## _wp04195

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---

### Introduction and central hypothesis
- Reexamines consequences of the loss of monetary credibility in the 1970s and the subsequent regaining of stability, focusing on interactions between policymakers and the private sector.
- Central hypothesis: the main impact of changes in monetary stance comes through its bearing on inflation inertia. Monetary stability allows pricing decisions by the private sector to become more focused on expectations of future inflation, reducing inflation inertia and improving supply responses.
- Claim: benefits from shifts in the Phillips curve (reduced inflation inertia) overwhelm benefits from changes in the monetary policy rule itself.
- Companion paper (Bayoumi and Sgherri, 2004) finds half life on the error correction term is around 5 years.

### Stylized facts (empirical background)
- U.S. CPI inflation since 1965: hump shaped — increases to 1973, rises through 1979 oil shock, then rapid fall in early 1980s and gradual trend to lower inflation thereafter.
- Broad consensus: changes in Federal Reserve conduct played the central role in taming inflation; pivotal event: appointment of Paul Volcker in 1979.
- Observed macro developments:
  - Inflation has become less volatile and more predictable.
  - Inflation has become less persistent.
  - Marked fall in U.S. output volatility in the 1990s.
- Theoretical implication: greater monetary stability (and fall in inflation) reduces inflation inertia through improved information and expectations, lowering volatility of inflation and output.

### Theoretical model specification
- Small rational-expectations monetary model with three equations: monetary policy reaction function, Phillips curve, aggregate demand (IS).
- Key variables:
  - it: Federal Funds interest rate.
  - π4t: annual rate of inflation over the last year (fourth difference in log prices).
  - yt: output gap (log ratio of actual output to potential).
  - πt: annualized rate of inflation over the last quarter (four times quarterly change in log price level).
- Monetary reaction function: Taylor-type including expected future inflation and current output gap (coefficients α1 and α2), plus two lagged interest-rate smoothing terms (ρ1 and ρ2).
- Phillips curve: current inflation depends on weighted average of future and past inflation (weights sum to one).
- Aggregate demand (IS): output gap linked to short-term real interest rate, forward- and backward-looking persistence terms (habit persistence interpretation).
- Additional relationship: nominal inertia depends on signal-to-noise ratio of the interest rate forecast versus aggregate demand uncertainty (equation (4)). χ1 and χ2 are estimated coefficients in the linear relationship.
- Model properties: linear (in logs) and saddlepath stable in each sub-period (two eigenvalues outside the unit circle equals number of non-predetermined variables).

### Estimation strategy and rolling-regression results
- Rolling regressions over successive fifty-quarter periods identify parameter evolution over time.
- Two approaches to expectations/real-time information:
  - “Classical”: GMM with instrumented future inflation and HP-filtered output gap (smoothing parameter 1600).
  - “Real time”: Federal Reserve estimates of the output gap and Michigan Survey of Consumers inflation expectations; real time output gap available 1965Q4 through 1995Q4 and extended using HP-filter for endpoints.
- Key empirical findings:
  - Monetary reaction function:
    - Long-run coefficient on inflation falls through 1960s–1970s, rises after 1979, peaks over samples involving the 1980s and early 1990s, then falls somewhat thereafter.
    - Standard error on the coefficient increases during transitions.
    - Coefficient on output gap displays broadly inverse pattern to inflation coefficient.
    - Interest-rate smoothing coefficients show dynamic shifts: first lag coefficient U-shaped; second lag initially significantly negative, rises toward zero, then falls back.
  - Phillips curve:
    - Coefficient on forward-looking inflation falls early in the sample from under three-quarters to around one-third, then gradually rises back.
    - Coefficient on the output gap is small, hardly significant, and relatively stable.
  - IS curve: no evidence of a significant structural break; semi-elasticity of aggregate spending to real interest rate is low and barely significant; persistence in output fluctuations remains about 0.5 over the whole sample.
- Four sub-periods used in analysis:
  - “1960s” (Bretton Woods): late 1950s through the early 1970s.
  - “1970s” (post-Bretton Woods/pre-Volcker): 1972:1 to 1979:3.
  - “1980s” (Volcker): 1979:4 to 1987:3.
  - “1990s” (Greenspan): 1987:4 through the end of sample.

### Simulation design and parameter choices
- Simulations use coefficient estimates obtained with real-time data.
- To reduce noise, only parameters that change significantly across sub-periods are allowed to vary:
  - IS-curve invariant.
  - Response of inflation to real output in Phillips curve invariant.
  - Monetary response function and coefficient on forward-looking inflation allowed to vary across the four sub-periods.
- For the 1970s, monetary response output-gap coefficient set to zero in simulations because it was perverse and not statistically significant.
- Model stability: eigenvalue analysis indicates stability for all time periods; speed of convergence to equilibrium is lowest over the 1970s.

