On the Identification of Peer Effect Models of Cognitive Achievement

The identification problems of general peer effect models have been studied in depth. But cognitive achievement studies suffer two additional sources of bias that arise because the behavioral variable - student effort - is unobserved. This paper studies both sources of bias and analyzes the relative success of the identification strategies most commonly used. In a quadratic model, the equilibrium parameters suffer endogeneity bias except in three particular cases, which are fairly restrictive. Even in these three cases, the structural peer effects are not identified. The most common strategies achieve partial identification at best, even after assuming a unique mechanism for peer effort, and additional assumptions are needed on the production and cost function. This implies that the current empirical studies overestimate the true effect of peers on achievement