Sufficient information in structural VARs

Necessary and sufficient conditions under which a VAR contains sufficient information to estimate the structural shocks are derived. On the basis of this theoretical result we propose two simple tests to detect informational deficiency and a procedure to amend a deficient VAR. A simulation based on a DSGE model with fiscal foresight suggests that our method correctly identifies and fixes the informational problem. In an empirical application, we show that a bivariate VAR including unemployment and labor productivity is informationally deficient. Once the relevant information is included into the model, technology shocks appear to be contractionary.