Accessible Version
Optimal Monetary Policy in a DSGE Model with Attenuated Forward Guidance Effects Accessible Data
Figure 1: Impulse responses to unanticipated and expected monetary policy shocks under various assumptions about discounting
Unanticipated shock
Y-axis: Fed Funds Rate and 4Q Inflation Rate are percentage points; Output is percent deviation.
| Quarter | Federal Funds Rate [Top-Left panel] | Output [Top-middle panel] | 4Q Inflation Rate [Top-right panel] | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Standard | Discounting | Strong Discounting | Standard | Discounting | Strong Discounting | Standard | Discounting | Strong Discounting | |
| 1 | -0.94 | -0.94 | -0.94 | 0.41 | 0.39 | 0.37 | 0.00 | 0.00 | 0.00 |
| 2 | -0.72 | -0.72 | -0.73 | 0.53 | 0.50 | 0.48 | 0.00 | 0.00 | 0.00 |
| 3 | -0.53 | -0.54 | -0.55 | 0.52 | 0.49 | 0.48 | 0.00 | 0.00 | 0.00 |
| 4 | -0.39 | -0.40 | -0.40 | 0.45 | 0.44 | 0.42 | 0.00 | 0.00 | 0.00 |
| 5 | -0.27 | -0.28 | -0.29 | 0.37 | 0.36 | 0.36 | 0.00 | 0.00 | 0.00 |
| 6 | -0.19 | -0.20 | -0.20 | 0.30 | 0.29 | 0.29 | 0.00 | 0.00 | 0.00 |
| 7 | -0.13 | -0.13 | -0.14 | 0.23 | 0.23 | 0.23 | -0.01 | 0.00 | 0.00 |
| 8 | -0.08 | -0.09 | -0.09 | 0.18 | 0.18 | 0.18 | -0.01 | 0.00 | 0.00 |
| 9 | -0.05 | -0.06 | -0.06 | 0.13 | 0.13 | 0.13 | -0.01 | 0.00 | 0.00 |
| 10 | -0.03 | -0.03 | -0.04 | 0.10 | 0.10 | 0.10 | -0.01 | 0.00 | 0.00 |
| 11 | -0.02 | -0.02 | -0.02 | 0.07 | 0.07 | 0.07 | -0.01 | 0.00 | 0.00 |
| 12 | -0.01 | -0.01 | -0.01 | 0.05 | 0.05 | 0.05 | -0.01 | -0.01 | 0.00 |
| 13 | 0.00 | -0.01 | -0.01 | 0.03 | 0.03 | 0.03 | -0.01 | -0.01 | 0.00 |
| 14 | 0.00 | 0.00 | 0.00 | 0.02 | 0.02 | 0.02 | -0.01 | -0.01 | 0.00 |
| 15 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | -0.01 | -0.01 | 0.00 |
| 16 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | -0.01 | -0.01 | 0.00 |
| 17 | 0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 | -0.01 | -0.01 | 0.00 |
| 18 | 0.00 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 |
| 19 | 0.00 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | -0.01 | 0.00 |
| 20 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 21 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 22 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 23 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 24 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 25 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 26 | -0.01 | -0.01 | -0.01 | 0.00 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 |
| 27 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | -0.01 | 0.00 | 0.00 |
| 28 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 |
| 29 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 |
| 30 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 |
