Monetary Policy Shocks

Definition

A monetary policy shock $\varepsilon_t^s$ is the exogenous, unexpected component of the central bank's policy action — the part of the policy instrument $S_t$ not explained by the central bank's systematic reaction to its information set $\Omega_t$ . Formally, the policy rule is:

$S_t = f(\Omega_t,\, \varepsilon_t^s)$

where $f(\cdot)$ is the feedback rule and $\varepsilon_t^s$ is mean-zero, serially uncorrelated, and orthogonal to all variables in $\Omega_t$ . The challenge is that neither $\varepsilon_t^s$ nor $\Omega_t$ is directly observable — both must be inferred from an identified vector autoregression (VAR).

Key Ideas

Identification is the central problem: Without a structural assumption on $A_0$ , VAR residuals are a mixture of all structural shocks and no monetary policy shock can be separately identified.
Three leading instruments: Federal funds rate (FF), non-borrowed reserves (NBR), or the ratio of non-borrowed to total reserves (NBR/TR) have each been used as $S_t$ ; qualitative results are robust across choices.
Price puzzle: A well-specified model should show prices falling after a contractionary shock; a rising price level indicates misspecification — typically, omission of forward-looking commodity prices from $\Omega_t$ .
Liquidity effect: A contractionary shock raises interest rates while initially increasing money demand (M1, M2 rise briefly then fall persistently); the short-run positive co-movement of rates and money aggregates is the "liquidity effect."
Qualitative robustness: Across recursiveness, non-recursive (Sims-Zha), and narrative (Romer-Romer) identification strategies, the qualitative dynamic responses agree: output falls persistently, prices eventually fall, financial quantities initially rise then fall.

How It Works

VAR Framework

Stack the variables as $Z_t = (X_t, S_t, X_{2t})$ where:

$X_t$ (slow block): variables the Fed observes contemporaneously — output ( $Y_t$ ), price level ( $P_t$ ), commodity price index ( $PCOM_t$ )
$S_t$ : the policy instrument (FF, NBR, or NBR/TR)
$X_{2t}$ (fast block): variables affected by monetary policy contemporaneously but not in the Fed's real-time information set — e.g., money aggregates (M1, M2)

The structural VAR is:

$A_0 Z_t = A_+(L)\, Z_{t-1} + \varepsilon_t, \qquad E[\varepsilon_t \varepsilon_t'] = I$

Recursiveness Assumption

The recursiveness assumption (Christiano-Eichenbaum-Evans [CEE] 1999) states:

The Fed observes $X_t$ but not $X_{2t}$ contemporaneously.
Shocks to $S_t$ do not affect $X_t$ within the period (output and prices do not respond to monetary policy instantaneously).

Under this assumption, $A_0$ is block lower-triangular:

$A_0 = \begin{pmatrix} A_{11} & 0 & 0 \\ a_{21} & a_{22} & 0 \\ A_{31} & a_{32} & A_{33} \end{pmatrix}$

Identification is Cholesky (lower-triangular with positive diagonal). The policy shock $\varepsilon_t^s$ is the innovation to $S_t$ orthogonalized to $X_t$ .

Identification invariance (CEE 1999 §4): Any $A_0$ satisfying the recursiveness assumption (block lower-triangular with positive diagonal) generates the same dynamic response of $Z_t$ to $\varepsilon_t^s$ , regardless of the orthogonal rotation $W$ applied to the lower-right block. Cholesky is one member of a large equivalence class, all producing the same policy impulse response function (IRF).

Benchmark Specifications

Name	Policy instrument $S_t$	Source
FF	Federal funds rate	Bernanke-Blinder (1992)
NBR	Non-borrowed reserves	Christiano-Eichenbaum (1992)
NBR/TR	Ratio of non-borrowed to total reserves	Strongin (1995)

Benchmark Impulse Response Results

After a one-standard-deviation contractionary monetary policy shock:

Federal funds rate rises persistently (several quarters)
Real gross domestic product (GDP) falls with a hump-shaped trough around 4–8 quarters after the shock
Price level eventually falls (with or without price puzzle resolved)
M1 and M2 initially rise (liquidity effect), then persistently fall
NBR/TR specification implies a faster recovery of output than FF or NBR

Price Puzzle

Without $PCOM_t$ in $X_t$ , the estimated $A_0$ implies prices rise after a contractionary shock — contradicting theory. Sims (1992) showed that including a commodity price index (a leading indicator of inflation) in the slow block resolves this: the Fed raises rates partly in anticipation of commodity-price-driven inflation, and once $PCOM_t$ is controlled for, prices fall as expected.

