Student Sorting and Bias in Value Added Estimation: Selection on Observables and Unobservables

45 Pages Posted: 25 Jan 2009 Last revised: 30 Jul 2022

See all articles by Jesse Rothstein

Jesse Rothstein

University of California, Berkeley, The Richard & Rhoda Goldman School of Public Policy; University of California, Berkeley, College of Letters & Science, Department of Economics; National Bureau of Economic Research (NBER)

Date Written: January 2009

Abstract

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.

Suggested Citation

Rothstein, Jesse, Student Sorting and Bias in Value Added Estimation: Selection on Observables and Unobservables (January 2009). NBER Working Paper No. w14666, Available at SSRN: https://ssrn.com/abstract=1332605

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