A public college in Mexico City randomly assigns applicants into a group that can immediately enroll and a group that can only do so after one year. The author shows that the standard model of educational decisions predicts no (or minimal) effect of deferral on educational attainment. He surveyed the applicants to this college for the 2007/2008 academic year. Using data from that survey, he finds that, one and a half years after the first group enrolled, individuals in that group were 19 percentage points more likely to be enrolled than those that had to wait. This implies that offering more slots in a public college increases educational attainment. He finds that one additional slot increases the attainment of at least 0.3 individuals of the applicant pool and that offering them to individuals of poorer backgrounds has an even larger effect. To account for these results, he extends the standard model by placing the education decision in a model of labor market search. This suggests the importance of variability in opportunity costs for explaining who enrolls in college at any given moment. He derives testable implications of the model and show that they are verified empirically. He estimates the parameters of the model and show that the model can explain the observed patterns under reasonable assumptions. He also discusses alternative explanations of the impact of deferral and show they are inconsistent with observed patterns. The conclusion is twofold. First, public supply of college slots can impact the attainment of the target population. Second, within-individual variation in opportunity costs is an important element in determining educational attainment. This latter point can have implications for how systems of higher education systems should be designed. Bounding the Effect of Admission on Enrollment is appended. (Contains 3 figures, 17 tables, and 28 footnotes.)