## 1. Interest Rates, Inflation, Exchange Rate, Growth and Unemployment Rate, 2001–04... 18

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### I. Introduction and purpose
- Small-scale structural macro models produce coherent forecast scenarios and policy analysis inside policy institutions.
- Model basis and scope:
  - Model developed based on the small linear model of the Israeli economy documented in Epstein and others (2006).
  - Resembles standard New Keynesian open-economy models (Svensson (2000); Gali and Monacelli (2005)) but lacks explicit micro foundations.
- Limitations of linear models highlighted:
  - Simulation properties are independent of initial conditions.
  - Impulse responses are linear functions of disturbance magnitudes.
  - May not capture effects of large shocks or policy decisions that induce loss of monetary policy credibility.

### II. Extension of the linear model: nonlinearity and endogenous credibility — objectives and approach
- Purpose of extension:
  - Capture strong reaction of the Israeli economy to sharp policy interest rate cuts and prolonged erosion in policy credibility, focusing on the 2001–2003 episode.
  - Argue that loss of policy credibility was costly and prevented the central bank from properly responding to fundamentals.
- Methodology:
  - Extend the small linear model with features of nonlinearity (in the Phillips curve) and endogenous policy credibility.
  - Allow the model to revert to the standard linear case with minimal changes if calibrated accordingly.
- Claimed model performance:
  - Standard linear model cannot explain the 2001–2003 episode very well.
  - Extended model, permitting nonlinearities in the output-inflation process and endogenous credibility, better replicates the stylized facts of the historical episode.

### III. Concept and measurement of credibility
- Definitions and measures of monetary policy credibility cited:
  - (i) deviations of inflation expectations from the central bank’s target;
  - (ii) variation in long-term interest rates, long-term inflation expectations and the public’s assessment of the central bank’s ability to achieve the target;
  - (iii) the extent to which the public believes the announced target is the central bank’s actual target;
  - (iv) the gap between central bank’s objectives and the public’s perception of these objectives.
- Literature references informing the credibility concept include Cukierman and Meltzer (1986); Bomfim and Rudebusch (2000); Faust and Svensson (2001); Laxton and N'Diaye (2002); Stiver (2003); Rebucci and Rossi (2006).

### IV. Channels through which credibility affects outcomes
- Three main channels modeled:
  - First: Lack of credibility causes a positive inflation expectations bias, increasing inflation through the expectations term in the Phillips Curve (Isard, Laxton and Eliasson, 2001).
  - Second: Buildup in credibility shifts public expectations of future inflation closer to announced targets rather than past inflation, lowering the weight on backward-looking expectations and improving the inflation-output tradeoff.
  - Third: Credibility affects the risk premium in the interest parity (IP) condition, influencing exchange rate dynamics.

### V. Standard FPAS model structure for Israel — key equations and calibration
- Model blocks:
  - Domestic (small Israeli economy) and Rest of the World (U.S.) blocks.
- Domestic output gap equation:
  - Output gap depends on real interest rate (RR), real exchange rate (z, logs, increase = depreciation), U.S. output gap (yusgap), and dynamics via past and future domestic output gaps.
  - Output gap measured in percentage points as deviation of actual output from trend.
- Domestic Phillips curve:
  - Inflation (4tπ = four-quarter CPI change) depends on expected four-quarter inflation (4etπ), lagged inflation, output gap, exchange rate gap, and movements in the real (relative) price of oil.
  - Inflation measurement: annualized quarterly change in percent via log differences.
  - Inflation expectations combine model-consistent and backward-looking components; lead and lag weights (ldπα and eπα) determine responsiveness and persistence.
- Exchange rate equation:
  - Real interest parity condition: deviations of home and U.S. real interest rates from equilibrium and equilibrium risk premium (*)tρ drive deviations of real exchange rate z; residual interpreted as temporary shock to risk premium.
- Monetary policy rule:
  - Forward-looking Taylor-variant: interest rate set as a function of expected future inflation (4[+4]tπ), the output gap (t ygap), with smoothing (lag term); instrument is short-term nominal rate; policy anchors inflation to target *π.
- Calibration scenarios (from Epstein and others (2006) and alternatives used here):
  - Baseline aggregated lead weight: ldπα=0.1 and eπα=1.
  - “Increased credibility” alternative: ldπα=0.70 and eπα=0.5 giving an aggregated lead weight of 0.35.
  - Interpretation: higher lead weights imply inflation equals sum of future output and exchange rate gaps; low lead weights imply strong inertia and slow monetary effectiveness.

