Measuring the dependence among dimensions of welfare: a study based on spearman´s footrule and Gini´s Gamma

Abstract

Welfare is multidimensional as it involves not only income, but also education, health or labour. The composite indicators of welfare are usually based on aggregating somehow the information across dimensions and individuals. However, this approach ignores the relationship between the dimensions being aggregated. To face this goal, in this paper we analyse the dependence between the dimensions included in the Human Development Index (HDI), namely income, health and schooling, through three copula-based measures of multivariate association: Spearman’s footrule, Gini’s gamma and Spearman’s rho. We discuss their properties and prove new results on Spearman’s footrule. The copula approach focuses on the positions of the individuals across dimensions, rather than the values that the variables attain for such individuals. Thus, it allows for more general types of dependence than the linear correlation. We base our study on data from 1980 till 2014 for the countries included in the 2015 Human Development Report. We find out that though the overall HDI has increased over this period, the dependence between its dimensions remains high and nearly unchanged so that the richest countries tend to be also the best ranked in both health and education.