Copula-based measurement of dependence between dimensions of well-being.

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).

Copula-based orderings of multivariate dependence

In this paper I investigate the problem of defining a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with fixed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non- fixed margins, I impose a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearmanís rank correlation coefficient belongs.copula, concordance ordering, dependence measures, dependence orderings, multivariate stochastic dominance, supermodular ordering

Copula-based measurement of dependence between dimensions of well-being

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).copula, complex inequality, concordance, HDI, multidimensional inequality, Russia, well-being.

Global inequality: a multidimensional perspective

This paper investigates the evolution of global well-being inequality between 1980 and 2010 based on three dimensions: income, health and education. The inequality of each of these dimensions shows a different pattern over time. To make an overall assessment of the evolution of well-being inequality, I make use of a recently developed multidimensional inequality index which reflects the implicit value judgments of the revised Human Development Index. Multidimensional well-being inequality has decreased over the considered period. However, this result is shown to depend crucially on the weighting scheme selected, the aggregation procedure and the transformation of the income dimension.

Copula-based orderings of multivariate dependence

In this paper I investigate the problem of defining a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with fixed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non-fixed margins, I impose a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearman’s rank correlation coefficient belongs.copula, concordance ordering, dependence measures, dependence orderings, multivariate stochastic dominance, supermodular ordering.

Global inequality: a multidimensional perspective.

This paper investigates the evolution of global well-being inequality between 1980 and 2010 based on three dimensions: income, health and education. The inequality of each of these dimensions shows a different pattern over time. To make an overall assessment of the evolution of well-being inequality, I make use of a recently developed multidimensional inequality index which reflects the implicit value judgments of the revised Human Development Index. Multidimensional well-being inequality has decreased over the considered period. However, this result is shown to depend crucially on the weighting scheme selected, the aggregation procedure and the transformation of the income dimension.

Weights in multidimensional indices of well-being: an overview

Multidimensional indices are becoming increasingly important instruments to assess the well-being of societies. They move beyond the focus on a single indicator and yet, are easy to present and communicate. A crucial step in the construction of a multidimensional index of well-being is the selection of the relative weights for the different dimensions. The aim of this paper is to study the role of these weights and to critically survey eight different approaches to set them. We categorize the approaches in three classes: data-driven, normative and hybrid weighting, and compare their respective advantages and drawbacks.composite indicator, multidimensional well-being index, weights.

Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index

We propose to measure inequality of well-being with a multidimensional generalization of the Gini coefficient. We derive two inequality indices from their underlying social evaluation functions. These functions are conceived as a double aggregation functions: one across the dimensions of well-being, and another across the individuals. They differ only with respect to the sequencing of aggregations. We argue that the sequencing that does not exclude the Gini index to be sensitive to the correlation between the dimensions is more attractive. We illustrate both Gini indices using Russian household data on three dimensions of well-being: expenditure, health and education.multidimensional inequality, single parameter Gini index, correlation increasing majorization, Russia.

The evolution of world inequality in well-being.

In this paper we investigate the evolution of the inequality in well-being across different countries between 1975 and 2000. We treat well-being as a multidimensional concept focusing on three important dimensions of life: standard of living, health and education. Inequality in the three dimensions shows a different trend between 1975 and 2000. We propose a flexible measure of well-being and use the tools offered by the recent literature on multidimensional inequality measurement to quantify the evolution of overall intercountry well-being inequality. The empirical results are nuanced, and sensitive to different normative choices on the trade-offs between the different dimensions. In particular the concave transformation of income turns out to be decisive for the evolution of world inequality in well-being.Belgium; Effects; Income taxes; Personal; World;