Consistent instrumental variables (IV) estimation requires instruments uncorrelated with model errors, but this assumption is usually both suspect and untestable. Here the asymptotic sampling distribution of the IV parameter estimator is derived for any specified instrument-error covariance vector. This result makes it possible to quantify the sensitivity of any particular IV inference result to instrument-error correlations, allowing one to assess the robustness of such inferential conclusions to uncertainty in the validity of the instruments. An application illustrating the value of this sensitivity analysis is given to a study by Acemoglu et al. (2001).