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Proposing indicators to measure achievement and shortfall inequality consistently

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  • Lasso de la Vega, Casilda
  • Aristondo, Oihana

Abstract

In several economic fields, such as those related to health or education, 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. In this note we propose a procedure to define indicators that measure equally the achievement and shortfall inequality. Specifically, we derive measures which are invariant under ratio-scale or translation transformations, and a decomposable measure is also obtained. As the indicators proposed depend on the distribution bounds, families of indices that guarantee the same inequality rankings regardless of the distribution maximal levels are identified.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Health Economics.

Volume (Year): 31 (2012)
Issue (Month): 4 ()
Pages: 578-583

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Handle: RePEc:eee:jhecon:v:31:y:2012:i:4:p:578-583

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Web page: http://www.elsevier.com/locate/inca/505560

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Keywords: Inequality measurement; Health inequality; Achievements; Shortfalls;

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References

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  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. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, vol. 91(2), pages 199-222, April.
  3. Adam Wagstaff, 2005. "The bounds of the concentration index when the variable of interest is binary, with an application to immunization inequality," Health Economics, John Wiley & Sons, Ltd., vol. 14(4), pages 429-432.
  4. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
  6. Bosmans, Kristof & Cowell, Frank A., 2010. "The class of absolute decomposable inequality measures," Economics Letters, Elsevier, vol. 109(3), pages 154-156, December.
  7. Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, 02.
  8. Wagstaff, Adam, 2009. "Correcting the concentration index: A comment," Journal of Health Economics, Elsevier, vol. 28(2), pages 516-520, March.
  9. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  10. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, vol. 28(2), pages 521-524, March.
  11. Erreygers, Guido, 2009. "Can a single indicator measure both attainment and shortfall inequality?," Journal of Health Economics, Elsevier, vol. 28(4), pages 885-893, July.
  12. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  13. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  14. Lambert, Peter & Zheng, Buhong, 2011. "On the consistent measurement of attainment and shortfall inequality," Journal of Health Economics, Elsevier, vol. 30(1), pages 214-219, January.
  15. Erreygers, Guido, 2009. "Correcting the Concentration Index," Journal of Health Economics, Elsevier, vol. 28(2), pages 504-515, March.
  16. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  17. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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Cited by:
  1. Satya R. Chakravarty & Nachiketa Chattopadhyay & Conchita D’Ambrosio, 2013. "On a family of achievement and shortfall inequality indices," Working Papers 300, ECINEQ, Society for the Study of Economic Inequality.
  2. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables," Working Papers 2013:18, Lund University, Department of Economics, revised 02 Jan 2014.
  3. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "On correcting the concentration index for binary variables," Journal of Health Economics, Elsevier, vol. 32(3), pages 659-670.

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