## _wp09101 — 1. Oil Price Developments

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---

### Inflationary context and stylized facts
- Crude oil inflation (cumulative change in the spot price of a barrel of West Texas Intermediate measured in U.S. dollars) rose by almost 160 percent between 2003 Q1 and 2008 Q1.
- In both nominal and real (normalized by the U.S. GDP deflator) terms, this increase is about double the increase in oil prices experienced during either the first or the second oil shock of the 1970s.
- Food prices (average of Reuters-Jefferies Commodity Research Bureau three key food sub indices: grains and oilseeds, livestock and foodstuff) rose by over 900 percent in the five years to 2008 Q1.
- Drivers of the food-price surge: higher demand in large emerging markets; oil price hike raising production costs; increased demand for crops used to produce cheaper-than-oil bio-fuels.
- Oil and some base-metal prices dropped considerably in the second half of 2008 following deepening international financial turmoil and expectations of a global slowdown.
- Despite the drop, supply constraints and projected demand growth in emerging markets imply continued risk of generalized CPI inflation.
- Projected increase in world crude oil demand by emerging markets: 3 ¾ percent a year during 2008- 2012.
- Table 1 methodology note: oil shock episodes are determined based on a cumulative change in the log price of oil of above 50%, sustained for more the four quarters.

### Transmission to inflation and welfare
- Supply shock from high oil and food prices spread to headline CPI with heterogeneous effects:
  - Net importers of oil and food were hit most.
  - Non-food-producing poor countries experienced severe cuts in real income and living conditions due to the large weight of food in final expenditure.

### Research questions and approaches
- How should interest rates be set in response to a severe but transient supply shock?
  - Approach: small structural open-economy model with Phillips curve explicitly accounting for oil shocks (Batini, Jackson and Nickell (BJN, 2005); Blanchard and Galí (BG, 2007)).
- What is the appropriate horizon of monetary policy under a shock like this?
  - Approach: apply Batini and Nelson (2001) methodology to impulse responses to obtain optimal policy and feedback horizons for economies with different degrees of nominal rigidities.
  - Previewed finding: length of the horizon is a function of inflation volatility, agents’ forward-lookingness, and target credibility.
- How does loss of credibility affect optimal policies?
  - Approach: Kalman-learning version of the model where agents learn the target after a shock in target confidence; simulate adjustments to rein in inflation expectations.
- How should central banks prepare for future oil-price developments?
  - Approach: stochastic simulations where the future path for the price of oil is a Markov chain.
  - Previewed result: adequate policy response is rather independent of the future mean of real oil prices, but under a symmetric target depends on the extent of oil price fluctuations; continuing high oil-price volatility demands bold policy-rate responses.

### Methodology, calibration, and key model definitions
- Model: small-scale, forward-looking open economy with structural equations (IS, Phillips, UIP) and oil as explicit supply input.
- Key variable definitions:
  - yt = log output
  - Rt = nominal interest rate (quarterly fraction)
  - πt = quarterly inflation
  - Δroilt = first difference in the log-level real price of oil
  - qt = log real exchange rate (rise = depreciation)
  - ∑3 j=0 q~t−j = four-quarter moving average of qt
- Shock processes and calibration values:
  - eyt AR(1) coefficient = 0.3; innovation standard deviation = 1%
  - σ = 0.2; δ = 0.05
  - Phillips-curve mixed backward/forward calibration: α = 0.8 (baseline); alternative α = 0.3 explored
  - φy = 0.1; φq = 0.025
  - eπt white noise with standard deviation = 1%
  - κt AR(1) coefficient = 0.75; innovation standard deviation = 0.9%
- Oil process and pass-through:
  - roilt follows AR(1) with coefficient ρroil set to two values: 0.71 (stable 1980s–1990s) and 0.99 (quasi-explosive 2002 onward)
  - Oil pass-through parameter calibrated to 0.02 (recent evidence); experiments also use 0.1 (1970s average)
  - Estimated dependent-variable standard deviations: 0.2 (1980–1990), 0.4 (post-2002)
- Policymaker loss function (asymptotic-variance quadratic form):
  - β = 0.99; λy = λπ = 1; λR = 0.5
- Simple Taylor-style rule used for comparison (optimized for each k): Rt = γRt−1 + ψπ(Etπt+k − π*) + ψΔyΔyt−1 + ... with ψπ, ψΔy > 1

### Optimal policy responses — mechanics and calibrated quantitative findings
- Complex optimal rule: full-commitment rule derived from structural equations and policymakers’ first-order conditions; Lagrange multipliers included in state vector.
- Simple optimized rule: parsimonious feedback rule with ψπ, ψΔy, γ chosen to minimize loss.
- General behaviors:
  - Under complex optimal rule, quasi-explosive 2000s regime resembles 1970s shocks in optimal responses.
  - With low pass-through (0.02), inflation increases only by 15 of a percent in some impulse response descriptions; output falls below potential and remains prolonged.
  - Under ‘stable’ regime output returns to potential in less than two years with contained inflation.
  - Simple rules produce more volatile responses and more cyclical output; output never remains longer than a year below potential in those scenarios.
  - In all examined scenarios, optimal policy raises nominal rates so real rates become strongly positive; nominal rates grow on average around 5 times more than inflation.

