The authors examine ways to measure how “segregated” is a school district. One could imagine complete segregation as being the case where each school in a district hosts a different ethnic group, and nonsegregation as the case where all schools in a district have the same ethnic distribution. <\/p>\n
The authors propose a set of 6 axiomatic desiderata for measures of segregation, desiderata that appeal to intuitions about how a measure should be affected or not by certain changes in underlying conditions. For example, one axiomatic desideratum is called “symmetry”, which amounts to an ordering produced by a segregation measure being invariant to the renaming of the ethnic groups in question. <\/p>\n
On these grounds, they find that a measure producing an ordering equivalent to that of the so-called Atkinson index (link<\/a>) is necessary and sufficient to satisfy 5 out of the 6 desiderata, with the symmetry property being the one that is not satisfied. This strikes me as a major problem with Atkinson-type indices, as they require ad hoc decisions to combine or exclude ethnic categories in cases where districts differ in the combinations of groups that they contain. <\/p>\n The authors then discuss the appealing properties of orderings that are equivalent to that which is produced by the Mutual Information index. This index is an entropy (link<\/a>) based measure that quantifies the reduction in uncertainty about a student’s race that comes from learning about what school she comes from; in a symmetric manner, it also equals “the reduction in uncertainty about a student\u2019s school that comes from learning her race.” Measures that always produce an ordering equivalent to that which is produced by mutual information are necessary and sufficient for all 6 desiderata except the so-called “composition invariance” property. Composition invariance is a controversial property. It implies that the ordering imposed by the measure does not change when the size of an ethnic group in a given district is increased in a uniform manner in all schools in that district (e.g., if the number of whites increases by 10% in all schools in a district). Composition invariance runs counter to conceptualizations of segregation that emphasize “contact” between people of different ethnicities (the authors cite work by Coleman, Hoffer, and Kilgore). For this reason, I find mutual information-based measures to be especially appealing.<\/p>\n Clearly these measures can be applied to measuring any kind of segregation. A useful discussion.<\/p>\n Full citation:<\/p>\n David M. Frankel and Oscar Volij (2011) “Measuring school segregation,” Journal of Economic Theory<\/em>, 146:1-38. (gated link<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":" The authors examine ways to measure how “segregated” is a school district. One could imagine complete segregation as being the case where each school in a district hosts a different ethnic group, and nonsegregation as the case where all schools in a district have the same ethnic distribution. The authors propose a set of 6 … <\/p>\n