Partial Identification in Two-sided Matching Models

In this paper we propose a methodology for estimating preference parameters in matching models. Our estimator applies to repeated observations of matchings among a fixed group of individuals, which is a similar data structure as in Fox (2010). Our estimator is based on stability conditions in the matching models; we consider both transferable (TU) and non-transferable utility (NTU) models. In both cases, the stability conditions yield moment inequalities which can be taken to the data. The preference parameters are partially identified. We consider simple illustrative examples, and also an empirical application to aggregate marriage markets.