Introduction: This study examines the influence of major fluctuations in the number of students enrolling at university on the probability of dropout or a switch to a different course of study. Findings from the US show that a pronounced increase in student numbers leads to more dropouts. Materials and methods: This article provides an analysis of this relationship for the first time outside the US and for an entire university system. We use administrative data for all the students who started studying at Swiss universities between 1980 and 2001. Results: The results suggest a significant relationship between positive cohort growth and the probability of dropout. A reduction in student numbers, on the other hand, does not increase the probability of persistence. Discussion: Despite the negative influence of a big cohort on the probability of persistence, no statistically significant relationship exists, by contrast, between the change in student numbers and the probability of a student switching to a different course of study.