### VI. Historical perspective on 2001−03 and limits of the standard model
- Key observed events (2001−03, preserved magnitudes and chronology):
  - Late 2001: central bank cut policy rate by 200 basis points.
  - First half 2002: sheqel depreciated; headline inflation rose to 7 percent (y-o-y) by July, 2002.
  - Subsequent hikes: 450 basis points in three steps over five months.
  - Year-on-year inflation > 6 percent by second half 2002; nominal depreciation peaked at 16 percent.
  - Central bank held policy rate around 9 percent until mid-2003 despite recession.
  - Real GDP: contracted by 0.6 percent in 2001 and 0.9 percent in 2002; grew by 1.5 percent in 2003; recovery in 2004 with real GDP growth of 4.8 percent.
  - Long-run inflation expectations (3−4 years ahead) rose well above the 3 percent upper level of the target band from Q2 2002 to end-2003 even when actual inflation was below the 1−3 percent band for most of 2003.
  - Real market interest rates (policy rate minus one-year-ahead inflation expectations) rose to 6 percent during second half 2002 and remained around that level through mid-2003.
  - Unemployment rate reached 11 percent by end-2003.
  - By 2006: headline inflation overshot upper band due to exchange depreciation, record oil prices, reduced spare capacity; central bank response in 2006 was measured; long-run expectations descended toward midpoint of targeting range.
- Standard model simulation shortfalls:
  - Simulated temporary interest rate cut of 200 basis points for two quarters yields depreciation and gradual increases in output and inflation, but effects are much smaller than observed.
  - Standard model does not generate the large cumulative costs, sharp contractions, and persistent loss of credibility witnessed in 2001−03.

### VII. Extensions introduced — nonlinear Phillips curve and endogenous credibility (model specifics)
- Two main extensions:
  - Nonlinear effect of the output gap on inflation to produce severe inflationary and real costs following overly expansionary policy.
  - Endogenous credibility: raise backward-looking weight (1−eπα) in inflation expectations when credibility is low; allow higher exchange rate risk premium when credibility falls.
- Nonlinear Phillips curve specification:
  - Replace linear output gap term by maxmax t ygap t ygap y yygap α ⎛⎞ ⎜⎟ − ⎝⎠ .
  - Maximum output gap max y calibrated to equal 6 percent.
  - When output gap near zero, marginal effect equals linear case; as gap approaches max y, marginal effect on inflation becomes much stronger, inducing potential long periods of negative output gaps to return inflation to target.
- Credibility stock tγ:
  - Range: 0 (no credibility) to 1 (full credibility).
  - Two hypothetical inflation regimes define credibility:
    - ‘L’ (Low inflation) scenario: inflation converges to announced target *tπ via *1 40.54(1 0.5) L L tttt π ππ πε − =∗ +− ∗+ (equation (6)); calibrated coefficient on target set to 0.5.
    - ‘H’ (High inflation) scenario: inflation converges to *H tπ = 10.8 percent with estimated eπα = 0.45 via 1 40.554(1 0.55) 10.8 H H ttt π ππε − =∗ +− ∗+ (equation (7)); based on 1992−1996 data.
  - Credibility stock autoregression: 11 0.7(1 0.7) tttt γ γγλε −− =∗+− ∗+ (equation (8)); λt defined by 2 22 (44) (44) (44) H tt t HL tttt ππ λ ππ ππ − = − + − (equation (9)).
  - Interpretation of extremes:
    - ‘L’ case: λt = 1 → tγ converges to 1 (full credibility).
    - ‘H’ case: λt = 0 → tγ converges to 0 (no credibility).
- Channels of interaction:
  - Credibility affects a ‘bias’ factor in inflation expectations.
  - Credibility alters the weight of forward-looking behavior in pricing (Phillips curve lead weight).
  - Credibility affects the risk premium in the IP condition (exchange rate dynamics).

