Kevin’s post on peer effects mentioned the problem of identification, an example of a less standard approach to this issue is the paper by Graham (IDENTIFYING SOCIAL INTERACTIONS THROUGH CONDITIONAL VARIANCE RESTRICTIONS, BRYAN S. GRAHAM, Econometrica, Vol.76, No. 3 (May, 2008), 643–660), which uses variance restrictions to argue that peer effects were important for participants in the Tennessee STAR class size experiment. The intuition is described below (from p.4):
“The application examines the effect of peer quality on kindergarten achievement using data from the Tennessee class size reduction experiment Project STAR. Classrooms of two sizes are observed in the data set: small and large. Students and teachers within participating schools were randomly assigned to one of the two types of classrooms. In large classrooms, clusters of talented students are typically offset by corresponding clusters of below average students, resulting in little variation in mean student ability. In small classrooms, however, groups composed of mostly above or below average students are more frequently observed, generating greater variation in mean ability. As a result, the variance of peer quality (as measured by average student ability in a classroom) is greater across the set of small than it is across the set of large classrooms. In contrast to peer quality, random assignment ensures that the distribution of teacher characteristics is similar across the two types of classrooms. Under some additional restrictions on the educational production function, discussed in detail below, class type provides a plausible source of exogenous variation in the variance of peer quality”.