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Editor: Universidad Carlos III de Madrid. Departamento de Economía

Issued date: 2007-11

ISSN: 2340-5031

Serie-No.: UC3M Working papers. Economics07-44

Other version: http:-hdl.handle.net-10016-4716

Keywords: Gender segregation measurement , Axiomatic properties , Econometric models

JEL Classification: J16 , J24

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:In the context of educational segregation by ethnic group, it has been argued that rigorous pairwise segregation comparisons over time or across space should be invariant in two situations:when the ethnic composition of the population changes while the disIn the context of educational segregation by ethnic group, it has been argued that rigorous pairwise 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 groupover the schools remains constant (invariance 1), or when the size distribution of schools changeswhile the ethnic composition of each school remains constant (invariance 2). This paper makesthree contributions to this literature. First, it presents a testing strategy for choosing between thetwo properties. Second, it argues that both properties have strong implications, and that there arereasons to defend that the overall segregation index need not satisfy either one. In particular, thecontrast between invariant segregation indices and the Mutual Information segregation index thatviolates both properties is illustrated with a number of examples. Third, nevertheless, it is shownthat pair wise segregation comparisons using this index can be expressed in terms of (i) changes inthe 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 toreach the analogous ones obtained in Deutsch et al. (2006).+-





Author: Mora, Ricardo; Ruiz-Castillo, Javier

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Economía DE - Working Papers.
Economics.
WE 2007-11 The invariance properties of the Mutual Information index of multigroup segregation Mora, Ricardo http:--hdl.handle.net-10016-1086 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Working Paper 07-75 Economic Series (44) November 2007 Departamento de Economía Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 916249875 THE INVARIANCE PROPERTIES OF THE MUTUAL INFORMATION INDEX OF MULTIGROUP SEGREGATION Ricardo Mora and Javier Ruiz-Castillo1 Departamento de Economía, Universidad Carlos III de Madrid 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.
Th...





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