### VIII. Credibility mechanism, calibration, and expectation equations (detailed mechanics)
- Calibration and dynamics:
  - Credibility convergence rate calibrated to 0.7 (i.e., it takes 1.5−2.0 years for credibility to rebuild from below-full levels).
  - Credibility stock evolution restated: 11 0.7(1 0.7) tttt γ γ γλε −− = ∗ + − ∗ +  (equation A2).
  - Credibility indicator tλ defined via high/low expectation errors: 2 22 () () () H HL t t tt π π π ε λ ε ε = + (equation A3).
- Inflation expectations bias tb:
  - Defined as proportion of deviation of weighted average of the two forecasts from the inflation target with weights reflecting tγ:
    - () () ,, * 0.15414 eLeH tttttt bγπγππ = ∗ + − ∗ −  (equation 13 / A9).
  - As tγ → 1, bias b → 0; as tγ → 0, bias equals difference between high inflation expectations and target.
- One-year-ahead inflation expectations:
  - Combine backward- and forward-looking components and the bias term via 41 4414 22 e e tt ttttt b π γ γ π π πε +− ⎛⎞ ⎛ ⎞ = + − ++ ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠  (equation 10 / A6).
  - Hypothetical implied expectations:
    - (A7) 3 , * 4 0 4(1 0.5)0.50.54 eLi ttt i π π π = = − ∗ ∗ + ⋅ ∑
    - (A8) 3 , 4 0 4(1 0.55) 10.80.550.554 eHi tt i π π = = − ∗ ∗ + ⋅ ∑
  - Hypothetical L and H state processes reiterated:
    - (A4) * 1 40.54(1 0.5) L L t t t t π π π πε − = ∗ + − ∗ + .
    - (A5) 1 40.554(1 0.55) 10.8 H H t t t π π πε − = ∗ + − ∗ + .

### IX. Modified interest parity and quantitative linkage from credibility to risk premium
- Modified IP condition (including tb):
  - * 11 [] / 4 0.662.3() eusz tttt ttttt zzRRRRbbbρε +− = − − − + + − +  (equation 14 / A12).
- Quantitative example from model text:
  - A loss of credibility that generates a 1-percentage-point expectations bias will, temporarily, cause a 3 percent real depreciation and thereafter leave the country risk premium higher by 0.66 percent.

### X. Main model equations (as listed)
- Nonlinear inflation equation (A1) includes Phillips-curve elements plus credibility, backward-looking terms, real exchange rate, oil-price terms, and max output gap effects.
- Stock of credibility: A2 (convergence calibration 0.7).
- Indicator of credibility: A3.
- Hypothetical L and H processes: A4 and A5 (High case contains 10.8 value).
- One-year-ahead inflation expectations and bias: A6, A7, A8, A9.
- Output gap equation: A10.
- Monetary policy reaction function (inflation-forecast-based Taylor rule): A11.
- Modified interest parity (IP) including tb: A12.

### XI. Dynamic responses to shocks — principal quantitative findings (preserving stated magnitudes)
- Interest rate shock: 200 basis points cut for two quarters (extended model results):
  - Initial credibility = 1.0:
    - Credibility drops by 12 percent at its peak after 5 quarters.
    - Nominal exchange rate depreciates and peaks at 5.5 percent (above control).
    - Inflation peaks at 2.5 percentage points above control.
    - Interest rates must be raised to 350 basis points above control to rebuild credibility and return inflation to target (versus 150 basis points in the base-case linear scenario).
    - Peak output gap (boom) = 2.1 percentage points (versus 1.6 percentage points in base case).
    - Negative output gap trough = -0.8 percentage point below control during bust.
  - Initial credibility = 0.8:
    - Inflation peaks at more than 3.5 percentage points.
    - Exchange rate depreciation peaks at 8 percent.
    - Nominal interest rates reach 6 percentage points above control.
    - Output gap trough = -1.7 percentage points.
  - Initial credibility = 0.5:
    - Larger nominal and real responses; credibility falls less immediately but larger further deviations are required to restore credibility.
- Credibility shocks (no interest-rate shock):
  - Initial credibility = 1.0 versus 0.8:
    - Lower initial credibility (0.8) produces a larger expectations bias and higher risk premium.
    - Inflation peaks at 0.35 percentage points above control after one year (lower credibility scenario).
    - Regaining control requires nominal (and real) interest rate increases and causes output losses with a trough of -0.13 percentage point after six quarters.
    - Once credibility is disturbed, it takes over 2 years before monetary authorities can bring it back to control (text statement).
- Inflation (cost-push) shock: 1 percentage point for one quarter:
  - Linear model (no endogenous credibility): baseline behavior shown in Figure 9.
  - Endogenous credibility, initial credibility = 1.0 (Figure 10): only moderate loss in credibility with appropriate monetary response; inflation and interest rates only moderately higher.
  - Endogenous credibility, initial credibility = 0.5 (Figure 11): inflation outcomes somewhat higher but remain moderate.
  - General conclusion: credibility is usually lost as a result of policy errors, not normal economy shocks, provided the central bank reacts consistently and timely.

