Inequality Indices as Tests of Fairness
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."
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References listed on IDEAS
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- 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.
- Corak, Miles, 2013. "Income Inequality, Equality of Opportunity, and Intergenerational Mobility," IZA Discussion Papers 7520, Institute for the Study of Labor (IZA).
- Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047, April.
- 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.
- Ferreira , Francisco H. G. & Gignoux, Jeremie, 2008. "The measurement of inequality of opportunity : theory and an application to Latin America," Policy Research Working Paper Series 4659, The World Bank.
- 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.
- Kanbur, Ravi & Stiglitz, Joseph E., 2015. "Dynastic Inequality, Mobility And Equality Of Opportunity," Working Papers 250014, Cornell University, Department of Applied Economics and Management.
- Kanbur, Ravi & Stiglitz, Joseph E, 2015. "Dynastic Inequality, Mobility and Equality of Opportunity," CEPR Discussion Papers 10542, C.E.P.R. Discussion Papers.
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