## Appendix I & II — Policy Credibility; New‑Keynesian Model for Canada (_wp16192)

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### Introduction and summary
- Bank of Canada: flexible inflation targeting (FIT) for a quarter century; inflation-control targets defined in agreements with Government and embody Bank of Canada Act objectives (stabilizing output and inflation).
- Proposal: increase transparency via Conventional Forward Guidance (CFG) — routine publication of the forecast path of the policy rate and relevant macro variables (e.g., output gap and inflation) following policy decision meetings.
- Key historical/numerical facts:
  - Since 1994 headline CPI inflation has averaged just less than the target of 2 percent; expectations anchored at 2 percent.
  - Overnight rate reduced as negative output gap widened since 2014; overnight rate at 0.5 percent (as reported).
  - Bank revised its ELB estimate down to -0.5 percent from the previous 0.25 percent (Witmer and Yang, 2015).
  - Global equilibrium real interest rate post-crisis likely less than 1 percent (Box 1).

### Inflation‑forecast targeting (IFT), transparency, and international comparisons
- IFT central banks publish a central-bank inflation forecast as an operational intermediate target explaining policy management of the short-run output‑inflation trade-off.
- Selected entries (as presented):
  - Canada: 2016 1.7  2017 2.1  2018 (0.1)  2.0 (0.0)  0.1  Yes (1994)
  - Czech Republic: 2016 0.6  2017 1.7  2018 (-0.3)  2.1 (0.1)  -0.2  Yes (2002)
  - New Zealand: 2016 0.7  2017 1.7  2018 (-0.3)  2.0 (0.0)  -0.3  Yes (1997)
  - Sweden: 2016 1.0  2017 1.5  2018 (-0.5)  2.2 (0.2)  -0.3  Yes (2007)
  - United States: 2016 1.3  2017 2.3  2018 (0.0)  2.3 (0.0)  0.0  Yes (2012)
  - Euro Area: 2016 0.3  2017 1.3  2018 (-0.7)  1.5 (-0.5)  -1.2  No
  - Japan: 2016 -0.1  2017 0.6  2018 (-1.4)  0.9 (-1.1)  -2.5  No
- Most transparent FIT central banks rank highly on Dincer‑Eichengreen index; top three: Sweden, Czech Republic, New Zealand — these have overtaken Bank of Canada on that index.

### Factors contributing to Canada’s FIT success
- Exchange rate flexibility: CAD/USD allowed to vary widely, absorbing large terms‑of‑trade shocks and buffering domestic output and inflation.
- Fiscal policy: surpluses pre-2008; large deficits post-global crisis (including 2009‑10 stimulus); consolidation over 2012‑15 restored declining government debt‑to‑GDP; fiscal policy in 2016 adopted stimulative stance.
- Commodity-driven expansion: early‑decade commodity boom (oil demand from China and other EMs) supported domestic investment and output.
- Financial regulation/supervision: regular 5‑year updates of banking legislation and well‑capitalized banks reduced financial‑sector stress in 2008‑09.

### Neutral rate, ELB, and policy constraints
- Neutral/equilibrium real interest rate substantially below pre‑2008 levels; in 2016 neutral rate may be around zero.
- Even maximum feasible policy rate cuts may provide limited stimulus without other measures.
- Bank signaled readiness for unconventional measures (large‑scale asset purchases, funding for credit) but efficacy uncertain.
- Prolonged negative rates raise concerns about financial system efficiency and stability.

### Conventional forward guidance (CFG): rationale, advantages, and objections
- Rationale and mechanics:
  - Policy works through expectations of the future path of the overnight rate, influencing longer‑term rates, exchange rate, and asset prices.
  - Publishing the implied interest‑rate path aligns public expectations with the central bank’s forecast and can make the instrument more effective.
  - CFG can enable temporary inflation overshoots to reduce real interest rates and escape low‑inflation/deflation scenarios if communicated clearly.
- Advantages:
  - If markets share the central bank’s forecast, longer‑term interest rates, exchange rate, and asset prices move to support monetary objectives.
  - Under ELB constraints, publishing the inflation path and interest‑rate path shapes expected real rates when nominal rates are constrained.
  - CFG improves accountability via quantitative forecast paths and confidence bands.
- Main objection and mitigation:
  - Objection: conditionality — deviations from published path to offset shocks could impair credibility.
  - Mitigation: effective communications, model‑derived confidence bands, alternative conditional scenarios; evidence from Czech Republic, New Zealand, Norway, Sweden suggests markets adjust and can buffer shocks.

### Downward trend in global equilibrium real interest rate (Box 1 summary)
- Definition: equilibrium real interest rate = rate consistent with equality of actual and potential output in absence of cyclical shocks (medium‑term concept).
- For a very open economy like Canada, U.S./global equilibrium rate drives domestic rate.
- Empirical evidence:
  - Inflation‑adjusted bond yields have trended down since early 1980s; renewed drop after 2008‑09 led to substantial downward revisions.
  - No consensus on decline magnitude; surveyed estimates vary:
    - Summers (2015): -3 to 1.75 percent range from U.S. studies.
    - Mendes (2014): Canada range 1‑2 percent; translates to nominal 3‑4 percent.
- Authors’ inclination: treat persistent negative headwinds as part of the environment → materially lower neutral rate perceived with lag by policymakers.

### Expectations, the ELB “dark corner,” and model illustrations (Section IV)
- At the ELB, a weakened transmission mechanism can still operate via expected inflation affecting real interest rates and the real exchange rate; forward guidance can stimulate through these channels.
- If monetary policy is active and credible:
  - Commitment to hold the interest rate at the ELB for an extended period raises expected future inflation → reduces longer‑term real rates → real exchange rate depreciation and higher asset prices → amplifies stimulus in an open economy.
- If monetary policy is passive and not credible:
  - Expected inflation falls (expected deflation rises), real interest rates rise at the ELB, real exchange rate appreciates, asset prices fall → deflation trap.
- Model illustration (Figure 5):
  - A more aggressive CFG causes inflation to overshoot the target; at peak inflation reaches 2.5 percent.
  - Medium‑term increase in inflation peaks at 0.7 percentage point versus a smoother credible path.
  - That translates into a temporarily lower real interest rate of 70 basis points.
  - Aggressive strategy achieves the target at lower overall cost: smaller cumulative output gap and quicker exit from the deflation‑ELB dark corner.

