| Title:
|
A note on a property of the Gini coefficient (English) |
| Author:
|
Genčev, Marian |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
81-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Gini coefficient |
| Keyword:
|
finite sums |
| Keyword:
|
estimates |
| MSC:
|
26B35 |
| MSC:
|
91B82 |
| idZBL:
|
Zbl 1467.91107 |
| idMR:
|
MR4058167 |
| . |
| Date available:
|
2020-02-20T08:58:54Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147983 |
| . |
| Reference:
|
[1] Allison, P.D.: Measures of inequality.American Sociological Review, 43, 1978, 865-880, 10.2307/2094626 |
| Reference:
|
[2] Atkinson, A.B., Bourguignon, F.: Handbook of Income Distribution.2015, New York: Elsevier, |
| Reference:
|
[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, |
| Reference:
|
[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). 10.18267/j.polek.1232 |
| Reference:
|
[5] Gini, C.: Variabilit¸ e Mutuabilit¸. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche.1912, Bologna: C. Cuppini, |
| Reference:
|
[6] Lambert, P.J.: The Distribution and Redistribution of Income.2002, Manchester: Manchester University Press, |
| Reference:
|
[7] Musgrave, R.A., Thin, T.: Income tax progression, 1929--48.Journal of Political Economy, 56, 1948, 498-514, 10.1086/256742 |
| Reference:
|
[8] Plata-Peréz, L., Sánchez-Peréz, J., Sánchez-Sánchez, F.: An elementary characterization of the Gini index.Mathematical Social Sciences, 74, 2015, 79-83, MR 3314225, 10.1016/j.mathsocsci.2015.01.002 |
| Reference:
|
[9] Sen, A.K.: On Economic Inequality.1997, Oxford: Oxford University Press, |
| Reference:
|
[10] Zenga, M., Polisicchio, M., Greselin, F.: The variance of Gini's mean difference and its estimators.Statistica, 64, 3, 2004, 455-475, MR 2279894 |
| . |
