Fair asks how accurate VAR models are likely to be when used to answer structural questions — the use for policy analysis advocated by Sims (1982). His test is a controlled experiment: data are generated from the dynamic deterministic solution of a known large-scale structural model, a VAR is estimated on a subset of those variables, and the VAR's properties are compared to the structural model's known properties. Because the data come from a deterministic simulation, error-term noise is eliminated and any gap reflects approximation error. The result is negative — the VAR models do not appear to be good structural approximations.
"This paper presents a way of estimating how accurate VAR models are likely to be for answering structural questions … The results show that the VAR models do not seem to be good structural approximations."
A sharp, underrated methodological probe from the height of the VAR-vs-structural-models debate. Fair's design is the clever part: by running the true structural model deterministically he removes the "but you just estimated it badly" defense, so the VAR's failure to reproduce structural multipliers is a statement about the approximation, not the data. It is the empirical complement to the structural-vs-atheoretic arguments — where Keane argues the case in principle, Fair measures the gap in a rigged-to-be-fair experiment. The obvious caveat is external validity: the conclusion is only as general as Fair's particular US model and the variable subsets he chose, and a VAR advocate would reply that policy analysis rarely needs the full structural multiplier, only the response to identified shocks. Still, it is a durable reason to be skeptical of reading large structural counterfactuals off small VARs.