Educational interventions are often narrowly targeted and temporary, and evaluations often focus on the short-run impacts of the intervention. Insofar as the positive effects of educational interventions fade out over time, however, such assessments may be misleading. In this paper, we develop a simple statistical framework to empirically assess the persistence of treatment effects in education. To begin, we present a simple model of student learning that incorporates permanent as well as transitory learning gains. Using this model, we demonstrate how the parameter of interest--the persistence of a particular measurable education input--can be recovered via instrumental variables as a particular local average treatment effect. We initially motivate this strategy in the context of teacher quality, but then generalize the model to consider educational interventions more generally. Using administrative data that links students and teachers, we construct measures of teacher effectiveness and then estimate the persistence of these teacher value-added measures on student test scores. We find that teacher-induced gains in math and reading achievement quickly erode. In most cases, our point estimates suggest a one-year persistence of about one-fifth and rule out a one-year persistence rate higher than one-third.