# Partial Identification in Matching Models for the Marriage Market

## TL;DR

This paper develops a method for partially identifying preference parameters in matching models without relying on parametric assumptions, revealing that previous findings were often driven by such restrictions.

## Contribution

It introduces a nonparametric approach to characterize the identified set in matching models, challenging prior reliance on parametric assumptions like the Logit model.

## Key findings

- Many empirical results are sensitive to parametric assumptions.
- The methodology provides bounds on preference parameters without distributional restrictions.
- Re-examination of marriage market data shows previous conclusions may be parametric artifacts.

## 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 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.