## 5. Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply Shock in an Economy with High Inflation and Low Initial Credibility (No Delay Triangle; Delay Circle)

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### Model structure, calibration, and key mechanics
- Core model:
  - Expectations-augmented Phillips curve, an output gap equation, and a real exchange rate (real uncovered interest parity) equation.
  - Monetary policy chosen by minimizing a loss function rather than via a Taylor rule.
- Selected calibration parameters (as reported in the text):
  - Phillips-curve parameters: 1 = 0.75; 2 = 0.25; 3 = 0.10.
  - Output-gap dynamics: 1 = 0.75; 2 = 0.10; 3 = 0.20; 4 = 0.10; 5 = 0.20.
  - Expected real exchange-rate inertial weight: ' = 0.90.
  - Credibility-convergence parameter:  = 0.18.
  - Maximum output gap: y_max = 5 percent.
- Monetary policy loss function (two cases shown):
  - Loss_t = Σ_{t=1}^{T} [!1 (π_t - π^*)^2 + !2 y_t^2 + !3 (rs_t - rs_{t-1})^2].
  - Case 1 weights: !1 = 1; !2 = 1; !3 = 1.
  - Case 2 weights: !1 = 1; !2 = 0.25; !3 = 0.25.
- Endogenous credibility:
  - Expectations weight on forward-looking component, τ_t, evolves between 0 and 1 and is driven by a credibility coefficient (_t) that compares hypothetical `L' (convergence to target) and `H' (convergence to 40 percent) inflation scenarios.
  - Credibility stock evolves: τ_t =  τ_{t-1} + (1 - ) _{t-1} + error.

### Optimal disinflation: initial conditions and quantified outcomes
- Representative initial economy for disinflation exercises:
  - Initial inflation: 8 percent.
  - Long-term target (π^*): 3 percent.
  - Equilibrium real interest rate: 2.5 percent.
  - Initial nominal interest rate: 10.5 percent.
  - Initial output gap: 0.
  - Central bank announces target at period 0 and adjusts policy starting period 1.
- Disinflation outcomes by initial credibility (all numbers preserved exactly):
  - Initial credibility = 0:
    - Nominal interest rates rise by about two percentage points and remain above initial level for over a year.
    - Output gap declines to below minus 2% and excess supply persists for six years.
    - It takes more than four years to reach the 3% inflation target.
    - Sacrifice ratio ≈ 1.35 (foregone output ≈ 6 3/4 percent of GDP for the five percentage point decline in inflation).
  - Initial credibility = 1 (full credibility):
    - Inflation declines to 3 percent about two years after commitment.
    - Excess supply never falls below 1 percent; output returns to potential fairly quickly.
    - Sacrifice ratio just under 0.25 (foregone output = 1 1/4 percent of GDP).
    - Nominal rate declines throughout the disinflation phase because expected inflation premium falls.
  - Initial credibility = 0.5:
    - About three years to reach the 3% target.
    - Sacrifice ratio ≈ 0.75.
    - Nominal interest rates decline very little over much of the first year.
  - Exogenously held credibility = 0 for eight quarters vs. endogenous τ starting at 0:
    - Exogenous zero-credibility case takes about two years longer to reach 3% than endogenous-zero case.
    - Sacrifice ratio rises from about 1.35 (endogenous) to about 2 (exogenous-zero).
- Sensitivity to loss-function weights:
  - When policymakers place much less weight on output deviations and interest-rate variability (Case 2), simulations produce higher interest rates, greater excess supply, and a higher sacrifice ratio, but somewhat faster movement of inflation to equilibrium.

