## _wp09232 - 1. Estimation Results

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### Introduction and main findings
- Focus: Japan entering a liquidity trap in the mid-1990s and the subsequent “Lost Decade” of slow growth, deflation, and output persistently below potential.
- Core questions:
  - What policy was the Bank of Japan following?
  - What “exceptional mistakes” did it make?
  - What could it have done to avoid the “Lost Decade?”
- Empirical approach:
  - Tests whether Bank of Japan interest-rate policy is described by a forward-looking Taylor-type reaction function that implicitly targets inflation.
  - Uses a stylized structural New Keynesian model with time-varying implicit inflation target π*_t and time-varying natural rate r*_t.
- Key empirical findings:
  - Japanese interest rates fit a forward-looking Taylor rule that implicitly targets inflation.
  - Implicit inflation target declined from about 2.5 percent in the early 1980s to near 1 percent in the mid-1990s.
  - Natural rate of interest declined sharply in the early 1990s (from about 4 percent in the early 1980s to about 1 percent by the mid-1990s; estimate not significantly different from zero by 1995Q4).
  - The 1990s are characterized by contractionary demand shocks.
  - Monetary policy was not identified as the primary cause of poor performance, though alternative policy could have materially stabilized the economy.

### Model specification (stylized New Keynesian model)
- Endogenous variables and notation:
  - x_t: output gap (deviation of output from potential)
  - r_t: nominal interest rate
  - π_t: rate of inflation (quarterly)
  - π_tˆ: deviation of inflation from its steady-state level (π_t − π*)
- Observational frequency: quarterly; each period t corresponds to a quarter.
- Core structural equations:
  - Intertemporal IS equation: output depends on lagged real interest rate, past and expected future output; includes habit persistence and exogenous real-demand disturbance g_t.
  - Aggregate supply / Phillips-type equation: inflation depends on past and expected future inflation and the output gap; includes Calvo-style price stickiness and indexation.
  - Forward-looking Taylor rule with zero lower bound: policy responds to deviations of four-quarter-average inflation from the implicit target and can respond to the output gap; includes interest-rate smoothing φ_r and exogenous policy shock ε_r; a "max" operator enforces non-negativity of nominal interest rates.
- Stochastic processes:
  - g_t: AR(1) g_t = ḡ + g_ρ (g_{t-1} − ḡ) + ε^g_t.
  - z_t: AR(1) z_t = z_ρ z_{t-1} + ε^z_t.
  - r*_t: AR(1) with persistence r*_ρ and long-run value r*.
  - π*_t: AR(1) with persistence π*_ρ and long-run value π*.
- Zero lower bound treatment:
  - Linear model solved abstracting from zero lower bound (Sims (2002)).
  - Zero lower bound imposed using Reifschneider and Williams (2000) by augmenting the nominal interest-rate equation with additive disturbances over current and N future periods (disturbances equal zero if unconstrained rate is positive, otherwise equal absolute value of unconstrained negative rate).

### Estimation results — policy, targets, and structural parameters
- Policy-rule estimates (posterior summaries):
  - πφ (long-run reaction to inflation): Posterior Mean 1.715; Lower Bound 1.358; Upper Bound 2.078.
  - xφ (output gap-stabilization): Posterior Mean 0.092; Lower Bound 0.041; Upper Bound 0.144.
  - rφ (interest-rate smoothing): Posterior Mean 0.738; Lower Bound 0.648; Upper Bound 0.823.
- Implicit inflation target:
  - Estimated downward drift from about 2.5 percent in the early 1980s to about 1 percent by 1995.
  - Measurement bias in CPI inflation in Japan estimated by Shiratsuka (1999) about 0.9 percent per annum (cited).
- Natural rate of interest:
  - Estimated decline from about 4 percent in the early 1980s to about 1 percent by the mid-1990s; estimate not significantly different from zero by 1995Q4.
  - Sharp decline particularly after 1991, coinciding with bursting of asset-price bubble.
  - On average during 1991-1995, actual real policy rate remained above the natural rate despite interest-rate cuts.
- Structural parameters (selected posterior means and intervals):
  - σ: Posterior Mean 0.424; Lower Bound 0.317; Upper Bound 0.526.
  - γ: Posterior Mean 0.751; Lower Bound 0.651; Upper Bound 0.860.
  - κ: Posterior Mean 0.019; Lower Bound 0.016; Upper Bound 0.022.
  - λ (degree of price indexation): Posterior Mean 0.623; Lower Bound 0.474; Upper Bound 0.775.
- Shock standard deviations (posterior means and intervals; note expressed in percent in source):
  - σεg: Posterior Mean 0.280; Lower Bound 0.200; Upper Bound 0.350.
  - σεz: Posterior Mean 0.150; Lower Bound 0.120; Upper Bound 0.170.
  - σεr: Posterior Mean 0.150; Lower Bound 0.130; Upper Bound 0.180.
  - σεπ*: Posterior Mean 0.050; Lower Bound 0.030; Upper Bound 0.070.
  - σεr*: Posterior Mean 0.100; Lower Bound 0.040; Upper Bound 0.170.
- Persistence parameters (posterior means and intervals):
  - gρ (Normal prior): Posterior Mean 0.005; Lower Bound 0.003; Upper Bound 0.006.
  - zρ (Normal prior): Posterior Mean 0.007; Lower Bound 0.006; Upper Bound 0.009.
  - ρ ε g: Posterior Mean 0.643; Lower Bound 0.539; Upper Bound 0.749.
  - ρ ε z: Posterior Mean 0.290; Lower Bound 0.193; Upper Bound 0.388.
  - ρ π*: Posterior Mean 0.957; Lower Bound 0.924; Upper Bound 0.991.
  - ρ r*: Posterior Mean 0.961; Lower Bound 0.933; Upper Bound 0.991.
- Model implications:
  - σ posterior mean 0.4 implies monetary policy has relatively modest effect on output.
  - γ posterior mean 0.7 implies substantial persistence in consumption/expenditure.
  - Model replicates autocorrelation functions of inflation and interest rates closely; model generates less output persistence than implied by data.