### Role and mechanics of published central bank forecasts (CFG)
- CFG = publication of a complete central bank macro forecast with an endogenous interest‑rate path and confidence bands.
- Under IFT, at minimum publish forecast paths for inflation and the output gap/growth — in Canada, 8 times per year.
- Benefits:
  - Continuous information on how changing states affect policy.
  - Helps steer expectations for medium/long‑term rates and inflation.
  - Improves accountability; deviations can be explained relative to forecast assumptions.
- Communication caveats:
  - Present policy‑rate path as a conditional forecast, not a promise.
  - Publish confidence bands and alternative scenarios to indicate uncertainty and non‑normal risk ranges.
  - Avoid oversimplified threshold‑based messaging.

### Unconventional forward guidance (UFG) and international experience
- UFG used post‑crisis to talk down expected policy paths and term premiums; reduced longer‑term rates in several advanced economies.
- Communication difficulties: conditionality and horizon problematic; numerical thresholds risk oversimplifying decision framework.
- Examples:
  - UK (August 2013): unemployment threshold 7 percent; threshold breached but inflation below 2 percent → reversion to qualitative guidance by February 2014.
  - US: guidance changed multiple times (2008–2015); 2013 taper tantrum highlighted volatility from shifting perceptions.
- Empirical assessments:
  - Filardo and Hoffmann (2014): moderately beneficial results.
  - Charbonneau and Rennison (2015): lower expectations of future policy rates; improved predictability; reduced sensitivity of financial variables to news.
  - Engen, Laubach, Reifschneider (2015): net stimulus limited by gradual expectation changes; clearer public understanding could have reduced recession severity.

### Canada’s historical experience (post‑2008) and Bank of Canada forward guidance example
- Crisis onset: inflation about 2 percent; policy rate above 4 percent; Bank cut policy rate to near zero over 2 years.
- Canadian dollar depreciated; exports fell but GDP decline limited to 2.7 percent due to domestic demand; inflation remained positive.
- Bank of Canada forecasting performance: Monetary Policy Reports repeatedly revised back date when output would reach potential — from 2011Q4 (July 2010) to 2017Q3 (April 2016).
- Bank of Canada forward guidance (Press Release, April 9th, 2009) quote:
  - “With monetary policy now operating at the effective lower bound for the overnight policy rate, it is appropriate to provide more explicit guidance than is usual regarding its future path so as to influence rates at longer maturities. Conditional on the outlook for inflation, the target overnight rate can be expected to remain at its current level until the end of the second quarter of 2010 in order to achieve the inflation target.”
- Outcome: Bank forecast return to 2 percent in 2011; forecast aided by 2010‑11 global energy and food price rise; output gap closure forecast was overoptimistic.

### New‑Keynesian model simulations for Canada — model features and monetary policy specification
- Model features:
  - Core equations: output gap, core inflation, policy interest rate, exchange rate.
  - Expectations: forward‑looking and model‑consistent; behavioral equations include lagged adjustments.
  - Additional equations: headline inflation, food and energy inflation, commodity terms of trade, trade and financial linkages, bond yields of various maturities.
  - Nonlinearities: Phillips curve flattens with negative output gap; ELB constraint and reaction function introduce nonlinearities.
- Monetary policy in simulations:
  - Loss‑minimizing strategy with quadratic loss function.
  - Loss function weights:
    - weight 1 on squared inflation gap (deviation from 2 percent),
    - weight 1 on squared output gap,
    - weight 0.5 on squared change in policy interest rate (implying smoothed interest rate policy).
  - Quadratic loss imposes increasing loss for larger deviations, making strategy risk‑averse toward “dark corners.”
- Simulation context:
  - Start in 2009Q2 to evaluate CFG performance post‑global financial crisis.
  - CFG that commits to a lower‑for‑longer rate path reduces medium‑ and long‑term rates more than overnight cuts alone by affecting expectations for both nominal policy rate (down) and inflation (up).
  - CFG’s advantages are clearest in the ELB zone.

### Policy implications and recommended framework
- Recommended elements to avoid ELB‑deflation trap:
  - Loss‑minimizing monetary policy with quadratic loss that penalizes deviations from inflation target and potential output.
  - Full publication of central bank forecast, including endogenous policy‑rate path and confidence bands (CFG).
  - Clear role for fiscal stimulus near the ELB (2016 view).
- Compared effectiveness:
  - Combined strategy (loss‑minimizing policy + full forecast publication + targeted fiscal stimulus) could be more effective than:
    - unconventional monetary measures alone,
    - negative interest rates,
    - or raising the inflation target alone.
- On equilibrium real rates and policy design:
  - Estimates of equilibrium world real rate falling since crisis; recent estimates around zero.
  - If equilibrium real rate near zero, ELB on nominal rate implies a floor of about -2 percent on the gap between actual and equilibrium real interest rate — limited expansionary room.
  - Raising inflation target by 1 percentage point would provide more space but is difficult given strong expectations anchored at 2 percent — actions required, not just announcement.
  - Expansionary fiscal policy is a preferable alternative for below‑par activity: raises output and makes monetary policy more effective in short‑run output‑inflation trade‑off.
- Recommended combined strategy (2016 view):
  - CFG combined with well‑designed fiscal stimulus is potent for recovery despite ELB.
  - This avoids financial stability issues from prolonged negative rates, is stronger than QE‑type interventions in Canada, and preserves 2 percent inflation target as nominal anchor.

