A Decomposable Index of Multidimensional Inequality of Opportunity

This paper proposes a measure of multidimensional inequality of opportunity - the Kullback Leibler divergence index, based on the opportunity equality definition of Roemer (1993, 1998, 2016). We prove theoretically and numerically that this measure satisfies a larger set of properties mainly the additive decomposability by dimensions. We show that the Kullback Leibler divergence index for multiple dimensions can be decomposed into Kullback Leibler divergence index for each of these dimensions along with a measure of association which is interpreted as the mutual information Sugiyama et al. (2013). We provide an empirical application of our proposed method using the Indian Demographic and Health Survey 2015/16 data for adult males.