Four elementary points about multidimensional poverty Francisco H. G. Ferreira Deputy Chief Economist, LCR

1.It’s the correlations. When might you want to analyze poverty “multi-dimentionally”? 1.When there are at least two welfare dimensions of interest between which there are no natural aggregators (e.g. prices)… 2.…and when correlations between them matter. “It is possible for a set of univariate analyses done independently for each dimension of well-being to conclude that poverty in A is lower than poverty in B while a multivariate analysis concludes the opposite, and vice-versa. The key to these possibilities is the interaction of the various dimensions of well-being in the poverty measure and their correlation in the sampled populations” (Duclos, Sahn and Younger, EJ 2006, p.945)

2.What about MP indices? Whether one views the (say) two dimensions as complements or substitutes affects what kind of index you want to build. For instance, Alkire and Foster’s (2008) index only satisfies the Bourguignon & Chakravarty (2003) NDCIS axiom weakly. Correlation-increasing switches will not generally increase the MPI. Two versions of the transfer principle (OTP and MTP), imply very different indices.

3.The MPI has its uses. Although insensitive to correlations (that imply no z crossing), the MPI is: – An elegant aggregator of multiple deprivations, based on averages (over entire population) of entries in the censored deprivation matrix: – That can shed useful light on the composition of poverty. E.g. “health deprivation” is a relatively bigger component of the Latino share of MP in the US, while income poverty is more important for African-Americans. Typical entries into which are

4.Indices require measures of robustness to weights (at least). Source: Foster, McGillivray and Seth (2008) “Inescapably, the choice of a specific well-being index entails important value judgements about … the respective contribution of its components.” (Decancq and Lugo, forthcoming). - dimension weights - transformation functions - elasticity of substitution across dimensions Foster, McGillivray and Seth (2008) propose a robustness criterion for assessing the rank robustness of such indices. - This should, in my view, be as mandatory as reporting SEs for regression coefficients…

Summary 1.Multidimensional poverty analysis is useful because the joint distribution contains more information than the marginal distributions. 2.As in unidimensional poverty and inequality measurement, dominance relationships are often more informative than specific indices, but indices can still be useful. 3.How indices are constructed reflect important value judgments. – In the MP context, judgments about how to value correlations are particularly important. 4.All multidimensional indices using arbitrary weights (MPI, HDI, HOI, etc.) should report rank-robustness information.