Copula-based Measurement
of Dependence
Between Dimensions of
Well-being
Koen Decancq
December 2, 2009
Abstract
Well-being consists of
many dimensions such as income, health and education. A society exhibits
greater dependence between its dimensions of well-being when the positions of
the individuals in the different dimensions are more aligned or correlated. Differences
in dependence may lead to very different societies, even when the dimension-wise
distributions are identical. I propose to use a copula-based framework to order
societies with respect to their dependence. A class of measures of dependence
is derived to which the multidimensional rank correlation coefficient belongs.
I illustrate the usefulness of the approach by showing that Russian dependence between
three dimensions of well-being has increased significantly between 1995 and 2003.
Unfortunately, the aspect of dependence is missed by all composite well-being measures
based on dimension-specific summary statistics such as the popular Human Development
Index (HDI).
Keywords: copula, complex inequality, concordance, HDI,
multidimensional inequality,
JEL Classification: D31, D63, I31, O50.