## 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1

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### Major empirical components
- Sections estimated jointly: time-varying output gap (1966:1–2002:1), Phillips curve (1967:2–2002:1), GARCH for Phillips disturbances, monetary rule (1967:2–2002:1), GARCH for monetary-rule disturbances, and equilibrium/Granger causality between inflation persistence and relative monetary-policy uncertainty (1967:4–2002:1).
- Alternative output-gap measures compared: KL_ (Kalman-filter decomposition), HP_ (Hodrick-Prescott), ORP_ (Orphanides real-time).

### Methodology and identification
- Structural form: New-Keynesian aggregate supply with empirical augmentation including backward-looking inertia (λ) and time-varying signal-to-noise κ_t (equations (1), (1′), (1′′)).
- Demand link: (y_t - y_t^*) = φ (r_t - r_t^*) + ε^D_t with φ<0 and var(ε^D_t)=σ^2_{εD}.
- κ_t expression (signal-to-noise / Kalman gain): κ_t = [σ^2_{φ r_{t|t-1}}] / [σ^2_{φ r_{t|t-1}} + σ^2_{εD}] (formula (3)/(3′)).
- Monetary rule: time-varying Taylor-type with partial adjustment and monetary shock r^ε_t (equations (4), (5)); conditional variance decomposition per equation (8).
- Time variation modeled as independent random walks for parameters (transition equations (6), (7)); GARCH(1,1) for disturbance variances (equation (9)).
- Joint estimation via Kalman filter of two measurement equations: time-varying Phillips curve (η_t, λ_t, γ_t) and time-varying monetary rule (μ_t, ρ_t, φ1_t, φ2_t).
- Test of long-run link: cointegration λ_t = χ_0 + χ_1 κ_t (equation (10)); Granger causality tests in VAR with two lags.

### Key estimated parameters and statistics
- Output-gap estimation (Table 1, Model 1 KL):
  - σ_y~ = 0.0085  (0.0005)
  - σ_{y*} = 0.0009  (0.0020)
  - θ = 0.9229  (0.0212)
  - g = 0.0074  (0.0002)
  - Log likelihood = 484.6667
- Phillips-curve time-varying-parameter variances (Table 2):
  - Model 1 (Kalman Filter): σ_η = 0.0000 (0.1039); σ_λ = 0.0497 (0.0166); σ_γ = 0.0000 (0.0159)
  - Model 2 (HP): σ_η = 0.0000 (0.1043); σ_λ = 0.0397 (0.0170); σ_γ = 0.0000 (0.0267)
  - Model 3 (Real-time): σ_η = 0.2580 (0.2140); σ_λ = 0.0413 (0.0167); σ_γ = 0.0000 (0.0254)
- Phillips-curve GARCH(1,1) estimates (Table 3):
  - α_0: KL 0.0881 (0.0633); HP 0.0709 (0.0594); ORP 0.0600 (0.0502)
  - α_1: KL 0.1999 (0.0916); HP 0.2424 (0.1109); ORP 0.3126 (0.1344)
  - α_2: KL 0.7696 (0.0924); HP 0.7472 (0.1024); ORP 0.6839 (0.1312)
  - Interpretation: average α_1 ~ one-quarter and α_2 ~ three-quarters implying a half life of about one year; residual variance accounts for over three-quarters of total inflation variance.
- Monetary-rule time-varying-parameter variances (Table 4):
  - σ_μ: KL 0.4321 (0.2510); HP 0.4199 (0.3598); ORP 0.3708 (0.2456)
  - σ_ρ: KL 0.0371 (0.0187); HP 0.0446 (0.0312); ORP 0.0266 (0.0173)
  - σ_φ1: KL 0.1251 (0.0158); HP 0.0576 (0.0373); ORP 0.0374 (0.0213)
  - σ_φ2: KL 0.0653 (0.0353); HP 0.1216 (0.0211); ORP 0.1325 (0.0140)
- Monetary-rule GARCH estimates (Table 5):
  - α_0: KL 0.0016 (0.0092); HP 0.0008 (0.0006); ORP 0.0024 (0.0332)
  - α_1: KL 0.1554 (0.7836); HP 0.2445 (1.6649); ORP 0.0000 (0.0002)
  - α_2: KL 0.3848 (0.3699); HP 0.5319 (2.9470); ORP 0.8452 (2.1045)
  - Empirical implication: “no significant evidence of GARCH heteroscedasticity in the disturbances to the real interest rate,” implying uncertainty about policy arises mainly from parameter uncertainty rather than unexpected deviations.

