Two-Sided Matching Without Transfers: A Unifying Empirical Framework

This paper provides a unifying framework of one-to-one and many-to-one matching without transfers and investigates how data on realized matches can be leveraged to identify preferences of participating agents. I find that, under parsimonious assumptions on preferences, one can only identify the joint surplus function both in the one-to-one and many-to-one case. While this negative identification result was already established for the one-to-one case, I reconcile this finding with the recent literature showing that preferences are separately identified when having data on many-to-one matchings. I find that these positive identification results are mostly driven by restrictions imposed on preferences rather than the additional identification power made available through the many-to-one structure of the data. I then show that by imposing similar restrictions on preferences, one can recover identification of preferences both in the one-to-one and many-to-one case. Finally, I show that the additional data brought by many-to-one matchings can alternatively be used to estimate more precisely the distribution of un-observed preference heterogeneity