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Interpreting Inequality Measures and Changes in Inequality

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This paper explores, in the context of the Atkinson inequality measure, attempts to make interpretations of orders of magnitude transparent. One suggestion is that the analogy of sharing a cake among a very small number of people provides a useful intuitive description for people who want some idea of what an inequality measure ‘actually means’. In contrast with the Gini measure, for which a simple ‘cake-sharing’ result is available, the Atkinson measure requires a nonlinear equation to be solved. Comparisons of ‘excess shares’ (the share obtained by the richer person in excess of the arithmetic mean) for a range of assumptions are provided. The implications for the ‘leaky bucket’ experiments are also examined. An additional approach is to obtain the ‘pivotal income’, above which a small increase for any individual increases inequality. The properties of this measure for the Atkinson index are also explored.

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  • John Creedy, 2014. "Interpreting Inequality Measures and Changes in Inequality," Treasury Working Paper Series 14/20, New Zealand Treasury.
    • Handle: RePEc:nzt:nztwps:14/20
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    1. S. Subramanian, 2002. "An Elementary Interpretation of the Gini Inequality Index," Theory and Decision, Springer, vol. 52(4), pages 375-379, June.
    2. Alejandro Corvalan, 2014. "The Impact of a Marginal Subsidy on Gini Indices," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(3), pages 596-603, September.
    3. Hoffmann, Rodolfo, 2001. "Effect of the rise of a person's income on inequality," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 21(2), November.
    4. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(3), pages 253-277, December.
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. Yoram Amiel & John Creedy & Stan Hurn, 1999. "Measuring Attitudes Towards Inequality," Scandinavian Journal of Economics, Wiley Blackwell, vol. 101(1), pages 83-96, March.
    7. Luisa Tibiletti & S. Subramanian, 2015. "Inequality Aversion and the Extended Gini in the Light of a Two-person Cake-sharing Problem," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 16(2), pages 237-244, May.
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    Cited by:

    1. Creedy, John, 2019. "The Atkinson Inequality Measure and Inequality Aversion," Working Paper Series 8015, Victoria University of Wellington, Chair in Public Finance.
    2. Creedy, John, 2019. "The Atkinson Inequality Measure and Inequality Aversion," Working Paper Series 20918, Victoria University of Wellington, Chair in Public Finance.
    3. Creedy, John, 2021. "Comparing Income Distributions Using Atkinson’s Measure of Inequality," Working Paper Series 9469, Victoria University of Wellington, Chair in Public Finance.
    4. Guillaume Saint-Jacques & Amir Sepehri & Nicole Li & Igor Perisic, 2020. "Fairness through Experimentation: Inequality in A/B testing as an approach to responsible design," Papers 2002.05819, arXiv.org.
    5. John Creedy, 2023. "Distributional Comparisons Using the Gini Inequality Measure," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 56(4), pages 538-550, December.
    6. John Creedy, 2023. "Comparing Income Distributions Using Atkinson's Measure of Inequality," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 56(1), pages 141-155, March.
    7. Rehan Akram & Nasir Ayub & Imran Khan & Fahad R. Albogamy & Gul Rukh & Sheraz Khan & Muhammad Shiraz & Kashif Rizwan, 2021. "Towards Big Data Electricity Theft Detection Based on Improved RUSBoost Classifiers in Smart Grid," Energies, MDPI, vol. 14(23), pages 1-17, December.
    8. Creedy, John, 2021. "Distributional Comparisons Using the Gini Inequality Measure," Working Paper Series 9471, Victoria University of Wellington, Chair in Public Finance.
    9. Alinaghi, Nazila & Creedy, John & Gemmell, Norman, 2022. "Income Inequality and the Accounting Period in New Zealand: Evidence from Administrative Data," Working Paper Series 21899, Victoria University of Wellington, Chair in Public Finance.
    10. Gemmell, Norman, 2021. "Economic Lessons for Tax Policy Advisers," Working Paper Series 21109, Victoria University of Wellington, Chair in Public Finance.
    11. Gemmell, Norman, 2021. "Economic Lessons for Tax Policy Advisers," Working Paper Series 9463, Victoria University of Wellington, Chair in Public Finance.

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    More about this item

    Keywords

    Inequality; Atkinson Measure; Excess Share;
    All these keywords.

    JEL classification:

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

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