Positive skill clustering in role-assignment matching models

Kremer and Maskin (1996, NBER Working Paper) explore matching when production involves defined roles. Despite underlying Cobb-Douglas production functions, the induced maximum production function is not supermodular (SPM), and positive sorting does not arise. This article introduces and solves a general class of role-assignment matching models with general SPM production functions. The unique equilibrium entails a novel blend of positive sorting in the large, and locally negative sorting that I call positive clustering. I show how the equilibrium matching changes as the production function changes. In a dynamic extension, sorting, mobility, and wage inequality positively covary with changes in production across matching markets.