IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality

  • Oihana Aristondo

    ()

    (Universidad del País Vasco)

  • José Luis García-Lapresta

    ()

    (Universidad Valladolid)

  • Casilda Lasso de la Vega

    ()

    (Universidad del País Vasco)

  • Ricardo Alberto Marques Pereira

    ()

    (Universita degli Studi di Trento)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.ecineq.org/milano/WP/ECINEQ2011-203.pdf
Download Restriction: no

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 203.

as
in new window

Length: 24 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2011-203
Contact details of provider: Web page: http://www.ecineq.org
Email:


More information through EDIRC

References listed on IDEAS
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.:

as in new window
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  7. 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.
  8. Sen, Amartya, 1979. " Issues in the Measurement of Poverty," Scandinavian Journal of Economics, Wiley Blackwell, vol. 81(2), pages 285-307.
  9. 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.
  10. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

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 you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.