Scale vs. Translation Invariant Measures of Inequality of Opportunity When the Outcome is Binary

Abstract

This paper discusses the measurement of ex-ante inequality of opportunity for binary outcome variables. We argue that the use of scale but not translation invariant inequality measures such as the dissimilarity index might be problematic depending on the aim of the study. The main concern is that these measures heavily rely on the on the average level of access and therefore comparisons across countries or time might become difficult. We propose a translation invariant alternative and illustrate the differences between the two measures with Mexican data. We find substantial differences in the results when comparing the two methods. We do not claim that our measure is preferable in all situations, but we suggest at least the use of both measures to assess the situation more clearly.

Keywords: inequality of opportunity, binary indicator, HOI, ordered variables, translation invariance

JEL Classification: C18, D63, I24, O54