Identification in Separable Matching with Observed Transfers

Imposing a separability assumption on the joint surplus in transferable utility matching models has proved very useful in empirical work. Yet when only “who matches whom” is observed, the distributions of unobserved heterogeneity cannot be identified separately. This note derives the distribution of equiilibrium transfers and shows that if the distribution of transfers within cells is observed, the distribution of heterogeneity can often be recovered, separability can be tested, and complementarities in surplus inferred