We study a structural model of college admissions framed as a contest between a continuum of students for enrollment in a continuum of colleges where the contest outcome is decided by the students' choice of human capital (HC). Students have private information about their learning costs, and colleges have heterogeneous, observable qualities. Our economic model is inspired by methods from the empirical auctions literature and allow us to separately identify the roles of school quality, HC, and unobserved learning costs on post-college household income. We use our estimates to conduct counterfactual experiments comparing different college admissions rules including color-blind admissions, a proportional quota for minority students, and means-tested affirmative action (AA). An AA ban would result in a large migration of minority students out of the best schools and into the lowest quality schools with a corresponding reduction in household income and mean graduation rates. However, the signs and magnitudes of changes to HC investment and individual graduation rate depend on the demographics and learning cost type of the particular student in question. We also argue that a means-tested AA plan does not significantly increase racial diversity. Finally, our estimates imply that the competitive incentive to accrue HC is stronger than the productive incentive for all but the top 4% achieving students.