Inequality of Wellbeing: A Multidimensional Approach By KOEN DECANCQ† and MARI ´ A ANA LUGO‡ †Katholieke Universiteit Leuven, Universite´ catholique de Louvain, University of Antwerp ‡University of Oxford and World Bank Final version received 29 March 2011. An important aspect of multidimensional wellbeing distributions is the correlation between different dimensions. We propose two indices for measuring multidimensional inequality, derived from two underly- ing 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. INTRODUCTION In their report on the measurement of economic performance and social progress, Sti- glitz et al. (2009, p. 14) argue that individual wellbeing is a multidimensional notion. 1 Individuals care about many different aspects of their lives, including their material standard of living, health and schooling. These non-monetary dimensions are neither freely tradable nor perfectly correlated with income. If we want to take the multidimen- sionality of individual wellbeing seriously, it follows that we need to incorporate the various dimensions explicitly into the analysis of inequality. Yet most analyses of inequality have confined themselves to the analysis of a sole dimension, namely income (or expenditure). A straightforward approach to take the multidimensionality of wellbeing into account is to consider each dimension separately, that is, to study the evolution of inequality dimension by dimension. (For examples of this approach, see Atkinson et al. 2002; World Bank 2005; Fahey et al. 2005.) 2 This method clearly goes beyond a sole focus on incomes and may provide additional insights. Unfortunately, a dimension-by- dimension approach leads us to ignore the interrelationships and possible correlations between the dimensions of wellbeing. A society where one individual is top-ranked in all dimensions, another second-ranked, and so on, is arguably more unequal than a society with the same distributional profiles in each dimension but where some individuals are top-ranked in some dimensions, and other individuals in other dimensions. To neglect these interrelationships would be to abandon one of the primary motivations for a multi- dimensional approach to inequality. 3 The concerns about multidimensionality of wellbeing and the correlation between its dimensions are not merely academic. In this paper we use household data from the Russian Longitudinal Monitoring Survey of HSE (RLMS-HSE) to show that these issues lie at the heart of the evolution of inequality during the recent transition from a centrally planned economy to a free market economy. Figures 1 and 2 summarize two stylized facts about that transition in the period between 1995 and 2005. The first figure presents the evolution of inequality in four dimensions of wellbeing: expenditures, health, education and housing quality. (For every dimension, inequality is measured by © 2012 The London School of Economics and Political Science. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA Economica (2012) 79, 721–746 doi:10.1111/j.1468-0335.2012.00929.x