Valid Inference in Partially Unstable Generalized Method of Moments Models

This paper considers time series Generalized Method of Moments (GMM) models where a subset of the parameters are time varying. We focus on an empirically relevant case with moderately large instabilities, which are well approximated by a local asymptotic embedding that does not allow the instability to be detected with certainty, even in the limit. We show that for many forms of the instability and a large class of GMM models, usual GMM inference on the subset of stable parameters is asymptotically unaffected by the partial instability. In the empirical analysis of presumably stable parameters-such as structural parameters in Euler conditions-one can thus ignore moderate instabilities in other parts of the model and still obtain approximately correct inference. Copyright © 2009 The Review of Economic Studies Limited.