We consider the case in which the number of seats in a program is limited, such as a job training program or a supplemental tutoring program, and explore the implications that peer effects have for which individuals should be assigned to the limited seats. In the frequently-studied case in which all applicants are assigned to a group, the average outcome is not changed by shuffling the group assignments if the peer effect is linear in the average composition of peers. However, when there are fewer seats than applicants, the presence of linear-in-means peer effects can dramatically influence the optimal choice of who gets to participate. We illustrate how peer effects impact optimal seat assignment, both under a general social welfare function and under two commonly used social welfare functions. We next use data from a recent job training RCT to provide the first evidence of large peer effects in the context of job training for disadvantaged adults. Finally, we combine the two results to show that the program's effectiveness varies greatly depending on whether the assignment choices account for or ignore peer effects.
Researchers often include covariates when they analyze the results of randomized controlled trials (RCTs), valuing the increased precision of the estimates over the potential of inducing small-sample bias when doing so. In this paper, we develop a sufficient condition which ensures that the inclusion of covariates does not cause small-sample bias in the effect estimates. Using this result as a building block, we develop a novel approach that uses machine learning techniques to reduce the variance of the average treatment effect estimates while guaranteeing that the effect estimates remain unbiased. The framework also highlights how researchers can use data from outside the study sample to improve the precision of the treatment effect estimate by using the auxiliary data to better model the relationship between the covariates and the outcomes. We conclude with a simulation, which highlights the value of using the proposed approach.