### Impulse responses and key simulation findings
- One percentage point one-off shocks (demand and supply):
  - All period parameterizations are stable.
  - 1970s parameterization displays larger, more elongated, and more cyclical responses than other periods.
  - 1980s responses show generally larger volatility than 1990s; 1990s show the least volatility.
- Permanent 1 percentage point disinflation (sacrifice ratios ordering):
  - Highest in the 1970s, followed by the 1980s, the 1960s, and the 1990s (lowest).
- Announcement effects: inflation typically falls on announcement of a new inflation target; size of announcement effect is roughly inversely proportional to degree of nominal inertia in the Phillips curve.
- Holding inflation inertia fixed at 1990s level across periods (panel b of Figure 7): responses across time periods become extremely similar — indicates changes in private sector responses (inflation inertia) drive differences across periods more than changes in monetary rules.
- Temporary one percentage point reduction in nominal interest rates:
  - With varying inflation inertia, 1990s model generates larger boost to output and a relatively modest increase in inflation.
  - 1970s model exhibits the largest degree of cycling and instability.

### Asymptotic standard deviations and simulated statistics (selected exact figures)
- 1990s model asymptotic standard deviations:
  - output: 1.3 percent
  - inflation: 1.7 percent
  - nominal interest rates: 2.6 percent
- Historical values:
  - output: 1.2 percent
  - inflation: 1.5 percent
  - nominal interest rates: 2.1 percent
- Table 4 (real-time model parameters by period, exact values):
  - α0 = 0 across Bretton Woods, Post Bretton Woods, Volcker, Greenspan
  - α1: Bretton Woods = 1.062; Post Bretton Woods = .635; Volcker = 1.824; Greenspan = 1.405
  - α2: Bretton Woods = .253; Post Bretton Woods = .241; Volcker = 0; Greenspan = .375
  - ρ1: Bretton Woods = 1.185; Post Bretton Woods = .871; Volcker = .840; Greenspan = 1.484
  - ρ2: Bretton Woods = -.424; Post Bretton Woods = -.213; Volcker = -.107; Greenspan = -.646
  - β: Bretton Woods = .620; Post Bretton Woods = .470; Volcker = .623; Greenspan = .726
  - γ = .014 for all periods
  - δ0 = 0 for all periods
  - δ1 = -.018 for all periods
  - δ2 = .486 for all periods
- Historical standard deviations by period (percent):
  - Inflation: Bretton Woods = 1.79; Post Bretton Woods = 2.89; Volcker = 3.87; Greenspan = 1.49
  - Output: Bretton Woods = 1.70; Post Bretton Woods = 2.31; Volcker = 1.83; Greenspan = 1.20
  - Interest rate: Bretton Woods = 1.83; Post Bretton Woods = 2.58; Volcker = 3.53; Greenspan = 2.08
- Simulated standard deviations and sacrifice ratios using 1990s-specific shocks and β's estimates (as listed in source; values correspond to periods in order):
  - Inflation: 1.72; 1.74; 1.70; 1.72
  - Output: 1.22; 1.05; 1.50; 1.34
  - Interest rate: 2.00; 1.40; 2.47; 2.61
  - Sacrifice Ratios: 5.84; 7.26; 6.58; 4.96
- Simulated standard deviations and sacrifice ratios using estimated parameters but 1990s-specific shocks:
  - Inflation: 2.23; 4.76; 2.17; 1.72
  - Output: 1.51; 3.89; 1.88; 1.34
  - Interest rate: 2.88; 6.74; 3.67; 2.61
  - Sacrifice Ratios: 6.22; 10.20; 7.28; 4.96
- Note: Under the 1970s parameterization, the model does not converge to steady state by the end of the simulation horizon; the sacrifice ratio is therefore calculated over the first 24 quarters.

### Main conclusions
- A model allowing the monetary rule and inflation inertia to vary over time, while keeping underlying shocks at their 1990s level, exhibits highest macroeconomic volatility in the 1970s and lowest in the 1990s.
- The model including inflation inertia tracks broad patterns of macroeconomic volatility over time—particularly output volatility—without requiring large changes in the size of underlying disturbances.
- Almost all of the observed fall in both inflation and output volatility is explained through changes in inflation inertia induced by monetary policies.
- Reducing inflation inertia reduces volatility of inflation, output, and the interest rate for all relevant parameter values; changes in inflation persistence overwhelm effects from changing the monetary rule.
- Trade-offs across monetary rules (changes in α1 and α2) produce much smaller changes in macroeconomic stability than shifts in inflation persistence; higher α2 lowers output volatility but raises inflation instability.
- Mechanism implies significant lags: full impact of a change in monetary policy on nominal inertia and volatility may take substantial time to be realized. Early stages of returning to monetary stability can involve substantial output losses.
- IS curve is found to be stable over the period examined.