### Appendix II — Model structure (high‑level summary of equations and parameterization)
- Model timing and baseline (starting 2009Q2):
  - Quasi‑real time information with historical data revisions unrolled one quarter at a time.
  - Baseline initial conditions:
    - output gap = -4.5 percent,
    - inflation rate = 1 percent,
    - policy interest rate = effective ELB of 0.25 percent,
    - real equilibrium interest rate estimate = 1.7 percent (revised downward thereafter).
  - ELB constraint historically assumed 0.25 percent in simulations.
  - Rolling filter determines latent variable estimates.
- IS equation:
  - Output gap linked to past and expected future output gaps, lagged one‑year real interest rate deviations, real effective exchange rate deviations, rest‑of‑world output gap, terms‑of‑trade gap, with coefficients and β parameters including (0.65), (0.15), (0.15), (0.05), (0.3), (0.5).
- Phillips curve:
  - Core inflation depends on expectation, past year‑on‑year core inflation, lagged output gap nonlinearly, real effective exchange rate depreciation, pass‑through from oil and food.
  - Base‑case numerical weights include (0.75), (0.25), (0.05), (0.05), (0.01), (0.01).
  - Expectation formation includes weightings (example: (0.8) combination).
- Policy interest rate options:
  - IFB: linear inflation‑forecast‑based form with coefficients including (0.75), (1.5), (0.5) and γ‑terms.
  - OPT (loss‑minimizing): minimizes discounted loss with discount factor (0.98) and loss weights (1.0)(1.0)(0.5).
  - ELB constraint: floor i ≥ (0.25).
- Real rates and exchange rates:
  - Real interest rate r_t = i_t − 1 C_t π+ (nominal minus expected core inflation).
  - Real exchange rate definitions and decompositions with coefficients and weightings for trade regions: (0.68), (0.07), (0.02), (0.08), (0.04), (0.05), (0.05) enter reer calculation.
  - Risk‑adjusted UIP includes time‑varying country risk premium ctry_t σ and terms‑of‑trade premium; expectation formation mixes model‑consistent and backward‑looking components.
- Relative prices, term structure, unemployment, potential output, rest of the world, and commodity terms of trade:
  - Relative price, Oil, Food, and tot equations include parameters such as (0.43), (0.012), (0.02), persistence (0.9).
  - Term structure: Gov_k_t i equals average expected short rates k quarters ahead plus term premia σ_Term_k_t and measurement shock ε for maturities 4, 8, 20, 40 quarters.
  - Unemployment/Okun’s law: one percentage‑point unemployment gap ~ two percentage‑point decrease in output gap; autoregressive coefficients (0.4), (0.4), NAIRU AR dynamics include (0.9).
  - Potential output dynamics include persistence coefficients (0.97) and (2) in AR structure.
  - Rest‑of‑world output gap is weighted average across seven regions with weights (0.79), (0.04), (0.02), (0.04), (0.04), (0.02), (0.05).
  - Commodity price dynamics: Oil and Food AR(1) growth persistence (0.95) and level persistence (0.7); terms‑of‑trade gap uses coefficients (0.03) for Oil and (0.002) for Food.
  - Terms‑of‑trade premium and real exchange rate linkage specified with decomposition and autoregressive relations.

### Key simulation results and counterfactuals
- OPT (loss‑minimizing) vs IFB (inflation‑forecast‑based):
  - OPT keeps policy rate at floor for two years, 2009Q2‑2011Q2; expected Canadian dollar depreciation ~4.5 percent, 2009Q1‑2012Q4; output gap closed to zero by 2010Q4; core inflation peaks at 2.8 percent (2011Q4‑2012Q2) then returns to 2 percent.
  - IFB keeps policy rate at floor ~2009Q3‑2010Q2; output gap closed in 2011Q3 and stays there; unemployment at 2011Q3 is 1 percentage point higher than under OPT; inflation returns to target only by 2012Q3.
  - Conclusion: OPT preferable given initial conditions and quadratic loss with ELB constraint.
- Counterfactual with historical shocks under OPT:
  - Policy rate at ELB until 2013Q1 under OPT (historical Bank raised to 1 percent in 2010).
  - Under OPT, core inflation peaks above 3.5 percent in 2010; headline above 4 percent; output gap closes in second half 2011 before negative shocks reopen gap.
  - OPT yields narrower output gap and unemployment up to 0.8 percentage points lower in 2010–2011 relative to historical.
  - Drawback: inflation overshoot under OPT (authors view acceptable given medium‑term deviations and FIT experience).
- Fiscal stimulus and negative policy rate experiments (forecasts as of 2009Q2):
  - Negative interest rate case: cut to -0.5 percent leads to quicker output gap closure than control; effects modest relative to positive ELB case; requires smaller inflation overshoot to achieve decline in real interest rates.
  - Fiscal policy case (1 percent of GDP stimulus): more direct demand impact; smaller implied inflation overshoot than baseline; fiscal stimulus appreciates CAD vs base but raises output because monetary policy holds interest rate at ELB and focuses on inflation/output objectives; exchange rate appreciation not large enough to choke off stimulus.
- Alternative scenario: IFB with backward‑looking expectations:
  - IFB with high weight on lagged inflation yields worse outcomes: wider output gap, higher unemployment, lower inflation relative to history from 2009Q2.
  - Counterfactual policy rate lower for a couple of years in response to weaker economy, not due to more aggressive policy.

*Source: IMF Working Paper — Appendix I & Appendix II (new‑Keynesian model for Canada) — _wp16192.*

### Appendix I. Policy Credibility: Exchange Rate and Asset Prices as Shock Absorbers or

### Appendix I. Policy Credibility: Exchange Rate and Asset Prices as Shock Absorbers or Amplifiers

### Introduction and summary
- For a quarter century, the Bank of Canada has pursued flexible inflation targeting (FIT).
- Inflation-control targets are defined in agreements between the Bank of Canada and the Government of Canada and embody the preamble objectives of the Bank of Canada Act (stabilizing output and inflation).
- The paper argues that the framework could be improved with increased transparency about the future path of the policy rate via conventional forward guidance (CFG): routine publication of the forecast path of the policy rate and other relevant macro variables (e.g., output gap and inflation) following policy decision meetings.
- Since 1994 headline CPI inflation has averaged just less than the target of 2 percent; expectations have been firmly anchored at 2 percent.
- The Bank of Canada’s overnight rate was reduced in response to widening negative output gap since 2014; the overnight rate is now at 0.5 percent.
- The Bank revised its estimate of the effective lower bound (ELB) on the overnight rate down to -0.5 percent, from the previous 0.25 percent (Witmer and Yang, 2015).
- The global equilibrium real interest rate has declined considerably since the global financial crisis and is likely less than 1 percent (Box 1).