### Time paths and qualitative dynamics reported
- Inflation inertia (λ_t):
  - Rose rapidly in early 1970s from under one-quarter to around three-quarters, stayed high through late 1970s, then declined through 1990 and stabilized below 0.5.
- Output-gap sensitivity (γ_t):
  - Moved less dramatically; increased in 1970s, declined subsequently.
- Implied E_t π_{t+1}:
  - Around 5 percent in 1970s, rising to double-digit in mid- to late 1970s (much higher in ORP), falling to low single digits by late 1980s.
- Monetary-rule coefficients:
  - Coefficient on inflation fell below stability threshold in late 1970s (KL and HP), rose rapidly after Volcker to about unity by mid-1980s, fell to around one-half in late 1990s, with a recent decline at sample end.
  - Coefficient on output gap mirrored inflation coefficient movements (opposite sign), became negative early 1980s, returned to 1970s levels afterwards.
  - Derived steady-state inflation ~ two percent (assuming natural real rate = 4 percent).
  - Smoothing parameter ρ decreased in 1970s, rose through 1980s/1990s, fell recently.

### Decomposition of uncertainty and variance results
- Decomposition of real interest rate conditional variance (Figure 5 & text):
  - “Virtually all uncertainty about the path of interest rates derives from uncertainty about underlying parameters in the rule, not from unexpected deviations.”
  - Monetary uncertainty peaks in mid-1970s and early 1980s; falls to extremely low levels in the 1990s.
- Phillips-curve conditional variance decomposition:
  - Residual-driven inflation variance dominates (over three-quarters), with GARCH dynamics implying a half life of about one year for volatility shocks.

### Long-run relationship and Granger causality (cointegration and VAR results, 1967:4–2002:1)
- Trace test (T-nm) for r=0:
  - Model 1 (Kalman): 19.15 [0.00]**
  - Model 2 (HP): 16.61 [0.01]**
  - Model 3 (Real-time): 5.21 [0.54]
- Estimated cointegrating vectors (β_uncertainty):
  - KL -1.4116 (0.1570); HP -1.2032 (0.1158); ORP -1.4133 (0.2652)
- Error-correction coefficients α_persistence:
  - KL -0.0657 (0.0161); HP -0.0790 (0.0179); ORP -0.0380 (0.0190) — implying slow mean reversion (order of five years).
- Identification restrictions p-values:
  - KL 0.6235 [0.43]; HP 0.7682 [0.38]; ORP 0.9815 [0.32]
- Granger causality tests:
  - Persistence does not Granger-cause Uncertainty: KL F=0.4073 [0.82]; HP 0.5252 [0.77]; ORP 2.0979 [0.35] (no rejection).
  - Uncertainty Granger-causes Persistence: KL F=13.461 [0.00]*; HP 13.193 [0.00]**; ORP 8.4475 [0.01]* (reject null — uncertainty → persistence).

### Core empirical claims and robustness
- Main empirical claims:
  - Strong, statistically significant long-term link between κ_t (portion of aggregate-demand uncertainty due to uncertainty about the real interest rate) and inflation persistence λ_t.
  - Uncertainty about monetary policy Granger-causes inflation persistence; no evidence of reverse causation.
  - Reduction in monetary policy uncertainty over time is associated with a gradual decline in nominal inertia of the Phillips curve and with reduced output volatility.
- Robustness:
  - Results reported for three output-gap measures (KL_, HP_, ORP_) with broadly similar qualitative patterns though some quantitative differences (ORP often shows larger movements).
  - Inferences depend on the Kalman-filter learning framework and GARCH specification for variances.

