IDEAS home Printed from https://ideas.repec.org/a/eee/jhecon/v30y2011i1p214-219.html
   My bibliography  Save this article

On the consistent measurement of attainment and shortfall inequality

Author

Listed:
  • Lambert, Peter
  • Zheng, Buhong

Abstract

In measuring inequality of a bounded variable such as health status, one can focus on attainments or shortfalls. However, rankings of social states by attainment and shortfall inequality do not necessarily mirror one another. We propose a requirement, that attainment inequality and shortfall inequality be measured consistently, and we examine the performance of partial orderings and indices of inequality in this respect. For relative inequality and all currently documented intermediate inequality concepts, the orderings fail our consistency requirement, as do all indices which respect these orderings. However, the absolute inequality partial ordering satisfies consistency. We identify two classes of indices of absolute inequality, one containing rank-independent and the other rank-dependent indices, which measure attainment and shortfall inequality consistently (in fact identically). The only subgroup decomposable inequality index, of any type, which measures attainment and shortfall inequality consistently is the variance. We discuss implications for the study of pure health inequality.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jhecon:v:30:y:2011:i:1:p:214-219
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6296(10)00140-2
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. ERREYGERS, Guido & CLARKE, Philip & VAN OURTI, Tom, 2010. "Mirror, mirror, on the wall, who in this land is fairest of all? Revisiting the extended concentration index," Working Papers 2010015, University of Antwerp, Faculty of Business and Economics.
    2. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    3. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    4. Wagstaff, Adam, 2009. "Correcting the concentration index: A comment," Journal of Health Economics, Elsevier, vol. 28(2), pages 516-520, March.
    5. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, vol. 28(2), pages 521-524, March.
    6. 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.
    7. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    8. Tateo Yoshida, 2005. "Social welfare rankings of income distributions A new parametric concept of intermediate inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 557-574, June.
    9. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 485-497.
    10. Besley, Timothy J & Preston, I P, 1988. "Invariance and the Axiomatics of Income Tax Progression: A Comment," Bulletin of Economic Research, Wiley Blackwell, vol. 40(2), pages 159-163, April.
    11. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    12. 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.
    13. Erreygers, Guido, 2009. "Correcting the Concentration Index," Journal of Health Economics, Elsevier, vol. 28(2), pages 504-515, March.
    14. Buhong Zheng, 2007. "Unit‐Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, February.
    15. Pfingsten, Andreas, 1986. "Distributionally-neutral tax changes for different inequality concepts," Journal of Public Economics, Elsevier, vol. 30(3), pages 385-393, August.
    16. Bleichrodt, Han & van Doorslaer, Eddy, 2006. "A welfare economics foundation for health inequality measurement," Journal of Health Economics, Elsevier, vol. 25(5), pages 945-957, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Paul Makdissi & Myra Yazbeck, 2014. "Robust Wagstaff Orderings of Distributions of Self-Reported Health Status," Discussion Papers Series 533, School of Economics, University of Queensland, Australia.
    2. Paul Allanson & Dennis Petrie, 2014. "Understanding The Vertical Equity Judgements Underpinning Health Inequality Measures," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1390-1396, November.
    3. MUSSARD Stéphane & PI ALPERIN Maria Noel & THIREAU Véronique, 2016. "Aggregable Health Inequality Indices," LISER Working Paper Series 2016-11, LISER.
    4. Asadullah, M. Niaz & Trannoy, Alain & Tubeuf, Sandy & Yalonetzky, Gaston, 2021. "Measuring educational inequality of opportunity: pupil’s effort matters," World Development, Elsevier, vol. 138(C).
    5. Gaston Yalonetzky, 2020. "Inequality of ratios," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 193-217, August.
    6. Makdissi, Paul & Yazbeck, Myra, 2016. "Avoiding blindness to health status in health achievement and health inequality measurement," Social Science & Medicine, Elsevier, vol. 171(C), pages 39-47.
    7. Satya R. Chakravarty & Nachiketa Chattopadhyay & Conchita D'Ambrosio, 2016. "On a Family of Achievement and Shortfall Inequality Indices," Health Economics, John Wiley & Sons, Ltd., vol. 25(12), pages 1503-1513, December.
    8. Paul Makdissi & Myra Yazbeck, 2017. "Robust rankings of socioeconomic health inequality using a categorical variable," Health Economics, John Wiley & Sons, Ltd., vol. 26(9), pages 1132-1145, September.
    9. Paul Allanson & Dennis Petrie, 2013. "On The Choice Of Health Inequality Measure For The Longitudinal Analysis Of Income‐Related Health Inequalities," Health Economics, John Wiley & Sons, Ltd., vol. 22(3), pages 353-365, March.
    10. Makdissi, Paul & Yazbeck, Myra, 2014. "Measuring socioeconomic health inequalities in presence of multiple categorical information," Journal of Health Economics, Elsevier, vol. 34(C), pages 84-95.
    11. 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.
    12. Stéphane Mussard & Maria Noel Pi Alperin & Véronique Thireau, 2018. "Health inequality indices and exogenous risk factors: an illustration on Luxembourgish workers," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 19(9), pages 1285-1301, December.
    13. Iñaki Permanyer, 2016. "Measuring Achievement and Shortfall Improvements in a Consistent Way," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(4), pages 758-774, December.