### Identified shocks and baseline findings
- Baseline model uses σ = 0.4 as comparison benchmark.
- Supply shocks that reduce inflation can, when nominal interest rates are at the zero lower bound, raise real interest rates and depress output.
- Exogenous interest rate shocks εr are close to zero during the 1990s.
- Estimated output response coefficient in the baseline rule is xφ = 0.09.
- Implicit inflation target in estimated policy rule declined over time, reaching about 1 percent in the early 1990s.

### Counterfactual policy experiments and outcomes (simulation period 1993Q1–2006Q1)
- Simulation design:
  - Start 1993Q1, end 2006Q1.
  - Report outcomes: average inflation during 1993Q1-2006Q1 and cumulative output loss defined as sum of output gaps from 1993Q1-2006Q1 in percent of annual potential GDP.
  - Shock extraction uses estimated model while respecting zero bound.
  - Post-1995Q4 assumptions: structural parameters unchanged; implicit inflation target and natural rate follow estimated paths up to 1995Q4 and remain at values reached at 1995Q4 (about 1 percent) thereafter.
  - Robustness checks include natural rate falling to -1 percent per year after 1995Q4 and reducing σ to 0.2.
- Table 2 (1993Q1–2006Q1): Actual and Counterfactual outcomes (average inflation in percent per year; cumulative output loss in percent of annual potential GDP)
  - Actual: Average Inflation = -0.01; Output Loss = -22.6
  - Counterfactual — Higher Inflation Target: Average Inflation = 2.6; Output Loss = -19.4
  - Counterfactual — Stronger Output-gap Response: Average Inflation = 0.2; Output Loss = -15.8
  - Counterfactual — Higher Inflation Target and Stronger Output-gap Response: Average Inflation = 2.7; Output Loss = -10.8
  - Counterfactual — Price Target: Average Inflation = 1.1; Output Gain/Loss = 1.4

- Higher inflation target (raise implicit target to 4 percent from 1993Q1):
  - Average inflation = 2.6 percent per year (counterfactual).
  - Cumulative output loss reduced from -22.6 to -19.4 percent of potential GDP (a reduction of one seventh).
  - Limited and short-lived output improvement because output response coefficient remains xφ = 0.09.

- Stronger output-gap response (raise xφ to 1.0 from 1993Q1):
  - Average inflation = 0.2 percent per year.
  - Cumulative output loss declines to -15.8 percent of potential GDP (about a 30 percent reduction versus actual -22.6 percent).
  - Counterfactual policy rate falls faster, reaches zero by 1995Q4 (about three years before the actual policy rate reached zero).
  - Stimulus operates mainly via expectations that policy rates will remain at zero longer; when policy rate is at zero bound after contractionary shocks it cannot respond further.

- Combined higher inflation target (4 percent) and stronger output-gap response (xφ = 1.0):
  - Average inflation = 2.7 percent per year.
  - Nominal interest rates hit the zero bound in only three quarters: 2001Q4–2002Q2.
  - Cumulative output loss = -10.8 percent of potential GDP (less than half the actual estimated loss).
  - Improvement equals 11.8 percentage points of annual potential GDP, noted as greater than the sum of individual component effects.

- Price-level targeting (price target with 1 percent trend, implemented from 1993Q1):
  - Policy targets price level p_t with trend p*_t evolving at about 1 percent per year.
  - Price-level response parameter reported as pφ = 7.1 in the source.
  - Average inflation = 1.1 percent per year.
  - Policy interest rate is held at zero for all but two quarters during 1995Q2–2006Q1.
  - Cumulative outcome: replaces actual estimated cumulative output loss with a cumulative output gain of 1.4 percent of potential GDP.
  - Price-level targeting yields superior stabilization in these simulations compared with combined inflation-target and stronger output-gap response.

- Robustness checks:
  - Assuming natural rate falls to and remains at -1 percent per year after 1995Q4 — counterfactual improvements do not decline under this assumption.
  - Reducing σ by half (σ = 0.2) — improvement in output performance from alternative interest-rate rules declines but remains substantial.

### Policy implications and comparative insights
- Single-policy changes:
  - Raising the inflation target alone to 4 percent would have limited, short-lived benefits: average inflation = 2.6 percent; cumulative output loss reduced to -19.4 percent.
  - Strengthening the output-gap response alone (xφ = 1.0) reduces cumulative output loss to -15.8 percent and raises average inflation to 0.2 percent but large output losses remain.
- Combined policy:
  - Combining a higher inflation target of about 4 percent with a stronger output-gap response (xφ = 1.0) yields average inflation = 2.7 percent and cumulative output loss = -10.8 percent (less than half the actual loss).
  - The combination produces an effect larger than the sum of individual effects.
- Price-level targeting:
  - Price-level targeting with an upward trend of about 1 percent per year produces average inflation = 1.1 percent and a cumulative output gain = 1.4 percent of potential GDP in the simulation.
  - Price-level targeting reduces time spent at the zero bound and requires future higher inflation to offset past deflation.
  - Potential concern: price-level targeting may imply costly monetary contractions following one-time increases in the price level; further assessment suggested.
- Credibility caveat:
  - Counterfactuals assume authorities have sufficient credibility so that policy announcements are believed; demonstrating resolve is important for announcement effectiveness.
- General takeaway for central banks:
  - Central banks that target very low inflation (0–2 percent) may need greater insurance against large contractionary shocks by raising inflation targets, increasing active stabilization of output, or adopting price-level targeting.

