The main purpose of the paper is to estimate the efficiency of a big public university in Italy using individual student-level data, modeling exogenous variables in human capital formation through a heteroscedastic stochastic frontier approach. Specifically, a production function for tertiary education has been estimated with emphasis on inefficiency and its determinants, taking explicitly into account the role played by students' socio-economic and educational background. The empirical evidence, based on 48,338 freshmen, leads towards the use of individual-level data in order to control for the portion of the student academic achievement affected by the personal characteristics and effort, and the portion ascribable to the resources or organization of the institutional activities. Within the limit of external validity allowed by operating within only one university, efficiency scores derived from using both individual-level and aggregate level data do offer an important instrument to the university and governance structures.