### Welfare statistics (asymptotic variances and loss — Table 2)
- ‘Stable’ Oil Regime (1986 Q1−2001 Q4)
  - Complex: AsyVar(y) = 0.27; AsyVar(π) = 0.37; AsyVar(R) = 0.011; AsyVar(q) = 0.34; Loss = 2.27
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘Explosive’ Oil Regime (2002 Q2−2008 Q2)
  - Complex: AsyVar(y) = 0.26; AsyVar(π) = 0.36; AsyVar(R) = 0.011; AsyVar(q) = 0.37; Loss = 2.12
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘1970s-Shocks’ Oil Regime (1970 Q2−1980 Q2) — Low Passthrough
  - Complex: AsyVar(y) = 0.27; AsyVar(π) = 0.37; AsyVar(R) = 0.011; AsyVar(q) = 0.85; Loss = 2.19
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘1970s-Shocks’ Oil Regime (1970 Q2−1980 Q2) — High Passthrough
  - Complex: AsyVar(y) = 0.38; AsyVar(π) = 0.58; AsyVar(R) = 0.017; AsyVar(q) = 3.98; Loss = 5.47
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- Key inference: complex rule yields lower loss than simple rules (loss on average 33% smaller), but with high pass-through the loss under complex rule can increase substantially relative to low pass-through.

### Optimized simple-rule coefficients and behavior
- Unit-shock optimized simple-rule coefficients: ψπ = 4.55; ψΔy = 0.02; γ = 1.15
- Feedback parameters across oil regimes are virtually identical in optimized simple rules when only oil shock variance/persistence changes and pass-through is small.

### Optimal policy horizons (OPH) — definitions and calibrated results
- OPH definitions:
  - Absolute criterion: kA* = periods to return permanently within ±0.01 percentage points of target.
  - Relative criterion: kR* = periods until 90% of the peak effect of the shock on inflation is extinguished.
- Table 3: OPHs (kA*, kR*)
  - ‘Stable’: kA* = 6; kR* = 11
  - ‘Quasi-Explosive’: kA* = 3; kR* = 28
  - ‘1970s’: kA* = 3; kR* = 20
  - ‘1970s with High Pass-through’: kA* = 10; kR* = 12
- Interpretation:
  - Under the absolute criterion, minimum efficient horizon ~ 1½ years (3 quarters) and maximum ~ 2½ years (10 quarters) depending on pass-through.
  - Under the relative criterion, horizons can be much longer (e.g., 28 quarters) when initial impacts are small but persistence is large.
- Sensitivity to forward-looking expectations (α = 0.3; Table 4)
  - Table 4: OPHs with α = 0.3
    - ‘Stable’: kA* = 6; kR* = 6
    - ‘Quasi-Explosive’: kA* = 6; kR* = 10
    - ‘1970s’: kA* = 6; kR* = 11
    - ‘1970s with High Passthrough’: kA* = 10; kR* = 10
  - With α = 0.3, absolute horizons lengthen in low pass-through cases; relative horizons shorten.

### Optimal feedback horizons (OFH) for simple rules
- OFH: the k in the simple rule Rt responding to Etπt+k that minimizes loss.
- Table 5 results:
  - ‘Stable’: kF* = 0
  - ‘Quasi-Explosive’: kF* = 0
  - ‘1970s’: kF* = 0
  - ‘1970s with High Passthrough’: kF* = 0
- Interpretation: model favors current-looking (zero feedback horizon) simple rules across parametrizations; zero feedback horizon does not imply instantaneous return to target — e.g., under the optimal zero-feedback rule inflation returns to target within 4 quarters for the ‘stable’ regime (other regimes: 4, 2, and 4 quarters respectively under their optimally chosen parameters).

### Imperfect credibility — modeling and quantitative consequences
- Credibility model:
  - Agents face signal-extraction about the inflation target π*t with two zero-mean stochastic components (πpt, πqt) dynamics in a VAR(1).
  - Calibrations: ρp = 0.9 (persistent); ρq = 0.05 (transitory)
  - Persistent target innovation correlated with oil shock: cross-correlation coefficient = 0.3
  - Agents use Kalman filter; Kalman gain and learning follow Erceg and Levin (2003) calibration.
- Quantitative impacts under imperfect credibility:
  - A unit oil shock with imperfect credibility produces much larger inflation peaks: inflation increases up to 50 times as much even with low pass-through (implication: a 100 percent oil increase could yield inflation peaks between 83 and 86 percent a few quarters after the shock in impulse-response discussion).
  - Output gap drops three times deeper relative to full-credibility case after necessary interest-rate spike.
  - Shock to target credibility dominates differences across oil regimes: inflation, output, and interest-rate paths become quasi-identical across regimes under imperfect credibility.
  - Efficient horizon for returning inflation to target lengthens enormously (narrative suggests ten-year period), though after 2½ years deviation may already be below ½ of a percent.
- Policy corollaries:
  - Earlier, stronger action can reduce overall shock magnitude and output-variability costs.
  - Central bank communication is crucial: transparent explanation of strategy and horizon for returning inflation to target can reduce target disbelief and associated costs.