### Appendix — implementation of the zero interest-rate floor in simulations
- Method:
  - Non-negativity constraint imposed using Reifschneider and Williams (2000).
  - Linear model augmented with anticipated shocks to policy interest rate over current and N future periods.
  - Disturbances equal zero if unconstrained rule implies positive rate; otherwise equal absolute value of unconstrained negative rate.
  - Simulations use N = 12; results not sensitive to exact value of N.
- Interpretation:
  - Procedure ensures nominal interest rate respects zero floor for current and N future periods.
  - Assumption consistent with notion that fiscal policy could eventually be expected to provide necessary stimulus to prevent unstable deflationary spiral.

*Source: _wp09232 - 1. Estimation Results (PDF chapter content provided).*

### 1. Estimation Results ..................................................................................................

### _wp09232 - 1. Estimation Results ..................................................................................................

### Introduction and main findings
- Focus: the experience of Japan entering a liquidity trap in the mid-1990s and the subsequent “Lost Decade” of slow growth, deflation, and output persistently below potential.
- Core questions addressed:
  - What policy was the Bank of Japan following?
  - What “exceptional mistakes” did it make?
  - What could it have done to avoid the “Lost Decade?”
- Empirical approach:
  - Investigates whether the Bank of Japan’s interest-rate policy is well described by a standard Taylor-type monetary policy reaction function.
  - Uses a stylized structural New Keynesian model with the implicit inflation target and the natural rate of interest allowed to vary over time.
- Key empirical findings:
  - Japanese interest rates fit a forward-looking Taylor rule that implicitly targets inflation (consistent with Ahearne et al. (2002)).
  - The implicit inflation target declined from about 2.5 percent in the early 1980s to near 1 percent in the mid-1990s.
  - The natural rate of interest declined sharply in the early 1990s.
  - The 1990s are characterized by contractionary demand shocks.
  - These results suggest monetary policy was not the primary cause of poor performance, though alternative policy could have helped stabilize the economy.

### Counterfactual policy experiments and outcomes
- Alternative policy rules evaluated (counterfactual simulations):
  - (i) A policy rule with a higher inflation target (as suggested by Krugman (1998)).
  - (ii) A policy rule with a strong response to the output gap.
  - (iii) A policy rule that combines a higher inflation target with a strong response to the output gap.
  - (iv) A price-level targeting rule along the lines of Eggertsson and Woodford (2003).
- Counterfactual results:
  - Raising the inflation target to 4 percent while keeping everything else unchanged: only a short-lived positive effect on output.
  - Responding more aggressively to the output gap while keeping the low estimated inflation target: would not have avoided deflation and would yield limited output improvement.
  - Combining a higher inflation target of about 4 percent with a stronger response to the output gap: would have provided substantial support to output and avoided deflation.
  - A price-level targeting rule: would have provided superior stabilization results.
- Credibility caveat:
  - The analysis assumes authorities have already established sufficient credibility so that their policy announcements are believed; demonstrating resolve is important for announcement effectiveness.

### Model specification (stylized New Keynesian model)
- Key endogenous variables and notation:
  - x_t: output gap (deviation of output from potential)
  - r_t: nominal interest rate
  - π_t: rate of inflation (quarterly)
  - π_tˆ: deviation of inflation from its steady-state level (π_t − π*)
- Observational frequency: quarterly; each period t corresponds to a quarter.
- Core structural equations (as presented):
  - Intertemporal IS equation (equation (1)): output depends on lagged real interest rate, past and expected future output; includes habit persistence and exogenous real-demand disturbance g_t.
  - Aggregate supply / Phillips-type equation (equation (2)): inflation depends on past and future expected inflation and the output gap; includes Calvo-style price stickiness and indexation.
  - Forward-looking Taylor rule with zero lower bound (equation (3)): policy responds to deviations of four-quarter-average inflation from the implicit target and can respond to the output gap; includes interest-rate smoothing (φ_r) and an exogenous policy shock ε_r; the "max" operator enforces non-negativity of nominal interest rates.
- Stochastic processes included:
  - g_t follows AR(1): g_t = ḡ + g_ρ (g_{t-1} − ḡ) + ε^g_t  (notation and parameter names as in the source).
  - z_t (supply disturbance) follows AR(1): z_t = z_ρ z_{t-1} + ε^z_t.
  - r*_t (time-varying natural rate of interest) follows AR(1) with persistence r*_ρ and long-run value r*.
  - π*_t (time-varying implicit inflation target) follows AR(1) with persistence π*_ρ and long-run value π*.
- Solution method:
  - Linear model solved abstracting from zero lower bound (following Sims (2002)).
  - Zero lower bound imposed using Reifschneider and Williams (2000) by augmenting the nominal interest-rate equation with additive disturbances for current and a finite number of future periods (disturbances equal zero if unconstrained rate is positive, otherwise equal absolute value of unconstrained negative rate).
  - Expectations of future nominal interest rate cannot be negative up to a finite number of future periods under this procedure.

