Balancing Efficiency and Equity in Classroom Assignment under Endogenous Peer Effects

Abstract: This paper presents a three-step empirical framework for optimizing classroom assignments under endogenous peer effects, using data from the China Education Panel Survey (CEPS). We design \textit{PeerNN}, a neural network that mimics endogenous network formation as a discrete choice model, generating a friendship-intensity matrix ($\Omega$) that captures student popularity. \textbf{Step 2: Estimating Peer Effects.} We measure the peer effect friends' average 6th-grade class rank weighted by $\Omega$ on 8th-grade cognitive test score. Incorporating $\Omega$ into the linear-in-means model induces endogeneity. Using quasi-random classroom assignments, we instrument friends' average 6th-grade class rank with the average classmates' 6th-grade class rank (unweighted by $\Omega$). Our main regression result shows that a 10\% improvement in friends' 6th-grade class rank raises 8th-grade cognitive test scores by 0.13 SD. Positive $\beta$ implies maximizing (minimizing) the popularity of high (low) achievers optimizes outcomes. \textbf{Step 3: Simulating Policy Trade-offs.} We use estimates from Step 1 and Step 2 to simulate optimal classroom assignments. We first implement a genetic algorithm (GA) to maximize average peer effect and observe a 1.9\% improvement. However, serious inequity issues arise: low-achieving students are hurt the most in the pursuit of the higher average peer effect. We propose an \textit{Algorithmically Fair GA} (AFGA), achieving a 1.2\% gain while ensuring more equitable educational outcomes. These results underscore that efficiency-focused classroom assignment policies can exacerbate inequality. We recommend incorporating fairness considerations when designing classroom assignment policies that account for endogenous spillovers.