Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach

Standard VARs identify monetary policy shocks from only a handful of observable variables, even though “Fed policymakers and others who make decisions about monetary policy typically utilize information from a wide range of economic and financial data” — and this sparse-information problem generates three distinct problems. First, omitting relevant conditioning information biases the identified policy shock, which the authors argue produces the “price puzzle” (a spurious rise in the price level after an identified tightening). Second, the choice of which few observable variables to include in a small VAR is arbitrary yet consequential for the results. Third, a small VAR can only generate impulse responses for the variables it explicitly includes, even though researchers and policymakers care about the effects of policy on many more series than that.

The FAVAR links an M×1 vector of observable economic variables Y_t (in the benchmark, only the federal funds rate) and a K×1 vector of unobserved latent factors F_t through a joint transition equation, [F_t; Y_t] = Φ(L)[F_{t-1}; Y_{t-1}] + v_t, while a separate observation equation X_t = Λ^f F_t + Λ^y Y_t + e_t relates the large N×1 panel of informational data (N=120) to the factors and the observable, with e_t having a diagonal covariance matrix to allow for measurement error in each series. The key identifying assumption is that the economic space relevant to the Fed’s decisions is spanned by {F_t, Y_t} jointly — i.e., the latent factors are meant to proxy for the full breadth of information the Fed actually conditions on, not just the single observed policy rate.

Factors are estimated in a first step using only the subset of the 120 series marked as “slow-moving” — series that do not respond contemporaneously to monetary policy shocks — specifically so that the factor estimates are not contaminated by the policy shock itself. If fast-moving variables (e.g., asset prices) that react within the month to a policy surprise were used to construct the factors, the factors would partly reflect the policy shock, undermining the recursive identification described below. The two estimation approaches used to obtain factors are: (1) a two-step principal-components (PC) procedure following Stock and Watson (2002), where the K+M principal components of X_t are extracted first and then used as data in a VAR with Y_t; and (2) a one-step Bayesian approach using Gibbs sampling (10,000 iterations, first 2,000 discarded as burn-in, diffuse priors, Carter-Kohn 1994 state-space sampler) that jointly estimates the factors and the VAR dynamics.

The policy shock is identified recursively via a Cholesky ordering in which the federal funds rate is ordered last among all variables in {F_t, Y_t} — meaning the latent factors are assumed not to respond contemporaneously to a monetary policy shock, while the funds rate is allowed to respond contemporaneously to the factors. Factor normalization follows the standard principal-components convention (C’C/T = I, where C = [Λ^f, Λ^y]); the paper notes this normalization is not unique, and the Cholesky ordering imposes an additional specific rotation on top of it — the paper does not test the exclusion-restriction/ordering assumption directly.

A standard three-variable VAR (industrial production, CPI, and the federal funds rate) produces a strong price puzzle — a persistent rise in the price level after an identified tightening, together with unusually persistent, slow-to-recover industrial production — but adding even a single latent factor to the VAR “considerably” reduces the price puzzle. The benchmark three-factor FAVAR (estimated by two-step PC) goes further, generating impulse responses across 20 shown variables that are “broadly consistent with what standard economic theory implies”: real activity declines, prices eventually fall (rather than rise), money aggregates decline, the dollar appreciates on impact, and dividends rise initially before falling.

No — using five factors instead of three leaves the qualitative conclusions unchanged, with the estimated factors continuing to capture similar informational content, and the one-step Bayesian (Gibbs sampling) estimation approach produces qualitatively similar impulse responses to the two-step PC approach, though quantitatively more imprecise. The authors state they “prefer the two-step approach for its greater plausibility” given this added precision, even though the Gibbs-sampling approach is, in principle, the more theoretically rigorous of the two since it estimates factors and VAR dynamics jointly rather than sequentially. A seven-lag VAR is also reported as a robustness check against the benchmark thirteen-lag specification.

In the variance decomposition at a 60-month horizon, the policy shock explains a large share of the variance of interest-rate variables — 45.4% of the federal funds rate itself, 43.3% of the 3-month T-bill, and 40.3% of the 5-year bond — but a much smaller share of real activity and prices, including 5.4% of industrial production, 3.8% of CPI, 10.0% of capacity utilization, 10.3% of unemployment, and 6.6% of employment. The shares attributed to monetary aggregates and the exchange rate are smaller still: 0.5% of the monetary base, 0.5% of M2, 0.7% of the exchange rate, and 4.9% of a commodity price index.

The R² of the common component is high for real activity and price variables — 70.7% for industrial production, 72.3% for employment, 81.6% for unemployment, and 86.9% for CPI — indicating the factors capture most of the variation in these series, but it is low for monetary aggregates, at 10.4% for the monetary base and 5.2% for M2. Because of this low explanatory power, the authors explicitly state that the FAVAR-implied impulse responses for the monetary quantity aggregates “should be interpreted with some caution,” since those series are poorly summarized by the estimated factors even though the model still generates an impulse response for them.

No — the authors hedge, describing their result as providing only “some support for the view that the ‘price puzzle’ results from the exclusion of conditioning information,” not a definitive resolution. They also note that factor normalization is not unique (different normalizations give observationally equivalent FAVAR representations, and the Cholesky identification imposes an additional specific rotation), that the exclusion-restriction/ordering assumption underlying the recursive identification is not directly tested, and that their formal backward-looking IS-AS motivation for the model (in which only the interest rate is observable and output, inflation, and potential output are treated as latent factors) is offered as an approximation — the authors note the FAVAR framework applies equally well to forward-looking or estimated-parameter variants of the model. Finally, the sample runs only through August 2001, so the paper does not address whether the FAVAR’s price-puzzle resolution holds up during the 2008 financial crisis or the zero-lower-bound period that followed.