Bernanke-Boivin-Eliasz (2005) Measuring the Effects of Monetary Policy: A FAVAR Approach

Summary

Bernanke, Boivin and Eliasz address the "sparse information set" problem of structural VARs — that a small VAR omits information the central bank and private sector actually use, contaminating the measured policy shock (the price puzzle being the symptom) and limiting impulse responses to the handful of included variables. Their solution, the factor-augmented VAR (FAVAR), summarizes a large panel of macro series (≈120) by a few estimated factors and runs the VAR on those factors jointly with the observed policy instrument (the federal funds rate). This lets the VAR condition on a rich information set while staying low-dimensional, resolves the price puzzle, and delivers impulse responses for all series in the panel.

Key Claims

• The problem: omitted information. Standard VARs use <20 variables, so (i) the policy innovation is contaminated whenever agents see information the VAR omits, and (ii) impulse responses exist only for included variables — yet "economic activity" or "prices" are latent constructs no single series captures.
• FAVAR model. A vector of latent factors $F_t$ plus the observed policy variable $Y_t$ follow a VAR: $[F_t', Y_t']' = \Phi(L)[F_{t-1}', Y_{t-1}']' + v_t$. A large panel of "informational" series $X_t$ loads on both: $X_t = \Lambda^f F_t + \Lambda^y Y_t + e_t$ — i.e. $X_t$ is a dynamic-factor observation equation and the FAVAR is its state transition.
• Two-step estimation. Extract $F_t$ from $X_t$ by principal components (the space spanned by the factors is consistently estimated when $N,T$ are large), then estimate the VAR in $(\hat F_t, Y_t)$ by OLS; impulse responses for any $X$-series follow from its factor loadings. Bootstrap (Kilian) for inference to account for the generated regressors.
• One-step Bayesian estimation. Alternatively estimate factors and VAR jointly by a Gibbs sampler with a Carter-Kohn (multimove) state-space smoother for the latent factors — internally consistent but computationally heavier; the two methods give broadly similar answers.
• Identification (slow vs. fast). To identify the policy shock recursively, the informational series are split into slow-moving (real activity, prices — predetermined within the month) and fast-moving (financial, forward-looking); the fed funds rate is ordered after the slow factors, so the policy shock is orthogonal to contemporaneous slow variables — a factor-space analogue of the standard recursive scheme.
• Results. Adding factors resolves the price puzzle (no anomalous price increase after a contractionary shock) and yields economically sensible, comprehensive impulse responses across the ≈120 variables; three to five factors capture most of the incremental information. Conclusion: the extra information matters materially for identifying the monetary transmission mechanism.

Concepts Introduced or Extended

• Factor-Augmented VAR (FAVAR)
• Dynamic Factor Model
• Price Puzzle

Entities Mentioned

• Ben Bernanke
• Jean Boivin
• Piotr Eliasz

Quotes

"To the extent that central banks and the private sector have information not reflected in the VAR, the measurement of policy innovations is likely to be contaminated."

"Impulse responses can be observed only for the included variables, which generally constitute only a small subset of the variables that the researcher and policymaker care about."

My Take

FAVAR is the clean resolution of a tension the monetary-VAR literature had lived with for a decade: you want the parsimony and identification of a small VAR, but small VARs are informationally starved, and the price puzzle is the smoking gun that the missing information biases the shock. Bernanke-Boivin-Eliasz make the latent-construct point explicit — "economic activity" and "the price level" are exactly the sort of things a factor is built to represent — and then get impulse responses for the entire panel essentially for free from the loadings. The two estimation routes frame a trade-off the field still lives with: fast, transparent principal-components-then-VAR (with generated-regressor caveats) versus the internally-consistent but heavier one-step Gibbs sampler. The slow/fast recursive identification is the part most open to challenge (it is still a timing assumption), and later work — sign restrictions, the informative-prior approach, external instruments — can be read as relaxing exactly that. For the wiki it anchors the new FAVAR concept and ties the dynamic factor and monetary-shock literatures together.