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.