In this paper, we develop inference procedures to detect both parameter instability and changes in the strength of identification, or strength of instrumental variables. If parameter instability is not linked to changes in instrument strength, we show consistency of standard GMM inference methods. We also show that incorporating information about the break- point leads to more efficient GMM estimators. On the other hand, if parameter instability is linked to changes in instrument strength, we develop methods to estimate the location and magnitude of such changes. We derive the asymptotic distribution of 2SLS and GMM structural parameter estimates in different subsamples, and show which inference methods are valid and efficient. We also provide a step-by-step guide for practitioners on how to detect and locate these changes. We illustrate our methods via the New Keynesian Phillips Curve for the US. Joint with Bertille Antoine.