### Policy implications and recommendations
- Emphasize policies that reduce inflation inertia (improve private sector flexibility) as the main channel to lower volatility of inflation and output.
- Changes in monetary rules alone are likely to have only small effects on macroeconomic stability.
- Central banks should recognize long lags in the transmission of policy via changes in nominal inertia; short-term output costs can precede longer-term stability gains.
- Central bank communication and convincing the public that interest rate policy is credible are crucial given the role of private sector perceptions.
- Policymakers should account for collective social memory: emphasis may differ across countries depending on historical experiences (e.g., output control emphasis in countries recalling the Great Depression versus inflation control emphasis where hyperinflations are recalled).

*Source: _wp04195 (PDF chapter/section).*

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

### _wp04195 - References

### Tables
- 1.         Estimated Monetary Policy Rule  .................................................................................32
- 2.         Estimated         Phillips         Curve..............................................................................................33
- 3.         Estimated Aggregate Demand Function  ......................................................................34
- 4.         Simulated Standard Deviations and Sacrifice Ratios...................................................35

### Figures
- 1.         United States: Inflation Dynamics and Macroeconomic Volatility, 1957–2003.........23
- 2. Rolling GMM Estimates of the U.S. Monetary  
                  Policy Rule (Using Real-Time Data).....................................................................24
- 3. Rolling GMM Estimates of the U.S. Phillips Curve 
                  (Using Real-Time Data).........................................................................................25
- 4. Rolling GMM Estimates of the U.S. Aggregate Demand 
                  (Using Real-Time Data).........................................................................................26 
- 5a.       Impulse Responses to a Negative One-Percent One-Off Demand Shock  ...................27 
- 5b.       Impulse Responses to a Negative One-Percent One-Off Supply Shock......................27
- 6.         Model-Generated         Auto-         and Cross-Correlation Functions for a One-Off 
                        Supply            Shock  .........................................................................................................28            
- 7a.       Impulse Responses to a Negative One-Percent Permanent Disinflation Shock  ..........29 
- 7b. Impulse Response Functions to a One-Percent Permanent Disinflation Shock 
                        under            Constant            β’s (β=0.726)  ................................................................................29

*Source: _wp04195 - References (PDF).*

### 8.         Impulse Response Functions to a One-Percent One-Off Interest Rate Shock.............30

### 8.         Impulse Response Functions to a One-Percent One-Off Interest Rate Shock.............30

### Introduction and central hypothesis
- The paper reexamines the consequences of the loss of monetary credibility in the 1970s and the subsequent regaining of stability, focusing on interactions between policymakers and the private sector.
- Hypothesis: the main impact of changes in monetary stance comes through its bearing on inflation inertia. Monetary stability allows pricing decisions by the private sector to become more focused on expectations of future inflation, reducing inflation inertia and improving supply responses.
- Claim: benefits from shifts in the Phillips curve (reduced inflation inertia) overwhelm benefits from changes in the monetary policy rule itself.
- Companion paper (Bayoumi and Sgherri, 2004) analyses theoretically the link between monetary policy uncertainty and inflation inertia; half life on the error correction term is around 5 years.

### Stylized facts (empirical background)
- U.S. CPI inflation since 1965 is hump shaped: increases to 1973, rises through 1979 oil shock, then rapid fall in early 1980s and gradual trend to lower inflation thereafter.
- Broad consensus: changes in Federal Reserve conduct played the central role in taming inflation; pivotal event: appointment of Paul Volcker in 1979 leading to tougher response to increases in inflation.
- Observed macro developments:
  - Inflation has become less volatile and more predictable.
  - Inflation has become less persistent.
  - Marked fall in U.S. output volatility in the 1990s.
- Theoretical implication: greater monetary stability (and fall in inflation) reduces inflation inertia through improved information and expectations, lowering volatility of inflation and output.

