A New Multiplicative Decomposition for the Foster–greer–thorbecke Poverty Indices

Abstract

This paper shows that Foster-Greer-Thorbecke poverty indices can be written as the product of components summarizing the incidence, intensity and inequality dimensions of poverty and provides an empirical illustration of the decomposition using Spanish household budget surveys data.

The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality

“…[2] − y [1] − y [2] ) + w 3 (x [3] − y [3] [2] − y [1] − y [2] ) + w 3 (x [3] − y [3] [3] − y [1] − y [2] − y [3] …”

“…where g [1] ≥ · · · ≥ g [q] are the positive normalized poverty gaps generated by the income distribution x , the remaining normalized poverty gaps…”

“…We think this is a serious drawback which may distort the conclusions in the 1 For comprehensive surveys on poverty and inequality measures see Silber [25] and Chakravarty [4]. 2 Besides Clark et al [5], Osberg and Xu [21], Xu and Osberg [29] and Aristondo et al [1], some of them may be found in Kakwani [17]. 3 For instance, whereas in the original proposals of Sen [22] and Shorrocks [24] the "Gini index of the poor income" takes part in the decompositions, Osberg and Xu [21] and Xu and Osberg [29] derive alternative decompositions in which the "Gini index of the gaps" is included.…”

“…Accordingly, whenever a relative or intermediate inequality index is involved in the decomposition of a poverty index, the inequality component is not consistent. We think this is a serious drawback which may distort the conclusions in the 1 For comprehensive surveys on poverty and inequality measures see Silber [25] and Chakravarty [4]. 2 Besides Clark et al [5], Osberg and Xu [21], Xu and Osberg [29] and Aristondo et al [1], some of them may be found in Kakwani [17].…”

“…3 For instance, whereas in the original proposals of Sen [22] and Shorrocks [24] the "Gini index of the poor income" takes part in the decompositions, Osberg and Xu [21] and Xu and Osberg [29] derive alternative decompositions in which the "Gini index of the gaps" is included. Similarly, the "inequality among the poor" is captured in term of gaps in the TIP curves introduced by Jenkins and Lambert [15] and in the decomposition for the FGT indices (Foster et al [9]) proposed by Aristondo et al [1].…”