It is common in the implementation of teacher accountability systems to use a procedure known as Empirical Bayes shrinkage to adjust the teacher value-added estimates by their level of precision. Because value-added estimates based on fewer students and students with "hard-to-predict" achievement will be less precise, the procedure could have differential impacts on the probability that the teachers of fewer students or students with hard-to-predict achievement will be assigned consequences.
This paper investigates how shrinkage affects the value-added estimates of teachers of hard-to-predict students, focusing on the context of threshold-based accountability systems. We found that the achievement of particular groups of students -- students with low prior achievement and who receive free lunch -- is harder to predict. Teachers of these types of students tend to have less precise value-added estimates, and shrinkage increases their estimates' precision.
Shrinkage also reduces the absolute value of the value-added estimates of teachers of hard-to-predict students. However, in our data, we found that shrinkage has no statistically significant effect on the relative probability that teachers of hard-to-predict students receive consequences.