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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 difficulty 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. Keywords AbstractIn 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 difficulty 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.

This paper shows that Foster-Greer-Thorbecke poverty indices can be written as the product of components summarizing the incidence, intensity and inequality dimensions of poverty and provides an empirical illustration of the decomposition using Spanish household budget surveys data.

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In several economic fields, such as those related to health or education, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty 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. In this note we propose a procedure to define indicators that measure equally the achievement and shortfall inequality. Specifically, we derive measures which are invariant under ratio-scale or translation transformations, and a decomposable measure is also obtained. As the indicators proposed depend on the distribution bounds, families of indices that guarantee the same inequality rankings regardless of the distribution maximal levels are identified.