Frictions Lead to Sorting: a Model of Bilateral On-the-Match Search∗

We present a partnership model where heterogeneous agents bargain over the gains from trade and are allowed to search on the match. Because of frictions, agents extract higher rents from more productive partners, generating an endogenous preference for high types. As individuals search while matched, more productive agents upgrade their partners more often, and therefore the equilibrium distribution becomes positively assortative. Frictions are commonly understood to hamper sorting. In contrast, our mechanism highlights the role of frictions as a driving force towards positive sorting. Our results invalidate the interpretation of positive assortative matching as evidence of complementarity since such a sorting pattern arises even with a submodular production function. JEL Classification: C78; D83; J63; J64