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* If matching based on observed characteristics is found to be important, it is a reasonable conjecture that matching based on unobserved characteristics is also important. * This paper investigates what data on the sorting patterns between agents can tell us about the distributions of unobserved agent characteristics relevant for sorting.  Foundations:* We use data on many markets with finite numbers of players and different realizations of observables and unobservables in each market.

* In the baseline transferable utility matching game, the primitive that governs sorting is the matrix that collects the production values for each potential match in a matching market. The *Our key assumption is that the production level of each match is additively -separable in observable and unobservable terms. *