### Theoretical model (specification)
- Small rational-expectations monetary model with three equations: monetary policy reaction function, Phillips curve, aggregate demand (IS).
- Key variables:
  - it: Federal Funds interest rate.
  - π4t: annual rate of inflation over the last year (fourth difference in log prices).
  - yt: output gap (log ratio of actual output to potential).
  - πt: annualized rate of inflation over the last quarter (four times quarterly change in log price level).
- Monetary reaction function (Taylor-type) includes expected future inflation, current output gap (coefficients α1 and α2), and two lagged interest-rate smoothing terms (ρ1 and ρ2).
- Phillips curve: current inflation depends on weighted average of future and past inflation (weights sum to one).
- Aggregate demand (IS): output gap linked to short-term real interest rate, forward- and backward-looking persistence terms (habit persistence interpretation).
- Key additional relationship: nominal inertia depends on signal-to-noise ratio of the interest rate forecast versus aggregate demand uncertainty (equation (4) in the source). χ1 and χ2 are estimated coefficients in the linear relationship.
- The model is linear (in logs) and saddlepath stable in each sub-period: number of eigenvalues outside the unit circle (two) equals number of non-predetermined variables.

### Estimation strategy and rolling-regression results
- Rolling regressions over successive fifty-quarter periods identify parameter evolution over time.
- Two approaches to expectations/real-time information:
  - “Classical”: GMM with instrumented future inflation and HP-filtered output gap (smoothing parameter 1600).
  - “Real time”: Federal Reserve estimates of the output gap and Michigan Survey of Consumers inflation expectations (future output gap instrumented similarly). Real time output gap available 1965Q4 through 1995Q4 and extended using HP-filter for endpoints.
- Key empirical findings from rolling regressions:
  - Monetary reaction function: long-run coefficient on inflation falls through 1960s–1970s, rises after 1979, peaks over samples involving the 1980s and early 1990s, then falls somewhat thereafter. Standard error on the coefficient increases during transitions.
  - Coefficient on output gap displays broadly inverse pattern to inflation coefficient: rises through the 1970s, falls over the 1980s, rises over the 1990s.
  - Interest-rate smoothing coefficients show dynamic shifts:
    - First lag coefficient follows a U-shape: starts well above unity, falls below unity mid-sample, then rises above one in the 1990s.
    - Second lag coefficient initially significantly negative, rises toward zero, then falls back to a large negative value.
  - Phillips curve:
    - Coefficient on forward-looking inflation falls rapidly early in the sample from under three-quarters to around one-third, then gradually rises back to its initial value.
    - Coefficient on the output gap is small, hardly significant, and relatively stable.
  - IS curve: no evidence of a significant structural break; semi-elasticity of aggregate spending to real interest rate is low and barely significant; persistence in output fluctuations remains about 0.5 over the whole sample.
- Four distinct sub-periods identified for analysis:
  - “1960s” (Bretton Woods): late 1950s through the early 1970s.
  - “1970s” (post-Bretton Woods/pre-Volcker): 1972:1 to 1979:3.
  - “1980s” (Volcker): 1979:4 to 1987:3.
  - “1990s” (Greenspan): 1987:4 through the present day (end of sample).

### Simulation design
- Simulations use coefficient estimates obtained with real-time data.
- To reduce noise, only parameters that change significantly across sub-periods are allowed to vary:
  - IS-curve invariant.
  - Response of inflation to real output in Phillips curve invariant.
  - Monetary response function and coefficient on forward-looking inflation allowed to vary across the four sub-periods.
- For the 1970s, the coefficient on the output gap in the monetary response was perverse and not statistically significant, so it was set to zero in simulations.
- Model stability: eigenvalue analysis indicates stability for all time periods; speed of convergence to equilibrium is lowest over the 1970s.

### Impulse responses and key simulation findings
- Impulse responses to a one percentage point one-off shocks:
  - Experiments: one-off 1 percentage point shock to aggregate demand (IS) and one-off 1 percentage point shock to aggregate supply (Phillips).
  - Results:
    - All period parameterizations are stable.
    - 1970s parameterization displays larger, more elongated, and more cyclical responses than other periods—consistent with loss of monetary stability.
    - 1980s responses show generally larger volatility than 1990s; 1990s show the least volatility.
- Disinflation (credibly lowering the inflation target permanently by 1 percentage point):
  - Sacrifice ratio ordering (loss in output associated with 1 percentage point permanent reduction in inflation target):
    - Highest in the 1970s, followed by the 1980s, the 1960s, and the 1990s (lowest).
  - Announcement effects: inflation typically falls on announcement of a new inflation target in anticipation of future monetary actions; the size of the announcement effect is roughly inversely proportional to the degree of nominal inertia in the Phillips curve.
- Experiment holding inflation inertia fixed:
  - Panel b of Figure 7: disinflation shock with inflation inertia held at its 1990s level across all periods (monetary response function allowed to change).
  - Finding: responses across time periods become extremely similar—illustrates that changes in private sector responses (inflation inertia) drive differences across periods more than changes in monetary rules.
- Temporary one percentage point reduction in nominal interest rates:
  - When inflation inertia varies over time, the 1990s model generates a larger boost to output and a relatively modest increase in inflation (reflecting more pronounced easing after initial reduction and low inflation inertia).
  - 1970s model exhibits the largest degree of cycling and instability.
- Asymptotic standard deviations (1990s model vs historical):
  - 1990s model asymptotic standard deviation:
    - output: 1.3 percent
    - inflation: 1.7 percent
    - nominal interest rates: 2.6 percent
  - Historical values:
    - output: 1.2 percent
    - inflation: 1.5 percent
    - nominal interest rates: 2.1 percent
  - Interpretation: model numbers are relatively similar to historical values; slightly higher modeled volatilities may reflect disturbances that mirror relationships that altered over time.
- Role of changing monetary rules versus changing inflation inertia:
  - Holding underlying disturbances and inflation inertia at 1990s levels and varying only the monetary response function shows trivial impact of changing monetary rules alone on inflation volatility over time.
  - When ignoring the role of changing inflation inertia, conclusions about volatility and stability can be misleading (for example, output and interest-rate volatility appear most stable during the 1970s in such an exercise, contrary to historical data).