| 31 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | -0.01 | 0.00 | 0.00 | 0.00 |
| 32 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 33 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 34 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 35 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 36 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 37 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 38 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 39 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 40 | -0.01 | -0.01 | -0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Exp shock 20 qtrs ahead
Y-axis: Fed Funds Rate and 4Q Inflation Rate are percentage points; Output is percent deviation.
| Quarter | Federal Funds Rate [Bottom-Left panel] | Output [Bottom-middle panel] | 4Q Inflation Rate [Bottom-right panel] | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Standard | Discounting | Strong Discounting | Standard | Discounting | Strong Discounting | Standard | Discounting | Strong Discounting | |
| 1 | 0.00 | 0.00 | 0.00 | 0.60 | 0.25 | 0.13 | 0.02 | 0.01 | 0.00 |
| 2 | 0.00 | 0.00 | 0.00 | 0.92 | 0.40 | 0.21 | 0.05 | 0.02 | 0.01 |
| 3 | 0.00 | 0.00 | 0.00 | 1.09 | 0.50 | 0.28 | 0.07 | 0.03 | 0.01 |
| 4 | 0.00 | 0.00 | 0.00 | 1.18 | 0.57 | 0.33 | 0.10 | 0.04 | 0.02 |
| 5 | 0.00 | 0.00 | 0.00 | 1.23 | 0.62 | 0.37 | 0.10 | 0.04 | 0.02 |
| 6 | 0.00 | 0.00 | 0.00 | 1.26 | 0.66 | 0.41 | 0.10 | 0.04 | 0.02 |
| 7 | 0.00 | 0.00 | 0.00 | 1.27 | 0.69 | 0.45 | 0.10 | 0.04 | 0.02 |
| 8 | 0.00 | 0.00 | 0.00 | 1.27 | 0.72 | 0.48 | 0.09 | 0.04 | 0.02 |
| 9 | 0.00 | 0.00 | 0.00 | 1.26 | 0.74 | 0.51 | 0.09 | 0.04 | 0.02 |
| 10 | 0.00 | 0.00 | 0.00 | 1.24 | 0.77 | 0.54 | 0.08 | 0.04 | 0.02 |
| 11 | 0.00 | 0.00 | 0.00 | 1.22 | 0.78 | 0.57 | 0.08 | 0.04 | 0.02 |
| 12 | 0.00 | 0.00 | 0.00 | 1.20 | 0.80 | 0.60 | 0.08 | 0.04 | 0.02 |
| 13 | 0.00 | 0.00 | 0.00 | 1.17 | 0.81 | 0.63 | 0.07 | 0.04 | 0.02 |
| 14 | 0.00 | 0.00 | 0.00 | 1.14 | 0.82 | 0.65 | 0.07 | 0.03 | 0.02 |
| 15 | 0.00 | 0.00 | 0.00 | 1.11 | 0.83 | 0.68 | 0.06 | 0.03 | 0.02 |
| 16 | 0.00 | 0.00 | 0.00 | 1.08 | 0.84 | 0.70 | 0.06 | 0.03 | 0.02 |
| 17 | 0.00 | 0.00 | 0.00 | 1.04 | 0.83 | 0.71 | 0.06 | 0.03 | 0.02 |
| 18 | 0.00 | 0.00 | 0.00 | 0.99 | 0.82 | 0.72 | 0.05 | 0.03 | 0.01 |
| 19 | 0.00 | 0.00 | 0.00 | 0.94 | 0.81 | 0.72 | 0.05 | 0.02 | 0.01 |
| 20 | -0.86 | -0.88 | -0.89 | 0.88 | 0.78 | 0.72 | 0.04 | 0.02 | 0.01 |
| 21 | -0.61 | -0.64 | -0.66 | 0.73 | 0.66 | 0.61 | 0.04 | 0.02 | 0.01 |
| 22 | -0.43 | -0.46 | -0.49 | 0.56 | 0.52 | 0.48 | 0.04 | 0.02 | 0.01 |
| 23 | -0.29 | -0.33 | -0.36 | 0.41 | 0.38 | 0.36 | 0.03 | 0.02 | 0.01 |
| 24 | -0.20 | -0.24 | -0.27 | 0.28 | 0.27 | 0.25 | 0.03 | 0.02 | 0.01 |
| 25 | -0.14 | -0.17 | -0.20 | 0.18 | 0.17 | 0.16 | 0.03 | 0.01 | 0.01 |
