Crowding in School Choice, By William Phan, Ryan Tierney, and Yu Zhou

 Here's an innovative paper in the latest AER.

The authors use North Carolina's Wake County Public School System as a motivating example of crowding and the information available to parents about crowding.

Crowding in School Choice, By William Phan, Ryan Tierney, and Yu Zhou, American Economic Review 2024, 114(8): 2526–2552, https://doi.org/10.1257/aer.20220626

Abstract: "We consider the market design problem of matching students to schools in the presence of crowding effects. These effects are salient in parents’ decision-making and the empirical literature; however, they cause difficulties in the design of satisfactory mechanisms and, as such, are not currently considered. We propose a new framework and an equilibrium notion that accommodates crowding, no-envy, and respect for priorities. The equilibrium has a student-optimal element that induces an incentive-compatible mechanism and is implementable via a novel algorithm. Moreover, analogs of fundamental structural results of the matching literature (the rural hospitals theorem, welfare lattice, etc.) survive."

"In our model, each student has a preference over the two dimensions of school identity and the total amount of educational resources that they consume at each school. The more crowded a school is, the fewer resources each student enjoys, and so the value of this second dimension at each school will emerge endogenously. 

...

"We propose a new equilibrium concept: rationing crowding equilibrium (RCE). The core of our innovation is in realizing that the vector of resource levels can function like a price. Consider a competitive solution applied in our context. We may imagine that an auctioneer announces a resource vector, which then determines a (finite) list of school and resource-level pairs. Each student will then demand (generically) one of these pairs, and we can ask the usual market clearing question: Does there exist a resource vector at which, for each school, the demand for educational resources is equal to its supply? We show that the answer is yes, if we allow for an error of at most one seat.9,10 Since each student faced the same budget set, the resulting allocation satisfies no-envy, at least for schools that have not reached their enrollment cap