Finance and Economics Discussion Series: Accessible versions of figures for 2026-055

Inflation Uncertainty and Endogenous Planning Horizons

Accessible version of figures

Figure 1: Planning horizon and the trend-adjusted reference point.
Note: The figure solves the endogenous-planning stopping rule under the stylized linear planning-cost schedule \((\tau_0=0.012)\), with the supply disturbance \(\hat\epsilon_{s,t}=0\). The black line sets \(\bar\pi_t=0\); the red dashed line sets \(\bar\pi_t=0.50\). In both cases \(\beta=1.03^{-1/4}\), \(\theta = 0.60, \rho_y=0.90\), and \(\kappa=0.0104\).

demand_gap_from_reference y_hat_trend_0 k_star_trend_0 y_hat_trend_0p50 k_star_trend_0p50
-1.6 -1.6 11 -1.245 18
-1.59 -1.59 10 -1.235 18
-1.58 -1.58 10 -1.225 18
-1.57 -1.57 10 -1.215 18
-1.56 -1.56 10 -1.205 18
-1.55 -1.55 10 -1.195 18
-1.54 -1.54 10 -1.185 18
-1.53 -1.53 10 -1.175 18
-1.52 -1.52 10 -1.165 18
-1.51 -1.51 10 -1.155 17
-1.5 -1.5 10 -1.145 17
-1.49 -1.49 10 -1.135 17
-1.48 -1.48 10 -1.125 17
-1.47 -1.47 10 -1.115 17
-1.46 -1.46 10 -1.105 17
-1.45 -1.45 10 -1.095 17
-1.44 -1.44 10 -1.085 17
-1.43 -1.43 10 -1.075 17
-1.42 -1.42 9 -1.065 17
-1.41 -1.41 9 -1.055 17
-1.4 -1.4 9 -1.045 17
-1.39 -1.39 9 -1.035 17
-1.38 -1.38 9 -1.025 17
-1.37 -1.37 9 -1.015 16
-1.36 -1.36 9 -1.005 16
-1.35 -1.35 9 -0.995 16
-1.34 -1.34 9 -0.985 16
-1.33 -1.33 9 -0.975 16
-1.32 -1.32 9 -0.965 16
-1.31 -1.31 9 -0.955 16
-1.3 -1.3 9 -0.945 16
-1.29 -1.29 9 -0.935 16
-1.28 -1.28 9 -0.925 16
-1.27 -1.27 8 -0.915 16
-1.26 -1.26 8 -0.905 16
-1.25 -1.25 8 -0.895 15
-1.24 -1.24 8 -0.885 15
-1.23 -1.23 8 -0.875 15
-1.22 -1.22 8 -0.865 15
-1.21 -1.21 8 -0.855 15
-1.2 -1.2 8 -0.845 15
-1.19 -1.19 8 -0.835 15
-1.18 -1.18 8 -0.825 15
-1.17 -1.17 8 -0.815 15
-1.16 -1.16 8 -0.805 15
-1.15 -1.15 8 -0.795 15
-1.14 -1.14 7 -0.785 14
-1.13 -1.13 7 -0.775 14
-1.12 -1.12 7 -0.765 14
-1.11 -1.11 7 -0.755 14
-1.1 -1.1 7 -0.745 14
-1.09 -1.09 7 -0.735 14
-1.08 -1.08 7 -0.725 14
-1.07 -1.07 7 -0.715 14
-1.06 -1.06 7 -0.705 14
-1.05 -1.05 7 -0.695 14
-1.04 -1.04 7 -0.685 13
-1.03 -1.03 7 -0.675 13
-1.02 -1.02 7 -0.665 13
-1.01 -1.01 6 -0.655 13
-1 -1 6 -0.645 13
-0.99 -0.99 6 -0.635 13
-0.98 -0.98 6 -0.625 13
-0.97 -0.97 6 -0.615 13
-0.96 -0.96 6 -0.605 12
-0.95 -0.95 6 -0.595 12
-0.94 -0.94 6 -0.585 12
-0.93 -0.93 6 -0.575 12
-0.92 -0.92 6 -0.565 12
-0.91 -0.91 5 -0.555 12
-0.9 -0.9 5 -0.545 12
-0.89 -0.89 5 -0.535 12
-0.88 -0.88 5 -0.525 11
-0.87 -0.87 5 -0.515 11
-0.86 -0.86 5 -0.505 11
-0.85 -0.85 5 -0.495 11
-0.84 -0.84 5 -0.485 11
-0.83 -0.83 5 -0.475 11
-0.82 -0.82 5 -0.465 10
-0.81 -0.81 4 -0.455 10
-0.8 -0.8 4 -0.445 10
-0.79 -0.79 4 -0.435 10
-0.78 -0.78 4 -0.425 10
-0.77 -0.77 4 -0.415 10
-0.76 -0.76 4 -0.405 9
-0.75 -0.75 4 -0.395 9
-0.74 -0.74 4 -0.385 9
-0.73 -0.73 4 -0.375 9
-0.72 -0.72 3 -0.365 9
-0.71 -0.71 3 -0.355 8
-0.7 -0.7 3 -0.345 8
-0.69 -0.69 3 -0.335 8
-0.68 -0.68 3 -0.325 8
-0.67 -0.67 3 -0.315 7
-0.66 -0.66 3 -0.305 7
-0.65 -0.65 3 -0.295 7
-0.64 -0.64 2 -0.285 7
-0.63 -0.63 2 -0.275 6
-0.62 -0.62 2 -0.265 6
-0.61 -0.61 2 -0.255 6
-0.6 -0.6 2 -0.245 6
-0.59 -0.59 2 -0.235 5
-0.58 -0.58 2 -0.225 5
-0.57 -0.57 1 -0.215 5
-0.56 -0.56 1 -0.205 4
-0.55 -0.55 1 -0.195 4
-0.54 -0.54 1 -0.185 3
-0.53 -0.53 1 -0.175 3
-0.52 -0.52 1 -0.165 3
-0.51 -0.51 0 -0.155 2
-0.5 -0.5 0 -0.145 2
-0.49 -0.49 0 -0.135 1
-0.48 -0.48 0 -0.125 1
-0.47 -0.47 0 -0.115 0
-0.46 -0.46 0 -0.105 0
-0.45 -0.45 0 -0.095 0
-0.44 -0.44 0 -0.085 0
-0.43 -0.43 0 -0.075 0
-0.42 -0.42 0 -0.065 0
-0.41 -0.41 0 -0.055 0
-0.4 -0.4 0 -0.045 0
-0.39 -0.39 0 -0.035 0
-0.38 -0.38 0 -0.025 0
-0.37 -0.37 0 -0.015 0
-0.36 -0.36 0 -0.005 0
-0.35 -0.35 0 0.005 0
-0.34 -0.34 0 0.015 0
-0.33 -0.33 0 0.025 0
-0.32 -0.32 0 0.035 0
-0.31 -0.31 0 0.045 0
-0.3 -0.3 0 0.055 0
-0.29 -0.29 0 0.065 0
-0.28 -0.28 0 0.075 0
-0.27 -0.27 0 0.085 0
-0.26 -0.26 0 0.095 0
-0.25 -0.25 0 0.105 0
-0.24 -0.24 0 0.115 0
-0.23 -0.23 0 0.125 0
-0.22 -0.22 0 0.135 0
-0.21 -0.21 0 0.145 0
-0.2 -0.2 0 0.155 0
-0.19 -0.19 0 0.165 0
-0.18 -0.18 0 0.175 0
-0.17 -0.17 0 0.185 0
-0.16 -0.16 0 0.195 0
-0.15 -0.15 0 0.205 0
-0.14 -0.14 0 0.215 0
-0.13 -0.13 0 0.225 0
-0.12 -0.12 0 0.235 0
-0.11 -0.11 0 0.245 0
-0.1 -0.1 0 0.255 0
-0.09 -0.09 0 0.265 0
-0.08 -0.08 0 0.275 0
-0.07 -0.07 0 0.285 0
-0.06 -0.06 0 0.295 0
-0.05 -0.05 0 0.305 0
-0.04 -0.04 0 0.315 0
-0.03 -0.03 0 0.325 0
-0.02 -0.02 0 0.335 0
-0.01 -0.01 0 0.345 0
0 0 0 0.355 0
0.01 0.01 0 0.365 0
0.02 0.02 0 0.375 0
0.03 0.03 0 0.385 0
0.04 0.04 0 0.395 0
0.05 0.05 0 0.405 0
0.06 0.06 0 0.415 0
0.07 0.07 0 0.425 0
0.08 0.08 0 0.435 0
0.09 0.09 0 0.445 0
0.1 0.1 0 0.455 0
0.11 0.11 0 0.465 0
0.12 0.12 0 0.475 0
0.13 0.13 0 0.485 0
0.14 0.14 0 0.495 0
0.15 0.15 0 0.505 0
0.16 0.16 0 0.515 0
0.17 0.17 0 0.525 0
0.18 0.18 0 0.535 0
0.19 0.19 0 0.545 0
0.2 0.2 0 0.555 0
0.21 0.21 0 0.565 0
0.22 0.22 0 0.575 0
0.23 0.23 0 0.585 0
0.24 0.24 0 0.595 0
0.25 0.25 0 0.605 0
0.26 0.26 0 0.615 0
0.27 0.27 0 0.625 0
0.28 0.28 0 0.635 0
0.29 0.29 0 0.645 0
0.3 0.3 0 0.655 0
0.31 0.31 0 0.665 0
0.32 0.32 0 0.675 0
0.33 0.33 0 0.685 0
0.34 0.34 0 0.695 0
0.35 0.35 0 0.705 0
0.36 0.36 0 0.715 0
0.37 0.37 0 0.725 0
0.38 0.38 0 0.735 0
0.39 0.39 0 0.745 0
0.4 0.4 0 0.755 0
0.41 0.41 0 0.765 0
0.42 0.42 0 0.775 0
0.43 0.43 0 0.785 0
0.44 0.44 0 0.795 0
0.45 0.45 0 0.805 0
0.46 0.46 0 0.815 0
0.47 0.47 0 0.825 0
0.48 0.48 0 0.835 0
0.49 0.49 0 0.845 0
0.5 0.5 0 0.855 0
0.51 0.51 0 0.865 0
0.52 0.52 1 0.875 0
0.53 0.53 1 0.885 0
0.54 0.54 1 0.895 0
0.55 0.55 1 0.905 0
0.56 0.56 1 0.915 1
0.57 0.57 1 0.925 1
0.58 0.58 2 0.935 1
0.59 0.59 2 0.945 1
0.6 0.6 2 0.955 1
0.61 0.61 2 0.965 1
0.62 0.62 2 0.975 1
0.63 0.63 2 0.985 1
0.64 0.64 2 0.995 1
0.65 0.65 3 1.005 1
0.66 0.66 3 1.015 1
0.67 0.67 3 1.025 2
0.68 0.68 3 1.035 2
0.69 0.69 3 1.045 2
