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The Law of Large Numbers for Large Stable Matchings

Jacob Schwartz, Kyungchul Song

arXiv 2 Jan 2021 · Econometrics · publishedJournal of Econometrics (2024) · 1 citations (OpenAlex)

arXiv:2101.00399 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In this paper, we consider a setting in which the researcher observes either all or a nontrivial fraction of outcomes from a stable matching. We establish a concentration inequality for empirical matching probabilities assuming strong correlation among the colleges' preferences while allowing students' preferences to be fully heterogeneous. Our concentration inequality yields laws of large numbers for the empirical matching probabilities and other statistics commonly used in empirical analyses of a large matching market. To illustrate the usefulness of our concentration inequality, we prove consistency for estimators of conditional matching probabilities and measures of positive assortative matching.

Citation extraction

54
references
127
in-text mentions
62
distinct cited
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33,880
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Roth and Sotomayor (1990) Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis0.693241100%
2Blum and Rothblum (2002) “Timing is Everything” and Marital Bliss0.69371100%
3Blum, Roth, and Rothblum (1997) Vacancy Chains and Equilibration in Senior-Level Labor Markets0.69361100%
4Fack, Grenet, and He (2019) Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions0.69361100%
5Menzel (2015) Large Matching Markets as Two-Sided Demand Systems0.69361100%
6Chung and Lu (2002) Connected Components in Random Graphs with Given Expected Degree Sequences0.69351100%
7Massart (2007) Concentration Inequalities and Model Selection0.64441100%
Wu/Roth:2018:GEBunmatched citation key Wu/Roth:2018:GEB0.64441100%
9He, Sinha, and Sun (2023) Identification and Estimation in Many-to-One Two-Sided Matching without Transfers0.58531100%
Abdulkadiroglu/Agarwal/Pathak:2017:AERunmatched citation key Abdulkadiroglu/Agarwal/Pathak:2017:AER0.51121100%

Showing the top 10 of 62 scored citations. 2 of these could not be matched to a bibliography entry, so only the citation key is shown.