Consider a group consisting of S members facing a common budget constraint p'ξ=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto-efficient outcomes; neither individual consumptions nor intragroup transfers are observable. The paper analyzes when, to what extent, and under which conditions it is possible to recover the underlying structure—individual preferences and the decision process—from the group's aggregate behavior. We show that the general version of the model is not identified. However, a simple exclusion assumption (whereby each member does not consume at least one good) is sufficient to guarantee generic identifiability of the welfare-relevant structural concepts.