Dynamic College Admissions and the Determinants of Students’ College Retention

Abstract

We analyze the relevance of incorporating dynamic incentives and eliciting private information about students’ preferences to improve their welfare and outcomes in dynamic centralized assignment systems. We show that the most common assignment mechanism, the Deferred Acceptance (DA) algorithm, can result in significant inefficiencies as it fails to elicit cardinal information on students’ preferences. We collect novel data about students’ preferences, their beliefs on admission chances, and their college outcomes for the Chilean college system. We analyze two main behavioral channels that explain students’ dynamic decisions. First, by exploiting discontinuities on admission cutoffs, we show that not being assigned to ones’ top-reported preference has a positive causal effect on the probability of re-applying to the centralized system and switching one’s major/college, suggesting that students switch to more preferred programs due to initial mismatches. Second, we find that a significant fraction of students change their preferences during their college progression, and that these changes are correlated with their grades, suggesting that students may learn about their match-quality. Based on these facts, we build and estimate a structural model of students’ college progression in the presence of a centralized admission system, allowing students to learn about their match-quality over time and re-apply to the system. We use the estimated model to disentangle how much of students’ switching behavior is due to initial mismatches and learning, and we analyze the impact of changing the assignment mechanism and the re-application rules on the efficiency of the system. Our counterfactual results show that policies that provide score bonuses that elicit information on students’ cardinal preferences and leverage dynamic incentives can significantly decrease switchings, dropouts, and increase students’ overall welfare.