A note on a property of the Gini coefficient

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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

|G(σ1, . . ., σn) − G(γ1, . . . , γn)| ,

where (γ1, . . . , γn) represents the vector of the gross wages and (σ1, . . . , σn) 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) σi = 100 ⎡ 1.34 γi/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.

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