Modeling multidimensional inequality in well-being: the case of Spain

The aim of this paper is to assess the evolution of multidimensional inequality in well-being using Lorenz curves. Closed expressions for the bivariate Lorenz curve defined by Arnold (1983) are given. We assume a relevant type of models based on the class of distributions with given marginals described by Sarmanov and Lee (Lee, 1996; Sarmanov, 1966). This specification of the bivariate Lorenz curve can be easily interpreted as a convex linear combination of products of classical and concentrated Lorenz curves (Sarabia and Jordá, 2014). Using this methodology, we present a closed expression for the bivariate Gini index (Arnold, 1987) in terms of the classical and concentrated Gini indices of the marginal distributions, which are modeled using a convenient model. This index is especially useful and can be decomposed in two factors, corresponding to inequality within variables and the degree of correlation between dimensions (Sarabia and Jordá, 2014). Finally, we illustrate all the previous methodology by analyzing multidimensional inequality in well-being in Spain during the period 2004-2012. We focus on three dimensions, namely income, health and education. Our results point out that inequality levels decreased over the study period, especially for non-income components. Keywords— bivariate Lorenz curve; Sarmanov-Lee distribution; bivariate Gini index; well-being.