  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.