### Model estimation details
- Estimation method: Bayesian estimation jointly of the interest-rate reaction function and the structural model.
- Sample period: quarterly data for 1981Q3-1995Q4.
  - Rationale: sample starts after inflation had declined to 4 percent from double-digit levels in the 1970s; sample ends in 1995Q4 because interest rates were at or near the zero bound after that date.
- Data series and adjustments:
  - Price series: seasonally-adjusted consumer price index (CPI) excluding fresh food (from Bank of Japan).
  - Consumption-tax adjustments: two jumps in the price level in 1989Q2 and in 1997Q2 due to changes in the consumption tax; the analysis uses the Bank of Japan’s consumption- and tax-adjusted inflation series.
  - Output-gap: Bank of Japan staff estimates using a production-function approach and data on capital and labor (Hara et al., 2006) to avoid using the Hodrick-Prescott filter for Japan.
  - Policy instrument: uncollateralized interbank overnight nominal call money rate corresponds to the model’s policy rate.
- Prior choices and Bayesian implementation:
  - Bayesian approach chosen because it outperforms maximum likelihood in small samples and combines observable data with prior information.
  - Selection of priors follows existing literature.
  - Standard errors of innovations assumed to follow inverse-gamma distributions.
  - Prior means have loose priors with standard deviations of two.
  - Prior means for standard errors of innovations to r* and π* are one-tenth of those for the other shocks.
  - Persistence parameters for demand and supply shocks are beta distributed to ensure values between zero and one.
- Estimation outcomes (summary of empirical interpretations rather than full posterior details):
  - Estimated time-varying implicit inflation target fell from about 2.5 percent in the early 1980s to near 1 percent in the mid-1990s.
  - Estimated sharp decline in the natural rate of interest in the early 1990s.
  - Evidence of contractionary demand shocks dominating the 1990s.

### Policy implications emphasized in the text
- Raising the implicit inflation target alone to 4 percent (holding other policy coefficients unchanged) would have limited, short-lived benefits.
- Strengthening the policy response to the output gap alone (with a low inflation target) would have been insufficient to avoid deflation and would have yielded limited output gains.
- Combining a higher inflation target of about 4 percent with a stronger output-gap response could have substantially supported output and avoided deflation.
- Price-level targeting would have provided superior stabilization compared with simple inflation-targeting rules in the counterfactuals considered.
- Credibility of announcements is crucial; the analysis assumes sufficient credibility so announcements are believed.

*Source: _wp09232 - 1. Estimation Results (PDF chapter content provided).*

### 0.5 and a standard deviation of 0.2. For the

### _wp09232 - 0.5 and a standard deviation of 0.2. For the

### Priors and estimation setup
- Natural rate of interest (quarterly long-run) prior: Normal distribution with mean of 0.75 percent per quarter and standard deviation 0.1 (corresponds to 3 percent on an annual basis; close to average observed over 1981-1995).
- Steady-state inflation target, π*: Normal distribution with mean of 0.5 percent per quarter (2 percent per annum) and standard deviation of 0.1 percent.
- Interest-rate policy function priors (based on Taylor (1993) rule):
  - Long-run reaction to inflation (πφ): Normal distribution mean 1.5 and standard deviation 0.125.
  - Output response parameter (xφ): inverse-gamma distribution mean 0.125 and standard deviation 0.125.
  - Interest-rate smoothing parameter (rφ): beta distribution mean 0.75 and standard error 0.1.
- Structural parameter priors:
  - Habit-persistence parameter γ: beta distribution mean 0.5.
  - Intertemporal elasticity of substitution σ: set at 0.5 (prior).
  - Phillips curve slope κ: prior mean 0.02.
  - Degree of price indexation prior mean 0.5.
  - β fixed at 0.995.
- Estimation approach:
  - Vector of parameters Φ estimated by standard Bayesian methods.
  - Mode of posterior found by maximizing log posterior.
  - Posterior distribution (mean and 95-percent confidence interval) obtained using a Metropolis-Hastings algorithm.
  - Estimation details: two blocks of 100,000 replications each, first 20 percent discarded, step size 0.5, rejection rate 0.70. Estimation conducted using DYNARE.
- Ex-post real interest rate over 1981Q3-1995Q4: 3.6 percent.

### Estimation results — monetary policy parameters and targets
- Estimated interest-rate reaction function:
  - Long-run reaction to inflation (πφ): estimated mean 1.7; 95-percent confidence interval greater than one.
  - Output gap-stabilization parameter (xφ): estimated mean 0.09.
  - Interest-rate smoothing coefficient (rφ): estimated mean 0.7.
- Implicit inflation target:
  - Estimated downward drift from about 2.5 percent in the early 1980s to about 1 percent by 1995.
  - Implicit target about 1 percent by 1995 is consistent with narrative evidence and Bank of Japan material cited.
  - Measurement bias in CPI inflation in Japan estimated by Shiratsuka (1999) about 0.9 percent per annum (cited).
- Natural rate of interest:
  - Estimated decline from about 4 percent in the early 1980s to about 1 percent by the mid-1990s.
  - Estimate not significantly different from zero by 1995Q4.
  - Sharp decline particularly after 1991; coincides with bursting of asset-price bubble.
  - On average during 1991-1995, actual real policy rate remained above the natural rate despite interest-rate cuts.

- Policy-rule fit:
  - Estimated target rate differs from fitted policy rate because target sets interest-rate smoothing parameter to zero.
  - Actual policy rate tends to follow target with a lag; substantial gradualism noted during late 1980s boom and after 1992.

