We advance current knowledge of school punishment by examining (1) the prevalence of exclusionary discipline in elementary school, (2) racial disparities in exclusionary discipline in elementary school, and (3) the association between exclusionary discipline and aggressive behavior in elementary school. Using child and parent reports from the Fragile Families Study, we estimate that more than 1 in 10 children born 1998-2000 in large US cities were suspended or expelled by age nine, when most were in third grade. We also find extreme racial disparity; about 40% of non-Hispanic black boys were suspended or expelled, compared to 8% of non-Hispanic white or other-race boys. Disparities are largely due to differences in children's school and home environments rather than to behavior problems. Next, consistent with social stress and strain theories, we find suspension or expulsion associated with increased aggressive behavior in elementary school. This association does not vary by race but is robust to a rich set of covariates, individual fixed-effects, and matching methods. In conjunction with what we find for racial disparities, our results imply that school discipline policies relying heavily on exclusionary punishment may be fostering childhood inequality.