Free college proposals have become increasingly popular in many countries of the world. To evaluate their potential effects, we develop and estimate a dynamic model of college enrollment, performance, and graduation. A central piece of the model, student effort, has a direct effect on class completion, and an indirect effect in mitigating the risk of not completing a class or not remaining in college. We estimate the model using rich, student-level administrative data from Colombia, and use the estimates to simulate free college programs that differ in eligibility requirements. Among these, universal free college expands enrollment the most, but it does not affect graduation rates and has the highest per-graduate cost. Performance-based free college, in contrast, delivers a slightly lower enrollment expansion yet a greater graduation rate at a lower per-graduate cost. Relative to universal free college, performance-based free college places greater risk on students, but precisely for this reason leads them to better outcomes. Nonetheless, even performance-based free college fails to deliver a large increase in graduation rate, suggesting that additional, complementary policies might be required to elicit the large effort increase needed to raise graduation rates.