Non-Recursive Alternative (Sims-Zha)

The Sims-Zha model relaxes recursiveness by allowing the Fed's information set to include contemporaneous prices and output. $A_0$ has a block-simultaneous structure. Qualitative results are similar to the benchmark recursive schemes.

Narrative Approach (Romer-Romer)

Romer and Romer (1989) identified contractionary episodes from Federal Open Market Committee (FOMC) minutes (dates when the Fed deliberately tried to induce a recession to reduce inflation). Their dummy variable is approximately the innovation to NBR orthogonal to FF. Dynamic responses under narrative identification are qualitatively similar to recursive VAR results, providing cross-method validation.

Bernanke-Mihov Critique

Bernanke and Mihov (1998) propose a structural model of the federal funds market and impose $\gamma = 0$ (borrowed reserves are insensitive to NBR) as an overidentifying restriction, then use a likelihood-ratio test to discriminate among the FF, NBR, and NBR/TR benchmark schemes. CEE (1999) show this restriction is empirically rejected ( $F = 3.48$ , $p < 0.001$ ) and theoretically unjustified — Goodfriend (1983) implies a positive NBR–borrowed-reserves link is expected — leaving the three benchmark schemes on equal footing.

Variance Decomposition

FF shocks account for 21%, 44%, and 38% of output forecast-error variance at 4, 8, and 12 quarter horizons; NBR shocks account for only 7–10%. Both measures explain negligible fractions of price-level forecast variance. Policy shocks dominate variance of the policy instrument itself at short horizons but are not the dominant source of business cycle fluctuations overall.

Why It Matters

Identifying monetary policy shocks is the first step in understanding monetary transmission mechanisms. The qualitative facts — output falls persistently, prices eventually fall, liquidity temporarily rises — are robust stylized facts that structural models (Dynamic Stochastic General Equilibrium (DSGE), limited-participation models, sticky-price models) must replicate. The CEE framework is foundational for the modern DSGE literature on monetary policy, where models are calibrated to match these impulse responses.

The CEE (1997b) exogenous policy rule proposal operationalises this: structural DSGE models should be evaluated by matching the VAR-estimated impulse response of money growth to the identified shock, rather than the interest-rate path. Specifying the monetary experiment as an exogenous money-growth trajectory removes endogenous feedback and ensures model and data experiments are truly comparable.

Open Questions

Quantitative disagreement: While qualitative results are robust, the size and persistence of output responses vary substantially across identification schemes and sample periods.
Real-time data pitfall: Estimated monetary policy rules can appear forward-looking due to measurement error between the Fed's real-time data and published data — disentangling genuine forward-looking behavior from data revision artifacts remains difficult.
Non-linearity: Standard VARs impose linear dynamics; monetary transmission may be non-linear (asymmetric effects of tightening vs. loosening, state-dependence near zero lower bound).
Sign restrictions and the role of implicit assumptions: Uhlig (2004) shows that dropping Cholesky's implicit zero contemporaneous restriction on GDP makes the output response statistically indeterminate — within $\pm 0.2\%$ with 2/3 probability. Monetary policy shocks explain only ~5–10% of GDP forecast variance under sign restrictions vs. ~50% under Cholesky, suggesting the latter's large effects are driven by the identifying assumption, not the data. See Sign Restriction Identification.
High-frequency identification and partial identification: Faust-Swanson-Wright (2004) impose the funds rate term structure estimated from FOMC-day futures changes as restrictions on the CEE VAR. The restriction matrix $R$ has rank $\approx 3$ — not full rank — so the impulse vector is only partially identified; valid inference requires Stock-Wright (2000) S-set confidence sets. Key findings: CEE recursive identification rejected; zero contemporaneous price effect rejected (confidence set becomes empty); output forecast-error-variance (FEV) share 0–29% at 60 months confirmed under weaker assumptions. See Faust-Swanson-Wright (2004).