### Responses to shocks — quantified scenarios and asymmetries
- Shock setups:
  - Supply shocks: one-off ±3 percent shocks to the inflation-equation disturbance.
  - Demand shocks: one-off ±1.0 percent of GDP shocks to the output-gap disturbance.
  - Two economy types for shock experiments:
    - High-credibility economy: credibility = 0.75; nominal rate = 4.0%; real rate = 2.0%; output gap = +1%.
    - Low-credibility economy: inflation = 8%; credibility = 0.25; nominal rate = 7% (real = -1% given equilibrium real = 2.5%); output gap = +1%.
- Supply shocks — high credibility (0.75):
  - Unfavorable supply shock (+3 percent):
    - Nominal rate peak about 2 percentage points above baseline; less than 100 basis points above baseline after about a year.
    - Domestic currency appreciates just over 1% for about a year.
    - Inflation reverses after about a year and returns to baseline after about two years, followed by a small undershoot.
    - Output gap moves into excess supply by less than one percentage point.
  - Favorable supply shock (−3 percent):
    - Interest rates hardly adjust because shock reduces inflation and offsets positive initial output gap pressures.
- Supply shocks — low credibility (0.25) and problematic initial conditions:
  - Unfavorable supply shock (+3 percent):
    - Nominal interest rate rises from 7% to almost 15% subsequent to the shock.
    - Inflation rises to almost 10% over the first year.
    - Output gap falls to -3% during the second year and remains below baseline for over six years.
    - Exchange-rate appreciation accompanies policy tightening for a couple of years.
    - Credibility stock rises only slowly because high inflation increases skepticism.
  - Favorable supply shock (−3 percent):
    - Helps the disinflating economy: smaller output gaps, lower nominal rates, and lower transitional inflation than baseline, though interest rates still must rise because of initial negative real rates and excess demand.
- Demand shocks:
  - Expansionary demand shock (+1.0 percent of GDP):
    - Appropriate policy: prompt, sharp interest-rate rise of 2–3 percentage points above baseline in periods 2 and 3.
    - Implied peak policy rate: about 7 1/2% for the high-credibility economy; about 15% for the low-credibility economy.
    - Real exchange rate appreciates as much as 3% relative to baseline, then depreciates back.
    - Robust tightening eliminates the positive output gap within a year and keeps inflation close to baseline while maintaining credibility.
  - Contractionary demand shock (−1.0 percent of GDP):
    - Requires less policy action; effects align with closing the initial positive output gap.
- General asymmetry and interpretation:
  - Policy must respond more vigorously to unfavorable supply shocks (inflationary) than to favorable ones.
  - High credibility greatly mitigates the amplification and persistence of supply shocks because expectations are better anchored.
  - Low credibility creates self-reinforcing inflation-expectation dynamics that amplify policy costs and generate prolonged output losses (stagflation).

### Costs of delaying interest-rate increases (primary explicit finding)
- Scenario: low-credibility economy hit by an unfavorable supply shock in period 1 but the central bank delays required interest-rate increases until period 3.
- Quantified consequences:
  - Delayed response produces serious inflationary consequences relative to the optimal immediate response: inflation deviates considerably above the optimal path for several years.
  - After the two-quarter hesitation, interest rates must “catch up” and ultimately rise to higher levels than in the optimal-response scenario and remain higher for more than five years.
  - Short-run demand support from delay is bought at the cost of much higher inflation and higher nominal interest rates for a considerable length of time.
  - The delay leads to an erosion of credibility: the stock of credibility remains below baseline as inflation rises above baseline.
  - Net macroeconomic outcome: several years of stagflation (higher inflation, prolonged negative output gaps), and greater exposure to subsequent unfavorable supply shocks.

### Policy implications and recommendations emphasized by the simulations
- Credibility matters critically:
  - Greater initial credibility reduces both the necessary short-run output sacrifice and the required peak interest-rate adjustments in disinflation.
  - Building and communicating credibility early reduces long-run costs of disinflation.
- Policy timing and firmness:
  - When confronted with unfavorable supply shocks during disinflation under imperfect credibility, prompt and sufficiently large interest-rate hikes are required; postponing tightening converts a short-run policy easing into a long-run high-rate regime and prolonged stagflation.
- Communications and target-setting:
  - Announce a long-run inflation target and present intermediate disinflation paths as conditional forecasts rather than rigid interim targets.
  - Explain to the public how shocks (especially unfavorable supply shocks) alter the optimal path and the trade-offs between inflation and output in the medium term.
- Flexibility within commitment:
  - Flexible inflation targeting that recognizes short-run trade-offs (output and interest-rate variability) is preferable to rigid adherence to narrow short-run targets, but flexibility must be consistent with the long-run low-inflation objective.
- Opportunistic disinflation caveat:
  - Waiting for favorable supply shocks to reduce disinflation costs (“opportunistic disinflation”) risks undermining credibility in a stochastic environment, potentially worsening outcomes.

