Yanqin Fan, Marc Henry, Brendan Pass, Jorge A. Rivero
arXiv 17 Mar 2022 · Econometrics · 1 citations (OpenAlex)
arXiv:2203.09000 · PDF · DOI · OpenAlex · Extracted main text
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 with 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, which is equivalent to preference by any social planner with inequality averse multivariate rank dependent social evaluation functional. We define a family of multi-attribute Gini index and complete ordering based on the Lorenz map. 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 2022.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | G. Koshevoy and K. Mosler (1996) The Lorenz zonoid of a multivariate distribution | 1.000 | 13 | 3 | 100% |
| 2 | J. L. Gastwirth (1971) A general definition of the Lorenz curve | 1.000 | 9 | 3 | 100% |
| 3 | B. C. Arnold (1983) Pareto Distributions | 1.000 | 8 | 3 | 100% |
| 4 | B. C. Arnold and J. M. Sarabia (2018) Majorization and the Lorenz order with Applications in Applied Mathematics and Economics | 0.928 | 4 | 3 | 100% |
| 5 | V. Chernozhukov, A. Galichon, M. Hallin, and M. Henry (2017) Monge-Kantorovich depth, quantiles, ranks and signs | 0.909 | 8 | 5 | 75% |
| 6 | T. Taguchi (1972) On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dime… | 0.874 | 10 | 2 | 100% |
| 7 | A. Galichon and M. Henry (2012) Dual theory of choice under multivariate risks | 0.874 | 6 | 3 | 67% |
| 8 | T. Taguchi (1972) On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dime… | 0.874 | 5 | 2 | 100% |
| 9 | A. Banerjee (2016) Multidimensional Lorenz dominance: A definition and an example | 0.811 | 4 | 2 | 100% |
| 10 | A. W. Marshall, I. Olkin, and B. C. Arnold (2011) Inequalities: Theory of Majorization and Its Applications | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 81 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | An econometrician's guide to optimal transport | 0.693 | 5 | 1 |