### XII. Policy implications and conclusions
- Model improvements and interpretive insights:
  - Nonlinear Phillips curve plus endogenous credibility improves ability to reproduce Israeli dynamics for late 2001.
  - Extended model captures deterioration in credibility and resulting movements in exchange rate, inflation and output following a policy-related shock.
  - Model reproduces relatively long time to rebuild credibility.
  - Bringing inflation back to target and rebuilding credibility can be very costly—interest rates must be raised substantially higher, inducing greater variability in output.
- Policy message:
  - Normal economic shocks, even large ones, need not erode credibility if the central bank reacts appropriately and timely.
  - Credibility is most at risk when policy itself is the source of the shock; policy errors can generate large exchange depreciation, higher inflation, and prolonged output costs through weakened credibility.

*IMF staff working-paper content from the supplied PDF excerpt.*

### 1. Interest Rates, Inflation, Exchange Rate, Growth and Unemployment Rate, 2001–04... 18

### 1. Interest Rates, Inflation, Exchange Rate, Growth and Unemployment Rate, 2001–04... 18

### I. Introduction and purpose
- Small-scale structural macro models help produce coherent forecast scenarios and policy analysis inside policy institutions.
- The model developed here is based on the small linear model of the Israeli economy documented in Epstein and others (2006).
- The model resembles standard New Keynesian open-economy models (examples cited: Svensson (2000) and Gali and Monacelli (2005)), but does not have explicit micro foundations.
- Key limitations of linear models:
  - Simulation properties are independent of initial conditions.
  - Impulse responses are linear functions of disturbance magnitudes.
  - May not fully capture effects of large shocks or policy decisions that lead to a loss of monetary policy credibility.

### Extension of the linear model: nonlinearity and endogenous credibility
- Purpose of extension:
  - Capture strong reaction of the Israeli economy to sharp policy interest rate cuts and prolonged erosion in policy credibility.
  - Pay particular attention to the period from 2001 to 2003, when a larger-than-normal policy rate cut led to large movements in the exchange rate and inflation and subsequent sharp reversals in rate settings.
- Methodology:
  - Extend the small linear model with features of nonlinearity and endogenous policy credibility.
  - Use the extended model to argue that loss of policy credibility was costly and prevented the central bank from properly responding to economic fundamentals.
- Model performance claims:
  - The standard linear model cannot explain the 2001–2003 episode very well.
  - The extended model, allowing for nonlinearities in the output-inflation process and endogenous monetary policy credibility, does a much better job in replicating the stylized facts of this historical episode.

### Concept and measurement of credibility
- Various studies define monetary policy credibility using notions such as:
  - (i) deviations of inflation expectations from the central bank’s target;
  - (ii) variation in long-term interest rates, long-term inflation expectations and the public’s assessment of the central bank’s ability to achieve the target;
  - (iii) the extent to which the public believes that the announced target is indeed the central bank’s actual target;
  - (iv) the gap between central bank’s objectives and the public’s perception of these objectives.
- Citations referenced for credibility concepts include Cukierman and Meltzer (1986), Bomfin and Rudebusch (2000), Faust and Svensson (2001), Laxton and N'Diaye (2002), Stiver (2003) and Rebucci and Rossi (2006).

### Channels through which credibility affects outcomes
- The approach gauges credibility effects via three main channels:
  - First: Lack of credibility causes a positive inflation expectations bias, putting upward pressure on inflation through the expectations term in the Phillips Curve (see Isard, Laxton and Eliasson, 2001).
  - Second: A buildup in credibility can shift public expectations of future inflation closer to announced targets rather than to past inflation.
    - In the extended model, enhanced credibility lowers the weight on backward-looking expectations and this improves the inflation-output tradeoff.
  - Third: Credibility also affects the risk premium in the interest parity (IP) condition.

### Modeling assumptions and regime specification
- Credibility dynamics:
  - Credibility builds up when actual inflation converges to the target rather than diverges to some higher level.
  - Analysis is based on a two-regime definition (high and low inflation).
  - This two-regime specification allows credibility to increase even if past inflation is high (but falling) and even if it is not expected to return to the target for some time (for example, due to interest rate smoothing or lags in the transmission mechanism).

*Source: Excerpt from IMF Working Paper chapter "1. Interest Rates, Inflation, Exchange Rate, Growth and Unemployment Rate, 2001–04... 18"*

