Koen Decancq

Weights in Multidimensional Indices of Wellbeing: An Overview

Multidimensional indices are becoming increasingly important instruments to assess the wellbeing of societies. They move beyond the focus on a single indicator and yet they are easy to present and communicate. A crucial step in the construction of a multidimensional index of wellbeing is the selection of the relative weights for the different dimensions. The aim of this article 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.

Inequality of Wellbeing: A Multidimensional Approach

An important aspect of multidimensional wellbeing distributions is the correlation between different dimensions. We propose two indices for measuring multidimensional inequality, derived from two underlying social evaluation functions. These functions aggregate both across dimensions and across individuals. The social evaluation functions differ only with respect to the sequencing of aggregation. Aggregating first across dimensions is more attractive since it allows the inequality index to depend on the correlation between dimensions. We illustrate both indices, and the impact of correlation sensitivity, using Russian household data between 1995 and 2005 for four dimensions of wellbeing: expenditure, health, schooling and housing quality.

Inequality, income and well-being

Individual well-being depends not only on income but also on other dimensions of life, such as health, the quality of social relations and of the environment, employment, and job satisfaction. In this paper we survey the economic literature on how to construct such overall measures of well-being. We distinguish three approaches: the capability (and functionings) approach, the use of subjective life satisfaction measures and the calculation of equivalent incomes. We discuss the normative assumptions underlying these three approaches, focusing on two issues: the degree to which individual preferences are respected and where in each approach the boundaries of individual responsibility are drawn. We compare the measurement of inequality in well-being with the use of multidimensional inequality measures. We illustrate the general theoretical issues in three domains of application: measuring the effects of household size and composition in the literature on equivalence scales, valuing publicly provided goods and services, and making international comparisons of well-being involving international PPP comparisons.

Elementary multivariate rearrangements and stochastic dominance on a Fréchet class

A Frechet class collects all multivariate joint distribution functions that have the same marginals. Members of a Frechet class only differ with respect to the interdependence between their marginals. In this paper, I study orders of interdependence on a Frechet class using two multivariate generalizations of the bivariate rearrangement proposed by Epstein and Tanny (1980) [4] and Tchen (1980) [16]. I show how these multivariate rearrangements are underlying multivariate first order stochastic dominance in terms of the joint distribution function and the survival function. A combination of both rearrangements is shown to be equivalent to the concordance order proposed by Joe (1990) [9].