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We study estimation and non-parametric identiﬁcation of preferences in two-sided matching markets using data from a single market with many agents. We consider a model in which preferences of each side of the market are vertical, utility is non-transferable and the observed matches are pairwise stable. We show that preferences are not identiﬁed with data on one-to-one matches but are non-parametrically identiﬁed when data from many-to-one matches are observed. The additional empirical content in many-to-one matches is illustrated by comparing two simulated objective functions, one that does and the other that does not use information available in many-to-one matching. We also prove consistency of a method of moments estimator for a parametric model under a data generating process in which the size of the matching market increases, but data only on one market is observed. Since matches in a single market are interdependent, our proof of consistency cannot rely on observations of independent matches. Finally, we present Monte Carlo studies of a simulation based estimator.
Agarwal, Nikhil and Diamond, William, "Identification and Estimation in Two-Sided Matching Markets" (2013). Cowles Foundation Discussion Papers. 2289.