### Inflation-forecast targeting (IFT) and transparency
- IFT central banks publish a central-bank inflation forecast as an operational intermediate target that explains how policy manages the short-run output-inflation trade-off.
- Table 1 (selected entries, as presented in source) — Inflation Expectations Better Anchored in IFT Countries:
  - Canada: 2016 1.7  2017 2.1  2018 (0.1)  2.0 (0.0)  0.1  Yes (1994)
  - Czech Republic: 2016 0.6  2017 1.7  2018 (-0.3)  2.1 (0.1)  -0.2  Yes (2002)
  - New Zealand: 2016 0.7  2017 1.7  2018 (-0.3)  2.0 (0.0)  -0.3  Yes (1997)
  - Sweden: 2016 1.0  2017 1.5  2018 (-0.5)  2.2 (0.2)  -0.3  Yes (2007)
  - United States: 2016 1.3  2017 2.3  2018 (0.0)  2.3 (0.0)  0.0  Yes (2012)
  - Euro Area: 2016 0.3  2017 1.3  2018 (-0.7)  1.5 (-0.5)  -1.2  No
  - Japan: 2016 -0.1  2017 0.6  2018 (-1.4)  0.9 (-1.1)  -2.5  No
  - Note: The implicit CPI inflation objective for the U.S. is estimated by the authors at about 0.3 percentage points above the Fed's official PCE inflation objective of 2.0 percent (based on difference in long-term CPI and PCE inflation forecasts from Philadelphia Fed's Survey of Professional Forecasters).
- The most transparent FIT central banks rank highly on the Dincer-Eichengreen index; the top three are Sweden, Czech Republic, and New Zealand (Figure 2). These have overtaken the Bank of Canada on this index.

### Factors contributing to Canada’s FIT success
- Exchange rate flexibility:
  - The CAD/USD exchange rate has been allowed to vary over a wide range, absorbing large terms-of-trade shocks and buffering domestic output and inflation (Figure 3).
- Fiscal policy:
  - Fiscal policy played a supportive role: surpluses pre-2008, switching to large deficits post-global-crisis (including 2009-10 fiscal stimulus). Budgetary consolidation over 2012-15 restored a declining government debt-to-GDP ratio. Fiscal policy in 2016 adopted a stimulative stance given macro circumstances.
- Commodity-driven expansion:
  - Early-decade commodity boom (oil demand from China and other EMs) stimulated domestic investment and output, shielding Canada from the negative effects of the global decline in equilibrium real interest rates post-2008.
- Sound financial regulation and supervision:
  - Regular 5-year updating of banking legislation and well-capitalized banks helped Canada avoid severe financial-sector stress during 2008-09; post-crisis credit tightening was less severe than in many countries.

### Neutral rate, ELB, and policy constraints
- The global level of nominal rates consistent with maintaining output at potential given inflation targets is well below pre-2008 levels; in 2016 the neutral rate may be around zero.
- Even maximum feasible policy rate cuts may provide limited stimulus unless supplemented by other measures.
- The Bank has signaled readiness to adopt unconventional measures (large-scale asset purchases, funding for credit), but their efficacy is uncertain.
- Concerns exist about implications of prolonged negative rates for financial system efficiency and stability.

### Conventional forward guidance (CFG): rationale, advantages, and objections
- Rationale:
  - The overnight rate setting for the next 6 weeks has no material direct impact on inflation or output; policy works through expectations of the future path of the overnight rate which influence longer-term interest rates, exchange rate, and asset prices.
  - Central banks already produce a forecast path for inflation implicitly when setting policy; publishing the interest-rate path (CFG) would align public expectations with the central bank’s own best-informed forecast.
  - CFG would make the interest rate instrument more effective, improving management of medium-term trade-offs and potentially obviating the need for negative policy rates or expanded unconventional measures.
  - CFG would restore Canada closer to the forefront of IFT economies in terms of transparency.
- Advantages:
  - If markets share the central bank’s rate forecast, longer-term interest rates, exchange rate, and asset prices move to support monetary objectives.
  - Under ELB constraints, publishing the forecast inflation path (and interest-rate path) helps shape expected real interest rates, which is important when nominal rates are constrained.
  - CFG allows communication of strategies such as temporary overshoots of inflation to reduce the real interest rate and escape low-inflation/dangerous-deflation scenarios while preserving credibility if communicated clearly.
- Main objection and mitigation:
  - Objection: Conditionality of the interest-rate forecast—if the Bank must deviate from a published path to offset shocks, credibility may be impaired.
  - Mitigation: Effective communications, model-derived confidence bands, and alternative forecasts that illustrate conditionality and shock impacts can preserve credibility; evidence from countries publishing interest-rate forecasts (e.g., Czech Republic, New Zealand, Norway, Sweden) suggests markets adjust and can buffer shocks more effectively.

### Box 1 — Downward trend in global equilibrium real interest rate (summary)
- Definition: equilibrium real interest rate = rate consistent with equality of actual and potential output in absence of short-run/cyclical shocks (medium-term concept).
- For a very open economy like Canada, the global (or U.S.) equilibrium rate drives the domestic rate.
- Empirical evidence:
  - Inflation-adjusted bond yields have trended down since the early 1980s; renewed drop after 2008-09 crisis led to substantial downward revisions of the equilibrium real rate.
  - No consensus on how far the rate has declined since the crisis.
  - Surveyed and cited estimates:
    - Summers (2015) cites a -3 to 1.75 percent range from a survey of U.S. studies.
    - Mendes (2014) puts the range for Canada at 1-2 percent.
  - Mendes (2014) translates a 1-2 percent real neutral rate to nominal terms of 3-4 percent.
- Interpretation differences:
  - Higher equilibrium estimates (>1 percent) treat repeated negative headwinds as shocks.
  - Lower estimates (near or below zero) treat repeated headwinds as a permanent change in the medium-term environment.
- Authors’ inclination:
  - Favor treating persistent negative headwinds as part of the environment rather than temporary shocks; repeated forecast downgrades, below-target inflation, and declines in actual real rates support a materially lower neutral rate that policymakers may perceive only with a lag.

