Identifying Social Interactions through Excess Variance Contrasts

Abstract

This paper outlines a new method for detecting and assessing the strength of social interactions based on contrasts in excess variance across social groups of exogenously differing sizes. An attractive feature of the approach is its robustness to the presence of group-level heterogeneity and sorting. The proposed estimation strategy is used to test for the presence of peer effects in learning using data from the Tennessee class size reduction experiment Project STAR. Size-induced contrasts of excess variance provide a powerful mechanism for detecting peer group effects in this dataset. Switching from classroom where mean peer ability is at the 25th percentile of the ability distribution to one where it is at the 75th percentile is associated with changes in math and reading achievement scores of 0.9 and 1.1 standard deviations respectively. These estimates suggest that, at minimum, differences in peer composition are at least as important as those in teacher quality for explaining variation in academic achievement within Project STAR schools. While tests based on excess variance contrasts provide strong evidence of peer group effects, conventional regression-based excess sensitivity tests do not. Calibrating asymptotic power functions for the two tests to the Project STAR data suggests that across repeated samples the odds of detecting social interactions are roughly 20 to 30 times greater with the proposed excess variance test. Generalized method of moments provides a unified framework for estimation and inference. The proposed approach is straightforward to implement using standard software.