The Identification and Estimation of Structural Dynamic Factor Models

Description

High-dimensional structural dynamic factor models are useful tools to analyze theeffects of an economic shock over time. A structural dynamic factor model (SDFM)extracts factors from a large number of variables to recover the space spanned by theunobserved economic shocks and fits the estimated factors using a conventionalstructural VAR model. Compared to a conventional low-dimensional VAR, a SDFM hasthe advantage that it uses much more information and does not lose the parsimony.Since the economic shocks are not observed, additional assumptions are required foridentification purposes. The most commonly used identification strategy is to assumethat the contemporaneous effects of the shock follow a recursive structure. This is ajust-identified scheme where the number of restrictions is equal to the number ofunknown parameters. In a factor model, however, the number of valid restrictions can belarger than the number of unknown parameters due to the high-dimensionality. Thus,the SDFM is often over-identified. Compared with a just-identified SDFM, using overidentifyingrestrictions have two main advantages. First, the estimation of the unknownparameters will be more accurate under over-identifying restrictions. Second, overidentifyingrestrictions can be tested so that practitioners can know if the identificationconditions are satisfied or not.This project will generalize the existing method in several dimensions. It focuses on theidentification and estimation of SDFMs under over-identified schemes, which improvethe estimation accuracy. Also, we will use various types of identification conditions,which are more general than the commonly used recursive setups. The new method canestimate the parameters of interests under a combination of multiple identificationstrategies, such as short-run restrictions, long-run restrictions, external instruments,and heteroscedasticity.