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More Reliable Inference for Segregation Indices

Author

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  • Rebecca Allen
  • Simon Burgess
  • Frank Windmeijer

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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.

Suggested Citation

  • Rebecca Allen & Simon Burgess & Frank Windmeijer, 2009. "More Reliable Inference for Segregation Indices," The Centre for Market and Public Organisation 09/216, Department of Economics, University of Bristol, UK.
  • Handle: RePEc:bri:cmpowp:09/216
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    File URL: http://www.bristol.ac.uk/cmpo/publications/papers/2009/wp216.pdf
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    References listed on IDEAS

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    1. Judith K. Hellerstein & David Neumark, 2008. "Workplace Segregation in the United States: Race, Ethnicity, and Skill," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 459-477, August.
    2. Mora, Ricardo & Ruiz-Castillo, Javier, 2007. "The invariance properties of the Mutual Information index of multigroup segregation," UC3M Working papers. Economics we077544, Universidad Carlos III de Madrid. Departamento de Economía.
    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 402-409, 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 276-277, September.
    5. Rebecca Allen & Anna Vignoles, 2006. "What Should an Index of School Segregation Measure?," CEE Discussion Papers 0060, Centre for the Economics of Education, LSE.
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    Citations

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    Cited by:

    1. Seong-Yun Hong & Yukio Sadahiro, 2014. "Measuring geographic segregation: a graph-based approach," Journal of Geographical Systems, Springer, vol. 16(2), pages 211-231, April.
    2. 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.
    3. Rebecca Allen & Simon Burgess & Tomas Key, 2010. "Choosing secondary school by moving house: school quality and the formation of neighbourhoods," DoQSS Working Papers 10-21, Department of Quantitative Social Science - UCL Institute of Education, University College London.
    4. Anna Makles & Kerstin Schneider, 2015. "Much Ado about Nothing? The Role of Primary School Catchment Areas For Ethnic School Segregation: Evidence From a Policy Reform," German Economic Review, Verein für Socialpolitik, vol. 16(2), pages 203-225, May.
    5. Schneider, Kerstin & Schuchart, Claudia & Weishaupt, Horst & Riedel, Andrea, 2012. "The effect of free primary school choice on ethnic groups — Evidence from a policy reform," European Journal of Political Economy, Elsevier, vol. 28(4), pages 430-444.
    6. Anna Maria Altavilla & Angelo Mazza & Antonio Punzo, 2014. "A comparison of bias correction methods for the dissimilarity index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 68(3-4), pages 159-166, July-Dece.

    More about this item

    Keywords

    segregation; dissimilarity index; bootstrap methods; hypothesis testing;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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