### Table 1 — Prior and posterior summaries (selected rows preserved exactly as in source)
- Prior Distribution / Posterior Distribution (Mean, St. Dev., Lower Bound, Upper Bound) — parameters shown below as reported:

  - πφ: Normal | Mean 1.500 St. Dev. 0.250 → Posterior Mean 1.715 Lower Bound 1.358 Upper Bound 2.078
  - xφ: Invgamma | Mean 0.125 St. Dev. 0.125 → Posterior Mean 0.092 Lower Bound 0.041 Upper Bound 0.144
  - rφ: Beta | Mean 0.750 St. Dev. 0.100 → Posterior Mean 0.738 Lower Bound 0.648 Upper Bound 0.823
  - σ: Invgamma | Mean 0.500 St. Dev. 0.100 → Posterior Mean 0.424 Lower Bound 0.317 Upper Bound 0.526
  - γ: Beta | Mean 0.500 St. Dev. 0.100 → Posterior Mean 0.751 Lower Bound 0.651 Upper Bound 0.860
  - κ: Invgamma | Mean 0.020 St. Dev. 0.001 → Posterior Mean 0.019 Lower Bound 0.016 Upper Bound 0.022
  - λ (degree of price indexation): Beta | Mean 0.500 St. Dev. 0.100 → Posterior Mean 0.623 Lower Bound 0.474 Upper Bound 0.775
  - σεg: Invgamma | Mean 1.000 St. Dev. 2.000 → Posterior Mean 0.280 Lower Bound 0.200 Upper Bound 0.350
  - σεz: Invgamma | Mean 1.000 St. Dev. 2.000 → Posterior Mean 0.150 Lower Bound 0.120 Upper Bound 0.170
  - σεr: Invgamma | Mean 1.000 St. Dev. 2.000 → Posterior Mean 0.150 Lower Bound 0.130 Upper Bound 0.180
  - σεπ*: Invgamma | Mean 0.100 St. Dev. 2.000 → Posterior Mean 0.050 Lower Bound 0.030 Upper Bound 0.070
  - σεr*: Invgamma | Mean 0.100 St. Dev. 2.000 → Posterior Mean 0.100 Lower Bound 0.040 Upper Bound 0.170
  - gρ (Normal): Mean 0.005 St. Dev. 0.001 → Posterior Mean 0.005 Lower Bound 0.003 Upper Bound 0.006
  - zρ (Normal): Mean 0.007 St. Dev. 0.001 → Posterior Mean 0.007 Lower Bound 0.006 Upper Bound 0.009
  - ρ ε g: Beta | Mean 0.500 St. Dev. 0.100 → Posterior Mean 0.643 Lower Bound 0.539 Upper Bound 0.749
  - ρ ε z: Beta | Mean 0.500 St. Dev. 0.100 → Posterior Mean 0.290 Lower Bound 0.193 Upper Bound 0.388
  - ρ π*: Beta | Mean 0.950 St. Dev. 0.025 → Posterior Mean 0.957 Lower Bound 0.924 Upper Bound 0.991
  - ρ r*: Beta | Mean 0.950 St. Dev. 0.025 → Posterior Mean 0.961 Lower Bound 0.933 Upper Bound 0.991

- Note from table: parameters denoting standard deviations of shocks are expressed in percent.

### Structural-model parameter estimates and dynamics
- IS equation and habit:
  - σ (intertemporal elasticity of substitution): posterior mean 0.4 (noted as estimated posterior mean 0.4 in text).
  - γ (habit-formation): posterior mean 0.7 (text: estimated posterior mean of 0.7).
  - Implication: monetary policy has a relatively modest effect on output given σ estimate; substantial persistence in expenditure given γ estimate.
- Aggregate supply:
  - Degree of price indexation: estimated prior mean 0.6 (text reports estimated prior mean of 0.6).
  - κ (slope): estimated mean 0.02, consistent with Sugo and Ueda (2008).
- Model persistence:
  - Model replicates autocorrelation functions of inflation and interest rates closely; generates less output persistence than implied by the data.

### Counterfactual analysis design and assumptions
- Simulation period: start 1993Q1 and end 2006Q1.
- Reported outcomes for each simulation: average level of inflation during 1993Q1-2006Q1, cumulative output loss defined as sum of output gaps from 1993Q1-2006Q1 in percent of annual potential GDP.
- Shock extraction: time series for exogenous disturbances {g, z, εr} extracted using estimated model while respecting zero bound on nominal interest rates.
- Post-1995Q4 assumptions for counterfactuals:
  - Structural parameters from Table 1 remain unchanged after 1995Q4.
  - Implicit inflation target and natural rate of interest follow estimated paths up to 1995Q4 and remain at values reached at 1995Q4 (about 1 percent) thereafter.
  - Robustness checks:
    - Assuming natural rate falls to and remains at -1 percent per year after 1995Q4 — counterfactual improvements in output performance achieved by alternative policy rules do not decline under this assumption.
    - Reducing σ by half (σ=0.2) — improvement in output performance from alternative interest-rate rules declines but remains substantial.
- Interpretation of shocks:
  - Real demand shocks (gt) in early 1990s reflect decline in investment after bursting of stock- and land-price bubbles in 1991–92.
  - Shocks during 1997-99 associated with banking crisis, consumption tax hike, and Asian financial crisis.
  - Contractionary shocks starting in 2001 may reflect U.S. dot-com bubble collapse recession.
  - Supply shocks (zt) indicate deflationary disturbances starting in late 1990s, interpreted as declining markups and firm monopoly power in benign circumstances, but potentially problematic when interacting with other dynamics.

### Key qualitative findings and implications
- Estimated monetary policy for Japan in early 1990s:
  - No evidence of "exceptional" interest-rate policy during early 1990s relative to international norms.
  - Implicit inflation target declined to near 1 percent; consistent with contemporaneous central banking consensus favoring low inflation.
- Decline in natural rate of interest:
  - Large decline complicates easing monetary policy because actual real policy rate remained above natural rate on average during 1991-1995 despite cuts.
- Policy inertia and smoothing:
  - Actual policy rate exhibits inertia and tends to lag the model-implied target rate, especially during the late 1980s boom and post-1992 periods.
- Counterfactuals indicate that alternative interest-rate rules can materially affect average inflation and cumulative output loss over 1993Q1-2006Q1, with robustness to plausible alternative assumptions about the post-1995 natural rate and smaller σ.

