  Vector autoregressions (VARs) with multivariate stochastic volatility are
widely used for structural analysis. Often the structural model identified
through economically meaningful restrictions--e.g., sign restrictions--is
supposed to be independent of how the dependent variables are ordered. But
since the reduced-form model is not order invariant, results from the
structural analysis depend on the order of the variables. We consider a VAR
based on the factor stochastic volatility that is constructed to be order
invariant. We show that the presence of multivariate stochastic volatility
allows for statistical identification of the model. We further prove that, with
a suitable set of sign restrictions, the corresponding structural model is
point-identified. An additional appeal of the proposed approach is that it can
easily handle a large number of dependent variables as well as sign
restrictions. We demonstrate the methodology through a structural analysis in
which we use a 20-variable VAR with sign restrictions to identify 5 structural
shocks.
