| Empirical studies of the allocation of consumption within the family have often failed to reject the null hypothesis of Pareto efficiency. To study the power of these tests, I construct two models of public goods allocation. One model is cooperative and leads to efficient allocations, and the other is noncooperative and leads to inefficient allocations. In the noncooperative models, variations in the economic or social circumstances outside of the household ("distribution factors") cause variations in implicit property rights within the household. If these variations go unobserved by the econometrician, then noncooperative models imply the same restrictions on household demand as do the cooperative ones. Therefore, many tests in the literature cannot identify inefficiency when it is present. I then show that without restrictions on preferences or data on individual consumption, the hypothesis of Pareto efficiency is not well-separated from the noncooperative alternative. So in a nonparametric setting, there can be no tests that both reject all inefficient models and do not reject any efficient models. However, if the effective wealth of each partner is observed without error and satisfies a large support condition, and if the consumption of a public good and at least one assignable private good can be observed, then it is possible to reject efficiency. |
