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Finance and Economics Discussion Series: Data for FEDS 2012-54 ♣

The Aggregate Demand Effects of Short- and Long-Term Interest Rates

Michael T. Kiley

Figure 1: Inflation and Interest Rate Data 1964Q1 to 2007Q4

Date (YY:Q) Output (natural logarithm of real GDP 2005cw dollars with trend removed by Hodrick-Prescott filter as described in text_ Inflation (percent change in GDP price index at an annual rate) Nominal Federal Funds Rate annual rate quarterly average Yield on 10-yr Treasury Note BBB corporate bond rate Expected inflation next 10 years
64:1 -5.1191 1.4408 3.5733 4.0202 4.7054 NaN
64:2 -4.7244 1.3332 3.6018 4.0427 4.7259 NaN
64:3 -4.1235 1.9814 3.5667 4.0362 4.6986 NaN
64:4 -4.597 1.8296 3.6934 4.016 4.6849 NaN
65:1 -2.9225 1.7001 4.1103 4.0458 4.6611 NaN
65:2 -2.3284 1.7734 4.2199 4.0516 4.6952 NaN
65:3 -1.0747 1.7455 4.2169 4.0921 4.7668 NaN
65:4 0.5521 2.4549 4.3156 4.324 4.8453 NaN
66:1 2.2179 2.4597 4.7265 4.6282 5.0502 NaN
66:2 1.7889 3.7594 5.1072 4.6365 5.3818 NaN
66:3 1.6807 3.705 5.638 5.0092 5.7689 NaN
66:4 1.7212 3.5171 5.8 4.8575 6.0467 NaN
67:1 1.8289 1.9577 5.0053 4.4296 5.7826 NaN
67:2 1.0771 2.4432 4.1275 4.6839 5.8854 NaN
67:3 1.0959 3.6371 4.025 5.1126 6.2459 NaN
67:4 1.0765 4.3698 4.3223 5.5178 6.6517 NaN
68:1 2.3334 4.2857 4.9743 5.4861 6.7619 NaN
68:2 3.2302 4.441 6.2516 5.625 6.9618 NaN
68:3 3.1215 3.8504 6.2125 5.3297 6.7963 NaN
68:4 2.7595 5.5109 6.183 5.6472 6.9652 NaN
69:1 3.524 4.0089 6.8823 6.0621 7.3275 NaN
69:2 3.0129 5.3125 8.812 6.2537 7.5452 NaN
69:3 2.8377 5.7582 9.5325 6.7696 7.8877 NaN
69:4 1.5578 4.9819 9.4875 7.2388 8.3625 NaN
70:1 0.5882 5.5064 9.0653 7.3058 8.7619 NaN
70:2 -0.0464 5.6955 8.3171 7.653 8.9915 NaN
70:3 0.0215 3.1531 7.0369 7.3916 9.4443 NaN
70:4 -1.8657 5.0391 5.8054 6.7584 9.3049 NaN
71:1 0.0313 5.9802 3.9923 5.8855 8.5257 NaN
71:2 -0.2281 5.3272 4.7359 6.1451 8.6055 NaN
71:3 -0.2593 3.9688 5.7049 6.3862 8.7063 NaN
71:4 -0.8089 3.1747 4.9316 6.0927 8.4042 NaN
72:1 0.1358 6.4873 3.6599 6.2012 8.2168 NaN
72:2 1.6521 2.3002 4.4555 6.3113 8.2064 NaN
72:3 1.7787 3.6501 4.9214 6.3967 8.151 NaN
72:4 2.586 4.653 5.3537 6.4216 7.9673 NaN
73:1 4.2867 5.1981 6.8498 6.6645 7.9396 NaN
73:2 4.613 6.6122 8.2471 6.82 8.1648 NaN
73:3 3.2559 7.5621 11.2964 7.2988 8.7443 NaN
73:4 3.3851 6.7993 10.665 6.8884 8.5916 NaN
74:1 1.6862 8.1805 9.9258 7.1849 9.0366 NaN
74:2 1.126 8.8532 12.081 7.9378 10.6719 NaN
74:3 -0.6813 12.2673 13.0479 8.3223 12.2953 NaN
74:4 -1.8871 12.1644 9.9374 7.6855 11.7953 NaN
75:1 -3.9199 9.1062 6.6012 7.4647 10.7223 NaN
