The Effects of Class Size and Composition on Student Achievement: New Evidence from Natural Population Variation

I use natural population variation to identify the effects of class size and composition on student achievement. I isolate the credibly random component of population variation in each grade and school district and use this component to generate instrumental variables for class size and composition. I also exploit the discontinuous changes in class size that occur when natural population variation triggers a change in the number of classes in a grade in a school. Discontinuity-based results are both consistent and precise only when applied to within-district changes in class size and population. I find that reductions in class size from a base of 15 to 30 students have no effect on student achievement. The estimates are precise enough to identify improvements in math, reading, or writing achievement of just 3/100ths of a standard deviation. I find that the presence of black students in a class, in an of itself, has no effect on achievement. I demonstrate that estimates of the effect of racial composition that rely on between-district comparisons suffer from substantial bias. Finally, I show that more female classes perform significantly better in writing in the 4th through 8th grades and in math in the 4th grade. Comparison of the effects to average male-female differences in test scores suggest that gender composition alters classroom conduct.