### Stochastic scenarios for future oil prices and optimized simple-rule coefficients
- Back-of-envelope demand-price relation: every 1 quadrillion Btu increase in world liquid-fuel demand produced a US$5 increase in oil prices over past 5 years; at current projected demand growth, this implies additional crude price increase of about US$ 90 over next 5 years (other things equal).
- Markov-chain scenarios for next 12 quarters (two-state low/high mean and volatility; low→high switch probability 0.02; high state persistence 0.9999; high state maintained for 12 quarters then scenario-specific evolution):
  - Scenario 1 (L-H-H): jump to 2008 Q2 level and remain
  - Scenario 2 (L-H-HH): jump to 2008 Q2 level then to a higher level
  - Scenario 3 (L-H-M): jump to 2008 Q2 level then revert to an intermediate level
  - Scenario 3A (L-H-L): revert to low state
- Optimized simple-rule coefficients under scenarios (Table 6):
  - Scenario 1 (L-H-H): ψπ = 3.61; ψΔy = 0.052; γ = 1.15
  - Scenario 2 (L-H-HH): ψπ = 4.13; ψΔy = 0.048; γ = 1.14
  - Scenario 3 (L-H-M): ψπ = 4.12; ψΔy = 0.049; γ = 1.10
  - Scenario 3A (L-H-L): ψπ = 4.00; ψΔy = 0.050; γ = 1.15
  - Memo: unit shock: ψπ = 4.55; ψΔy = 0.020; γ = 1.15
- Scenario findings:
  - Central bank needs to react strongly to close inflation gap quickly in all scenarios.
  - Interest-rate smoothing (γ > 1) is necessary to ensure determinacy and strengthen policy signaling.
  - Feedback on output growth remains small.
  - Little difference in optimal reaction between some scenarios (e.g., Scenario 2 vs Scenario 3A): remain aggressive responding to inflation deviations even after a drop in real oil price if inflation volatility remains high.

### Concluding policy implications and actionable findings
- Optimal response to a 2000s-type oil shock: aggressive increases in real interest rates to close the inflation gap over the minimum efficient policy horizon; repeated nominal-rate rises strengthen determinacy and anti-inflation signaling.
- Failure to raise real rates promptly has contributed to inflation rises and unanchored inflation expectations in several emerging markets.
- Under a symmetric inflation target, policy should remain aggressive even if an adverse supply shock is followed by favorable ones, because objective minimization is in absolute deviations.
- Repeated shocks take time to rein in; overlapping impulse responses substantially lengthen efficient horizons (potentially 2–3 times longer for multiple shocks).
- Loss of target credibility dramatically worsens policy dilemmas: requires larger interest-rate gyrations and larger output-gap losses.
  - Policy recommendation: act more aggressively early to contain overall shock magnitude and reduce output costs.
  - Policy recommendation: clear, transparent central bank communication on strategy and horizon for returning inflation to target to minimize target disbelief and materially improve outcomes.

*Source: _wp09101 - 1. Oil Price Developments (PDF).*

### 1. Oil Price Developments  ............................................................................................4

### 1. Oil Price Developments

### Inflationary context and stylized facts
- Over the five years to 2008 Q1, crude oil inflation (cumulative change in the spot price of a barrel of West Texas Intermediate measured in U.S. dollars) rose by almost 160 percent between 2003 Q1 and the same quarter in 2008.
- Both in nominal and in real (normalized by the U.S. GDP deflator) terms, this increase is about double the increase in oil prices experienced during either the first or the second oil shock of the 1970s (Table 1).
- Food prices measured by the average of Reuters-Jefferies Commodity Research Bureau three key food sub indices (grains and oilseeds, livestock and foodstuff) rose by over 900 percent in the five years to 2008 Q1.
- The surge in food prices reflected higher demand in large emerging markets and the oil price hike, which raised production costs and boosted demand for specific food crops used to produce cheaper-than-oil bio-fuels.
- Table 1: Oil Price Developments is based on the methodology in Blanchard-Galí (2007). Oil shock episodes are determined based on a cumulative change in the log price of oil of above 50%, sustained for more the four quarters.
- Prices of oil and some base metals dropped considerably in the second half of 2008 following the deepening of the international financial turmoil and expectations of a global slowdown.
- Despite the drop, supply constraints (disruptions in producing areas, weak non-OPEC supply, and slow development of alternative fuels) and projected demand growth in emerging markets imply continued risk of generalized CPI inflation.
- Projected increase in world crude oil demand by emerging markets: 3 ¾ percent a year during 2008- 2012.