### Section II discusses the features of a standard linear model for Israel. Section III reviews the

### _wp07207 - Section II discusses the features of a standard linear model for Israel. Section III reviews the

### II. STANDARD FPAS MODEL FOR ISRAEL — model structure and key equations
- Model split:
  - Domestic (small Israeli economy) and Rest of the World (U.S.) blocks.
- Output gap equation (domestic):
  - Domestic output gap depends on real interest rate (RR), real exchange rate (z, logs, increase = depreciation), U.S. output gap (yusgap), and dynamics via past and future domestic output gaps.
  - Output gap is deviation (in percentage points) of actual output from trend; positive = above trend.
- Phillips curve (domestic):
  - Inflation (4tπ = four-quarter CPI change) depends on expected four-quarter inflation (4etπ), lagged inflation, the output gap, exchange rate gap, and movements in the real (relative) price of oil.
  - Inflation measurement: annualized quarterly change, in percent: ()()[]1loglog400 − −= ttt cpicpiπ.
  - Inflation expectations combine model-consistent and backward-looking components via equation (3).
  - Lead and lag weights (ldπα and eπα) critically determine responsiveness to policy and persistence.
- Exchange rate equation:
  - Real interest parity (real IP) condition: deviations of home and U.S. real interest rates from equilibrium and equilibrium risk premium (*)tρ drive deviations of real exchange rate z from equilibrium; residual interpreted as temporary shock to risk premium.
  - Exchange rate expectations allowed to be model-consistent but not imposed (δ1z≠).
- Monetary policy rule:
  - Forward-looking Taylor-variant: interest rate set as a function of expected future inflation (4[+4]tπ), the output gap (t ygap), with smoothing (lag term); instrument is short-term nominal rate; policy anchors inflation to target *π.
- Rest of World (U.S.) block:
  - Similar behavioral equations (output gap, Phillips curve, policy rule) but without world influences.
- Calibration and key parameter scenarios:
  - Epstein and others (2006) baseline uses ldπα=0.1 and eπα=1 for aggregated lead weight; alternative “increased credibility” scenario in this paper sets ldπα=0.70 and eπα=0.5 giving an aggregated lead weight of 0.35.
  - Higher lead weights imply inflation equals sum of future output and exchange rate gaps; low lead weights imply strong inertia and slow monetary effectiveness.

### III. HISTORICAL PERSPECTIVE ON 2001−03 AND LIMITS OF THE STANDARD MODEL — observed events and model shortfalls
- Key historical events (2001−03):
  - Late 2001: central bank cut policy rate by 200 basis points in face of weakening economy.
  - First half 2002: sheqel depreciated; headline inflation rose to 7 percent (y-o-y) by July, 2002.
  - Subsequent hikes: 450 basis points in three steps over five months; policy intentions questioned; exchange depreciation exacerbated amid security deterioration and recession.
  - Year-on-year inflation hit over 6 percent by second half 2002; nominal depreciation peaked at 16 percent.
  - Central bank held policy rate around 9 percent until mid-2003 despite recession.
  - Real GDP: contracted by 0.6 percent in 2001 and 0.9 percent in 2002; grew by 1.5 percent in 2003; recovery in 2004 with real GDP growth of 4.8 percent.
  - Long-run inflation expectations (3−4 years ahead) rose well above the 3 percent upper level of the target band from Q2 2002 to end-2003 even when actual inflation was below the 1−3 percent band for most of 2003.
  - Real market interest rates (policy rate minus one-year-ahead inflation expectations) rose to 6 percent during second half 2002 and remained around that level through mid-2003.
  - Unemployment rate reached 11 percent by end-2003.
  - By 2006: headline inflation overshot upper band due to exchange depreciation, record oil prices, reduced spare capacity; central bank response in 2006 was measured and did not ratchet up long-term inflation expectations; real market rates remained broadly stable; long-run expectations descended toward midpoint of targeting range.
- Standard model simulation and limitations:
  - Shock simulated: temporary interest rate cut of 200 basis points for two quarters (base-case).
  - Standard model immediate responses: significant depreciation of nominal and real exchange rates; combined with rate cut, gradual increases in output and inflation.
  - Over time: interest rates rise to contain inflationary pressures; output and inflation return gradually to control values.
  - Differences from 2001−03 experience:
    - Inflation and exchange rate effects are much smaller in model.
    - Sharp rate reductions do not generate large cumulative costs; short-run output expands and is not followed by a large contraction as observed historically.
  - Conclusion: standard linear model cannot replicate large exchange depreciation, strong business cycle downturn, and persistent loss of credibility observed in 2001−03.

