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The invariance properties of the Mutual Information index of multigroup segregation

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  • Ricardo Mora
  • Javier Ruiz-Castillo

Abstract

In the context of educational segregation by ethnic group, it has been argued that rigorous pair wise segregation comparisons over time or across space should be invariant in two situations: when the ethnic composition of the population changes while the distribution of each ethnic group over the schools remains constant (invariance 1), or when the size distribution of schools changes while the ethnic composition of each school remains constant (invariance 2). This paper makes three contributions to this literature. First, it presents a testing strategy for choosing between the two properties. Second, it argues that both properties have strong implications, and that there are reasons to defend that the overall segregation index need not satisfy either one. In particular, the contrast between invariant segregation indices and the Mutual Information segregation index that violates both properties is illustrated with a number of examples. Third, nevertheless, it is shown that pair wise segregation comparisons using this index can be expressed in terms of (i) changes in the ethnic composition of the population, (ii) changes in the school size distribution, and (iii) changes in a third term that is invariant 1 or invariant 2. These decompositions can be used to reach the analogous ones obtained in Deutsch et al. (2006).

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we077544.

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Date of creation: Nov 2007
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Handle: RePEc:cte:werepe:we077544

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  1. Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers, Iowa State University, Department of Economics 12818, Iowa State University, Department of Economics.
  2. Robert Hutchens, 2004. "One Measure of Segregation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 555-578, 05.
  3. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, Elsevier, vol. 42(1), pages 13-29, July.
  4. Ricardo Mora & Javier Ruiz-Castillo, 2008. "A defense of an entropy based index of multigroup segregation," Economics Working Papers we074645, Universidad Carlos III, Departamento de Economía.
  5. Karmel, T & Maclachlan, M, 1988. "Occupational Sex Segregation--Increasing or Decreasing?," The Economic Record, The Economic Society of Australia, The Economic Society of Australia, vol. 64(186), pages 187-95, September.
  6. Francine D. Blau & Wallace E. Hendricks, 1979. "Occupational Segregation by Sex: Trends and Prospects," Journal of Human Resources, University of Wisconsin Press, vol. 14(2), pages 197-210.
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Cited by:
  1. Coral Río & Olga Alonso-Villar, 2010. "Gender Segregation in the Spanish Labor Market: An Alternative Approach," Social Indicators Research, Springer, Springer, vol. 98(2), pages 337-362, September.
  2. Van Puyenbroeck, Tom & De Bruyne, Karolien & Sels, Luc, 2010. "More than 'Mutual Information': Educational and Sectoral Gender Segregation and their Interaction on the Flemish Labour Market," Working Papers, Hogeschool-Universiteit Brussel, Faculteit Economie en Management 2010/29, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  3. Rebecca Allen & Simon Burgess & Frank Windmeijer, 2009. "More Reliable Inference for Segregation Indices," The Centre for Market and Public Organisation, Department of Economics, University of Bristol, UK 09/216, Department of Economics, University of Bristol, UK.
  4. Carlos Gradín, 2010. "Conditional occupational segregation of minorities in the U.S," Working Papers 185, ECINEQ, Society for the Study of Economic Inequality.
  5. Luiz Dias Bahia & Danilo Coelho & Alexandre Messa Silva & Sergei Soares, 2009. "A Evolução da Segregação por Qualificação Profissional ao Nível das Firmas," Discussion Papers, Instituto de Pesquisa Econômica Aplicada - IPEA 1406, Instituto de Pesquisa Econômica Aplicada - IPEA.

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