Approximating Singular by Means of Non-singular Structural VARs

In applications of dynamic factor models to structural macroeconomic analysis, r, the number of static factors, is typically larger than q, the number of shocks driving the macroeconomy, so that the spectral density matrix of the factors is singular. Singularity is an important advantage with respect to standard structural VARs, because it ensures that generically the Structural Shocks are fundamental and the factors have a finite VAR representation in the Structural Shocks. However, a serious difficulty with this approach is that singular VARs are not necessarily unique. We show that, despite this, the Structural Shocks and the corresponding Impulse-Response Functions are approximated consistently using a non-singular VAR.