Frictions Lead to Sorting: a Partnership Model with On-the-Match Search

We present a partnership model where heterogeneous agents bargain over the gains from trade and search on the match. Frictions allow agents to extract higher rents from more productive partners, generating an endogenous preference for high types. More productive agents upgrade their partners faster, therefore the equilibrium match distribution features positive assortative matching. Frictions are commonly understood to hamper sorting. Instead, we show how frictions generate positive sorting even with a submodular production function. Our results challenge the interpretation of positive assortative matching as evidence of complementarity.