### Transmission to inflation and welfare
- The supply shock originating in high oil and food prices spread to headline CPI in most countries, with heterogeneous effects:
  - Net importers of oil and food were hit most.
  - Non-food-producing poor countries experienced severe cuts in real income and living conditions due to the large weight of food in final expenditure.

### Research questions addressed in the paper
- How should interest rates be set in response to a severe but transient supply shock?
  - Approach: small structural open-economy model with a Phillips curve that accounts explicitly for oil shocks as in Batini, Jackson and Nickell (BJN, 2005) and Blanchard and Galí (BG, 2007).
  - Tasks: Revisit mechanics of monetary intervention, derive optimal monetary policy response to a protracted supply shock of the 2007–2008 type, and compare to policies optimal for the 1970s shocks.
- What is the appropriate horizon of monetary policy under a shock like this?
  - Approach: Apply methodology in Batini and Nelson (2001) to impulse responses of the model to a 2007–2008-type supply shock to obtain optimal policy and feedback horizons for economies with different degrees of nominal rigidities.
  - Finding preview: Length of the horizon is a function of inflation volatility, agents’ forward-lookingness, and target credibility.
- How does the choice of optimal policies get affected if the target loses credibility?
  - Approach: Use a version of the model where agents Kalman-learn the target following a shock in target confidence from persistent target misses; simulate adjustments needed to rein in inflation expectations when commitment to low inflation is eroded.
- How should central banks prepare for future developments in the price of oil?
  - Approach: Evaluate robustness of monetary policies to future oil shocks using stochastic simulations where the future path for the price of oil takes the form of a Markov chain.
  - Previewed result: Adequate policy response is rather independent of the future mean of real oil prices, but under a symmetric target depends on the extent of oil price fluctuations over a given period. Continuing high oil price volatility demands bold policy rate responses going forward.

### Methodology and organization
- Model features highlighted:
  - Small structural open-economy framework.
  - Phillips curve that explicitly incorporates oil shocks (BJN, 2005; BG, 2007).
  - Impulse-response analysis and optimal-policy/feedback-horizon derivations using Batini and Nelson (2001) methodology.
  - Kalman-learning setup to model erosion of target credibility.
  - Stochastic Markov-chain representations of future oil price paths to test policy robustness.
- Paper organization:
  - Section 2: brief literature review.
  - Section 3: stylized facts, model description, and oil shock process.

*Source: _wp09101 - 1. Oil Price Developments (PDF).*

### Section 4 summarizes results on optimal policy rules and optimal horizons. Section 5 revisits

### _wp09101 - Section 4 summarizes results on optimal policy rules and optimal horizons. Section 5 revisits

### Methodology, data and calibration
- Model: small-scale, forward-looking open economy with structural equations (IS, Phillips, UIP) and oil as an explicit supply input.
- Key variable definitions:
  - yt = log output
  - Rt = nominal interest rate (quarterly fraction)
  - πt = quarterly inflation
  - Δroilt = first difference in the log-level real price of oil
  - qt = log real exchange rate (rise = depreciation)
  - ∑3 j=0 q~t−j = four-quarter moving average of qt
- Shock processes and calibrations:
  - eyt AR(1) coefficient = 0.3; innovation standard deviation = 1%
  - σ = 0.2; δ = 0.05
  - Phillips-curve mixed backward/forward calibration: α = 0.8 (baseline); alternative α = 0.3 explored
  - φy = 0.1; φq = 0.025
  - eπt white noise with standard deviation = 1%
  - κt AR(1) coefficient = 0.75; innovation standard deviation = 0.9%
- Oil process:
  - roilt follows AR(1) with coefficient ρroil set to two values: 0.71 (stable 1980s–1990s) and 0.99 (quasi-explosive 2002 onward)
  - Oil pass-through parameter calibrated to 0.02 (recent evidence); experiments also use 0.1 (1970s average)
  - Estimated dependent-variable standard deviations: 0.2 (1980–1990), 0.4 (post-2002)
- Policymaker loss function (asymptotic-variance quadratic form):
  - β = 0.99; λy = λπ = 1; λR = 0.5
- Simple rule (Taylor-style) used for comparison:
  - Rt = γRt−1 + ψπ(Etπt+k − π*) + ψΔyΔyt−1 + ... with ψπ, ψΔy > 1 and optimized for each k

### Optimal policy responses to a 2000s-type oil shock — main quantitative calibrations and mechanics
- Complex rule: full commitment optimal rule derived using model structural equations plus policymakers’ first-order conditions; Lagrange multipliers enter the state vector.
- Simple optimized rule: parsimonious feedback rule like Eq. (6); parameters ψπ, ψΔy, γ chosen to minimize loss.
- General behaviors across rules and regimes:
  - Under complex optimal rule, quasi-explosive 2000s regime resembles 1970s shocks in optimal responses.
  - With low pass-through (0.02), inflation increases only by 15 of a percent in some impulse response descriptions; output falls below potential and remains prolonged.
  - Under ‘stable’ regime output returns to potential in less than two years with contained inflation.
  - Simple rules produce more volatile responses and more cyclical output; output never remains longer than a year below potential in those scenarios.
  - In all examined scenarios, optimal policy raises nominal rates so real rates become strongly positive; nominal rates grow on average around 5 times more than inflation.

