Sufficient Information in Structural VARs

We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. contains enough information to estimate the structural shocks with a VAR
model. Based on such conditions, we provide a procedure to test for informational sufficiency.
If sufficiency is rejected, we propose a strategy to amend the VAR. Our method can be applied
to FAVAR models and can be used to determine how many factors to include in such models.
We apply our procedure to a VAR including TFP, unemployment and per-capita hours worked.
We find that the three variables are not informationally sufficient. When adding missing information, the effects of technology shocks change dramatically.