*Source: Excerpted content from the provided IMF PDF chapter/section.*

### conclusions that the macroeconomic volatility of the 1970s came entirely from large

### _wp04195 - conclusions that the macroeconomic volatility of the 1970s came entirely from large

### Main findings
- A model that allows the monetary rule and inflation inertia to vary over time, while keeping underlying shocks at their 1990s level, exhibits highest macroeconomic volatility in the 1970s and lowest in the 1990s.
- The model including inflation inertia tracks broad patterns of macroeconomic volatility over time—particularly output volatility—without requiring large changes in the size of underlying disturbances.
- Almost all of the observed fall in both inflation and output volatility is explained through changes in inflation inertia induced by monetary policies.

### Role of inflation inertia versus monetary rule
- Varying the coefficient on forward-looking inflation expectations in the Phillips curve (β) and the long-run monetary response to inflation (α1) shows:
  - Reducing inflation inertia reduces volatility of inflation, output, and the interest rate for all relevant values.
  - Changes in inflation persistence overwhelm effects from changing the monetary rule.
- Trade-offs across monetary rules (changes in α1 and the long-term response to the output gap, α2):
  - Resulting changes in macroeconomic stability are much smaller than those implied by shifts in inflation persistence.
  - Larger response to the output gap (higher α2) leads to lower output volatility but higher inflation instability.
  - Increases in the long-term response to inflation (α1) also produce similar trade-offs beyond a certain point.

### Model evidence and comparison with other studies
- The model sometimes overestimates interest rate volatility, suggesting disturbances to the monetary reaction function may be overestimated.
- The estimated instability in the 1970s can be larger than historical data, possibly reflecting cycling in the impulse response functions.
- Comparison with other work:
  - Stock and Watson (2003): In their univariate framework reductions in output volatility can only be explained by changes in output inertia. They find lower persistence explains lower inflation volatility but do not link to output instability.
  - Cogley and Sargent (1993): Using a Bayesian VAR framework, they also link falls in real volatility to changes in inflation inertia.
- The IS curve is found to be stable over the period examined.

### Mechanism, timing, and quantitative interpretation
- The paper proposes that the primary transmission mechanism from monetary policy to macroeconomic stability operates through changes in nominal (inflation) inertia rather than large changes in the monetary rule itself.
- This mechanism implies significant lags: it may take a substantial amount of time for the full impact of a change in monetary policy to be realized.
- Early stages of returning to monetary stability can involve substantial output losses because public uncertainty keeps inflation inertia and the costs of deflation high for some time.
- In the longer term, lower nominal inertia reduces volatility of both output and inflation.
- The authors’ calculations suggest that most of the fall in U.S. output volatility between the early 1980s and now can be ascribed to improved supply-side responses resulting from better monetary policies.

### Policy implications and recommendations
- Emphasize policies that reduce inflation inertia (improve private sector flexibility) as the main channel to lower volatility of inflation and output.
- Changes in monetary rules alone are likely to have only small effects on macroeconomic stability.
- Central banks should recognize long lags in the transmission of policy via changes in nominal inertia; short-term output costs can precede longer-term stability gains.
- Given the importance of private sector perceptions, central bank communication and convincing the public that interest rate policy is in good hands are crucial.
- Policymakers should account for collective social memory:
  - In countries where memories of the Great Depression loom large (e.g., the United States), there may be greater emphasis on controlling output.
  - In countries recalling destructive hyperinflations (e.g., Germany, Japan, and many countries in Latin America), there may be greater emphasis on controlling inflation.

