A note on a property of the Gini coefficient

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 â ¡ 1.34 γi/100â ¤, 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.