A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Estimates of how monetary policy affects the economy tend to misbehave once interest rates are near zero. Does using a broad, usage-weighted measure of the money supply as the policy gauge fix that? Estimating a small United States model over samples ending in 1995, 2007 and 2015, this paper finds it does: output falls for three years after a tightening, prices fall with a lag, and money itself drops on impact, with results stable across samples, while three alternative substitutes for the interest rate all give implausible price responses. Why it matters: it offers a workable reading of policy when interest rates are stuck at the floor.
What this paper finds — and why it matters
This 2019 Journal of Money, Credit and Banking paper by John Keating, Logan Kelly, A. Lee Smith, and Victor Valcarcel asks whether replacing the federal funds rate with Divisia M4 (DM4) – a user-cost-weighted monetary aggregate – as the policy indicator in a Christiano-Eichenbaum-Evans (1999)-style block-recursive structural VAR can identify monetary policy shocks that behave sensibly in both normal times and financial-crisis/near-zero-lower-bound conditions, when standard funds-rate-based shocks are prone to implausible (“puzzle”) responses. The empirical model partitions macro variables into three ordered blocks – a slow-moving block (real GDP, the GDP deflator, a commodity price index), the policy indicator (DM4), and a fast-responding money-market block (the monetary base and DM4’s user cost) – estimated by Bayesian Gibbs sampling (following Sims and Zha 1999) with a noninformative prior and 90% probability intervals, at 5 lags quarterly (13 lags in a monthly robustness check), across three overlapping samples: 1967:Q1-1995:Q2 (replicating the original CEE funds-rate sample), 1967:Q1-2007:Q4 (precrisis), and 1967:Q1-2015:Q4 (full sample including the 2008-09 crisis and the ZLB period). A complementary small-scale New Keynesian model with money shows that when the Fed’s estimated interest-rate rule displays high inertia (rho approximately 0.94, estimated by nonlinear GMM on 1967-2007 quarterly data), its policy dynamics can be closely replicated by a non-inertial money-growth rule reacting to output and inflation – providing theoretical grounding for using DM4 in a Cholesky-ordered VAR even though the Fed never formally targeted it – whereas a low-inertia Taylor (1993) rule is not well replicated by a money-growth rule. Empirically, the DM4-based VAR produces no output, price, or liquidity puzzles in any of the three samples: GDP falls in a significant, hump-shaped (U-shaped) pattern for three years after a contractionary shock, the price level declines with a lag (becoming significantly negative after about two years), DM4 itself falls on impact with a significant liquidity effect, and its user cost rises on impact – a pattern the authors describe as “remarkably stable” across samples and broadly similar to the CEE funds-rate benchmark in the precrisis sample. By contrast, VARs built on three shadow short rates (Lombardi-Zhu, Krippner, Wu-Xia) all generate persistent, statistically significant price puzzles, with two of the three also generating liquidity puzzles. The cumulative identified DM4 shocks crest around QE1-QE3 and register the 2013:Q2 taper tantrum as a large negative shock, and a historical decomposition finds monetary policy shocks after 2008 were mildly net expansionary (real GDP 0.48% and the GDP deflator 0.50% higher than they otherwise would have been), with monetary policy shocks accounting for 8.44% (90% interval 1.73%-18.78%) of real GDP forecast-error variance at 8 quarters and 6.47% (0.66%-17.04%) of GDP-deflator variance at 20 quarters. A Great Depression counterfactual – applying the 1929:Q3-1937:Q3 pace of M2 collapse to DM4 starting in 2007:Q4 – implies a hypothetical 12.65% peak-to-trough GDP decline and 4.1% deflation, versus the actual -4.35% GDP decline and +0.26% inflation, which the authors interpret as evidence that post-2008 Fed actions, while not large departures from its historical policy rule, prevented a much deeper contraction. Long-run policy-rule coefficients on inflation are negative and significant in all three samples (-1.83, -2.26, and -0.88 respectively across the three samples) while the output-growth coefficient stays small and insignificant throughout, which the authors read as the Fed behaving “as if” it stabilized inflation via broad money growth. Results are robust to a monthly-frequency VAR (only 1 of 102 responses falls outside the quarterly model’s 90% bands, though the monthly liquidity effect is not statistically significant) and largely, though not entirely, to substituting DM2 for DM4 (DM2 shows a small, statistically insignificant price puzzle and a rising monetary base in the full crisis-inclusive sample). The authors attribute DM4’s puzzle-free performance in the crisis period to two features: its Divisia expenditure-weighting, which (per a DSGE decomposition) avoids the aggregation bias that afflicts simple-sum aggregates like M1 and M2 when asset substitutability is time-varying, and its breadth, since DM4 includes institutional money-market funds, repos, commercial paper, and Treasury bills – assets specifically targeted by the Fed’s 2008-09 liquidity facilities (PDCF, TSLF, CPFF, ABCPMMMFLF).
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Questions & answers
Q1. What problem motivates the paper, and what fix do the authors propose?
