Publication: The invariance properties of the Mutual Information index of multigroup segregation
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2007-11
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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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Keywords
Gender segregation measurement, Axiomatic properties, Econometric models