It turns out that you can get a lot more information about preferences from many to one (or many to many) matching than from one to one matching, because e.g. something about your employer's preferences (and why they wanted to hire you) can be deduced from who else they hired.
IDENTIFICATION AND ESTIMATION IN TWO-SIDED MATCHING MARKETS
By Nikhil Agarwal and William Diamond
Abstract: 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 nontransferable 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.
Here's my post on Nikhil's defense.
IDENTIFICATION AND ESTIMATION IN TWO-SIDED MATCHING MARKETS
By Nikhil Agarwal and William Diamond
Abstract: 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 nontransferable 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.
Here's my post on Nikhil's defense.
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