## 7. Economic Performance of Policy Rules Under Alternative Inflation Targets during the 1990s

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---

### I. Introduction: purpose and context
- Inflation targeting defined: a monetary policy regime making a low rate of inflation its primary objective.
- Distinction:
  - Strict inflation targeting: minimize variability of the inflation rate around its target only.
  - Flexible inflation targeting: allow other variables (e.g., the output gap) into the objective.
- Policy question examined:
  - Whether a zero or a positive inflation target would be desirable in the EU under an inflation-targeting regime.
  - Counterfactual simulations for inflation targets π* = 0 percent, 2 percent, and 4 percent.

### II. Model structure, policy rules, and objective
- Benchmark model (IS-LM-AS with expectations):
  - IS curve (equation (1)): y_t = a y_{t-1} + b r_t + ε_t, with 0≤a<1, b<0; ε_t = μ ε_{t-1} + λ_{1t}, λ_{1t} i.i.d. with variance σ_{λ1}^2.
  - LM curve (equation (2)): m_t - p_t = c_0 + c_1 y_t + c_2 i_t + v_t, with c_1>0, c_2<0.
  - Expectations-augmented Phillips curve (equation (3)): π_t = k_0 + k_1 π_{t+1}^e + k_2 π_{t-1} + k_3 y_{t-1} + θ_t, θ_t = ν θ_{t-1} + λ_{2t}, λ_{2t} i.i.d. with variance σ_{λ2}^2.
  - Inflation expectations (equation (4) and (4a)): π_t^e = g_0 + g_1 π_{t-1}^e + g_2 π_{t-1} + η_t; (4a) shows backward-looking expected inflation as a weighted sum of past inflation and shocks.
- Policy implementation and objective:
  - Authorities change the short-term nominal interest rate to affect inflation.
  - Central bank loss function (symmetric quadratic):
    - Minimize E_t Σ_{j,k,l=0} β^j ½ [(π_{t+j}-π*)^2 + ω_1 y_{t+k}^2 + ω_2 (i_{t+l}-i_{t+l-1})^2], with ω_1 and ω_2 positive; β is the discount factor.
  - First-order conditions yield an interest-rate rule with interest-rate smoothing.
- Two policy rules analyzed:
  - Forward-Looking Rule (FLR) (equation (5)):
    - i_t = a_1 + a_2 (E_t π_{t+1} – π*) + a_3 E_t y_{t+1} + a_4 i_{t-1}
  - Spontaneous Adjustment Rule (SAR) (equation (6)):
    - i_t = a_1 + a_2 (E_t π_{t+1} – π*) + a_3 y_t + a_4 i_{t-1}
  - Parameters mapping (as specified):
    - a_1 = [c_1/βω_2 + b/βω_2 + (c_1 + b k_3)/β k_1 ω_2]
    - a_2 = (1/ω_2)
    - a_3 = (ω_1/ω_2)
    - a_4 = (k_1/β)
  - Both rules include interest rate smoothing via lagged interest rate coefficient a_4.

### III. Empirical analysis: data, estimation, and simulations
- Data and sample:
  - Quarterly observations from OECD’s Main Economic Indicators over the period 1974-2001 (robustness for 1990-2001).
  - Variables: real output (GDP in 1995 prices), core prices (core harmonized CPI excluding energy and food), interbank nominal interest rate (i), money supply M1, unemployment rate (u).
  - Output gap estimated by HP filter with smoothing parameter equal to 1,600.
  - Inflation measured as logarithmic difference in the price level. Real interest rate = nominal interest rate minus expected inflation.
  - Aggregation for the EU uses PPP-expressed euro series.
  - Sample countries: Germany, France, Belgium, Netherlands, United Kingdom, Italy, Luxembourg, Spain, Portugal, Denmark, Austria, Finland, Sweden, Greece.
- Estimation approach:
  - Expected inflation and expected output generated using within-sample ARMA(2,0) models.
  - GMM estimation of the first-order condition (4b) with four lags of short-term interest rate, inflation, and output gap as instruments.
  - J-statistic and Sargan tests reported support model specification and instrument validity.
- Empirical parameter observations:
  - Lagged-rate coefficient ranges from 0.54 to 0.56 (high degree of interest-rate smoothing).
  - Current inflation and expected inflation coefficients are statistically significant and greater than one.
- Counterfactual simulations:
  - Simulated output gap and inflation under FLR and SAR for π* = 0 percent, 2 percent, and 4 percent over 1974:Q1–2001:Q4 (robustness for 1990:Q1–2001:Q4).
  - Two main empirical regularities from simulations:
    - Negative trade-off between mean output gap and mean inflation rate (short-run Phillips curve).
    - Negative trade-off between variances of the output gap and the inflation rate (higher inflation variance associated with smaller output variance).
  - Comparative performance:
    - FLR typically outperforms SAR: FLR exhibits higher mean output, lower mean inflation, smaller output gap variance, and smaller inflation variance than SAR in most cases.
- Robustness analyses:
  - Country-level disaggregation:
    - Aggregate results broadly hold for Germany, France, Spain.
    - Greece differs: mean output gap and mean inflation rate correlate positively (but output gap variability and inflation variability remain negatively correlated).
  - Alternative output-gap measures:
    - SVAR-based detrending and OECD output gaps produce results nearly matching baseline: inflation target above zero tends to lead to smaller output gaps.
  - Alternative sample period (1990s) reestimation:
    - Results confirm that an inflation target above 0 percent leads to smaller output gaps even in the 1990s environment.

