Abstract
A growing literature exploits a feature of centralized college admission systems where students with similar admission scores in a neighborhood of a school's admission threshold are or are not offered admission based on small quasi-random differences in admission scores. Assuming that the students at the margin of admission differ only in the treatment assignment, this literature relies on admission scores to instrument for admission or graduation.
We point out that non-compliance with the centralized matching assignment typically corresponds to enrolling in one's preferred program a year after the initial assignment, introducing significant non-compliance costs. We show that with costly non-compliance, the exclusion restriction, the key assumption of the LATE theorem, is violated, leading to biased estimates when instrumenting for graduation, i.e., for a treatment taking place after non-compliance costs are incurred.
We use data from a student-college matching market in Croatia to illustrate the empirical importance of this potential source of bias and propose a method inspired by Lee (2009), which recovers the treatment effect bounds under the assumption that the costs of non-compliance are not related to the treatment assignment.