### Welfare statistics (Table 2 — asymptotic variances and loss)
- ‘Stable’ Oil Regime (1986 Q1−2001 Q4)
  - Complex: AsyVar(y) = 0.27; AsyVar(π) = 0.37; AsyVar(R) = 0.011; AsyVar(q) = 0.34; Loss = 2.27
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘Explosive’ Oil Regime (2002 Q2−2008 Q2)
  - Complex: AsyVar(y) = 0.26; AsyVar(π) = 0.36; AsyVar(R) = 0.011; AsyVar(q) = 0.37; Loss = 2.12
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘1970s-Shocks’ Oil Regime (1970 Q2−1980 Q2) — Low Passthrough
  - Complex: AsyVar(y) = 0.27; AsyVar(π) = 0.37; AsyVar(R) = 0.011; AsyVar(q) = 0.85; Loss = 2.19
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- ‘1970s-Shocks’ Oil Regime (1970 Q2−1980 Q2) — High Passthrough
  - Complex: AsyVar(y) = 0.38; AsyVar(π) = 0.58; AsyVar(R) = 0.017; AsyVar(q) = 3.98; Loss = 5.47
  - Simple: AsyVar(y) = 1.55; AsyVar(π) = 0.34; AsyVar(R) = 0.002; AsyVar(q) = 2.23; Loss = 3.30
- Key inference: complex rule yields lower loss than simple rules (loss on average 33% smaller), but with high pass-through the loss under complex rule can increase substantially relative to low pass-through.

### Simple-rule optimized parameters (unit shock memo and findings)
- Optimized simple-rule coefficients (unit shock memo): ψπ = 4.55; ψΔy = 0.02; γ = 1.15
- Feedback parameters across oil regimes are virtually identical in optimized simple rules when only the oil shock variance/persistence changes and pass-through is small.

### Optimal policy horizons (OPH) — definitions and results
- Definitions:
  - OPH (Optimal Policy Horizon): time when inflation is brought back to a target range under an optimal rule.
  - Two operational criteria:
    - Absolute criterion: kA* = periods to return permanently within ±0.01 percentage points of target.
    - Relative criterion: kR* = periods until 90% of the peak effect of the shock on inflation is extinguished.
- Table 3: OPHs (kA*, kR*)
  - ‘Stable’: kA* = 6; kR* = 11
  - ‘Quasi-Explosive’: kA* = 3; kR* = 28
  - ‘1970s’: kA* = 3; kR* = 20
  - ‘1970s with High Pass-through’: kA* = 10; kR* = 12
- Interpretation:
  - Under the absolute criterion, minimum efficient horizon ~ 1½ years (3 quarters) and maximum ~ 2½ years (10 quarters) depending on pass-through.
  - Under the relative criterion, horizons can be much longer (e.g., 28 quarters) when initial impacts are small but persistence is large.
- Sensitivity to forward-looking expectations (α = 0.3; Table 4):
  - Table 4: OPHs with α = 0.3
    - ‘Stable’: kA* = 6; kR* = 6
    - ‘Quasi-Explosive’: kA* = 6; kR* = 10
    - ‘1970s’: kA* = 6; kR* = 11
    - ‘1970s with High Passthrough’: kA* = 10; kR* = 10
  - With α = 0.3, absolute horizons lengthen in low pass-through cases; relative horizons shorten.

### Optimal feedback horizons (OFH) for simple rules (Table 5)
- OFH: the k in the simple rule Rt responding to Etπt+k that minimizes loss when coefficients are optimized.
- Table 5 results:
  - ‘Stable’: kF* = 0
  - ‘Quasi-Explosive’: kF* = 0
  - ‘1970s’: kF* = 0
  - ‘1970s with High Passthrough’: kF* = 0
- Interpretation: model favors current-looking (zero feedback horizon) simple rules across parametrizations; a zero feedback horizon does not imply instantaneous return to target—e.g., under the optimal zero-feedback rule inflation returns to target within 4 quarters for the ‘stable’ regime (other regimes: 4, 2, and 4 quarters respectively under their optimally chosen parameters).

