Abstract: I present a method to jointly estimate social spillovers in the classroom and the distributions of teacher and student effects. This method is based on the covariance and higher-order moments restrictions of the test scores, requiring the random assignment of teachers and students to classrooms. Using the Tennessee Project STAR dataset, I estimate sizeable spillovers in kindergarten classrooms and departures from normality of the teacher and student ability distributions. The estimates also show that reducing class size has a positive effect on mean performance, but it increases the inequality. Based on these estimates, I perform several input-neutral policy counterfactuals involving teachers and students assignment rules, and changing the distribution of class sizes. For the latter, I derive an optimal class size distribution rule, which increases mean test scores and reduces the overall variance