| 26 | -0.09 | -0.13 | -0.16 | 0.11 | 0.10 | 0.09 | 0.03 | 0.01 | 0.00 |
| 27 | -0.07 | -0.10 | -0.13 | 0.05 | 0.05 | 0.04 | 0.03 | 0.01 | 0.00 |
| 28 | -0.05 | -0.08 | -0.11 | 0.01 | 0.01 | 0.00 | 0.02 | 0.01 | 0.00 |
| 29 | -0.04 | -0.07 | -0.09 | -0.02 | -0.02 | -0.02 | 0.02 | 0.01 | 0.00 |
| 30 | -0.03 | -0.06 | -0.08 | -0.04 | -0.04 | -0.04 | 0.02 | 0.01 | 0.00 |
| 31 | -0.03 | -0.06 | -0.08 | -0.05 | -0.05 | -0.05 | 0.02 | 0.01 | 0.00 |
| 32 | -0.03 | -0.06 | -0.08 | -0.05 | -0.05 | -0.06 | 0.02 | 0.01 | 0.00 |
| 33 | -0.03 | -0.05 | -0.07 | -0.06 | -0.06 | -0.06 | 0.02 | 0.01 | 0.00 |
| 34 | -0.03 | -0.05 | -0.07 | -0.05 | -0.06 | -0.06 | 0.02 | 0.01 | 0.00 |
| 35 | -0.03 | -0.05 | -0.07 | -0.05 | -0.06 | -0.06 | 0.02 | 0.01 | 0.00 |
| 36 | -0.03 | -0.05 | -0.07 | -0.05 | -0.05 | -0.06 | 0.02 | 0.01 | 0.00 |
| 37 | -0.03 | -0.05 | -0.06 | -0.05 | -0.05 | -0.06 | 0.02 | 0.01 | 0.00 |
| 38 | -0.03 | -0.05 | -0.06 | -0.04 | -0.04 | -0.05 | 0.01 | 0.01 | 0.00 |
| 39 | -0.02 | -0.04 | -0.06 | -0.04 | -0.04 | -0.05 | 0.01 | 0.01 | 0.00 |
| 40 | -0.02 | -0.04 | -0.06 | -0.03 | -0.04 | -0.04 | 0.01 | 0.01 | 0.00 |
Figure 2: A recession scenario and optimal outcomes under different assumptions about the discounting in the Euler equation
Y-axis: Percent
| Quarter | Federal Funds Rate [Left panel] | Output Gap [Middle panel] | 4Q Inflation Rate [Right panel] | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | |
| 1 | 0.53 | 1.61 | 1.04 | 0.66 | -4.25 | -0.46 | -2.16 | -3.40 | 1.87 | 2.08 | 2.00 | 1.93 |
| 2 | 0.13 | 0.58 | 0.14 | 0.13 | -6.83 | -0.97 | -3.50 | -5.43 | 1.72 | 2.18 | 2.00 | 1.84 |
| 3 | 0.13 | 0.15 | 0.13 | 0.13 | -8.45 | -1.48 | -4.38 | -6.67 | 1.56 | 2.29 | 2.00 | 1.75 |
| 4 | 0.13 | 0.13 | 0.13 | 0.13 | -9.41 | -1.91 | -4.88 | -7.37 | 1.41 | 2.40 | 2.02 | 1.67 |
| 5 | 0.13 | 0.13 | 0.13 | 0.13 | -9.90 | -2.18 | -5.08 | -7.65 | 1.39 | 2.43 | 2.04 | 1.68 |
| 6 | 0.13 | 0.13 | 0.13 | 0.13 | -10.01 | -2.27 | -5.00 | -7.60 | 1.40 | 2.44 | 2.07 | 1.70 |
| 7 | 0.13 | 0.13 | 0.13 | 0.13 | -9.82 | -2.18 | -4.71 | -7.28 | 1.42 | 2.44 | 2.09 | 1.73 |
| 8 | 0.13 | 0.13 | 0.13 | 0.13 | -9.39 | -1.93 | -4.22 | -6.73 | 1.44 | 2.44 | 2.12 | 1.76 |
| 9 | 0.13 | 0.13 | 0.13 | 0.13 | -8.76 | -1.54 | -3.58 | -6.00 | 1.47 | 2.45 | 2.15 | 1.80 |
| 10 | 0.12 | 0.13 | 0.13 | 0.13 | -7.97 | -1.04 | -2.81 | -5.13 | 1.49 | 2.45 | 2.18 | 1.83 |
| 11 | 0.12 | 0.13 | 0.13 | 0.13 | -7.13 | -0.52 | -2.02 | -4.22 | 1.51 | 2.45 | 2.20 | 1.86 |
| 12 | 0.12 | 0.13 | 0.13 | 0.13 | -6.30 | -0.01 | -1.24 | -3.31 | 1.54 | 2.45 | 2.22 | 1.89 |
| 13 | 0.12 | 0.13 | 0.13 | 0.13 | -5.49 | 0.46 | -0.50 | -2.43 | 1.56 | 2.45 | 2.24 | 1.91 |
| 14 | 0.12 | 0.13 | 0.13 | 0.13 | -4.75 | 0.87 | 0.17 | -1.61 | 1.58 | 2.45 | 2.26 | 1.94 |
