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Measuring Segregation

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  • Frankel, David M.
  • Volij, Oscar

Abstract

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.

Suggested Citation

  • Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers Archive 12818, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genres:12818
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    2. Victor Ginsburgh & Shlomo Weber, 2016. "Linguistic Diversity, Standardization, and Disenfranchisement: Measurement and Consequences," ULB Institutional Repository 2013/277407, ULB -- Universite Libre de Bruxelles.
    3. Federico Echenique & Roland G. Fryer Jr., 2005. "On the Measurement of Segregation," Labor and Demography 0503006, University Library of Munich, Germany.
    4. Ricardo Mora & Javier Ruiz-Castillo, 2009. "The invariance properties of the mutual information index of multigroup segregation," Research on Economic Inequality, in: Occupational and Residential Segregation, pages 33-53, Emerald Group Publishing Limited.
    5. Frankel, David M. & Volij, Oscar, 2008. "An axiomatization of the multigroup Atkinson segregation indices," ISU General Staff Papers 200804140700001164, Iowa State University, Department of Economics.
    6. Victor Ginsburgh & Shlomo Weber, 2013. "Linguistic diversity, standardization and disenfranchisement. Measurement and consequences," ULB Institutional Repository 2013/152436, ULB -- Universite Libre de Bruxelles.
    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. 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. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. David Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij.
    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; measurement; schools; education; indices; peer effects; equal opportunity;
    All these keywords.

    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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