The decomposition of multidimensional poverty measures

Decomposition is arguably the most useful property of poverty measures for the purposes of empirical research and policy making as it allows to disaggregate the sources of observed poverty. Decomposition by population subgroups allows to express overall poverty as a sum of poverty levels in variously defined groups, e.g., based on sex, race, place of origin, etc. In a multidimensional setting, however, another form of decomposition is possible, namely, decomposition by factors in which individuals are deprived. The additive factor decomposition means that overall poverty is a sum of poverty levels in individual attributes. Classes of multidimensional measures that can be decomposed additively into groups and attributes are presented. This allows for a very precise decomposition where the determinants of poverty can be assigned to particular groups and particular attributes. However, the additive factor decomposition neglects the dependence between dimensions of poverty, and therefore poverty measures that are sensitive to dimensions' substitution or complementarity cannot be decomposed in this way. For such measures, the decomposition can be obtained utilizing the so-called Shapley decomposition. The chapter presents this methodology that is very general and may be applied to all poverty indices.