Identification of independent structural shocks in the presence of multiple Gaussian components

Several recently developed identification techniques for structural VAR models are based on the assumption of non-Gaussianity. So-called independence based identification provides unique structural shocks (up to scaling and ordering) under the assumption of at most one Gaussian component. While non-Gaussianity of certain interesting shocks appears rather natural, not all macroeconomic shocks in the system might show this clear difference from Gaussianity. Identifiability can be generalized by noting that even in the presence of multiple Gaussian shocks the non-Gaussian ones are still unique. Consequently, independence based identification allows to uniquely determine the (non-Gaussian) shocks of interest irrespective of the distribution of the remaining system. Furthermore, studying settings close to normality or with multiple Gaussian components highlights the performance of normality diagnostics and their applicability to decide on the identifiability of the structural shock components. In an illustrative five dimensional model the identified monetary policy and stock price shock confirm the results of previous studies on the monetary policy asset price nexus.