IDEAS home Printed from https://ideas.repec.org/p/nid/ovolij/018.html
   My bibliography  Save this paper

Scale-Invariant Measures of Segregation

Author

Listed:
  • David Frankel

    (Department of Economics, Iowa State University.)

  • Oscar Volij

    (Department of Economics, Ben-Gurion University.)

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 affect 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 Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij.
    • Handle: RePEc:nid:ovolij:018
    as

    Download full text from publisher

    File URL: http://volij.co.il/publications/papers/atkinsonFull.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    6. 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.
    7. 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.
    8. Jonathan Guryan, 2004. "Desegregation and Black Dropout Rates," American Economic Review, American Economic Association, vol. 94(4), pages 919-943, September.
    9. 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.
    10. Barbara S. Zoloth, 1976. "Alternative Measures of School Segregation," Land Economics, University of Wisconsin Press, vol. 52(3), pages 278-298.
    11. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
    12. Charles T. Clotfelter, 1999. "Public School Segregation in Metropolitan Areas," Land Economics, University of Wisconsin Press, vol. 75(4), pages 487-504.
    13. 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.
    14. Philipson Tomas, 1993. "Social Welfare and Measurement of Segregation," Journal of Economic Theory, Elsevier, vol. 60(2), pages 322-334, August.
    15. Caroline Hoxby, 2000. "Peer Effects in the Classroom: Learning from Gender and Race Variation," NBER Working Papers 7867, National Bureau of Economic Research, Inc.
    16. 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.
    17. 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.
    18. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Oscar Volij & David Frankel, 2004. "Measuring Segregation," Econometric Society 2004 North American Summer Meetings 210, Econometric Society.
    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. Tugce, Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," SIRE Discussion Papers 2013-49, Scottish Institute for Research in Economics (SIRE).
    4. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    5. Tugce Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," Discussion Paper Series, School of Economics and Finance 201308, School of Economics and Finance, University of St Andrews.
    6. 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.
    7. Olof Åslund & Per-Anders Edin & Peter Fredriksson & Hans Grönqvist, 2011. "Peers, Neighborhoods, and Immigrant Student Achievement: Evidence from a Placement Policy," American Economic Journal: Applied Economics, American Economic Association, vol. 3(2), pages 67-95, April.
    8. Federico Echenique & Roland G. Fryer Jr., 2005. "On the Measurement of Segregation," Labor and Demography 0503006, University Library of Munich, Germany.
    9. Robert Bifulco & Jason Fletcher & Stephen Ross, 2008. "The Effect of Classmate Characteristics on Individual Outcomes: Evidence from the Add Health," Working papers 2008-21, University of Connecticut, Department of Economics, revised Jan 2009.
    10. 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.
    11. Robert Bifulco & Delia Furtado & Stephen L. Ross, 2009. "Why Are Ghettos Bad? Examining the Role of the Metropolitan Educational Environment," Working papers 2009-30, University of Connecticut, Department of Economics.
    12. Roland G. Fryer, Jr, 2010. "The Importance of Segregation, Discrimination, Peer Dynamics, and Identity in Explaining Trends in the Racial Achievement Gap," NBER Working Papers 16257, National Bureau of Economic Research, Inc.
    13. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    14. Martin Nordin, 2013. "Immigrant School Segregation in Sweden," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 32(3), pages 415-435, June.
    15. Jacob L. Vigdor, 2006. "The New Promised Land: Black-White Convergence in the American South, 1960-2000," NBER Working Papers 12143, National Bureau of Economic Research, Inc.
    16. 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..
    17. Jacob Vigdor & Jens Ludwig, 2007. "Segregation and the Black-White Test Score Gap," NBER Working Papers 12988, National Bureau of Economic Research, Inc.
    18. Olof Åslund & Per-Anders Edin & Peter Fredriksson & Hans Grönqvist, 2011. "Peers, Neighborhoods, and Immigrant Student Achievement: Evidence from a Placement Policy," American Economic Journal: Applied Economics, American Economic Association, vol. 3(2), pages 67-95, April.
    19. Shen, Menghan, 2018. "How I met your mother: The effect of school desegregation on birth outcomes," Economics of Education Review, Elsevier, vol. 63(C), pages 31-50.
    20. Oscar Volij, 2018. "Segregation: theoretical approaches," Chapters, in: Conchita D’Ambrosio (ed.), Handbook of Research on Economic and Social Well-Being, chapter 21, pages 480-503, Edward Elgar Publishing.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nid:ovolij:018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oscar Volij (email available below). General contact details of provider: http://volij.co.il/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.