The law of large numbers for large stable matchings

Jacob Schwartz, Kyungchul Song

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number105742
JournalJournal of Econometrics
Issue number1
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© 2024


  • Concentration inequality
  • Correlated preferences
  • Law of large numbers
  • Stable matching
  • Two-sided matching

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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