Repeated selection with heterogeneous individuals and relative age effects

In many contexts, skill-accumulation over time crucially depends on the amount of training received, which is often allocated through repeated selection. We analyze optimal selection when individuals differ with respect to their ability to transform training into skills and relative age. The latter is considered a major determinant for initial within-cohort performance differentials. The optimal policy is pro-competitive at later selection stages in the sense of selecting the individuals with the higher skill signals. In early stages, pro-competitive selection, counter-competitive selection or no selection can be the optimal policy, depending on the size of the relative age differences and on the degree of heterogeneity with respect to ability in the population. We show that under the optimal selection policy the probability of allocating high intensity training to the individuals with highest ability is not monotone with respect to the size of the relative age advantage. Finally, the (empirical) observation of persistent relative age effects does not necessarily hint at suboptimal selection policies.