0.7 0.7 3 1.055 2
0.71 0.71 3 1.065 2
0.72 0.72 3 1.075 2
0.73 0.73 4 1.085 2
0.74 0.74 4 1.095 2
0.75 0.75 4 1.105 2
0.76 0.76 4 1.115 2
0.77 0.77 4 1.125 2
0.78 0.78 4 1.135 2
0.79 0.79 4 1.145 3
0.8 0.8 4 1.155 3
0.81 0.81 4 1.165 3
0.82 0.82 5 1.175 3
0.83 0.83 5 1.185 3
0.84 0.84 5 1.195 3
0.85 0.85 5 1.205 3
0.86 0.86 5 1.215 3
0.87 0.87 5 1.225 3
0.88 0.88 5 1.235 3
0.89 0.89 5 1.245 3
0.9 0.9 5 1.255 3
0.91 0.91 5 1.265 3
0.92 0.92 6 1.275 4
0.93 0.93 6 1.285 4
0.94 0.94 6 1.295 4
0.95 0.95 6 1.305 4
0.96 0.96 6 1.315 4
0.97 0.97 6 1.325 4
0.98 0.98 6 1.335 4
0.99 0.99 6 1.345 4
1 1 6 1.355 4
1.01 1.01 6 1.365 4
1.02 1.02 7 1.375 4
1.03 1.03 7 1.385 4
1.04 1.04 7 1.395 4
1.05 1.05 7 1.405 4
1.06 1.06 7 1.415 5
1.07 1.07 7 1.425 5
1.08 1.08 7 1.435 5
1.09 1.09 7 1.445 5
1.1 1.1 7 1.455 5
1.11 1.11 7 1.465 5
1.12 1.12 7 1.475 5
1.13 1.13 7 1.485 5
1.14 1.14 7 1.495 5
1.15 1.15 8 1.505 5
1.16 1.16 8 1.515 5
1.17 1.17 8 1.525 5
1.18 1.18 8 1.535 5
1.19 1.19 8 1.545 5
1.2 1.2 8 1.555 5
1.21 1.21 8 1.565 5
1.22 1.22 8 1.575 5
1.23 1.23 8 1.585 6
1.24 1.24 8 1.595 6
1.25 1.25 8 1.605 6
1.26 1.26 8 1.615 6
1.27 1.27 8 1.625 6
1.28 1.28 9 1.635 6
1.29 1.29 9 1.645 6
1.3 1.3 9 1.655 6
1.31 1.31 9 1.665 6
1.32 1.32 9 1.675 6
1.33 1.33 9 1.685 6
1.34 1.34 9 1.695 6
1.35 1.35 9 1.705 6
1.36 1.36 9 1.715 6
1.37 1.37 9 1.725 6
1.38 1.38 9 1.735 6
1.39 1.39 9 1.745 6
1.4 1.4 9 1.755 6
1.41 1.41 9 1.765 7
1.42 1.42 9 1.775 7
1.43 1.43 10 1.785 7
1.44 1.44 10 1.795 7
1.45 1.45 10 1.805 7
1.46 1.46 10 1.815 7
1.47 1.47 10 1.825 7
1.48 1.48 10 1.835 7
1.49 1.49 10 1.845 7
1.5 1.5 10 1.855 7
1.51 1.51 10 1.865 7
1.52 1.52 10 1.875 7
1.53 1.53 10 1.885 7
1.54 1.54 10 1.895 7
1.55 1.55 10 1.905 7
1.56 1.56 10 1.915 7
1.57 1.57 10 1.925 7
1.58 1.58 10 1.935 7
1.59 1.59 10 1.945 7
1.6 1.6 11 1.955 7

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Figure 2: Planning horizon and planning costs.
Note: The figure varies \(\tau_0\) while holding the other parameters and the aggregate-supply shock process at their baseline values. Average planning costs are costs paid by firms that receive a Calvo price-reset opportunity, expressed as a share of those firms’ steady-state per-period profits.

model tilde_tau0 tau0 mean_k_star mode_k_star sd_k_star share_k_gt_free mean_planning_cost cost_reset_profits_pct beta_cg sd_pi_quarterly mean_sigma_pi_model sd_sigma_pi_model cv_sigma_pi_model cv_sigma_ratio_to_data k_counts
RE endpoint 0 0 40 40 0 1 0 0 0.665 0.637 0.236 0 0 0 k=40: 50000
Endogenous planning 0.25 0.009 12.83 2 12.009 0.884 0 0.016 0.382 0.837 0.257 0.034 0.131 0.22 k=2: 5790; k=3: 4591; k=4: 4749; k=5: 3795; k=6: 2850; k=7: 2326; k=8: 1908; k=9: 1750; k=10: 1633; k=11: 1407; k=12: 1436; k=13: 1320; k=14: 1267; k=15: 1121; k=16: 990; k=17: 904; k=18: 841; k=19: 731; k=20: 646; k=21: 565; k=22: 505; k=23: 430; k=24: 380; k=25: 348; k=26: 274; k=27: 246; k=28: 192; k=29: 209; k=30: 194; k=31: 176; k=32: 139; k=33: 143; k=34: 117; k=35: 113; k=36: 98; k=37: 103; k=38: 90; k=39: 88; k=40: 5535
Endogenous planning 0.5 0.019 7.664 2 7.613 0.775 0 0.033 0.49 0.88 0.245 0.035 0.142 0.238 k=2: 11263; k=3: 6292; k=4: 5525; k=5: 4268; k=6: 3273; k=7: 2658; k=8: 2080; k=9: 1870; k=10: 1553; k=11: 1428; k=12: 1310; k=13: 1125; k=14: 952; k=15: 872; k=16: 722; k=17: 566; k=18: 521; k=19: 374; k=20: 357; k=21: 276; k=22: 235; k=23: 204; k=24: 184; k=25: 125; k=26: 132; k=27: 90; k=28: 99; k=29: 89; k=30: 78; k=31: 48; k=32: 64; k=33: 41; k=34: 44; k=35: 48; k=36: 33; k=37: 30; k=38: 25; k=39: 52; k=40: 1094
Endogenous planning 0.75 0.028 5.317 2 4.81 0.669 0 0.043 0.659 0.929 0.233 0.03 0.127 0.213 k=2: 16556; k=3: 7167; k=4: 5983; k=5: 4415; k=6: 3320; k=7: 2372; k=8: 1895; k=9: 1530; k=10: 1309; k=11: 1078; k=12: 893; k=13: 690; k=14: 567; k=15: 453; k=16: 348; k=17: 241; k=18: 174; k=19: 143; k=20: 98; k=21: 89; k=22: 74; k=23: 58; k=24: 44; k=25: 37; k=26: 42; k=27: 35; k=28: 29; k=29: 20; k=30: 21; k=31: 19; k=32: 17; k=33: 19; k=34: 17; k=35: 9; k=36: 10; k=37: 9; k=38: 9; k=39: 11; k=40: 199
Endogenous planning 1 0.038 4.096 2 3.204 0.568 0 0.048 0.828 0.967 0.224 0.024 0.109 0.182 k=2: 21581; k=3: 7789; k=4: 6052; k=5: 4196; k=6: 2767; k=7: 1915; k=8: 1487; k=9: 1070; k=10: 834; k=11: 623; k=12: 452; k=13: 328; k=14: 232; k=15: 152; k=16: 102; k=17: 77; k=18: 76; k=19: 44; k=20: 42; k=21: 28; k=22: 19; k=23: 11; k=24: 13; k=25: 14; k=26: 6; k=27: 8; k=28: 11; k=29: 9; k=30: 7; k=31: 3; k=32: 5; k=33: 2; k=34: 2; k=35: 2; k=36: 6; k=37: 2; k=38: 1; k=39: 2; k=40: 30
Endogenous planning 1.25 0.047 3.396 2 2.282 0.477 0 0.05 0.967 0.994 0.217 0.021 0.096 0.162 k=2: 26145; k=3: 8079; k=4: 5753; k=5: 3530; k=6: 2198; k=7: 1363; k=8: 941; k=9: 658; k=10: 450; k=11: 294; k=12: 184; k=13: 127; k=14: 85; k=15: 56; k=16: 37; k=17: 20; k=18: 21; k=19: 9; k=20: 7; k=21: 6; k=22: 5; k=23: 5; k=24: 3; k=25: 2; k=26: 1; k=27: 2; k=28: 2; k=29: 5; k=30: 2; k=31: 1; k=33: 1; k=34: 1; k=35: 1; k=36: 1; k=38: 1; k=40: 4
Endogenous planning 1.5 0.057 2.958 2 1.7 0.397 0 0.05 1.073 1.014 0.211 0.019 0.089 0.149 k=2: 30128; k=3: 8203; k=4: 5088; k=5: 2781; k=6: 1498; k=7: 904; k=8: 570; k=9: 336; k=10: 176; k=11: 124; k=12: 64; k=13: 48; k=14: 19; k=15: 14; k=16: 15; k=17: 8; k=18: 5; k=19: 4; k=20: 1; k=21: 4; k=22: 3; k=23: 1; k=25: 3; k=28: 1; k=29: 1; k=35: 1
Endogenous planning 1.75 0.066 2.669 2 1.298 0.325 0 0.047 1.159 1.029 0.206 0.017 0.084 0.142 k=2: 33740; k=3: 7828; k=4: 4294; k=5: 2021; k=6: 1009; k=7: 542; k=8: 241; k=9: 144; k=10: 73; k=11: 37; k=12: 27; k=13: 12; k=14: 14; k=15: 7; k=16: 2; k=17: 3; k=18: 2; k=19: 2; k=21: 1; k=22: 1
Endogenous planning 2 0.075 2.471 2 1.018 0.26 0 0.044 1.229 1.041 0.201 0.016 0.081 0.135 k=2: 36976; k=3: 7128; k=4: 3408; k=5: 1395; k=6: 603; k=7: 243; k=8: 111; k=9: 59; k=10: 34; k=11: 14; k=12: 12; k=13: 7; k=14: 6; k=15: 2; k=16: 1; k=17: 1
