"When a distribution of income is decomposed into component distributions of classes in a population, it is often interesting to ask what fraction of income inequality is due to between- as opposed to within-class inequality. Certain inequality measures allow a precise answer to this question. In the equal-opportunity literature, one often decomposes income distributions into component distributions associated with types, which are characterized as consisting of individuals having different circumstances. The degree of inequality attributed to circumstances is often quite low, according to this statistical approach. Here, we compute how much inequality could possibly be attributed to circumstances, and give an example. The question has been studied by Elbers et al. [2008] for discrete distributions; the present contribution solves the problem for continuous distributions, which gives a simpler computational approach, and one that is more appropriate for large population samples."

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