Class size, class composition, and the distribution of student achievement

Using richly detailed data on fourth‐ and fifth‐grade students in the North Carolina public school system, I find evidence that students are assigned to classrooms in a non‐random manner based on observable characteristics for a substantial portion of classrooms. Moreover, I find that this non‐random assignment is statistically related to class size for a number of student characteristics and that failure to control for classroom composition can severely bias traditionally estimated class size effects. Teacher‐fixed effects and classroom composition controls appear to be effective at addressing selection related to classroom composition. I find heterogeneity in class size effects by student characteristics – students who struggle in school appear to benefit more from class size reductions than students in the top of the achievement distribution. I find that smaller classes have smaller achievement gaps on average and that class size reductions may be relatively more effective at closing achievement gaps than raising average achievement; however, class size effects on both average achievement and achievement gaps are small.