### Abstract

This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed-point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

Original language | English (US) |
---|---|

Pages (from-to) | 897-941 |

Number of pages | 45 |

Journal | Econometrica |

Volume | 83 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2015 |

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### Keywords

- Discrete choice
- Large games
- Matching markets
- Multiple equilibria
- Pairwise stability

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Econometrica*,

*83*(3), 897-941. https://doi.org/10.3982/ECTA12299

**Large Matching Markets as Two-Sided Demand Systems.** / Menzel, Konrad.

Research output: Contribution to journal › Article

*Econometrica*, vol. 83, no. 3, pp. 897-941. https://doi.org/10.3982/ECTA12299

}

TY - JOUR

T1 - Large Matching Markets as Two-Sided Demand Systems

AU - Menzel, Konrad

PY - 2015/5/1

Y1 - 2015/5/1

N2 - This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed-point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

AB - This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed-point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

KW - Discrete choice

KW - Large games

KW - Matching markets

KW - Multiple equilibria

KW - Pairwise stability

UR - http://www.scopus.com/inward/record.url?scp=84930706392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930706392&partnerID=8YFLogxK

U2 - 10.3982/ECTA12299

DO - 10.3982/ECTA12299

M3 - Article

VL - 83

SP - 897

EP - 941

JO - Econometrica

JF - Econometrica

SN - 0012-9682

IS - 3

ER -