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More Reliable Inference for Segregation Indices

Author

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  • 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.

Suggested Citation

  • Rebecca Allen & Simon Burgess & Frank Windmeijer, 2009. "More Reliable Inference for Segregation Indices," The Centre for Market and Public Organisation 09/216, The Centre for Market and Public Organisation, 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. Stephen Gibbons & Shqiponja Telhaj, 2007. "Are Schools Drifting Apart? Intake Stratification in English Secondary Schools," Urban Studies, Urban Studies Journal Limited, vol. 44(7), pages 1281-1305, June.
    3. Ricardo Mora & Javier Ruiz-Castillo, 2009. "The invariance properties of the mutual information index of multigroup segregation," Research on Economic Inequality, in: Occupational and Residential Segregation, pages 33-53, Emerald Group Publishing Limited.
    4. Martin Söderström & Roope Uusitalo, 2010. "School Choice and Segregation: Evidence from an Admission Reform," Scandinavian Journal of Economics, Wiley Blackwell, vol. 112(1), pages 55-76, March.
    5. Michael R. Ransom, 2000. "Sampling Distributions of Segregation Indexes," Sociological Methods & Research, , vol. 28(4), pages 454-475, May.
    6. 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.
    7. 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.
    8. 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, Quantitative Social Science - UCL Social Research Institute, University College London.
    4. Roland Rathelot, 2012. "Measuring Segregation When Units are Small: A Parametric Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 546-553, June.
    5. Angelo Mazza & Antonio Punzo, 2015. "On the Upward Bias of the Dissimilarity Index and Its Corrections," Sociological Methods & Research, , vol. 44(1), pages 80-107, February.
    6. 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.
    7. Makles Anna & Schneider Kerstin, 2015. "Much Ado about Nothing? The Role of Primary School Catchment Areas For Ethnic School Segregation: Evidence From a Policy Reform," German Economic Review, De Gruyter, vol. 16(2), pages 203-225, May.
    8. Federico Benassi & Francesca Bitonti & Angelo Mazza & Salvatore Strozza, 2023. "Sri Lankans’ residential segregation and spatial inequalities in Southern Italy: an empirical analysis using fine-scale data on regular lattice geographies," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(2), pages 1629-1648, April.
    9. Angelo Mazza, 2017. "Dealing With The Bias Of The Dissimilarity Index Of Segregation1," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 71(2), pages 11-20, April-Jun.
    10. 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 - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 68(3-4), pages 159-166, July-Dece.

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    More about this item

    Keywords

    segregation; dissimilarity index; bootstrap methods; hypothesis testing;
    All these keywords.

    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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