Efficient Intra-Household Allocations: a General Characterization and Empirical Tests
The neo-classical theory of demand applies to individuals yet in empirical work it is usually taken as valid for households with many members (or even for whole economies!). This paper explores what the theory of individual members of the household resolve conflicts. All we assume is that however decisions are made, outcomes are efficient. We refer to this as the collective setting. The main result we derive shows that in the collective setting household demands must satisfy a symmetry and rank condition on the slutsky matrix. This condition includes the usualsymmetry condition as a special case. We also present some further results on the effects on demands of variables that do not modify oreferences but that do affect how decisions are made. The prime candidates for such variables are the incomes of the individual in the household. We apply our theory to a series of surveys of household expenditures from Canada. We use a flexible quadratic log demand system as out maintained model. The tests of the usual symmetry conditions are rejected for two person households but not for one person households. Moreover we show that the estimates for the two person housholds, assmuing a single utility function for the household, display problems that are absent for single person households. We then test for our collective setting conditions on the couples data. None of the collective setting restrictions are rejected. We conclude that the collective setting is a plausible and tractable next step to take in the analysis of household demand and labour supply behaviour.
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