*Source: IMF Working Paper — Appendix I. Policy Credibility: Exchange Rate and Asset Prices as Shock Absorbers or Amplifiers (excerpt).*

### Section IV contains policy simulations of a new-Keynesian model for Canada. These indicate

### _wp16192 - Section IV contains policy simulations of a new-Keynesian model for Canada. These indicate

### Expectations and the ELB “dark corner”
- At the ELB a weakened transmission mechanism can still operate via real interest rates and the real exchange rate, because expected inflation provides a channel through which forward guidance can stimulate the economy.
- If monetary policy is active and credible:
  - The public can be persuaded that inflation will eventually be brought back to the long-run target.
  - A commitment to hold the interest rate at the ELB for an extended period raises expected future inflation, reducing longer-term real rates even if the nominal rate is at the ELB.
  - Real exchange rate depreciation and higher asset prices follow, amplifying the real interest rate channel in an open economy (Appendix I).
- If monetary policy is passive and not credible:
  - Expected inflation falls (expected deflation rises), real interest rates rise at the ELB, the real exchange rate appreciates, and asset prices fall — the classic deflation trap.
- Illustration from model/calculations (Figure 5):
  - A more aggressive conventional forward guidance causes inflation to overshoot the target for several quarters — at the peak, inflation reaches 2.5 percent.
  - The medium-term increase in the inflation rate peaks at 0.7 percentage point versus a smoother credible path.
  - That translates into a temporarily lower real interest rate of 70 basis points.
  - The aggressive strategy achieves the inflation target at a lower overall cost: smaller cumulative output gap and quicker exit from the deflation-ELB dark corner.

### Role and mechanics of published central bank forecasts (Conventional Forward Guidance — CFG)
- CFG derives from publication of a complete central bank macroeconomic forecast with an endogenous interest rate path and confidence bands around key variables.
- Under inflation-targeting frameworks (IFT), at a minimum forecast paths for inflation and the output gap or growth are published—i.e. 8 times per year in Canada.
- Benefits of publishing the endogenous policy rate path and confidence bands:
  - Provides market participants with continuous information on how changing economic states affect monetary policy actions.
  - Helps steer public expectations for medium- and longer-term interest rates and inflation in support of policy objectives.
  - Improves accountability via quantitative forecast paths and confidence bands; deviations can be explained in terms of specific deviations from forecast assumptions.
- Communication caveats:
  - The policy-rate path should be presented as a conditional forecast, not a promise.
  - Publish confidence bands and alternative scenarios to indicate uncertainty and the non-normal range of risks.
  - Avoid oversimplified threshold-based messaging that could mislead markets about conditionality.

### Unconventional Forward Guidance (UFG) and international experience
- UFG was used after the global financial crisis to talk down expected policy rate paths and term premiums and succeeded in reducing longer-term rates in several advanced economies.
- Communication difficulties with UFG:
  - Conditionality and the time horizon over which guidance applies proved problematic.
  - Announced numerical thresholds risk oversimplifying policymakers’ actual complex decision framework and can misguide markets.
  - Examples:
    - United Kingdom (August 2013): announced thresholds including unemployment below 7 percent; within months unemployment fell below the threshold but inflation remained below 2 percent and the Bank reverted to qualitative guidance in February 2014.
    - United States: guidance changed forms multiple times between 2008 and 2015, and the 2013 taper tantrum highlighted market volatility from shifting perceptions.
- Empirical assessments:
  - Filardo and Hoffmann (2014): forward guidance had moderately beneficial results.
  - Charbonneau and Rennison (2015): found lower expectations of future policy rates, improved predictability of short-term yields, and reduced sensitivity of financial variables to news.
  - Engen, Laubach, and Reifschneider (2015): suggest the net stimulus was limited by the gradual nature of expectation changes; better public understanding of FOMC accommodation would have reduced recession severity.

### Canada’s historical experience (post-2008)
- At crisis onset inflation was about 2 percent and the policy rate was above 4 percent; the Bank cut the policy rate to near zero over the next 2 years.
- The Canadian dollar depreciated; exports fell but GDP decline was limited to 2.7 percent due to domestic demand; inflation remained positive.
- Bank of Canada forecasting performance:
  - Monetary Policy Reports repeatedly revised back the date at which output was expected to reach potential — from 2011Q4 in the July 2010 Report to 2017Q3 in the April 2016 Report (Table 3).
  - In retrospect, persistent negative output shocks imply the Bank was overestimating the equilibrium real interest rate.
- Bank of Canada forward guidance example (Press Release, April 9th, 2009) quoted:
  - “With monetary policy now operating at the effective lower bound for the overnight policy rate, it is appropriate to provide more explicit guidance than is usual regarding its future path so as to influence rates at longer maturities. Conditional on the outlook for inflation, the target overnight rate can be expected to remain at its current level until the end of the second quarter of 2010 in order to achieve the inflation target.”
- Outcome:
  - The Bank forecast that policy would return inflation to the 2 percent target in 2011; the forecast was not far off largely due to one-off rise in global energy and food prices in 2010-11, while the output gap closure forecast was overoptimistic.

### New-Keynesian model simulations for Canada (Section IV)
- Model features:
  - Standard core with equations for the output gap, core inflation, the policy interest rate, and the exchange rate.
  - Expectations are forward-looking and consistent with the model’s projections; behavioral equations also include lagged adjustments.
  - Additional equations for headline inflation, food and energy inflation, the commodity terms of trade, trade and financial linkages, and bond yields of various maturities.
  - Nonlinearities: Phillips curve becomes quite flat when there is a negative output gap; ELB constraint and monetary policy reaction function introduce nonlinearities.
- Monetary policy specification in simulations:
  - Loss-minimizing strategy with quadratic loss function.
  - Loss function weights:
    - weight of 1 on the squared inflation gap (deviation from 2 percent),
    - weight of 1 on the squared output gap,
    - weight of 0.5 on the squared change in the policy interest rate (implying smoothed interest rate policy).
  - The quadratic loss imposes an increasingly heavy loss as deviations from target increase, making the strategy risk-averse toward “dark corners.”
- Simulation context:
  - Start in 2009Q2 to evaluate how CFG would have performed following the global financial crisis.
  - The model suggests that during ELB episodes, publication of an endogenous forecast (CFG) that commits to a lower-for-longer rate path can reduce medium- and long-term rates more than the overnight rate cut alone by affecting expectations for both the nominal policy rate (down) and for inflation (up).
  - CFG’s advantages are most clear in the ELB zone: a transparent lower-for-longer strategy combined with a published forecast acts as an additional instrument to steer expectations and support recovery.