*Source: _wp09232 - 0.5 and a standard deviation of 0.2. For the (PDF chapter/section).*

### 1.8 percent per year.

### _wp09232 - 1.8 percent per year.

### Identified shocks and baseline findings
- The model with the estimated value of σ=0.4 is used as the comparison benchmark.
- Supply shocks that reduce inflation can, when nominal interest rates are at the zero lower bound, raise real interest rates and thus depress output.
- Exogenous interest rate shocks, εr, are close to zero during the 1990s.
- The estimated output response coefficient in the baseline/estimated rule is xφ = 0.09.
- The implicit inflation target in the estimated policy rule declined over time, reaching about 1 percent in the early 1990s.

### Counterfactual experiments — summary table (1993Q1–2006Q1)
- Table 2: Actual and Counterfactual Inflation and Output Loss (average inflation in percent per year; cumulative output loss relative to potential in percent of annual potential GDP)
  - Actual: Average Inflation = -0.01; Output Loss = -22.6
  - Counterfactual — Higher Inflation Target: Average Inflation = 2.6; Output Loss = -19.4
  - Counterfactual — Stronger Output-gap Response: Average Inflation = 0.2; Output Loss = -15.8
  - Counterfactual — Higher Inflation Target and Stronger Output-gap Response: Average Inflation = 2.7; Output Loss = -10.8
  - Counterfactual — Price Target: Average Inflation = 1.1; Output Gain/Loss = 1.4

### Higher inflation target (4 percent from 1993Q1)
- Policy change:
  - Implicit inflation target raised to 4 percent per year starting 1993Q1.
- Mechanisms raising inflation to a counterfactual average of 2.6 percent:
  - Anchoring inflation expectations at 4 percent (forward-looking aggregated supply equation).
  - Short-run decline in real interest rates as nominal rates rise gradually toward a higher long-run level, stimulating output during 1993–1995.
  - Persistent deflationary unexpected shocks keep current-quarter inflation below 4 percent.
- Macro outcomes:
  - Average inflation = 2.6 percent per year (counterfactual).
  - Cumulative output loss reduced from -22.6 percent to -19.4 percent of potential GDP (a reduction of one seventh).
  - Limited and short-lived output improvement because the output response coefficient remains at xφ = 0.09.

### Stronger output-gap response (xφ raised to 1.0 from 1993Q1)
- Policy change:
  - Output-response parameter increased from estimated 0.09 to xφ = 1.0 in 1993Q1.
- Dynamics:
  - Counterfactual policy rate falls faster in 1993 and reaches zero by 1995Q4 (about three years before the actual policy rate reached zero).
  - Additional stimulus raises output during 1993–1997 and increases inflation above actual levels, though several quarters of deflation remain.
  - After contractionary shocks in 1997 and 2001, output falls by less but the policy rate—already at the zero bound—cannot respond further.
  - Stimulus operates primarily via expectations that policy rates will remain at zero longer.
- Macro outcomes:
  - Average inflation = 0.2 percent per year.
  - Cumulative output loss declines to -15.8 percent of potential GDP (about a 30 percent reduction versus actual -22.6 percent).
  - The output loss remains substantial at almost -16 percent of potential GDP.

### Combined higher inflation target and stronger output-gap response
- Policy change:
  - Inflation target = 4 percent per year; output-response parameter xφ = 1.0 starting 1993Q1.
- Dynamics:
  - Higher inflation target anchors expectations at 4 percent and provides greater policy space for cuts.
  - Announcement stimulates output during first two years; inflation rises toward 4 percent during this period.
  - When contractionary shocks hit (1997 and after 2001), the central bank uses additional policy space for interest-rate cuts; output rebounds faster after shocks.
- Macro outcomes:
  - Average inflation = 2.7 percent per year.
  - Nominal interest rates hit the zero bound in only three quarters: 2001Q4–2002Q2.
  - Cumulative output loss = -10.8 percent of potential GDP (less than half the actual estimated loss); loss reduction equals 11.8 percentage points of annual potential GDP, which the author notes is greater than the sum of individual component effects.

### Price-level targeting (price target with 1 percent trend)
- Policy change:
  - Central bank targets price level p_t with a trend equal to the estimated inflation target (about 1 percent per year); target evolves via p*_t = p*_(t-1) + π*_(t).
  - Interest-rate reaction function uses expected deviation of price level from target; price-level response parameter pφ is stated as 7.1 = pφ in the source (implying an expected 1 percent increase in the price level above the target is associated with a 1.7 percentage-point increase in the policy rate as described in the text).
  - No interest-rate smoothing and no additional explicit output-gap response in the baseline specification.
- Dynamics and rationale:
  - Price-level targeting requires future higher inflation to offset past deflation, lowering real rates during deflationary spells and moderating output contractions.
  - Introduced in 1993Q1 in the simulation.
- Macro outcomes:
  - Average inflation = 1.1 percent per year (broadly in line with the targeted price trend).
  - Policy interest rate is held at zero for all but two quarters during 1995Q2–2006Q1.
  - Cumulative outcome replaces the actual estimated cumulative output loss with a cumulative output gain of 1.4 percent of potential GDP.
  - The simulation suggests price-level targeting would have delivered more stable macroeconomic performance than the combined higher inflation target and stronger output-gap response in this setting.

