This paper presents a model where students have cognitive and non-cognitive ability, and a teacher’s effect on long-run outcomes is a combination of her effects on both ability-types. Conditional on cognitive scores, an underlying non-cognitive factor associated with student absences, suspensions, grades, and grade progression, is strongly correlated with long-run educational attainment, arrests, and earnings in survey data. In administrative data, teachers have meaningful causal effects on both cognitive-scores and this non-cognitive factor. Calculations indicate that teacher effects based on test scores alone fail to identify many excellent teachers, and may greatly understate the importance of teachers for adult outcomes.