| 15 | 0.12 | 0.13 | 0.13 | 0.13 | -4.07 | 1.21 | 0.78 | -0.85 | 1.60 | 2.44 | 2.27 | 1.96 |
| 16 | 0.13 | 0.13 | 0.13 | 0.13 | -3.46 | 1.48 | 1.30 | -0.16 | 1.62 | 2.44 | 2.28 | 1.98 |
| 17 | 0.13 | 0.13 | 0.13 | 0.13 | -2.94 | 1.68 | 1.75 | 0.44 | 1.63 | 2.43 | 2.29 | 1.99 |
| 18 | 0.13 | 0.13 | 0.13 | 0.13 | -2.50 | 1.81 | 2.11 | 0.98 | 1.65 | 2.42 | 2.30 | 2.01 |
| 19 | 0.16 | 0.13 | 0.13 | 0.13 | -2.13 | 1.87 | 2.40 | 1.43 | 1.66 | 2.41 | 2.31 | 2.02 |
| 20 | 0.24 | 0.13 | 0.13 | 0.13 | -1.84 | 1.86 | 2.60 | 1.81 | 1.67 | 2.41 | 2.32 | 2.03 |
| 21 | 0.34 | 0.14 | 0.13 | 0.13 | -1.60 | 1.79 | 2.74 | 2.11 | 1.68 | 2.40 | 2.32 | 2.04 |
| 22 | 0.46 | 0.14 | 0.13 | 0.13 | -1.42 | 1.67 | 2.80 | 2.35 | 1.69 | 2.39 | 2.32 | 2.05 |
| 23 | 0.58 | 0.14 | 0.13 | 0.13 | -1.27 | 1.51 | 2.80 | 2.52 | 1.71 | 2.38 | 2.33 | 2.06 |
| 24 | 0.71 | 0.16 | 0.13 | 0.13 | -1.15 | 1.30 | 2.74 | 2.63 | 1.72 | 2.37 | 2.33 | 2.07 |
| 25 | 0.83 | 0.25 | 0.13 | 0.13 | -1.06 | 1.07 | 2.62 | 2.68 | 1.72 | 2.37 | 2.33 | 2.07 |
| 26 | 0.95 | 0.50 | 0.13 | 0.13 | -0.98 | 0.83 | 2.46 | 2.68 | 1.73 | 2.36 | 2.33 | 2.08 |
| 27 | 1.06 | 0.85 | 0.14 | 0.13 | -0.92 | 0.61 | 2.26 | 2.64 | 1.74 | 2.35 | 2.33 | 2.09 |
| 28 | 1.17 | 1.21 | 0.15 | 0.13 | -0.87 | 0.43 | 2.02 | 2.54 | 1.75 | 2.35 | 2.33 | 2.09 |
| 29 | 1.26 | 1.51 | 0.18 | 0.13 | -0.82 | 0.31 | 1.77 | 2.41 | 1.76 | 2.34 | 2.34 | 2.10 |
| 30 | 1.36 | 1.74 | 0.38 | 0.13 | -0.78 | 0.25 | 1.49 | 2.25 | 1.77 | 2.33 | 2.34 | 2.10 |
| 31 | 1.44 | 1.89 | 0.74 | 0.13 | -0.75 | 0.24 | 1.24 | 2.06 | 1.78 | 2.33 | 2.34 | 2.11 |
| 32 | 1.52 | 1.97 | 1.14 | 0.14 | -0.71 | 0.27 | 1.02 | 1.84 | 1.79 | 2.32 | 2.34 | 2.11 |
| 33 | 1.59 | 2.00 | 1.50 | 0.18 | -0.68 | 0.32 | 0.88 | 1.61 | 1.80 | 2.32 | 2.34 | 2.11 |
| 34 | 1.66 | 2.01 | 1.76 | 0.44 | -0.65 | 0.38 | 0.80 | 1.37 | 1.81 | 2.31 | 2.35 | 2.12 |
| 35 | 1.73 | 2.00 | 1.93 | 0.79 | -0.62 | 0.43 | 0.79 | 1.16 | 1.81 | 2.31 | 2.35 | 2.12 |
| 36 | 1.79 | 2.00 | 2.01 | 1.14 | -0.60 | 0.48 | 0.83 | 0.99 | 1.82 | 2.30 | 2.35 | 2.13 |
| 37 | 1.85 | 2.00 | 2.04 | 1.43 | -0.57 | 0.51 | 0.89 | 0.89 | 1.83 | 2.30 | 2.35 | 2.14 |
| 38 | 1.90 | 2.02 | 2.02 | 1.63 | -0.55 | 0.53 | 0.97 | 0.85 | 1.84 | 2.29 | 2.35 | 2.14 |
| 39 | 1.95 | 2.05 | 1.99 | 1.73 | -0.52 | 0.53 | 1.05 | 0.87 | 1.84 | 2.29 | 2.35 | 2.15 |
| 40 | 2.00 | 2.09 | 1.96 | 1.77 | -0.50 | 0.53 | 1.11 | 0.92 | 1.85 | 2.28 | 2.35 | 2.15 |
| 41 | 2.05 | 2.13 | 1.94 | 1.76 | -0.48 | 0.51 | 1.16 | 0.99 | 1.86 | 2.28 | 2.36 | 2.16 |
| 42 | 2.09 | 2.18 | 1.93 | 1.73 | -0.46 | 0.50 | 1.19 | 1.06 | 1.87 | 2.27 | 2.35 | 2.16 |
| 43 | 2.13 | 2.24 | 1.95 | 1.70 | -0.43 | 0.48 | 1.20 | 1.13 | 1.87 | 2.27 | 2.35 | 2.16 |
| 44 | 2.17 | 2.29 | 1.98 | 1.66 | -0.41 | 0.46 | 1.20 | 1.19 | 1.88 | 2.26 | 2.35 | 2.17 |
