From Household to Individual Welfare Comparisons : a Double Concavity Test  HØlLne Couprie y , Eugenio Peluso z and Alain Trannoy x April 19, 2006 Abstract 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 dis- tribution of individual incomes, the GL ranking is said to be preserved. The concavity of the expenditures devoted to public goods relatively to household income is a necessary condition for the preservation result. This condition also becomes su¢cient, 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 Bour- guignons dominance analysis (1989) when considering a more general framework with households of di/erent 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 individual level. JEL Classication : D63, D13, C14. Key Words : Lorenz comparisons, intra-household inequality, sharing functions, non-parametric estimation.  We thank Jean-Yves Duclos, Marc Fleurbaey, Peter Lambert, Arthur Lewbel, Michel Le Breton, Federico Perali, Nathalie Picard, Nicolas Ruiz and the participants at CHILD International Workshop in Garda, CIRPEE 2004 Conference and 2005 Econometric Society World Meeting for useful comments. INSEE data were made available through an agreement with IRESCO-Lasmas. The usual caveat applies. y Corresponding author. GREMAQ, UniversitØ Toulouse 1, helene.couprie@univ-tlse1.fr. z THEMA UniversitØ de Cergy- Pontoise and Dipartimento di Scienze Economiche, Universit degli Studi di Verona Viale dellUniversit 4, 37129 Verona (Italy). E-mail: eugenio.peluso@univr.it x EHESS, GREQAM-IDEP, Centre de la vieille charitØ, Marseille. alain.trannoy@eco.u-cergy.fr 1