More Reliable Inference for Segregation Indices
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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- Judith Hellerstein & David Neumark, 2007.
"Workplace Segregation in the United States: Race, Ethnicity, and Skill,"
07-02, Center for Economic Studies, U.S. Census Bureau.
- 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.
- Judith Hellerstein & David Neumark, 2004. "Workplace Segregation in the United States: Race, Ethnicity, and Skill," PPIC Working Papers 2004.05, Public Policy Institute of California.
- Judith Hellerstein & David Neumark, 2005. "Workplace Segregation in the United States: Race, Ethnicity, and Skill," NBER Working Papers 11599, National Bureau of Economic Research, Inc.
- Judith Hellerstein & David Neumark, 2006. "Workplace Segregation in the United States: Race, Ethnicity, and Skill," Working Papers 060710, University of California-Irvine, Department of Economics.
- 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.
- 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.
- 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.
- 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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