Partial Identification in Matching Models for the Marriage Market

Abstract

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 as-sumptions 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 distribu-tional 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.