Endogenous planning 2.25 0.085 2.333 2 0.807 0.206 0 0.039 1.29 1.05 0.198 0.015 0.077 0.129 k=2: 39692; k=3: 6336; k=4: 2574; k=5: 873; k=6: 300; k=7: 106; k=8: 57; k=9: 29; k=10: 11; k=11: 13; k=12: 8; k=13: 1
Endogenous planning 2.5 0.094 2.236 2 0.642 0.16 0 0.034 1.34 1.058 0.194 0.014 0.072 0.121 k=2: 42000; k=3: 5425; k=4: 1819; k=5: 505; k=6: 142; k=7: 60; k=8: 19; k=9: 17; k=10: 11; k=11: 2
Endogenous planning 2.75 0.104 2.168 2 0.519 0.122 0 0.029 1.379 1.063 0.191 0.013 0.067 0.112 k=2: 43891; k=3: 4453; k=4: 1247; k=5: 285; k=6: 73; k=7: 26; k=8: 15; k=9: 8; k=10: 2
Endogenous planning 3 0.113 2.119 2 0.42 0.092 0 0.025 1.412 1.07 0.189 0.012 0.061 0.103 k=2: 45396; k=3: 3583; k=4: 810; k=5: 144; k=6: 42; k=7: 16; k=8: 7; k=9: 2
Endogenous planning 3.5 0.132 2.059 2 0.278 0.05 0 0.017 1.464 1.075 0.185 0.009 0.049 0.082 k=2: 47515; k=3: 2125; k=4: 296; k=5: 50; k=6: 8; k=7: 6
Endogenous planning 4 0.151 2.028 2 0.184 0.025 0 0.01 1.493 1.078 0.182 0.007 0.037 0.062 k=2: 48743; k=3: 1135; k=4: 106; k=5: 13; k=6: 3
Endogenous planning 4.5 0.17 2.013 2 0.12 0.012 0 0.006 1.512 1.082 0.181 0.005 0.026 0.044 k=2: 49404; k=3: 559; k=4: 32; k=5: 5
Fixed-planning endpoint 5   2 2 0 0 0 0 1.536 1.085 0.179 0 0 0 k=2: 50000

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Figure 3: Inflation forecast predictability across models.
Note: The data bar reports the point estimate from regressing the average SPF forecast error on the average SPF forecast revision over the 1969:Q4–2007:Q4 sample period. The point estimate is \(\hat{\beta}_{CG}=1.25\) with an approximate 95 percent confidence interval of \([0.28,2.22]\). Model bars report simulated population moments using 200,000 observations.

label kind beta_cg beta_cg_hac_se ci_95_lower ci_95_upper sample_start sample_end model_n_obs source plotted
Data Data 1.248 0.494 0.28 2.217 1969Q4 2007Q4   Replicated CG regression 1
Rational Expectations Model 0           200000 Fixed-horizon approximation, k=1000 1
Fixed Planning Model 1.304           200000 Fixed planning, k=4 1
Endogenous Planning, Linear Cost Model 0.857           200000 Linear cost, k_underbar=2, tau0=1 1
Endogenous Planning, Exponential Cost Model 0.971           200000 Exponential cost, b0=0.80, b1=0.25 1

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Figure 4: Forecast revisions and inflation uncertainty in the data and model.
Note: The left panel uses the empirical one-quarter-ahead density-uncertainty series for core PCE inflation and the average SPF four-quarter forecast revision over the 1969:Q1–2007:Q1 survey-quarter sample. The right panel uses simulated data from the baseline endogenous-planning model. The red line in the data panel is an OLS fitted line; the red line in the model panel reports equal-count binned means. \(\rho\) denotes the Pearson correlation between the two series.

panel bin n min_abs_forecast_revision max_abs_forecast_revision mean_abs_forecast_revision mean_sigma_pi mean_k_star
Data 1 12 0 0.024 0.014 0.243  
Data 2 12 0.024 0.051 0.035 0.173  
Data 3 13 0.051 0.081 0.067 0.194  
Data 4 12 0.085 0.123 0.104 0.274  
Data 5 12 0.128 0.158 0.143 0.168  
Data 6 13 0.16 0.194 0.171 0.323  
Data 7 12 0.201 0.264 0.228 0.208  
Data 8 12 0.268 0.307 0.291 0.295  
Data 9 13 0.307 0.391 0.35 0.287  
Data 10 12 0.395 0.514 0.463 0.352  
Data 11 12 0.522 0.847 0.654 0.374  
Data 12 13 0.899 1.489 1.135 0.444  
Endogenous-planning model 1 5714 0 0.003 0.001 0.216 2.312
Endogenous-planning model 2 5714 0.003 0.005 0.004 0.215 2.294
Endogenous-planning model 3 5714 0.005 0.008 0.007 0.215 2.294
Endogenous-planning model 4 5715 0.008 0.011 0.01 0.216 2.307
Endogenous-planning model 5 5714 0.011 0.014 0.012 0.216 2.347
Endogenous-planning model 6 5714 0.014 0.017 0.015 0.216 2.354
Endogenous-planning model 7 5715 0.017 0.02 0.018 0.216 2.379
Endogenous-planning model 8 5714 0.02 0.023 0.021 0.216 2.422
Endogenous-planning model 9 5714 0.023 0.026 0.024 0.217 2.509
Endogenous-planning model 10 5714 0.026 0.029 0.027 0.217 2.508
Endogenous-planning model 11 5715 0.029 0.032 0.031 0.217 2.568
Endogenous-planning model 12 5714 0.032 0.036 0.034 0.218 2.675
Endogenous-planning model 13 5714 0.036 0.039 0.037 0.218 2.716
Endogenous-planning model 14 5715 0.039 0.043 0.041 0.218 2.821
Endogenous-planning model 15 5714 0.043 0.047 0.045 0.22 2.961
Endogenous-planning model 16 5714 0.047 0.051 0.049 0.22 3.111
Endogenous-planning model 17 5714 0.051 0.055 0.053 0.221 3.188
Endogenous-planning model 18 5715 0.055 0.059 0.057 0.22 3.299
Endogenous-planning model 19 5714 0.059 0.064 0.062 0.221 3.489
Endogenous-planning model 20 5714 0.064 0.069 0.067 0.221 3.665
Endogenous-planning model 21 5715 0.069 0.074 0.072 0.222 3.842
Endogenous-planning model 22 5714 0.074 0.08 0.077 0.223 4.045
Endogenous-planning model 23 5714 0.08 0.086 0.083 0.223 4.22
Endogenous-planning model 24 5714 0.086 0.092 0.089 0.224 4.477
Endogenous-planning model 25 5715 0.092 0.099 0.096 0.224 4.67
Endogenous-planning model 26 5714 0.099 0.107 0.103 0.226 4.887
Endogenous-planning model 27 5714 0.107 0.115 0.11 0.227 5.1
Endogenous-planning model 28 5715 0.115 0.123 0.119 0.228 5.381
Endogenous-planning model 29 5714 0.123 0.133 0.128 0.229 5.593
Endogenous-planning model 30 5714 0.133 0.145 0.139 0.232 6.016
Endogenous-planning model 31 5714 0.145 0.159 0.152 0.234 6.434
Endogenous-planning model 32 5715 0.159 0.177 0.167 0.236 6.94
Endogenous-planning model 33 5714 0.177 0.2 0.188 0.239 7.442
Endogenous-planning model 34 5714 0.2 0.239 0.217 0.244 8.339
Endogenous-planning model 35 5715 0.239 0.873 0.301 0.262 11.478

Return to text


Figure 5: Empirical and model-based measures of inflation uncertainty.
