Poverty measurement: the critical comparison value

The Foster–Greer–Thorbecke (FGT) family of poverty-measures is commonly used when comparing income distributions with respect to poverty. Within this framework, the poverty ranking will be sensitive to the choice of poverty aversion parameter (defining a particular FGT poverty-measure). If we content ourselves with applying a few specific parameter values, then we may demand too little in order to claim robustness in our poverty comparisons. On the other hand, we may demand too much if we only work with FGT poverty-measure quasi orderings established by considering every possible parameter value. An alternative approach may be to report the number of parameter values representing possible reversal points in our poverty ranking—what we call critical comparison values—and leave the final evaluative step to the relevant decision-makers. By applying a generalized version of Descartes’ Rule of Signs, we show that the number of critical comparison values depends on the number of times the cumulative distribution functions intersect.

---

Bertil TungoddenEmail: