Teacher Quality in Educational Production: Tracking, Decay, and Student Achievement

An emerging consensus holds that teacher quality is an extremely important determinant of student achievement and a promising lever by which educational outcomes can be improved. "Value-Added Models" (VAMs) attempt to distinguish good from bad teachers, using observational data to measure teachers' effects on student achievement. I develop falsification tests for the assumptions about student-to-teacher assignments on which VAMs rely, using the idea that teachers in later grades cannot have causal effects in students' test scores in earlier grades. A simple VAM indicates that 5th grade teachers have nearly as large "effects" on 4th grade gains as on 5th grade gains, implying that assignments are not ignorable. An extension of this test shows that VAMs that allow for tracking on the basis of students' permanent ability are similiarly misspecified: Teacher assignments evidently respond dynamicallt to year-to-year fluctuations in student achievement. I propose models of the assignment process that permit identification. Estimates that are consistant in the presence of (some forms of) dynamic tracking yield very different assessments of teacher quality than those obtained from common VAMs. VAMs need further development and validation before they can support causal interpretations or policy applications.