Note: The middle panel reports the selected planning horizon \(k_t^\star\), with the dashed line showing its sample mean. The trend-inflation line is \(\pi^{Avg}+\bar{\pi}_t\), where \(\bar{\pi}_t\) is the demeaned model trend state and \(\pi^{Avg}\) is the sample mean of quarterly core PCE inflation.

quarter date sigma_melosi_1q sigma_model demand_sigma_allocation supply_sigma_allocation demand_variance_share supply_variance_share demand_variance_contribution supply_variance_contribution k_continuous k_rounded pi pi_avg pi_level y trend trend_level supply
1970Q1 1970-01-01 00:00:00 0.239 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 0.287 0.796 1.083 0.56 0.283 1.079 -0.003
1970Q2 1970-04-01 00:00:00 0.211 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 0.33 0.796 1.125 -0.171 0.284 1.08 0.03
1970Q3 1970-07-01 00:00:00 0.199 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 0.311 0.796 1.106 -0.094 0.293 1.089 0.014
1970Q4 1970-10-01 00:00:00 0.182 0.214 0.011 0.202 0.053 0.947 0.002 0.043 2.175 2 0.599 0.796 1.395 -1.982 0.297 1.092 0.19
1971Q1 1971-01-01 00:00:00 0.256 0.205 0.009 0.196 0.042 0.958 0.002 0.04 2 2 0.463 0.796 1.259 -0.1 0.357 1.153 0.062
1971Q2 1971-04-01 00:00:00 0.237 0.21 0.01 0.2 0.047 0.953 0.002 0.042 2 2 0.339 0.796 1.134 -0.357 0.378 1.174 -0.011
1971Q3 1971-07-01 00:00:00 0.205 0.211 0.013 0.199 0.06 0.94 0.003 0.042 3.002 3 0.142 0.796 0.938 -0.332 0.37 1.166 -0.099
1971Q4 1971-10-01 00:00:00 0.21 0.223 0.016 0.207 0.07 0.93 0.003 0.046 4.849 5 -0.226 0.796 0.569 -0.891 0.325 1.12 -0.223
1972Q1 1972-01-01 00:00:00 0.342 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 0.159 0.796 0.955 0.133 0.215 1.01 -0.029
1972Q2 1972-04-01 00:00:00 0.289 0.206 0.009 0.197 0.043 0.957 0.002 0.041 2.568 3 -0.122 0.796 0.674 1.576 0.203 0.999 -0.185
1972Q3 1972-07-01 00:00:00 0.265 0.209 0.009 0.2 0.045 0.955 0.002 0.042 2 2 -0.047 0.796 0.749 1.706 0.138 0.934 -0.122
1972Q4 1972-10-01 00:00:00 0.224 0.212 0.011 0.202 0.05 0.95 0.002 0.043 2 2 -0.17 0.796 0.626 2.545 0.101 0.897 -0.18
1973Q1 1973-01-01 00:00:00 0.22 0.246 0.028 0.217 0.115 0.885 0.007 0.053 2 2 -0.101 0.796 0.694 4.157 0.047 0.843 -0.139
1973Q2 1973-04-01 00:00:00 0.193 0.238 0.032 0.206 0.136 0.864 0.008 0.049 8.742 9 0.557 0.796 1.353 4.381 0.017 0.813 0.113
1973Q3 1973-07-01 00:00:00 0.403 0.231 0.023 0.208 0.099 0.901 0.005 0.048 5.978 6 0.525 0.796 1.32 2.992 0.125 0.921 0.109
1973Q4 1973-10-01 00:00:00 0.389 0.23 0.022 0.208 0.098 0.902 0.005 0.048 5.85 6 0.587 0.796 1.383 3.063 0.205 1.001 0.103
1974Q1 1974-01-01 00:00:00 0.397 0.221 0.014 0.207 0.066 0.934 0.003 0.046 4.74 5 0.907 0.796 1.702 1.319 0.282 1.077 0.259
1974Q2 1974-04-01 00:00:00 0.468 0.221 0.014 0.206 0.065 0.935 0.003 0.046 5.403 5 1.659 0.796 2.455 0.675 0.407 1.202 0.55
1974Q3 1974-07-01 00:00:00 0.731 0.216 0.011 0.206 0.05 0.95 0.002 0.045 4.691 5 2.022 0.796 2.818 -1.14 0.657 1.453 0.651
1974Q4 1974-10-01 00:00:00 0.91 0.224 0.017 0.207 0.075 0.925 0.004 0.046 3.127 3 1.618 0.796 2.414 -2.376 0.93 1.726 0.384
1975Q1 1975-01-01 00:00:00 0.895 0.309 0.053 0.256 0.171 0.829 0.016 0.079 14.021 14 1.139 0.796 1.935 -4.421 1.068 1.863 0.229
1975Q2 1975-04-01 00:00:00 0.784 0.292 0.05 0.241 0.172 0.828 0.015 0.07 14.312 14 0.717 0.796 1.513 -4.507 1.082 1.878 0.046
1975Q3 1975-07-01 00:00:00 0.663 0.271 0.048 0.224 0.175 0.825 0.013 0.061 11.96 12 0.693 0.796 1.489 -3.592 1.009 1.805 0.018
1975Q4 1975-10-01 00:00:00 0.565 0.266 0.037 0.229 0.139 0.861 0.01 0.061 10.029 10 0.82 0.796 1.616 -3.029 0.946 1.741 0.068
1976Q1 1976-01-01 00:00:00 0.527 0.239 0.026 0.213 0.109 0.891 0.006 0.051 5.513 6 0.712 0.796 1.508 -1.567 0.921 1.716 -0.038
1976Q2 1976-04-01 00:00:00 0.482 0.239 0.029 0.21 0.123 0.877 0.007 0.05 6.595 7 0.397 0.796 1.193 -1.603 0.879 1.675 -0.151
1976Q3 1976-07-01 00:00:00 0.413 0.238 0.026 0.211 0.111 0.889 0.006 0.05 2 2 0.758 0.796 1.554 -1.838 0.783 1.578 0.023
1976Q4 1976-10-01 00:00:00 0.408 0.238 0.026 0.212 0.108 0.892 0.006 0.05 2 2 0.757 0.796 1.553 -1.904 0.778 1.573 0.026
1977Q1 1977-01-01 00:00:00 0.389 0.228 0.023 0.206 0.099 0.901 0.005 0.047 2 2 0.873 0.796 1.669 -1.531 0.774 1.569 0.084
1977Q2 1977-04-01 00:00:00 0.415 0.215 0.014 0.202 0.063 0.937 0.003 0.043 2 2 0.721 0.796 1.516 -0.427 0.794 1.589 -0.023
1977Q3 1977-07-01 00:00:00 0.387 0.205 0.009 0.196 0.043 0.957 0.002 0.04 2 2 0.854 0.796 1.65 0.536 0.779 1.575 0.041
1977Q4 1977-10-01 00:00:00 0.389 0.216 0.014 0.203 0.064 0.936 0.003 0.044 2.636 3 0.647 0.796 1.443 -0.302 0.794 1.59 -0.058
1978Q1 1978-01-01 00:00:00 0.352 0.218 0.016 0.202 0.073 0.927 0.003 0.044 2 2 0.752 0.796 1.548 -0.837 0.765 1.56 0.015
1978Q2 1978-04-01 00:00:00 0.338 0.21 0.011 0.199 0.053 0.947 0.002 0.042 2.686 3 0.915 0.796 1.71 2.092 0.762 1.558 0.051
1978Q3 1978-07-01 00:00:00 0.37 0.209 0.011 0.198 0.052 0.948 0.002 0.042 2.306 2 0.905 0.796 1.701 2.213 0.793 1.588 0.033
1978Q4 1978-10-01 00:00:00 0.366 0.216 0.012 0.204 0.056 0.944 0.003 0.044 3.261 3 0.983 0.796 1.779 2.659 0.815 1.611 0.045
1979Q1 1979-01-01 00:00:00 0.385 0.206 0.009 0.197 0.043 0.957 0.002 0.041 2.517 3 0.561 0.796 1.357 1.931 0.849 1.645 -0.164
1979Q2 1979-04-01 00:00:00 0.332 0.216 0.011 0.205 0.052 0.948 0.002 0.044 4.152 4 1.379 0.796 2.175 1.171 0.791 1.587 0.26
1979Q3 1979-07-01 00:00:00 0.479 0.208 0.009 0.199 0.042 0.958 0.002 0.041 2 2 1.033 0.796 1.829 1.1 0.909 1.705 0.06
1979Q4 1979-10-01 00:00:00 0.453 0.208 0.01 0.198 0.049 0.951 0.002 0.041 2.933 3 1.269 0.796 2.064 0.604 0.934 1.729 0.165
