Chapter 4: Frontiers of Poverty Measurement
to identifying the poor that depends on a simple measure of the breadth or multiplicity of deprivation the person experiences. In this approach, every deprivation has a value. The overall breadth of deprivation experienced by a person is measured by summing the values of deprivations experienced. A poverty cutoff is selected, and if the breadth of deprivation is above or equal to the poverty cutoff, then the person is identified as being poor. The union approach is obtained at one extreme where the poverty cutoff is very low, while the intersection approach arises at the other where the cutoff is very high. An intermediate poverty cutoff identifies as poor those who are sufficiently multiply deprived. This is the dual cutoff approach to identification suggested by Alkire and Foster (2011). For aggregation, Alkire and Foster (2011) extend the FGT class of indices to the multidimensional context. They do this by constructing three matrices analogous to the vectors used in the FGT definitions, except that now each person has a vector containing information to be aggregated into the overall measure. The matrices are censored in that the data of anyone who is not poor are replaced by a vector of zeroes. The censored deprivation matrix g0 contains deprivation values (when a person is deprived in a dimension and poor) or zeroes (when the person is not deprived in the dimension or not poor). The adjusted headcount ratio M0 = m(g0) is its mean. The measure can be equivalently expressed as M0 = HA, where H is the population percentage identified as poor and A is the average breadth of deprivation they experience. Analogous definitions yield the adjusted poverty gap M1 and the adjusted FGT M2, as part of a family Ma of measures where a ≼ 0. The methodology of Alkire and Foster combines a dual cutoff identification approach and an adjusted FGT index. The adjusted headcount ratio has several properties that make it particularly attractive in practical applications. It can be used when the underlying data are ordinal or even categorical. Its interpretation as H × A is similar to the interpretation of PG, the traditional poverty gap, because PG = PH × PIG, where PH is the traditional headcount ratio and PIG is the average normalized income gap of the poor. M0 augments the information in H using A, which is a measure of breadth rather than depth. It is decomposable by population subgroup. It can dig down into the aggregate numbers to understand the key deprivations that are behind the measured poverty level. Related examples can be found in Alkire and Foster (2011) and the recent Human Development Reports of the United Nations Development Programme, which implemented
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