Shock Restricted Structural Vector-Autoregressions

It is well known that the covariance structure of the data alone is not enough to identify an SVAR, and the conventional approach is to impose restrictions on the parameters of the model based on a priori theoretical considerations. This paper suggests that much can be gained by requiring the properties of the identified shocks to agree with major economic events that have been realized. We first show that even without additional restrictions, the data alone are often quite informative about the quantitatively important shocks that have occurred in the sample. We propose shrinking the set of solutions by imposing two types of inequality constraints on the shocks. The first restricts the sign and possibly magnitude of the shocks during unusual episodes in history. The second restricts the correlation between the shocks and variables external to the SVAR. The methodology provides a way to assess the validity of assumptions imposed as equality constraints. The effectiveness and limitations of this approach are exemplified with three applications.