75:2 -3.9652 5.7773 5.6463 7.9405 10.8709 NaN
75:3 -3.0991 7.3985 6.4432 8.1908 10.7026 NaN
75:4 -2.6029 6.9974 5.6437 8.1058 10.47 NaN
76:1 -1.1541 4.464 5.0164 7.7919 9.6688 NaN
76:2 -1.2012 4.1878 5.4108 7.7938 9.5939 NaN
76:3 -1.506 5.3223 5.5028 7.7496 9.3467 NaN
76:4 -1.5731 6.7971 5.0639 7.2237 8.9666 NaN
77:1 -1.2066 6.6727 4.8371 7.3612 8.962 NaN
77:2 -0.0233 6.3394 5.3693 7.4268 8.8776 NaN
77:3 0.9679 5.4947 6.0742 7.4239 8.7586 NaN
77:4 0.1691 6.7044 6.8261 7.7003 9.0587 NaN
78:1 -0.2649 6.5532 7.0891 8.1376 9.2265 NaN
78:2 2.8223 7.6369 7.6641 8.4028 9.6757 NaN
78:3 3.03 6.8665 8.554 8.5933 9.5458 6.2
78:4 3.5795 8.0699 10.2006 8.917 10.3193 NaN
79:1 2.9858 7.2689 10.7519 9.2255 10.5632 NaN
79:2 2.3223 9.6168 10.872 9.2203 10.6115 6.75
79:3 2.2848 8.1828 11.7302 9.1933 10.5931 NaN
79:4 1.8093 7.8417 14.7597 10.6369 12.9447 NaN
80:1 1.3839 8.6712 16.5009 12.1891 15.3259 NaN
80:2 -1.4306 8.8349 13.7026 10.6517 12.947 NaN
80:3 -2.3574 9.0253 10.4735 11.1019 13.706 8.61
80:4 -1.2627 11.1134 17.4333 12.7046 14.8353 8.82
81:1 0.0585 10.3735 18.3148 13.2448 15.3007 8.28
81:2 -1.4758 7.083 19.7585 14.0385 16.7713 7.87
81:3 -0.9993 7.2781 19.5246 15.1605 18.3991 7.62
81:4 -2.9825 6.9172 14.7698 14.4164 17.4946 7.73
82:1 -5.3655 5.5973 15.4915 14.6257 17.4155 7.16
82:2 -5.5525 4.9258 15.8484 14.1764 17.2634 6.76
82:3 -6.6656 5.5173 11.8127 13.3233 16.1794 6.765
82:4 -7.3133 4.2196 9.8729 11.1466 14.0771 6.6
83:1 -6.8037 3.4113 9.174 11.0245 13.2648 6.32
83:2 -5.3077 2.909 9.3328 10.987 12.6921 6.58
83:3 -4.0821 4.0621 10.0652 12.0649 13.6384 6.63
83:4 -2.7638 2.8794 10.0327 12.0623 13.6769 6.65
84:1 -1.571 4.9338 10.3206 12.2951 13.7599 6.58
84:2 -0.5881 3.5955 11.2924 13.6103 15.4948 6.505
84:3 -0.3505 3.2577 12.2405 13.2651 14.8227 6.05
84:4 -0.2699 2.3467 9.8476 12.0959 13.5769 5.7
85:1 -0.0617 4.548 8.9726 11.9624 13.3988 5.36
85:2 0.0497 2.0532 8.3645 11.2142 12.6454 5.475
85:3 0.8671 1.894 8.338 10.7568 12.1948 5.695
85:4 0.8898 2.445 8.5625 10.2009 11.564 5.615
86:1 1.112 2.0272 8.2566 8.9883 10.6422 5.285
86:2 0.778 1.9915 7.2665 8.0758 10.3077 5.2533
86:3 1.0018 2.5135 6.4982 7.886 10.0848 5.12
86:4 0.7475 2.8811 6.562 7.7578 9.7782 5.1067
87:1 0.5632 3.1349 6.5132 7.5545 9.2631 5.285
87:2 0.8832 2.2375 6.9766 8.6532 10.1813 5.295
87:3 1.0082 3.1424 7.1796 9.1595 10.7463 5.48
87:4 1.9657 2.8554 7.2664 9.4259 10.7997 5.14
88:1 1.7418 3.2049 6.9906 8.7736 10.0293 5.235
88:2 2.2775 3.8338 7.5242 9.2413 10.5552 5.045
88:3 2.0512 4.7175 8.4274 9.4238 10.5331 4.92
88:4 2.6355 3.2124 8.9675 9.2482 10.4004 4.6667
89:1 2.827 4.1542 10.0495 9.4948 10.6918 4.69
