Inequality indices as tests for fairness

Ravi Kanbur and Andy Snell

No 432, Working Papers from ECINEQ, Society for the Study of Economic Inequality

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; Bayes Factor. (search for similar items in EconPapers)
JEL-codes: A10 A13 C01 C12 D63 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2017-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Inequality Indices as Tests of Fairness (2019)
Working Paper: Inequality Indices as Tests of Fairness (2017)
Working Paper: Inequality Indices as Tests of Fairness (2017)
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