*Source: IMF Working Paper chapter "5. Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply Shock in an Economy with High Inflation and Low Initial Credibility" (content unit: _wp0994 - 5).*

### References..............................................................................................................

### _wp0994 - References..............................................................................................................

### References
- References................................................................................................................................23

### Figures
- 1. Disinflation with Equal Weights on Inflation, Output and 
  Interest Rate Variability ......................................................................................26
- 2. Disinflation with Lower Weights on Output and Interest Rate Variability .................27
- 3. Responses to Unfavorable and Favorable Supply Shocks (Positive Shock 
  Circle; Negative Shock Triangle) .......................................................................28
- 4. Responses to Positive and Negative Demand Shocks (Positive Shock Circle 
  Negative Shock Triangle.....................................................................................29

*_wp0994 - References_*>

### 5. Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply

### 5. Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply Shock in an Economy with High Inflation and Low Initial Credibility (No Delay Triangle; Delay Circle)

### Model structure, calibration, and key mechanics
- Core model: expectations-augmented Phillips curve, an output gap equation, and a real exchange rate (real uncovered interest parity) equation; monetary policy chosen by minimizing a loss function rather than via a Taylor rule.
- Selected calibration parameters (as reported in the text):
  - Phillips-curve parameters: 1 = 0.75; 2 = 0.25; 3 = 0.10.
  - Output-gap dynamics: 1 = 0.75; 2 = 0.10; 3 = 0.20; 4 = 0.10; 5 = 0.20.
  - Expected real exchange-rate inertial weight: ' = 0.90.
  - Credibility-convergence parameter:  = 0.18.
  - Maximum output gap: y_max = 5 percent.
- Monetary policy loss function (two cases shown):
  - Loss_t = Σ_{t=1}^{T} [!1 (π_t - π^*)^2 + !2 y_t^2 + !3 (rs_t - rs_{t-1})^2].
  - Case 1 weights: !1 = 1; !2 = 1; !3 = 1.
  - Case 2 weights: !1 = 1; !2 = 0.25; !3 = 0.25.
- Endogenous credibility:
  - Expectations weight on forward-looking component, τ_t, evolves between 0 and 1 and is driven by a credibility coefficient (_t) that compares hypothetical `L' (convergence to target) and `H' (convergence to 40 percent) inflation scenarios.
  - Credibility stock evolves: τ_t =  τ_{t-1} + (1 - ) _{t-1} + error.

### Optimal disinflation: initial conditions and quantified outcomes
- Representative initial economy for disinflation exercises:
  - Initial inflation: 8 percent.
  - Long-term target (π^*): 3 percent.
  - Equilibrium real interest rate: 2.5 percent.
  - Initial nominal interest rate: 10.5 percent.
  - Initial output gap: 0.
  - Central bank announces target at period 0 and adjusts policy starting period 1.
- Disinflation outcomes by initial credibility (all numbers preserved exactly):
  - Initial credibility = 0:
    - Nominal interest rates rise by about two percentage points and remain above initial level for over a year.
    - Output gap declines to below minus 2% and excess supply persists for six years.
    - It takes more than four years to reach the 3% inflation target.
    - Sacrifice ratio ≈ 1.35 (foregone output ≈ 6 3/4 percent of GDP for the five percentage point decline in inflation).
  - Initial credibility = 1 (full credibility):
    - Inflation declines to 3 percent about two years after commitment.
    - Excess supply never falls below 1 percent; output returns to potential fairly quickly.
    - Sacrifice ratio just under 0.25 (foregone output = 1 1/4 percent of GDP).
    - Nominal rate declines throughout the disinflation phase because expected inflation premium falls.
  - Initial credibility = 0.5:
    - About three years to reach the 3% target.
    - Sacrifice ratio ≈ 0.75.
    - Nominal interest rates decline very little over much of the first year.
  - Exogenously held credibility = 0 for eight quarters vs. endogenous τ starting at 0:
    - Exogenous zero-credibility case takes about two years longer to reach 3% than endogenous-zero case.
    - Sacrifice ratio rises from about 1.35 (endogenous) to about 2 (exogenous-zero).
- Sensitivity to loss-function weights:
  - When policymakers place much less weight on output deviations and interest-rate variability (Case 2), simulations produce higher interest rates, greater excess supply, and a higher sacrifice ratio, but somewhat faster movement of inflation to equilibrium.