### Imperfect credibility: modeling and quantitative consequences
- Credibility model:
  - Agents face a signal-extraction problem about the inflation target π*t, which has two zero-mean stochastic components (πpt, πqt) with dynamics in a VAR(1).
  - Calibrations: ρp = 0.9 (persistent); ρq = 0.05 (transitory)
  - Persistent target innovation correlated with oil shock: cross-correlation coefficient = 0.3
  - Agents use Kalman filter; the Kalman gain and learning process follow Erceg and Levin (2003) calibration.
- Quantitative impacts under imperfect credibility:
  - A unit oil shock with imperfect credibility produces much larger inflation peaks: inflation increases up to 50 times as much even with low pass-through (interpreted as near full pass-through; a 100 percent oil increase could yield inflation peaks between 83 and 86 percent a few quarters after the shock in the impulse-response discussion).
  - Output gap drops three times deeper relative to full credibility case after necessary interest-rate spike.
  - The shock to target credibility dominates differences across oil regimes: inflation, output, and interest-rate paths become quasi-identical across regimes under imperfect credibility.
  - The efficient horizon for returning inflation to target lengthens enormously (suggested ten-year period in the narrative), though the path implies that after 2½ years the deviation may already be below ½ of a percent.
- Policy corollaries under imperfect credibility:
  - Cross-correlation between credibility shock and oil shock is endogenous; earlier, stronger action can reduce the overall shock magnitude and output variability costs.
  - Central bank communication is crucial: transparent explanation of strategy and horizon for returning inflation to target can reduce target disbelief and associated costs.

### Bracing for future shocks — stochastic scenarios and optimized simple-rule coefficients
- Back-of-envelope: every 1 quadrillion Btu increase in world liquid-fuel demand produced a US$5 increase in oil prices over past 5 years; at current projected demand growth, this implies additional crude price increase of about US$ 90 over next 5 years (other things equal).
- Markov-chain scenarios for the next 12 quarters (two-state low/high mean and volatility; low→high switch probability 0.02; high state persistence 0.9999; high state maintained for 12 quarters then scenario-specific evolution):
  - Scenario 1 (L-H-H): jump to 2008 Q2 level and remain
  - Scenario 2 (L-H-HH): jump to 2008 Q2 level then to a higher level
  - Scenario 3 (L-H-M): jump to 2008 Q2 level then revert to an intermediate level
  - Scenario 3A (L-H-L): revert to low state
- Optimized simple-rule coefficients under scenarios (Table 6):
  - Scenario 1 (L-H-H): ψπ = 3.61; ψΔy = 0.052; γ = 1.15
  - Scenario 2 (L-H-HH): ψπ = 4.13; ψΔy = 0.048; γ = 1.14
  - Scenario 3 (L-H-M): ψπ = 4.12; ψΔy = 0.049; γ = 1.10
  - Scenario 3A (L-H-L): ψπ = 4.00; ψΔy = 0.050; γ = 1.15
  - Memo: unit shock: ψπ = 4.55; ψΔy = 0.020; γ = 1.15
- Key scenario findings:
  - Central bank needs to react strongly to close inflation gap quickly in all scenarios.
  - Interest-rate smoothing (γ > 1) is necessary to ensure determinacy and strengthen policy signaling.
  - Feedback on output growth remains small.
  - No large difference in optimal reaction between some scenarios (e.g., Scenario 2 vs Scenario 3A): bank should remain aggressive responding to inflation deviations even after a drop in real oil price if inflation volatility remains high.

### Concluding policy implications and actionable findings
- Optimal response to a 2000s-type oil shock: aggressive increases in real interest rates to close the inflation gap over the minimum efficient policy horizon; repeated nominal-rate rises strengthen determinacy and anti-inflation signaling.
- Failure to raise real rates promptly has contributed to inflation rises and unanchored inflation expectations in several emerging markets.
- Under a symmetric inflation target, policy should remain aggressive even if adverse supply shock is followed by favorable ones, because objective minimization is in absolute deviations.
- It takes time to rein in large oil shocks; repeated shocks imply accumulation and overlapping impulse responses, substantially lengthening efficient horizons (potentially 2–3 times longer for multiple shocks).
- Loss of target credibility dramatically worsens policy dilemmas: requires larger interest-rate gyrations and larger output-gap losses; therefore:
  - Acting more aggressively early can contain overall shock magnitude and reduce output costs.
  - Clear, transparent central bank communication on strategy and horizon for returning inflation to target can minimize target disbelief and materially improve outcomes.

*Source: _wp09101 - Section 4 summarizes results on optimal policy rules and optimal horizons. Section 5 revisits — IMF working paper content provided in the prompt.*

