7 research outputs found
The Gini index and the consistent measurement of inequality among the poor
In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A diculty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor
Multidistances and Dispersion Measures
ProducciĂłn CientĂficaIn this paper, we provide a formal notion of absolute dispersion measure that
is satisfied by some classical dispersion measures used in Statistics, such as the
range, the variance, the mean deviation and the standard deviation, among others,
and also by the absolute Gini index, used in Welfare Economics for measuring
inequality. The notion of absolute dispersion measure shares some properties
with the notion of multidistance introduced and analyzed by Mart´ın and
Mayor in several recent papers. We compare absolute dispersion measures and
multidistances and we establish that these two notions are compatible by showing
some functions that are simultaneously absolute dispersion measures and
multidistances. We also establish that remainders obtained through the dual decomposition
of exponential means, introduced by Garc´ıa-Lapresta and Marques
Pereira, are absolute dispersion measures up to signMinisterio de EconomĂa, Industria y Competitividad (ECO2012-32178)Junta de Castilla y LeĂłn (programa de apoyo a proyectos de investigaciĂłn – Ref. VA066U13