COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1905 Identification and Estimation in Two-Sided Matching Markets Nikhil Agarwal and William Diamond August 2013 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 is homogeneous, utility is non-
transferable utility 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. This difference in the
identifiability of the model 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. |
