Identification and estimation of dynamic factor models

We consider a set of minimal identification conditions for dynamic factor models. These conditions have economic interpretations, and require fewer number of restrictions than when putting in a static-factor form. Under these restrictions, a standard structural vector autoregression (SVAR) with or without measurement errors can be embedded into a dynamic factor model. More generally, we also consider overidentification restrictions to achieve efficiency. General linear restrictions, either in the form of known factor loadings or cross-equation restrictions, are considered. We further consider serially correlated idiosyncratic errors with heterogeneous coefficients. A numerically stable Bayesian algorithm for the dynamic factor model with general parameter restrictions is constructed for estimation and inference. A square-root form of Kalman filter is shown to improve robustness and accuracy when sampling the latent factors. Confidence intervals (bands) for the parameters of interest such as impulse responses are readily computed. Similar identification conditions are also exploited for multi-level factor models, and they allow us to study the spill-over effects of the shocks arising from one group to another.