Estimating Intra-household Bargaining Power When Outside Options Are Endogenous

We generalize the collective model of the family to let partners choose their outside options, whether to act on them, and how to allocate shared resources. To do so, we apply Harsanyi's (1986) generic games framework to a limited-commitment collective model where a family's real consumption opportunities depend on each partners' specified outside option. We demonstrate uniqueness and existence of the solution by applying Rubinstein, Safra, and Thomson's (1992) appeals-immunity solution concept. We demonstrate that the expected value of bargaining power is semi-parametrically identified in an ordinal framework; the research need not assume specific utility or social welfare functional forms. In addition to empirical tractability and analytical precision, this update to the collective model provides a more nuanced view of intra-household bargaining power: partners with a greater capacity to specify more damaging threats will have more control over the decision-making process, regardless of whether they act on those threats.