Estimation and Inference of Dynamic Structural Factor Models with Over-identifying Restrictions

During the past decade, high-dimensional factor models have been widely used for structural analysis in the literature, where the effects of structural shocks are often estimated under just-identifying restrictions. However, as the number of restrictions in a factor model setup can be large due to its high dimensionality, the structural shocks are over-identified. This paper develops a new estimator for the impulse response functions with a fixed number of over-identifying restrictions. The proposed identification scheme nests the conventional just-identified recursive scheme as a special case. We establish the asymptotic distributions of the new estimator and develop test statistics for the over-identifying restrictions. Simulation results show that adding a few more over-identifying restrictions can lead to a substantial improvement in estimation accuracy for impulse response functions at both zero and nonzero horizons. We estimate the effects of the monetary policy shock based on a U.S. macroeconomic data set. The result shows that our over-identified scheme can help to improve estimation efficiency and eliminate incorrect restrictions that lead to spurious impulse responses.