Multilevel interterritorial convergence and additive multidimensional inequality decomposition

In this paper we justify the use of the between-groups S-convex relative inequality indices to measure interterritorial convergence. In addition, we provide two appealing extensions to the use of the additive decomposable General Entropy inequality indices. First, multilevel decomposition along several subpartitions is satisfied and a natural application to convergence decomposition along different territorial level arises. Second, further general inequality decomposition along several dimensions is also satisfied. Thus, this framework provides a better explanation of the determinants of convergence (and inequality) when it is decomposed into different dimensions in comparison with other indices available in the literature.