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- ÁἸσαάκ Βασιλειάδης
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22 Table 1: FIML estimate of the econometric models Panel A: The US Panel B: Germany Parameter Estimate Std dev. t-statistic Estimate Std dev. t-statistic Phillips curve α π α π α π α π α y I-S curve β 0 (x100) β y β y β ρ Reaction function (1968:1-79:2) δ 0 (x100) δ π δ y δ i (1979:3-98:4) δ 0 (x100) δ π δ y δ i Likelihood σ y σ ε LBc(8) (p-value) LM(8) (p-value) σ y σ ε LBc(8) (p-value) LM(8) (p-value) Phillips curve (0.909) (0.095) (0.468) (0.452) I-S curve (0.714) (0.071) (0.049) (0.102) Reaction function (1968:1-79:2) (0.133) (0.011) (0.072) (0.590) Reaction function (1979:3-98:4) (0.179) (0.000) (0.038) (0.009) Real rate Inflation (79:3-98:4) Nominal rate Real rate Inflation (79:3-98:4) Nominal rate Steady-state values Note: LBc(8) is the Ljung-Box statistic, corrected for heteroskedasticity, obtained by regressing residuals on 8 lags. LM(8) is the Engle statistic for heteroskedasticity, obtained by regressing squared residuals on 8 lags. These statistics are distributed as χ 2 (8). Steady-state values are defined in Section 2.4.
23 Table 2: Stability tests The US Germany Panel A: Test for global stability p Sup-LR Avg-LR Exp-LR p Sup-LR Avg-LR Exp-LR Unknown date a a a b b Break in 1979: a b Panel B: Test for stability of policy-rule parameters p Sup-LR Avg-LR Exp-LR p Sup-LR Avg-LR Exp-LR Unknown date a a a a 8.14 a Break in 1979: a Panel C: Test for stability of non-policy parameters p Sup-LR Avg-LR Exp-LR p Sup-LR Avg-LR Exp-LR Unknown date b b Break in 1979: Note: Asymptotic critical values for the Sup-LR statistic are from Andrews (1993) and asymptotic critical values for the Exp-LR and the Avg-LR statistics are from Andrews and Ploberger (1994). p denotes the number of parameters allowed to shift at the break point. We assume that the break may occur over the subsample [π 0 T,(1-π 0 )T], with π 0 = a and b denote that the statistic is significant at the 1 percent and 5 percent levels, respectively.
24 Table 3: Implied parameters for optimal monetary-policy rules using program (9) Weights in the Optimal parameter values Unconditional standard deviations loss function (λ;1 λ) δ π 1 δ y δ i σ π σ y σ i (k) Panel A: The US k=6 (0.00;1.00) (0.50;0.50) (1.00;0.00) k=5 (0.00;1.00) (0.50;0.50) (1.00;0.00) k=4.7 (0.00;1.00) (0.50;0.50) (1.00;0.00) Model estimate Panel B: Germany k=6 (0.00;1.00) (0.50;0.50) (1.00;0.00) k=5 (0.00;1.00) (0.50;0.50) (1.00;0.00) k=4.7 (0.00;1.00) (0.50;0.50) (1.00;0.00) Model estimate
25 Table 4: Implied parameters for optimal monetary-policy rules using program (8) Weights in the Optimal parameter values Unconditional standard deviations loss function (µ π ; µ y ; 1 µ π µ y ) δ π 1 δ y δ i σ π σ y σ i Panel A: The US Inflation targeter (0.95;0.00;0.05) Output-gap targeter (0.00;0.95;0.05) Interest-rate targeter (0.00;0.00;1.00) Balanced preferences (0.35;0.35;0.30) Model estimate Panel B: Germany Inflation targeter (0.95;0.00;0.05) Output-gap targeter (0.00;0.95;0.05) Interest-rate targeter (0.00;0.00;1.00) Balanced preferences (0.35;0.35;0.30) Model estimate
26 Table 5: Implied parameters for the German optimal monetary-policy rules for various values of α y, using program (9) Weights in the Optimal parameter values Unconditional standard deviations loss function (µ π ; µ y ; 1 µ π µ y ) δ π 1 δ y δ i σ π σ y σ i Model estimate Optimal rule with the estimated nonpolicy parameters (α y =0.106) (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with α y =0.158 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with α y =0.054 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30)
27 Table 6: Implied parameters for the German optimal monetary-policy rules for various values of β ρ, using program (9) Weights in the Optimal parameter values Unconditional standard deviations loss function (µ π ; µ y ; 1 µ π µ y ) δ π 1 δ y δ i σ π σ y σ i Model estimate Optimal rule with the estimated nonpolicy parameters (β ρ =-0.508) (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with β ρ =-0.84 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with β ρ =-0.17 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30)
28 Table 7: Implied parameters for the German optimal monetary-policy rules for various values of β y1 +β y2, using program (9) Weights in the Optimal parameter values Unconditional standard deviations loss function (µ π ; µ y ; 1 µ π µ y ) δ π 1 δ y δ i σ π σ y σ i Model estimate Optimal rule with the estimated nonpolicy parameters (β y1 +β y2 =0.98) (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with β y1 +β y2 =1.05 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30) Optimal rule with β y1 +β y2 =0.91 (0.00;0.70;0.30) (0.35;0.35;0.30) (0.70;0.00;0.30)
29 Fig. 1: Inflation rate, output gap and short-term interest rate The US Short-term interest rate Inflation rate Output gap Germany Short-term interest rate Inflation rate Output gap
30 Fig. 2a: The US optimal policy frontier Model estimate ( ) (σ π=3.4, σ y =3.1, σ i =4.8) k=4.7 k =5.0 k= Standard deviation of inflation Fig. 2b: The German optimal policy frontier Model estimate ( ) (σ π=3.8, σ y =4.0, σ i =4.9) k= k = k = Standard deviation of inflation
31 Fig. 3: Simulation of a temporary I-S shock under estimated rule (ER) and optimal rule (OR) The US Output gap (ER) Output gap (OR) Inflation (ER) Inflation (OR) Short nominal rate (ER) Short nominal rate (OR) Long real rate (ER) Long real rate (OR) Germany Output gap (ER) Output gap (OR) Inflation (ER) Inflation (OR) Short nominal rate (ER) Short nominal rate (OR) Long real rate (ER) Long real rate (OR)
32 Fig. 4: Shifts in German optimal policy frontier (with µ i =0.3) - Change in the sensitivity of inflation to movements in the output gap Model estimate ( ) (σ π=3.8, σ y =4.0, σ i =4.9) 3 α y =0.054 α y =0.158 Estimated α y Standard deviation of inflation
33 Fig. 5: Shifts in German optimal policy frontier (with µ i =0.3) - Change in the interestsensitivity of the I-S curve Model estimate ( ) (σ π=3.8, σ y =4.0, σ i =4.9) 3.5 Estimated β ρ 3.0 β ρ = β ρ = Standard deviation of inflation
34 Fig. 6: Shifts in German optimal policy frontier (with µ i =0.3) - Change in the persistence of the output-gap equation Model estimate ( ) (σ π=3.8, σ y =4.0, σ i =4.9) 3.5 β y1 +β y2 =0.91 β y1 +β y2 = Estimated β y1 and β y Standard deviation of inflation
22 .5 Real consumption.5 Real residential investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.5 Real house prices.5 Real fixed investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.3 Inflation
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.5 Real consumption.5 Real residential investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.5 Real house prices.5 Real fixed investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.3 Inflation rate.3
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