Graduation rates (GRs) remain one of the most frequently applied measures of institutional performance. This paper analyzes the relationship between university characteristics and GRs in Spain, using a dataset for the entire public university system over the period 1998-2008. Since we observe the same university over several years, we address the problem of institutional unobserved heterogeneity for the first time. The main findings that can be drawn from our results are that university features, such as expenditure, student-teacher ratio and financial-aid to students are important in accounting for GRs. Surprisingly, student ability has no significant impact explaining graduation, a result that can be justified given the features of the Spanish university system.