The recentered influence function and unidimensional poverty measurement
I discuss the applicability of the recentered influence function (RIF) to the analysis of poverty differentials between distributions (regression-based decomposition into composition and income structure effects).
I show that the predominant approach in the empirical literature estimates the relationship between individual poverty functions of additive measures, particularly the head-count ratio, and household attributes. Given that the recentered influence function of these measures is also their poverty function, this approach is simply a specific case of the one-stage recentered influence function decomposition, using non-linear probability models.
However, the use of recentered influence function provides a more general approach that better accounts for individual contributions to poverty for non-additive poverty measures (such as that of Sen and its extensions) as well. At the same time, the use of reweighting in a first stage allows to avoid imposing any functional form on the relationship between poverty and characteristics at the aggregate level.