Student Sorting and Bias in Value Added Estimation: Selection on Observables and Unobservables
Non-random assignment of students to teachers can bias value added estimates of teachers’ causal effects. Rothstein (2008) shows that typical value added models indicate large counter-factual effects of 5th grade teachers on students’ 4th grade learning, implying that assignments do not satisfy the imposed assumptions. 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. Under selection on observables, models for gain scores without controls or with only a single lagged score control are subject to important bias, but models with controls for the full test score history are nearly free of bias. I consider several scenarios for selection on unobservables, using the across-classroom variance of observed variables to calibrate each. Results indicate that even well-controlled models may be substantially biased, with the magnitude of the bias depending on the amount of information available for use in classroom assignments.
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