Title:Â Identification in Many-to-Many Matching Markets
by Yiran Xie
Abstract: This paper analyzes identification in a random utility model of many-to-many matching markets, where agents on both sides can form multiple links and market sizes grow at potentially different rates. The number of links formed by each agent is endogenously determined within the equilibrium.
I propose a utility structure that satisfies the stability conditions necessary for many-to-many matchings and is tractable for empirical implementation. A central challenge in these markets is that expanding the capacity of agents on either side can significantly affect the set of stable outcomes. I show that, under specific conditions, the number of firms willing to match with a given worker (and vice versa) grows at a rate independent of capacity expansions. This property enables the use of the inclusive value framework introduced by Menzel (2015) to characterize agents’ opportunity sets and facilitate identification.