Job matching under constraints by Kojima, Sun, and Yu in the September AER

 From the September AER, the latest in a distinguished string of papers initially motivated by aspects of the clearinghouse for new doctors in Japan:

Kojima, Fuhito, Ning Sun, and Ning Neil Yu. 2020. "Job Matching under Constraints." American Economic Review, 110 (9): 2935-47.  DOI: 10.1257/aer.20190780

Abstract: Studying job matching in a Kelso-Crawford framework, we consider arbitrary constraints imposed on sets of doctors that a hospital can hire. We characterize all constraints that preserve the substitutes condition (for all revenue functions that satisfy the substitutes condition), a critical condition on hospitals' revenue functions for well-behaved competitive equilibria. A constraint preserves the substitutes condition if and only if it is a "generalized interval constraint," which specifies the minimum and maximum numbers of hired doctors, forces some hires, and forbids others. Additionally, "generalized polyhedral constraints" are precisely those that preserve the substitutes condition for all "group separable" revenue functions.

Here's the first paragraph:

"Hiring entities often face various types of constraints. In the United States, firms that receive favorable treatments from governments often promise to hire at least a certain number of workers (Byrnes, Marvel, and Sridhar 1999): floor constraints. In Chinese cities, the household registration system distributes quotas to employers for transferring  employees’ registrations from other places (Chan and Zhang 1999): type-specific ceiling constraints on hiring nonlocals. In rural India, a health subcenter is often required to be staffed by exactly one male and one female (Kapoor 2011): type-specific constraints with exact quotas. These are restrictions on the set of employees that an employer is allowed to hire. Inspired by a classical framework for studying job markets (Kelso and Crawford 1982), this paper studies how all possible restrictions of this type impact the substitutes condition on revenue functions of the employers, a condition known to be critical for the existence and certain regularity properties of competitive equilibria (Kelso and Crawford 1982; Gul and Stacchetti 1999; Milgrom 2000; Hatfield et al. 2019; Kojima, Sun, and Yu 2020a)"

and, from the Conclusions section:

"In a classical paper on the difficulty for rural hospitals in filling all of their positions in the National Resident Matching Program, Roth (1986) concludes that “this maldistribution seems unlikely to be changed by any system that does not involve some element of compulsion, or some change in the relative numbers of available positions and eligible students.” Our analysis suggests that in job matching with adjustable salaries, a compulsion in the form of floor or ceiling constraints may be a possible solution: one of the appealing properties of such a policy is that it preserves the substitutes condition and thus the existence of competitive equilibria under standard assumptions (Kojima, Sun, and Yu 2020a)."