More Reliable Inference for Segregation Indices
AbstractThe 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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Bibliographic InfoPaper provided by Department of Economics, University of Bristol, UK in its series The Centre for Market and Public Organisation with number 09/216.
Length: 27 pages
Date of creation: Apr 2009
Date of revision:
segregation; dissimilarity index; bootstrap methods; hypothesis testing;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-04-25 (All new papers)
- NEP-ECM-2009-04-25 (Econometrics)
- NEP-URE-2009-04-25 (Urban & Real Estate Economics)
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