IDEAS home Printed from https://ideas.repec.org/p/isu/genres/12818.html
   My bibliography  Save this paper

Measuring Segregation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www2.econ.iastate.edu/papers/p3868-2007-05-24.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. 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.
    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. 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.

    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. David Frankel & Oscar Volij, 2005. "Scale-Invariant Measures of Segregation," Economic theory and game theory 018, Oscar Volij.
    2. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    3. 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.
    4. Tugce, Cuhadaroglu, 2013. "My Group Beats Your Group: Evaluating Non-Income Inequalities," SIRE Discussion Papers 2013-49, Scottish Institute for Research in Economics (SIRE).
    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. 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.
    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 & 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.
    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. 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.
    12. 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.
    13. 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.
    14. repec:cte:werepe:we034014 is not listed on IDEAS
    15. 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.
    16. Luca Paolo Merlino & Max Friedrich Steinhardt & Wren-Lewis Liam, 2022. "The long run impact of childhood interracial contact on residential segregation," Working Papers halshs-03754124, HAL.
    17. Szulkin, Ryszard & Jonsson, Jan O., 2007. "Ethnic Segregation and Educational Outcomes in Swedish Comprehensive Schools," SULCIS Working Papers 2007:2, Stockholm University, Linnaeus Center for Integration Studies - SULCIS.
    18. Mele, Angelo, 2013. "Poisson indices of segregation," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 65-85.
    19. Xavier D'Haultfœuille & Roland Rathelot, 2017. "Measuring segregation on small units: A partial identification analysis," Quantitative Economics, Econometric Society, vol. 8(1), pages 39-73, March.
    20. Amine Ouazad & Romain Rancière, 2016. "Credit Standards and Segregation," The Review of Economics and Statistics, MIT Press, vol. 98(5), pages 880-896, December.
    21. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:isu:genres:12818. 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: Curtis Balmer (email available below). General contact details of provider: https://edirc.repec.org/data/deiasus.html .

    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.