| 45 | 2.21 | 2.34 | 2.03 | 1.64 | -0.39 | 0.44 | 1.19 | 1.23 | 1.89 | 2.25 | 2.35 | 2.17 |
| 46 | 2.25 | 2.38 | 2.08 | 1.65 | -0.38 | 0.43 | 1.17 | 1.25 | 1.89 | 2.25 | 2.35 | 2.17 |
| 47 | 2.29 | 2.42 | 2.13 | 1.66 | -0.36 | 0.41 | 1.15 | 1.26 | 1.90 | 2.24 | 2.35 | 2.18 |
| 48 | 2.32 | 2.46 | 2.19 | 1.70 | -0.34 | 0.40 | 1.12 | 1.25 | 1.90 | 2.24 | 2.35 | 2.18 |
| 49 | 2.35 | 2.50 | 2.24 | 1.75 | -0.32 | 0.39 | 1.10 | 1.23 | 1.91 | 2.23 | 2.34 | 2.18 |
| 50 | 2.38 | 2.53 | 2.29 | 1.80 | -0.31 | 0.38 | 1.07 | 1.21 | 1.91 | 2.23 | 2.34 | 2.18 |
| 51 | 2.41 | 2.56 | 2.34 | 1.86 | -0.29 | 0.37 | 1.05 | 1.18 | 1.92 | 2.22 | 2.34 | 2.18 |
| 52 | 2.44 | 2.58 | 2.38 | 1.91 | -0.28 | 0.36 | 1.03 | 1.16 | 1.92 | 2.22 | 2.34 | 2.18 |
| 53 | 2.47 | 2.61 | 2.42 | 1.96 | -0.27 | 0.35 | 1.01 | 1.13 | 1.93 | 2.21 | 2.33 | 2.18 |
| 54 | 2.50 | 2.63 | 2.45 | 2.01 | -0.25 | 0.34 | 0.99 | 1.11 | 1.93 | 2.21 | 2.33 | 2.18 |
| 55 | 2.52 | 2.65 | 2.48 | 2.05 | -0.24 | 0.33 | 0.98 | 1.08 | 1.94 | 2.20 | 2.33 | 2.18 |
| 56 | 2.55 | 2.67 | 2.51 | 2.09 | -0.23 | 0.33 | 0.96 | 1.06 | 1.94 | 2.20 | 2.32 | 2.18 |
| 57 | 2.57 | 2.69 | 2.53 | 2.12 | -0.22 | 0.32 | 0.95 | 1.04 | 1.94 | 2.19 | 2.32 | 2.18 |
| 58 | 2.59 | 2.71 | 2.56 | 2.16 | -0.21 | 0.31 | 0.93 | 1.02 | 1.95 | 2.19 | 2.32 | 2.18 |
| 59 | 2.61 | 2.73 | 2.58 | 2.19 | -0.20 | 0.30 | 0.92 | 1.00 | 1.95 | 2.19 | 2.31 | 2.18 |
| 60 | 2.63 | 2.75 | 2.60 | 2.22 | -0.19 | 0.30 | 0.90 | 0.98 | 1.96 | 2.18 | 2.31 | 2.18 |
| 61 | 2.65 | 2.76 | 2.62 | 2.24 | -0.18 | 0.29 | 0.89 | 0.97 | 1.96 | 2.18 | 2.31 | 2.18 |
| 62 | 2.67 | 2.78 | 2.64 | 2.27 | -0.17 | 0.28 | 0.87 | 0.95 | 1.96 | 2.17 | 2.30 | 2.18 |
| 63 | 2.69 | 2.79 | 2.66 | 2.30 | -0.16 | 0.28 | 0.86 | 0.93 | 1.96 | 2.17 | 2.30 | 2.18 |
| 64 | 2.70 | 2.81 | 2.68 | 2.32 | -0.16 | 0.27 | 0.84 | 0.92 | 1.97 | 2.16 | 2.30 | 2.18 |
| 65 | 2.72 | 2.82 | 2.70 | 2.34 | -0.15 | 0.26 | 0.83 | 0.90 | 1.97 | 2.16 | 2.29 | 2.18 |
| 66 | 2.73 | 2.83 | 2.71 | 2.37 | -0.14 | 0.26 | 0.82 | 0.88 | 1.97 | 2.16 | 2.29 | 2.18 |
| 67 | 2.75 | 2.84 | 2.73 | 2.39 | -0.13 | 0.25 | 0.80 | 0.87 | 1.97 | 2.15 | 2.28 | 2.18 |
| 68 | 2.76 | 2.85 | 2.75 | 2.41 | -0.13 | 0.24 | 0.79 | 0.85 | 1.98 | 2.15 | 2.28 | 2.17 |
| 69 | 2.77 | 2.87 | 2.76 | 2.43 | -0.12 | 0.24 | 0.78 | 0.84 | 1.98 | 2.15 | 2.28 | 2.17 |
| 70 | 2.79 | 2.87 | 2.77 | 2.45 | -0.12 | 0.23 | 0.76 | 0.82 | 1.98 | 2.14 | 2.27 | 2.17 |
| 71 | 2.80 | 2.88 | 2.79 | 2.47 | -0.11 | 0.23 | 0.75 | 0.81 | 1.98 | 2.14 | 2.27 | 2.17 |
| 72 | 2.81 | 2.89 | 2.80 | 2.49 | -0.11 | 0.22 | 0.74 | 0.79 | 1.99 | 2.13 | 2.26 | 2.17 |
| 73 | 2.82 | 2.90 | 2.81 | 2.51 | -0.10 | 0.22 | 0.72 | 0.78 | 1.99 | 2.13 | 2.26 | 2.17 |
| 74 | 2.83 | 2.91 | 2.82 | 2.52 | -0.10 | 0.21 | 0.71 | 0.76 | 1.99 | 2.13 | 2.26 | 2.17 |
| 75 | 2.84 | 2.91 | 2.83 | 2.54 | -0.09 | 0.21 | 0.70 | 0.75 | 1.99 | 2.12 | 2.25 | 2.16 |
