On dissimilarity and equalization of opportunity.

Summary This thesis focuses on the measurement of dissimilarities in the distribution of economic attributes, and the implications for inequality of opportunity. Equality of opportunity has gained popularity for defining the goal of distributing a wide range of economic outcomes across social groups. This thesis is motivated by the fact that public policy evaluation based on equal opportunity always relies on comparisons of dissimilarity between conditional distributions, and we propose empirical criteria for testing these comparisons. In the first chapter, we axiomatically characterize the pre-order of dissimilarity for classifying distributions conditional on the original group, which are defined over discrete outcome classes. When the classes are permutable, we show that the dissimilarity is rationalized by a matrix majorization order and implemented by checking the inclusion of zonotopes. When the classes are ordered we base the dissimilarity judgment on a finite number of comparisons within the Lorenz majorization between the proportions of the groups, verified at different stages of aggregation of the aggregate population. In the second chapter, we examine the relevance of the dissimilarity pre-order to study segregation at the individual level. A complete characterization of a well-defined family of segregation indicators is obtained and we study one of them, the Gini exposure index, using Italian data. The last chapter presents a criterion of equalization of opportunity. Equalization of opportunity is achieved when there is no consensus, according to a given preference class, on the identity of the disadvantaged group. We use changes in (lack of) consensus about the existence and extent of disadvantage to characterize the equalization of opportunity criterion. The necessary restrictions, as well as possible aggregation procedures, are also discussed. We show that this criterion is identified according to the class of preferences represented by the rank-dependent utility functions and we obtain innovative inference results on the inverse stochastic dominance that allow us to test this criterion. Two applications on French data illustrate the impact in terms of equalization of opportunities of educational policies that take place early in the life of students.