I study a many-to-many, two-sided, transferable utility matching game. Consider
data on matches or relationships between agents but not on the choice set of
each agent. I investigate what economic parameters can be learned from data on
equilibrium matches and agent characteristics. Features of a production function,
which gives the surplus from a match, are nonparametrically identified. In partic-
ular, the ratios of complementarities from multiple pairs of inputs are identified.
Also, the production function is identified up to a positive monotonic transforma-
tion.
Keywords. Matching, identification, complementarities, two-sided matching,
assignment games, vertical relationships.
JEL classification. C14, C78.