The size of the core in school choice

JEL Classification: C78, D82, C71We study the determinants of the size of the core in the school choice problem using three years of data from a large higher education application clearinghouse. The clearinghouse uses a variation of the college-optimal stable mechanism (COSM) to assign applicants to slots in Finnish polytechnics. If the core is large, switching to a student-optimal stable mechanism (SOSM) could yield large improvements for applicants at a cost to schools. We however find that the core is either a singleton or very small each year. This suggests that the student/school trade-off is relatively unimportant within the set of stable matchings in Finnish polytechnic assignments. We show that the similarity of COSM and SOSM matchings is due to correlated school priorities, differing numbers of students and slots, and to students only applying to a small number of programs each. Because these properties are common to other higher education school choice problems, our conclusions are likely to generalize. In spite of the fact that Finnish polytechnics jointly only accept a third of applicants, accepted applicants' average matriculation exam grades are not much better than those of the median applicant. We attribute this to the low effective number of programs applied to, and suggest that details in the design of the application process affect the trade-off in match quality