| 76 | 2.85 | 2.92 | 2.84 | 2.55 | -0.09 | 0.20 | 0.69 | 0.73 | 1.99 | 2.12 | 2.25 | 2.16 |
| 77 | 2.86 | 2.93 | 2.85 | 2.57 | -0.08 | 0.20 | 0.68 | 0.72 | 1.99 | 2.12 | 2.24 | 2.16 |
| 78 | 2.86 | 2.93 | 2.86 | 2.58 | -0.08 | 0.19 | 0.66 | 0.71 | 1.99 | 2.12 | 2.24 | 2.16 |
| 79 | 2.87 | 2.94 | 2.86 | 2.60 | -0.08 | 0.19 | 0.65 | 0.69 | 2.00 | 2.11 | 2.23 | 2.16 |
| 80 | 2.88 | 2.94 | 2.87 | 2.61 | -0.07 | 0.18 | 0.64 | 0.68 | 2.00 | 2.11 | 2.23 | 2.15 |
Figure 3: A recession scenario and optimal outcomes under different assumptions about the discounting in both the Euler equation and the Phillips curve
Y-axis: Percent
| Quarter | Federal Funds Rate [Left panel] | Output Gap [Middle panel] | 4Q Inflation Rate [Right panel] | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | Inertial Taylor Rule (All Models) | Optimal (Standard) | Optimal (Discounting) | Optimal (Discounting-Stronger) | |
| 1 | 0.53 | 1.61 | 1.17 | 0.99 | -4.25 | -0.46 | -1.49 | -2.22 | 1.87 | 2.08 | 2.10 | 2.10 |
| 2 | 0.13 | 0.58 | 0.13 | 0.13 | -6.83 | -0.97 | -2.48 | -3.58 | 1.72 | 2.18 | 2.23 | 2.23 |
| 3 | 0.13 | 0.15 | 0.13 | 0.13 | -8.45 | -1.48 | -3.20 | -4.46 | 1.56 | 2.29 | 2.37 | 2.37 |
| 4 | 0.13 | 0.13 | 0.13 | 0.13 | -9.41 | -1.91 | -3.65 | -4.97 | 1.41 | 2.40 | 2.51 | 2.51 |
| 5 | 0.13 | 0.13 | 0.13 | 0.13 | -9.90 | -2.18 | -3.85 | -5.18 | 1.39 | 2.43 | 2.54 | 2.55 |
| 6 | 0.13 | 0.13 | 0.13 | 0.13 | -10.01 | -2.27 | -3.84 | -5.15 | 1.40 | 2.44 | 2.56 | 2.57 |
| 7 | 0.13 | 0.13 | 0.13 | 0.13 | -9.82 | -2.18 | -3.63 | -4.89 | 1.42 | 2.44 | 2.57 | 2.58 |
| 8 | 0.13 | 0.13 | 0.13 | 0.13 | -9.39 | -1.93 | -3.24 | -4.46 | 1.44 | 2.44 | 2.58 | 2.60 |
| 9 | 0.13 | 0.13 | 0.13 | 0.13 | -8.76 | -1.54 | -2.71 | -3.87 | 1.47 | 2.45 | 2.58 | 2.61 |
| 10 | 0.12 | 0.13 | 0.13 | 0.13 | -7.97 | -1.04 | -2.08 | -3.17 | 1.49 | 2.45 | 2.59 | 2.62 |
| 11 | 0.12 | 0.13 | 0.13 | 0.13 | -7.13 | -0.52 | -1.41 | -2.44 | 1.51 | 2.45 | 2.60 | 2.63 |
| 12 | 0.12 | 0.13 | 0.13 | 0.13 | -6.30 | -0.01 | -0.76 | -1.72 | 1.54 | 2.45 | 2.60 | 2.64 |
| 13 | 0.12 | 0.13 | 0.13 | 0.13 | -5.49 | 0.46 | -0.16 | -1.05 | 1.56 | 2.45 | 2.60 | 2.64 |
| 14 | 0.12 | 0.13 | 0.13 | 0.13 | -4.75 | 0.87 | 0.38 | -0.43 | 1.58 | 2.45 | 2.60 | 2.65 |
| 15 | 0.12 | 0.13 | 0.13 | 0.13 | -4.07 | 1.21 | 0.86 | 0.13 | 1.60 | 2.44 | 2.60 | 2.65 |
| 16 | 0.13 | 0.13 | 0.13 | 0.13 | -3.46 | 1.48 | 1.26 | 0.61 | 1.62 | 2.44 | 2.60 | 2.65 |
| 17 | 0.13 | 0.13 | 0.13 | 0.13 | -2.94 | 1.68 | 1.58 | 1.02 | 1.63 | 2.43 | 2.60 | 2.66 |
| 18 | 0.13 | 0.13 | 0.13 | 0.13 | -2.50 | 1.81 | 1.83 | 1.36 | 1.65 | 2.42 | 2.60 | 2.66 |
| 19 | 0.16 | 0.13 | 0.13 | 0.13 | -2.13 | 1.87 | 2.01 | 1.62 | 1.66 | 2.41 | 2.59 | 2.65 |
| 20 | 0.24 | 0.13 | 0.13 | 0.13 | -1.84 | 1.86 | 2.12 | 1.82 | 1.67 | 2.41 | 2.58 | 2.65 |