### Comparative policy insights and implications
- Single policy changes:
  - Raising the inflation target alone (to 4 percent) would have warded off deflation but only modestly reduced cumulative output losses (from -22.6 to -19.4 percent).
  - Strengthening the output-gap response alone (xφ = 1.0) reduces the cumulative output loss to -15.8 percent and raises average inflation to 0.2 percent, but significant output losses would remain.
- Combined policy:
  - Combining a higher inflation target (4 percent) with a stronger output-gap response (xφ = 1.0) reduces the cumulative output loss to -10.8 percent and raises average inflation to 2.7 percent.
  - The combination yields a greater improvement than the sum of the individual improvements.
- Price-level targeting:
  - Price-level targeting with an upward trend of about 1 percent per year yields superior stabilization in the simulations, producing an average inflation of 1.1 percent and a cumulative output gain of 1.4 percent of potential GDP.
  - Potential concern: price-level targeting implies potentially costly monetary contractions following one-time increases in the price level; a more comprehensive assessment is left for future research.
- Policy takeaway for other central banks:
  - Central banks that target very low inflation (0–2 percent) may need greater insurance against large contractionary shocks by raising inflation targets, increasing efforts to stabilize output, or adopting price-level targeting.

_Italic: Source — content unit "_wp09232 - 1.8 percent per year." (PDF chapter/section)_

