Copula-based measurement of interdependence for discrete distributions

We focus on a question that has been long addressed in economics, namely, of one distribution being better than another according to a normative criterion. Our criterion distinguishes between interdependence and behaviour in the margins. Many economics contexts concern interdependence only e.g. complementarities in production function, intergenerational mobility, social gradient in health. We prove that the proposed relations, namely, increasing discordance (concordance) orderings, are equivalent to first order stochastic (survival) dominance. We generalize to three dimensions for which dependence becomes a more complex notion. We measure interdependence via a most general measure, namely, a copula. Main challenge is that in a discrete setting there are many copulas associated with a given distribution. Drawing on a copula theory (Carley, 2002) we offer an algorithm which generates distributions that are more increasing concordant.