Testing for Sufficient Information in Structural VARs

We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. it contains enough information to estimate the structural shocks with a VAR model. Based on such conditions, we suggest a procedure to test for informational sufficiency. Moreover, we show how to amend the VAR if informational sufficiency is rejected. 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.