    14. Paul Makdissi & Myra Yazbeck, 2012. "Avoiding Blinding to Health Status: A New Class of Health Achievement and Inequality Indices," Working Papers 1207E, University of Ottawa, Department of Economics.
    15. Guido Erreygers & Tom Van Ourti, 2011. "Putting the cart before the horse. A comment on Wagstaff on inequality measurement in the presence of binary variables," Health Economics, John Wiley & Sons, Ltd., vol. 20(10), pages 1161-1165, October.
    16. Baeten, Steef & Van Ourti, Tom & van Doorslaer, Eddy, 2013. "Rising inequalities in income and health in China: Who is left behind?," Journal of Health Economics, Elsevier, vol. 32(6), pages 1214-1229.
    17. Oihana Aristondo & Francisco J. Goerlich Gisbert & Casilda Lasso De La Vega, 2015. "A Proposal to Compare Consistently the Inequality Among the Poor," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 561-572, September.
    18. Erreygers, Guido & Van Ourti, Tom, 2011. "Measuring socioeconomic inequality in health, health care and health financing by means of rank-dependent indices: A recipe for good practice," Journal of Health Economics, Elsevier, vol. 30(4), pages 685-694, July.
    19. Owen O'Donnell & Eddy Van Doorslaer & Tom Van Ourti, 2013. "Health and Inequality," Tinbergen Institute Discussion Papers 13-170/V, Tinbergen Institute.
    20. Lasso de la Vega, Casilda & Aristondo, Oihana, 2012. "Proposing indicators to measure achievement and shortfall inequality consistently," Journal of Health Economics, Elsevier, vol. 31(4), pages 578-583.
    21. Gaston Yalonetzky, 0. "Inequality of ratios," METRON, Springer;Sapienza Università di Roma, vol. 0, pages 1-25.
    22. Kristof Bosmans, 2016. "Consistent Comparisons of Attainment and Shortfall Inequality: A Critical Examination," Health Economics, John Wiley & Sons, Ltd., vol. 25(11), pages 1425-1432, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lasso de la Vega, Casilda & Aristondo, Oihana, 2012. "Proposing indicators to measure achievement and shortfall inequality consistently," Journal of Health Economics, Elsevier, vol. 31(4), pages 578-583.
    2. Paul Allanson & Dennis Petrie, 2014. "Understanding The Vertical Equity Judgements Underpinning Health Inequality Measures," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1390-1396, November.
    3. Paul Allanson & Dennis Petrie, 2013. "On The Choice Of Health Inequality Measure For The Longitudinal Analysis Of Income‐Related Health Inequalities," Health Economics, John Wiley & Sons, Ltd., vol. 22(3), pages 353-365, March.
    4. 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.
    5. Erreygers, Guido & Van Ourti, Tom, 2011. "Measuring socioeconomic inequality in health, health care and health financing by means of rank-dependent indices: A recipe for good practice," Journal of Health Economics, Elsevier, vol. 30(4), pages 685-694, July.
    6. Satya Chakravarty & Swami Tyagarupananda, 2009. "The subgroup decomposable intermediate indices of inequality," Spanish Economic Review, Springer;Spanish Economic Association, vol. 11(2), pages 83-97, June.
    7. Makdissi, Paul & Yazbeck, Myra, 2016. "Avoiding blindness to health status in health achievement and health inequality measurement," Social Science & Medicine, Elsevier, vol. 171(C), pages 39-47.
    8. Zhong, Hai, 2009. "A multivariate analysis of the distribution of individual's welfare in China: What is the role of health?," Journal of Health Economics, Elsevier, vol. 28(6), pages 1062-1070, December.
    9. Makdissi, Paul & Yazbeck, Myra, 2014. "Measuring socioeconomic health inequalities in presence of multiple categorical information," Journal of Health Economics, Elsevier, vol. 34(C), pages 84-95.
    10. Kristof Bosmans, 2016. "Consistent Comparisons of Attainment and Shortfall Inequality: A Critical Examination," Health Economics, John Wiley & Sons, Ltd., vol. 25(11), pages 1425-1432, November.
    11. Allanson, Paul, 2010. "Longitudinal analysis of income-related health inequality: welfare foundations and alternative measures," SIRE Discussion Papers 2010-71, Scottish Institute for Research in Economics (SIRE).
    12. Claudio Zoli, 2017. "A note on progressive taxation and inequality equivalence," Working Papers 19/2017, University of Verona, Department of Economics.
    13. FLEURBAEY, Marc & SCHOKKAERT, Erik, 2011. "Equity in health and health care," LIDAM Discussion Papers CORE 2011026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    15. Erreygers, Guido & Clarke, Philip & Van Ourti, Tom, 2012. "“Mirror, mirror, on the wall, who in this land is fairest of all?”—Distributional sensitivity in the measurement of socioeconomic inequality of health," Journal of Health Economics, Elsevier, vol. 31(1), pages 257-270.
    16. D. Jayaraj & S. Sreenivasan, 2015. "Growth and inequality in the distribution of India's consumption expenditure: 1983 to 2009-10," WIDER Working Paper Series 025, World Institute for Development Economic Research (UNU-WIDER).
    17. Teixidó Figueras, Jordi & Duro Moreno, Juan Antonio, 2012. "Ecological Footprint Inequality: A methodological review and some results," Working Papers 2072/203168, Universitat Rovira i Virgili, Department of Economics.
    18. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 555-577, December.
    19. 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.
    20. H. Eme Ichoku & William Fonta & Michael Thiede, 2011. "Socioeconomic gradients in self-rated health: a developing country case study of Enugu State, Nigeria," Economic Change and Restructuring, Springer, vol. 44(3), pages 179-202, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jhecon:v:30:y:2011:i:1:p:214-219. 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: (Haili He). General contact details of provider: http://www.elsevier.com/locate/inca/505560 .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.