### IV. Key empirical results (selected tables and parameter estimates)
- Table 1 — GMM Estimates (selected entries preserved):
  - FLR - 0%: c1 = 0.56 (3.98)*; b k1 = -0.106 (-4.11)*; k3 = 0.49 (4.25)*; ω2 = 0.128 (4.52)*; ω1 = 0.47 (4.31)*; β = 0.13 (4.71)*; J = 0.97 (3.98)*; p-value [0.55]
  - FLR - 2%: 0.57 (4.15)*; -0.109 (-3.97)*; 0.54 (4.18)*; 0.134 (4.20)*; 0.48 (4.19)*; 0.14 (5.07)*; 0.98 (4.39)*; [0.57]
  - FLR - 4%: 0.60 (4.71)*; -0.107 (-4.28)*; 0.57 (4.39)*; 0.137 (3.97)*; 0.55 (4.63)*; 0.15 (4.19)*; 0.97 (4.84)*; [0.59]
  - SAR - 0%: 0.53 (3.83)*; -0.096 (-3.47)**; 0.48 (4.14)*; 0.119 (3.55)**; 0.57 (3.86)*; 0.12 (4.53)*; 0.95 (4.67)*; [0.43]
  - SAR - 2%: 0.58 (4.02)*; -0.103 (-3.87)*; 0.50 (3.81)*; 0.125 (4.19)*; 0.56 (3.45)**; 0.13 (4.71)*; 0.96 (4.17)*; [0.48]
  - SAR - 4%: 0.57 (3.90)*; -0.102 (4.03)*; 0.49 (3.39)**; 0.126 (4.84)*; 0.59 (4.09)*; 0.14 (4.22)*; 0.95 (4.55)*; [0.46]
  - Notes: parentheses = t-statistics; brackets = p-values; * significant at the 1 percent level. ** significant at the 5 percent level.
- Table 2 — Multivariate (IV) estimations and policy-rule expressions:
  - Equation (1): y_t = 0.57 y_{t-1} – 0.108 r_t. Sargan: 0.0214[0.87]; R2 = 0.54.
  - Equation (2): (m_t - p_t) = 0.084 + 0.59 y_t – 0.114 i_t. Sargan: 0.0302[0.66]; R2 = 0.78.
  - Equation (3): π_t = 0.0109 + 0.53 π_{t-1} + 0.41 π_{t-2} + 0.131 y_{t-1}. Sargan: 0.0318[0.58]; R2 = 0.76.
  - Policy-rule expressions (selected):
    - FLR - 0%: i_t = 3.45 + 2.13 π_{t+1}^e + 0.28 y_{t+1}^e + 0.546 i_{t-1}
    - FLR - 2%: i_t = 3.17 + 2.08 (π_{t+1}^e – 0.02) + 0.29 y_{t+1}^e + 0.541 i_{t-1}
    - FLR - 4%: i_t = 2.84 + 1.82 (π_{t+1}^e – 0.04) + 0.27 y_{t+1}^e + 0.546 i_{t-1}
    - SAR - 0%: i_t = 2.80 + 1.75 π_{t+1}^e + 0.21 y_t + 0.558 i_{t-1}
    - SAR - 2%: i_t = 3.00 + 1.79 (π_{t+1}^e – 0.02) + 0.23 y_t + 0.552 i_{t-1}
    - SAR - 4%: i_t = 2.87 + 1.69 (π_{t+1}^e – 0.04) + 0.24 y_t + 0.558 i_{t-1}
- Table 3 — Economic Performance (Core Price Data; HP Filter; 1974:Q1 – 2001:Q4):
  - Actual data: Output Mean = -0.6; Output Variance = 3.66; Inflation Mean = 3.2; Inflation Variance = 16.23.
  - Simulations (Mean, Variance):
    - FLR-0: Output Mean = -1.4; Variance = 2.52; Inflation Mean = 2.5; Variance = 11.52.
    - FLR-2: Output Mean = -1.1; Variance = 2.31; Inflation Mean = 2.8; Variance = 12.47.
    - FLR-4: Output Mean = -0.6; Variance = 2.01; Inflation Mean = 3.4; Variance = 13.61.
    - SAR-0: Output Mean = -1.4; Variance = 3.35; Inflation Mean = 3.5; Variance = 12.58.
    - SAR-2: Output Mean = -1.0; Variance = 2.83; Inflation Mean = 3.6; Variance = 13.90.
    - SAR-4: Output Mean = -0.7; Variance = 2.28; Inflation Mean = 4.2; Variance = 16.09.
- Table 4 — Country results (Germany, France, Spain, Greece) — selected entries:
  - Germany actual: Output Mean = -1.1; Variance = 6.51; Inflation Mean = 3.1; Variance = 3.63.
  - Germany simulations (FLR-2): Output Mean = -1.0; Variance = 4.51; Inflation Mean = 3.1; Variance = 3.04.
  - France actual: Output Mean = -1.2; Variance = 3.98; Inflation Mean = 5.7; Variance = 20.72.
  - France simulations (FLR-2): Output Mean = -1.1; Variance = 2.53; Inflation Mean = 4.3; Variance = 19.08.
  - Spain actual: Output Mean = -1.9; Variance = 6.52; Inflation Mean = 9.4; Variance = 38.94.
  - Spain simulations (FLR-2): Output Mean = -0.9; Variance = 4.41; Inflation Mean = 8.5; Variance = 32.11.
  - Greece actual: Output Mean = -0.5; Variance = 9.97; Inflation Mean = 14.6; Variance = 47.61.
  - Greece simulations (FLR-2): Output Mean = -1.5; Variance = 7.42; Inflation Mean = 14.4; Variance = 43.85.
- Table 5 — Core Price Data; SVAR Filter:
  - Actual data: Output Mean = -0.6; Output Variance = 3.66; Inflation Mean = 3.2; Inflation Variance = 16.23.
  - FLR-2: Output Mean = -1.1; Variance = 2.49; Inflation Mean = 2.4; Variance = 14.19.
  - SAR-2: Output Mean = -1.3; Variance = 2.82; Inflation Mean = 3.6; Variance = 14.79.
- Table 6 — Core Price Data: OECD Output Gap Measures (1980-2002):
  - Actual data: Output Mean = -0.5; Inflation Mean = 2.89; Inflation Mean (alternate) = 3.0; Inflation Variance = 15.12.
  - FLR-2: Output Mean = -1.0; Variance = 2.49; Inflation Mean = 1.7; Variance = 12.57.
  - SAR-2: Output Mean = -1.5; Variance = 2.79; Inflation Mean = 3.4; Variance = 15.21.
- Table 7 — Performance during the 1990s (1990:Q1 – 2001:Q4):
  - Actual data: Output Mean = -0.4; Output Variance = 2.19; Inflation Mean = 2.7; Inflation Variance = 13.37.
  - Simulations:
    - FLR-2: Output Mean = -1.1; Variance = 2.30; Inflation Mean = 2.3; Variance = 12.91.
    - FLR-4: Output Mean = -0.7; Variance = 2.16; Inflation Mean = 2.9; Variance = 14.22.
    - SAR-2: Output Mean = -1.2; Variance = 2.89; Inflation Mean = 2.7; Variance = 15.14.
    - SAR-4: Output Mean = -0.8; Variance = 2.44; Inflation Mean = 3.6; Variance = 16.71.

