We model a higher education system that admits students according to their admission signal, which is, in turn, affected by their cognitive ability and socioeconomic background. We show that only policies aimed at compensating for low backgrounds result in a higher consumption and a favorable income distribution. We test the model using a unique dataset of open admission university and standard universities students. We demonstrate that high school GPA is explained by cognitive ability and socioeconomic background, while academic GPA is explained by cognitive ability. Results confirm that the current admission system misses capable students, especially from lower backgrounds.