The factor-augmented vector autoregressive (FAVAR) model, first proposed by Bernanke, Bovin, and Eliasz (2005, QJE), is now widely used in macroeconomics and finance. In this model, observable and unobservable factors jointly follow a vector autoregressive process, which further drives the comovement of a large number of observable variables. We study the identification restrictions in the presence of observable factors. We propose a likelihood-based two-step method to estimate the FAVAR model that explicitly accounts for factors being partially observed. We then provide an inferential theory for the estimated factors, factor loadings and the dynamic parameters in the VAR process. We show how and why the limiting distributions are different from the existing results.

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