We present evidence that the positive relationship between kindergarten entrance age and school achievement primarily reflects skill accumulation prior to kindergarten, rather than a heightened ability to learn in school among older children. The association between achievement test scores and entrance age appears during the first months of kindergarten, declines sharply in subsequent years, and is especially pronounced among children from upper-income families, a group likely to have accumulated the most skills prior to school entry. Finally, having older classmates boosts a child's test scores but increases the probability of grade repetition and diagnoses of learning disabilities such as ADHD. (Contains 5 figures, 8 tables and 34 footnotes.)