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A defense of an entropy based index of multigroup segregation

  • Ricardo Mora
  • Javier Ruiz-Castillo

This paper defends the use of the entropy based Mutual Information index of multigroup segregation for the following five reasons. (1) It satisfies 14 basic axioms discussed in the literature when segregation takes place along a single dimension. (2) It is additively decomposable into between- and within-group terms for any partition of the set of occupations (or schools) and the set of demographic groups in the multigroup case. (3) The underlying segregation ordering has been recently characterized in terms of 8 properties. (4) It is a monotonic transformation of log-likelihood tests for the existence of segregation in a general model. (5) It can be decomposed so that a term independent of changes in either of the two marginal distributions can be isolated in pair wise segregation comparisons. Other existing measures of segregation have not been characterized, fail to satisfy one or more of the basic axioms, do not admit a between- within-group decomposition, have not been motivated from a statistical approach, or are based on more restricted econometric models.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we074645.

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Date of creation: Nov 2008
Date of revision:
Handle: RePEc:cte:werepe:we074645
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  1. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  2. David Card & Jesse Rothstein, 2005. "Racial Segregation and the Black-White Test Score Gap," Working Papers 879, Princeton University, Department of Economics, Industrial Relations Section..
  3. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March.
  4. Butler, Richard J., 1987. "New indices of segregation," Economics Letters, Elsevier, vol. 24(4), pages 359-362.
  5. Boisso, Dale & Hayes, Kathy & Hirschberg, Joseph & Silber, Jacques, 1994. "Occupational segregation in the multidimensional case : Decomposition and tests of significance," Journal of Econometrics, Elsevier, vol. 61(1), pages 161-171, March.
  6. Alonso-Villar, Olga & del Río, Coral, 2010. "Local versus overall segregation measures," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 30-38, July.
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