From household to individual’s welfare: does the Lorenz criteria still hold? Theory and Evidence from French Data

Consider an income distribution among households of the same size in which individuals, equally needy from the point of view of an ethical observer, are treated unfairly within the household. In the first part of the paper, we look for necessary and sufficient conditions under which the Generalized Lorenz test is preserved from household to individual level. We find that the concavity of the expenditures devoted to public goods relatively to household income is a necessary condition. This condition also becomes sufficient, if joined with the concavity of the expenditure devoted to private goods of the dominated individual. The results are extended to the case of heterogeneous populations, when more complex Lorenz comparisons are involved. In the second part of the paper, we propose a new method to identify the intra-family sharing rule. The double concavity condition is then non-parametrically tested on French households.