When Should Children Start School?

Kindergarten-entrance-age effects are difficult to identify due to the nonrandom allocation of entrance-age and simultaneous relative-age effects. This paper presents evidence that instrumental variable frameworks do not identify age effects for the youngest children of a cohort using the results of statistical tests for essential heterogeneity in initial enrollment decisions. Restricting attention to the oldest children in a cohort yields a sample with quasirandom variation in entrance and relative ages. This variation is used to identify the parameters of education production functions in which both entrance and relative ages are inputs for achievement. Estimates of entrance-age parameters from the ECLS-K data set are positive, large, and persist until the spring of third grade. Relative-age parameters are smaller, tend to be negative, and fade-out for math achievement by third grade. For the average child in our sample these estimates imply that both an earlier entrance cutoff date and an earlier birthdate will increase achievement if the child remains eligible. There is extreme heterogeneity in effects by gender and home environment, and these results are likely to be the most relevant for policy.