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

Author

Listed:
  • 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.

Suggested Citation

  • Oihana Aristondo & José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2011. "The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality," Working Papers 203, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2011-203
    as

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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2011-203.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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, July.
    4. 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.
    5. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    6. Sen, Amartya, 1979. " Issues in the Measurement of Poverty," Scandinavian Journal of Economics, Wiley Blackwell, vol. 81(2), pages 285-307.
    7. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-526, June.
    8. 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.
    9. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-759, May.
    10. 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.
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    Cited by:

    1. Roy Cerqueti & Marcel Ausloos, 2015. "Statistical assessment of regional wealth inequalities: the Italian case," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2307-2323, November.
    2. Oihana Aristondo & José Luis García-Lapres & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2012. "Classical inequality indices, welfare functions, and the dual decomposition," Working Papers 253, ECINEQ, Society for the Study of Economic Inequality.
    3. Roy Cerqueti & Marcel Ausloos, 2014. "Assessing the Inequalities of Wealth in Regions: the Italian Case," Papers 1410.4922, arXiv.org.
    4. 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.

    More about this item

    Keywords

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

    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, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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