### REFERENCES

### _wp09101 - REFERENCES

### Bibliographic references (selected topical groupings)
- Monetary policy rules and interest rate rules:
  - Ball, L., 1999. Policy rules for open economies. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 127-144.
  - Batini, N., Haldane, A.G., 1999. “Forward-looking rules for monetary policy”. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 157-192.
  - McCallum, B.T., Nelson, E., 1999a. “Performance of operational policy rules in an estimated semi-classical structural model”. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 15-45.
  - McCallum, B.T., Nelson, E., 1999b. “Nominal income targeting in an open-economy optimizing model”, Journal of Monetary Economics 43: 553-578.
  - Rotemberg, J.J., Woodford, M., 1999. “Interest rate rules in an estimated sticky-price model”. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 57-119.
  - Rudebusch, G.D., Svensson, L.E.O., 1999. “Policy rules for inflation targeting”. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 203-246.
  - Taylor, J.B., 1993. “Discretion versus policy rules in practice”. Carnegie-Rochester Series on Public Policy 39: 195-214.
  - Taylor, J.B., 1999. “The robustness and efficiency of monetary policy rules as guidelines for interest rate setting by the European Central Bank”, Journal of Monetary Economics, Elsevier, vol. 43(3): 655-679.
  - King, R.G., Wolman, A.L., 1999. “What should the monetary authority do when prices are sticky?”. In: Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago: 349-398.
  - McCallum, B. T., 2001. "Should Monetary Policy Respond Strongly to Output Gaps?" American Economic Review Papers and Proceedings, 91(2) (May) pp. 258-262.
  - Rudebusch, G.D., 2000. “Assessing nominal income rules for monetary policy with model and data uncertainty”, ECB Working Paper No. 14.

- Oil price shocks, pass-through, and macroeconomic effects:
  - Bernanke, B., Gertler, M. and M. Watson, 1997. “Systematic Monetary Policy and the Effect of Oil price Shocks”, Brooking Papers on Economic Activity, 1997 (1): 91-142.
  - Bernanke, B., Gertler, M. and M. Watson, 2004. "Reply to Oil Shocks and Aggregate Macroeconomic Behavior: The Role of Monetary Policy: Comment”, Journal of Money, Credit, and Banking, 36 (2): 286-291.
  - Blanchard, O., Galí, J., 2007. “The Macroeconomic Effects of Oil Shocks: Why are the 2000s So Different from the 1970s?” NBER Working Papers 13368, National Bureau of Economic Research.
  - Hamilton, J. and A. M. Herrera, 2004. “Oil Shocks and Aggregate Macroeconomic Behavior: The Role of Monetary Policy”, Journal of Money, Credit and Banking, 36(2): 265-86.
  - Hooker, M., 1996. “What Happened to the Oil Price Macroeconomy Relationship?” Journal of Monetary Economics, 38: 195-213.
  - Hooker, M., 2002. “Are Oil Shocks Inflationary? Asymmetric and Nonlinear Specifications versus Changes in Regime”, Journal of Money, Credit and Banking, vol. 34(2): 540-561.
  - Kilian, L., 2007. “The Economic Effects of Energy Price Shocks”, CEPR Discussion Papers 6559.
  - De Gregorio, J., Landerretche, O., Neilson, C., 2007. “Another Pass-Through Bites the Dust? Oil Prices and Inflation”. Central Bank of Chile Working Papers 417, Central Bank of Chile.
  - Davis, M. and J. Hamilton, 2003. “Why Are Prices Sticky?” The Dynamics of Wholesale Gasoline Prices”, NBER Working Papers 9741, Cambridge, Mass.: National Bureau of Economic Research.
  - Edelstein, P. and L. Kilian, 2007. “Retail Energy Prices and Consumer Expenditures”, CEPR Discussion Paper No. 6255.
  - Energy Information Administration, 2008, 2008 International Energy Outlook, Office of Integrated Analysis and Forecasting, U.S. Department of Energy, Washington, D.C..

- Modeling, DSGE, credibility, and pass-through:
  - Batini, N., Nelson, E., 2001. "Optimal horizons for inflation targeting", Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7): 891-910.
  - Batini, N., Jackson, B., Nickell, S., 2005. “An open-economy new Keynesian Phillips curve for the U.K.”, Journal of Monetary Economics, Elsevier, vol. 52(6): 1061-1071.
  - Batini, N., Justiniano, A., Levine, P., and J. Pearlman, 2006. “Robust Control Monetary Policy Rules to Shield Against Indeterminacy”, Journal of Economic Dynamics and Control, 30(9-10): 1491-1526.
  - Batini, N., Levine, P., Pearlman, J., 2007. “Monetary Rules in Emerging Economies with Financial Market Imperfections”, Presented to the NBER Conference on International Dimensions of Monetary Policy, S'Agaro, Catalonia, Spain, June 11-13, 2007 and forthcoming in NBER Conference Volume, International Dimensions of Monetary Policy, ed. J. Gali and M. Gertler.
  - Medina, J. P. and C. Soto, 2005. “Oil Shocks and Monetary Policy in an Estimated DSGE Model for a Small Open Economy”, Central Bank of Chile WP No. 353.
  - Montoro, C., 2007. “Oil Shocks and Optimal Monetary Policy”, Central Bank of Peru Working Papers 2007-010, Lima.
  - Erceg, C., Levin, A., 2003. “Imperfect credibility and inflation persistence”. Journal of Monetary Economics, Elsevier, vol. 50(4): 915-944.
  - Fuhrer, J. 2000. “Habit Formation in Consumption and Its Implications for Monetary-Policy Models”. American Economic Review, American Economic Association, vol. 90(3): 367-390.
  - Fuhrer, J.C., 1997. “The (un)importance of forward-looking behavior in price specifications”. Journal of Money, Credit, and Banking 29: 338-350.
  - Galí, J., Gertler, M. 1999. “Inflation dynamics: A structural econometric analysis”. Journal of Monetary Economics, Elsevier, vol. 44(2): 195-222.
  - Carlstrom, C. and T. S. Fuerst, 2006. “Oil prices, Monetary Policy, and Counterfactual Experiments”, Journal of Money, Credit and Banking, vol. 38(7): 1945-1958.
  - De Fiore, F., Lombardo, G. and V. Stebunovs, 2006. “Oil Price Shocks, Monetary Policy Rules and Welfare”. Computing in Economics and Finance 2006, Society for Computational Economics.
  - Herrera, A. M. and E. Pesavento, 2007. “Oil price Shocks, Systematic Monetary Policy and the ‘Great Moderation’”. Mimeo, Michigan State University.
  - Bernanke, B., Gertler, M. and M. Watson (2004) — reply piece on role of monetary policy in oil shocks (Journal of Money, Credit, and Banking, 36 (2): 286-291).

