We study partial identification of the preference parameters in models of
one-to-one matching with perfectly transferable utilities, without imposing
parametric distributional restrictions 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 Multinomial Logit
assumption