### IV. EXTENDING THE STANDARD MODEL — nonlinear Phillips curve and endogenous credibility
- Objectives for extension:
  - Introduce endogenous credibility and a nonlinear Phillips curve with minimal changes to revert to the standard model if needed.
  - Capture worsening inflation-output tradeoff and higher inflation persistence under low credibility.
- Two main extensions:
  - Introduce nonlinear effect of the output gap on inflation to induce severe inflationary and real costs following overly expansionary policy.
  - Raise the backward-looking weight (1−eπα) in the inflation expectations equation to reflect stronger “show-me” skepticism; exchange rate risk premium also allowed to be higher.
- Nonlinear Phillips curve:
  - Replace linear output gap term by maxmax t ygap t ygap y yygap α ⎛⎞ ⎜⎟ − ⎝⎠ .
  - Imposes a maximum output gap max y calibrated to equal 6 percent.
  - When output gap is near zero, marginal effect equals linear case (ygapt ygapα∗); as gap approaches max y, marginal effect on inflation becomes much stronger, creating potential long periods of negative output gaps to return inflation to target.
- Credibility stock (tγ):
  - Credibility stock ranges between 0 (no credibility) and 1 (full credibility).
  - Two hypothetical inflation regimes define credibility:
    - ‘L’ (Low inflation) scenario: inflation converges to announced target *tπ via equation:
      - *1 40.54(1 0.5) L L tttt π ππ πε − =∗ +− ∗+  (equation (6))
      - Calibrated coefficient on target set to 0.5 (authors consider 0.2 estimated during 1997−2006 too low for a high-credibility scenario).
      - A value of 0.5 coincides with baseline eπα.
    - ‘H’ (High inflation) scenario: inflation converges to *H tπ = 10.8 percent with estimated eπα = 0.45 via:
      - 1 40.554(1 0.55) 10.8 H H ttt π ππε − =∗ +− ∗+  (equation (7))
      - Based on 1992−1996 data when inflation averaged above 10 percent.
  - Credibility stock autoregression:
    - 11 0.7(1 0.7) tttt γ γγλε −− =∗+− ∗+  (equation (8))
    - λt defined as: 2 22 (44) (44) (44) H tt t HL tttt ππ λ ππ ππ − = − + −  (equation (9))
    - Disturbance tγε considered a shock to central bank credibility.
  - Interpretation of extremes:
    - ‘L’ case: λt = 1 (since (44)L tt ππ − = 0), tγ converges to 1 → full credibility.
    - ‘H’ case: λt = 0 (since (40)H tt ππ − = ), tγ converges to 0 → complete lack of credibility.
    - In general, credibility is lost if inflation diverges above the announced target.
- Channels through which credibility stock interacts with model:
  - Through a ‘bias’ factor in inflation expectations (affecting expectations formation).
  - Through the weight of forward-looking behavior in agents’ pricing decisions (affecting Phillips curve lead weight).
  - Via the risk premium embedded in the IP condition (affecting exchange rate dynamics).
- Inflation expectations with credibility effects:
  - One-year-ahead expectations from equation (3) are a weighted combination of model-consistent prediction (4 tπ +) and past inflation, with the backward vs forward weights influenced by credibility (raising backward weight when credibility falls).

*Italic source attribution: IMF working paper content from the supplied PDF excerpt.*

### 10.8 percent in the 'H' case. The parameter values on lagged inflation are indicative of the rate of convergence

### _wp07207 - 10.8 percent in the 'H' case. The parameter values on lagged inflation are indicative of the rate of convergence

### Credibility mechanism, calibration, and interpretation
- The convergence rate parameter of the credibility stock was calibrated to 0.7, i.e., it takes 1.5−2.0 years for credibility to rebuild from some below-full level of initial credibility.
- The stock of credibility, tγ, evolves according to: 11 0.7(1 0.7) tttt γ γ γλε −− = ∗ + − ∗ +  (equation A2).
- Indicator of credibility, tλ, is based on the High and Low inflation states and their expectation errors: 2 22 () () () H HL t t tt π π π ε λ ε ε = + (equation A3).
- The inflation expectations ‘bias’ term, tb, is defined as a proportion of the deviation of a weighted average of the two forecasts from the inflation target, where weights reflect tγ:
  - () () ,, * 0.15414 eLeH tttttt bγπγππ = ∗ + − ∗ −  (equation 13 / A9).
- As credibility approaches unity, the bias converges to zero; under no-credibility (0 t γ = ), the inflation bias equals the difference between the high hypothetical inflation expectations and the target.

