I build a model of many‐to‐one matching with nontransferable utility involving many agents on both sides of the market, for example, workers and firms. Under parsimonious assumptions on preferences and assuming that matches are stable, I provide a tractable asymptotic characterization of the joint distribution of match characteristics. I find that one can identify the joint surplus of a match, but cannot separately identify workers' and firms' preferences from data on realized matches. Within‐firm variation in matched worker characteristics, only available in many‐to‐one matching data, can help identifying and estimating unobserved firm heterogeneity in the surplus function.
Tim Ederer (Thu,) studied this question.