### Conclusions and policy implications
- Principal conclusion: monetary policy uncertainty affects supply-side inflation inertia; more stable, predictable monetary policy gradually reduces backward-looking behavior in inflation (reduces λ_t).
- Policy implications highlighted:
  - Monetary policy affects not only aggregate demand but also the supply-side through evolving private-sector behavior linked to policy predictability.
  - Evaluations of monetary rules assuming fixed private-sector behavior may be misleading for long-term analysis.
  - The public’s learning process about the policy rule explains why disinflation can be costly and slow (multi-year mean reversion).
  - The U.S. decline in inflation persistence and output volatility since the 1980s can be partly attributed to improvements in monetary policy credibility and predictability.
  - Interactive dynamics: disinflation (Volcker) increased credibility → reduced inertia → expectations channel more effective → Fed increased smoothing (Greenspan), illustrating two-way feedback between policy and private behavior.

*Source: _wp0424 - 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1 (PDF chapter/section).*

### 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1...............18

### 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1

### Major empirical components (section-level inventory)
- 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1
- 2. Estimation of the Time-Varying Parameters of U.S. Phillips Curve, 1967:2–2002:1
- 3. Estimates of the GARCH Process Characterizing Disturbances to the Phillips Curve
- 4. Estimates of the Time-Varying Parameters of U.S. Monetary Rule, 1967:2–2002:1
- 5. Estimates of the GARCH Process Characterizing Disturbances to the Monetary Rule
- 6. Equilibrium Relationship Between Inflation Persistence and Relative Uncertainty About Monetary Policy: Indentification and Granger Causality Test, 1967:4–2002:1

### Figures and empirical diagnostics listed
- Figure 1. Comparing Time-Series Properties of Alternative Output Gap Measures
- Figure 2. Kalman-Filter Estimates of the Time-Varying Regression Coefficients of U.S. Phillips Curve
- Figure 3. Decomposition of Inflation Conditional Variance
- Figure 4. Kalman-Filter Estimates of the Time-Varying Regression Coefficients of U.S. Monetary Rule
- Figure 5. Decomposition of Real Interest Rate Conditional Variance
- Figure 6. Time-Varying Estimates of Inflation Persistence and Relative Uncertainty About Monetary Policy Based on Three Alternative Models

### Temporal coverage and methodological signals
- Sample periods explicitly cited:
  - Output gap estimates: 1966:1–2002:1
  - Phillips curve estimation: 1967:2–2002:1
  - Monetary rule estimation: 1967:2–2002:1
  - Granger causality and inflation–uncertainty equilibrium test: 1967:4–2002:1
- Methodological approaches signaled by section and figure titles:
  - Time-varying parameter estimation (Kalman-filter implied)
  - GARCH modeling of disturbance processes for Phillips curve and monetary rule
  - Decomposition of conditional variances for inflation and real interest rate
  - Identification and Granger causality testing for relationships between inflation persistence and relative monetary-policy uncertainty
  - Comparison of alternative output gap measures via time-series properties

*Source: _wp0424 - 1. Estimates of the Time-Varying Parameters of U.S. Output Gap, 1966:1–2002:1 (PDF chapter/section).*

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

### _wp0424 - References

### I. Introduction — framing and motivation
- Central observation: success in restoring low inflation in the United States and elsewhere reflects multiple factors but “changes in monetary policy have played a central role.”
- Historical narrative summarized:
  - Through much of the 1970s the Federal Reserve “accommodated inflationary shocks,” contributing to instability; this ended with Paul Volcker’s appointment in 1979.
- Research question: reexamine disinflation since the 1970s focusing on the interaction between monetary policy and supply-side (Phillips curve) responses, linking uncertainty about aggregate demand to instability in monetary policy.
- Key theoretical insight invoked: imperfect information about the future path of monetary aggregates/noisy signals can generate inflation inertia (Mankiw and Reis, 2001; Woodford, 2003; Amato and Shin, 2003; Lucas, 1979; Phelps, 1983).
- Empirical strategy preview: estimate time-varying perceptions of the Phillips curve and the monetary reaction function using Kalman filters to examine the link between monetary stability and inflationary persistence.
- Core empirical claim previewed: reductions in uncertainty about the path of the real interest rate produce a gradual reduction of nominal inertia in the Phillips curve; monetary policy uncertainty Granger causes persistence (no reverse causation found).

