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Inequality and negative income


  • Stich, Andreas


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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    References listed on IDEAS

    1. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
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    3. Diego Battiston & Guillermo Cruces & Luis Lopez-Calva & Maria Lugo & Maria Santos, 2013. "Income and Beyond: Multidimensional Poverty in Six Latin American Countries," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 112(2), pages 291-314, June.
    4. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 7-34, January.
    5. Gert Wagner & Jan Göbel & Peter Krause & Rainer Pischner & Ingo Sieber, 2008. "Das Sozio-oekonomische Panel (SOEP): Multidisziplinäres Haushaltspanel und Kohortenstudie für Deutschland – Eine Einführung (für neue Datennutzer) mit einem Ausblick (für erfahrene Anwender)," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 2(4), pages 301-328, December.
    6. Sabina Alkire & James Foster & Maria Santos, 2011. "Where did identification go?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 501-505, September.
    7. Jiantuo Yu, 2013. "Multidimensional Poverty in China: Findings Based on the CHNS," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 112(2), pages 315-336, June.
    8. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    9. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    10. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 25-49, April.
    11. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7), pages 476-487.
    12. Christopher J. Bennett & Shabana Mitra, 2013. "Multidimensional Poverty: Measurement, Estimation, and Inference," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 57-83, January.
    13. Zheng, Buhong, 1997. " Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    14. Mitra, Sophie & Posarac, Aleksandra & Vick, Brandon, 2013. "Disability and Poverty in Developing Countries: A Multidimensional Study," World Development, Elsevier, vol. 41(C), pages 1-18.
    15. Satya R. Chakravarty & Pietro Muliere, 2004. "Welfare indicators: a review and new perspectives. 2. Measurement of poverty," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 247-281.
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    Cited by:

    1. Giorgio Calcagnini & Francesco Perugini, 2016. "A Well-Being Indicator for the Italian Provinces a," Working Papers 1608, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2016.
    2. 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.
    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. 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.
    5. 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.
    6. 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).
    7. repec:psl:pslqrr:2017:22 is not listed on IDEAS

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