### Hypothetical Low and High inflation state processes and expectations
- Hypothetical Low inflation state (A4): * 1 40.54(1 0.5) L L t t t t π π π πε − = ∗ + − ∗ + .
- Hypothetical High inflation state (A5): 1 40.554(1 0.55) 10.8 H H t t t π π πε − = ∗ + − ∗ + .
  - Note: the High-state equation includes the coefficient/value "10.8" as presented in the source.
- One-year-ahead inflation expectations combine backward- and forward-looking components and the bias term:
  - 41 4414 22 e e tt ttttt b π γ γ π π πε +− ⎛⎞ ⎛ ⎞ = + − ++ ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠  (equation 10 / A6).
- One-year-ahead expectations implied by the hypothetical ‘L’ and ‘H’ equations:
  - (A7) 3 , * 4 0 4(1 0.5)0.50.54 eLi ttt i π π π = = − ∗ ∗ + ⋅ ∑
  - (A8) 3 , 4 0 4(1 0.55) 10.80.550.554 eHi tt i π π = = − ∗ ∗ + ⋅ ∑

### Modified interest parity and role of the bias in the risk premium
- The modified IP condition includes tb and links credibility losses to exchange rate depreciation and an increase in the country risk premium:
  - * 11 [] / 4 0.662.3() eusz tttt ttttt zzRRRRbbbρε +− = − − − + + − +  (equation 14 / A12).
- Quantitative example from the model text:
  - A loss of credibility that generates a (high) 1-percentage-point expectations bias will, temporarily, cause a 3 percent real depreciation, thereafter leaving the country risk premium higher by 0.66 percent.

### Main model structure and key equations (as presented)
- Nonlinear inflation equation (A1) retains standard Phillips-curve elements and adds credibility, backward-looking terms, real exchange rate, oil-price terms, and constrained maximum output gap effects.
- Stock of credibility: see A2 (calibration to 0.7).
- Indicator of credibility: see A3.
- Hypothetical L and H processes: see A4 and A5 (High case contains 10.8 value).
- One-year-ahead inflation expectations: see A6, A7, A8 and bias definition A9.
- Output gap equation: A10.
- Monetary policy reaction function (inflation-forecast-based Taylor rule): A11.
- Modified interest parity (IP) including tb: A12.
- Backward-looking and model-consistent expectations for the exchange rate when δz ≠ 1: equation at end of A12 section.

### Dynamic responses to shocks — principal findings (preserving stated magnitudes)
- Interest rate shock (200 basis points cut for two quarters):
  - Under extended model with endogenous credibility and initial credibility 1.0:
    - Credibility drops by 12 percent at its peak after 5 quarters.
    - Nominal exchange rate depreciates and peaks at 5.5 percent (above control).
    - Inflation peaks at 2.5 percentage points above control.
    - To rebuild credibility and return inflation to target, interest rates must be raised to 350 basis points above control (versus 150 basis points in the base-case linear scenario).
    - Peak output gap (boom) is 2.1 percentage points (versus 1.6 percentage points in base case); negative output gap trough is -0.8 percentage point below control during bust.
- Interest rate shock with lower initial credibility:
  - Initial credibility = 0.8 (Figure 5):
    - Inflation peaks at more than 3.5 percentage points.
    - Exchange rate depreciation peaks at 8 percent.
    - Nominal interest rates reach 6 percentage points above control.
    - Output gap trough of the negative gap is -1.7 percentage points.
  - Initial credibility = 0.5 (Figure 6):
    - Larger nominal and real responses; credibility falls less immediately and further falls require larger deviations.
- Credibility shocks (no interest-rate shock):
  - Initial credibility = 1.0 (Figure 7) vs 0.8 (Figure 8):
    - Lower initial credibility (0.8) produces a larger expectations bias and higher risk premium.
    - Inflation peaks at 0.35 percentage points above control after one year (in the lower credibility scenario).
    - Regaining control requires nominal (and real) interest rate increases and causes output losses with a trough of -0.13 percentage point after six quarters.
    - Once credibility is disturbed, it takes over 2 years before monetary authorities can bring it back to control (text statement).
- Inflation (cost-push) shock (1 percentage point for one quarter) — Figures 9–11:
  - Linear model (no endogenous credibility): Figure 9 (baseline).
  - Endogenous credibility with initial credibility = 1.0 (Figure 10):
    - Only moderate loss in credibility due to immediate and appropriate monetary policy response; inflation and interest rates only moderately higher.
  - Endogenous credibility with initial credibility = 0.5 (Figure 11):
    - Inflation outcomes somewhat higher but remain moderate.
  - General conclusion: credibility is usually lost as a result of policy errors, not normal economy shocks, provided the central bank reacts consistently and timely.

### Policy implications and conclusions (as stated)
- Extending the standard small structural model by making the Phillips curve nonlinear and introducing endogenous credibility improves the model’s ability to reproduce observed Israeli dynamics (late 2001 episode).
- The extended model captures:
  - The deterioration in credibility and resulting movements in exchange rate, inflation and output following a policy-related shock.
  - The relatively long time to rebuild credibility.
  - That bringing inflation back to target and rebuilding credibility can be very costly—interest rates must be raised substantially higher, inducing greater variability in output.
- Normal economic shocks, even large ones, need not erode credibility if the central bank is seen to react appropriately; credibility is most at risk when policy itself is the source of the shock.

