A Topological View on the Identification of Vector Autoregressions

The notion of the group of orthogonal matrices acting on the set of all feasible identification schemes is used to characterize the identification problem arising in structural vector autoregressions. This approach presents several conceptual advantages. First, it provides a fundamental justification for the use of the normalized Haar measure as the natural uninformative prior. Second, it allows to derive the joint distribution of blocks of parameters defining an identification scheme. Finally, it provides a coherent way for studying perturbations of identification schemes which becomes relevant, among other things, for the specification of vector autoregressions with time-varying covariance matrices.