### Responses to shocks — quantified scenarios and asymmetries
- Shock setups:
  - Supply shocks: one-off ±3 percent shocks to the inflation-equation disturbance (e.g., permanent world food-price shock).
  - Demand shocks: one-off ±1.0 percent of GDP shocks to the output-gap disturbance.
  - Two economy types for shock experiments:
    - High-credibility economy: credibility = 0.75; nominal rate = 4.0%; real rate = 2.0%; output gap = +1%.
    - Low-credibility economy: inflation = 8%; credibility = 0.25; nominal rate = 7% (real = -1% given equilibrium real = 2.5%); output gap = +1%.
- Supply shocks — high credibility (0.75):
  - Unfavorable supply shock (+3 percent):
    - Nominal rate peak about 2 percentage points above baseline; less than 100 basis points above baseline after about a year.
    - Domestic currency appreciates just over 1% for about a year.
    - Inflation reverses after about a year and returns to baseline after about two years, followed by a small undershoot.
    - Output gap moves into excess supply by less than one percentage point.
  - Favorable supply shock (−3 percent):
    - Interest rates hardly adjust because shock reduces inflation and offsets positive initial output gap pressures.
- Supply shocks — low credibility (0.25) and problematic initial conditions:
  - Unfavorable supply shock (+3 percent):
    - Nominal interest rate rises from 7% to almost 15% subsequent to the shock.
    - Inflation rises to almost 10% over the first year.
    - Output gap falls to -3% during the second year and remains below baseline for over six years.
    - Exchange-rate appreciation accompanies policy tightening for a couple of years.
    - Credibility stock rises only slowly because high inflation increases skepticism.
  - Favorable supply shock (−3 percent):
    - Helps the disinflating economy: smaller output gaps, lower nominal rates, and lower transitional inflation than baseline, though interest rates still must rise because of initial negative real rates and excess demand.
- Demand shocks:
  - Expansionary demand shock (+1.0 percent of GDP):
    - Appropriate policy: prompt, sharp interest-rate rise of 2–3 percentage points above baseline in periods 2 and 3.
    - Implied peak policy rate: about 7 1/2% for the high-credibility economy; about 15% for the low-credibility economy (due in part to low real rates initially).
    - Real exchange rate appreciates as much as 3% relative to baseline, then depreciates back.
    - Robust tightening eliminates the positive output gap within a year and keeps inflation close to baseline while maintaining credibility.
  - Contractionary demand shock (−1.0 percent of GDP):
    - Requires less policy action; effects align with closing the initial positive output gap.
- General asymmetry and interpretation:
  - Policy must respond more vigorously to unfavorable supply shocks (inflationary) than to favorable ones.
  - High credibility greatly mitigates the amplification and persistence of supply shocks because expectations are better anchored.
  - Low credibility creates self-reinforcing inflation-expectation dynamics that amplify policy costs and generate prolonged output losses (stagflation).

### Costs of delaying interest-rate increases (primary explicit finding)
- Scenario: low-credibility economy hit by an unfavorable supply shock in period 1 but the central bank delays required interest-rate increases until period 3.
- Quantified consequences (as described in the text and figures):
  - Delayed response produces serious inflationary consequences relative to the optimal immediate response: inflation deviates considerably above the optimal path for several years.
  - After the two-quarter hesitation, interest rates must “catch up” and ultimately rise to higher levels than in the optimal-response scenario and remain higher for more than five years.
  - Short-run demand support from delay is bought at the cost of much higher inflation and higher nominal interest rates for a considerable length of time.
  - The delay leads to an erosion of credibility: the stock of credibility remains below baseline as inflation rises above baseline.
  - Net macroeconomic outcome: several years of stagflation (higher inflation, prolonged negative output gaps), and greater exposure to subsequent unfavorable supply shocks.

