The Matching Function: A Unified Look into the Black Box

2026-05-10

AI Summary

This study uncovers the microfoundations of matching functions, demonstrating that their functional form is determined by the fine-grained network structure of connections between job seekers and vacancies. Drawing on network theory, the authors model the matching process as a two-sided search network and develop a unified framework—incorporating distributions of search intensity and inequality measures such as the Gini coefficient—that encompasses CES and other canonical matching functions. The paper innovatively introduces “CES-like” approximation conditions and establishes a theory of matching efficiency centered on inequality in search intensity. Key findings reveal that increased dispersion in search intensity on either side reduces matching efficiency; moreover, even when average search intensity rises, greater inequality can lead to an overall decline in matching effectiveness.

Abstract

In this paper, we use tools from network theory to trace the properties of the matching function to the structure of granular connections between applicants and vacancies. We unify seemingly disparate parts of the literature by recovering multiple functional forms as special cases including the CES. We derive a testable condition under which matching in any network from the broad class we analyze can be thought "as if" it comes from a CES matching function, up to a first-order approximation. We provide a theory of match efficacy in which inequality in search intensities is the key determinant of how well the matching process works. A robust finding of our analysis is that dispersion of search intensities on either side of the market is bad for the matching process. We also show that a rise in the market's mean search intensity can reduce match efficacy when it is associated with a higher Gini coefficient of search intensities.

Problem

• matching function
• search intensity
• network structure
• match efficacy
• inequality

Innovation

• matching function
• network theory
• search intensity inequality
• CES matching
• match efficacy