Standard structural VARs that use the federal funds rate to identify monetary policy shocks can misbehave once the sample includes the 2008-09 financial crisis and its aftermath, so the authors propose replacing the funds rate with Divisia M4 (DM4) – a user-cost-weighted monetary aggregate – as the policy indicator in an otherwise standard recursive VAR. The funds rate effectively hit its zero lower bound during the crisis, which is one of several reasons funds-rate-based shock measures can generate output, price, or liquidity “puzzles” (responses with counterintuitive signs). The paper’s specific question is whether a DM4-based VAR, keeping the timing/ordering assumptions of Christiano, Eichenbaum, and Evans (1999) (CEE), can produce impulse responses free of these puzzles across samples that both exclude and include the crisis.
Q2. What theoretical result justifies using a monetary aggregate, rather than an interest rate, as the policy indicator?
A small-scale New Keynesian model with money shows that when the Fed’s estimated interest-rate rule has high inertia (rho approximately 0.94, estimated by nonlinear GMM on quarterly 1967-2007 data, together with responses phi_pi = 2.20 and phi_y = 2.69), the resulting policy dynamics can be closely replicated by a money-growth rule with no inertia (rho-tilde = 0) and positive responses to output and inflation (phi-tilde_y = 0.54, phi-tilde_pi = 0.65). By contrast, when the calibration instead uses the low-inertia Taylor (1993) rule (rho = 0, phi_pi = 1.5, phi_y = 0.13), the fit for the price level “deteriorates more significantly.” The authors conclude that “interest rate inertia is the primary factor determining whether monetary policy impulses under interest rate rules can be well approximated by money growth rules” (p. 235), which is the theoretical bridge that lets them treat DM4 as a legitimate Cholesky-ordered policy indicator even though the Federal Reserve never formally targeted it.
Q3. How is the empirical block-recursive SVAR structured, and over what samples and data is it estimated?
The VAR follows CEE’s (1999) block-recursive structure, partitioning variables into three ordered blocks with a block-lower-triangular impact matrix: a slow-moving macro block (real GDP, the GDP deflator, and a commodity price index) ordered first, the policy indicator (DM4) ordered second, and a fast-responding money-market block (the monetary base and DM4’s user cost) ordered last. This ordering assumes the policy indicator responds contemporaneously to the slow macro variables but monetary policy has no contemporaneous effect on output or prices, while the fast block reacts immediately to both other blocks but affects them only with a lag. Unlike the CEE funds-rate benchmark, nonborrowed reserves are dropped (they turn negative after 2007) and the monetary base replaces total reserves. The model is estimated with a Bayesian Gibbs sampler (Sims and Zha 1999 / Koop and Korobilis 2010), noninformative prior, 90% probability intervals, and 5 lags at quarterly frequency (13 lags in the monthly robustness check), over three overlapping U.S. samples: 1967:Q1-1995:Q2 (matching CEE’s original funds-rate sample), 1967:Q1-2007:Q4 (precrisis), and 1967:Q1-2015:Q4 (full sample spanning the financial crisis and the ZLB period).
Q4. Does the DM4-based VAR avoid the output, price, and liquidity puzzles, and how stable is this across samples?
Yes: in all three sample periods the DM4 VAR produces no output, price, or liquidity puzzles. Real GDP falls in a statistically significant, hump-shaped (U-shaped) pattern for three years after a contractionary shock; the price level declines with inertia, with the point estimate never positive and turning significantly negative after about two years; DM4 itself falls on impact (a statistically significant liquidity effect); and DM4’s user cost rises on impact. The authors later summarize this pattern as “remarkable stability in the qualitative effects of monetary policy shocks across samples” (p. 249), with the specific impulse responses reported in Section 2.1 (pp. 238-240).
Q5. How does the DM4 model compare to the federal-funds-rate benchmark and to shadow-rate models once the crisis period is included?
Over the CEE replication sample (1967:Q1-1995:Q2), the DM4 and funds-rate models give “remarkably similar impulse responses from both a qualitative and quantitative standpoint,” but they diverge once the precrisis-extended sample (1967:Q1-2007:Q4) is used: the funds-rate benchmark develops an initially significant price puzzle, while DM4’s price response stays nonpositive throughout and turns significantly negative after 10 quarters. Models built instead on three shadow short-rate series (Lombardi-Zhu 2014, Krippner 2015, Wu-Xia 2016, spliced with the effective funds rate before 2008:Q4) each generate a persistent, statistically significant price puzzle, and the Krippner and Wu-Xia versions also generate a liquidity puzzle (the monetary base initially rises after an expansionary shock). The authors note the price puzzles from the shadow-rate models “lead to uncomfortable implications when considering counterfactual monetary policy regimes” (p. 246).
Q6. What do the identified DM4 shocks imply about the stance and real effects of post-2008 monetary policy?
