The invariance properties of the Mutual Information index of multigroup segregation
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).
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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, vol. 45(2), pages 555-578, 05.
- Oscar Volij & David Frankel, 2004.
Econometric Society 2004 North American Summer Meetings
210, Econometric Society.
- Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers Archive 12818, Iowa State University, Department of Economics.
- Frankel, David M. & Volij, Oscar, 2010. "Measuring Segregation," Staff General Research Papers Archive 32130, Iowa State University, Department of Economics.
- David M. Frankel & Oscar Volij, 2007. "Measuring Segregation," Working Papers 0703, Ben-Gurion University of the Negev, Department of Economics.
- David Frankel & Oscar Volij, 2005. "Measuring Segregation," Economic theory and game theory 017, Oscar Volij.
- Ruiz-Castillo, Javier & Mora, Ricardo, 2008. "A defense of an entropy based index of multigroup segregation," UC3M Working papers. Economics we074645, Universidad Carlos III de Madrid. Departamento de Economía.
- Karmel, T & Maclachlan, M, 1988. "Occupational Sex Segregation--Increasing or Decreasing?," The Economic Record, The Economic Society of Australia, vol. 64(186), pages 187-195, September.
- Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
- 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. Full references (including those not matched with items on IDEAS)