A note on a property of the Gini coefficient

Marian Genčev

Communications in Mathematics (2019)

  • Volume: 27, Issue: 2, page 81-88
  • ISSN: 1804-1388

Abstract

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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 G ( σ 1 , ⋯ , σ n ) - G ( γ 1 , ⋯ , γ n ) , where ( γ 1 , ⋯ , γ n ) represents the vector of the gross wages and ( σ 1 , ⋯ , σ 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) σ i = 100 · 1 . 34 γ i / 100 , 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.

How to cite

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Genčev, Marian. "A note on a property of the Gini coefficient." Communications in Mathematics 27.2 (2019): 81-88. <http://eudml.org/doc/295024>.

@article{Genčev2019,
abstract = {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.},
author = {Genčev, Marian},
journal = {Communications in Mathematics},
keywords = {Gini coefficient; finite sums; estimates},
language = {eng},
number = {2},
pages = {81-88},
publisher = {University of Ostrava},
title = {A note on a property of the Gini coefficient},
url = {http://eudml.org/doc/295024},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Genčev, Marian
TI - A note on a property of the Gini coefficient
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 2
SP - 81
EP - 88
AB - 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.
LA - eng
KW - Gini coefficient; finite sums; estimates
UR - http://eudml.org/doc/295024
ER -

References

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  9. Sen, A.K., On Economic Inequality, 1997, Oxford: Oxford University Press, (1997) 
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