I perform the joint estimation of a reduced-form dynamic model of the transition from one grade level to the next, and a Mincer wage equation, using panel data taken from the NLSY. A very high degree of flexibility is achieved by approximating the distributions of idiosyncractic grade transition shocks and wage shocks with high dimensional normal mixtures. The model rejects all simplifying assumptions common in the empirical literature. In particular, the log wage regression is highly convex, even after conditioning on unobserved and observed skills. Skill heterogeneity is also found to be over-estimated when non-linearity is ignored. After conditioning on skill heterogeneity, I also find evidence of non-separability between the effect of schooling and experience (schooling has a positive effect on wage growth). Finally, the variance of the idiosyncratic wage shock is reduced by obtaining higher education.