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Inequality Indices as Tests of Fairness

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  • Kanbur, Ravi

    (Cornell University)

  • Snell, Andy

    (University of Edinburgh)

Abstract

Standard income inequality indices can be interpreted as a measure of welfare loss entailed in departures from equality of outcomes, for egalitarian social welfare functions defined on the distribution of outcomes. But such a welfare interpretation has been criticized for a long time on the grounds that these indices are snap shot outcomes-based measures which do not take into account the process generating the observed distribution. Rather than focusing on outcomes, it is argued, we should be interested in whether the underlying process is "fair." Following this line of argument, this paper develops statistical tests for fairness within well-defined income distribution generating processes and a well specified notion of fairness. We find that the likelihood ratio (LR) test for fairness versus unfairness within two such processes are proportional to Theil's first and second inequality indices respectively. The LR values may either be used as a test statistic or to approximate a Bayes factor that measures the posterior probabilities of the fair version of the processes over that of the unfair. The answer to the process versus outcomes critique is thus not to stop calculating inequality measures, but to interpret their values differently – to compare them to critical values for a test of the null hypothesis of fairness, or to use them directly as a measure of the chance that the process was fair relative to the chance it was unfair. We also apply this perspective to measurement of "inequality of opportunity."

Suggested Citation

  • Kanbur, Ravi & Snell, Andy, 2017. "Inequality Indices as Tests of Fairness," IZA Discussion Papers 10721, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp10721
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    References listed on IDEAS

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    1. Ravi Kanbur & Adam Wagstaff, 2016. "How Useful Is Inequality of Opportunity as a Policy Construct?," International Economic Association Series, in: Kaushik Basu & Joseph E. Stiglitz (ed.), Inequality and Growth: Patterns and Policy, chapter 4, pages 131-150, Palgrave Macmillan.
    2. Ravi Kanbur & Joseph E. Stiglitz, 2016. "Dynastic inequality, mobility and equality of opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(4), pages 419-434, December.
    3. Kaushik Basu & Joseph E. Stiglitz (ed.), 2016. "Inequality and Growth: Patterns and Policy," International Economic Association Series, Palgrave Macmillan, number 978-1-137-55454-3, June.
    4. Miles Corak, 2013. "Income Inequality, Equality of Opportunity, and Intergenerational Mobility," Journal of Economic Perspectives, American Economic Association, vol. 27(3), pages 79-102, Summer.
    5. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    6. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1553-1623.
    7. Francisco H. G. Ferreira & Jérémie Gignoux, 2011. "The Measurement Of Inequality Of Opportunity: Theory And An Application To Latin America," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(4), pages 622-657, December.
    8. Francisco H.G. Ferreira & Jérémie Gignoux, 2011. "The Measurement of Inequality of Inequality of Opportunity: Theory and an Application to Latin America," PSE-Ecole d'économie de Paris (Postprint) halshs-00754503, HAL.
    9. Kaushik Basu & Joseph E. Stiglitz (ed.), 2016. "Inequality and Growth: Patterns and Policy," International Economic Association Series, Palgrave Macmillan, number 978-1-137-55459-8, June.
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    Cited by:

    1. Hansen, Kristian S. & Moreno-Ternero, Juan D. & Østerdal, Lars P., 2023. "Productivity and quality-adjusted life years: QALYs, PALYs and beyond," Working Papers 11-2023, Copenhagen Business School, Department of Economics.
    2. Kanbur, Ravi, 2024. "Shannon-Theil-Rawls: Information Theory, Inequality and the Veil of Ignorance," CEPR Discussion Papers 18864, C.E.P.R. Discussion Papers.
    3. Seungwoo Han, 2022. "Identifying the roots of inequality of opportunity in South Korea by application of algorithmic approaches," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-10, December.
    4. Ji-Won Park & Chae Un Kim, 2020. "Getting to a feasible income equality," Papers 2011.09119, arXiv.org, revised Mar 2021.
    5. Ji-Won Park & Chae Un Kim, 2021. "Getting to a feasible income equality," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-16, March.
    6. Ji-Won Park & Jaeup U. Kim & Cheol-Min Ghim & Chae Un Kim, 2021. "The Boltzmann fair division for distributive justice," Papers 2109.11917, arXiv.org, revised Nov 2021.

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    More about this item

    Keywords

    likelihood ratio tests of fairness; fair versus unfair process; process versus outcomes; snapshot inequality indices; Bayes Factor;
    All these keywords.

    JEL classification:

    • A10 - General Economics and Teaching - - General Economics - - - General
    • A13 - General Economics and Teaching - - General Economics - - - Relation of Economics to Social Values
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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