Adjusting Incomes for Needs: Can One Avoid Equivalence Scales?

The aim of the paper is to provide guidelines in order to make meaningful comparisons of heterogeneous distributions when incomes are adjusted in order to accommodate differences in needs. We emphasize that the choice of the equivalent income function and the system of weights associated to the equivalent incomes affects significantly the conclusions to be drawn. Introducing simple but intuitively appealing normative conditions, we show that adjusting incomes by a scale factor and weighting the resulting equivalent incomes by the same factor -- as was proposed by Pyatt, ``Social evaluation criteria'', in C. Dagum and M. Zenga (Eds.), Income and Wealth Distribution, Inequality and Poverty, Springer-Verlag, 1990 -- does constitute the only consistent method of making comparisons of relative inequality and/or welfare across populations of heterogeneous households. When the focus is on comparisons in terms of absolute inequality, then lump-sum equivalent income functions and equal weights constitute the only admissible adjustment procedure.