### Framing and broader insights
- The paper frames monetary management as partly an “artistic” exercise: influencing private sector perceptions matters and optimal policy choices can depend on societal memory and the public’s trust in central banks.
- Trade-offs inherent in monetary responses (α1 and α2) imply policy design must balance objectives across inflation and output volatility rather than rely solely on rule changes.

*Source: _wp04195 - conclusions that the macroeconomic volatility of the 1970s came entirely from large*

### REFERENCES

### _wp04195 - REFERENCES

### Major empirical parameters and estimates (from tables and figures)

- Table 1. Estimated Monetary Policy Rule (Generalized Method of Moments; Newey-West; up to four-quarter serial correlation)
  - Using HP filter (sample periods and estimates; robust standard errors in parentheses; P-values for Hansen’s J-test in square brackets)
    - Bretton Woods (1957:1-1972:2): α0 = .018 (.004); α1 = 1.004 (.157); α2 = .343 (.130); ρ1 = 1.104 (.139); ρ2 = -.385 (.102); Overidentifying Restrictions [.55]; SEE = 6.9; SEE (percent) = .54%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): α0 = .026 (.021); α1 = .608 (.265); α2 = .594 (.330); ρ1 = .799 (.061); ρ2 = -.138 (.044); Overidentifying Restrictions [.85]; SEE = 4.1; SEE (percent) = 1.01%
    - Volcker (1980:1-1987:3): α0 = .033 (.021); α1 = 1.641 (.461); α2 = -.101 (.238); ρ1 = .828 (.072); ρ2 = -.074 (.060); Overidentifying Restrictions [.74]; SEE = 5.2; SEE (percent) = 2.00%
    - Greenspan (1987:4-2003:2): α0 = .010 (.007); α1 = 1.563 (.218); α2 = .333 (.196); ρ1 = 1.476 (.048); ρ2 = -.673 (.054); Overidentifying Restrictions [.80]; SEE = 4.6; SEE (percent) = .37%
    - Full sample (1957:1-2003:2): α0 = .021 (.010); α1 = 1.047 (.272); α2 = 1.064 (.385); ρ1 = 1.057 (.057); ρ2 = -.178 (.055); Overidentifying Restrictions [.25]; SEE = 10.3; SEE (percent) = 1.03%
  - Using real-time data
    - Bretton Woods (1957:1-1972:2): α0 = .018 (.004); α1 = 1.062 (.124); α2 = .253 (.112); ρ1 = 1.185 (.110); ρ2 = -.424 (.085); Overidentifying Restrictions [.77]; SEE = 4.9; SEE (percent) = .52%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): α0 = .044 (.032); α1 = .635 (.264); α2 = .241 (.120); ρ1 = .871 (.075); ρ2 = -.213 (.069); Overidentifying Restrictions [.77]; SEE = 4.9; SEE (percent) = 1.04%
    - Volcker (1980:1-1987:3): α0 = -.007 (.019); α1 = 1.824 (.298); α2 = -.467 (.258); ρ1 = .840 (.079); ρ2 = -.107 (.058); Overidentifying Restrictions [.77]; SEE = 4.9; SEE (percent) = 1.99%
    - Greenspan (1987:4-2003:2): α0 = .017 (.007); α1 = 1.405 (.211); α2 = .375 (.102); ρ1 = 1.484 (.044); ρ2 = -.646 (.044); Overidentifying Restrictions [.93]; SEE = 3.1; SEE (percent) = .36%
    - Full sample (1957:1-2003:2): α0 = .004 (.013); α1 = 1.715 (.373); α2 = .289 (.163); ρ1 = 1.054 (.052); ρ2 = -.156 (.053); Overidentifying Restrictions [.47]; SEE = 7.6; SEE (percent) = 1.04%
  - Instrument set for real-time estimates: lags 1-4 of annual inflation, output gap, and effective federal funds rate.

