Socioeconomic-based affirmative action in higher education has gained importance following controversies over race-based alternatives. In many settings, these interventions use a school-based criterion that selects beneficiaries relative to their peers. Exploiting a nationwide quota policy in Brazil that reserved a large share of vacancies in higher education for public-school students, I show that the reform increases movements from private to public schools by 31% and that movers come disproportionately from low-SES and low-quality private schools. An exploration of the mechanisms shows that movers increase their future probability of higher education attendance at the expense of attending poorer and lower-performing public schools. The reform also leads to changes in school choice of indirectly exposed cohorts and general-equilibrium effects in the form of school closure.