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Measuring income inequality based on unequally distributed income

Author

Listed:
  • Joongyang Park

    (Gyeongsang National University)

  • Youngsoon Kim

    (Gyeongsang National University)

  • Ae-Jin Ju

    (Gyeongsang National University)

Abstract

This paper proposes a new framework for measuring income inequality. The framework is based on the unequally distributed (UD) incomes that are obtained by removing the equally distributed parts from incomes. We then derive the normalized norm indexes from the cumulative distribution function and the unscaled Lorenz curve of the UD incomes. The relation between the normalized norm indexes and the popular Gini coefficient and coefficient of variation (CV) shows that the Gini coefficient and CV represent only parts of income inequality. We analyze example income distributions and the Luxembourg Income Study datasets to show that the normalized norm indexes evaluate income inequality appropriately and solve the negative income problem.

Suggested Citation

  • Joongyang Park & Youngsoon Kim & Ae-Jin Ju, 2021. "Measuring income inequality based on unequally distributed income," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 309-322, April.
    • Handle: RePEc:spr:jeicoo:v:16:y:2021:i:2:d:10.1007_s11403-020-00295-1
    DOI: 10.1007/s11403-020-00295-1
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    References listed on IDEAS

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Fabio Clementi & Mauro Gallegati & Lisa Gianmoena & Simone Landini & Joseph E. Stiglitz, 2019. "Mis-measurement of inequality: a critical reflection and new insights," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(4), pages 891-921, December.
    3. Chen, Chau-Nan & Tsaur, Tien-Wang & Rhai, Tong-Shieng, 1982. "The Gini Coefficient and Negative Income," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 473-478, November.
    4. Emanuela Raffinetti & Elena Siletti & Achille Vernizzi, 2015. "On the Gini coefficient normalization when attributes with negative values are considered," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 507-521, September.
    5. Dorfman, Robert, 1979. "A Formula for the Gini Coefficient," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 146-149, February.
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    7. Emanuela Raffinetti & Elena Siletti & Achille Vernizzi, 2017. "Analyzing the Effects of Negative and Non-negative Values on Income Inequality: Evidence from the Survey of Household Income and Wealth of the Bank of Italy (2012)," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 133(1), pages 185-207, August.
    8. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
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    10. Joongyang Park & YoungSoon Kim & Seon‐ja Heo, 2018. "Dual‐Index Measurement Of Income Inequality," Bulletin of Economic Research, Wiley Blackwell, vol. 70(3), pages 277-284, July.
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    More about this item

    Keywords

    Coefficient of variation; Gini coefficient; Income inequality; $$ell _1$$ ℓ 1 Norm; $$ell _2$$ ℓ 2 Norm; Normalized norm index; Rawlsian index; Unequally distributed income;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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