We study the consequences of affirmative action in centralized college admissions systems. We develop an empirical framework to examine the effects of a large-scale program in Brazil that required all federal institutions to reserve half their seats for socioeconomically and racially marginalized groups. By exploiting admissions cutoffs, we find that marginally benefited students are more likely to attend college and are enrolled at higher-quality degrees four years later. Meanwhile, there are no observed impacts for marginally displaced non-targeted students. To study the effects of larger changes in affirmative action, we estimate a joint model of school choices and potential outcomes. We find that the policy has impacts on college attendance and persistence that imply a virtually one-toone income transfer from the non-targeted to the targeted group. These findings indicate that introducing affirmative action can increase equity without affecting efficiency