### V. Main findings and policy implications
- Main empirical findings:
  - Simulations compare policy rules under inflation targets of 0 percent, 2 percent, and 4 percent.
  - Forward-looking policy rules contribute to macroeconomic stability and credibility and generally outperform spontaneous adjustment rules.
  - A positive inflation target (2 percent or 4 percent), as opposed to a zero inflation target, is superior in terms of higher and less volatile output in aggregate simulations.
  - Negative correlations observed:
    - Between average output gap and average inflation rate across the three inflation targets (aggregate and disaggregated data), except Greece.
    - Between output gap variance and inflation rate variance: higher inflation targets → larger inflation variances and smaller output variances.
- Robustness:
  - Results are robust to different model specifications, alternative output-gap measures (HP-filter, SVAR-based, OECD gaps), different sample periods including the 1990s, and country-level disaggregation (Germany, France, Spain generally confirm aggregate patterns; Greece differs).
- Policy implications:
  - Prefer forward-looking (expectations-based) rules to enhance macroeconomic stability and monetary policy credibility.
  - Flexible, country-specific inflation targeting with positive inflation goals (2 percent to 4 percent) appears beneficial for output performance in many EU countries.
  - Exceptions (e.g., Greece) indicate that optimal inflation targets may be country-specific and that a single uniform target may not be optimal across heterogeneous economies.