1980Q1 1980-01-01 00:00:00 0.491 0.211 0.01 0.201 0.048 0.952 0.002 0.042 3.717 4 1.621 0.796 2.417 0.253 1.001 1.796 0.3
1980Q2 1980-04-01 00:00:00 0.605 0.251 0.018 0.233 0.071 0.929 0.004 0.058 2 2 1.417 0.796 2.212 -2.414 1.125 1.921 0.203
1980Q3 1980-07-01 00:00:00 0.603 0.283 0.047 0.236 0.167 0.833 0.013 0.067 2 2 1.406 0.796 2.202 -3.031 1.183 1.979 0.176
1980Q4 1980-10-01 00:00:00 0.589 0.238 0.017 0.221 0.071 0.929 0.004 0.053 2.33 2 1.611 0.796 2.407 -1.701 1.228 2.023 0.237
1981Q1 1981-01-01 00:00:00 0.623 0.219 0.013 0.207 0.058 0.942 0.003 0.045 2 2 1.399 0.796 2.194 -0.332 1.304 2.1 0.07
1981Q2 1981-04-01 00:00:00 0.609 0.26 0.037 0.223 0.141 0.859 0.01 0.058 8.432 8 1.076 0.796 1.872 -1.686 1.323 2.119 -0.022
1981Q3 1981-07-01 00:00:00 0.543 0.245 0.03 0.214 0.124 0.876 0.007 0.052 6.07 6 1.029 0.796 1.825 -1.138 1.274 2.07 -0.053
1981Q4 1981-10-01 00:00:00 0.486 0.281 0.042 0.239 0.15 0.85 0.012 0.067 11.789 12 0.967 0.796 1.763 -2.911 1.225 2.021 0.029
1982Q1 1982-01-01 00:00:00 0.428 0.266 0.056 0.21 0.209 0.791 0.015 0.056 16.085 16 0.657 0.796 1.453 -5.178 1.173 1.969 0.02
1982Q2 1982-04-01 00:00:00 0.381 0.266 0.056 0.211 0.209 0.791 0.015 0.056 15.782 16 0.548 0.796 1.344 -5.439 1.07 1.866 0.019
1982Q3 1982-07-01 00:00:00 0.393 0.338 0.028 0.31 0.082 0.918 0.009 0.105 16.645 17 0.795 0.796 1.59 -6.548 0.966 1.761 0.211
1982Q4 1982-10-01 00:00:00 0.369 0.332 0.049 0.283 0.148 0.852 0.016 0.094 17.285 17 0.587 0.796 1.383 -7.246 0.932 1.727 0.164
1983Q1 1983-01-01 00:00:00 0.326 0.319 0.05 0.268 0.158 0.842 0.016 0.086 16.192 16 0.509 0.796 1.305 -6.668 0.863 1.658 0.128
1983Q2 1983-04-01 00:00:00 0.291 0.245 0.044 0.2 0.181 0.819 0.011 0.049 13.683 14 -0.034 0.796 0.762 -5.157 0.792 1.588 -0.149
1983Q3 1983-07-01 00:00:00 0.682 0.269 0.037 0.233 0.136 0.864 0.01 0.063 2 2 0.713 0.796 1.508 -3.932 0.627 1.423 0.111
1983Q4 1983-10-01 00:00:00 0.624 0.239 0.031 0.207 0.131 0.869 0.007 0.049 8.126 8 0.001 0.796 0.797 -2.647 0.644 1.44 -0.19
1984Q1 1984-01-01 00:00:00 0.562 0.229 0.019 0.21 0.083 0.917 0.004 0.048 4.865 5 0.209 0.796 1.005 -1.517 0.515 1.311 -0.096
1984Q2 1984-04-01 00:00:00 0.483 0.21 0.013 0.198 0.06 0.94 0.003 0.042 2 2 0.368 0.796 1.164 -0.635 0.454 1.25 -0.031
1984Q3 1984-07-01 00:00:00 0.42 0.216 0.013 0.203 0.058 0.942 0.003 0.044 3.644 4 0.139 0.796 0.934 -0.52 0.437 1.233 -0.123
1984Q4 1984-10-01 00:00:00 0.4 0.221 0.014 0.207 0.062 0.938 0.003 0.046 4.353 4 -0.087 0.796 0.709 -0.558 0.377 1.173 -0.193
1985Q1 1985-01-01 00:00:00 0.443 0.207 0.009 0.198 0.045 0.955 0.002 0.041 2.515 3 0.559 0.796 1.355 -0.451 0.285 1.08 0.148
1985Q2 1985-04-01 00:00:00 0.424 0.216 0.012 0.204 0.055 0.945 0.003 0.044 3.331 3 0.068 0.796 0.863 -0.43 0.339 1.135 -0.116
1985Q3 1985-07-01 00:00:00 0.397 0.207 0.008 0.199 0.039 0.961 0.002 0.041 2 2 0.226 0.796 1.022 0.234 0.285 1.081 -0.031
1985Q4 1985-10-01 00:00:00 0.345 0.211 0.011 0.199 0.053 0.947 0.002 0.042 3.366 3 -0.081 0.796 0.715 0.13 0.273 1.069 -0.166
1986Q1 1986-01-01 00:00:00 0.385 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 0.278 0.796 1.074 0.223 0.202 0.998 0.039
1986Q2 1986-04-01 00:00:00 0.338 0.211 0.011 0.199 0.054 0.946 0.002 0.042 3.373 3 -0.112 0.796 0.683 -0.154 0.218 1.013 -0.15
1986Q3 1986-07-01 00:00:00 0.358 0.208 0.01 0.197 0.049 0.951 0.002 0.041 2.888 3 -0.111 0.796 0.684 -0.023 0.152 0.947 -0.125
1986Q4 1986-10-01 00:00:00 0.347 0.208 0.009 0.199 0.043 0.957 0.002 0.041 2 2 0.015 0.796 0.811 -0.302 0.099 0.895 -0.039
1987Q1 1987-01-01 00:00:00 0.302 0.21 0.011 0.199 0.052 0.948 0.002 0.042 2.934 3 -0.164 0.796 0.631 -0.367 0.082 0.878 -0.112
1987Q2 1987-04-01 00:00:00 0.297 0.208 0.009 0.199 0.042 0.958 0.002 0.041 2 2 0.17 0.796 0.966 -0.085 0.033 0.829 0.074
1987Q3 1987-07-01 00:00:00 0.279 0.205 0.009 0.196 0.044 0.956 0.002 0.04 2 2 0.096 0.796 0.892 0.002 0.06 0.856 0.02
1987Q4 1987-10-01 00:00:00 0.248 0.209 0.011 0.198 0.052 0.948 0.002 0.041 2.384 2 0.215 0.796 1.011 0.935 0.068 0.863 0.061
1988Q1 1988-01-01 00:00:00 0.236 0.208 0.009 0.199 0.044 0.956 0.002 0.041 2 2 0.165 0.796 0.96 0.694 0.097 0.893 0.027
1988Q2 1988-04-01 00:00:00 0.215 0.215 0.012 0.203 0.057 0.943 0.003 0.044 3.676 4 0.409 0.796 1.205 1.251 0.111 0.906 0.118
1988Q3 1988-07-01 00:00:00 0.257 0.21 0.011 0.199 0.052 0.948 0.002 0.042 2.71 3 0.349 0.796 1.145 1.1 0.17 0.966 0.073
1988Q4 1988-10-01 00:00:00 0.244 0.214 0.013 0.201 0.059 0.941 0.003 0.043 2.376 2 0.315 0.796 1.111 1.694 0.206 1.002 0.032
1989Q1 1989-01-01 00:00:00 0.223 0.215 0.013 0.202 0.062 0.938 0.003 0.043 2 2 0.29 0.796 1.085 1.983 0.228 1.024 0.006
1989Q2 1989-04-01 00:00:00 0.205 0.209 0.01 0.199 0.048 0.952 0.002 0.042 2 2 0.11 0.796 0.906 2.029 0.24 1.036 -0.096
1989Q3 1989-07-01 00:00:00 0.201 0.207 0.01 0.197 0.05 0.95 0.002 0.041 2.138 2 -0.054 0.796 0.741 2.06 0.214 1.01 -0.168
1989Q4 1989-10-01 00:00:00 0.242 0.21 0.009 0.201 0.043 0.957 0.002 0.042 2 2 0.116 0.796 0.911 1.555 0.161 0.956 -0.045
1990Q1 1990-01-01 00:00:00 0.215 0.219 0.015 0.204 0.069 0.931 0.003 0.045 3.617 4 0.349 0.796 1.145 1.948 0.152 0.947 0.059
1990Q2 1990-04-01 00:00:00 0.25 0.214 0.013 0.201 0.059 0.941 0.003 0.043 2.528 3 0.315 0.796 1.111 1.624 0.191 0.987 0.039
1990Q3 1990-07-01 00:00:00 0.232 0.208 0.008 0.199 0.04 0.96 0.002 0.041 2 2 0.21 0.796 1.005 1.019 0.216 1.012 -0.016
1990Q4 1990-10-01 00:00:00 0.208 0.21 0.011 0.198 0.053 0.947 0.002 0.042 2.598 3 0.04 0.796 0.836 -0.553 0.215 1.01 -0.075
1991Q1 1991-01-01 00:00:00 0.208 0.219 0.015 0.204 0.069 0.931 0.003 0.045 2.539 3 0.088 0.796 0.884 -1.669 0.18 0.976 -0.017
