Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2024, Volume 92, Issue 3

Identification and Estimation in Many-to-one Two-sided Matching without Transfers
p. 749-774

YingHua He, Shruti Sinha, Xiaoting Sun

In a setting of many‐to‐one two‐sided matching with nontransferable utilities, for example, college admissions, we study conditions under which preferences of both sides are identified with data on one single market. Regardless of whether the market is centralized or decentralized, assuming that the observed matching is stable, we show nonparametric identification of preferences of both sides under certain exclusion restrictions. To take our results to the data, we use Monte Carlo simulations to evaluate different estimators, including the ones that are directly constructed from the identification. We find that a parametric Bayesian approach with a Gibbs sampler works well in realistically sized problems. Finally, we illustrate our methodology in decentralized admissions to public and private schools in Chile and conduct a counterfactual analysis of an affirmative action policy.

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Supplemental Material

Supplement to "Identification and Estimation in Many-to-one Two-sided Matching without Transfers"

YingHua He, Shruti Sinha, and Xiaoting Sun

This supplemental appendix contains material not found within the manuscript.

Supplement to "Identification and Estimation in Many-to-one Two-sided Matching without Transfers"

YingHua He, Shruti Sinha, and Xiaoting Sun

The replication package for this paper is available at The authors were granted an exemption to publish parts of their data because either access to these data is restricted or the authors do not have the right to republish them. However, the authors included in the package, on top of the codes and the parts of the data that are not subject to the exemption, a simulated or synthetic dataset that allows running the codes. The Journal checked the data and the codes for their ability to generate all tables and figures in the paper and approved online appendices. Whenever the available data allowed, the Journal also checked for their ability to reproduce the results. However, the synthetic/simulated data are not designed to produce the same results. Given the highly demanding nature of the algorithms, the reproducibility checks were run on a simplified version of the code, which is also available in the replication package.