Four elementary points about multidimensional poverty

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

2. 1. It’s the correlations. • When might you want to analyze poverty “multi-dimentionally”? • When there are at least two welfare dimensions of interest between which there are no natural aggregators (e.g. prices)… • …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)

3. 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.

4. 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

5. 4. Indices require measures of robustness to weights (at least). “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… Source: Foster, McGillivray and Seth (2008)

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