- Table 2. Estimated Phillips Curve (Generalized Method of Moments; Newey-West; up to four-quarter serial correlation)
  - Using HP filter (β, γ; robust standard errors in parentheses; P-values for Hansen’s J-test in square brackets; SEE in percent)
    - Bretton Woods (1957:1-1972:2): β = .640 (.092); γ = .047 (.058); Overidentifying Restrictions [.51]; SEE = 10.3; SEE (percent) = 1.12%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): β = .470 (.038); γ = .005 (.060); Overidentifying Restrictions [.90]; SEE = 5.7; SEE (percent) = 1.64%
    - Volcker (1980:1-1987:3): β = .551 (.055); γ = .018 (.080); Overidentifying Restrictions [.90]; SEE = 5.5; SEE (percent) = 2.35%
    - Greenspan (1987:4-2003:2): β = .905 (.070); γ = .260 (.115); Overidentifying Restrictions [.54]; SEE = 9.9; SEE (percent) = 1.26%
    - Full sample (1957:1-2003:2): β = .594 (.059); γ = .056 (.053); Overidentifying Restrictions [.20]; SEE = 14.6; SEE (percent) = 1.49%
  - Using real-time data
    - Bretton Woods (1957:1-1972:2): β = .620 (.077); γ = .148 (.047); Overidentifying Restrictions [.48]; SEE = 10.6; SEE (percent) = 1.05%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): β = .470 (.040); γ = .003 (.015); Overidentifying Restrictions [.90]; SEE = 5.7; SEE (percent) = 1.64%
    - Volcker (1980:1-1987:3): β = .623 (.068); γ = -.030 (.016); Overidentifying Restrictions [.92]; SEE = 5.3; SEE (percent) = 2.36%
    - Greenspan (1987:4-2003:2): β = .726 (.066); γ = .005 (.038); Overidentifying Restrictions [.72]; SEE = 7.9; SEE (percent) = 1.23%
    - Full sample (1957:1-2003:2): β = 0.558 (0.055); γ = 0.014 (0.019); Overidentifying Restrictions [.22]; SEE = 14.1; SEE (percent) = 1.48%
  - Instrument set for real-time estimates: lags 1-4 of annual inflation, output gap, and federal funds rate.

- Table 3. Estimated Aggregate Demand Function (Generalized Method of Moments; Newey-West; up to four-quarter serial correlation)
  - Using HP filter (δ1, δ2; robust standard errors in parentheses; P-values for Hansen’s J-test in square brackets; SEE in percent)
    - Bretton Woods (1957:1-1972:2): δ1 = .021 (.021); δ2 = .555 (.035); Overidentifying Restrictions [.63]; SEE = 8.0; SEE (percent) = .64%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): δ1 = -.062 (.018); δ2 = .569 (.038); Overidentifying Restrictions [.91]; SEE = 4.8; SEE (percent) = .67%
    - Volcker (1980:1-1987:3): δ1 = -.022 (.005); δ2 = .468 (.035); Overidentifying Restrictions [.86]; SEE = 5.4; SEE (percent) = .57%
    - Greenspan (1987:4-2003:2): δ1 = -.000 (.006); δ2 = .481 (.041); Overidentifying Restrictions [.76]; SEE = 6.6; SEE (percent) = .33%
    - Full sample (1957:1-2003:2): δ1 = -.013 (.006); δ2 = .499 (.026); Overidentifying Restrictions [.61]; SEE = 8.2; SEE (percent) = .54%
  - Using real-time data
    - Bretton Woods (1957:1-1972:2): δ1 = .013 (.023); δ2 = .582 (.031); Overidentifying Restrictions [.69]; SEE = 7.4; SEE (percent) = .63%
    - Post Bretton Woods / Pre Volcker (1972:3-1979:4): δ1 = -.146 (.021); δ2 = .567 (.023); Overidentifying Restrictions [.90]; SEE = 4.8; SEE (percent) = .94%
    - Volcker (1980:1-1987:3): δ1 = -.029 (.005); δ2 = .458 (.025); Overidentifying Restrictions [.85]; SEE = 5.5; SEE (percent) = 1.13%
    - Greenspan (1987:4-2003:2): δ1 = -.007 (.008); δ2 = .515 (.039); Overidentifying Restrictions [.62]; SEE = 8.1; SEE (percent) = .49%
    - Full sample (1957:1-2003:2): δ1 = -.018 (.007); δ2 = .486 (.028); Overidentifying Restrictions [.49]; SEE = 9.4; SEE (percent) = .74%
  - Instrument set for real-time estimates: lags 1-4 of annual inflation, output gap, and federal funds rate.

