The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality
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.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.ecineq.org|
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Oihana Aristondo & Casilda Lasso de la Vega & Ana Urrutia, 2010.
"A New Multiplicative Decomposition For The Foster-Greer-Thorbecke Poverty Indices,"
Bulletin of Economic Research,
Wiley Blackwell, vol. 62(3), pages 259-267, 07.
- Oihana Aristondo & Casilda Lasso de la Vega & Ana Urrutia, 2008. "A New Multiplicative Decomposition For The Foster-Greer-Thorbecke Poverty Indices," Working Papers 91, ECINEQ, Society for the Study of Economic Inequality.
- Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
- Sen, Amartya, 1979. " Issues in the Measurement of Poverty," Scandinavian Journal of Economics, Wiley Blackwell, vol. 81(2), pages 285-307.
- Maes, Koen C. & Saminger, Susanne & De Baets, Bernard, 2007. "Representation and construction of self-dual aggregation operators," European Journal of Operational Research, Elsevier, vol. 177(1), pages 472-487, February.
- Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-59, May.
- Clarke, Philip M. & Gerdtham, Ulf-G. & Johannesson, Magnus & Bingefors, Kerstin & Smith, Len, 2002. "On the measurement of relative and absolute income-related health inequality," Social Science & Medicine, Elsevier, vol. 55(11), pages 1923-1928, December.
- Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
- Lars Osberg & Kuan Xu, 2000.
"International Comparisons of Poverty Intensity: Index Decomposition and Bootstrap Inference,"
Journal of Human Resources,
University of Wisconsin Press, vol. 35(1), pages 51-81.
- Osberg, L & Xu, K, 1997. "International Comparisons of Poverty Intensity : Index Decomposition and Bootstrap Inference," Department of Economics at Dalhousie University working papers archive 97-03, Dalhousie, Department of Economics.
- Kuan Xu & Lars Osberg, 2000.
"The Social Welfare Implications, Decomposability, and Geometry of the Sen Family of Poverty Indices,"
Department of Economics at Dalhousie University working papers archive
sendeco, Dalhousie, Department of Economics.
- Kuan Xu & Lars Osberg, 2002. "The social welfare implications, decomposability, and geometry of the Sen family of poverty indices," Canadian Journal of Economics, Canadian Economics Association, vol. 35(1), pages 138-152, February.
- Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-26, June.
When requesting a correction, please mention this item's handle: RePEc:inq:inqwps:ecineq2011-203. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maria Ana Lugo)
If references are entirely missing, you can add them using this form.