Inequality Indices as Tests of Fairness

21 Pages Posted: 1 May 2017

See all articles by Ravi Kanbur

Ravi Kanbur

Cornell University; Centre for Economic Policy Research (CEPR); IZA Institute of Labor Economics

Andy Snell

University of Edinburgh - Economics

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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."

Keywords: snapshot inequality indices, process versus outcomes, fair versus unfair process, likelihood ratio tests of fairness, BayesFactor

JEL Classification: A10, A13, C01, C12, D63

Suggested Citation

Kanbur, Ravi and Snell, Andy, Inequality Indices as Tests of Fairness. IZA Discussion Paper No. 10721. Available at SSRN: https://ssrn.com/abstract=2960530

Ravi Kanbur (Contact Author)

Cornell University ( email )

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HOME PAGE: http://www.kanbur.dyson.cornell.edu

Centre for Economic Policy Research (CEPR)

London
United Kingdom

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Andy Snell

University of Edinburgh - Economics ( email )

50 George Square
Edinburgh, EH8 9JY
United Kingdom

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