Global identification, estimation and inference of structural impulse response functions in factor models: A unified framework

This paper develops a theory for the global identification, estimation and inference of impulse response functions (IRFs) in structural factor models (SFMs). We examine the impact of normalization choices on IRF identification and propose to use identification restrictions robust to such choices. A new theorem is established to address IRF identification under both recursive and nonrecursive schemes in SFMs. Moreover, we develop two new estimators for structural IRFs under principal component normalization and establish their asymptotic distributions. We also propose a test for overidentifying restrictions. Simulation results demonstrate the validity of the asymptotic approximations and the favorable finite-sample properties of the overidentification test. To illustrate the flexibility of our methodology, we employ a hybrid identification scheme and analyze the dynamic effects of oil shocks using a US dataset.