Differentiating Between Dimensionality and Duration in Multidimensional Measures of Poverty: Methodology with an Application to China

We develop a multidimensional poverty measure that is sensitive to the within-individual distribution of deprivations across dimensions and time. Our measure combines features from a static multidimensional measure (Alkire and Foster, 2011a) and a time-dependent unidimensional measure (Foster, 2009). The proposed measure separately identifies—and can therefore be decomposed according to—the proportion of the poverty score attributable to: (i) the concentration of deprivations within periods; (ii) the concentration of deprivations within dimensions. In doing so it allows for a poverty ranking that is robust to assumptions about the trade-off between the two components. Previous measures have not allowed for the features proposed here due to the inability to calculate the exact contribution of each dimension to overall poverty. We overcome this by adapting to our measure the Shapley decomposition proposed in Shorrocks (2013) (based on Shapley, 1953). The measure is applied to data from China, 2000-2011.