Geodesic
A note on a property of the Gini coefficient
Communications in Mathematics, Tome 27 (2019) no. 2, pp. 81-88 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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/

[1] Allison, P.D.: Measures of inequality. American Sociological Review, 43, 1978, 865-880, | DOI

[2] Atkinson, A.B., Bourguignon, F.: Handbook of Income Distribution. 2015, New York: Elsevier,

[3] Ceriani, L., Verme, P.: The origins of the Gini index: extracts from Variabilità Mutabilità (1912) by Corrado Gini. The Journal of Economic Inequality, 10, 3, 2012, 1-23,

[4] Genčev, M., Musilová, D., Široký, J.: A Mathematical Model of the Gini Coefficient and Evaluation of the Redistribution Function of the Tax System in the Czech Republic. Politická ekonomie, 66, 6, 2018, 732-750, (in Czech). | DOI

[5] Gini, C.: Variabilit¸ e Mutuabilit¸. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. 1912, Bologna: C. Cuppini,

[6] Lambert, P.J.: The Distribution and Redistribution of Income. 2002, Manchester: Manchester University Press,

[7] Musgrave, R.A., Thin, T.: Income tax progression, 1929--48. Journal of Political Economy, 56, 1948, 498-514, | DOI

[8] Plata-Peréz, L., Sánchez-Peréz, J., Sánchez-Sánchez, F.: An elementary characterization of the Gini index. Mathematical Social Sciences, 74, 2015, 79-83, | DOI | MR

[9] Sen, A.K.: On Economic Inequality. 1997, Oxford: Oxford University Press,

[10] Zenga, M., Polisicchio, M., Greselin, F.: The variance of Gini's mean difference and its estimators. Statistica, 64, 3, 2004, 455-475, | MR