Valid Inference in Partially Unstable GMM Models

The paper considers time series GMM models where a subset of the parameters are time varying. The magnitude of the time variation in the unstable parameters is such that efficient tests detect the instability with (possibly high) probability smaller than one, even in the limit. We show that for many forms of the instability and a large class of GMM models, standard GMM inference on the subset of stable parameters, ignoring the partial instability, remains asymptotically valid.