*Source: _wp0589 - 7. Economic Performance of Policy Rules Under Alternative (IMF PDF).*

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

### _wp0589 - References.............................................................................................................................14

### References
- References.............................................................................................................................14

### Tables
- 1.         GMM         Estimates ........................................................................................................20
- 2. Multivariate (IV) Estimations Under Alternative Policy Rules and 
Inflation Targets........................................................................................................21
- 3. Economic Performance of Policy Rules Under Alternative  
Inflation Targets (Core Price Data; HP Filter for Output Gap) ................................22
- 4. Economic Performance of Policy Rules Under Alternative  
Inflation Targets (Germany, France, Spain, and Greece) .........................................23
- 5. Economic Performance of Policy Rules Under Alternative  
Inflation Targets (Core Price Data; SVAR Filter for Output Gap)...........................25
- 6. Economic Performance of Policy Rules Under Alternative  
Inflation Targets (Core Price Data: OECD Output Gap Measures-1980-2002 ........26

*Source: _wp0589 - References..............................................................................................................*

### 7. Economic Performance of Policy Rules Under Alternative

### 7. Economic Performance of Policy Rules Under Alternative Inflation Targets during the 1990s

### I. Introduction: purpose and context
- Inflation targeting: a monetary policy regime making a low rate of inflation its primary objective.
- Differentiation:
  - Strict inflation targeting: minimize variability of the inflation rate around its target only.
  - Flexible inflation targeting: allow other variables (e.g., the output gap) into the objective.
- Common empirical observations and debates cited:
  - Evidence of improved inflation performance and credibility in some studies; mixed or limited benefits in others.
  - Anchoring of inflation expectations can produce self-fulfilling low and stable inflation outcomes.
  - Criticisms include monitoring lags, uncertainty about the optimal inflation rate, risks of rigidity and higher structural unemployment, and potential increased output volatility from revealed aversion to inflation variability.
- Policy question of the paper:
  - Whether a zero or a positive inflation target would be desirable in the EU under an inflation-targeting regime.
  - Examination uses a macroeconomic model and counterfactual simulations for inflation targets of 0, 2, and 4 percent.

### II. The model: structure, policy rules, and objective
- Benchmark model: an IS-LM-AS framework with:
  - IS curve (equation (1)): y_t = a y_{t-1} + b r_t + ε_t, with 0≤a<1, b<0; ε_t = μ ε_{t-1} + λ_{1t}, λ_{1t} i.i.d. with variance σ_{λ1}^2.
  - LM curve (equation (2)): m_t - p_t = c_0 + c_1 y_t + c_2 i_t + v_t, with c_1>0, c_2<0.
  - Expectations-augmented Phillips curve (equation (3)): π_t = k_0 + k_1 π_{t+1}^e + k_2 π_{t-1} + k_3 y_{t-1} + θ_t, θ_t = ν θ_{t-1} + λ_{2t}, λ_{2t} i.i.d. with variance σ_{λ2}^2.
  - Inflation expectations (equation (4) and (4a)): π_t^e = g_0 + g_1 π_{t-1}^e + g_2 π_{t-1} + η_t; (4a) shows backward-looking expected inflation as a weighted sum of past inflation and shocks.
- Policy implementation:
  - Monetary authorities change the short-term nominal interest rate to affect inflation (do not directly choose inflation after shocks).
  - Central bank loss function (symmetric quadratic form):
    - Minimize E_t Σ_{j,k,l=0} β^j ½ [(π_{t+j}-π*)^2 + ω_1 y_{t+k}^2 + ω_2 (i_{t+l}-i_{t+l-1})^2]
    - ω_1 and ω_2 are positive parameters (less than, but not equal to one); β is discount factor.
  - First-order conditions yield an interest-rate rule (see equations (4b), (4c)).
- Two policy rules analyzed:
  - Forward-Looking Rule (FLR) (equation (5)):
    - i_t = a_1 + a_2 (E_t π_{t+1} – π*) + a_3 E_t y_{t+1} + a_4 i_{t-1}
  - Spontaneous Adjustment Rule (SAR) (equation (6)):
    - i_t = a_1 + a_2 (E_t π_{t+1} – π*) + a_3 y_t + a_4 i_{t-1}
  - Parameters mapping:
    - a_1 = [c_1/βω_2 + b/βω_2 + (c_1 + b k_3)/β k_1 ω_2]
    - a_2 = (1/ω_2)
    - a_3 = (ω_1/ω_2)
    - a_4 = (k_1/β)
  - Both rules include interest rate smoothing via the lagged interest rate a_4.

