🤖 AI Summary
This paper addresses the failure of conventional task assignment models when skill-mismatch costs are concave—rendering the output function neither supermodular nor submodular. To resolve this, we propose a novel structured matching model. Methodologically, we introduce the concept of “composite sorting,” which relaxes the supermodularity/submodularity assumptions and explicitly models firms’ mismatch-mitigation behavior via concave cost functions; we further develop an interpolation framework that bridges supermodular and submodular structures. Our contributions are threefold: (i) we unify the explanation of within-occupation and cross-occupation labor sorting; (ii) we demonstrate that workers of the same type can simultaneously engage in both positive and negative sorting, and that heterogeneous worker types may coexist within a single occupation; and (iii) we quantitatively replicate earnings dispersion both within and across occupations, precisely identifying patterns missed by standard models—thereby offering a new mechanism for understanding labor market inequality.
📝 Abstract
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.
