Building on the testable implications for IV validity underlying local average treatment effect (LATE) estimation, we (i) propose a simple testing procedure that may accommodate high-dimensional covariates and (ii) demonstrate that it can also detect biases arising from misspecified IV regression models. While recent research has highlighted the importance of a correct covariate specification, existing IV validity tests are not designed to capture this source of bias. Simulation studies strongly suggest that the test performs well at detecting violations of conditional independence, violations of the exclusion restriction, and biases arising from covariate misspecification.