IDEAS home Printed from https://ideas.repec.org/a/spr/jeicoo/v16y2021i2d10.1007_s11403-020-00295-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11403-020-00295-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11403-020-00295-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    6. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    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.
    9. Corrado Gini, 2005. "On the measurement of concentration and variability of characters," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-38.
    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.
    11. Salverda, Wiemer & Nolan, Brian & Smeeding, Timothy M. (ed.), 2011. "The Oxford Handbook of Economic Inequality," OUP Catalogue, Oxford University Press, number 9780199606061, Decembrie.
    12. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    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. 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.
    2. 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.
    3. Camacho Cuena, Eva & Neugebauer, Tibor & Seidl, Christian, 2005. "Compensating justice beats leaky buckets: an experimental investigation," Economics Working Papers 2005-06, Christian-Albrechts-University of Kiel, Department of Economics.
    4. 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.
    5. Eva Camacho-Cuena & Tibor Neugebauer & Christian Seidl, 2007. "Leaky Buckets Versus Compensating Justice: An Experimental Investigation," Working Papers 74, ECINEQ, Society for the Study of Economic Inequality.
    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. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    8. Casilda Lasso de la Vega & Ana Urrutia & Oscar Volij, 2011. "An Axiomatic Characterization Of The Theil Inequality Order," Working Papers 1103, Ben-Gurion University of the Negev, Department of Economics.
    9. Pedro Salas-Rojo & Juan Gabriel Rodríguez, 2022. "Inheritances and wealth inequality: a machine learning approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 27-51, March.
    10. Guido Erreygers & Roselinde Kessels & Linkun Chen & Philip Clarke, 2016. "Decomposing Socioeconomic Inequality of Health," EcoMod2016 9574, EcoMod.
    11. Peter J. Lambert & Helen T. Naughton, 2009. "The Equal Absolute Sacrifice Principle Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 23(2), pages 328-349, April.
    12. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    13. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.
    14. Stéphane Mussard & Pauline Mornet, 2019. "A Note on α‐Gini Measures," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(3), pages 675-682, September.
    15. repec:ebl:ecbull:v:3:y:2003:i:19:p:1-16 is not listed on IDEAS
    16. Sorger, Gerhard & Stark, Oded, 2013. "Income redistribution going awry: The reversal power of the concern for relative deprivation," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 1-9.
    17. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    18. Kleiber, Christian, 1997. "The existence of population inequality measures," Economics Letters, Elsevier, vol. 57(1), pages 39-44, November.
    19. Marko Ledić & Ivica Rubil & Ivica Urban, 2023. "Tax progressivity and social welfare with a continuum of inequality views," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 30(5), pages 1266-1296, October.
    20. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    21. Udo Ebert & Heinz Welsch, 2009. "How Do Europeans Evaluate Income Distributions? An Assessment Based On Happiness Surveys," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(3), pages 803-819, September.

    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

    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:spr:jeicoo:v:16:y:2021:i:2:d:10.1007_s11403-020-00295-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.