Multivariate Ranks-Based Concordance Indexes

The theoretical contributions to a “good” taxation have put the attention on the relations between the efficiency and the vertical equity without considering the “horizontal equity” notion: only recently, measures connected to equity (iniquity) of a taxation have been introduced in literature. The taxation problem is limited to the study of two quantitative characters: however the concordance problem can be extended in a more general context as we present in the following sections. In particular, the aim of this contribution consists in defining concordance indexes, as dependence measures, in a multivariate context. For this reason a k-variate (k > 2) concordance index is provided recurring to statistical tools such as ranks-based approach and multiple linear regression function. All the theoretical topics involved are shown through a practical example.