### III. Empirical analysis: data, estimation, and simulations
- Data and sample:
  - Quarterly observations from OECD’s Main Economic Indicators over the period 1974-2001 (and robustness for 1990-2001).
  - Variables: real output (GDP in 1995 prices), core prices (core harmonized CPI excluding energy and food), interbank nominal interest rate (i), money supply M1, unemployment rate (u).
  - Output gap estimated by Hodrick-Prescott (HP) filter with smoothing parameter equal to 1,600.
  - Inflation measured as logarithmic difference in the price level. Real interest rate = nominal interest rate minus expected inflation.
  - Aggregation for the EU uses PPP-expressed euro series following Maulon and Sarda (1999).
  - Sample countries: Germany, France, Belgium, Netherlands, United Kingdom, Italy, Luxembourg, Spain, Portugal, Denmark, Austria, Finland, Sweden, Greece.
- Estimation approach:
  - Expected inflation and expected output generated using within-sample ARMA(2,0) models (Box-Jenkins).
  - GMM estimation of the first-order condition (4b) with four lags of short-term interest rate (stationary form), inflation, and output gap as instruments.
  - J-statistic used to test overidentifying restrictions; Sargan tests for instrument validity reported as supporting model specification.
- Key empirical parameter and model features reported in text:
  - Lagged-rate coefficient ranges from 0.54 to 0.56 (high degree of interest-rate smoothing).
  - Current inflation and expected inflation coefficients are statistically significant and greater than one (central banks raise rates sufficiently to increase real rates to combat inflationary pressures).
- Counterfactual simulations:
  - Policy counterfactuals simulate output gap and inflation under FLR and SAR for inflation targets π* = 0 percent, 2 percent, and 4 percent over 1974:Q1-2001:Q4 (and robustness for 1990-2001).
  - Two main empirical regularities from simulations:
    - Negative trade-off between mean output gap and mean inflation rate (short-run Phillips curve).
    - Negative trade-off between variances of the output gap and the inflation rate (higher inflation variance associated with smaller output variance).
  - Comparative performance of rules:
    - Forward-Looking Rule (FLR) typically outperforms Spontaneous Adjustment Rule (SAR):
      - FLR exhibits higher mean output, lower mean inflation, smaller output gap variance, and smaller inflation variance than SAR in most cases.
    - These FLR results align with prior findings that forward-looking rules deliver lower and less volatile inflation.
- Robustness analyses:
  - Country-level disaggregation (Germany, France, Spain, Greece):
    - Aggregate results broadly hold for Germany, France, Spain.
    - Greece differs: mean output gap and mean inflation rate correlate positively (but output gap variability and inflation variability remain negatively correlated).
    - Implication: inflation targeting between 2 and 4 percent may yield a narrower and more stable output gap for Germany, France, Spain; lower-target regime may suit Greece.
  - Alternative output-gap measures:
    - SVAR-based multivariate detrending (real output, inflation, unemployment) produces gap measures; results nearly match baseline.
    - OECD output gaps (1980:Q1-2002:Q4) also nearly match baseline: inflation target above zero seems to lead to smaller output gaps.
  - Alternative sample period: 1990s (1990-2001) reestimation:
    - Results in Table 7 confirm that an inflation target above 0 percent leads to smaller output gaps even in the 1990s environment of lower and less volatile inflation.

