This paper studies the effect of graduating from college on lifetime earnings. We develop a quantitative model of college choice with uncertain graduation. Departing from much of the literature, we model in detail how students progress through college. This allows us to parameterize the model using transcript data. College transcripts reveal substantial and persistent heterogeneity in students' credit accumulation rates that are strongly related to graduation outcomes. From this data, the model infers a large ability gap between college graduates and high school graduates that accounts for 54% of the college lifetime earnings premium.