Sharing Rule Identification for General Collective Consumption Models

Abstract

We propose a method to identify bounds (i.e. set identi…cation) on the shar- ing rule for a general collective household consumption model. Unlike the eects of distribution factors, it is well known that the level of the sharing rule cannot be uniquely identi…ed without strong assumptions on preferences across households of dierent compositions. Our new results show that, though not point identi…ed without these assumptions, narrow bounds on the sharing rule can be obtained. We get these bounds by applying revealed preference restrictions implied by the collective model to the household's continuous aggregate demand functions. We obtain informative bounds even if nothing is known about whether each good is public, private, or assignable within the household, though having such infor- mation tightens the bounds. We apply our method to US 1999-2009 PSID data. This application obtains tight sharing rule bounds that yield useful conclusions regarding the eects of income and wages on intrahousehold resource sharing, and on the prevalence of individual (as opposed to household level) poverty.