WSEAS Transactions on Business and Economics
Print ISSN: 1109-9526, E-ISSN: 2224-2899
Volume 19, 2022
Relation Between Two Income Inequality Measures: The Gini coefficient and the Robin Hood Index
Author:
Abstract: The objective of this investigation is to study the relation between two common measures of income
inequality, the Gini coefficient and the Robin Hood index. An approximate formula for the Robin Hood index
in terms of the Gini coefficient is developed from 100,000 Lorenz curves that are randomly generated based on
100 twenty-parameter families of income distributions. The approximate formula is tested against Robin Hood
indexes of commonly-used one-parameter Lorenz curves, income data of several countries, and reported results
of Robin Hood indexes. The approximate formula is also tested against results of a stochastic income-wealth
model that is introduced in the present investigation. The formula is useful conceptually in understanding why
Gini coefficients and Robin Hood indexes are correlated in distribution data and is useful practically in providing
accurate estimates of Robin Hood indexes when Gini coefficients are known. The continuous piecewise-linear
approximation is generally within 5% of standard one-parameter Lorenz curves and income distribution data and
has the form: $$R \approx 0.74G$$ for $$0\leqslant G \leqslant 0.5, R \approx 0.37+0.90(G-0.5)$$ for $$0.5\leqslant G \leqslant 0.8$$ and $$ R \approx 0.64 + 1.26 (G- 0.8)$$ for $$ 0.8\leqslant G \leqslant 0.95$$ where $$ R$$ is the Robin Hood index and $$G $$ is the Gini coefficient.
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Keywords: Robin Hood index, Gini coefficient, income inequality, Lorenz curve, Pietra index, Hoover index,
Schutz index
Pages: 760-770
DOI: 10.37394/23207.2022.19.67