### Policy implications and recommended framework
- A strong policy framework to avoid macroeconomic quagmires (ELB-deflation trap) would include:
  - A loss-minimizing monetary policy with a quadratic loss function that places increasing penalty on deviations from the inflation target and from potential output.
  - Full publication of the central bank forecast, including an endogenous policy-rate path and confidence bands (CFG).
  - Near the ELB in 2016, a clear role for fiscal stimulus is identified by the simulations.
- These features (loss-minimizing policy + full forecast publication + targeted fiscal stimulus near the ELB) could be more effective than:
  - unconventional monetary policy measures alone,
  - negative interest rates,
  - or raising the target inflation rate,
  for avoiding the ELB-deflation “dark corner.”
- Publication of the forecast functions as an additional instrument by influencing medium- and long-term market expectations and thereby reducing real interest rates and supporting exchange rate adjustment and asset prices.

*Source: _wp16192 - Section IV contains policy simulations of a new-Keynesian model for Canada. These indicate*

### Appendix II outlines the model structure.

### _wp16192 - Appendix II outlines the model structure.

### Model setup and baseline assumptions
- Policymakers operate in quasi-real time: information available in any quarter is limited to what could have been available at the time, but the series used contain revisions to historical data (current historical dataset unrolls one quarter at a time).
- Starting point: 2009Q2 with
  - output gap = -4.5 percent,
  - inflation rate = 1 percent,
  - policy interest rate = effective ELB of 0.25 percent,
  - real equilibrium interest rate estimate = 1.7 percent (revised downward thereafter on the basis of incoming new data).
- Monetary policy is constrained by an ELB of 0.25 percent (the Bank of Canada view at the time).
- A rolling filter determines estimates of latent variables.

### Forecast as per 2009Q2 plan — comparison of OPT (loss-minimizing) and IFB (inflation-forecast-based) strategies
- Figure 8 shows forecasts in 2009Q2 for policy rate, output gap, inflation, exchange rate and unemployment under:
  - OPT: derived loss-minimizing strategy (red line).
  - IFB: linear inflation-forecast-based reaction function (blue line).
- Key aspects:
  1. OPT keeps the policy rate at the floor for two years, 2009Q2-2011Q2.
     - Expected exchange rate movement: rise (Canadian dollar depreciates) about 4.5 percent, 2009Q1-2012Q4.
     - Output gap: closed to zero by 2010Q4; an excess demand gap opens thereafter.
     - Unemployment falls at same pace as output gap closure.
     - Year-on-year core inflation peaks at 2.8 percent, 2011Q4-2012Q2, then returns to 2 percent. Headline peaks slightly lower.
     - Mechanism: anticipated medium-term increase in inflation reduces real interest rates and causes a real depreciation.
  2. IFB keeps policy rate at floor for about one year, 2009Q3-2010Q2.
     - Exchange rate depreciation in medium term is relatively modest.
     - Output gap closed more slowly, reaching zero in 2011Q3 and staying there.
     - Unemployment at 2011Q3 is 1 percentage point higher than under OPT.
     - Inflation (core and headline) does not return to target until 2012Q3.
  - Conclusion: OPT would generally be regarded as the better strategy given the initial conditions and quadratic loss function, with ELB constraint adding incentive for stimulative policy to avoid a deflation-dark-corner equilibrium.

### Counterfactual history with loss-minimizing strategy (allowing historical unanticipated shocks)
- Global financial crisis and subsequent negative shocks produced a weaker historical path than either illustrative 2009Q2 policy envisaged; negative output gap never completely closed historically.
- Simulations re-run with historical shocks; quasi-real time results compared to history (Figure 9).
- Key aspects:
  1. Under loss-minimizing response to historical shocks, policy rate remains at the ELB until 2013Q1 (entire period shown). In contrast, the Bank of Canada raised the policy rate to 1 percent in 2010.
     - Canadian dollar appreciates less under the counterfactual OPT strategy.
  2. Under OPT, inflation overshoots target substantially:
     - Core inflation peaks above 3.5 percent in 2010.
     - Headline inflation, driven by energy and food price shocks, peaks above 4 percent.
     - Output gap closes to zero in second half of 2011 before further negative shocks in 2012 re-open a gap.
  3. OPT delivers a considerably narrower output gap than historical; unemployment consistently below historical rate—up to 0.8 percentage points lower in 2010 and 2011.
  4. Summary: OPT implies an aggressive response (long ELB horizon) that moves the economy away from the deflation dark corner and closer to potential output and full employment.
  5. Drawback: inflation overshoot under OPT, exacerbated in headline inflation by 2010-11 oil and food price increases; authors view medium-term overshoot as acceptable given expected deviations on both sides of target over time and consistency with Canadian inflation-targeting experience.

### Fiscal stimulus and negative policy rate experiments (Figure 10)
- Simulated shock: fiscal stimulus equivalent to 1 percent of GDP, and a cut in policy rate from 0.25 to -0.5 percent (reflecting Bank of Canada’s latest estimate of the ELB).
- All cases under the loss-minimizing strategy; forecasts as of 2009Q2.
- Key aspects:
  1. Negative interest rate case:
     - Policy rate cut to new floor (-0.5 percent) and stays there a little less time than base case with 0.25 percent ELB.
     - Lower rate causes a quick rise in the price of foreign exchange; these changes close the output gap faster than the control.
     - Because nominal rate declines more, the decline in real interest rates requires a smaller inflation overshoot than in the base case.
     - Effects are relatively modest compared to those achieved at the positive ELB.
  2. Fiscal policy case (cross-hatched lines):
     - Fiscal policy has a more direct impact through the demand channel; implied inflation overshoot is smaller than baseline.
     - Fiscal stimulus appreciates the Canadian dollar relative to base (classic Mundell-Fleming result for a small open economy with perfect capital mobility).
     - Unlike Mundell-Fleming’s neutralization by higher rates, in this model fiscal policy increases output because monetary policy holds the interest rate at the ELB and focuses on inflation and output gap objectives.
     - The exchange rate appreciation relative to control is not large enough to choke off the stimulus.

