Testing for Additive Separability of Student Achievement Function

Josh Kinsler

Is it possible to isolate the contribution of an individual teacher in the production of student achievement? Value-added models purport to do just this by estimating the component of test score gains attributable to the current teacher. However, a foundational assumption of these models, additive separability of teacher inputs, has never been investigated. Additive separability implies that the current teacher’s value-added is independent of the string of previous teachers. This does not mean that past teachers have no impact on student performance, only that the value-added of the current teacher is invariant to different teacher histories. Additive separability would fail to hold if, for example, there exists complementarity in teaching styles across grades. In other words, the effectiveness of the current teacher varies according to whether the string of previous teachers have a similar instructional approach. Failure of additive separability means that estimates of individual teacher value-added are contaminated by interactions with past teacher inputs. As a result, it is inappropriate to use these measures for individual personnel decisions. In this proposal, I describe a methodology for testing whether additive separability is supported in the data. The empirical strategy is to estimate multiple measures of teacher value-added and then test whether the restrictions implied by additive separability hold.

About Josh Kinsler

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