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This paper empirically studies the distributional consequences of affirmative action in the context of a centralized college admission system. We examine the effects of a large-scale program in Brazil that mandated all federal public institutions to reserve half their seats for public high school students, prioritizing those from socioeconomically and racially marginalized groups. After the policy was put in place, the representation of public high school students of color in the most selective federal degrees increased by 73%. We exploit degree admission cutoffs to estimate the effects of increasing affirmative action by one reserved seat on the quality of the degree attended four years later. Our estimates indicate that the gains for bene ted students are 1.6 times the costs experienced by displaced students. To study the effects of larger changes in affirmative action, we estimate a joint model of school choice and potential outcomes. We identify the parameters of the model using exogenous variation in test scores|arising from random assignment to graders of varying strictness|that changes the availability of degrees for otherwise identical individuals. We find that the policy creates impacts on college attendance and persistence that imply overall income gains of 1.16% for the average targeted student, and losses of 0.93% for the average non-targeted student. Overall, the policy prompted a negligible increase in predicted income of 0.1% across all students in the population. Taken together, we find that the affirmative action policy had important distributional consequences, which resulted in almost one-to-one transfers from the non-targeted to the targeted group. These results indicate that introducing affirmative action can increase equity without affecting the overall efficiency of the education system.