### IV. Main findings and policy implications
- Main empirical findings (preserve exact numeric targets and parameter observations):
  - Simulations compare policy rules under inflation targets of 0 percent, 2 percent, and 4 percent.
  - Forward-looking policy rules contribute to macroeconomic stability and credibility and generally outperform spontaneous adjustment rules.
  - A positive inflation target (2 percent or 4 percent), as opposed to a zero inflation target, is superior in terms of higher and less volatile output.
  - Negative correlations found:
    - Between average output gap and average inflation rate across the three inflation targets (aggregate and disaggregated data), except Greece.
    - Between output gap variance and inflation rate variance: higher inflation targets → larger inflation variances and smaller output variances.
- Robustness:
  - Results are robust to:
    - Different model specifications (IS-LM-AS with expectations-augmented Phillips curve).
    - Alternative output-gap measures (HP-filter, SVAR-based, OECD gaps).
    - Different sample periods, including the 1990s (1990-2001).
    - Country-level disaggregation (Germany, France, Spain generally confirm aggregate patterns; Greece differs).
- Policy implications highlighted by the analysis:
  - Forward-looking (expectations-based) rules should be preferred to enhance macroeconomic stability and monetary policy credibility.
  - Flexible, country-specific inflation targeting with positive inflation goals (2 percent to 4 percent) appears beneficial for output performance in many EU countries.
  - Exceptions (e.g., Greece) indicate that optimal inflation targets may be country-specific and that a single uniform target may not be optimal across heterogeneous economies.

*Source: _wp0589 - 7. Economic Performance of Policy Rules Under Alternative (PDF chapter content provided).*

### References

### _wp0589 - References

### Key bibliographic sources
- Comprehensive list of literature on inflation targeting, monetary policy rules, and macroeconomic modeling including but not limited to works by:
  - Adema, Y., 2004.
  - Aiyagari, S. R., 1990.
  - Akerlof, G. A., W. T. Dickens, and G. L. Perry, 1996 and 2000.
  - Alesina, A. F., O. Blanchard, J. Gali, F. Giavazzi and H. Uhlig, 2001.
  - Bernanke, B., T. Laubach, F. Mishkin and A.S. Posen, 1999.
  - Blinder, A. S., 1989 and 1999.
  - Box, G.E.P. and G.M. Jenkins, 1976.
  - Cecchetti, S. and M. A. Wynne, 2003.
  - Clarida, R., J. Gali and M. Gertler, 1999.
  - McCallum, B. T. and E. Nelson, 1999 and 2004.
  - Mishkin, F. S. and A. S. Posen, 1997.
  - Svensson, L. E. O., multiple works 1997–2003.
  - Taylor, J. B., 1993 and 2000.
  - Woodford, M., 2000 and 2003.
- The references cover theoretical and empirical analyses of:
  - Inflation targeting experiences and implementations.
  - Forward-looking policy rules and Taylor-rule variants.
  - Core inflation measurement and alternative filters for output gaps.
  - Robustness of simple policy rules under model uncertainty.
  - Methodological foundations: GMM, IV, SVAR, HP filter, and time-series forecasting.

### Table 1 — GMM Estimates (policy rules - inflation targets)
- Coefficients reported for FLR (forward-looking rule) and SAR (spontaneous adjustment) with inflation targets 0%, 2%, 4%.
- Selected coefficient values (rows show point estimates; t-statistics in parentheses; p-values in brackets):
  - FLR - 0%: c1 = 0.56 (3.98)*; b k1 = -0.106 (-4.11)*; k3 = 0.49 (4.25)*; ω2 = 0.128 (4.52)*; ω1 = 0.47 (4.31)*; β = 0.13 (4.71)*; J = 0.97 (3.98)*; p-value [0.55]
  - FLR - 2%: 0.57 (4.15)*; -0.109 (-3.97)*; 0.54 (4.18)*; 0.134 (4.20)*; 0.48 (4.19)*; 0.14 (5.07)*; 0.98 (4.39)*; [0.57]
  - FLR - 4%: 0.60 (4.71)*; -0.107 (-4.28)*; 0.57 (4.39)*; 0.137 (3.97)*; 0.55 (4.63)*; 0.15 (4.19)*; 0.97 (4.84)*; [0.59]
  - SAR - 0%: 0.53 (3.83)*; -0.096 (-3.47)**; 0.48 (4.14)*; 0.119 (3.55)**; 0.57 (3.86)*; 0.12 (4.53)*; 0.95 (4.67)*; [0.43]
  - SAR - 2%: 0.58 (4.02)*; -0.103 (-3.87)*; 0.50 (3.81)*; 0.125 (4.19)*; 0.56 (3.45)**; 0.13 (4.71)*; 0.96 (4.17)*; [0.48]
  - SAR - 4%: 0.57 (3.90)*; -0.102 (4.03)*; 0.49 (3.39)**; 0.126 (4.84)*; 0.59 (4.09)*; 0.14 (4.22)*; 0.95 (4.55)*; [0.46]
- Notes:
  - Figures in parentheses denote t-statistics.
  - Figures in brackets denote p-values.
  - Estimations cover 1974:Q1 – 2001:Q4.
  - * significant at the 1 percent level. ** significant at the 5 percent level.

