Inequality Measures as Tests of Fairness in an Economy

Abstract

Standard measures of inequality have been criticized for a long time on the grounds that they are snap shot 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 a well defined income distribution generating process and a well specified notion of “fairness”. We find that standard test procedures, such as LR, LM and Wald, lead to test statistics which are closely related to standard measures of inequality. 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.