Copula-based Orderings of Multivariate Dependence

In this paper I investigate the problem of de…ning a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with …xed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non…xed margins, I impose a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearman’s rank correlation coe¢ cient belongs. Keywords: copula, concordance ordering, dependence measures, dependence orderings, multivariate stochastic dominance, supermodular ordering. JEL Classi…cation: C14 Koen Decancq: Center for Economic Studies, Katholieke Universiteit Leuven, Naamsestraat 69, B3000 Leuven, Belgium and CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. E-mail: [email protected]. This is a revised version of a chapter of my PhD dissertation. I gratefully thank André Decoster, James E. Foster, Luc Lauwers, Erwin Ooghe, Casey Quinn, Erik Schokkaert, Suman Seth, Dirk Van de Gaer, Tom Van Ourti, John A. Weymark and participants at seminars in Leuven, Berlin, Montreal, Verona, Oxford, and Louvain-La-Neuve for very helpful comments and suggestions to this or an ealier version of the paper. Remaining errors are mine.