Lorenz regressions : a statistical contribution to the quantification of explained inequality
(2023)
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- Economics is increasingly interested in attributing the inequality of an outcome to a set of explanatory factors. For example, in the context of inequality of opportunity, one wishes to determine whether income inequality is related to a number of circumstances beyond the individuals’ control. This thesis offers a novel procedure that combines statistical rigor and economic interpretability. The starting point is the explained Gini coefficient. Formally, it is the Gini coefficient of the conditional expectation of an outcome given certain explanatory factors, assuming a single-index model. Informally, it combines the Gini coefficient, a widely used measure of economic inequality, with the single-index model, a flexible statistical model. The methodology developed in this work, and summarized under the term Lorenz regression, proposes an inferential procedure for the explained Gini coefficient. Compared to the existing procedures, the Lorenz regression benefits from a number of advantages. The single-index is a flexible semiparametric model. Besides, the Lorenz regression does not entail to estimate all the elements of the model; only the parametric part needs to be estimated. The explained Gini coefficient is optimized for the Gini criterion, in the sense that it gives weights to the explanatory factors in order to maximize their power in explaining the inequality of the outcome. In the penalized procedure, the overestimation of the explained inequality is avoided, even when many explanatory factors are included. Also, the method yields an automatic selection of the relevant variables. The first chapters introduce the Lorenz and penalized Lorenz regression. The methodology is then applied in the context of inequality of opportunity and illustrated with a publicly available library from the statistical software R.
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Jacquemain, A. (2023). Lorenz regressions : a statistical contribution to the quantification of explained inequality. https://hdl.handle.net/2078.5/27389