SUMMARY AND CONCLUSIONS

Since the 1990s, the measurement of multidimensional inequality and poverty has turned into a thriving research area. Novel analytical results have accompanied a massive pro­duction of applied research.

The informational basis of the analysis is indeed crucial: tools intended for cardinal or categorical variables need not be appropriate for dichotomous variables, which often rep­resent the bulk of the available information. This is one reason why we have paid special attention to the counting approach. Another one is expository convenience: the role of marginal distributions and the association between the attributes are particularly transpar­ent for dichotomous variables, especially in the two-dimensional case, although the descriptive and normative issues are similar to those of continuous variables. However, the main motivation for this choice has been the attempt to bridge the gap between a copious empirical literature and a still relatively underdeveloped analytical elaboration.

The opposite situation characterizes the axiomatic treatment of poverty and inequal­ity for continuous and categorical variables: a fairly rich theoretical apparatus does not appear to have yet made an impact on empirical investigations, except in sporadic appli­cations. This may be due to the scarcity of suitable variables and databases, but it may also reflect the difficulty of discriminating among many equally sensible alternative tools. In addition to further developing and refining theoretical analysis, in this case, empirical work may play an important role in screening the most effective tools.

Yet, is it really worth devoting so much intellectual effort to develop the multidimen­sional analysis of poverty and inequality? It is an odd question at the end of such a long chapter, but as discussed in the introduction, the widely shared view that well-being, and hence poverty, is multidimensional does not necessarily imply that the social evaluation must itself be multidimensional. It may be for philosophical reasons or, more practically, because too much is lost in the process of aggregation. Once Sen (1987, p. 33) remarked that “the passion for aggregation makes good sense in many contexts, but it can be futile or pointless in others.... When we hear of variety, we need not invariably reach for our aggregator.” On the other hand, the “eye-catching property” of the Human Develop­ment Index was praised by Streeten (1994, p. 235) as a powerful feature for its affirmation in the public debate, in spite of the theoretical weaknesses pointed out by its critics.⁴ Three points may help us to find an answer to the question.

First, there is a pervasive demand by media commentators and policy-makers for mul­tidimensional analyses. This demand must be met, not the least in order to avoid that such analyses are left to practitioners that conceive them as a bunching together of living stan­dard indicators through some simple averaging or multivariate technique easily available in statistical and econometric packages. Empirical research confirms that broadening the evaluative space to include variables other than income can modify the picture drawn on

48

For a recent example, see the exchange between Klugman et al. (2011a,b) and Ravallion (2011b, 2012a,b). See also Chakravarty (2011).

the basis of income alone. There is distinct informative value in adopting a multidimen­sional perspective. The theoretical work surveyed in this chapter facilitates the interpre­tation of empirical findings by bringing to the fore the implicit measurement assumptions and their economic meaning. If we estimate a lower deprivation index in the United Kingdom than in Italy using concave social preferences, as in Section 3.3.2.4, it is because we favor the union criterion, and hence, we tend to be relatively more worried by the spreading of a given number of deprivations across many people than by their concen­tration on fewer people who are hit more. If, on the contrary, we have convex prefer­ences and are particularly concerned about those suffering from severe deprivations, we cannot unequivocally rank one country ahead of the other.

Second, the difficulties of multidimensional measurement should not be overstated. The choice of the degree of poverty or inequality aversion and the proper definition of indicators less familiar to us than income also arise in the univariate context. The prob­lems that are new to the multivariate case are the weighting structure of the attributes and their degree of substitutability. Both these aspects are not technical hitches but rather the expression of implicit value judgements. Far from being a weakness of multidimensional approaches, the investigation of alternative assumptions is necessary to allow for the dif­ferent views in the society. This is a sufficient reason for not devolving the resolution of these measurement problems to some statistical algorithm.

Third, the battery of instruments in our toolbox is ample. If we are reluctant to use a summary poverty or inequality index, we may fruitfully use sequential dominance anal­ysis: it may yield a partial ordering, but it may sometimes be sufficient to evaluate, say, the impact on the distribution of well-being of alternative policies. The variety of our tool­box means that there is a middle ground between multidimensional summary indices and the dashboard approach, as stressed by Ferreira and Lugo (2013).

These are all good arguments in favor of multidimensional social evaluation. Are they also compelling enough to push us as far as to accept summary indices? Probably not, but two further comments are in order. The first is a pragmatic suggestion drawn from Bourguignon (1999, p. 483): when their building assumptions are properly understood, these indices can provide valuable insights if used “more as a dominance instrument than a strictly cardinal rule of comparison.” The second is a somewhat deeper point. Ina sense, the uneasiness with such a summary index in sectors of the economics profession may stem from the reluctance of those economists to abandon a utility-based conception of well-being. Only individuals are able to assess the trade-offs between the different con­stituents of well-being, and prices are the best available way to reveal such trade-offs, because they derive from the interactions of individuals in a market economy. If exter­nalities, distortions, and missing markets prevent us from relying on prices as the aggre­gator of well-being dimensions, then the dashboard approach may be preferable, because no arbitrary weighting is imposed. The most developed conceptualization of multidi­mensional well-being to date, the capability approach, originates exactly from the rejection of a utility-based conception: “valuing a life and measuring the happiness gen­erated in that life are two different exercises” (Sen, 1985, p. 12). If this is the founding aspect of multidimensional analysis, then the weighting of the different dimensions is an integral part of the evaluation exercise, and the reference to market prices loses much of its appeal. Social evaluation may attach more weight to work effort than that revealed by the wage, because jobs are characterized by other attributes that might contribute to rein­forcing social integration. From this perspective, the practical solutions given to the selec­tion of weights, which often boil down to equal weighting, may miss a decisive part of the evaluation.

ACKNOWLEDGMENTS

We are very grateful to Tony Atkinson and Francois Bourguignon for their inspiring discussions, insightful comments, and generous patience. We would also like to thank Sabina Alkire, Conchita D’Ambrosio, Jean-Yves Duclos, StephenJenkins, Eugenio Peluso, Luigi Federico Signorini, Henrik Sigstad and Claudio Zoli for their helpful comments. The views expressed here are solely ours; in particular, they do not necessarily reflect those of the Bank of Italy and Statistics Norway.

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