Baumeister-Hamilton (2019) Structural Interpretation of Vector Autoregressions with Incomplete Identification

Summary

This paper reframes structural VAR identification as a fully Bayesian problem in which the identifying assumptions themselves carry uncertainty. Traditional SVARs take an "all-or-nothing" stance — treating some features of the contemporaneous structure as known with certainty (zero/recursive restrictions) while claiming complete ignorance about others (agnostic sign restrictions). Baumeister and Hamilton show both are special cases of Bayesian inference with extreme priors (dogmatic point masses, or completely uninformative priors) and advocate the "vast middle ground": place informative but non-dogmatic priors directly on the structural parameters (e.g., supply and demand elasticities). The resulting posterior error bands reflect not only sampling uncertainty but also genuine doubt about the structure. Revisiting the oil market, they estimate a short-run oil-supply elasticity near 0.15 and find supply shocks more important — and inventory/speculative demand less important — than earlier studies that imposed very tight prior beliefs.

Key Claims

• Identification is a prior, not a fact. In the structural form $A\,y_t = \text{(lags)} + u_t$, traditional identification fixes elements of the contemporaneous matrix $A$ (zeros → recursive; inequality regions → sign restrictions). These are just dogmatic priors (point masses) or uninformative priors on $A$; the honest position is an informative proper prior somewhere between.
• Priors on economically interpretable parameters. Rather than restricting an abstract rotation, put priors on the objects economists actually have beliefs about — price elasticities of supply and demand, and the equilibrium impacts of structural shocks — so identification draws on all available (imperfect) information.
• Uncertainty about identification enters the error bands. Posterior credible sets for impulse responses widen to reflect doubt about the structure itself, unlike frequentist SVARs whose bands condition on the identifying restrictions being exactly true.
• Critique of agnostic sign restrictions. Uninformative priors over the rotation are not "assumption-free" — they impose an implicit, often influential, prior on the structural parameters; results can be prior-driven even when the analyst believes they are letting the data speak.
• Measurement error and structural stability. The framework generalizes the SVAR to allow measurement error in the observed variables (important for poorly measured world oil inventories) and to downweight earlier data when structural stability is in doubt.
• Oil findings. Short-run oil-supply elasticity $\approx 0.15$ (well above the tight upper bounds of Kilian-Murphy 2012); supply disruptions were a larger factor and inventory demand a smaller factor in historical oil price movements than previously estimated; supply shocks reduce global activity only after a significant lag, demand shocks do not.

Concepts Introduced or Extended

• Bayesian SVAR Identification
• Structural Identification
• Sign Restriction Identification

Entities Mentioned

• Christiane Baumeister
• James D. Hamilton
• Oil Price Shocks
• Kilian (2009) Not All Oil Price Shocks Are Alike

Quotes

"Traditional approaches to structural vector autoregressions can be viewed as special cases of Bayesian inference arising from very strong prior beliefs."

"There is vast middle ground between these two extremes. We advocate that analysts should both relax [dogmatic restrictions] and draw on all available information about the structure, while acknowledging that this information, too, is imperfect."

My Take

The reframing is the contribution: once you see a Cholesky ordering as a degenerate prior and Uhlig-style sign restrictions as a diffuse one, the natural question is why an economist with real (if fuzzy) knowledge of an elasticity should use either extreme. Putting the prior on interpretable structural parameters is both more honest and more disciplined, and — crucially — it makes the sensitivity of conclusions to identification visible in the width of the bands rather than hidden in an assumption. It complements the wiki's sign-restriction and narrative pages by supplying the general Bayesian scaffolding of which they are limiting cases. The practical cost is elicitation: the method is only as good as the priors on elasticities, and defending those priors (and their sensitivity) becomes the new locus of debate — arguably where it belongs.