Exploring Student-Teacher Interactions in Longitudinal Achievement Data

This article develops a model for longitudinal student achievement data designed to estimate heterogeneity in teacher effects across students of different achivement levels. The model specifies interactions between teacher effects and students’ predicted scores on a test, estimating both average effects of individual teachers and interaction terms indicating whether individual teachers are differentially effective with students of different predicted scores. Using various longitudinal data sources, we find evidence of these interactions that are of relatively consistent but modest magnitude across different contexts, accounting for about 10% of the total variation in teacher effects across all students. However, the amount that the interactions matter in practice depends on how different are the groups of students taught by different teachers. Using empirical estimates of the heterogeneity of students across teachers, we find that the interactions account for about 3%-4% of total variation in teacher effects on different classes, with somewhat larger values in middle school mathematics. Our findings suggest that ignoring these interactions is not likely to introduce appreciable bias in estimated teacher effects for most teachers in most settings. The results of this study should be of interest to policymakers concerned about the validity of VAM teacher effect estimates. Modeling Student-Teacher Interactions 1