We present an equilibrium model of the market for higher education. Our model simultaneously predicts student selection into institutions of higher education, financial aid, educational expenditures, and educational outcomes. We show that the model gives rise to a strict hierarchy of colleges that differ by the educational quality provided to the students. We also develop a new estimation procedure that exploits the observed variation in prices within colleges. Identification is based on variation in endowments and technology. It does not rely on observed variation in potentially endogenous characteristics of colleges such as peer quality measures and expenditures. We estimate the structural parameters using data collected by the National Center for Education Statistics and aggregate data from Peterson's and the National Science Foundation.