### Key model calibrations and simulated statistics (Table 4 and figures)

- Table 4. Simulated standard deviations and sacrifice ratios (real-time model; parameterizations by decade)
  - Estimated parameters over the periods (real-time model)
    - α0 = 0 across Bretton Woods, Post Bretton Woods, Volcker, Greenspan
    - α1: Bretton Woods = 1.062; Post Bretton Woods = .635; Volcker = 1.824; Greenspan = 1.405
    - α2: Bretton Woods = .253; Post Bretton Woods = .241; Volcker = 0; Greenspan = .375
    - ρ1: Bretton Woods = 1.185; Post Bretton Woods = .871; Volcker = .840; Greenspan = 1.484
    - ρ2: Bretton Woods = -.424; Post Bretton Woods = -.213; Volcker = -.107; Greenspan = -.646
    - β: Bretton Woods = .620; Post Bretton Woods = .470; Volcker = .623; Greenspan = .726
    - γ = .014 for all periods
    - δ0 = 0 for all periods
    - δ1 = -.018 for all periods
    - δ2 = .486 for all periods
  - Historical standard deviations over the periods (percent)
    - Inflation: Bretton Woods = 1.79; Post Bretton Woods = 2.89; Volcker = 3.87; Greenspan = 1.49
    - Output: Bretton Woods = 1.70; Post Bretton Woods = 2.31; Volcker = 1.83; Greenspan = 1.20
    - Interest rate: Bretton Woods = 1.83; Post Bretton Woods = 2.58; Volcker = 3.53; Greenspan = 2.08
  - Simulated standard deviations and sacrifice ratios using 1990s-specific shocks and β's estimates (Asymptotic standard errors (percent))
    - Inflation: 1.72; 1.74; 1.70; 1.72 (listed as four values corresponding to periods)
    - Output: 1.22; 1.05; 1.50; 1.34
    - Interest rate: 2.00; 1.40; 2.47; 2.61
    - Sacrifice Ratios: 5.84; 7.26; 6.58; 4.96
  - Simulated standard deviations and sacrifice ratios using estimated parameters but 1990s-specific shocks (Asymptotic standard errors (percent))
    - Inflation: 2.23; 4.76; 2.17; 1.72
    - Output: 1.51; 3.89; 1.88; 1.34
    - Interest rate: 2.88; 6.74; 3.67; 2.61
    - Sacrifice Ratios: 6.22; 10.20; 7.28; 4.96
  - Note: Under the 1970s parameterization, the model does not converge to steady state by the end of the simulation horizon. The sacrifice ratio is therefore calculated over the first 24 quarters (periods during which the output gap remains below baseline).

- Figures (selected descriptions and measurement definitions)
  - Figure 1. United States: Inflation Dynamics and Macroeconomic Volatility, 1957–2003
    - Inflation measured by annual percentage changes in the Consumer Price Index.
    - Inflation volatility measured by twenty-quarter rolling standard deviation of annualized the quarterly inflation rate, as measured by CPI.
    - Output volatility measured by twenty-quarter rolling standard deviation of the real output gap.
    - Data source: International Financial Statistics.
  - Rolling GMM estimates (Figures 2–4) report time series estimates of monetary policy rule parameters (first- and second-order smoothing parameters, long-term feedback parameters on inflation and output gap, intercept, SEE), Phillips curve parameters (forward-looking inflation coefficient, output gap coefficient, SEE), and aggregate demand parameters (forward-looking output gap, real interest rate, SEE) across sample windows (e.g., 1957:1-1969:3 through 1999:3-2001:3).
  - Impulse response figures (Figures 5–8) display:
    - Responses to a negative one-percent one-off demand shock and a negative one-percent one-off supply shock (panel a and b): inflation responses (percentage points), output gap responses (percent), nominal and real interest rate responses (percentage points), plotted for decades labeled 1960s, 1970s, 1980s, 1990s.
    - Responses to a one-percent permanent disinflation shock (Figure 7) and to a one-percent one-off interest-rate shock (Figure 8).
  - Figure 6. Model-generated autocorrelation and cross-correlation functions for a one-off supply shock:
    - Autocorrelation function: Inflation (lags 1–4) across decades 1960s–1990s.
    - Cross correlation: Inflation x Output Gap (lags 1–4) across decades 1960s–1990s.
  - Figure 9 (panels a and b). Sensitivity analyses:
    - Sensitivity of inflation, output, and interest-rate volatilities to alternative degrees of forward-lookingness in pricing (α) and conservativeness in monetary policy (β).
    - Sensitivity of inflation, output, and interest-rate volatilities to alternative degrees of conservativeness (α1/α2 axes shown) and activism in monetary policy (β axis shown).

### Measurement notes and estimation details referenced in tables and figures

- Estimation method: Generalized Method of Moments using the Newey-West weighting matrix and allowing for up to four-quarter serial correlation.
- Robust standard errors are reported in parentheses; P-values for Hansen’s J-test are reported in square brackets.
- Instrument sets (real-time estimates): lags 1-4 of annual inflation, output gap, and effective federal funds rate (Table 1) or federal funds rate (Tables 2 and 3).

*Source: _wp04195 - REFERENCES (figures and tables as presented in the supplied PDF content).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04195.pdf_