Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for parameters of interest in this model under both strict and weak exogeneity assumptions. The key identification insight is that other periods' treatment variables are instruments for the unobserved fixed effects. We apply our proposed estimator to matched student-teacher data used to estimate value-added models of teacher quality. We show that the common assumption that the return to unobserved teacher quality is the same for all students is rejected by the data. We also present evidence that No Child Left Behind-era school accountability increased the effectiveness of teacher quality for lower performing students.