Geodesic
A note on a property of the Gini coefficient
Communications in Mathematics, Tome 27 (2019) no. 2, pp. 81-88.

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The scope of this note is a self-contained presentation of a~mathematical method that enables us to give an absolute upper bound for the difference of the Gini coefficients \[ \left |G(\sigma _1,\dots ,\sigma _n)-G(\gamma _1,\dots ,\gamma _n)\right |, \] where $(\gamma _1,\dots ,\gamma _n)$ represents the vector of the gross wages and $(\sigma _1,\dots ,\sigma _n)$ represents the vector of the corresponding super-gross wages that is used in the Czech Republic for calculating the net wage. Since (as of June 2019) $\sigma _i=100\cdot \left \lceil 1.34\gamma _i/100\right \rceil $, the study of the above difference seems to be somewhat inaccessible for many economists. However, our estimate based on the presented technique implies that the introduction of the super-gross wage concept does not essentially affect the value of the Gini coefficient as sometimes expected.
Classification : 26B35, 91B82
Keywords: Gini coefficient; finite sums; estimates 
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Genčev, Marian. A note on a property of the Gini coefficient. Communications in Mathematics, Tome 27 (2019) no. 2, pp. 81-88. http://geodesic.mathdoc.fr/item/COMIM_2019__27_2_a1/