### II. The model — theoretical structure
- Aggregate supply (full-information New-Keynesian pricing) baseline:
  - Equation (1) (full-information): πt + Ωt = β E_t π_{t+1} + γ (y_t - y_t^*) + ε^π_t  (as in text)
- Empirical augmentation to capture inflation inertia:
  - Equation (1′): adds backward-looking element with coefficient λ on lagged inflation.
- Imperfect information formulation:
  - Equation (1′′): introduces time-varying κ_t capturing signal-to-noise in agents’ information; λ becomes a function of κ_t.
- Simple aggregate demand link to real interest rate (equation (2)):
  - (y_t - y_t^*) = φ (r_t - r_t^*) + ε^D_t  with φ<0 and var(ε^D_t)=σ^2_{εD}.
- Signal-to-noise (Kalman gain) expression (equation (3)):
  - κ_t = [σ^2_{φ r_{t|t-1}}] / [σ^2_{φ r_{t|t-1}} + σ^2_{εD}]  (presented in text as formula (3) and later simplified to (3’))
- Monetary reaction function: time-varying Taylor-type rule with partial adjustment (equations (4) and (5)):
  - r_t depends on past r and on deviations of inflation from desired π^*_t and estimated output gap; monetary shock r^ε_t included.
- Key identification: conditional variance of r_t based on t-1 information equals |1 Σ_{t|t-1} β X_{t-1}| + σ^2_{εr} (equation (8) in text) — uncertainty decomposed into parameter uncertainty and policy shock uncertainty.
- Disturbances assumed to follow GARCH(1,1) to allow time-varying variances (equation (9)).

### II.B Estimation strategy — state-space and learning
- Two measurement equations estimated jointly (linearized):
  - Phillips curve estimating time-varying η_t, λ_t, γ_t (equation (1′′′)).
  - Monetary rule estimating time-varying μ_t, ρ_t, φ1_t, φ2_t (equation (5′)).
- Time variation: parameters follow independent random walks with iid innovations (transition equations (6) and (7)).
- Unobserved components (e.g., E_t π_{t+1}, derived long-run coefficients δ_{1t}, δ_{2t}, and π^*_t) recovered from estimated time-varying parameters.
- Output gap measurement sensitivity: three alternative gap measures used
  - (a) Kalman-filter decomposition (KL_), (b) Hodrick-Prescott filter (HP_), and (c) Orphanides “real time” series (ORP_).
- Testing long-run link: cointegrating relationship λ_t = χ_0 + χ_1 κ_t (equation (10)); test whether χ_1>0 and whether causation runs from κ_t to λ_t.

