The Foster–Greer–Thorbecke Poverty Measures Reveal More

In this paper we propose new multiplicative decompositions of the Foster–Greer–Thorbecke (FGT) family of poverty measures with poverty aversion parameters 3 and 4. Our decomposition results reveal that skewness (i.e., the location of the bulk of the poor in relation to the poverty line) is introduced when the poverty aversion is 3, to augment poverty incidence, poverty intensity, and inequality among the poor. When the poverty aversion parameter is 4, both skewness and kurtosis (i.e., extremities in the distribution of the incomes of the poor) are introduced. The empirical benefits of introducing skewness and kurtosis are stated and illustrated using real data derived from the 2016 Canadian census. We also propose simpler alternative multiplicative decompositions of the FGT poverty measures for which the variance of the normalized incomes of the poor, which has a fixed upper bound of 1/4, is used as the inequality measure. The fixed upper bound of the variance inequality measure is then exploited to derive the bounds of the FGT measure with a poverty aversion parameter of 2, the empirical usefulness of which is also articulated in the paper.