IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/127974.html
   My bibliography  Save this paper

Inequality measurement for bounded variables

Author

Listed:
  • Permanyer, Inaki
  • Seth, Suman
  • Yalonetzky, Gaston

Abstract

Many health indicators are bounded, that is, their values lie between a lower and an upper bound. Inequality measurement with bounded variables faces two normative challenges well‐known in the health inequality literature. One is that inequality rankings may or may not be consistent across admissible attainment and shortfall representations of the variable. The other is that the set of maximum‐inequality distributions for bounded variables is different from the respective set for variables with no upper bound. Therefore, the ethical criteria for ranking maximum‐inequality distributions with unbounded variables may not be appropriate for bounded variables. In a novel proposal, we justify an axiom requiring maximum‐inequality distributions of bounded variables to be ranked equally, irrespective of their means. Then, our axiomatic characterization naturally leads to indices that measure inequality as an increasing function of the observed proportion of maximum attainable inequality for a given mean. Additionally, our inequality indices rank distributions consistently when switching between attainment and shortfall representations. In our empirical illustration with three health indicators, a starkly different picture of cross‐country inter‐temporal inequality emerges when traditional inequality indices give way to our proposed normalized inequality indices.

Suggested Citation

  • Permanyer, Inaki & Seth, Suman & Yalonetzky, Gaston, 2025. "Inequality measurement for bounded variables," LSE Research Online Documents on Economics 127974, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:127974
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/127974/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, vol. 28(2), pages 521-524, March.
    3. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    4. 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.
    5. Fields, Gary S, 1993. "Inequality in Dual Economy Models," Economic Journal, Royal Economic Society, vol. 103(420), pages 1228-1235, September.
    6. 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.
    7. repec:zbw:hohpro:325 is not listed on IDEAS
    8. Suman Seth & Mark McGillivray, 2018. "Composite indices, alternative weights, and comparison robustness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 657-679, December.
    9. 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.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    11. repec:old:wpaper:325 is not listed on IDEAS
    12. Fields, Gary S., 1987. "Measuring inequality change in an economy with income growth," Journal of Development Economics, Elsevier, vol. 26(2), pages 357-374, August.
    13. Erreygers, Guido, 2009. "Correcting the Concentration Index," Journal of Health Economics, Elsevier, vol. 28(2), pages 504-515, March.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Mohammad Abu‐Zaineh & Ramses H. Abul Naga, 2023. "Bread and Social Justice: Measurement of Social Welfare and Inequality Using Anthropometrics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 69(2), pages 265-288, June.
    3. Inaki Permanyer & Suman Seth & Gaston Yalonetzky, 2022. "Inequality measurement for bounded variables," Working Papers 602, ECINEQ, Society for the Study of Economic Inequality.
    4. 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.
    5. Gustav Kjellsson & Ulf-G. Gerdtham, 2013. "Lost in Translation: Rethinking the Inequality Equivalence Criteria for Bounded Health Variables," Research on Economic Inequality, in: Health and Inequality, volume 21, pages 3-32, Emerald Group Publishing Limited.
    6. 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.
    7. 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.
    8. 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.
    9. Guido Erreygers & Roselinde Kessels, 2017. "Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality," IJERPH, MDPI, vol. 14(7), pages 1-23, June.
    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. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Gaston Yalonetzky, 2020. "Inequality of ratios," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 193-217, August.
    16. Pulok, Mohammad Habibullah & van Gool, Kees & Hall, Jane, 2020. "Horizontal inequity in the utilisation of healthcare services in Australia," Health Policy, Elsevier, vol. 124(11), pages 1263-1271.
    17. Bénédicte H. Apouey & Jacques Silber, 2016. "Performance and Inequality in Health: A Comparison of Child and Maternal Health across Asia," Research on Economic Inequality, in: Inequality after the 20th Century: Papers from the Sixth ECINEQ Meeting, volume 24, pages 181-214, Emerald Group Publishing Limited.
    18. Gerdtham, Ulf-G & Lundborg, Petter & Lyttkens, Carl Hampus & Nystedt, Paul, 2012. "Do Socioeconomic Factors Really Explain Income-Related Inequalities in Health? Applying a Twin Design to Standard Decomposition Analysis," Working Papers 2012:21, Lund University, Department of Economics.
    19. Conrad Murendo & Gamuchirai Murenje & Pepukai Prince Chivenge & Rumbidzai Mtetwa, 2021. "Financial Inclusion, Nutrition and Socio‐Economic Status Among Rural Households in Guruve and Mount Darwin Districts, Zimbabwe," Journal of International Development, John Wiley & Sons, Ltd., vol. 33(1), pages 86-108, January.
    20. 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.

    More about this item

    Keywords

    bounded variables; inequality measurement; consistency;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being
    • O57 - Economic Development, Innovation, Technological Change, and Growth - - Economywide Country Studies - - - Comparative Studies of Countries

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ehl:lserod:127974. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.