### III. Results — estimated dynamics and tests
- Data and estimation setup:
  - Quarterly data from 1961:1; filters started in early 1967; Kalman filters started in early 1967; estimation window for time-varying parameters frequently noted as 1967:2–2002:1 or 1967:4–2002:1 in tests.
- Output gap time-varying-parameter estimates (Table 1, Model 1 KL):
  - σ_y~ = 0.0085  (0.0005)
  - σ_{y*} = 0.0009  (0.0020)
  - θ = 0.9229  (0.0212)
  - g = 0.0074  (0.0002)
  - Log likelihood = 484.6667
- Phillips curve time-varying-parameter variances (Table 2):
  - Model 1 (Kalman Filter): σ_η = 0.0000 (0.1039); σ_λ = 0.0497 (0.0166); σ_γ = 0.0000 (0.0159)
  - Model 2 (HP): σ_η = 0.0000 (0.1043); σ_λ = 0.0397 (0.0170); σ_γ = 0.0000 (0.0267)
  - Model 3 (Real-time): σ_η = 0.2580 (0.2140); σ_λ = 0.0413 (0.0167); σ_γ = 0.0000 (0.0254)
- Time paths (qualitative) documented:
  - λ_t (coefficient on lagged inflation) rose rapidly in early 1970s from under one-quarter to around three-quarters, stayed high through late 1970s, then declined through 1990 and stabilized below 0.5.
  - γ_t (output-gap coefficient) moved less dramatically; increased sensitivity in 1970s, declined subsequently.
  - Implied E_t π_{t+1}: around 5 percent in 1970s rising to double-digit in mid- to late 1970s (much higher in ORP), falling to low single digits by late 1980s.
- GARCH estimates for Phillips-curve disturbances (Table 3):
  - α_0: KL 0.0881 (0.0633); HP 0.0709 (0.0594); ORP 0.0600 (0.0502)
  - α_1: KL 0.1999 (0.0916); HP 0.2424 (0.1109); ORP 0.3126 (0.1344)
  - α_2: KL 0.7696 (0.0924); HP 0.7472 (0.1024); ORP 0.6839 (0.1312)
  - Interpretation: average α_1 ~ one-quarter and α_2 ~ three-quarters implying a half life of about one year; residual variance dominates total inflation variance (over three-quarters).
- Monetary rule time-varying-parameter variances (Table 4):
  - σ_μ: KL 0.4321 (0.2510); HP 0.4199 (0.3598); ORP 0.3708 (0.2456)
  - σ_ρ: KL 0.0371 (0.0187); HP 0.0446 (0.0312); ORP 0.0266 (0.0173)
  - σ_φ1: KL 0.1251 (0.0158); HP 0.0576 (0.0373); ORP 0.0374 (0.0213)
  - σ_φ2: KL 0.0653 (0.0353); HP 0.1216 (0.0211); ORP 0.1325 (0.0140)
- Monetary-rule coefficient dynamics (qualitative):
  - Coefficient on inflation fell below stability threshold in late 1970s (KL and HP), rose rapidly after Volcker to about unity by mid-1980s, fell to around one-half in late 1990s, with a recent decline at sample end.
  - Coefficient on output gap mirrored inflation coefficient movements (opposite sign), became negative early 1980s, returned to 1970s levels afterwards.
  - Derived steady-state inflation ~ two percent (assuming natural real rate = 4 percent).
  - Smoothing parameter ρ decreased in 1970s, rose through 1980s/1990s, fell recently (zero bound effects).
- GARCH on monetary-rule disturbances (Table 5):
  - α_0: KL 0.0016 (0.0092); HP 0.0008 (0.0006); ORP 0.0024 (0.0332)
  - α_1: KL 0.1554 (0.7836); HP 0.2445 (1.6649); ORP 0.0000 (0.0002)
  - α_2: KL 0.3848 (0.3699); HP 0.5319 (2.9470); ORP 0.8452 (2.1045)
  - Empirical implication emphasized: “no significant evidence of GARCH heteroscedasticity in the disturbances to the real interest rate,” implying uncertainty about policy arises mainly from parameter uncertainty rather than unexpected random deviations from the rule.
- Decomposition of real interest rate conditional variance (Figure 5 & text):
  - Virtually all uncertainty about the path of interest rates derives from uncertainty about underlying parameters in the rule, not from unexpected deviations.
  - Monetary uncertainty peaks in mid-1970s and early 1980s; falls to extremely low levels in the 1990s.
- Long-run relationship and causality (Table 6; VAR with two lags, 1967:4–2002:1):
  - Trace test (T-nm): Model 1 (Kalman) reported statistic 19.15 [0.00]** for r=0; Model 2 (HP) 16.61 [0.01]** for r=0; Model 3 (Real-time) 5.21 [0.54] for r=0.
  - Estimated cointegrating vectors (reported as β_uncertainty): KL -1.4116 (0.1570); HP -1.2032 (0.1158); ORP -1.4133 (0.2652)
  - Error-correction coefficients α_persistence: KL -0.0657 (0.0161); HP -0.0790 (0.0179); ORP -0.0380 (0.0190) — implying slow mean reversion (order of five years).
  - Identification restrictions p-values: KL 0.6235 [0.43]; HP 0.7682 [0.38]; ORP 0.9815 [0.32].
  - Granger causality tests:
    - Persistence does not GC Uncertainty: KL F=0.4073 [0.82]; HP 0.5252 [0.77]; ORP 2.0979 [0.35] (no rejection).
    - Uncertainty does not GC Persistence: KL F=13.461 [0.00]*; HP 13.193 [0.00]**; ORP 8.4475 [0.01]* (reject null — uncertainty Granger-causes persistence).
- Summary empirical claims:
  - Strong, statistically significant long-term link between the portion of aggregate-demand uncertainty due to uncertainty about the real interest rate (κ_t) and inflation persistence (λ_t), with no evidence of reverse causation.
  - Reduction in monetary policy uncertainty over time is associated with a gradual decline in nominal inertia of the Phillips curve and with reduced output volatility.

