Zhenyuan Zhang Publications

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.

We propose a new sorting framework: composite sorting. Composite sorting comprises of (1) distinct worker types assigned to the same occupation, and (2) a given worker type simultaneously being part of both positive and negative sorting. Composite sorting arises when fixed investments mitigate variable costs of mismatch. We completely characterize optimal sorting and additionally show it is more positive when mismatch costs are less concave. We then characterize equilibrium wages. Wages have a regional hierarchical structure − relative wages depend solely on sorting within skill groups. Quantitatively, composite sorting can generate a sizable portion of within-occupations wage dispersion in the US.