1991Q2 1991-04-01 00:00:00 0.185 0.219 0.015 0.204 0.069 0.931 0.003 0.045 3.518 4 -0.028 0.796 0.768 -1.528 0.161 0.957 -0.059
1991Q3 1991-07-01 00:00:00 0.189 0.216 0.015 0.201 0.068 0.932 0.003 0.043 2 2 0.101 0.796 0.896 -1.655 0.124 0.919 0.014
1991Q4 1991-10-01 00:00:00 0.169 0.221 0.017 0.204 0.076 0.924 0.004 0.045 3.397 3 -0.012 0.796 0.784 -1.945 0.119 0.915 -0.025
1992Q1 1992-01-01 00:00:00 0.156 0.217 0.013 0.204 0.06 0.94 0.003 0.044 2.645 3 -0.033 0.796 0.762 -1.399 0.093 0.889 -0.039
1992Q2 1992-04-01 00:00:00 0.146 0.211 0.013 0.198 0.059 0.941 0.003 0.042 2.638 3 -0.092 0.796 0.703 -0.971 0.068 0.863 -0.063
1992Q3 1992-07-01 00:00:00 0.138 0.21 0.011 0.199 0.053 0.947 0.002 0.042 3.034 3 -0.205 0.796 0.591 -0.649 0.036 0.831 -0.104
1992Q4 1992-10-01 00:00:00 0.163 0.207 0.008 0.199 0.039 0.961 0.002 0.041 2 2 -0.066 0.796 0.73 -0.281 -0.013 0.783 -0.024
1993Q1 1993-01-01 00:00:00 0.148 0.208 0.011 0.198 0.052 0.948 0.002 0.041 2 2 -0.109 0.796 0.687 -0.798 -0.023 0.773 -0.034
1993Q2 1993-04-01 00:00:00 0.134 0.208 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.04 0.796 0.756 -0.907 -0.04 0.755 0.013
1993Q3 1993-07-01 00:00:00 0.124 0.214 0.013 0.201 0.059 0.941 0.003 0.043 2.996 3 -0.238 0.796 0.558 -1.126 -0.04 0.756 -0.077
1993Q4 1993-10-01 00:00:00 0.155 0.207 0.01 0.197 0.049 0.951 0.002 0.041 2.585 3 -0.283 0.796 0.513 -0.477 -0.08 0.716 -0.094
1994Q1 1994-01-01 00:00:00 0.157 0.208 0.01 0.197 0.049 0.951 0.002 0.041 2.568 3 -0.343 0.796 0.453 -0.22 -0.12 0.675 -0.109
1994Q2 1994-04-01 00:00:00 0.164 0.208 0.009 0.199 0.044 0.956 0.002 0.041 2 2 -0.125 0.796 0.671 0.417 -0.165 0.631 0.013
1994Q3 1994-07-01 00:00:00 0.16 0.205 0.009 0.196 0.042 0.958 0.002 0.04 2 2 -0.239 0.796 0.557 0.286 -0.157 0.639 -0.049
1994Q4 1994-10-01 00:00:00 0.145 0.204 0.009 0.195 0.045 0.955 0.002 0.04 2 2 -0.289 0.796 0.507 0.704 -0.173 0.622 -0.074
1995Q1 1995-01-01 00:00:00 0.142 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 -0.273 0.796 0.523 0.334 -0.196 0.599 -0.048
1995Q2 1995-04-01 00:00:00 0.129 0.204 0.009 0.195 0.043 0.957 0.002 0.04 2 2 -0.204 0.796 0.592 -0.097 -0.212 0.584 0.003
1995Q3 1995-07-01 00:00:00 0.115 0.206 0.009 0.197 0.042 0.958 0.002 0.041 2 2 -0.32 0.796 0.476 0.02 -0.21 0.586 -0.061
1995Q4 1995-10-01 00:00:00 0.12 0.206 0.009 0.197 0.042 0.958 0.002 0.041 2 2 -0.296 0.796 0.5 -0.046 -0.232 0.564 -0.036
1996Q1 1996-01-01 00:00:00 0.11 0.208 0.009 0.199 0.041 0.959 0.002 0.041 2 2 -0.403 0.796 0.392 -0.053 -0.245 0.551 -0.086
1996Q2 1996-04-01 00:00:00 0.117 0.21 0.009 0.2 0.044 0.956 0.002 0.042 2 2 -0.321 0.796 0.474 0.81 -0.277 0.519 -0.039
1996Q3 1996-07-01 00:00:00 0.105 0.21 0.009 0.2 0.044 0.956 0.002 0.042 2 2 -0.341 0.796 0.455 0.867 -0.286 0.51 -0.045
1996Q4 1996-10-01 00:00:00 0.093 0.214 0.013 0.201 0.061 0.939 0.003 0.043 2 2 -0.228 0.796 0.568 1.021 -0.297 0.499 0.018
1997Q1 1997-01-01 00:00:00 0.114 0.206 0.01 0.196 0.048 0.952 0.002 0.04 2 2 -0.404 0.796 0.392 0.749 -0.283 0.513 -0.078
1997Q2 1997-04-01 00:00:00 0.138 0.216 0.015 0.201 0.07 0.93 0.003 0.044 2 2 -0.275 0.796 0.52 1.457 -0.307 0.489 -0.008
1997Q3 1997-07-01 00:00:00 0.124 0.212 0.011 0.201 0.051 0.949 0.002 0.043 2.039 2 -0.563 0.796 0.233 1.724 -0.301 0.495 -0.167
1997Q4 1997-10-01 00:00:00 0.193 0.215 0.01 0.205 0.048 0.952 0.002 0.044 2 2 -0.48 0.796 0.316 1.578 -0.353 0.443 -0.094
1998Q1 1998-01-01 00:00:00 0.168 0.216 0.011 0.205 0.049 0.951 0.002 0.044 2 2 -0.502 0.796 0.294 1.563 -0.378 0.417 -0.093
1998Q2 1998-04-01 00:00:00 0.153 0.217 0.014 0.202 0.067 0.933 0.003 0.044 2 2 -0.49 0.796 0.306 1.452 -0.403 0.393 -0.072
1998Q3 1998-07-01 00:00:00 0.141 0.219 0.018 0.201 0.082 0.918 0.004 0.044 2 2 -0.441 0.796 0.354 1.663 -0.42 0.375 -0.041
1998Q4 1998-10-01 00:00:00 0.122 0.228 0.021 0.207 0.092 0.908 0.005 0.047 2 2 -0.477 0.796 0.318 2.209 -0.425 0.371 -0.065
1999Q1 1999-01-01 00:00:00 0.106 0.227 0.02 0.206 0.09 0.91 0.005 0.047 2 2 -0.545 0.796 0.25 2.082 -0.435 0.361 -0.094
1999Q2 1999-04-01 00:00:00 0.107 0.226 0.02 0.207 0.088 0.912 0.004 0.047 2 2 -0.449 0.796 0.347 1.853 -0.457 0.339 -0.028
1999Q3 1999-07-01 00:00:00 0.1 0.231 0.022 0.209 0.095 0.905 0.005 0.048 2 2 -0.428 0.796 0.368 2.114 -0.456 0.34 -0.022
1999Q4 1999-10-01 00:00:00 0.089 0.24 0.026 0.214 0.107 0.893 0.006 0.051 6.094 6 -0.326 0.796 0.469 2.683 -0.45 0.346 -0.018
2000Q1 2000-01-01 00:00:00 0.105 0.229 0.021 0.208 0.091 0.909 0.005 0.048 4.409 4 -0.273 0.796 0.523 1.991 -0.425 0.37 0.022
2000Q2 2000-04-01 00:00:00 0.098 0.239 0.028 0.212 0.115 0.885 0.007 0.051 2 2 -0.447 0.796 0.348 2.775 -0.395 0.401 -0.073
2000Q3 2000-07-01 00:00:00 0.13 0.227 0.02 0.208 0.086 0.914 0.004 0.047 3.358 3 -0.314 0.796 0.481 1.901 -0.405 0.39 0.003
2000Q4 2000-10-01 00:00:00 0.115 0.222 0.018 0.204 0.08 0.92 0.004 0.045 2.61 3 -0.302 0.796 0.494 1.57 -0.387 0.408 0.012
2001Q1 2001-01-01 00:00:00 0.104 0.211 0.013 0.199 0.06 0.94 0.003 0.042 2.986 3 -0.148 0.796 0.648 0.367 -0.37 0.426 0.096
2001Q2 2001-04-01 00:00:00 0.138 0.205 0.009 0.196 0.042 0.958 0.002 0.04 2 2 -0.418 0.796 0.377 0.173 -0.326 0.47 -0.055
2001Q3 2001-07-01 00:00:00 0.184 0.207 0.01 0.197 0.049 0.951 0.002 0.041 2.629 3 -0.538 0.796 0.258 -0.983 -0.344 0.452 -0.085
2001Q4 2001-10-01 00:00:00 0.197 0.206 0.009 0.198 0.043 0.957 0.002 0.041 2 2 -0.314 0.796 0.481 -1.407 -0.383 0.413 0.053
2002Q1 2002-01-01 00:00:00 0.17 0.208 0.011 0.197 0.051 0.949 0.002 0.041 2.042 2 -0.489 0.796 0.307 -1.224 -0.369 0.427 -0.049
