Solving the Reflection Problem in Social Interaction Models with Endogeneity

Abstract

We identify peer and contextual effects in social interactions models with endogenous covariates (e.g., self-selected treatments). Unobserved individual characteristics are correlated with these endogenous covariates and affect peer outcomes in the reduced form. Our method uses instruments for endogenous covariates, but does not require additional instruments for simultaneity in outcomes, which are often hard to find in linear-in-means models. Nor does it require any exclusion restriction that some covariates have no contextual effects. The method can be applied to relax the Stable Unit Treatment Value Assumption (SUTVA) in the program evaluation literature, allowing individual treatments to influence the outcomes of other group members through both peer and contextual effects. We apply our method to estimate social effects in Grade 3 math scores of elementary school students in the State of Tennessee. Using lagged class sizes, teacher qualifications and students' self-reported motivation scores as instruments for Grade 2 scores, we find significant evidence for positive peer effects and path dependence on G2 scores.