization of the Multigroup Atkinson Segregation Indices," Staff General Research Papers Archive 12902, Iowa State University, Department of Economics.
    3. 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.
    4. Pancs, Romans & Vriend, Nicolaas J., 2007. "Schelling's spatial proximity model of segregation revisited," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 1-24, February.
    5. 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.
    6. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    7. Coral Río & Olga Alonso-Villar, 2010. "Gender Segregation in the Spanish Labor Market: An Alternative Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 98(2), pages 337-362, September.
    8. repec:cte:werepe:we077544 is not listed on IDEAS
    9. David Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij.
    10. Victor Ginsburgh & Shlomo Weber, 2016. "Linguistic Diversity, Standardization, and Disenfranchisement: Measurement and Consequences," ULB Institutional Repository 2013/277407, ULB -- Universite Libre de Bruxelles.
    11. Victor Ginsburgh & Shlomo Weber, 2013. "Linguistic diversity, standardization and disenfranchisement. Measurement and consequences," ULB Institutional Repository 2013/152436, ULB -- Universite Libre de Bruxelles.
    12. Stepinski, Tomasz & Dmowska, Anna, 2019. "Imperfect melting pot – analysis of changes in diversity and segregation of US urban census tracts in the period of 1990-2010," SocArXiv uqj8x, Center for Open Science.
    13. 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.
    14. 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.
    15. 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.
    16. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.

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    More about this item

    Keywords

    Segregation; segregation indices.;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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