### References

### References

### Scholarly and policy literature cited
- Ahearne, Alan; Joseph Gagnon; Jane Haltmaier; Steve Kamin; and Christopher Erceg; Jon Faust; Luca Guerrieri; Carter Hemphill; Linda Kole; Jennifer Roush; John Rogers; Nathan Sheets; and Jonathan Wright, 2002, “Preventing Deflation: Lessons from Japan’s Experience in the 1990s,” International Finance Discussion Papers, Board of Governors of the Federal Reserve System.
- Baba, Naohiko; Motoharu Nakashima; Yosuke Shigemi; Kazuo Ueda; and Hiroshi Ugai, 2005, “Japan's Deflation, Problems in the Financial System, and Monetary Policy,” Monetary and Economic Studies 23(1), pp. 47–111.
- Ball, Laurence, 2000, Policy Panel on “Why Price Stability?” at the First ECB Central Banking Conference in Frankfurt am Main, November 2000.
- Bank of Japan, 2009, “Outlook for Economic Activity and Prices,” May 2009, http://www.boj.or.jp/en/type/release/teiki/tenbo/gor0904b.pdf
- Bernanke, Ben S., and Mark Gertler, 1999, “Monetary Policy and Asset Price Volatility,” in 1999 Symposium: New Challenges for Monetary Policy, pp. 77–128, Kansas City: Federal Reserve Bank of Kansas City.
- Bernanke, Ben S., 2000, “Japanese Monetary Policy: A Case of Self-Induced Paralysis?” in Ryoichi Mikitani and Adam S. Posen (eds.), Japan’s Financial Crisis and its Parallels to U.S. Experience, Special Report 13 (September 2000), Washington, DC: Institute for International Economics.
- Blanchard, Olivier, 2000, “Bubbles, Liquidity Traps, and Monetary Policy,” in Ryoichi Mikitani and Adam S. Posen (eds.), Japan’s Financial Crisis and its Parallels to U.S. Experience, Special Report 13 (September 2000), Washington, DC: Institute for International Economics.
- Blanchard, Olivier, 2003, Macroeconomics, Third Edition, Prentice-Hall.
- Boivin, Jean and Marc P. Giannoni, 2006, “Has Monetary Policy Become More Effective?,” The Review of Economics and Statistics, August 2006, 88(3): pp. 445-462.
- Clarida, R.; J. Gali; and M. Gertler, 1997, “Monetary Policy Rules in Practice: Some International Evidence,” European Economic Review, Vol. 42 (1998), pp. 1033–1067.
- Curdia, Vasco, and Michael Woodford, 2008, “Credit Frictions and Optimal Monetary Policy,” mimeo, Princeton University.
- Duisenberg, Wim, 2003, Remarks at Press Seminar on the Evaluation of the ECB’s Monetary Policy Strategy, http://www.ecb.int/press/pressconf/2003/html/is030508_1.en.html
- Eggertsson, Gauti, and Michael Woodford, 2003, “Optimal Monetary Policy in a Liquidity Trap,” Brookings Papers on Economic Activity 1:2003.
- Eggertsson, Gauti, 2006a, “Was the New Deal Contractionary?” Federal Reserve Bank of New York Staff Report No. 264, October 2006.
- Eggertsson, Gauti B., 2006b, “The Deflation Bias and Committing to Being Irresponsible,” Journal of Money, Credit and Banking, Vol. 38, No. 2 (Mar., 2006), pp. 283–321.
- Eggertsson, Gauti, 2008, “Great Expectations and the End of the Depression,” American Economic Review, 2008: 90(4).
- Feldstein, Martin, 1996, “Overview,” in Federal Reserve Bank of Kansas City, 1996, Achieving Price Stability.
- Friedman, Benjamin M., 2003, “Comments and Discussion,” Brookings Papers on Economic Activity 1:2003.
- Gertler, Mark, “Comments and Discussion,” Brookings Papers on Economic Activity 1:2003.
- Hara, Naoko; Naohisa Hirakata; Yusuke Inomata; Satoshi Ito; Takuji Kawamoto; Takushi Kurozumi; Makoto Minegishi; and Izumi Takagawa, 2006, “The New Estimates of Output Gap and Potential Growth Rate,” Bank of Japan Review 2006-E-3.
- Hayashi, Fumio and Edward C. Prescott, 2002, “The 1990s in Japan: A Lost Decade,” Review of Economic Dynamics, Vol. 5, pp. 206–235.
- Hunt, Benjamin L., and Douglas M. Laxton, 2003, “The Zero-Interest-Rate Floor and Its Implications for Monetary Policy in Japan,” in Tim Callen and Jonathan D. Ostry (eds.), 2003, Japan’s Lost Decade: Policies for Economic Revival (International Monetary Fund, 2003).
- International Monetary Fund, 2009, World Economic Outlook, April 2009, Washington, DC: International Monetary Fund.
- Iwamara, Mitsuru; Takeshi Kudo; Tsutomu Watanabe, 2006, “Monetary and Fiscal Policy in a Liquidity Trap: The Japanese Experience 1999-2004,” in Ito, Takatoshi and Andrew K. Rose (eds.), 2006, Monetary Policy with Very Low Inflation in the Pacific Rim, NBER-East Asia Seminar on Economics, Vol. 15. Chicago and London: University of Chicago Press, 2006.
- Jung, Taehun; Yuki Teranishi; and Tsutomu Watanabe, 2005, “Optimal Monetary Policy at the Zero-Interest-Rate Bound,” Journal of Money, Credit and Banking, Vol. 37(5), pp. 813–35.
- Kahn, George A., 1996, “Achieving Price Stability: a Summary of the Bank's 1996 Symposium,” Economic Review, Fourth Quarter 1996, Federal Reserve Bank of Kansas City.
- Krugman, Paul, 1998, “It’s Baaack! Japan’s Slump and the return of the Liquidity Trap,” Brookings Papers on Economic Activity 2:1998.
- Kuttner, Kenneth N., and Adam S. Posen, 2002, “Fiscal Policy Effectiveness in Japan,” Journal of the Japanese and International Economies, Volume 16, Issue 4, December 2002, pp. 536–558.
- Kuzin, Vladimir, 2006, “The Inflation Aversion of the Bundesbank: a State Space Approach, Journal of Economic Dynamics and Control, 30 (2006), pp. 1671–1686.
- Laubach, Thomas and John C. Williams, 2003, “Measuring the Natural Rate of Interest,” Review of Economics and Statistics, Vol. 85 (2003), pp. 1063–1070.
- Laxton, Douglas; Papa N'Diaye; and Paolo Pesenti, 2006, “Deflationary Shocks and Monetary Rules: An Open-Economy Scenario Analysis,” Journal of the Japanese and International Economies, Vol. 20, Issue 4 (2006).
- Leigh, Daniel, 2008, “Estimating the Federal Reserve’s Implicit Inflation Target: A State Space Approach,” Journal of Economic Dynamics and Control, 32 (2008), pp. 2013–2030.
- Ogaki, Masao, and Carmen M. Reinhart, 1998, “Measuring Intertemporal Substitution: The Role of Durable Goods,” Journal of Political Economy, 106, 1078–98.
- Okina, Kunio, and Shigneori Shiratsuka, 2004, “Policy Commitment and Expectation Formation: Japan's Experience Under Zero Interest Rates,” North American Journal of Economics and Finance 15(1) (March), pp. 75–100.
- Okubo, Masakatsu, 2008, “On the Intertemporal Elasticity of Substitution under Nonhomothetic Utility,” Journal of Money, Credit and Banking, Vol. 40, No. 5 (August 2008).
- Posen, Adam S., 2000, “The Political Economy of Deflationary Monetary Policy,” in Ryoichi Mikitani and Adam S. Posen (eds.), Japan’s Financial Crisis and its Parallels to U.S. Experience, Special Report 13 (September 2000), Washington, DC: Institute for International Economics.
- Posen, Adam S., 2002, “Deflation and the Bank of Japan,” Op-ed from The Japan Times, September 23, 2002.
- Rabanal, Pau, and Juan F. Rubio-Ramirez, 2005, “Comparing New Keynesian models of the business cycle: A Bayesian approach,” Journal of Monetary Economics, Vol. 52(6), pp. 1151–1166.
- Reifschneider, David, and John C. Williams, 2000, “Three Lessons for Monetary Policy in a Low-Inflation Era,” Journal of Money Credit and Banking, Vol. 32, No. 4, pp. 936–964.
- Shinotsuka, Eiko, 2000, Speech to the Japan Society of Monetary Economics on May 27, 2000, Bank of Japan Speeches and Statements.
- Shiratsuka, Shinegori, 1999, “Measurement Error in Japanese Consumer Price Index,” Federal Reserve Bank of Chicago, Working Paper No. WP/99/2.
- Sims, Christopher A., 2002, “Solving Linear Rational Expectations Models,” Computational Economics, Vol. 20(1-2), pp. 1–20.
- Smets, Frank, and Rafael Wouters, 2007, "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach." American Economic Review, 97(3): 586–606.
- Sugo, Tomohiro, and Kozo Ueda, 2008, “Estimating a Dynamic Stochastic General Equilibrium Model for Japan,” Journal of the Japanese and International Economies, Vol. 22(4), pp. 476–502.
- Taylor, John B., 1993, “Discretion Versus Policy Rules in Practice,” Carnegie-Rochester Series on Public Policy 39, 195–214.
- Woodford, Michael, 2003, Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press.
- Yamaguchi, Yukata, 2000, “Thinking behind Current Monetary Policy,” Remarks at the Japan National Press Club (4 August).

### Appendix — Implementation of the zero interest-rate floor in simulations
- Methodology:
  - The non-negativity constraint is imposed using the procedure of Reifschneider and Williams (2000).
  - The linear model described by equations (1)-(7) is augmented with anticipated shocks to the policy interest rate in the current period and N future periods.
  - These disturbances equal zero if the unconstrained policy-interest rates rule implies a positive rate, and the absolute value of the unconstrained rule if the rule implies a negative interest rate.
  - The nominal interest rate therefore respects the zero interest rate floor for the current and N future periods.
- Interpretation and consistency:
  - This assumption is consistent with the notion that fiscal policy could eventually be expected to provide the necessary stimulus to prevent an unstable deflationary spiral.
- Simulation parameter:
  - The simulations are based on N=12, but the results are not sensitive to the exact value of N.

*Source: _wp09232 - References*

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