The Sharing Rule: Where Is It?

The search for a robust and stable sharing rule has led us to novel results for identifying the rule governing the intra-household allocation of resources. We introduce an income proportionality property that directly connects distribution factors with individual incomes and implements this identifying condition to obtain an exact correspondence between the structural and reduced form of the collective demand equations. In our application, we appropriately exploit information about privately consumed goods, prices and distribution factor variation to exactly estimate how resources are shared between adults and children in a sample of Italian households. 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.