This paper introduces an empirical strategy to estimate dynamic treatment effects in randomized trials that provide treatment in multiple stages and in which various noncompliance problems arise, such as attrition and selective transitions between treatment and control groups. Our approach is applied to the highly influential four-year randomized class size study, Project STAR. We find benefits from attending small classes in all cognitive subject areas in kindergarten and first grade. We do not find any statistically significant dynamic benefits from continuous treatment versus never attending small classes following grade 1. Finally, statistical tests support accounting for both selective attrition and noncompliance with treatment assignment.

Peer effects have figured prominently in debates on school vouchers, desegregation, ability tracking, and antipoverty programs. Compelling evidence of their existence remains scarce for plaguing endogeneity issues such as selection bias and the reflection problem. This paper is among the first to firmly establish the link between peer performance and student achievement, using a unique data set from China. We find strong evidence that peer effects exist and operate in a positive and nonlinear manner; reducing the variation of peer performance increases achievement; and our semiparametric estimates clarify the trade-offs facing policymakers in exploiting positive peer effects to increase future achievement.