| 21 | 0.34 | 0.14 | 0.13 | 0.13 | -1.60 | 1.79 | 2.15 | 1.95 | 1.68 | 2.40 | 2.58 | 2.65 |
| 22 | 0.46 | 0.14 | 0.13 | 0.13 | -1.42 | 1.67 | 2.13 | 2.02 | 1.69 | 2.39 | 2.57 | 2.65 |
| 23 | 0.58 | 0.14 | 0.13 | 0.13 | -1.27 | 1.51 | 2.05 | 2.03 | 1.71 | 2.38 | 2.57 | 2.64 |
| 24 | 0.71 | 0.16 | 0.13 | 0.13 | -1.15 | 1.30 | 1.91 | 1.98 | 1.72 | 2.37 | 2.56 | 2.64 |
| 25 | 0.83 | 0.25 | 0.13 | 0.13 | -1.06 | 1.07 | 1.74 | 1.89 | 1.72 | 2.37 | 2.55 | 2.63 |
| 26 | 0.95 | 0.50 | 0.13 | 0.13 | -0.98 | 0.83 | 1.52 | 1.75 | 1.73 | 2.36 | 2.55 | 2.63 |
| 27 | 1.06 | 0.85 | 0.13 | 0.13 | -0.92 | 0.61 | 1.28 | 1.58 | 1.74 | 2.35 | 2.54 | 2.63 |
| 28 | 1.17 | 1.21 | 0.37 | 0.14 | -0.87 | 0.43 | 1.02 | 1.38 | 1.75 | 2.35 | 2.53 | 2.62 |
| 29 | 1.26 | 1.51 | 0.76 | 0.22 | -0.82 | 0.31 | 0.77 | 1.15 | 1.76 | 2.34 | 2.53 | 2.62 |
| 30 | 1.36 | 1.74 | 1.17 | 0.53 | -0.78 | 0.25 | 0.56 | 0.91 | 1.77 | 2.33 | 2.52 | 2.62 |
| 31 | 1.44 | 1.89 | 1.53 | 0.92 | -0.75 | 0.24 | 0.43 | 0.70 | 1.78 | 2.33 | 2.52 | 2.61 |
| 32 | 1.52 | 1.97 | 1.79 | 1.29 | -0.71 | 0.27 | 0.36 | 0.55 | 1.79 | 2.32 | 2.52 | 2.61 |
| 33 | 1.59 | 2.00 | 1.95 | 1.59 | -0.68 | 0.32 | 0.36 | 0.45 | 1.80 | 2.32 | 2.51 | 2.61 |
| 34 | 1.66 | 2.01 | 2.03 | 1.80 | -0.65 | 0.38 | 0.40 | 0.42 | 1.81 | 2.31 | 2.51 | 2.61 |
| 35 | 1.73 | 2.00 | 2.06 | 1.92 | -0.62 | 0.43 | 0.47 | 0.45 | 1.81 | 2.31 | 2.50 | 2.61 |
| 36 | 1.79 | 2.00 | 2.05 | 1.97 | -0.60 | 0.48 | 0.54 | 0.51 | 1.82 | 2.30 | 2.50 | 2.60 |
| 37 | 1.85 | 2.00 | 2.02 | 1.97 | -0.57 | 0.51 | 0.62 | 0.59 | 1.83 | 2.30 | 2.50 | 2.60 |
| 38 | 1.90 | 2.02 | 2.00 | 1.95 | -0.55 | 0.53 | 0.69 | 0.67 | 1.84 | 2.29 | 2.49 | 2.60 |
| 39 | 1.95 | 2.05 | 1.99 | 1.93 | -0.52 | 0.53 | 0.74 | 0.76 | 1.84 | 2.29 | 2.49 | 2.60 |
| 40 | 2.00 | 2.09 | 1.99 | 1.91 | -0.50 | 0.53 | 0.77 | 0.82 | 1.85 | 2.28 | 2.48 | 2.59 |
| 41 | 2.05 | 2.13 | 2.02 | 1.90 | -0.48 | 0.51 | 0.79 | 0.88 | 1.86 | 2.28 | 2.48 | 2.59 |
| 42 | 2.09 | 2.18 | 2.05 | 1.91 | -0.46 | 0.50 | 0.79 | 0.91 | 1.87 | 2.27 | 2.47 | 2.59 |
| 43 | 2.13 | 2.24 | 2.10 | 1.93 | -0.43 | 0.48 | 0.78 | 0.93 | 1.87 | 2.27 | 2.46 | 2.58 |
| 44 | 2.17 | 2.29 | 2.15 | 1.97 | -0.41 | 0.46 | 0.77 | 0.94 | 1.88 | 2.26 | 2.46 | 2.58 |
| 45 | 2.21 | 2.34 | 2.21 | 2.02 | -0.39 | 0.44 | 0.76 | 0.94 | 1.89 | 2.25 | 2.45 | 2.57 |
| 46 | 2.25 | 2.38 | 2.27 | 2.07 | -0.38 | 0.43 | 0.74 | 0.93 | 1.89 | 2.25 | 2.45 | 2.57 |
| 47 | 2.29 | 2.42 | 2.32 | 2.13 | -0.36 | 0.41 | 0.72 | 0.92 | 1.90 | 2.24 | 2.44 | 2.56 |
| 48 | 2.32 | 2.46 | 2.37 | 2.18 | -0.34 | 0.40 | 0.71 | 0.91 | 1.90 | 2.24 | 2.43 | 2.56 |
| 49 | 2.35 | 2.50 | 2.41 | 2.23 | -0.32 | 0.39 | 0.69 | 0.90 | 1.91 | 2.23 | 2.43 | 2.55 |
| 50 | 2.38 | 2.53 | 2.46 | 2.28 | -0.31 | 0.38 | 0.68 | 0.89 | 1.91 | 2.23 | 2.42 | 2.55 |