89:2 2.8284 3.9675 10.364 9.0563 10.2449 4.74
89:3 2.873 2.7053 9.6464 8.3745 9.841 4.53
89:4 2.3444 2.5109 9.1253 8.1874 9.7519 4.305
90:1 2.6355 4.8288 8.7237 8.7051 10.361 NaN
90:2 2.2822 4.6212 8.7152 8.9565 10.4474 4.27
90:3 1.5288 3.6997 8.6237 8.984 10.4203 4.39
90:4 -0.105 3.2838 8.1656 8.6663 10.5316 4.3
91:1 -1.3468 4.2576 6.7386 8.3257 10.151 4.315
91:2 -1.4326 2.7884 6.1235 8.4555 9.9086 4.34
91:3 -1.7732 3.0141 5.8904 8.2656 9.5321 NaN
91:4 -2.1456 2.2616 5.0045 7.6799 8.9977 4
92:1 -1.8201 2.2542 4.1625 7.67 8.9406 3.7
92:2 -1.532 2.3724 3.8967 7.691 8.7517 3.9
92:3 -1.2769 1.7753 3.3573 7.0415 8.0304 3.75
92:4 -1.0041 2.2651 3.126 7.1277 8.3933 3.6
93:1 -1.5971 2.4532 3.1304 6.6373 7.7121 3.5
93:2 -1.7383 2.1669 3.0883 6.3101 7.382 3.7
93:3 -1.9947 1.875 3.1507 5.8768 6.9158 3.45
93:4 -1.4664 2.0692 3.0775 5.8618 6.9439 3.45
94:1 -1.2833 2.1997 3.3102 6.3327 7.2922 3.45
94:2 -0.7126 1.9268 4.0762 7.3203 8.358 3.5
94:3 -0.8603 2.2421 4.6509 7.554 8.3716 3.5
94:4 -0.5475 2.1055 5.3762 8.0528 9.0652 3.5
95:1 -1.0958 2.3858 6.0632 7.7151 8.573 3.3
95:2 -1.676 1.7825 6.2931 6.8117 7.6996 3.35
95:3 -1.6355 1.6865 6.0528 6.5566 7.4281 3.2
95:4 -1.7386 2.0495 5.9695 6.0912 6.9537 3
96:1 -1.8551 2.1601 5.5913 6.1252 7.1138 3
96:2 -0.9413 1.469 5.4596 6.9417 7.7562 3
96:3 -0.8764 1.9775 5.5274 6.945 7.793 3
96:4 -0.5927 1.8245 5.4985 6.5232 7.1968 3
97:1 -0.6291 2.0302 5.4983 6.7435 7.5497 3
97:2 0.0397 1.7786 5.7591 6.9036 7.684 2.85
97:3 0.4839 1.1153 5.77 6.4642 7.2091 3
97:4 0.4449 1.5167 5.7413 6.1187 6.9611 2.65
98:1 0.5821 0.5966 5.7561 5.8187 6.7657 2.6
98:2 0.6745 0.9846 5.7342 5.8422 6.795 2.5
98:3 1.1831 1.4911 5.7704 5.4407 6.7292 2.5
98:4 2.0977 1.053 5.0509 5.0069 6.7478 2.5
99:1 2.1838 1.6902 4.9148 5.4255 6.9228 2.3
99:2 2.1626 1.6785 4.9299 5.9291 7.3315 2.5
99:3 2.6275 1.4003 5.2979 6.3335 7.857 2.5
99:4 3.6101 1.6382 5.526 6.5796 8.0989 2.5
00:1 3.0748 3.0337 5.9226 6.7817 8.3686 2.5
00:2 4.2123 2.0263 6.5665 6.5322 8.6449 2.5
00:3 3.5035 2.3534 6.8333 6.2089 8.3122 2.5
00:4 3.3031 2.0222 6.7824 5.855 8.0707 2.5
01:1 2.1846 2.7501 5.8381 5.371 7.5738 2.5
01:2 2.0503 2.7754 4.4828 5.5789 7.6298 2.5
01:3 0.9882 1.2772 3.6135 5.3261 7.3967 2.5
01:4 0.5535 1.1241 2.1869 5.1242 7.3151 2.55
02:1 0.6218 1.4444 1.7727 5.4609 7.7283 2.5
02:2 0.3719 1.7568 1.7901 5.4267 7.7568 2.5
02:3 0.0991 1.7491 1.7797 4.5967 7.4124 2.5
02:4 -0.6436 2.3017 1.4753 4.34 7.1689 2.45
03:1 -1.0027 2.8062 1.2751 4.2027 6.5753 2.5
03:2 -0.9327 1.1571 1.2721 3.8407 5.7329 2.5
03:3 -0.0725 2.2024 1.0362 4.4523 6.111 2.5