2002Q2 2002-04-01 00:00:00 0.165 0.205 0.008 0.196 0.041 0.959 0.002 0.04 2 2 -0.247 0.796 0.549 -1.229 -0.393 0.403 0.091
2002Q3 2002-07-01 00:00:00 0.167 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 -0.264 0.796 0.532 -1.417 -0.364 0.432 0.07
2002Q4 2002-10-01 00:00:00 0.144 0.214 0.012 0.201 0.058 0.942 0.003 0.043 2.218 2 -0.441 0.796 0.355 -1.875 -0.344 0.452 -0.026
2003Q1 2003-01-01 00:00:00 0.151 0.214 0.013 0.202 0.059 0.941 0.003 0.043 2.627 3 -0.488 0.796 0.308 -1.93 -0.363 0.432 -0.035
2003Q2 2003-04-01 00:00:00 0.157 0.211 0.011 0.2 0.051 0.949 0.002 0.042 2 2 -0.417 0.796 0.378 -1.634 -0.388 0.408 0.004
2003Q3 2003-07-01 00:00:00 0.134 0.205 0.008 0.196 0.041 0.959 0.002 0.04 2 2 -0.339 0.796 0.457 -0.576 -0.394 0.402 0.033
2003Q4 2003-10-01 00:00:00 0.12 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.349 0.796 0.447 -0.026 -0.383 0.413 0.014
2004Q1 2004-01-01 00:00:00 0.105 0.207 0.009 0.197 0.045 0.955 0.002 0.041 2 2 -0.247 0.796 0.549 -0.082 -0.376 0.42 0.065
2004Q2 2004-04-01 00:00:00 0.118 0.207 0.01 0.197 0.05 0.95 0.002 0.041 2 2 -0.226 0.796 0.57 0.061 -0.35 0.445 0.061
2004Q3 2004-07-01 00:00:00 0.104 0.205 0.009 0.196 0.042 0.958 0.002 0.04 2 2 -0.438 0.796 0.357 0.364 -0.325 0.47 -0.069
2004Q4 2004-10-01 00:00:00 0.155 0.21 0.013 0.198 0.06 0.94 0.003 0.042 2 2 -0.255 0.796 0.541 0.73 -0.348 0.448 0.034
2005Q1 2005-01-01 00:00:00 0.143 0.219 0.015 0.204 0.069 0.931 0.003 0.045 3.792 4 -0.087 0.796 0.709 1.194 -0.329 0.466 0.085
2005Q2 2005-04-01 00:00:00 0.182 0.211 0.011 0.2 0.053 0.947 0.002 0.042 2 2 -0.302 0.796 0.494 1.065 -0.281 0.515 -0.03
2005Q3 2005-07-01 00:00:00 0.176 0.209 0.01 0.199 0.048 0.952 0.002 0.042 2 2 -0.407 0.796 0.389 1.234 -0.285 0.511 -0.086
2005Q4 2005-10-01 00:00:00 0.183 0.219 0.014 0.204 0.066 0.934 0.003 0.045 3.267 3 -0.13 0.796 0.666 1.188 -0.309 0.486 0.06
2006Q1 2006-01-01 00:00:00 0.182 0.223 0.018 0.204 0.082 0.918 0.004 0.046 2.238 2 -0.218 0.796 0.577 1.94 -0.273 0.522 -0.005
2006Q2 2006-04-01 00:00:00 0.157 0.222 0.017 0.205 0.078 0.922 0.004 0.045 4.298 4 -0.002 0.796 0.793 1.631 -0.262 0.533 0.082
2006Q3 2006-07-01 00:00:00 0.184 0.211 0.009 0.201 0.045 0.955 0.002 0.042 2 2 -0.259 0.796 0.537 1.241 -0.21 0.585 -0.046
2006Q4 2006-10-01 00:00:00 0.172 0.211 0.011 0.2 0.052 0.948 0.002 0.042 2 2 -0.366 0.796 0.43 1.584 -0.22 0.576 -0.103
2007Q1 2007-01-01 00:00:00 0.185 0.219 0.015 0.204 0.068 0.932 0.003 0.045 2.982 3 -0.109 0.796 0.687 1.371 -0.249 0.547 0.041
2007Q2 2007-04-01 00:00:00 0.184 0.211 0.011 0.2 0.051 0.949 0.002 0.042 2 2 -0.38 0.796 0.415 1.468 -0.221 0.575 -0.109
2007Q3 2007-07-01 00:00:00 0.188 0.216 0.013 0.203 0.06 0.94 0.003 0.044 2 2 -0.306 0.796 0.49 1.53 -0.253 0.543 -0.054
2007Q4 2007-10-01 00:00:00 0.163 0.221 0.017 0.204 0.076 0.924 0.004 0.045 3.526 4 -0.107 0.796 0.689 1.653 -0.264 0.532 0.039
2008Q1 2008-01-01 00:00:00 0.175 0.209 0.009 0.2 0.043 0.957 0.002 0.042 2 2 -0.268 0.796 0.528 0.729 -0.232 0.564 -0.032
2008Q2 2008-04-01 00:00:00 0.158 0.206 0.01 0.196 0.048 0.952 0.002 0.04 2 2 -0.377 0.796 0.419 0.849 -0.239 0.556 -0.088
2008Q3 2008-07-01 00:00:00 0.165 0.204 0.009 0.195 0.043 0.957 0.002 0.04 2 2 -0.287 0.796 0.509 -0.123 -0.267 0.529 -0.012
2008Q4 2008-10-01 00:00:00 0.137 0.232 0.019 0.213 0.082 0.918 0.004 0.05 5.917 6 -0.875 0.796 -0.079 -2.75 -0.271 0.525 -0.209
2009Q1 2009-01-01 00:00:00 0.329 0.24 0.027 0.213 0.112 0.888 0.006 0.051 7.251 7 -0.797 0.796 -0.001 -4.267 -0.391 0.404 -0.078
2009Q2 2009-04-01 00:00:00 0.323 0.245 0.026 0.219 0.107 0.893 0.006 0.054 2 2 -0.405 0.796 0.391 -4.79 -0.473 0.323 0.101
2009Q3 2009-07-01 00:00:00 0.267 0.242 0.025 0.217 0.104 0.896 0.006 0.052 7.052 7 -0.441 0.796 0.354 -4.758 -0.459 0.337 0.116
2009Q4 2009-10-01 00:00:00 0.231 0.223 0.012 0.211 0.053 0.947 0.003 0.047 2 2 -0.175 0.796 0.621 -3.991 -0.456 0.34 0.202
2010Q1 2010-01-01 00:00:00 0.274 0.231 0.021 0.211 0.089 0.911 0.005 0.049 5.18 5 -0.454 0.796 0.342 -3.819 -0.399 0.396 0.05
2010Q2 2010-04-01 00:00:00 0.249 0.227 0.018 0.208 0.08 0.92 0.004 0.047 4.19 4 -0.527 0.796 0.269 -3.176 -0.41 0.385 0.002
2010Q3 2010-07-01 00:00:00 0.247 0.22 0.015 0.205 0.07 0.93 0.003 0.045 4.209 4 -0.642 0.796 0.154 -2.746 -0.434 0.362 -0.049
2010Q4 2010-10-01 00:00:00 0.258 0.216 0.015 0.201 0.068 0.932 0.003 0.043 2 2 -0.48 0.796 0.316 -2.575 -0.475 0.32 0.03
2011Q1 2011-01-01 00:00:00 0.221 0.219 0.016 0.202 0.075 0.925 0.004 0.044 2 2 -0.358 0.796 0.438 -3.18 -0.476 0.319 0.104
2011Q2 2011-04-01 00:00:00 0.196 0.211 0.011 0.2 0.051 0.949 0.002 0.042 2 2 -0.213 0.796 0.583 -2.882 -0.453 0.343 0.164
2011Q3 2011-07-01 00:00:00 0.21 0.224 0.017 0.207 0.078 0.922 0.004 0.046 2 2 -0.34 0.796 0.455 -3.291 -0.405 0.391 0.078
2011Q4 2011-10-01 00:00:00 0.184 0.218 0.015 0.204 0.067 0.933 0.003 0.044 2 2 -0.44 0.796 0.356 -2.573 -0.392 0.404 0.008
2012Q1 2012-01-01 00:00:00 0.18 0.207 0.009 0.197 0.045 0.955 0.002 0.041 2 2 -0.167 0.796 0.629 -2.151 -0.401 0.394 0.151
2012Q2 2012-04-01 00:00:00 0.192 0.213 0.012 0.201 0.058 0.942 0.003 0.043 2 2 -0.383 0.796 0.413 -2.128 -0.354 0.441 0.012
2012Q3 2012-07-01 00:00:00 0.178 0.219 0.015 0.205 0.066 0.934 0.003 0.045 3.406 3 -0.507 0.796 0.289 -2.412 -0.36 0.436 -0.032
2012Q4 2012-10-01 00:00:00 0.188 0.216 0.015 0.201 0.069 0.931 0.003 0.043 2 2 -0.355 0.796 0.441 -2.731 -0.39 0.406 0.054
2013Q1 2013-01-01 00:00:00 0.169 0.213 0.013 0.2 0.059 0.941 0.003 0.043 2 2 -0.406 0.796 0.39 -2.194 -0.383 0.413 0.016
2013Q2 2013-04-01 00:00:00 0.147 0.219 0.014 0.204 0.065 0.935 0.003 0.045 3.101 3 -0.514 0.796 0.282 -2.377 -0.387 0.409 -0.025