*IMF staff working-paper content as provided in the source unit.*

### References

### References

### Credibility, Disinflation, and Expectations
- Bomfim, A., and G.D. Rudebusch, 2000, “Opportunistic and Deliberate Disinflation under Imperfect Credibility,” Journal of Money, Credit and Banking, Vol. 32, No. 4, part 1 (Nov.), pp. 704-21.
- Cukierman, A., and A. Meltzer, 1986, “A Theory of Ambiguity, Credibility, and Inflation under Discretion and Asymmetric Information,” Econometrica, Vol. 54, No. 5 (sep.), pp. 1099-1128.
- Faust, J., and L.E.O. Svensson, 2001, “Transparency and Credibility: Monetary Policy with Unobserved Goals,” International Economic Review, Vol. 42 (May), pp. 369-397.
- Isard, P., D. Laxton, and A. Eliasson, 2001, “Inflation Targeting with NAIRU Uncertainty and Endogenous Policy Credibility,” Journal of Economic Dynamics & Control, Vol. 25, pp. 115-148.
- Laxton, D., and P. N'Diaye, 2002, “Monetary Policy Credibility and the Unemployment-Inflation Trade-Off: Some Evidence from 17 Industrial Countries,” IMF Working Paper (Washington: International Monetary Fund).
- Lalonde, R., 2005, “Monetary Endogenous Central Bank Credibility in a small Forward-Looking Model of the U.S. Economy,” Bank of Canada Working Paper 2005-16.
- Keen Meng, C. and E. Tanuwidjaja, 2005, “Central Bank Credibility and Monetary Policy: Evidence from Small Scale Macroeconomic Model of Indonesia,” Singapore Centre for Applied and Policy Economics Working Paper 2005/14.
- Rebucci, A. and M. Rossi, 2006, “Measuring Disinflation Credibility in Emerging Markets: A Bayesian Approach with an Application to Turkey’s IMF-Supported Program, Exonomics Bulletin, Vol 6, No. 11, pp. 1-8.
- Stiver, J.D., 2003, “Expectations, and Credibility in a Model of Monetary Policy,” University of Connecticut, Department of Economics Working Paper 2003−34.

### Phillips Curve, Inflation Dynamics, and Asymmetry
- Debelle, G., and D. Laxton, 1997, “Is the Phillips Curve Really a Curve? Some Evidence for Canada, The United Kingdom and the United States,” Staff Papers, International Monetary Fund, Vol. 44, No. 2, June, pp. 249–82.
- Laxton, D., G. Meredith, and D. Rose, 1995, “Asymmetric Effects of Economic Activity on Inflation: Evidence and Policy Implications,” IMF Staff Papers, Vol. 42, June, (Washington: International Monetary Fund).
- Laxton, D., D. Rose, and D. Tambakis, 1999,” The U.S. Phillips Curve The Case for Asymmetry,” Journal of Economic Dynamics and Control, Vol. 23, No. 9, pp. 1459–85.

### Model-Based Monetary Policy Analysis and DSGE Approaches
- Berg, A., P. Karam, and D. Laxton, 2006a, “A Practical Model-Based Approach to Monetary Policy Analysis—Overview,” IMF Working Paper (Washington: International Monetary Fund).
- ––––––, 2006b, “Practical Model-Based Monetary Policy Analysis—A How-to Guide,” IMF Working Paper (Washington: International Monetary Fund).
- Epstein, N., P. Karam, D. Laxton, and D. Rose, 2006, “A Simple Forecasting and Policy Analysis System for Israel: Structure and Applications,” in Israel: Selected Issues, ed. by Rick Haas, Country Report No. 06/121 (Washington: International Monetary Fund).
- Smets, F., and R. Wouters, 2003, “An Estimated Stochastic dynamic General Equilibrium Model of the Euro Area,” Journal of European Economics, Vol. 49, pp. 947-981.

### Small Open Economies and Exchange Rate Considerations
- Gali, J., and T. Monacelli, 2005, “Monetary Policy and Exchange Rate Volatility in a Small Open Economy ,” Review of Economic Studies, Vol. 72 (3), pp. 707-734.
- Laxton, D., and P. Pesenti, 2003,"Monetary Policy Rules for Small, Open, Emerging Economies," Journal of Monetary Economics, Vol. 50 (July), pp. 1109-46.
- Svensson, L.E.O., 2000, “Open-Economy Inflation Targeting,” Journal of International Economics, Vol. 50, pp. 155-183.

*Source: _wp07207 - References*

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