Inferring Optimal Peer Assignment From Experimental Data

Abstract

This article studies the problem of optimally dividing individuals into peer groups to maximize social gains from heterogeneous peer effects. The specific setting analyzed here concerns efficient ways of allocating roommates in college dormitories. Using confidential data on a sample of Dartmouth College freshmen who were randomly assigned to be roommates, the article derives efficient roommate pairing rules, based on demographic and academic background, which maximize different aggregate outcomes. Segregation by precollege academic standing and by race are seen to minimize mean enrolment into sororities and maximize mean enrolment into fraternities. Segregation has no effect on mean and median freshman year grade point average (GPA) but increases the higher and decreases the lower percentiles of the GPA distribution for both men and women. Efficiency loss due to legal constraints on allocations (e.g., race-blindness) is shown to be significant and also larger for women for whom peer effects are more nonlinear. The article develops large-sample inference methods for these optimal solutions and the resulting optimized values by using and extending insights from the mathematical programming literature. Applicability of these techniques extends beyond linear maximands such as the mean to other important policy objectives such as outcome quantiles, which, though nonlinear, are shown to be quasi-convex in the allocation probabilities.