Student Sorting and Bias in Value Added Estimation: Selection on Observables and Unobservables
Nonrandom assignment of students to teachers can bias value-added estimates of teachers’ causal effects. Rothstein (2008, 2010) shows that typical value-added models indicate large counterfactual effects of ﬁfthgrade teachers on students’ fourth-grade learning, indicating that classroom assignments are far from random.This article quantiﬁes the resulting biases in estimates of ﬁfth-grade teachers’ causal effects from several valueadded models, under varying assumptions about the assignment process. If assignments are assumed to depend only on observables, the most commonly used speciﬁcations are subject to important bias, but other feasible speciﬁcations are nearly free of bias. I also consider the case in which assignments depend on unobserved variables. I use the across-classroom variance of observables to calibrate several models of the sorting process. Results indicate that even the best feasible value-added models may be substantially biased, with the magnitude of the bias depending on the amount of information available for use in classroom assignments.