| 51 | 2.41 | 2.56 | 2.49 | 2.32 | -0.29 | 0.37 | 0.67 | 0.88 | 1.92 | 2.22 | 2.42 | 2.54 |
| 52 | 2.44 | 2.58 | 2.52 | 2.36 | -0.28 | 0.36 | 0.66 | 0.87 | 1.92 | 2.22 | 2.41 | 2.53 |
| 53 | 2.47 | 2.61 | 2.55 | 2.40 | -0.27 | 0.35 | 0.65 | 0.86 | 1.93 | 2.21 | 2.40 | 2.53 |
| 54 | 2.50 | 2.63 | 2.58 | 2.43 | -0.25 | 0.34 | 0.64 | 0.85 | 1.93 | 2.21 | 2.40 | 2.52 |
| 55 | 2.52 | 2.65 | 2.61 | 2.46 | -0.24 | 0.33 | 0.63 | 0.85 | 1.94 | 2.20 | 2.39 | 2.52 |
| 56 | 2.55 | 2.67 | 2.63 | 2.48 | -0.23 | 0.33 | 0.63 | 0.84 | 1.94 | 2.20 | 2.38 | 2.51 |
| 57 | 2.57 | 2.69 | 2.65 | 2.51 | -0.22 | 0.32 | 0.62 | 0.83 | 1.94 | 2.19 | 2.38 | 2.50 |
| 58 | 2.59 | 2.71 | 2.67 | 2.53 | -0.21 | 0.31 | 0.61 | 0.82 | 1.95 | 2.19 | 2.37 | 2.50 |
| 59 | 2.61 | 2.73 | 2.69 | 2.55 | -0.20 | 0.30 | 0.60 | 0.82 | 1.95 | 2.19 | 2.37 | 2.49 |
| 60 | 2.63 | 2.75 | 2.71 | 2.57 | -0.19 | 0.30 | 0.59 | 0.81 | 1.96 | 2.18 | 2.36 | 2.49 |
| 61 | 2.65 | 2.76 | 2.73 | 2.60 | -0.18 | 0.29 | 0.58 | 0.80 | 1.96 | 2.18 | 2.35 | 2.48 |
| 62 | 2.67 | 2.78 | 2.75 | 2.62 | -0.17 | 0.28 | 0.58 | 0.79 | 1.96 | 2.17 | 2.35 | 2.47 |
| 63 | 2.69 | 2.79 | 2.77 | 2.64 | -0.16 | 0.28 | 0.57 | 0.79 | 1.96 | 2.17 | 2.34 | 2.47 |
| 64 | 2.70 | 2.81 | 2.78 | 2.65 | -0.16 | 0.27 | 0.56 | 0.78 | 1.97 | 2.16 | 2.34 | 2.46 |
| 65 | 2.72 | 2.82 | 2.80 | 2.67 | -0.15 | 0.26 | 0.55 | 0.77 | 1.97 | 2.16 | 2.33 | 2.45 |
| 66 | 2.73 | 2.83 | 2.81 | 2.69 | -0.14 | 0.26 | 0.54 | 0.76 | 1.97 | 2.16 | 2.32 | 2.45 |
| 67 | 2.75 | 2.84 | 2.83 | 2.70 | -0.13 | 0.25 | 0.54 | 0.76 | 1.97 | 2.15 | 2.32 | 2.44 |
| 68 | 2.76 | 2.85 | 2.84 | 2.72 | -0.13 | 0.24 | 0.53 | 0.75 | 1.98 | 2.15 | 2.31 | 2.43 |
| 69 | 2.77 | 2.87 | 2.85 | 2.73 | -0.12 | 0.24 | 0.52 | 0.74 | 1.98 | 2.15 | 2.31 | 2.43 |
| 70 | 2.79 | 2.87 | 2.86 | 2.74 | -0.12 | 0.23 | 0.51 | 0.73 | 1.98 | 2.14 | 2.30 | 2.42 |
| 71 | 2.80 | 2.88 | 2.87 | 2.75 | -0.11 | 0.23 | 0.50 | 0.72 | 1.98 | 2.14 | 2.29 | 2.42 |
| 72 | 2.81 | 2.89 | 2.88 | 2.76 | -0.11 | 0.22 | 0.50 | 0.72 | 1.99 | 2.13 | 2.29 | 2.41 |
| 73 | 2.82 | 2.90 | 2.89 | 2.77 | -0.10 | 0.22 | 0.49 | 0.71 | 1.99 | 2.13 | 2.28 | 2.40 |
| 74 | 2.83 | 2.91 | 2.90 | 2.79 | -0.10 | 0.21 | 0.48 | 0.70 | 1.99 | 2.13 | 2.28 | 2.40 |
| 75 | 2.84 | 2.91 | 2.90 | 2.80 | -0.09 | 0.21 | 0.48 | 0.69 | 1.99 | 2.12 | 2.27 | 2.39 |
| 76 | 2.85 | 2.92 | 2.91 | 2.80 | -0.09 | 0.20 | 0.47 | 0.68 | 1.99 | 2.12 | 2.27 | 2.38 |
| 77 | 2.86 | 2.93 | 2.92 | 2.81 | -0.08 | 0.20 | 0.46 | 0.67 | 1.99 | 2.12 | 2.26 | 2.38 |
| 78 | 2.86 | 2.93 | 2.92 | 2.82 | -0.08 | 0.19 | 0.45 | 0.67 | 1.99 | 2.12 | 2.26 | 2.37 |
| 79 | 2.87 | 2.94 | 2.93 | 2.83 | -0.08 | 0.19 | 0.45 | 0.66 | 2.00 | 2.11 | 2.25 | 2.37 |
| 80 | 2.88 | 2.94 | 2.93 | 2.84 | -0.07 | 0.18 | 0.44 | 0.65 | 2.00 | 2.11 | 2.25 | 2.36 |
Last Update:
October 19, 2018