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Proposing indicators to measure achievement and shortfall inequality consistently

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  • Casilda Lasso de la Vega
  • Oihana Aristondo

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 to measure consistently the achievement and shortfall inequality. Specifically, we derive measures which are invariant under ratio-scale or translation transformations, and a decomposable measure also is proposed.

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File URL: http://www.bwpi.manchester.ac.uk/medialibrary/publications/working_papers/bwpi-wp-12010.pdf
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Paper provided by BWPI, The University of Manchester in its series Brooks World Poverty Institute Working Paper Series with number 12010.

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Date of creation: 2010
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Handle: RePEc:bwp:bwppap:12010

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  1. Erreygers, Guido, 2009. "Correcting the Concentration Index," Journal of Health Economics, Elsevier, Elsevier, vol. 28(2), pages 504-515, March.
  2. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, Elsevier, vol. 22(1), pages 67-86, February.
  3. Kristof Bosmans & Frank Cowell, 2009. "The class of absolute decomposable inequality measures," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 25434, London School of Economics and Political Science, LSE Library.
  4. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1369-85, November.
  5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(1), pages 82-111, August.
  6. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, Econometric Society, vol. 48(3), pages 613-25, April.
  7. 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.
  8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, Elsevier, vol. 12(3), pages 416-442, June.
  9. Erreygers, Guido, 2009. "Can a single indicator measure both attainment and shortfall inequality?," Journal of Health Economics, Elsevier, Elsevier, vol. 28(4), pages 885-893, July.
  10. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, Elsevier, vol. 28(2), pages 521-524, March.
  11. Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, London School of Economics and Political Science, vol. 74(293), pages 97-111, 02.
  12. Lambert, Peter & Zheng, Buhong, 2011. "On the consistent measurement of attainment and shortfall inequality," Journal of Health Economics, Elsevier, Elsevier, vol. 30(1), pages 214-219, January.
  13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(3), pages 244-263, September.
  14. 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.
  15. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  16. Foster, James E. & Shneyerov, Artyom A., 2000. "Path Independent Inequality Measures," Journal of Economic Theory, Elsevier, Elsevier, vol. 91(2), pages 199-222, April.
  17. Wagstaff, Adam, 2009. "Correcting the concentration index: A comment," Journal of Health Economics, Elsevier, Elsevier, vol. 28(2), pages 516-520, March.
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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. "On correcting the concentration index for binary variables," Journal of Health Economics, Elsevier, Elsevier, vol. 32(3), pages 659-670.
  3. Kjellsson, Gustav, 2014. "Extending Decomposition Analysis to Account for Socioeconomic Background: Income-Related Smoking Inequality among Swedish Women," Working Papers, Lund University, Department of Economics 2014:29, Lund University, Department of Economics.
  4. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables," Working Papers, Lund University, Department of Economics 2013:18, Lund University, Department of Economics, revised 02 Jan 2014.

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