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More reliable inference for the dissimilarity index of segregation

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  • Rebecca Allen
  • Simon Burgess
  • Russell Davidson
  • Frank Windmeijer

Abstract

The most widely used measure of segregation is the so‐called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. 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 adjustments 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 bias adjustments to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that the 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 & Russell Davidson & Frank Windmeijer, 2015. "More reliable inference for the dissimilarity index of segregation," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 40-66, February.
    • Handle: RePEc:wly:emjrnl:v:18:y:2015:i:1:p:40-66
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    File URL: http://hdl.handle.net/10.1111/ectj.12039
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    Cited by:

    1. Gwilym Owen & Yu Chen & Timothy Birabi & Gwilym Pryce & Hui Song & Bifeng Wang, 2023. "Residential segregation of migrants: Disentangling the intersectional and multiscale segregation of migrants in Shijiazhuang, China," Urban Studies, Urban Studies Journal Limited, vol. 60(1), pages 166-182, January.
    2. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    3. Marta Martínez Matute & Pedro S. Martins, 2022. "How representative are social partners in Europe? The role of dissimilarity," LABOUR, CEIS, vol. 36(4), pages 424-444, December.
    4. Rafiq Friperson & Hessel Oosterbeek & Bas van der Klaauw, 2023. "The Hidden Divide: School Segregation of Teachers in the Netherlands," Tinbergen Institute Discussion Papers 23-034/V, Tinbergen Institute.
    5. Filippo Temporin, 2019. "A multilevel structural equation modelling approach to study segregation of deprivation: an application to Bolivia," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(3), pages 1657-1674, May.
    6. Daniel Guinea-Martin & Ricardo Mora, 2022. "Computing decomposable multigroup indices of segregation," Stata Journal, StataCorp LP, vol. 22(3), pages 521-556, September.
    7. Kutscher, Macarena & Nath, Shanjukta & Urzúa, Sergio, 2023. "Centralized admission systems and school segregation: Evidence from a national reform," Journal of Public Economics, Elsevier, vol. 221(C).
    8. Kelvyn Jones & Ron Johnston & David Manley & Dewi Owen & Chris Charlton, 2015. "Ethnic Residential Segregation: A Multilevel, Multigroup, Multiscale Approach Exemplified by London in 2011," Demography, Springer;Population Association of America (PAA), vol. 52(6), pages 1995-2019, December.
    9. Oosterbeek, Hessel & Sóvágó, Sándor & van der Klaauw, Bas, 2021. "Preference heterogeneity and school segregation," Journal of Public Economics, Elsevier, vol. 197(C).
    10. Bertoli, Simone & Ozden, Caglar & Packard, Michael, 2021. "Segregation and internal mobility of Syrian refugees in Turkey: Evidence from mobile phone data," Journal of Development Economics, Elsevier, vol. 152(C).
    11. Renan Xavier Cortes & Sergio Rey & Elijah Knaap & Levi John Wolf, 2020. "An open-source framework for non-spatial and spatial segregation measures: the PySAL segregation module," Journal of Computational Social Science, Springer, vol. 3(1), pages 135-166, April.
    12. Coral Río & Olga Alonso-Villar, 2022. "On Measuring Segregation in a Multigroup Context: Standardized Versus Unstandardized Indices," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 163(2), pages 633-659, September.
    13. Ran Wei & Elijah Knaap & Sergio Rey, 2023. "American Community Survey (ACS) Data Uncertainty and the Analysis of Segregation Dynamics," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 42(1), pages 1-23, February.
    14. Joao Firmino & Luis C. Nunes & Silvia de Almeida & Susana Batista, 2020. "Student segregation across and within schools. The case of the Portuguese public school system," Nova SBE Working Paper Series wp633, Universidade Nova de Lisboa, Nova School of Business and Economics.
    15. Fahey, Éamonn & Russell, Helen & McGinnity, Frances & Grotti, Raffaele, 2019. "Diverse neighbourhoods: an analysis of the residential distribution of immigrants in Ireland," Research Series, Economic and Social Research Institute (ESRI), number BKMNEXT376, June.
    16. Austin, Andrea M. & Carmichael, Donald Q. & Bynum, Julie P.W. & Skinner, Jonathan S., 2019. "Measuring racial segregation in health system networks using the dissimilarity index," Social Science & Medicine, Elsevier, vol. 240(C).
    17. Mariana C Arcaya & Gabriel Schwartz & SV Subramanian, 2018. "A multi-level modeling approach to understanding residential segregation in the United States," Environment and Planning B, , vol. 45(6), pages 1090-1105, November.
    18. van der Klaauw, Bas & Oosterbeek, Hessel & Sóvágó, Sándor, 2019. "Why are schools segregated? Evidence from the secondary-school match in Amsterdam," CEPR Discussion Papers 13462, C.E.P.R. Discussion Papers.
    19. Burger, Kaspar, 2019. "The socio-spatial dimension of educational inequality: A comparative European analysis," MPRA Paper 95309, University Library of Munich, Germany, revised 2019.

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