03:4 0.0576 2.0976 1.0156 4.4846 5.922 2.5
04:1 -0.0543 3.3895 1.0223 4.1862 5.5269 2.5
04:2 -0.1801 3.3942 1.0292 4.8064 6.1767 2.5
04:3 -0.2041 2.9254 1.4618 4.4953 5.8539 2.5
04:4 -0.1529 2.9246 1.9969 4.3479 5.5135 2.5
05:1 0.111 3.6937 2.5348 4.4399 5.5046 2.45
05:2 -0.2056 2.6636 3.0297 4.2807 5.5325 2.5
05:3 -0.1738 4.0939 3.5683 4.3354 5.5579 2.5
05:4 -0.4192 3.3226 4.1173 4.6485 5.9689 2.5
06:1 0.0796 2.9504 4.6207 4.7241 6.0572 2.5
06:2 -0.2697 3.512 5.1007 5.2169 6.5889 2.5
06:3 -1.009 3.0036 5.4631 5.0242 6.5351 2.5
06:4 -1.0828 1.8275 5.4631 4.7545 6.215 2.5
07:1 -1.6967 4.542 5.4737 4.8128 6.1984 2.35
07:2 -1.549 2.7233 5.4667 4.9804 6.3963 2.4
07:3 -1.5671 1.2833 5.2796 4.9006 6.6433 2.4
07:4 -1.8895 1.8706 4.6644 4.4579 6.4712 2.4
Return to Figure 1

Figure 2: Impulse Response to Monetary Policy Shock (Blue-Optimization-based; Red-Semi-structural; Solid-Treasury Yields; Dashed-Corporate Bond Yields)

X-axis periods since shock Panel a policy rate at annual rate optimization-based model estimated using Treasury Yields Panel a policy rate at annual rate semi-structural model estimated using Treasury Yields Panel a policy rate at annual rate optimization-based model estimated using Private Yields Panel a policy rate at annual rate semi-structural model estimated using Private Yields Panel b long-term interest rate at annual rate optimization-based model estimated using Treasury Yields Panel b long-term interest rate at annual rate semi-structural model estimated using Treasury Yields Panel b long-term interest rate at annual rate optimization-based model estimated using Private Yields Panel b long-term interest rate at annual rate semi-structural model estimated using Private Yields Panel c output (percent) optimization-based model estimated using Treasury Yields Panel c output (percent) semi-structural model estimated using Treasury Yields Panel c output (percent) optimization-based model estimated using Private Yields Panel c output (percent) semi-structural model estimated using Private Yields Panel d inflation rate at annual rate optimization-based model estimated using Treasury Yields Panel d inflation rate at annual rate semi-structural model estimated using Treasury Yields Panel d inflation rate at annual rate optimization-based model estimated using Private Yields Panel d inflation rate at annual rate semi-structural model estimated using Private Yields
1 0.9727 0.9784 0.9814 0.9867 0.2049 0.208 0.2472 0.2534 -0.097 -0.0724 -0.079 -0.0619 -0.0061 -0.0158 -0.0009 -0.0069
2 1.0206 1.0088 1.0093 0.9973 0.1851 0.1882 0.2283 0.2346 -0.1784 -0.1505 -0.1444 -0.1293 -0.0104 -0.0269 -0.0016 -0.0117
