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Inequality and negative income

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  • Stich, Andreas

Abstract

This paper deals with some problems in the measurement of inequality when negative incomes are allowed. A helpful axiom is defined, called the Greatest Gets More axiom. Using this axiom it can be shown that the properties of some inequality measures depend on whether there are negative incomes or not. In this paper for the intermediate measures of Eichhorn and the centrist measures of Kolm a threshold value is given above which the Greatest Gets More axiom holds. Furthermore, a simple proof is given for the fact that there exists no function which fulfills the three axioms Pigou-Dalton, homogeneity and additive invariance when the data contain negative incomes.

Suggested Citation

  • Stich, Andreas, 1996. "Inequality and negative income," Discussion Papers in Econometrics and Statistics 4/96, University of Cologne, Institute of Econometrics and Statistics.
    • Handle: RePEc:zbw:ucdpse:9604
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    Cited by:

    1. Nkonya, Ephraim & Phillip, Dayo & Mogues, Tewodaj & Pender, John & Kato, Edward, 2012. "Impacts of Community-driven Development Programs on Income and Asset Acquisition in Africa: The Case of Nigeria," World Development, Elsevier, vol. 40(9), pages 1824-1838.
    2. Vladimir Hlasny & Lidia Ceriani & Paolo Verme, 2022. "Bottom Incomes and the Measurement of Poverty and Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 970-1006, December.
    3. Peter Lindner, 2015. "Factor decomposition of the wealth distribution in the euro area," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 42(2), pages 291-322, May.
    4. Lidia Ceriani & Vladimir Hlasny & Paolo Verme, 2021. "Bottom Incomes and the Measurement of Poverty: A Brief Assessment of the Literature," Working Papers 589, ECINEQ, Society for the Study of Economic Inequality.
    5. Nkonya, Ephraim & Phillip, Dayo & Mogues, Tewodaj & Pender, John & Yahaya, Muhammed Kuta & Adebowale, Gbenga & Arokoyo, Tunji & Kato, Edward, 2008. "From the ground up: Impacts of a pro-poor community-driven development project in Nigeria," IFPRI discussion papers 756, International Food Policy Research Institute (IFPRI).
    6. Laurent Piet & M Benoit & V Chatellier & K. Hervé Dakpo & N Delame & Yann Desjeux & P Dupraz & M Gillot & Philippe Jeanneaux & C Laroche-Dupraz & A Ridier & E Samson & P Veysset & P Avril & C Beaudoui, 2020. "Hétérogénéité, déterminants et trajectoires du revenu des agriculteurs français," Working Papers hal-02877320, HAL.
    7. Giorgio Calcagnini & Francesco Perugini, 2019. "A Well-Being Indicator for the Italian Provinces," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 142(1), pages 149-177, February.
    8. Ana Manero, 2017. "Income inequality within smallholder irrigation schemes in Sub-Saharan Africa," International Journal of Water Resources Development, Taylor & Francis Journals, vol. 33(5), pages 770-787, September.
    9. Loek Groot & Erik Zonneveld, 2013. "European Union Budget Contributions and Expenditures: A Lorenz Curve Approach," Journal of Common Market Studies, Wiley Blackwell, vol. 51(4), pages 649-666, July.
    10. 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.
    11. Ignazio Drudi & Giorgio Tassinari & Fabrizio Alboni, 2017. "Changes in wealth distribution in Italy (2002-2012) and who gained from the Great Recession," PSL Quarterly Review, Economia civile, vol. 70(281), pages 129-153.

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