Factor-Augmented VAR (FAVAR)

Definition

A factor-augmented VAR (FAVAR) is a structural VAR whose state vector is augmented with a small number of latent factors extracted from a large panel of time series, so that the VAR can condition on a rich information set while remaining low-dimensional. Introduced by Bernanke, Boivin and Eliasz (2005) to measure the effects of monetary policy, it couples a dynamic factor model (many observed series load on a few factors) with a VAR in those factors and a handful of observed policy variables — combining the identification transparency of small VARs with the informational breadth of large-panel factor methods.

Key Ideas

• Two blocks. Latent factors $F_t$ (dimension $K$, small) and observed variables $Y_t$ (e.g. the federal funds rate) jointly follow a VAR: $$\begin{bmatrix}F_t\\ Y_t\end{bmatrix}=\Phi(L)\begin{bmatrix}F_{t-1}\\ Y_{t-1}\end{bmatrix}+v_t.$$ A large "informational" panel $X_t$ ($N\gg K$ series) is the observation equation loading on both: $X_t=\Lambda^f F_t+\Lambda^y Y_t+e_t$. The FAVAR is the state transition, the factor model the measurement — a state-space system.
• Why augment. A small VAR omits information agents actually use, so the identified policy shock is contaminated (the price puzzle is the diagnostic) and impulse responses exist only for the few included series. Factors summarize the omitted information and let responses be read off for every series in $X_t$ via its loadings.
• Latent constructs. "Economic activity" or "the price level" are theoretical objects no single series measures; a factor is precisely a common index of many indicators, making it the natural representation.

How It Works

• Two-step (principal components). Estimate the factor space from $X_t$ by principal components, then estimate the VAR in $(\hat F_t, Y_t)$ by OLS. Consistent as $N,T\to\infty$; simple and transparent, but $\hat F_t$ are generated regressors, so inference uses a bootstrap. Care is needed to remove the part of the factors spanned by $Y_t$ (e.g. the slow/fast split below).
• One-step (Bayesian). Estimate factors and VAR jointly by a Gibbs sampler, drawing the latent factors with a Carter-Kohn multimove state-space smoother and the parameters from their conditionals. Internally consistent and propagates factor uncertainty, at higher computational cost; results are broadly similar to the two-step method.
• Identification (slow vs. fast). For a recursive policy shock, partition $X_t$ into slow-moving variables (real activity, prices — not reacting within the period to the policy shock) and fast-moving variables (financial, forward-looking). Order the policy instrument after the slow factors so its innovation is orthogonal to contemporaneous slow variables — a factor-space analogue of the standard recursive scheme.

Why It Matters

• Resolves the price puzzle and gives economically coherent, panel-wide impulse responses, showing the extra information genuinely matters for identifying the monetary transmission mechanism.
• Bridges literatures. Unifies dynamic factor models (Stock-Watson diffusion indexes) with structural VAR analysis; the Stock-Watson (2016) handbook chapter treats DFMs, FAVARs, and SVARs as one framework.
• Data-rich policy analysis. Enables monetary and macro analysis conditioned on hundreds of series without degrees-of-freedom collapse.

Open Questions

• The slow/fast recursive identification is still a timing assumption; sign-restriction, informative-prior, and external-instrument schemes relax it.
• Generated-regressor uncertainty in the two-step method vs. the cost of the one-step Gibbs sampler.
• Choosing the number of factors and ensuring they are structurally interpretable rather than merely statistical summaries.

Related

• Dynamic Factor Model
• Factor Model
• Price Puzzle
• Monetary Policy Shocks
• Bayesian VAR
• Bayesian SVAR Identification
• Bernanke-Boivin-Eliasz (2005) Measuring the Effects of Monetary Policy: A FAVAR Approach
• Ben Bernanke
• Jean Boivin
• Piotr Eliasz