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Characterizing Inequality Equivalence Criteria

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  • Claudio Zoli

    () (Department of Economics (University of Verona))

Abstract

We introduce an axiomatic framework to analyze the perception of inequality across distributions with different total income. The main result is the characterization of a new two parameters generalized version of the inequality equivalence criterion (IEC), the Flexible IEC (FIE). This criterion is able to encompass all the most used criteria of inequality equivalence and is sufficiently flexible to provide a perception consistent with recent evidence from questionnaire investigations, namely that the inequality perception goes from the relative view (focussing on income shares) to the absolute view (focussing on absolute income differentials) as incomes increase. One parameter of the FIE is associated with the Bossert and Pfingsten (Math. Soc. Sc. 1990) Intermediate IEC (IIE) while the other is shown to lead to an alternative single parameter version of the IEC, the Proportional IEC which is dual to the previous. We provide independent characterizations both of PIE and IIE. Also alternative IECs existing in the literature are characterized within the axiomatic framework suggested. These results are consistent with those obtained in the surplus sharing literature by Moulin (Int. J. Game Theory 1987), Young (Math. Op. Res. 1987, J. Econ. Theory 1988) and Pfingsten (Math. Soc. Sc. 1991), and with recent results in inequality measurement by Ebert (Math. Soc. Sc. 2004) and Zheng (Soc. Ch. Wel. 2007). We complete the analysis investigating the implications of extending the domain of the income distributions including negative incomes. The basic consistency properties suggested in order to characterize the IECs are sufficient to select the absolute IEC when unbounded negative incomes are included in the domain.

Suggested Citation

  • Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
  • Handle: RePEc:ver:wpaper:32/2012
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    References listed on IDEAS

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    1. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-20, January.
    2. Francisco Azpitarte & Olga Alonso-Villar, 2011. "Ray-invariant intermediate inequality measures: A Lorenz dominance criterion," Working Papers 226, ECINEQ, Society for the Study of Economic Inequality.
    3. Paul Allanson, 2010. "Longitudinal analysis of income-related health inequality: welfare foundations and alternative measures," Dundee Discussion Papers in Economics 240, Economic Studies, University of Dundee.
    4. Coral Río & Olga Alonso-Villar, 2010. "New unit-consistent intermediate inequality indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 505-521, March.
    5. Olga Alonso-Villar & Coral Del Río, 2017. "Local Segregation and Well-Being," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(2), pages 269-287, June.
    6. Florent Bresson & Jean-Yves Duclos, 2015. "Intertemporal poverty comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 567-616, March.
    7. Florent Bresson & Kelly Labar, 2007. "“Leftist”, “Rightist” and Intermediate Decompositions of Poverty: Variations with an Application to China from 1990 to 2003," Working Papers 76, ECINEQ, Society for the Study of Economic Inequality.
    8. Paul Allanson & Dennis Petrie, 2014. "Understanding The Vertical Equity Judgements Underpinning Health Inequality Measures," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1390-1396, November.
    9. Manfred Krtscha, 2017. "Some axiomatics of inequality measurement, with specific reference to intermediate indices," Working Papers 445, ECINEQ, Society for the Study of Economic Inequality.
    10. D. Jayaraj & S. Sreenivasan, 2015. "Growth and inequality in the distribution of India's consumption expenditure: 1983 to 2009-10," WIDER Working Paper Series 025, World Institute for Development Economic Research (UNU-WIDER).
    11. Ma Casilda Lasso de la Vega & Ana Urrutia & Henar Díez, 2010. "Unit Consistency And Bipolarization Of Income Distributions," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(1), pages 65-83, March.
    12. S. Subramanian, 2015. "Assessing Inequality in the Presence of Growth: an Expository Essay," The Review of Black Political Economy, Springer;National Economic Association, vol. 42(3), pages 179-199, September.
    13. Coral del Río & Olga Alonso-Villar, 2007. "Rankings of Income Distributions: A Note on Intermediate Inequality Indices," Working Papers 68, ECINEQ, Society for the Study of Economic Inequality.
    14. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables," Working Papers 2013:18, Lund University, Department of Economics, revised 02 Jan 2014.
    15. Claudio Zoli, 2017. "A note on progressive taxation and inequality equivalence," Working Papers 19/2017, University of Verona, Department of Economics.
    16. Sreenivasan Subramanian & D. Jayaraj, 2015. "Growth and Inequality in the Distribution of India's Consumption Expenditure: 1983 to 2009-10," WIDER Working Paper Series wp-2015-025, World Institute for Development Economic Research (UNU-WIDER).
    17. Subbu Subramanian, 2014. "Dividing a cake (or) Distributional values in the measurement of economic inequality: an expository note," The Journal of Philosophical Economics, Bucharest Academy of Economic Studies, The Journal of Philosophical Economics, vol. 7(2), May.
    18. Francisco Azpitarte & Olga Alonso-Villar, 2012. "A Dominance Criterion for Measuring Income Inequality from a Centrist View: The Case of Australia," Melbourne Institute Working Paper Series wp2012n03, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.

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    More about this item

    Keywords

    Inequality measurement; inequality equivalence; axiomatic surplus sharing; intermediate inequality.;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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