### IV. Conclusions — implications and interpretations
- Main conclusion: monetary policy uncertainty affects supply-side inflation inertia; a more stable, predictable monetary policy gradually reduces backward-looking behavior in inflation (reduces λ_t).
- Policy and conceptual implications:
  - Challenges the “central dogma” that monetary policy affects only aggregate demand; supply responses evolve with policy predictability.
  - Evaluations of monetary rules that assume fixed private-sector behavior may be misleading for long-term analysis.
  - The learning process by which the public infers the policy rule helps explain why disinflation can be costly (slow adjustment, multi-year mean reversion).
  - The decline in inflation persistence and output volatility in the U.S. since the 1980s can be partly attributed to improvements in monetary policy credibility and predictability.
  - The empirical pattern suggests interactive dynamics: disinflation (Volcker) increased credibility → reduced inertia → made expectations channel more effective → Fed increased smoothing (Greenspan period), illustrating two-way feedback between policy and private behavior.
- Robustness and caveats:
  - Results presented for three output-gap measures (KL_, HP_, ORP_) with broadly similar qualitative patterns though some quantitative differences (ORP often shows larger movements).
  - Empirical identification relies on Kalman-filter learning framework and GARCH specification for variances; inferences depend on these modeling choices.

*Italic line: Source: _wp0424 - References (PDF content provided).*

### References

### References

### Monetary policy theory and rules
- Amato, Jeffrey V., and Hyun Song Shin, 2003, “Public and private information in monetary policy models” BIS Working Papers, forthcoming (Basel: Bank of International Settlements).
- Barro, Robert, and David Gordon, 1983, “Rules, Discretion, and Reputation in a Model of Monetary Policy,” Journal of Monetary Economics, Vol. 12, pp. 101–21.
- Clarida, Richard, Jordi Galí, and Mark Gertler, 1998, “Monetary Policy Rules In Practice: Some International Evidence,” European Economic Review, pp. 1033–67.
- Clarida, Richard, Jordi Galí, and Mark Gertler, 1999, “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature, pp. 1661–07.
- Clarida, Richard, Jordi Galí, and Mark Gertler, 2000, “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory,” Quarterly Journal of Economics, Vol. 115, pp. 147–80.
- King, Robert, and Alexander Wolman, 1999, “What Should the Monetary Authority Do When Prices Are Sticky?,” in Monetary policy rules, ed. by John B. Taylor (Chicago, IL: University of Chicago Press).
- Levin, Andrew, Volker Wieland, and John C. Williams, 1999, “Robustness of Simple Monetary Policy Rules under Model Uncertainty,” in Monetary policy rules, ed. by John B. Taylor (Chicago, IL: University of Chicago Press).
- McCallum, Bennett, 2001, “Should Monetary Policy Respond Strongly to Output Gaps?,” NBER Working Paper 8226 (Cambridge, Mass., National Bureau of Economic Research).
- Orphanides, Athanasios, 2000, “Activist Stabilization Policy and Inflation: the Taylor Rule in the 1970s,” Finance and Economics Discussion Paper No. 2000-13 (Washington, DC: Board of Governors of the Federal Reserve System).
- Taylor, John B., 1993, “Discretion Versus Policy Rules in Practice,” Carnegie-Rochester Conference on Public Policy, Vol. 39, pp. 195-214.
- Taylor, John B., 1999, “Staggered Price and Wage Settings in Macroeconomics,” in Handbook of Macroeconomics, edited by John B. Taylor and Michael Woodford, Vol. 1B, pp. 1009–50.
- Taylor, John B., 2001, “Expectations, Open Market Operations, and Changes in the Federal Funds Rate,” in Proceedings of the 25th Annual Economic Conference of the Federal Reserve Bank of St. Louis, Federal Reserve Bank of St. Louis Review, Vol. 83, pp. 33–48.

