Weighting with individuals, equivalent individuals, or not weighting at all. Does it matter empirically?

To take into account heterogeneity in a social welfare function, Ebert (1997) and Shorrocks (1995) show that the only consistent way of welfare measurement consists of either constructing an artificial distribution in which each household is weighted by the number of equivalent individuals, or weighting by the number of individuals in the household. Both approaches are not only mutually exclusive on axiomatic grounds, they are also in sharp contrast with many empirical applications where there is no weighting at all. Since ultimately, the choice is a normative one between axioms, and hence not easily envisaged, an empirical test of the sensitivity of welfare evaluations for the choice of the different weighting schemes might prove useful. In this paper we apply the different methods to administrative microdata of the 2000 PIT reform in Belgium, obtained from the microsimulation model SIRe of the Belgian Ministery of Finance. We find indeed sensitivity of our results with respect to the different weighting methods. In addition, using the number of equivalent individuals as weights to perform dominance analysis leads to fanciful results with respect to the choice of equivalence scales.