Inference in linear models with structural changes and mixed identification strength

This paper considers estimation and inference in a linear model with endogenous regressors and parameter instability. We allow for structural changes in the parameters of the structural and reduced forms, and for mixed identification strength: the identification may not be strong over the whole sample, and may even change over time. In addition, we allow the second moments of the data generating process to change over time (e.g. changes in the variance of the structural errors, and/or in the variance of the instruments). We propose and derive the limiting distributions of two tests for parameter changes in the structural form: when the reduced form is stable and when the reduced form exhibits structural change. We also propose and derive new GMM estimators for the unstable structural form. We show that if the RF is stable, they are more efficient than the standard subsample GMM estimators, even in the presence of weaker identification patterns.