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A defense of an entropy based index of multigroup segregation

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  • Ricardo Mora
  • Javier Ruiz-Castillo

Abstract

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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Bibliographic Info

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
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Handle: RePEc:cte:werepe:we074645

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Keywords: Gender segregation measurement; Axiomatic properties;

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References

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  1. Olga Alonso-Villar & Coral del Río, 2008. "Local versus overall segregation measures," Working Papers, Universidade de Vigo, Departamento de Economía Aplicada 0802, Universidade de Vigo, Departamento de Economía Aplicada.
  2. Butler, Richard J., 1987. "New indices of segregation," Economics Letters, Elsevier, Elsevier, vol. 24(4), pages 359-362.
  3. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, Econometric Society, vol. 47(4), pages 901-20, July.
  4. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, Elsevier, vol. 53(2), pages 185-195, March.
  5. David Card & Jesse Rothstein, 2006. "Racial Segregation and the Black-White Test Score Gap," NBER Working Papers 12078, National Bureau of Economic Research, Inc.
  6. Boisso, Dale & Hayes, Kathy & Hirschberg, Joseph & Silber, Jacques, 1994. "Occupational segregation in the multidimensional case : Decomposition and tests of significance," Journal of Econometrics, Elsevier, Elsevier, vol. 61(1), pages 161-171, March.
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Cited by:
  1. 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.
  2. Alonso-Villar, Olga & del Río, Coral, 2010. "Local versus overall segregation measures," Mathematical Social Sciences, Elsevier, Elsevier, vol. 60(1), pages 30-38, July.
  3. Ricardo Mora & Javier Ruiz-Castillo, 2007. "The invariance properties of the Mutual Information index of multigroup segregation," Economics Working Papers, Universidad Carlos III, Departamento de Economía we077544, Universidad Carlos III, Departamento de Economía.

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