A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions

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).

Structural Approaches to Vector Autoregressions

This 1992 Federal Reserve Bank of St. Louis Review paper (a policy review, not peer-reviewed) by John W. Keating is an expository survey of structural vector autoregression (VAR) methods that shows how a reduced-form VAR, x_t = β(L)x_{t-1} + e_t, can be derived from an underlying structural simultaneous-equations model, Ax_t = C(L)x_{t-1} + Dz_t, and then develops two families of identifying restrictions needed to recover the structural parameters in A and D from the estimated reduced-form residual covariance matrix Σ_e = A^{-1}DΣ_εD’A^{-1’}: contemporaneous restrictions on the impact matrix A (of which the Choleski, or recursive, decomposition is a special, atheoretical case) and long-run restrictions on the cumulative multiplier matrix θ(1), following the Blanchard-Quah (1989) approach, which let the data determine short-run dynamics while theory constrains only shocks’ permanent effects. Keating illustrates both strategies with a 4-variable quarterly U.S. system — the GNP deflator, real GNP, the 3-month Treasury bill rate, and M1, all first-differenced, over 1959:Q1-1991:Q3 with 4 lags — specifying a contemporaneous model (a predetermined price/aggregate-supply equation, an IS equation, a money-supply reaction function, and a buffer-stock money-demand equation) and a long-run model that restricts aggregate-supply shocks to be the sole source of permanent output movements. For the long-run model only, the paper reports estimated structural shock standard deviations (aggregate supply 0.0144, IS 0.0092, money demand 0.0149, money supply 0.0172, all significant at 5%), finds the long-run money-demand and money-supply coefficients statistically significant at 5% while the long-run IS coefficient on output is not, and shows via impulse responses (with Runkle 1987 Monte Carlo confidence bands) that supply shocks raise output permanently and lower prices, IS shocks raise output only temporarily but raise prices and the interest rate permanently, money-demand shocks have essentially no effect on output, prices, or rates, and money-supply shocks have a “relatively small” effect on output that peaks at 13 percent of its variance about two years out; variance decompositions show supply shocks explaining 90 percent of output variance at a 48-quarter horizon. For the contemporaneous model, by contrast, all ten estimated structural coefficients (Table 3) are statistically insignificant even though several carry theory-consistent signs (money-demand coefficients of roughly one-half on nominal spending and almost -1.0 on the interest rate; a positive coefficient on money in the money-supply/interest-rate equation, read as evidence the Fed “attempts to stabilize money growth by raising interest rates”), and its impulse responses (Figures 5-8) and variance decomposition (Table 4) mix expected patterns — supply shocks dominating output and price variance, IS shocks dominating short-run output movement and long-run interest-rate variance, much as in the long-run model — with patterns Keating calls “inconsistent with most macroeconomic theories,” namely the money-demand shock’s effects concentrated on long-run output and short-run interest-rate variance rather than money itself, and the money-supply shock’s negligible effect on output paired with a large, persistent effect on real money. Keating’s own comparison concludes that “wherever a significant discrepancy exists between the two models, the model with long-run restrictions yields sensible results, while the results from the contemporaneous model are inconsistent with standard economic theories,” and that long-run parameters are estimated more precisely; he attributes this to macro theories often sharing long-run properties while differing in short-run dynamics, and to long-run identification avoiding contemporaneous exclusion restrictions that his 1990 paper argues can be invalid under rational expectations, while flagging that further research is needed to know whether this result generalizes beyond the paper’s illustrative system.

John W. Keating | Macro Paper Warehouse

A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions

Structural Approaches to Vector Autoregressions