### Policy implications and recommendations emphasized by the simulations
- Credibility matters critically:
  - Greater initial credibility reduces both the necessary short-run output sacrifice and the required peak interest-rate adjustments in disinflation.
  - Building and communicating credibility early reduces long-run costs of disinflation.
- Policy timing and firmness:
  - When confronted with unfavorable supply shocks during disinflation under imperfect credibility, prompt and sufficiently large interest-rate hikes are required; postponing tightening converts a short-run policy easing into a long-run high-rate regime and prolonged stagflation.
- Communications and target-setting:
  - Announce a long-run inflation target and present intermediate disinflation paths as conditional forecasts rather than rigid interim targets.
  - Explain to the public how shocks (especially unfavorable supply shocks) alter the optimal path and the trade-offs between inflation and output in the medium term.
- Flexibility within commitment:
  - Flexible inflation targeting that recognizes short-run trade-offs (output and interest-rate variability) is preferable to rigid adherence to narrow short-run targets, but flexibility must be consistent with the long-run low-inflation objective.
- Opportunistic disinflation caveat:
  - Waiting for favorable supply shocks to reduce disinflation costs (“opportunistic disinflation”) risks undermining credibility in a stochastic environment, potentially worsening outcomes.

*Source: IMF Working Paper chapter "5. Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply Shock in an Economy with High Inflation and Low Initial Credibility" (content unit: _wp0994 - 5).*

### References

### References

### Monetary policy credibility, inflation targeting, and disinflation
- Argov, E. N. Epstein, P. Karam, D. Laxton, and D. Rose, 2007, ìEndogenous Monetary Policy Credibility in a Small Macro Model of Israel,î IMF Working Paper 07/207 (Washington: International Monetary Fund).
- Batini, N., K. Kuttner, and D. Laxton, 2005, ìDoes Ination Targeting Work in Emerging Markets?î Chapter 4 (September 2005)World Economic Outlook,International Monetary Fund, available at www.imf.org.
- Batini, N. and D. Laxton, 2007, ìUnder What Conditions Can Ination Targeting Be Adopted? The Experience of Emerging Markets,'inMonetary Policy Under Ination Targeting,îed. by F. S. Mishkin and K. Schmidt-Hebbel (Chile: Banco Central de Chile), pp. 467ñ506.
- Debelle, G., and D. Laxton, 1997, ìIs the Phillips Curve Really A Curve? Some Evidence for Canada, The United Kingdom and the United States,î Staff Papers, International Monetary Fund, Vol. 44, No. 2, June, pp. 249ñ82.
- Freedman, C., D. Laxton, and I. ÷tker-Robe, 2009, ìInation Targeting: Saying What You Do and Doing What You Say,î forthcoming.
- Goretti, M. and D. Laxton, 2005, ìLong-Term Ination Expectations and Credibility,î Box 4.2 in Chapter 4 (September 2005),World Economic Outlook, International Monetary Fund, available at www.imf.org.
- Isard, P., D. Laxton, and A. Eliasson, 2001, ìInation Targeting with NAIRU Uncertainty and Endogenous Policy Credibility,îJournal of Economic Dynamics & Control, Vol. 25, pp. 115ñ48.
- Laxton, D., and P. N'Diaye, 2002, ìMonetary Policy Credibility and the Unemployment-Ination Trade-Off: Some Evidence from 17 Industrial Countries,î IMF Working Paper 02/220 (Washington: International Monetary Fund).
- Masson, P., M. Savastano, and S. Sharma, 1997, ìThe Scope for Ination Targeting in Developing Countries,î IMF Working Paper 97/130 (Washington: International Monetary Fund).
- Mishkin, F., and K. Schmidt-Hebbel, 2001, ìOne Decade of Ination Targeting in the World: What Do We Know and What Do We Need to Know?î in Norman Loayza and Raimundo Soto, eds., Ination Targeting: Design, Performance, Challenges (Central Bank of Chile: Santiago, 2001): pp. 117-219.
- Roger, S., and M. Stone, 2005, ìOn Target? The International Experience with Achieving Ination Targets,î IMF Working Paper 05/163 (Washington: International Monetary Fund).
- Svensson, L., 1997, ìInation Forecast Targeting: Implementing and Monitoring Ination Targets,îEuropean Economic Review41, pp. 1111-1146.

