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

This 2005 Quarterly Journal of Economics paper by Ben Bernanke, Jean Boivin, and Piotr Eliasz proposes the Factor-Augmented VAR (FAVAR) to address a specific problem with standard small monetary VARs: because Fed policymakers actually condition on a wide range of economic and financial data, a VAR built from only a handful of observable series omits conditioning information, which biases the identified policy shock (producing the “price puzzle,” a spurious rise in prices after a tightening), makes the choice of which few variables to include arbitrary, and limits impulse responses to only the included series. The FAVAR augments a standard VAR in observable variables (in the benchmark specification, just the federal funds rate) with a small number of latent factors extracted by principal components from a large panel of 120 monthly U.S. macroeconomic series (DRI/McGraw Hill Basic Economics Database, January 1959-August 2001); the factors and the observable are then modeled jointly in a VAR (13 lags, 3 factors in the benchmark), with the policy shock identified recursively (Cholesky) by ordering the federal funds rate last, and with the factors themselves estimated in a first step using only “slow-moving” variables that do not respond contemporaneously to policy shocks, so as not to contaminate the factor estimates with the policy shock itself. Two estimation approaches are compared: a computationally simple two-step principal-components procedure (following Stock and Watson 2002), which the authors prefer for its “greater plausibility,” and a one-step Bayesian likelihood approach via Gibbs sampling (10,000 draws, 2,000 discarded as burn-in) that is more rigorous but yields qualitatively similar, quantitatively more imprecise results. Moving from a standard three-variable VAR (industrial production, CPI, funds rate), which produces a strong and persistent price puzzle, to a FAVAR with even a single additional factor considerably reduces the puzzle; the preferred three-factor, two-step-PC FAVAR generates impulse responses for many more series that are broadly consistent with standard theory (real activity and prices eventually decline, money aggregates fall, the dollar appreciates on impact), and a five-factor version leaves these qualitative conclusions unchanged. At a 60-month horizon the identified policy shock accounts for a sizeable share of the variance of interest rates (45.4% of the funds rate itself, 43.3% of the 3-month T-bill, 40.3% of the 5-year bond) but a much smaller share of real activity and prices (5.4% of industrial production, 3.8% of CPI) and of monetary aggregates (0.5% of both the monetary base and M2); the authors note that IRFs for the monetary aggregates should be interpreted with caution given the low R² of their common components (10.4% and 5.2%, respectively), and they hedge their central claim, describing the price-puzzle result as offering only “some support” for the view that the puzzle stems from omitted conditioning information rather than a definitive resolution. The sample ends in August 2001, before the financial crisis and the zero lower bound, so the paper does not speak to whether the FAVAR’s resolution of the price puzzle extends to that later, constrained-policy environment.

Piotr Eliasz | Macro Paper Warehouse

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