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

This paper discusses the measurement of ex-ante inequality of opportunity when the outcome is binary. We argue that the use of scale but not translation invariant inequality measures such as the dissimilarity index are problematic, since they rely too much on the average level of access. We propose rst a decomposition of these measures in a level and a dispersion eect and second an adapted index satisfying translation invariance. In two short illustrations we show that the conclusions dier substantially between the two methods and