Multidimensional Comparisons

Another major development of the Atkinson (1970) results is their extension to comparisons of multidimensional distributions of economic status. This has proved important because of increasing recognition that peoples’ material wellbeing depends not only on their money income (or consumption expenditure), but also on other factors.

The key theoretical results were derived by Atkinson and Bourguignon (1982), who prove a series of dominance results concerning multidimensional comparisons of social welfare in a general setting. The nature of the correlations between the various dimensions is shown to play an important role. The results have been applied to a number of areas.

First, there is the treatment of differences in ‘needs’ in income distribution comparisons. The conventional approach to distributional comparisons (as in Atkinson 1970) supposes that incomes have been adjusted in advance to take account of differences in household size and composition using an equivalence scale. But this approach presupposes social agreement about how much greater the economies of size or ‘needs’ are of larger families compared to smaller families, or of adults compared to children, that is, about equivalence scale relativities across different households. The great insight of Atkinson and Bourguignon (1987) was that one could treat income and needs jointly as a bivariate distribution, and seek dominance conditions for unanimous social welfare rankings with weaker assumptions about equivalence scale relativities than is made using a particular equivalence scale. The checks for dominance are shown to require a sequence of generalised Lorenz curve comparisons. Tony’s 1992 article extended the same idea to comparisons of distributions of poverty and needs. Jenkins and Lambert (1993) relaxed the constraint that the marginal distribution of needs is the same in the two bivariate distributions being compared. (For other developments in this area, see the review by Aaberge and Brandolini (2015: 193).)

Longitudinal income mobility is a second important area of application: the multiple dimensions now refer to incomes at different points in time for these same individuals. As with inequality measurement, there is a large number of ‘statistical’ or ‘descriptive’ indices used to summarise mobility, but their welfare foundations are unclear (Jantti and Jenkins 2015). Tony provided these foundations with his framework for evaluation together with a set of conditions for checking mobility dominance (Atkinson 1981a).

The third and currently most active area of application is to the development of multidimensional measures of poverty—the multiple dimensions refer to not only income but also deprivations in other domains of people’s life. This interest coincided with widespread recognition that ‘poverty’, especially in developing countries, is not only about low income but also about other factors such as poor health or educational attainment. In the measurement of multidimensional poverty, Tony’s distinctive bridging of different strands of research comes to the fore again. He examines the relationship between, on the one hand, the social welfare approach pioneered by Tsui (2002) and Bourguignon and Chakravarty (2003) and, on the other hand, what he labelled the ‘counting approach’, ‘widely used in applied studies, which concentrate on counting the number of dimensions in which people suffer deprivation’ (Atkinson 2003: 51). The counting approach was subsequently developed in the influential paper by Alkire and Foster (2011), while Duclos et al. (2006a, b) are two illustrations of the first approach. (For a collection of papers on the topic, see Kakwani and Silber (2008), and for a comprehensive recent survey, see Aaberge and Brandolini (2015).)