Abstract We propose a framework for value-added models that flexibly characterizes heterogeneous teacher productivity based on multidimensional student characteristics. We show that teacher effectiveness heavily depends on the specific attributes of their students. For example, the difference in value-added between well-matched and poorlymatched students for the average teacher is approximately 0.1 standard deviations in test scores. Notably, these matching effects are particularly pronounced among lowachieving students. In language arts, the standard deviation in teacher value-added is one-third larger for low-achieving students compared to high-achieving students.

We examine differences in minority science graduation rates among University of California campuses when racial preferences were in place. Less prepared minorities at higher ranked campuses had lower persistence rates in science and took longer to graduate. We estimate a model of students' college major choice where net returns of a science major differ across campuses and student preparation. We find less prepared minority students at top ranked campuses would have higher science graduation rates had they attended lower ranked campuses. Better matching of science students to universities by preparation and providing information about students' prospects in different major-university combinations could increase minority science graduation.