From Household to Individual Welfare Comparisons: A Double Concavity Test

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: an individual is systematically disadvantaged in the intra-household allocation. If an improvement of the household income distribution in the sense of the Generalized Lorenz (GL) test generates a similar improvement in the distribution of individual incomes, the GL ranking is said to be preserved. The concavity of the expenditures devoted to public goods relative to household income is a necessary condition for the preservation result. This condition also becomes sufficient, if joined with the concavity of the expenditure devoted to private goods of the disadvantaged individual. This double concavity condition also proves to be crucial for Bourguignon’s dominance analysis (1989) when considering a more general framework with households of different size such as couples and single individuals. The double concavity condition is then non-parametrically tested on French data. The concavity of the public sharing function is rejected by the data and consequently we cannot avoid being concerned about intra-household allocation for assessing inequality at the individual level.