### Alternative scenario: IFB reaction function with backward-looking expectations (Figure 11)
- Illustrative assumptions:
  - Monetary policy follows IFB reaction function.
  - Expectations put a high weight on lagged inflation (backward-looking) due to imperfect credibility of inflation target (Appendix II details assumptions).
- Implications:
  - IFB does not strongly avoid dark corners; will not mount sharp corrective actions near deflation/ELB.
  - Backward-looking expectations reflect imperfect credibility; if target is missed for prolonged period, public gives high weight to observed rate.
  - Negative shocks produce worse outcomes relative to history starting 2009Q2:
    - Wider output gap, higher unemployment, lower inflation.
    - Counterfactual policy interest rate is lower for a couple of years—not due to more aggressive policy but endogenous response to weaker economy.

### Policy conclusions and recommendations
- Canada’s IFT regime has delivered stable inflation expectations at 2 percent for more than two decades; credibility of target and flexible exchange rate have stabilized economy against external disturbances.
- Framework could be strengthened to better avoid dark corners:
  - Strong case for Bank of Canada to use CFG (commit to publish forecast of short-term interest rate path as part of information following each of the 8 annual policy decision meetings).
  - Increased transparency would strengthen the framework in both normal times and times of heightened instability and improve accountability by allowing the Bank to justify divergences from the forecast path.
- On equilibrium real rates and policy design:
  - Estimates of equilibrium world real interest rate have been falling since global financial crisis; various recent estimates are about zero.
  - If equilibrium real rate is near zero, the ELB on nominal rate implies a floor of about -2 percent on the gap between actual and equilibrium real interest rate—limited room for expansionary monetary policy.
  - Raising the inflation target by 1 percentage point (to 3 percent) would provide more space, but merely announcing a higher target is insufficient; actions would be required to achieve it and Canada’s strong expectations at 2 percent make such a change difficult.
  - Expansionary fiscal policy is a better alternative for below-par activity: it raises output and makes monetary policy more effective in short-run output-inflation trade-off.
- Recommended combined strategy (2016 view):
  - CFG for monetary policy combined with a well-designed fiscal stimulus would be potent for getting the economy back on track, despite ELB.
  - This strategy avoids financial stability issues from prolonged negative rates, is stronger than unconventional monetary interventions (e.g., QE which works through bond yield term or risk premiums of relatively small size in Canada), and preserves the 2 percent inflation target as a firm nominal anchor.

### Appendix highlights — Exchange rate and asset prices as shock absorbers or amplifiers
- Risk-adjusted uncovered interest parity (UIP) condition (nominal and real versions) under perfect foresight relates interest differentials, exchange rate changes, and risk premium; real exchange rate z defined as nominal exchange rate adjusted for foreign (f_t p) and domestic (p_t) price differential: z_t = s_t + p_t^f - p_t.
- Real exchange rate as shock absorber:
  - With credible aggressive policy, negative demand shock leads to expected future inflation increase, larger decline in real interest rates than nominal, producing real depreciation (z_t up) that supports demand via exports and expenditure switching.
- Real exchange rate as shock amplifier:
  - If policy is passive and not credible, negative demand shock leads to expected future lower inflation, current and future short-term real interest rates could increase (sum of r_j up), producing real appreciation (z_t down) that reduces net exports and deepens recession.
- Asset prices (e.g., equity prices) behave similarly:
  - Credible aggressive policy → increases in equity prices (via currency depreciation benefits to profits and lower real discount rates → higher valuations).
  - Non-credible passive policy → decreases in asset prices, amplifying shocks.

*Source: Authors’ simulations and text in _wp16192 - Appendix II outlines the model structure.*

### APPENDIX II. THE NEW-KEYNESIAN MODEL FOR CANADA

### APPENDIX II. THE NEW-KEYNESIAN MODEL FOR CANADA

### A.II.1. IS Equation
- Output gap (t y) defined as log-level of output (t y) minus potential output (t y).
- IS equation links Canada’s output gap to past and expected future output gaps, deviations of the lagged one-year real interest rate (4 t r) and the real effective exchange rate (t reer) from equilibrium, the rest-of-the-world output gap (World t y), and the terms-of-trade gap (t tot).
- Structure and parameterization (as presented):
  - t t t y y y = + (equation framing)
  - Coefficients: (0.65), (0.15), (0.15), (0.05), (0.3), (0.5) appear in the IS relation alongside beta coefficients β1, β2, β3 and disturbance ε.
  - Lagged one-year real rate defined as: 4() / 4 t t t t t r r r r    =   +   +   +  (structural decomposition shown).

### A.II.2. Phillips Curve
- Core inflation (C t π) depends on:
  - Inflation expectation (C t E π)
  - Past year-on-year core inflation (1 4 C t π )
  - Lagged output gap in a non-linear way
  - Rate of real effective exchange rate depreciation and deviation from equilibrium
  - Small pass-through from oil and food price inflation via real oil and food prices adjusted for real exchange rate effects
- Parameterization and structure:
  - Weights on expectation and lag sum to one; base-case numerical weights shown: (0.75), (0.25), (0.05), (0.05), (0.01), (0.01) in the extended Phillips equation.
  - Expectation formation: *747 (0.8) 4(1) CC tt E π + λ π λ π = + − (shows combination of model-consistent one-year-ahead inflation and inflation target * π with small weight).
- Sensitivity analysis note:
  - Alternative with more inertia reduces a parameter from 0.75 to 0.65 and weight on the inflation target to 0.

