  We study partial identification of the preference parameters in the
one-to-one matching model with perfectly transferable utilities. We do so
without imposing parametric distributional assumptions on the unobserved
heterogeneity and with data on one large market. We provide a tractable
characterisation of the identified set under various classes of nonparametric
distributional assumptions on the unobserved heterogeneity. Using our
methodology, we re-examine some of the relevant questions in the empirical
literature on the marriage market, which have been previously studied under the
Logit assumption. Our results reveal that many findings in the aforementioned
literature are primarily driven by such parametric restrictions.