### Practical modeling, forecasting systems, and small open economy rules
- Berg, A., P. Karam, and D. Laxton, 2006a, ìA Practical Model-Based Approach to Monetary Policy AnalysisóOverview,î IMF Working Paper 06/080 (Washington: International Monetary Fund).
- óóó, 2006b, ìPractical Model-Based Monetary Policy AnalysisóA How-to Guide,î IMF Working Paper 06/081 (Washington: International Monetary Fund).
- Black, R., D. Laxton, D. Rose, and R. Tetlow, 1994, ìThe Steady-State Model: SSQPM,î The Bank of Canada's New Quarterly Projection System, Part 1, Bank of Canada, Technical Report No. 72.
- Coletti, D., Hunt, B., D. Rose, and R. Tetlow, 1996, ìThe Dynamic Model: QPM,î The Bank of Canada's New Quarterly Projection System, Part 3, Bank of Canada, Technical Report No. 75.
- Coats, W., D. Laxton and D. Rose, 2003, ìThe Czech National Bank's Forecasting and Policy Analysis System,î (Prague, Czech Republic: Czech National Bank).
- Hunt, B., D. Rose, and A. Scott, 2000, ìThe Core Model of the Reserve Bank of New Zealand's Forecasting and Policy System,î Economic Modelling 17, (April), pp. 247ñ74.
- Laxton, D., and P. Pesenti, 2003,ìMonetary Policy Rules for Small, Open, Emerging Economies,îJournal of Monetary Economics, Vol. 50 (July), pp. 1109ñ46.
- Smets, F., and R. Wouters, 2003, ìAn Estimated Stochastic Dynamic General Equilibrium Model of the Euro Area,îJournal of European Economics, Vol. 49, pp. 947ñ81.

### Supply and demand shocks, real wages, and macro dynamics
- Blanchard, O., and J. GalÌ, 2007, ìReal Wage Rigidities and the New Keynesian Model,îJournal of Money, Credit and Banking, Supplement to Vol. 39, No. 1, pp 35-65.
- Orphanides, A., and D. W. Wilcox, 2002, ìThe Opportunistic Approach to Disination,î International Finance, Vol. 5, pp. 47-71.
- Helbling, T., D. Laxton, V. Mercer-Blackman, and I. Tytell, 2008, ìIs Ination Back? Commodity Prices and Ination,î Chapter 3 (October 2008),World Economic Outlook, International Monetary Fund, available at www.imf.org.
- Levin, A., F. Natalucci and J. Piger, 2004, ìThe Macroeconomic Effects of Ination Targeting,î The Federal Reserve Bank of St. Louis Review, July/August, pp. 51-80.
- Woodford, M., 2003. ìOptimal Monetary Policy Inertia,îReview of Economic Studies, (2005), Vol. 70, pp. 861ñ86.
- óóó, 2005, ìCentral-Bank Communication and Policy Effectiveness,î Federal Reserve Bank of Kansas City, Jackson Hole Symposium The Greenspan Era: Lessons for the Future (August).

### Remarks, speeches, and overview pieces
- Meyer, L., 1996, ìMonetary Policy Objectives and Strategy,î Remarks Delivered at the National Association of Business Economists 38th Annual Meeting, Boston, Massachusetts September 8, 1996, http://www.federalreserve.gov/boarddocs/speeches/1996/19960908.htm
- Mishkin F., 2007, ìInation Dynamics,î Annual Macro Conference, Federal Reserve Bank of San Francisco, (March), http://www.federalreserve.gov/news events/speech/mishkin20070323a.htm
- The Economist, 2006, ìBig Questions and Big Numbers-Economic Models,î Special Report, (July), pp. 67ñ69.

### Figures listed in the source
- Figure 1: Disination with Equal Weights on Ination, Output and Interest Rate Variability
- Figure 2: Disination with Lower Weights on Output and Interest Rate Variability
- Figure 3: Responses to Unfavorable and Favorable Supply Shocks (Positive Shock Circle; Negative Shock Triangle)
- Figure 4: Responses to Positive and Negative Demand Shocks (Positive Shock Circle; Negative Shock Triangle)
- Figure 5: Cost of Delaying Interest Rate Hikes in Response to an Unfavorable Supply Shock in an Vulnerable Emerging-Market Economy with High Ination and Low Initial Credibility (No Delay Triangle; Delay Circle)

*Source: _wp0994 - References*

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