Student sorting and bias in value added estimation:

Non-random assignment of students to teachers can bias value added estimates of teachers’ causal effects. Rothstein (2008a, b) shows that typical value added models indicate large counter-factual effects of 5th grade teachers on students’ 4th grade learning, indicating that classroom assignments are far from random. This paper quantifies the resulting biases in estimates of 5th grade teachers’ causal effects from several value added 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 where 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. * Industrial Relations Section, Firestone Library, Princeton NJ 08544. [email protected]. I thank Nathan Wozny and Enkeleda Gjeci for research assistance. I am grateful to the North Carolina Education Data Research Center and the North Carolina Department of Public Instruction for assembling and making available the data used in this study. This work has benefited from helpful conversations with Jane Cooley, Gordon Dahl, Ed Glaeser, Brian Jacob, David Lee, and Diane Schanzenbach, and from comments from an anonymous referee. Financial support was generously provided by the Industrial Relations Section and the Center for Economic Policy Studies at Princeton and by the U.S. Department of Education (#R305A080560).