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Inequality Comparisons with Ordinal Data

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  • Stephen P. Jenkins

Abstract

Non‐intersection of appropriately defined Generalized Lorenz (GL) curves is equivalent to a unanimous ranking of distributions of ordinal data by all Cowell and Flachaire (Economica, 2017) indices of inequality and by a new index based on GL curve areas. Comparisons of life satisfaction distributions for six countries reveal a substantial number of unanimous rankings. The GL dominance criteria are compared with other criteria including the dual‐H dominance criteria of Gravel, Magdalou, and Moyes (Economic Theory, 2020).

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  • Stephen P. Jenkins, 2021. "Inequality Comparisons with Ordinal Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(3), pages 547-563, September.
    • Handle: RePEc:bla:revinw:v:67:y:2021:i:3:p:547-563
    DOI: 10.1111/roiw.12489
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    1. Benedicte Apouey, 2007. "Measuring health polarization with self‐assessed health data," Health Economics, John Wiley & Sons, Ltd., vol. 16(9), pages 875-894, September.
    2. Abul Naga, Ramses H. & Yalcin, Tarik, 2008. "Inequality measurement for ordered response health data," Journal of Health Economics, Elsevier, vol. 27(6), pages 1614-1625, December.
    3. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2014. "Ranking Distributions of an Ordinal Attribute," AMSE Working Papers 1450, Aix-Marseille School of Economics, France.
    4. Stephen P. Jenkins, 2020. "Better off? Distributional comparisons for ordinal data about personal well-being," New Zealand Economic Papers, Taylor & Francis Journals, vol. 54(3), pages 211-238, September.
    5. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    6. Frank A. Cowell & Emmanuel Flachaire, 2017. "Inequality with Ordinal Data," Economica, London School of Economics and Political Science, vol. 84(334), pages 290-321, April.
    7. Bénédicte Apouey & Jacques Silber & Yongsheng Xu, 2020. "On Inequality‐Sensitive and Additive Achievement Measures Based on Ordinal Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(2), pages 267-286, June.
    8. Stephen P. Jenkins, 2020. "Comparing distributions of ordinal data," Stata Journal, StataCorp LP, vol. 20(3), pages 505-531, September.
    9. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    10. Martyna Kobus, 2015. "Erratum to: Polarization measurement for ordinal data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 13(3), pages 485-485, September.
    11. Jenkins, Stephen P & Lambert, Peter J, 1997. "Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends," Oxford Economic Papers, Oxford University Press, vol. 49(3), pages 317-327, July.
    12. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-1230, September.
    13. Martyna Kobus, 2015. "Polarization measurement for ordinal data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 13(2), pages 275-297, June.
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    Cited by:

    1. Joan Costa-Font & Frank Cowell & Xuezhu Shi & Joan Costa-i-Font, 2023. "Health Inequality and Health Insurance Coverage: The United States and China Compared," CESifo Working Paper Series 10807, CESifo.
    2. Joan Costa-Font & Frank A. Cowell, 2022. "The measurement of health inequalities: does status matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(2), pages 299-325, June.
    3. Enza Simeone, 2023. "Inequality in health status during the COVID-19 in the UK: does the impact of the second lockdown policy matter?," Working Papers 661, ECINEQ, Society for the Study of Economic Inequality.
    4. Stephen P. Jenkins, 2020. "Better off? Distributional comparisons for ordinal data about personal well-being," New Zealand Economic Papers, Taylor & Francis Journals, vol. 54(3), pages 211-238, September.
    5. Stephen P. Jenkins, 2020. "Comparing distributions of ordinal data," Stata Journal, StataCorp LP, vol. 20(3), pages 505-531, September.
    6. Arthur Grimes & Stephen P. Jenkins & Florencia Tranquilli, 2023. "The Relationship Between Subjective Wellbeing and Subjective Wellbeing Inequality: An Important Role for Skewness," Journal of Happiness Studies, Springer, vol. 24(1), pages 309-330, January.
    7. Wesselbaum, Dennis & Smith, Michael D. & Barrett, Christopher B. & Aiyar, Anaka, 2023. "A food insecurity Kuznets Curve?," World Development, Elsevier, vol. 165(C).
    8. Silber, Jacques & Yalonetzky, Gaston, 2021. "Measuring welfare, inequality and poverty with ordinal variables," GLO Discussion Paper Series 962, Global Labor Organization (GLO).
    9. Bert Provan, 2022. "CASE Annual Report 2021," CASE Reports casereport142, Centre for Analysis of Social Exclusion, LSE.
    10. Fakih, Ali & Makdissi, Paul & Marrouch, Walid & Tabri, Rami V. & Yazbeck, Myra, 2022. "A stochastic dominance test under survey nonresponse with an application to comparing trust levels in Lebanese public institutions," Journal of Econometrics, Elsevier, vol. 228(2), pages 342-358.
    11. Anderson, Gordon & Fu, Rui & Leo, Teng Wah, 2022. "Health, loneliness and the ageing process in the absence of cardinal measure: Rendering intangibles tangible," The Journal of the Economics of Ageing, Elsevier, vol. 22(C).
    12. Costa-Font, Joan & Cowell, Frank & Shi, Xuezhu, 2024. "Health inequality and health insurance coverage: The United States and China compared," Economics & Human Biology, Elsevier, vol. 52(C).
    13. García-Peñalosa, Cecilia & Petit, Fabien & van Ypersele, Tanguy, 2023. "Can workers still climb the social ladder as middling jobs become scarce? Evidence from two British cohorts," Labour Economics, Elsevier, vol. 84(C).
    14. Jan Delhey & Stephanie Hess & Klaus Boehnke & Franziska Deutsch & Jan Eichhorn & Ulrich Kühnen & Christian Welzel, 2023. "Life Satisfaction During the COVID-19 Pandemic: The Role of Human, Economic, Social, and Psychological Capital," Journal of Happiness Studies, Springer, vol. 24(7), pages 2201-2222, October.
    15. Yalonetzky, Gaston, 2022. "Consistent and inconsistent inequality indices for ordinal variables," Economics Letters, Elsevier, vol. 219(C).

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    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • 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

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