### Credibility, expectations, and credibility imperfections
- Ball, Laurence, 1995, “Disinflation and Imperfect Credibility,” Journal of Monetary Economics, Vol. 35, pp. 5–24.
- Ball, Laurence, 2000, “Near-Rationality and Inflation in Two Monetary Regimes,” NBER Working Paper 7988 (Cambridge, Mass.: National Bureau of Economic Research).
- Erceg, Christopher J., and Andrew T. Levin, 2003, “Imperfect Credibility and Inflation Persistence,” Journal of Monetary Economics, Vol. 50, pp. 915–44.
- Ireland, Peter, 2000, “Expectations, Credibility, and Time-Consistent Monetary Policy,” Macroeconomic Dynamics, Vol. 4, pp. 448–66.
- Orphanides, Athanasios, 1998, “Monetary Policy Evaluation with Noisy Information,” Finance and Economics Discussion Series, 1998-50 (Washington: Board of Governors of the Federal Reserve System).
- Orphanides, Athanasios, and John Williams, 2002, “Imperfect Knowledge, Inflation Expectations, and Monetary Policy,” Finance and Economics Discussion Paper No. 2002-27 (Washington, DC: Board of Governors of the Federal Reserve System).
- Phelps, Edmund S., 1983, “The Trouble with ‘Rational Expectations’ and the Problem of Inflation Stabilization,” in Individual Forecasting and Aggregate Outcomes, edited by Roman Fryman and Edmund S. Phelps (Cambridge, England: Cambridge University Press, also New York: Cambridge University Press).
- Woodford, Michael, 2001, “Imperfect Common Knowledge and the Effects of Monetary Policy,” NBER Working Paper 8673 (Cambridge, Mass., National Bureau of Economic Research).

### Sticky prices, wages, and inflation dynamics
- Calvo, Guillermo A., 1983, “Staggered Prices in a Utility Maximizing Framework,” Journal of Monetary Economics, Vol. 12, pp. 383–88.
- Fuhrer, Jeffrey, and Mark Hooker, 1993, “Learning About Monetary Regime Shifts in an Overlapping Wage Contract Model,” Journal of Economic Dynamics and Control, Vol. 17, pp. 531–53.
- Fuhrer, Jeffrey, and George Moore, 1995, “Inflation Persistence,” Quarterly Journal of Economics, Vol. 110(1), pp. 127–60.
- Gertler, Mark, 1982. “Imperfect information and wage inertia in the business cycle,” Journal of Political Economy, Vol. 5, pp. 967–87.
- Rotemberg, Julio, 1996, “Prices, Output, and Hours: An Empirical Analysis Based on a Sticky Price Model,” Journal of Monetary Economics, Vol. 37, pp. 505–33.
- Rotemberg, Julio, and Michael Woodford, 1997, “An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy,” in: NBER Macroeconomics Annual, ed. by Ben Bernanke and Julio Rotemberg. MIT Press.
- Taylor, John B., 1980, “Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, Vol. 88, pp. 1-22.
- Buiter, W., and Jewitt, I., 1989, “Staggered Wage Setting and Relative Wage Rigidities: Variations on a Theme of Taylor,” Reprinted in: Macroeconomic Theory and Stabilization Policy, edited by W. Buiter (University of Michigan Press, Ann Arbor), pp. 183–99.

### Empirical studies on volatility, business cycles, and transmission
- Blanchard, Olivier, and John Simon, 2001, “The Long and Large Decline in U.S. Output Volatility,” Brookings Papers on Economic Activity I, pp. 135–64. (Washington: Brookings Institution).
- Boivin, Jean, and Marc Giannoni, 2002, “Assessing Changes in the Monetary Transmission Mechanism: A VAR Approach”, Federal Reserve Bank of New York Economic Policy Review, Vol 8, pp. 97-111.
- Cogley, Timothy, and Thomas Sargent, 2001, “Evolving Post-World War II U.S. Inflation Dynamics,” in NBER Macroeconomics Annual 2001, edited by B. Bernanke and K. Rogoff (Cambridge, MA: MIT Press), pp. 331–33.
- Harvey, Andres, Esther Ruiz, and Enrique Sentana, 1992, “Unobserved Component Time Series Models with ARCH Disturbances,” Journal of Econometrics, Vol. 52, pp. 129–57.
- Kim, Chang-Jin, 1993, “Sources of Monetary Growth Uncertainty and Economic Activity: The Time-Varying-Parameter Model with Heteroskedastic Disturbances,” Review of Economics and Statistics, Vol. 75, pp. 483–92.
- Kim, Chang-Jin, and Charles R. Nelson, 1999, State-Space Models with Regime Switching, (Cambridge, MA: The MIT Press).
- Kim, Chang-Jin, and Charles R. Nelson, 1989, “The Time-Varying-Parameter Model for Modeling Changing Conditional Variance: The Case for the Lucas Hypothesis,” Journal of Business and Economic Statistics, Vol. 74(4), pp. 433–40.
- Nelson, Charles, and Charles Plosser, 1982, “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications,” Journal of Monetary Economics, Vol. 10, pp.139–62.
- Stock, James, and Mark Watson, 2003, “Has the Business Cycle Changed?,” Harvard University, Cambridge. Paper presented at the symposium sponsored by the Federal Reserve Bank of Kansas City. Available at: www.kc.frb.org/publicat/sympos/2003/sym03prg.htm

