Estimates of the graduate earnings premium typically do not allow for the effect of non-cognitive skills. Since such skills are unobservable in most datasets there is a concern that existing estimates of the graduate premium are contaminated by selection on such unobservables. We use data on a young cohort of individuals that allows us to control for the effects of non-cognitive skills. We find that the inclusion of non-cognitive skills, themselves jointly significantly positive, reduces the estimated graduate premia by an insignificant 1-2 percentage points from an average of 10-12%. Our second contribution is motivated by the greater reliance on administrative datasets in recent research that has focused on annual earnings rather than hourly wages and our results show that the graduate earnings differential is significantly greater than the wage differential. Since we use estimation methods that are NOT robust to selection on unobservables, we adopt Oster (2016) tests to show that it would take an implausible degree of selection on unobservables to drive our estimated wage and earnings returns to zero, and that a plausible upper bound to returns is around one-quarter to one-third below the OLS returns. We further find heterogeneous returns by broad major group and elite university, and we find large degree class differentials.