Kernel estimation of the Quintile Share Ratio index of inequality for heavy-tailed income distributions

被引:0
作者
Kebe, Modou [1 ]
Deme, El Hadji [1 ]
Kpanzou, Tchilabalo Abozou [2 ]
Manou-Abi, Solym Mawaki [3 ,4 ]
Sisawo, Ebrima [1 ]
机构
[1] Univ Gaston Berger, UFR SAT, LERSTAD, BP 234, St Louis, Senegal
[2] Univ Kara, LaMMASD, Dept Math, Kara, Togo
[3] Inst Montpellierain Alexander Grothendieck, UMR CNRS 5149, Pl Eugene Bataillon, F-34090 Montpellier, France
[4] Ctr Univ Format & Rech, Mayotte, France
来源
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2023年 / 16卷 / 04期
关键词
Inequality Measures; QSR index; Kernel estimation; Heavy-tailed; Extreme value Theory; CAPITAL-INCOME; STATISTICAL-INFERENCE; GINI INDEX; PARAMETERS; TAXATION;
D O I
10.29020/nybg.ejpam.v16i4.4765
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non -parametric estimator. Hence, we need another estimator in the case of heavy-tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of the QSR index of economic inequality for heavy-tailed income distributions. Our methodology is based on the extreme value theory, which offers adequate statistical results for such distributions. We establish their asymptotic distribution, and through a simulation study, we illustrate their behavior in terms of the absolute bias and the median squared error. The simulation results clearly show that our estimators work well.
引用
收藏
页码:2509 / 2543
页数:35
相关论文
共 45 条
[1]  
Abel Andrew B., 2007, Technical Report 13354
[2]   ESTIMATING THE GINI INDEX FOR HEAVY-TAILED INCOME DISTRIBUTIONS [J].
Bari, Amina ;
Rassoul, Abdelaziz ;
Rouis, Hamid Ould .
SOUTH AFRICAN STATISTICAL JOURNAL, 2021, 55 (01) :15-28
[3]  
Beirlant J., 2002, EXTREMES, V5, P157, DOI [DOI 10.1023/A:, 10.1023/A:1022171205129, DOI 10.1023/A:1022171205129]
[4]  
Beirlant J., 1999, EXTREMES, V2, P177, DOI [DOI 10.1023/A:1009975020370, 10.1023/A:1009975020370]
[5]  
Bingham N. H., 1989, Encyclopedia Math. Appl., V27
[6]   OPTIMAL TAXATION OF CAPITAL INCOME IN GENERAL EQUILIBRIUM WITH INFINITE LIVES [J].
CHAMLEY, C .
ECONOMETRICA, 1986, 54 (03) :607-622
[7]   Extreme quantile estimation for β-mixing time series and applications [J].
Chavez-Demoulin, Valerie ;
Guillou, Armelle .
INSURANCE MATHEMATICS & ECONOMICS, 2018, 83 :59-74
[8]  
Cobham Alex, 2013, IS IT ALL TAILS PALM
[9]   WEIGHTED EMPIRICAL AND QUANTILE PROCESSES [J].
CSORGO, M ;
CSORGO, S ;
HORVATH, L ;
MASON, DM .
ANNALS OF PROBABILITY, 1986, 14 (01) :31-85
[10]   KERNEL ESTIMATES OF THE TAIL INDEX OF A DISTRIBUTION [J].
CSORGO, S ;
DEHEUVELS, P ;
MASON, D .
ANNALS OF STATISTICS, 1985, 13 (03) :1050-1077