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.