DP11930 | Inequality Indices as Tests of Fairness

Publication Date

03/23/2017

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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 egalitar- ian social welfare functions defi…ned 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 defi…ned income distribution generating processes and a well speci…fied notion of fairness. We fi…nd that the likelihood ratio (LR) test for fairness versus unfairness within two such processes are proportional to Theil’'s first… and second in- equality 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 cal- culating 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".”