[论文解读] Cupid's Invisible Hand: Social Surplus and Identification in Matching Models

Alfred Galichon, Bernard Salanié|arXiv (Cornell University)|Jun 4, 2021

Game Theory and Voting Systems参考文献 78被引用 34

一句话总结

本论文为可转移效用且存在未观测异质性的单对一匹配提供了一个通用框架，证明稳定匹配最大化在可观测互补性与未观测特征之间权衡的社会收益，并给出识别与计算方法。

ABSTRACT

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.

研究动机与目标

• Extend Choo and Siow's framework beyond their logit assumptions by allowing general unobserved heterogeneity distributions.
• Show that the equilibrium matching maximizes a social gain combining observable and unobservable components.
• Derive closed-form formulations to identify joint matching surplus and participant utilities.
• Develop efficient computational methods to compute stable matchings and estimate parametric models.
• Illustrate the approach with an empirical revisit of Choo and Siow’s marriage-pattern dataset.

提出的方法

• Introduce a separability assumption that decomposes joint surplus into observable and unobservable parts.
• Define an Emax (discrete choice) framework for one-sided decisions and its generalized entropy of choice.
• Use convex duality to express the social surplus and the matching problem as convex optimization problems.
• Characterize the generalized entropy of choice via an optimal transport problem and its dual.
• Derive identification results showing mean utilities are the gradient of the generalized entropy given observed matchings.
• Propose gradient, coordinate descent (IPFP), and linear programming algorithms for estimation and equilibrium computation.

实验结果

研究问题

• RQ1 How can a stable matching with transferable utility be characterized when unobserved heterogeneity is present and separable across sides?
• RQ2 Can the two-sided matching problem be decomposed into tractable one-sided discrete choice problems under separability?
• RQ3 How can the joint matching surplus and individual utilities be identified from observed match patterns under general unobserved heterogeneity?
• RQ4 What computational methods efficiently compute stable matchings and estimate model parameters in this general framework?
• RQ5 How does the extended framework perform relative to Choo and Siow’s original model in empirical applications?

主要发现

• The stable matching maximizes a social gain that trades off observable complementarities and unobserved characteristics.
• The generalized entropy of choice provides a convex, computable measure linking choice probabilities to mean utilities.
• Mean utilities are identified as the gradient of the generalized entropy given the distribution of unobservables, enabling identification from observed matchings.
• The social surplus can be computed via a dual convex program, revealing how surplus is split between men and women at equilibrium.
• Efficient algorithms (gradient methods, IPFP/coordinate descent, linear programming) enable computation of stable matchings and estimation of parametric models.
• The framework extends Choo and Siow’s results to more flexible distributions of unobserved heterogeneity and includes an empirical revisit of the original dataset.