### Figures and empirical displays (captions, axes, and formulas preserved exactly)
- Figure 1. Oil Developments 1970 Q1-2008 Q1
  - Axes and series labels preserved exactly:
    - "Oil price ($/barrel, left axis)"
    - "G3 inflation (GDPD,% yoy)"
    - "G3 inflation (CPI,% yoy)"
    - "IT EME inflation (CPI,% yoy)"
    - "Oil price and inflation"
    - "USA_GDPDIT EME (CPI)"
    - "G3 (GDPD)G3 (CPI)"
    - "Log Real Oil Price 1970=100"
    - "Oil price $/barrel"
    - "Real oil price log scale, 1970=100"
  - Time markers on charts preserved exactly: "70   73   76   79   82   85   88   91   94   97   00   03   06".

- Panel 1: Inflation Response to a Unit Shock to the Real Log-Level Price of Oil — Full Target Credibility Case
  - Plotted responses and series labels preserved exactly:
    - "Inflation Response--Complex Rule"
    - "Output Gap Response--Complex Rule"
    - "Interest Rate Response--Complex Rule"
    - "Inflation Response--Simple Rule"
    - "Output Gap  Response--Simple Rule"
    - "Interest Rate Response--Simple Rule"
  - Horizontal axis tick labels preserved exactly: "1  3  5  7  9 1113151719212325272931"
  - Regime labels preserved exactly: "Stable", "Quasi-", "Explosive".

- Panel 2: Inflation Response to a Unit Shock to the Real Log-Level Price of Oil (cont.) — Full Target Credibility Case
  - Additional scenario labels and series preserved exactly:
    - "1970s", "High Passthrough 1970s"
    - "Inflation Response--Complex Rule"
    - "Output Gap Response--Complex Rule"
    - "Interest Rate Response--Complex Rule"
    - "Inflation Response--Simple Rule"
    - "Output Gap  Response--Simple Rule"
    - "Interest Rate Response--Simple Rule"
  - Horizontal axis tick labels preserved exactly: "1   3   5   7   9  11 13 15 17 19 21 23 25 27 29 31" and "135791113151719212325272931".

- Panel 3: Inflation Response to a Unit Shock to the Real Log-Level Price of Oil (cont.) — Imperfect Target Credibility Case
  - Series and labels preserved exactly:
    - "Inflation Response--Simple Rule--Imperfect Target Credibility"
    - "Output Gap Response--Simple Rule--Imperfect Target Credibility"
    - "Interest Rate Response--Simple Rule--Imperfect Target Credibility"
    - "1970s", "High Passthrough 1970s"
  - Horizontal axis tick labels preserved exactly: "1  3  5  7  9 1113151719212325272931" and "1   3   5   7   9  11 13 15 17 19 21 23 25 27 29 31" and "135791113151719212325272931".

- Panel 4: Alternative Oil Price Scenarios
  - Charts and annotations preserved exactly:
    - Vertical/horizontal axis tick labels shown as numeric sequences: "50 100 150 200 250", and change axes values like "-5 0 5", "-10 0 10 20", "-2 0 2 4", "-4 -2 0 2 4".
    - Formula preserved exactly:
      - "Real oil price: roil_t = μ_M + σ_M * ε_roil_t; ε_roil_t = ρ * ε_roil_t + e_t"
    - Scenario labels preserved exactly:
      - "Scenario=1 ρ=0.99"
      - "Scenario=2 ρ=0.99"
      - "Scenario=3 ρ=0.99"
      - "Scenario=3 Alternative ρ=0.99"
    - Change and level labels preserved exactly:
      - "Change in real oil price: roil_t - roil_t-1"
      - "Real oil price: roil_t = μ_M + σ_M * ε_roil_t; ε_roil_t = ρ * ε_roil_t + e_t"
      - "roil_t - roil_t-1" and "roil_t"

*Source: _wp09101 - REFERENCES (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09101.pdf_