The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality
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.
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Bibliographic InfoPaper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 203.
Length: 24 pages
Date of creation: 2011
Date of revision:
Aggregation functions; dual decomposition; OWA operators; Gini index; consistent measures of achievement/shortfall inequality; Sen index; poverty measures.;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- I32 - Health, Education, and Welfare - - Welfare and Poverty - - - Measurement and Analysis of Poverty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-22 (All new papers)
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