### Central banking, communication, and low inflation environment
- Bayoumi, Tamim, and Silvia Sgherri, 2003, “Deconstructing the Art of Central Banking,” forthcoming IMF Working Paper (Washington: International Monetary Fund).
- IMF, 2002, World Economic Outlook, April 2002, Monetary Policy in a Low Inflation Era, (Washington: International Monetary Fund).
- Roberts, John, 1998. “Inflation Expectations and the Transmission of Monetary Policy,” Finance and Economics Discussion Paper No. 98-43 (Washington, DC: Board of Governors of the Federal Reserve System).
- Roberts, John, 2001, “How Well Does the New Keynesian Sticky-Price Model Fit the Data?,” Finance and Economics Discussion Paper No. 2001-13 (Washington, DC: Board of Governors of the Federal Reserve System).
- Sack, Brian, and Volker Wieland, 1999, “Interest Rate Smoothing and Optimal Monetary Policy: A Review of Recent Empirical Evidence,” Finance and Economics Discussion Paper No. 1999-39 (Washington, DC: Board of Governors of the Federal Reserve System).
- Svensson, Lars, 1997, “Inflation Forecast Targeting: Implementing and Monitoring Inflation Targets,” European Economic Review, Vol. 41, pp. 1111–46.
- Viñals, José, 2001, “Monetary Policy Issues in a Low Inflation Environment,” CEPR Working Paper No. 2945 (London, UK: Centre for Economic Policy Research).
- Walsh, Carl, 2003, “Implications of a Changing Economic Structure for the Strategy of Monetary Policy,” University of California, Santa Cruz. Paper presented at the symposium sponsored by the Federal Reserve Bank of Kansas City. Available at: www.kc.frb.org/publicat/sympos/2003/sym03prg.htm

### Methodology, econometrics, and theoretical foundations
- Friedman, Milton, and Anna Schwartz, 1963, A Monetary History of the United States 1867-1960 (NBER, Princeton University Press).
- Gertler, Mark, 1982. “Imperfect information and wage inertia in the business cycle,” Journal of Political Economy, Vol. 5, pp. 967–87.
- Kim, Chang-Jin, and Charles R. Nelson, 1999, State-Space Models with Regime Switching, (Cambridge, MA: The MIT Press).
- Mankiw, Gregory, and Ricardo Reis, 2001, “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” NBER Working Paper 8290 (Cambridge, Mass., National Bureau of Economic Research).
- Rudebusch, Glenn D., 1995, “Federal Reserve Interest Rate, Targeting Rational Expectations, and the Term Structure,” Journal of Monetary Economics, Vol. 35, pp. 245–74.
- Rudebusch, Glenn D., 2001, “Term Structure Evidence on Interest Rate Smoothing and Monetary Policy Inertia,” Federal Reserve Bank of San Francisco; unpublished.
- Sargent, Thomas, 1993, “The End of Four Great Inflations,” in Rational Inflations and Inflation 2nd Edition (Harper Collins).
- Sims, Christopher, 1999, “Monetary Policy, Drifts, (1999): “Drift and Breaks in Monetary Policy,” Discussion paper, Princeton University. Paper presented at the Australasian meeting of the Econometric Society. Available at: http://www.princeton.edu/~sims/.
- Stock, James, and Mark Watson, 2003, “Has the Business Cycle Changed?,” Harvard University, Cambridge. Paper presented at the symposium sponsored by the Federal Reserve Bank of Kansas City. Available at: www.kc.frb.org/publicat/sympos/2003/sym03prg.htm

*Source: _wp0424 - References*

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