3 0.8026 0.7757 0.7781 0.7555 0.1635 0.1672 0.2081 0.2151 -0.2446 -0.215 -0.1975 -0.1855 -0.0134 -0.0345 -0.002 -0.0151
4 0.7119 0.6868 0.7078 0.687 0.1471 0.1516 0.1934 0.2012 -0.2987 -0.2639 -0.2407 -0.2281 -0.0154 -0.0395 -0.0023 -0.0173
5 0.6811 0.6588 0.6994 0.6791 0.1325 0.1378 0.1801 0.1888 -0.3422 -0.2989 -0.2755 -0.2586 -0.0166 -0.0424 -0.0025 -0.0186
6 0.6369 0.6126 0.6659 0.6433 0.1183 0.1245 0.1667 0.1762 -0.3762 -0.3218 -0.3026 -0.2788 -0.0173 -0.0439 -0.0026 -0.0194
7 0.5829 0.5567 0.6198 0.5963 0.105 0.112 0.1538 0.1642 -0.4016 -0.3349 -0.323 -0.2907 -0.0175 -0.0441 -0.0027 -0.0196
8 0.5322 0.506 0.5787 0.5563 0.0927 0.1006 0.1417 0.1531 -0.4194 -0.3399 -0.3376 -0.296 -0.0175 -0.0435 -0.0027 -0.0195
9 0.4858 0.4607 0.5419 0.5212 0.0813 0.0902 0.1304 0.1428 -0.4308 -0.3386 -0.3471 -0.2962 -0.0172 -0.0423 -0.0026 -0.0192
10 0.4418 0.4181 0.5059 0.4873 0.0709 0.0807 0.1198 0.1331 -0.4364 -0.3325 -0.3523 -0.2926 -0.0167 -0.0407 -0.0026 -0.0186
11 0.3998 0.3782 0.4709 0.4549 0.0614 0.072 0.1098 0.124 -0.4371 -0.3225 -0.3539 -0.2861 -0.0161 -0.0387 -0.0025 -0.018
12 0.3602 0.3412 0.4374 0.4245 0.0527 0.0642 0.1005 0.1155 -0.4336 -0.3098 -0.3523 -0.2775 -0.0154 -0.0366 -0.0024 -0.0172
13 0.3231 0.3072 0.4057 0.396 0.0448 0.057 0.0918 0.1076 -0.4265 -0.2952 -0.348 -0.2674 -0.0147 -0.0343 -0.0023 -0.0165
14 0.2886 0.276 0.3755 0.3694 0.0376 0.0506 0.0837 0.1002 -0.4165 -0.2792 -0.3416 -0.2563 -0.0139 -0.032 -0.0022 -0.0156
15 0.2564 0.2474 0.347 0.3443 0.0311 0.0449 0.0762 0.0933 -0.4041 -0.2625 -0.3333 -0.2446 -0.0131 -0.0297 -0.0021 -0.0148
16 0.2265 0.2213 0.32 0.3209 0.0254 0.0397 0.0692 0.0869 -0.3897 -0.2454 -0.3236 -0.2326 -0.0122 -0.0275 -0.002 -0.014
17 0.199 0.1975 0.2946 0.299 0.0202 0.035 0.0627 0.0809 -0.3738 -0.2283 -0.3128 -0.2205 -0.0114 -0.0253 -0.0019 -0.0132
18 0.1737 0.176 0.2707 0.2786 0.0156 0.0308 0.0568 0.0753 -0.3568 -0.2115 -0.301 -0.2085 -0.0106 -0.0232 -0.0018 -0.0124
19 0.1505 0.1565 0.2483 0.2595 0.0115 0.0271 0.0512 0.0701 -0.3389 -0.1951 -0.2887 -0.1966 -0.0098 -0.0212 -0.0017 -0.0117
20 0.1293 0.1389 0.2273 0.2416 0.008 0.0238 0.0462 0.0652 -0.3205 -0.1793 -0.2758 -0.1852 -0.009 -0.0193 -0.0016 -0.011
21 0.11 0.123 0.2078 0.225 0.0048 0.0209 0.0415 0.0607 -0.3019 -0.1643 -0.2628 -0.1741 -0.0083 -0.0175 -0.0015 -0.0103
22 0.0926 0.1088 0.1895 0.2095 0.0022 0.0182 0.0372 0.0565 -0.2831 -0.1501 -0.2495 -0.1634 -0.0076 -0.0159 -0.0014 -0.0096
23 0.0769 0.096 0.1726 0.195 -0.0002 0.0159 0.0333 0.0525 -0.2645 -0.1367 -0.2363 -0.1532 -0.0069 -0.0144 -0.0013 -0.009