### A.II.3. Policy Interest Rate: Reaction Function Options
- Linear inflation-forecast-based (IFB) reaction function:
  - Standard IFB form with three-quarter-ahead inflation projection (3 4 C t π + and 3 4 H t π +) allowing discounting of shocks reversing within three-quarter policy horizon.
  - Coefficients in displayed form include (0.75), (1.5), (0.5) and γ-terms.
- Loss-minimizing strategy — risk management:
  - Minimizes discounted current and future losses from inflation deviations, output gaps, and changes in policy rate.
  - Loss function specification:
    - Discount factor and weights: (0.98) (1.0)(1.0)(0.5) appear in the Loss summation.
    - Quadratic penalties on inflation deviations and output gaps; penalty on squared change of policy rate to prevent sharp movements.
- Effective lower bound (ELB):
  - Interest rate subject to constraint floor i, historically assumed 0.25 percent in historical simulation.
  - Constraint: (0.25) floor t i i ≥

### A.II.4. Real Interest Rates and Real Exchange Rates
- Real interest rate definition:
  - t r = t i − 1 C t π + (nominal minus expected core inflation).
- Bilateral real exchange rate with U.S. (t z):
  - Defined using Canadian core CPI (C t p); increase implies Canadian-dollar depreciation.
  - Decomposition: t t z z z = + (equilibrium trend t z and deviation t z); equilibrium determined by equilibrium terms of trade (tot t z =).
  - USC tt t z s p p = + − (relationship with U.S. price levels).
- Real effective exchange rate (reer) entering output gap:
  - Trade-weighted bilateral real exchange rates versus seven regions with weights consistent with the Global Projection Model (GPM).
  - Weighting coefficients shown: (0.68), (0.07), (0.02), (0.08), (0.04), (0.05), (0.05) for regions USEUJA CHEALA etc., resulting in reer = sum of w z terms.
- Risk-adjusted UIP condition:
  - Links bilateral exchange rate (Canada–U.S.) with country interest rates (t i and US t i), includes time-varying country risk premium (ctry t σ) and terms-of-trade shocks (tot t σ).
  - Expectation formation for exchange rate: combination of model-consistent 1t s +, backward-looking 1t s −, and trend exchange rate depreciation *,* 2[() / 4] US t z π π Δ − −.
  - Numerical factorization: factors ¼ and 2 used to de-annualize/annualize inflation and nominal exchange rate growth consistent with annualized interest rates.
  - Autoregressive condition for the terms-of-trade premium consistent with equilibrium: 1 4() US ctry t t t t t r r z z σ + − = − + .

### A.II.5. Relative Prices
- Headline inflation driven by dynamics of relative price movements: core CPI (C t p) relative to headline CPI (H t p).
- Long-run assumption: headline inflation equals core inflation, though prolonged deviations possible due to relative price trends in non-core items.
- Relative price decomposition: t t r p p = C H (Core minus Headline); t t r p r p r p = + (trend plus gap).
- Relative price gap equation:
  - Parameters: (0.43), (0.012), (0.02) enter the equation linking relative price gap to Oil and Food real prices adjusted for exchange rate effects and an AR term.
  - Trend growth assumed AR(1) with mean zero and parameters shown: (0.9) in Δ dynamics.

### A.II.6. Term Structure of Interest Rates
- Long-term government bond yield Gov k t i (maturity k quarters: 4, 8, 20, 40) equals average expected short rates k quarters ahead plus a term σ Term k t capturing bond and term premia, plus measurement shock ε.
- Specific formulations shown:
  - ,4,4,4 4 Gov Term Gov t t t t i i σ ε = + + 
  - ,8,… with averaging expression ( 44 ) / 2 and analogous forms for 20 and 40 quarter maturities with coefficients and summations explicitly presented.
  - Short-rate decomposition across quarters: 123 4() / 4 t t t t t i i i i i    = + + + + (structural averaging).

### A.II.7. Unemployment Rate
- Unemployment rate (t u) modeled with gap version of Okun’s law:
  - A one percentage-point increase in the unemployment gap (t u) is associated with approximately two percentage-point decrease in the output gap.
- NAIRU (t u) follows stochastic process with shocks to level and growth rate.
- Parameterization and dynamics:
  - Autoregressive coefficients: (0.4), (0.4) in the u c y relation and NAIRU dynamics.
  - AR dynamics for level and growth include (0.9) in ΔΔ dynamics.

### A.II.8. Potential Output
- Potential growth rate (t y Δ) assumed to converge to steady state ss y Δ in the long run but can deviate for prolonged periods.
- Dynamics given with persistence coefficients: (0.97) and (2) and AR structure with shock ε.

### A.II.9. The Rest of the World
- Rest-of-the-world output gap relevant for Canada is a weighted average of output gaps across seven regions (U.S., Euro Area, Japan, China, Emerging Asia, Latin America, rest of world) using export-share weights.
- Weights shown explicitly: (0.79), (0.04), (0.02), (0.04), (0.04), (0.02), (0.05) combining into World = sum of Exp region gaps with these υ weights.
- Equilibrium real interest rate linkage to U.S.:
  - AR(1) relation with coefficient (0.6) and shock structure shown: 1 (0.6) (1) US r r r t t t t r r ρ ρ ε − = + − + .

### A.II.10. Commodity Terms of Trade
- Real price of oil (Oil t rp) defined as global oil price Oil t p in U.S. dollars relative to U.S. CPI US t p; equilibrium growth rate zero though actual growth can deviate.
- Oil and food real prices modeled with AR dynamics:
  - ΔΔ AR coefficient (0.95) for real-price growth, and level AR coefficient (0.7).
  - Same modeling approach applied to food: Food equations mirror Oil with identical persistence values (0.95) and (0.7).
- Terms-of-trade gap (t tot) determined by real price gaps of oil and food:
  - Coefficients: (0.03) for Oil and (0.002) for Food in the relation tot = c1 Oil rp + c2 Food rp.
- Real exchange rate depreciation consistent with terms-of-trade changes:
  - Coefficients in decomposition: (0.25), (0.03), (0.002) appear in the Δ relations linking tot z Δ to Oil z Δ and Food z Δ and their equilibrium counterparts.
- Terms-of-trade premium entering UIP:
  - Modeled as the “surprise” component in the real exchange rate movement consistent with the terms of trade: 1 4() tot tot tot t t t z E z σ − = − .

*Source: APPENDIX II. THE NEW-KEYNESIAN MODEL FOR CANADA*

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