DP11930 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 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".