Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating non-negatively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general.