The role of testing noise in the estimation of achievement-based peer effects

• Testing noise can generate a reversion bias in addition to the attenuation bias.
• The reversion bias is due to the presence of former peers in the current peer group.
• The reversion bias can be corrected by exploiting peer quality variation attributable to new peers only.
• The existence and correction of the reversion bias are illustrated with real-world data.

I demonstrate that in the value-added estimation of peer effects using lagged peer achievement, testing noise may generate another bias in addition to the well-known attenuation bias. Such a bias, which I refer to as the “reversion bias,” may arise when some of a student’s current peers happen to be his/her former peers whose performances in the baseline test were subject to the same common testing noise as the student's own. I propose a solution to overcome this problem by exploiting only the variation in the new peers’ portion of the overall peer quality. Using real-world data, I illustrate the existence of this bias and demonstrate the proposed solution.