The Sharing Rule: Where Is It? WP Series University of Verona Department of Economics (ISSN: 2036-2919 (paper), 2036-4679 (online)), 16/2012

The search for a robust and stable sharing rule has led us to novel results about identification of the rule governing the intra-household allocation of resources. We introduce an income proportionality property that directly connects distribution factors with individual incomes and implement this identifying condition to obtain an exact correspondence between the structural and reduced form of the adopted collective demand equations. The paper first reexamines the collective model of household consumption and shows that a) the collective model as traditionally de- veloped is not identified, b) illustrates the novel income proportionality condition, and c) derives a restriction allowing full identification. In the tradition of collective theory, we exploit information about private consumption of an assignable good, clothing for adults and children in our application, prices and distribution factor variation to estimate how resources are shared between adults and children in a sample of Italian households. Previous estimations of collective models where only limited to either the direct or indirect estimation of the structure. Our results open up the possibility of a direct structural estimation of a collective system of demand equations, and associated individual Engel curves, as easily as estimating a demand system based on a unitary framework.