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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.

Suggested Citation

  • David M. Frankel & Oscar Volij, 2008. "Scale-Invariant Measures of Segregation," Working Papers 0814, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:0814
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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. Matthew Gentzkow & Jesse M. Shapiro, 2011. "Ideological Segregation Online and Offline," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1799-1839.

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    More about this item

    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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