Composite Sorting

This paper introduces an assignment model with concave costs of skill gaps, which arise generally when firms mitigate costs of mismatch as in Stigler (1939) and Laffont and Tirole (1986, 1991). Concave costs of skill gaps imply that the output function is neither supermodular nor submodular. We thus introduce a tractable model that interpolates between the polar canonical cases of supermodularity and submodularity. We characterize sorting, wages, and comparative statics and show these substantively differ from traditional assignment models. Under composite sorting: (1) distinct worker types work in the same occupation, and (2) worker types are simultaneously part of both positive and negative sorting. Quantitatively, our model can generate and help explain earnings dispersion between and within occupations.