Amparo Baíllo, Javier Cárcamo, Carlos Mora-Corral
arXiv 4 Mar 2021 · Econometrics
arXiv:2103.03286 · PDF · DOI · OpenAlex · Extracted main text
We find the set of extremal points of Lorenz curves with fixed Gini index and compute the maximal $L^1$-distance between Lorenz curves with given values of their Gini coefficients. As an application we introduce a bidimensional index that simultaneously measures relative inequality and dissimilarity between two populations. This proposal employs the Gini indices of the variables and an $L^1$-distance between their Lorenz curves. The index takes values in a right-angled triangle, two of whose sides characterize perfect relative inequality-expressed by the Lorenz ordering between the underlying distributions. Further, the hypotenuse represents maximal distance between the two distributions. As a consequence, we construct a chart to, graphically, either see the evolution of (relative) inequality and distance between two income distributions over time or to compare the distribution of income of a specific population between a fixed time point and a range of years. We prove the mathematical results behind the above claims and provide a full description of the asymptotic properties of the plug-in estimator of this index. Finally, we apply the proposed bidimensional index to several real EU-SILC income datasets to illustrate its performance in practice.
appendix boundary found by appendix_titled_section at “Appendix” · 55% of the source is main text. Read the extracted text to check this.
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 | Sun, Z., and Beare, B. K (2021) Improved nonparametric bootstrap tests of Lorenz dominance | 0.874 | 6 | 2 | 100% |
| 2 | Arnold, B. C., and Sarabia, J. M (2018) Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics | 0.737 | 3 | 2 | 100% |
| 3 | Barrett, G. F., Donald, S. G., and Bhattacharya, D (2014) Consistent nonparametric tests for Lorenz dominance | 0.737 | 3 | 2 | 100% |
| 4 | Shapiro, A (1990) On concepts of directional differentiability | 0.644 | 3 | 2 | 67% |
| 5 | Yitzhaki, S., and Schechtman, E (2012) The Gini Methodology: A Primer on a Statistical Methodology | 0.644 | 2 | 2 | 100% |
| 6 | Zheng, B (2018) Almost Lorenz dominance | 0.644 | 2 | 2 | 100% |
| 7 | Kaji, T (2019) Asymptotic theory of $L$-statistics and integrable empirical processes | 0.585 | 3 | 1 | 100% |
| 8 | Kleiber, C., and Kotz, S (2003) Statistical Size Distributions in Economics and Actuarial Sciences (Vol | 0.585 | 3 | 1 | 100% |
| 9 | Simon, B (2011) Convexity | 0.575 | 7 | 2 | 29% |
| 10 | Bourguignon, F (2017) The Globalization of Inequality | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 113 scored citations.