Partial multidimensional inequality orderings

The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It is in the spirit of Sen (1970)'s partial orderings and follows the dominance approach to making inequality comparisons. By focusing on those below a multidimensional inequality “frontier”, we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual's multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. Our methods are also robust to choices of individual “utility” or aggregation functions. We apply our approach to data from India and Mexico to show inter alia how dependence between dimensions of well-being can influence relative poverty and inequality comparisons between two populations.