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Some axiomatics of inequality measurement, with specific reference to intermediate indices

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  • Manfred Krtscha

    (Karlsruher Institute of Technology, Germany)

Abstract

In this paper we consider properties for inequality measurement. A property that should be demanded for every inequality measure we call “axiom” otherwise we call it only “desideratum”. The most important new axiom (A6) and the desideratum “Cowell's Feature (CF)” are motivated carefully. (A6) is more restrictive than Zheng's (2007a) “unit consistency axiom” for partial inequality orderings, but it is not as restrictive as the overwhelmingly favoured “scale invariance” property. We will show that the combination of these two properties characterizes a type of differentiable inequality measure that the author had already introduced and characterized in 1994, but then with a stronger requirement. Since then, this measure has been widely employed in applied work because it has been perceived to possess some attractive properties. However, the aim of this paper is not only a better characterization of a single type of inequality measure, but also a numerical comparison of different “good” inequality measures that qualify under (A6). Our focus lies on the so-called intermediate measures, being a compromise between the scale invariant “relative inequality measures” and the translation invariant “absolute inequality measures”, where equal absolute changes in all incomes do not affect the inequality value. We present three methods to construct strictly intermediate or centrist inequality measures, which are explained with the help of three examples. Then we undertake a comparison of how these illustrative measures satisfy our axioms. Finally we give a complete summary table showing all the properties of these inequality measures. A last relevant example has been taken from true life.

Suggested Citation

  • 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.
    • Handle: RePEc:inq:inqwps:ecineq2017-445
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    1. S. Subramanian & D. Jayaraj, 2014. "Money-metric poverty, welfare, growth, and inequality in India: 1983 – 2011/12," Global Development Institute Working Paper Series 21114, GDI, The University of Manchester.
    2. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    4. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    5. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    6. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
    7. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    8. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    9. Subramanian, Subbu, 2011. "Inequality measurement with subgroup decomposability and level-sensitivity," Economics Discussion Papers 2011-7, Kiel Institute for the World Economy (IfW Kiel).
    10. Coral del RÎo & Javier Ruiz-Castillo, 2000. "Intermediate inequality and welfare," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 223-239.
    11. Tateo Yoshida, 2005. "Social welfare rankings of income distributions A new parametric concept of intermediate inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 557-574, June.
    12. Subramanian, Subbu, 2011. "Inequality measurement with subgroup decomposability and level-sensitivity," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-18.
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    Cited by:

    1. Subramanian S., 2017. "On Comprehensively Intermediate Measures of Inequality and Poverty, with an Illustrative Application to Global Data," Journal of Globalization and Development, De Gruyter, vol. 8(2), pages 1-18, December.
    2. D. Jayaraj & S. Subramanian, 2018. "The Distribution of Household Assets in India: 1991–1992 to 2012–2013," Indian Journal of Human Development, , vol. 12(2), pages 181-203, August.

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