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More Reliable Inference for Segregation Indices

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Author Info

  • Rebecca Allen
  • Simon Burgess
  • Frank Windmeijer

    ()

Abstract

The most widely used measure of segregation is the dissimilarity index, D. It is now well understood that this measure also reflects randomness in the allocation of individuals to units; that is, it measures deviations from evenness not deviations from randomness. This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce an adjustment to the index, based on an underlying statistical model. We specify the assignment problem in a very general way, with differences in conditional assignment probabilities underlying the resulting segregation. From this we derive a likelihood ratio test for the presence of any systematic segregation and a bootstrap bias adjustment to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that use of bootstrap methods can improve the size and power properties of test procedures considerably. We illustrate these methods by comparing dissimilarity indices across school districts in England to measure social segregation.

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File URL: http://www.bristol.ac.uk/cmpo/publications/papers/2009/wp216.pdf
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Bibliographic Info

Paper provided by Department of Economics, University of Bristol, UK in its series The Centre for Market and Public Organisation with number 09/216.

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Length: 27 pages
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:bri:cmpowp:09/216

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Related research

Keywords: segregation; dissimilarity index; bootstrap methods; hypothesis testing;

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References

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  1. Judith Hellerstein & David Neumark, 2007. "Workplace Segregation in the United States: Race, Ethnicity, and Skill," Working Papers 07-02, Center for Economic Studies, U.S. Census Bureau.
  2. Rebecca Allen & Anna Vignoles, 2006. "What Should an Index of School Segregation Measure?," CEE Discussion Papers 0060, Centre for the Economics of Education, LSE.
  3. Carrington, William J & Troske, Kenneth R, 1997. "On Measuring Segregation in Samples with Small Units," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 402-09, October.
  4. Silber, Jacques, 1992. "Occupational Segregation Indices in the Multidimensional Case: A Note," The Economic Record, The Economic Society of Australia, vol. 68(202), pages 276-77, September.
  5. Ricardo Mora & Javier Ruiz-Castillo, 2007. "The invariance properties of the Mutual Information index of multigroup segregation," Economics Working Papers we077544, Universidad Carlos III, Departamento de Economía.
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Cited by:
  1. Rebecca Allen & Simon Burgess & Tomas Key, 2010. "Choosing secondary school by moving house: school quality and the formation of neighbourhoods," The Centre for Market and Public Organisation 10/238, Department of Economics, University of Bristol, UK.
  2. Anna Makles & Kerstin Schneider, 2013. "Much Ado about Nothing? The Role of Primary School Catchment Areas for Ethnic School Segregation. Evidence from a Policy Reform," CESifo Working Paper Series 4520, CESifo Group Munich.
  3. Kerstin Schneider & Claudia Schuchart & Horst Weishaupt & Andrea Riedel, 2011. "The effect of free primary school choice on ethnic groups – Evidence from a policy reform," Schumpeter Discussion Papers sdp11007, Universitätsbibliothek Wuppertal, University Library.
  4. Xavier d'Haultfoeuille & Roland Rathelot, 2011. "Measuring Segregation on Small Units : A Partial Identification Analysis," Working Papers 2011-18, Centre de Recherche en Economie et Statistique.

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