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Lorenz Map, Inequality Ordering and Curves Based on Multidimensional Rearrangements

Y. FAN, M. Henry, B. Pass, J.A. Rivero

 

Séminaire d’économétrie de Montréal 2022-2023
conjoint avec les départements d’économique des universités de Montréal, du Québec à Montréal, Concordia et McGill ainsi que le CIRANO

Responsables : Marine Carrasco (U. de Montréal) et Saraswata Chaudhuri (McGill U.)

* Séminaire virtuel. Veuillez contacter un responsable pour obtenir les informations de connexion à Zoom.

RÉSUMÉ: We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated to a multivariate resource allocation. Each component of the Lorenz map is the cumulative share of each resource, as in the traditional univariate case. The pointwise ordering of such Lorenz maps defines a new multivariate majorization order. We define a multi-attribute Gini index and complete ordering based on the Lorenz map. We formulate income egalitarianism and show that the class of egalitarian allocations is maximal with respect to our inequality ordering over a large class of allocations. We propose the level sets of an Inverse Lorenz Function as a practical tool to visualize and compare inequality in two dimensions, and apply it to income-wealth inequality in the United States between 1989 and 2019.

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