Transferable Utility Matching Beyond Logit: Computation and Estimation with General Heterogeneity

TL;DR

This paper develops a flexible framework for transferable utility matching that handles arbitrary heterogeneity, introduces a scalable algorithm, and proposes an estimator robust to misspecification, advancing beyond traditional logit models.

Contribution

It provides a general linear programming approach for TU matching without logit assumptions, along with a scalable algorithm and a moment-matching estimator.

Findings

Algorithm is scalable and converges reliably.

Estimator is consistent under correct model specification.

Logit misspecification causes systematic bias.

Abstract

We present a general framework for matching with transferable utility (TU) that accommodates arbitrary heterogeneity without relying on the logit structure. The optimal assignment problem is characterized by tractable linear programming formulation, allowing flexible error distributions and correlation patterns. We introduce an iterative algorithm that solves large-scale assignment problems with guaranteed convergence and an intuitive economic interpretation, and we show how the same structure supports a simulated moment-matching estimator of the systematic surplus. Experiments using simulated data demonstrate the algorithm's scalability and the estimator's consistency under correct specification, as well as systematic bias arising from logit misspecification.