24 0.0627 0.0846 0.1568 0.1815 -0.0021 0.0139 0.0297 0.0489 -0.2462 -0.1241 -0.2232 -0.1435 -0.0063 -0.0129 -0.0012 -0.0084
25 0.0501 0.0744 0.1422 0.1689 -0.0038 0.012 0.0264 0.0455 -0.2282 -0.1124 -0.2103 -0.1343 -0.0057 -0.0116 -0.0011 -0.0079
26 0.0389 0.0653 0.1288 0.1572 -0.0052 0.0104 0.0234 0.0423 -0.2108 -0.1016 -0.1977 -0.1256 -0.0051 -0.0105 -0.001 -0.0073
27 0.029 0.0572 0.1163 0.1463 -0.0063 0.009 0.0207 0.0394 -0.194 -0.0916 -0.1854 -0.1174 -0.0045 -0.0094 -0.001 -0.0068
28 0.0203 0.05 0.1048 0.1362 -0.0072 0.0078 0.0183 0.0366 -0.1779 -0.0823 -0.1735 -0.1096 -0.0041 -0.0084 -0.0009 -0.0064
29 0.0127 0.0436 0.0943 0.1267 -0.0079 0.0067 0.016 0.0341 -0.1625 -0.0739 -0.162 -0.1023 -0.0036 -0.0075 -0.0008 -0.006
30 0.006 0.038 0.0846 0.1179 -0.0084 0.0058 0.014 0.0317 -0.1478 -0.0662 -0.151 -0.0955 -0.0032 -0.0066 -0.0007 -0.0055
31 0.0004 0.033 0.0757 0.1097 -0.0088 0.0049 0.0122 0.0295 -0.1339 -0.0592 -0.1405 -0.089 -0.0028 -0.0059 -0.0007 -0.0052
32 -0.0045 0.0286 0.0676 0.1021 -0.009 0.0042 0.0106 0.0274 -0.1209 -0.0528 -0.1304 -0.083 -0.0024 -0.0052 -0.0006 -0.0048
33 -0.0086 0.0248 0.0602 0.095 -0.0091 0.0036 0.0091 0.0255 -0.1086 -0.047 -0.1208 -0.0774 -0.0021 -0.0046 -0.0006 -0.0045
34 -0.012 0.0214 0.0534 0.0883 -0.0091 0.0031 0.0078 0.0237 -0.0971 -0.0417 -0.1118 -0.0721 -0.0018 -0.0041 -0.0005 -0.0042
35 -0.0148 0.0184 0.0473 0.0822 -0.0091 0.0026 0.0066 0.0221 -0.0864 -0.037 -0.1032 -0.0672 -0.0015 -0.0036 -0.0005 -0.0039
36 -0.017 0.0158 0.0417 0.0765 -0.0089 0.0022 0.0056 0.0206 -0.0765 -0.0328 -0.0951 -0.0626 -0.0013 -0.0032 -0.0004 -0.0036
37 -0.0188 0.0136 0.0366 0.0711 -0.0087 0.0018 0.0046 0.0191 -0.0674 -0.029 -0.0875 -0.0583 -0.001 -0.0028 -0.0004 -0.0034
38 -0.0201 0.0116 0.0321 0.0662 -0.0084 0.0015 0.0038 0.0178 -0.0589 -0.0255 -0.0803 -0.0543 -0.0008 -0.0025 -0.0004 -0.0031
39 -0.021 0.0099 0.0279 0.0616 -0.0081 0.0013 0.0031 0.0165 -0.0512 -0.0225 -0.0736 -0.0505 -0.0007 -0.0021 -0.0003 -0.0029
40 -0.0216 0.0084 0.0242 0.0573 -0.0078 0.0011 0.0024 0.0154 -0.0441 -0.0198 -0.0673 -0.047 -0.0005 -0.0019 -0.0003 -0.0027
Return to Figure 2

Figure 3: Long-run Inflation Expectations (Black) and Target Inflation (Blue-Optimization-based; Red-Semi-structural; Solid-Treasury Yields; Dashed-Corporate Bond Yields)

Date (YY:Q) Expected inflation next 10 years Target Inflation from optimization-based model estimated using Treasury Yields Target Inflation from semi-structural model estimated using Treasury Yields Target Inflation from optimization-based model estimated usingPrivate Yields Target Inflation from semi-structural model estimated using Private Yields
