A Re-scaled Version of the Foster-Greer-Thorbecke Poverty Indices based on an Association with the Minkowski Distance Function

This note advances a family of poverty measures, Πα, which are derived as simple, normalized Minkowski distance functions. The Πα indices turn out to be the αth roots of the corresponding Foster, Greer and Thorbecke Pα indices. The re-calibration of Pα in terms of Πα could have certain possible advantages, which are reviewed in the note. While the Πα indices are not decomposable in the ordinarily understood sense of that term, they are amenable to the completely general decomposition procedure advanced by Shorrocks (‘Decomposition Procedures for Distributional Analysis: A Unified Framework Based on the Shapley Value’) and discussed, here, as an application in the poverty context.