The cumulative sum of identified DM4 structural shocks crests at the start of each round of quantitative easing (QE1, QE2, QE3) and registers the 2013:Q2 taper tantrum as a large negative shock, which the authors read as supporting the shocks’ interpretation as genuine changes in the stance of policy. A historical decomposition over 1967:Q1-2015:Q4 finds that monetary policy shocks after 2008 were, on net, slightly expansionary: real GDP is estimated to be 0.48% higher and the GDP deflator 0.50% higher than they would have been absent those shocks. A variance decomposition over the same sample attributes 8.44% (90% interval 1.73%-18.78%) of real GDP forecast-error variance at the 8-quarter horizon, and 6.47% (0.66%-17.04%) of GDP-deflator forecast-error variance at the 20-quarter horizon, to monetary policy shocks (Table 2, p. 248).
Q7. What does the Great Depression counterfactual suggest about the Fed’s post-2008 policy response?
If DM4 had contracted from 2007:Q4 to 2015:Q4 at the same rate M2 contracted from 1929:Q3 to 1937:Q3, the model implies real GDP would have fallen 12.65% peak to trough with deflation reaching 4.1%, versus the actual outcomes of a 4.35% GDP decline and 0.26% inflation. The authors interpret this gap as evidence that the Federal Reserve’s post-2008 actions were not large deviations from its historical policy rule, but nonetheless prevented a much larger economic contraction (Section 2.4, p. 249).
Q8. What do the estimated long-run policy-rule coefficients say about how the Fed has behaved?
Long-run policy coefficients on output growth are small and statistically insignificant in all three samples, while the coefficients on price inflation are negative and significant throughout: -1.83 (90% interval -4.83 to -0.43) in 1967:Q1-1995:Q2, -2.26 (-4.87 to -0.92) in 1967:Q1-2007:Q4, and -0.88 (-1.80 to -0.20) in the full 1967:Q1-2015:Q4 sample. The authors “interpret this result as an indication that the Fed behaved ‘as if’ it stabilized inflation via broad money growth” (Section 2.4, pp. 248-249; Table 3).
Q9. How robust are the results to monthly data and to a narrower monetary aggregate (DM2), and why does DM4 specifically avoid the puzzles?
A monthly-frequency version of the DM4 VAR (1967:Q1-2015:Q4, 13 lags) is qualitatively and quantitatively similar to the quarterly baseline – only 1 of 102 quarterly-model responses falls outside the monthly model’s 90% probability bounds – though the monthly model does not display a statistically significant liquidity effect. Substituting DM2 (also expenditure-weighted) for DM4 mostly succeeds in the precrisis samples but shows marginal puzzles in the full sample: a DM2 shock causes the monetary base to rise for four of the first five quarters and produces a tiny, statistically insignificant price puzzle. The authors attribute DM4’s edge in the crisis period to two features (Section 2.6, pp. 251-254): breadth – DM4 includes institutional money-market funds, repos, commercial paper, and Treasury bills, assets specifically targeted by the Fed’s 2008-09 liquidity facilities (PDCF, TSLF, CPFF, ABCPMMMFLF) – and Divisia expenditure-weighting, which a DSGE-based decomposition shows avoids the aggregation bias that can give unweighted aggregates like M1 and M2 an upward-biased, even wrong-signed, impact response when asset substitutability is time-varying.
Key terms in this paper
Definitions below follow the paper's own usage.
- Divisia M4 (DM4)
- the paper's baseline policy indicator, an expenditure-weighted ("Divisia") monetary aggregate covering a broad set of assets -- including institutional money-market funds, repos, commercial paper, and Treasury bills -- that were specifically targeted by the Federal Reserve's 2008-09 liquidity facilities; its expenditure weighting is argued to track the theoretically correct monetary aggregate to second order and to avoid the substitution-driven aggregation bias of simple-sum aggregates like M1 or M2.
- Block-recursive (partially recursive) structural VAR
- the paper's identification scheme, following Christiano, Eichenbaum, and Evans (1999) and generalized by Keating (1996), in which variables are partitioned into ordered blocks with a block-lower-triangular impact matrix A_0 -- here a slow macro block, the policy indicator, and a fast money-market block -- so that the policy indicator responds contemporaneously to slower variables but not vice versa, while the Cholesky factorization within each block identifies that block's structural shocks.
- Output, price, and liquidity puzzles
- the paper's term for implausible impulse-response signs that standard funds-rate-based recursive VARs can generate -- e.g., prices rising or output rising after a contractionary policy shock (price/output puzzle), or the monetary base rising rather than falling after a contractionary shock (liquidity puzzle) -- which the authors use as the diagnostic criterion for judging whether a given policy indicator (DM4, the funds rate, or a shadow rate) is well identified.
- Shadow rate
- a model-based measure (here, Lombardi-Zhu 2014, Krippner 2015, or Wu-Xia 2016, each spliced with the effective federal funds rate before 2008:Q4) meant to proxy the stance of policy at the zero lower bound, when the funds rate itself is uninformative; the paper finds all three shadow-rate variants generate persistent price puzzles when used in place of DM4 or the funds rate.
- Historical decomposition
- the exercise of using the estimated VAR to compute how much of the actual path of a variable (here, real GDP and the GDP deflator after 2008) is attributable to the cumulative effect of the identified monetary policy shocks alone, holding other shocks at their estimated values, as distinct from a variance decomposition (which allocates forecast-error variance, not levels, across shocks).