2013Q3 2013-07-01 00:00:00 0.155 0.211 0.011 0.2 0.052 0.948 0.002 0.042 2 2 -0.403 0.796 0.393 -1.982 -0.413 0.383 0.029
2013Q4 2013-10-01 00:00:00 0.135 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.366 0.796 0.43 -1.576 -0.411 0.385 0.042
2014Q1 2014-01-01 00:00:00 0.122 0.218 0.014 0.203 0.066 0.934 0.003 0.044 2.366 2 -0.48 0.796 0.315 -2.391 -0.402 0.394 -0.008
2014Q2 2014-04-01 00:00:00 0.12 0.208 0.008 0.199 0.041 0.959 0.002 0.041 2 2 -0.36 0.796 0.436 -1.583 -0.417 0.378 0.049
2014Q3 2014-07-01 00:00:00 0.117 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.421 0.796 0.375 -0.86 -0.406 0.39 0
2014Q4 2014-10-01 00:00:00 0.109 0.206 0.009 0.197 0.044 0.956 0.002 0.041 2 2 -0.525 0.796 0.271 -0.848 -0.409 0.387 -0.054
2015Q1 2015-01-01 00:00:00 0.125 0.206 0.009 0.197 0.044 0.956 0.002 0.041 2.325 2 -0.629 0.796 0.167 -0.451 -0.432 0.364 -0.099
2015Q2 2015-04-01 00:00:00 0.142 0.208 0.009 0.199 0.044 0.956 0.002 0.041 2 2 -0.351 0.796 0.445 -0.338 -0.471 0.324 0.063
2015Q3 2015-07-01 00:00:00 0.17 0.204 0.009 0.195 0.043 0.957 0.002 0.04 2 2 -0.475 0.796 0.321 -0.446 -0.447 0.348 -0.013
2015Q4 2015-10-01 00:00:00 0.157 0.208 0.009 0.199 0.042 0.958 0.002 0.041 2 2 -0.547 0.796 0.249 -0.771 -0.453 0.343 -0.044
2016Q1 2016-01-01 00:00:00 0.156 0.207 0.008 0.199 0.039 0.961 0.002 0.041 2 2 -0.378 0.796 0.418 -0.706 -0.472 0.324 0.055
2016Q2 2016-04-01 00:00:00 0.146 0.206 0.009 0.197 0.044 0.956 0.002 0.041 2.225 2 -0.249 0.796 0.547 -0.895 -0.453 0.343 0.113
2016Q3 2016-07-01 00:00:00 0.161 0.205 0.009 0.196 0.045 0.955 0.002 0.04 2 2 -0.363 0.796 0.433 -0.694 -0.412 0.384 0.031
2016Q4 2016-10-01 00:00:00 0.142 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.452 0.796 0.344 -0.641 -0.402 0.394 -0.022
2017Q1 2017-01-01 00:00:00 0.14 0.205 0.008 0.196 0.041 0.959 0.002 0.04 2 2 -0.333 0.796 0.463 -0.653 -0.412 0.384 0.047
2017Q2 2017-04-01 00:00:00 0.126 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.462 0.796 0.334 -0.59 -0.396 0.4 -0.031
2017Q3 2017-07-01 00:00:00 0.133 0.206 0.009 0.197 0.042 0.958 0.002 0.041 2 2 -0.494 0.796 0.302 -0.3 -0.409 0.386 -0.045
2017Q4 2017-10-01 00:00:00 0.125 0.209 0.011 0.198 0.053 0.947 0.002 0.041 2 2 -0.352 0.796 0.444 0.322 -0.426 0.369 0.03
2018Q1 2018-01-01 00:00:00 0.125 0.216 0.013 0.203 0.059 0.941 0.003 0.044 3.412 3 -0.161 0.796 0.634 0.627 -0.411 0.384 0.1
2018Q2 2018-04-01 00:00:00 0.183 0.21 0.013 0.197 0.06 0.94 0.003 0.041 2 2 -0.26 0.796 0.535 0.645 -0.361 0.434 0.04
2018Q3 2018-07-01 00:00:00 0.155 0.206 0.01 0.196 0.048 0.952 0.002 0.04 2 2 -0.477 0.796 0.318 0.753 -0.341 0.455 -0.087
2018Q4 2018-10-01 00:00:00 0.194 0.21 0.01 0.2 0.047 0.953 0.002 0.042 2 2 -0.33 0.796 0.466 0.375 -0.368 0.427 0.011
2019Q1 2019-01-01 00:00:00 0.164 0.209 0.009 0.2 0.044 0.956 0.002 0.042 2 2 -0.395 0.796 0.4 0.47 -0.361 0.435 -0.029
2019Q2 2019-04-01 00:00:00 0.145 0.211 0.01 0.2 0.049 0.951 0.002 0.042 2 2 -0.374 0.796 0.422 0.774 -0.368 0.428 -0.019
2019Q3 2019-07-01 00:00:00 0.126 0.217 0.014 0.202 0.066 0.934 0.003 0.044 2 2 -0.425 0.796 0.371 1.412 -0.369 0.427 -0.055
2019Q4 2019-10-01 00:00:00 0.115 0.219 0.016 0.203 0.071 0.929 0.003 0.044 2 2 -0.445 0.796 0.351 1.583 -0.38 0.416 -0.062
2020Q1 2020-01-01 00:00:00 0.107 0.207 0.008 0.199 0.04 0.96 0.002 0.041 2 2 -0.346 0.796 0.45 -0.238 -0.393 0.403 0.024
2020Q2 2020-04-01 00:00:00 0.104 0.245 0.035 0.21 0.142 0.858 0.009 0.052 13.353 13 -0.984 0.796 -0.188 -8.922 -0.384 0.412 0.021
2020Q3 2020-07-01 00:00:00 0.301 0.208 0.009 0.199 0.043 0.957 0.002 0.041 3.088 3 -0.055 0.796 0.741 -1.897 -0.504 0.292 0.241
2020Q4 2020-10-01 00:00:00 0.489 0.204 0.009 0.195 0.044 0.956 0.002 0.04 2 2 -0.347 0.796 0.448 -1.226 -0.414 0.382 0.048
2021Q1 2021-01-01 00:00:00 0.388 0.213 0.012 0.201 0.057 0.943 0.003 0.043 3.769 4 0.055 0.796 0.85 -0.314 -0.401 0.395 0.211
2021Q2 2021-04-01 00:00:00 0.352 0.226 0.017 0.209 0.073 0.927 0.004 0.047 5.679 6 0.616 0.796 1.412 0.878 -0.31 0.486 0.383
2021Q3 2021-07-01 00:00:00 0.508 0.223 0.015 0.208 0.067 0.933 0.003 0.046 4.717 5 0.384 0.796 1.18 1.171 -0.125 0.671 0.202
2021Q4 2021-10-01 00:00:00 0.462 0.231 0.02 0.211 0.087 0.913 0.005 0.049 5.74 6 0.497 0.796 1.292 2.32 -0.023 0.773 0.177
2022Q1 2022-01-01 00:00:00 0.458 0.224 0.016 0.208 0.071 0.929 0.004 0.047 5.032 5 0.692 0.796 1.488 1.488 0.081 0.877 0.243
2022Q2 2022-04-01 00:00:00 0.5 0.209 0.011 0.198 0.052 0.948 0.002 0.042 2.722 3 0.391 0.796 1.187 1.046 0.203 0.999 0.078
2022Q3 2022-07-01 00:00:00 0.445 0.21 0.011 0.199 0.053 0.947 0.002 0.042 2.98 3 0.458 0.796 1.253 1.145 0.241 1.037 0.089
2022Q4 2022-10-01 00:00:00 0.429 0.208 0.011 0.197 0.052 0.948 0.002 0.041 2 2 0.356 0.796 1.151 1.196 0.284 1.08 0.023
2023Q1 2023-01-01 00:00:00 0.384 0.21 0.011 0.2 0.051 0.949 0.002 0.042 2 2 0.357 0.796 1.153 1.264 0.298 1.094 0.016
2023Q2 2023-04-01 00:00:00 0.349 0.205 0.009 0.196 0.042 0.958 0.002 0.04 2 2 0.177 0.796 0.973 1.225 0.31 1.106 -0.085
2023Q3 2023-07-01 00:00:00 0.306 0.209 0.01 0.198 0.048 0.952 0.002 0.041 3.216 3 -0.211 0.796 0.585 1.705 0.284 1.079 -0.261
2023Q4 2023-10-01 00:00:00 0.343 0.207 0.009 0.198 0.044 0.956 0.002 0.041 2.972 3 -0.267 0.796 0.529 1.879 0.185 0.98 -0.248
2024Q1 2024-01-01 00:00:00 0.326 0.211 0.013 0.198 0.059 0.941 0.003 0.042 2 2 0.184 0.796 0.98 1.426 0.094 0.89 0.028
2024Q2 2024-04-01 00:00:00 0.318 0.207 0.01 0.197 0.046 0.954 0.002 0.041 2 2 -0.085 0.796 0.711 1.653 0.112 0.908 -0.128

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