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Consistent comparisons of attainment and shortfall inequality: A critical examination

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  • Bosmans, K.G.M.

    (Microeconomics & Public Economics)

Abstract

An inequality measure is ‘consistent’ if it ranks distributions the same irrespective of whether health quantities are represented in terms of attainment or shortfalls. This consistency property severely restricts the set of admissible inequality measures. We show that, within a more general setting of separate measures for attainments and shortfalls, the consistency property is a combination of two conditions. The first is a compelling rationality condition that says that the attainment measure should rank attainment distributions as the shortfall measure ranks shortfall distributions. The second is an overly demanding condition that says that the attainment measure and the shortfall measure should be identical. By dropping the latter condition, the restrictions on the admissible inequality measures disappear.

Suggested Citation

  • Bosmans, K.G.M., 2013. "Consistent comparisons of attainment and shortfall inequality: A critical examination," Research Memorandum 064, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013064
    DOI: 10.26481/umagsb.2013064
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    Cited by:

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    2. Gaston Yalonetzky, 2020. "Inequality of ratios," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 193-217, August.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Yalonetzky, Gaston, 2022. "Consistent and inconsistent inequality indices for ordinal variables," Economics Letters, Elsevier, vol. 219(C).
    8. Inaki Permanyer & Suman Seth & Gaston Yalonetzky, 2022. "Inequality measurement for bounded variables," Working Papers 602, ECINEQ, Society for the Study of Economic Inequality.
    9. Rohde, Kirsten I.M. & Van Ourti, Tom & Soebhag, Amar, 2023. "Reducing socioeconomic health inequalities? A questionnaire study of majorization and invariance conditions," Journal of Health Economics, Elsevier, vol. 90(C).
    10. Nanak Kakwani & Hyun H. Son, 2015. "Income inequality and social well-being," Working Papers 380, ECINEQ, Society for the Study of Economic Inequality.
    11. Calara, Paul Samuel & Gerdtham, Ulf-G & Petrie, Dennis, 2016. "The Dynamics of Income-Related Health Inequalities in Australia versus Great Britain," Working Papers 2016:20, Lund University, Department of Economics.
    12. Glenn Sheriff & Kelly B. Maguire, 2020. "Health Risk, Inequality Indexes, and Environmental Justice," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2661-2674, December.

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