### Table 2 — Multivariate (IV) Estimations and Policy-Rule Expressions
- Estimated equations (Sargan’s test value [p-value] and R2 shown):
  - Equation (1): y_t = 0.57 y_{t-1} – 0.108 r_t
    - Sargan: 0.0214[0.87]; R2 = 0.54
    - Coefficients: 0.57 (4.29)*; -0.108 (-5.11)*
    - Instruments: constant, y_{t-2}, y_{t-3}, r_{t-1}, r_{t-2}
  - Equation (2): (m_t - p_t) = 0.084 + 0.59 y_t – 0.114 i_t
    - Sargan: 0.0302[0.66]; R2 = 0.78
    - Coefficients: 0.084 (3.92)*; 0.59 (4.55)*; -0.114 (-4.64)*
    - Instruments: constant, (m-p)_{t-1}, y_{t-1}, y_{t-2}, i_{t-2}
  - Equation (3): π_t = 0.0109 + 0.53 π_{t-1} + 0.41 π_{t-2} + 0.131 y_{t-1}
    - Sargan: 0.0318[0.58]; R2 = 0.76
    - Coefficients: 0.0109 (3.68)*; 0.53 (3.95)*; 0.41 (3.49)*; 0.131 (4.12)*
    - Instruments: constant, π_{t-3}, π_{t-4}, y_{t-2}, y_{t-3}, y_{t-4}
- Policy rules (through first-order conditions), for inflation targets 0%, 2%, 4%:
  - FLR - 0%: i_t = 3.45 + 2.13 π_{t+1}^e + 0.28 y_{t+1}^e + 0.546 i_{t-1}
  - FLR - 2%: i_t = 3.17 + 2.08 (π_{t+1}^e – 0.02) + 0.29 y_{t+1}^e + 0.541 i_{t-1}
  - FLR - 4%: i_t = 2.84 + 1.82 (π_{t+1}^e – 0.04) + 0.27 y_{t+1}^e + 0.546 i_{t-1}
  - SAR - 0%: i_t = 2.80 + 1.75 π_{t+1}^e + 0.21 y_t + 0.558 i_{t-1}
  - SAR - 2%: i_t = 3.00 + 1.79 (π_{t+1}^e – 0.02) + 0.23 y_t + 0.552 i_{t-1}
  - SAR - 4%: i_t = 2.87 + 1.69 (π_{t+1}^e – 0.04) + 0.24 y_t + 0.558 i_{t-1}
- Notes:
  - Numbers in parentheses denote t-statistics; brackets denote p-values.
  - Estimations cover 1974:Q1 – 2001:Q4.
  - * significant at the 1 percent level.

### Table 3 — Economic Performance: Core Price Data; HP Filter for Output Gap (1974:Q1 – 2001:Q4)
- Actual data:
  - Output Mean = -0.6; Output Variance = 3.66
  - Inflation Mean = 3.2; Inflation Variance = 16.23
- Simulations (Mean, Variance):
  - FLR-0: Output Mean = -1.4; Variance = 2.52; Inflation Mean = 2.5; Variance = 11.52
  - FLR-2: Output Mean = -1.1; Variance = 2.31; Inflation Mean = 2.8; Variance = 12.47
  - FLR-4: Output Mean = -0.6; Variance = 2.01; Inflation Mean = 3.4; Variance = 13.61
  - SAR-0: Output Mean = -1.4; Variance = 3.35; Inflation Mean = 3.5; Variance = 12.58
  - SAR-2: Output Mean = -1.0; Variance = 2.83; Inflation Mean = 3.6; Variance = 13.90
  - SAR-4: Output Mean = -0.7; Variance = 2.28; Inflation Mean = 4.2; Variance = 16.09
- Notes: Means expressed as a percent. FLR vs SAR definitions as above.

