July 2008

This paper develops a model for longitudinal student achievement data designed to estimate heterogeneity in teacher effects across students of different achievement 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, the authors find evidence of these interactions that are of relatively consistent but modest magnitude across different contexts, accounting for about 10 percent 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, they find that the interactions account for about three to four percent of total variation in teacher effects on different classes, with somewhat larger values in middle school mathematics. These 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 value-added measurement teacher effect estimates.

*This paper was presented at the Wisconsin Center for Education Research’s National Center on Value-Added Measurement in March 2008.

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