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

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Author Info

  • 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)

Abstract

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.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2011-203.pdf
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Bibliographic Info

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

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Length: 24 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2011-203

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Keywords: Aggregation functions; dual decomposition; OWA operators; Gini index; consistent measures of achievement/shortfall inequality; Sen index; poverty measures.;

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References

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  1. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, Econometric Society, vol. 47(3), pages 747-59, May.
  2. 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, Wiley Blackwell, vol. 62(3), pages 259-267, 07.
  3. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 91(362), pages 515-26, June.
  4. Osberg, L & Xu, K, 1997. "International Comparisons of Poverty Intensity : Index Decomposition and Bootstrap Inference," Department of Economics at Dalhousie University working papers archive, Dalhousie, Department of Economics 97-03, Dalhousie, Department of Economics.
  5. 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, Dalhousie, Department of Economics sendeco, Dalhousie, Department of Economics.
  6. Maes, Koen C. & Saminger, Susanne & De Baets, Bernard, 2007. "Representation and construction of self-dual aggregation operators," European Journal of Operational Research, Elsevier, Elsevier, vol. 177(1), pages 472-487, February.
  7. 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.
  8. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 761-66, May.
  9. Sen, Amartya, 1979. " Issues in the Measurement of Poverty," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 81(2), pages 285-307.
  10. 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, Elsevier, vol. 55(11), pages 1923-1928, December.
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Cited by:
  1. Oihana Aristondo & JosŽ Luis Garc’a-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2012. "Classical inequality indices, welfare functions, and the dual decomposition," DISA Working Papers, Department of Computer and Management Sciences, University of Trento, Italy 2012/06, Department of Computer and Management Sciences, University of Trento, Italy, revised Jun 2012.
  2. Silvia Bortot & Ricardo Alberto Marques Pereira, 2013. "The binomial Gini inequality indices and the binomial decomposition of welfare functions," Working Papers 305, ECINEQ, Society for the Study of Economic Inequality.

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