Inference in Nearly Nonstationary SVAR Models With Long-Run Identifying Restrictions

This paper considers inference for impulse responses in models with highly persistent variables. We show that the impulse responses of interest are not consistently estimable under the long-run identification scheme when the strongly dependent process is parameterized as local to unity. We employ the instrumental variable framework to argue that the inconsistency and the large sampling uncertainty associated with the impulse responses arise from a weak instrument problem. Furthermore, the structure of the model is used to impose additional statistical restrictions that are combined with the economic long-run, identifying constraints to obtain an improved estimator.