The systematic component of monetary policy in SVARs: An agnostic identification procedure

Questions & answers

Q1. What problem is this paper trying to solve in SVAR-based monetary policy identification?

Standard sign-restriction approaches to identifying monetary policy shocks, following Uhlig (2005), impose restrictions on the impulse responses the shock is supposed to produce (e.g., that a contractionary shock raises the funds rate and lowers prices) — but leave the contemporaneous response of output to the shock unrestricted, and Uhlig (2005) and Ramey (2016) argue that letting output respond freely is exactly what allows most of this literature to find monetary policy shocks are expansionary rather than contractionary. The authors’ response is to identify the shock instead through restrictions on the “systematic component” of policy — the monetary policy reaction function itself, i.e., how the Fed’s instrument normally responds to output, prices, and other variables — an approach they attribute to the emphasis on the policy equation in Leeper, Sims, and Zha (1996), Leeper and Zha (2003), and Sims and Zha (2006a).

Q2. What exactly is restricted, and on what data?

Two restrictions are placed on the contemporaneous coefficients of the federal-funds-rate equation in a six-variable, 12-lag monthly SVAR estimated over January 1965-June 2007 (chosen to exclude the financial crisis and unconventional policy period): Restriction 1 sets to zero the contemporaneous reactions of the funds rate to total reserves and nonborrowed reserves, and Restriction 2 requires the contemporaneous reactions of the funds rate to output and prices to be positive. The six variables are real GDP, the GDP deflator, a commodity price index, total reserves, nonborrowed reserves, and the federal funds rate (following the Bernanke-Mihov 1998 specification, with GDP and the deflator interpolated to monthly frequency); estimation uses a Bayesian uniform-normal-inverse-Wishart prior and the sign-and-zero-restriction techniques of Arias, Rubio-Ramírez, and Waggoner (2018b). Neither restriction constrains the contemporaneous response of output to the identified shock itself — the paper’s central departure from Uhlig (2005).

Q3. What are the posterior effects of a contractionary monetary policy shock under these restrictions?

Under Restrictions 1 and 2 over the full 1965-2007 sample, the posterior median response to a contractionary shock is an immediate decline in output that stays statistically significant for about 18 months (with the zero line near the edge of the 95% band around the 8-month trough), a protracted decline in the GDP deflator that builds over time, and an on-impact increase in the federal funds rate of roughly 20 basis points, while commodity prices and both reserve aggregates show little systematic reaction (reserves fall on impact but are near zero afterward). The authors note the deflator response is broadly in line with Smets and Wouters (2007). A posterior probability of a price puzzle is still present in some admissible models under the baseline restrictions.

Q4. How tight are the estimated policy-rule coefficients, and what do they imply about the systematic component?

The posterior median contemporaneous coefficient on output in the funds-rate rule is 0.84 (68% interval 0.24-2.33; 95% interval 0.04-5.25) and on prices is 2.73 (68% interval 0.75-7.87; 95% interval 0.12-24.23) — implying the funds rate reacts nearly one-for-one to output and more than one-for-one to prices, consistent with the Taylor principle — while the coefficient on commodity prices is centered near zero (median -0.02) and not precisely estimated. The authors describe the resulting posterior intervals as wide, a consequence of the fact that only one shock is identified out of a large class of admissible structural VARs — what they call the “double-edged sword” of set identification.

Q5. Do the results hold up in the Great Moderation sub-sample?

Restricting the sample to 1983:M1-2007:M6, the impulse responses remain qualitatively similar and the output response remains contractionary; the estimated standard deviation of the monetary policy shock falls from about 0.9 in the full sample to about 0.3 in the Great Moderation sub-sample, which the authors interpret as consistent with more systematic conduct of monetary policy over this period. The ratio of impact responses (an output elasticity to the funds rate) is about -2 in the Great Moderation sub-sample versus about -0.8 in the full sample, and the authors note the Great Moderation estimate is in line with Gertler and Karadi (2015).

Q6. How does imposing the systematic-component restrictions on Uhlig’s (2005) admissible set change the conclusions?

Applying only Uhlig’s (2005) Restriction 3 (negative responses of prices, commodity prices, and nonborrowed reserves, and a positive funds-rate response, at horizons 0 through 5) implies a posterior median contemporaneous output coefficient of -0.35 — the funds rate reacting negatively to output on average, which the authors say contradicts a Taylor rule — and implies, with posterior probability 1.00, that every structural parameter vector in Uhlig’s admissible set has the funds rate reacting contemporaneously to total or nonborrowed reserves, directly violating Restriction 1. The authors’ stated conclusion is that “the shocks identified by [Uhlig’s] Restriction 3 are not monetary policy shocks,” and that combining Uhlig’s IRF restrictions with the systematic-component Restriction 2 shifts the posterior on the output coefficient from centered near -0.57 to concentrated on positive values, recovering an output response that is negative “with very high posterior probability.”

Q7. What robustness checks does the paper report?

Adding a further zero restriction that the funds rate does not react contemporaneously to commodity prices produces slightly more pronounced output and price declines and a modest reduction in the incidence of the price puzzle; bounding the output and price coefficients to the interval (0,4) — a check motivated by the Kilian and Murphy (2012) concern that admissible sets can include implausible structural models — yields a posterior median output coefficient of 0.65 and price coefficient of 1.56, with a more persistent output decline through five years; and re-estimating the reduced-form VAR in first differences (with the same restrictions applied to the differenced policy equation) produces a broadly consistent but larger and more pronounced decline in output and prices. The authors also note the results are robust to estimating at quarterly frequency.

Q8. What are the paper’s acknowledged limitations?

The authors emphasize that identifying only the monetary policy shock leaves the admissible set of structural VARs large, producing wide posterior intervals (e.g., the 95% interval for the output coefficient spans 0.04 to 5.25) — the “double-edged sword” of set identification — and that this wide admissible set can, per the Kilian and Murphy (2012) critique, include structural models with implausible implications, which motivates their bounded-coefficient robustness check. The sample stops at June 2007 specifically to exclude the global financial crisis and the zero-lower-bound/unconventional-monetary-policy period, so the results do not speak to that later regime, and the policy indicator is the actual funds rate rather than a forward-guidance-augmented measure of the policy stance as in Gertler and Karadi (2015).