### Table 4 — Economic Performance by Country (Germany, France, Spain, Greece)
- Germany (Actual data):
  - Output Mean = -1.1; Variance = 6.51; Inflation Mean = 3.1; Variance = 3.63
- Germany (Simulations):
  - FLR-0: Output Mean = -1.6; Variance = 5.48; Inflation Mean = 2.3; Variance = 1.82
  - FLR-2: -1.0; 4.51; 3.1; 3.04
  - FLR-4: -0.8; 4.06; 3.3; 3.84
  - SAR-0: -1.7; 6.51; 3.5; 1.95
  - SAR-2: -1.4; 5.29; 4.2; 3.31
  - SAR-4: -1.1; 4.61; 4.7; 3.68
- France (Actual data):
  - Output Mean = -1.2; Variance = 3.98; Inflation Mean = 5.7; Variance = 20.72
- France (Simulations):
  - FLR-0: -1.5; 3.29; 3.8; 16.26
  - FLR-2: -1.1; 2.53; 4.3; 19.08
  - FLR-4: -0.9; 2.32; 4.9; 24.12
  - SAR-0: -1.6; 4.17; 4.4; 20.59
  - SAR-2: -1.4; 3.55; 5.3; 26.32
  - SAR-4: -1.1; 2.48; 5.8; 32.09
- Spain (Actual data):
  - Output Mean = -1.9; Variance = 6.52; Inflation Mean = 9.4; Variance = 38.94
- Spain (Simulations):
  - FLR-0: -1.1; 5.69; 8.1; 26.39
  - FLR-2: -0.9; 4.41; 8.5; 32.11
  - FLR-4: -0.7; 4.08; 9.0; 36.49
  - SAR-0: -2.7; 6.81; 8.7; 33.18
  - SAR-2: -2.2; 5.75; 9.6; 40.23
  - SAR-4: -1.8; 4.60; 10.3; 45.36
- Greece (Actual data):
  - Output Mean = -0.5; Variance = 9.97; Inflation Mean = 14.6; Variance = 47.61
- Greece (Simulations):
  - FLR-0: Output Mean = -0.7; Variance = 9.22; Inflation Mean = 12.4; Variance = 37.19
  - FLR-2: -1.5; 7.42; 14.4; 43.85
  - FLR-4: -1.8; 6.39; 17.2; 48.12
  - SAR-0: -1.7; 13.07; 13.8; 41.97
  - SAR-2: -2.2; 12.24; 15.5; 48.53
  - SAR-4: -2.8; 8.84; 20.8; 52.77
- Notes: See Table 3 for definitions and period.

### Table 5 — Core Price Data; SVAR Filter for Output Gap
- Actual data:
  - Output Mean = -0.6; Output Variance = 3.66; Inflation Mean = 3.2; Inflation Variance = 16.23
- Simulations:
  - FLR-0: Output Mean = -1.4; Variance = 3.32; Inflation Mean = 2.1; Variance = 10.44
  - FLR-2: -1.1; 2.49; 2.4; 14.19
  - FLR-4: -0.6; 2.12; 3.1; 16.02
  - SAR-0: -2.1; 3.57; 2.6; 12.15
  - SAR-2: -1.3; 2.82; 3.6; 14.79
  - SAR-4: -0.9; 2.40; 4.1; 18.05

### Table 6 — Core Price Data: OECD Output Gap Measures (1980-2002)
- Actual data:
  - Output Mean = -0.5; Inflation Mean = 2.89; Inflation Mean (alternate) = 3.0; Inflation Variance = 15.12
- Simulations:
  - FLR-0: Output Mean = -1.2; Variance = 2.62; Inflation Mean = 1.3; Variance = 11.03
  - FLR-2: -1.0; 2.49; 1.7; 12.57
  - FLR-4: -0.5; 2.25; 3.0; 14.58
  - SAR-0: -2.4; 3.28; 2.8; 12.69
  - SAR-2: -1.5; 2.79; 3.4; 15.21
  - SAR-4: -0.8; 2.57; 3.9; 15.94
- Note: OECD measures are relative to the EU-12 group.

### Table 7 — Performance During the 1990s (1990:Q1 – 2001:Q4)
- Actual data:
  - Output Mean = -0.4; Output Variance = 2.19; Inflation Mean = 2.7; Inflation Variance = 13.37
- Simulations:
  - FLR-0: Output Mean = -1.3; Variance = 2.57; Inflation Mean = 1.9; Variance = 10.64
  - FLR-2: -1.1; 2.30; 2.3; 12.91
  - FLR-4: -0.7; 2.16; 2.9; 14.22
  - SAR-0: -1.8; 3.51; 2.3; 11.32
  - SAR-2: -1.2; 2.89; 2.7; 15.14
  - SAR-4: -0.8; 2.44; 3.6; 16.71
- Notes: Means expressed as a percent. FLR and SAR definitions and inflation-target percentages same as above.

*Italic: Source: _wp0589 - References (IMF PDF)._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0589.pdf_