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LATE estimators under costly non-compliance in student-college matching markets
Drlje, M. ; Jurajda, Štěpán
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.
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Essays in Econometrics of Matching Markets: Identification, Estimation and Practice
Drlje, Marin ; Jurajda, Štěpán (advisor) ; Zimmerman, Seth (referee) ; Le Barbanchon, Thomas (referee)
A large literature estimates various school admission and graduation effects by employing variation in student admission scores around schools' admission cutoffs, assuming (quasi-) random school assignment close to the cutoffs. In this dissertation I focus on this variation, both from the theoretical and practical standpoints. In the first paper, I present evidence suggesting that the samples corresponding to typical applications of regression discontinuity design (RDD) fail to satisfy these assumptions. I distinguish ex-post randomization (as in admission lotteries applicable to those at the margin of admission) from ex-ante randomization, reflecting uncertainty about the market structure of applicants, which can be naturally quantified by resampling from the applicant population. Using data from the Croatian centralized college-admission system, I show that these ex-ante admission probabilities differ dramatically between treated and non-treated students within typical RDD bandwidths. Such unbalanced admission probability distributions suggest that bandwidths (and sample sizes) should be drastically reduced to avoid selection bias. I also show that a sizeable fraction of quasi-randomized assignments occur outside of the typical RDD bandwidths, suggesting that these are also inefficient. As an alternative,...
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