64:1 NaN 3.8833 3.0381 3.2395 2.7419
64:2 NaN 3.8828 3.0805 3.2363 2.7968
64:3 NaN 3.9066 3.1302 3.2808 2.8591
64:4 NaN 3.9296 3.1919 3.327 2.9308
65:1 NaN 3.9505 3.2296 3.3756 2.9872
65:2 NaN 3.9873 3.305 3.442 3.0785
65:3 NaN 4.0305 3.3756 3.516 3.17
65:4 NaN 4.0883 3.464 3.5794 3.2557
66:1 NaN 4.1423 3.5507 3.6372 3.3409
66:2 NaN 4.157 3.6127 3.7003 3.4441
66:3 NaN 4.2235 3.7063 3.7697 3.5378
66:4 NaN 4.2338 3.7433 3.8441 3.6349
67:1 NaN 4.2493 3.7839 3.9027 3.7147
67:2 NaN 4.3642 3.931 4.002 3.84
67:3 NaN 4.474 4.0613 4.1071 3.9606
67:4 NaN 4.569 4.1797 4.2049 4.0749
68:1 NaN 4.5838 4.2075 4.2589 4.138
68:2 NaN 4.5993 4.2459 4.2961 4.1941
68:3 NaN 4.6068 4.2793 4.335 4.256
68:4 NaN 4.6787 4.3729 4.3894 4.3307
69:1 NaN 4.7539 4.4565 4.4534 4.4047
69:2 NaN 4.7558 4.4835 4.4655 4.4402
69:3 NaN 4.8434 4.5811 4.5212 4.508
69:4 NaN 4.9534 4.708 4.6106 4.6131
70:1 NaN 5.0215 4.7835 4.7121 4.7208
70:2 NaN 5.1402 4.9073 4.8089 4.8206
70:3 NaN 5.2074 4.9751 4.957 4.9665
70:4 NaN 5.2164 5.0065 5.0444 5.0672
71:1 NaN 5.1825 4.9565 5.0717 5.0788
71:2 NaN 5.2315 5.0274 5.1056 5.1263
71:3 NaN 5.3022 5.1019 5.1638 5.1838
71:4 NaN 5.3585 5.1674 5.2352 5.2572
72:1 NaN 5.4411 5.2508 5.3018 5.3204
72:2 NaN 5.4933 5.3052 5.3526 5.3688
72:3 NaN 5.5577 5.3903 5.4119 5.4425
72:4 NaN 5.596 5.4348 5.4432 5.4788
73:1 NaN 5.6175 5.4613 5.4478 5.49
73:2 NaN 5.6277 5.4915 5.4673 5.5303
73:3 NaN 5.6345 5.5166 5.474 5.5562
73:4 NaN 5.6459 5.5217 5.5213 5.6028
74:1 NaN 5.7316 5.6247 5.6035 5.7008
74:2 NaN 5.7977 5.6856 5.7388 5.8315
74:3 NaN 5.8406 5.7377 5.8929 5.9888
74:4 NaN 5.8463 5.7364 5.9259 6.0108
75:1 NaN 5.9274 5.8192 5.9185 5.9953
75:2 NaN 6.06 5.9357 6.007 6.0573
75:3 NaN 6.0836 5.9558 6.0072 6.041
75:4 NaN 6.1025 5.9793 6.0272 6.0515
76:1 NaN 6.0759 5.9501 5.9814 5.9928
76:2 NaN 6.0778 5.9698 5.9919 6.0067
76:3 NaN 6.0841 5.987 5.9975 6.0102
76:4 NaN 6.0244 5.936 5.994 6.0011
77:1 NaN 6.0529 5.9703 6.0236 6.0214
77:2 NaN 6.0472 5.9689 6.0276 6.015
77:3 NaN 6.0326 5.966 6.0252 6.0093
77:4 NaN 6.0529 6.0107 6.0565 6.0468
78:1 NaN 6.1185 6.0841 6.0974 6.0793
78:2 NaN 6.1097 6.0649 6.1331 6.0941
78:3 6.2 6.0928 6.08 6.0945 6.0707
78:4 NaN 6.2264 6.2191 6.2544 6.2373
79:1 NaN 6.4061 6.411 6.3946 6.3896
79:2 6.75 6.5246 6.5368 6.5046 6.5079
79:3 NaN 6.8302 6.8358 6.8126 6.8185
79:4 NaN 7.283 7.2868 7.3023 7.3123
80:1 NaN 7.7965 7.7928 7.8333 7.8429
80:2 NaN 8.0215 8.0284 8.0187 8.0407
80:3 8.61 8.5196 8.5082 8.5191 8.5257
80:4 8.82 8.6728 8.7497 8.6178 8.6816
81:1 8.28 8.149 8.2459 8.0909 8.1715
81:2 7.87 7.9419 8.0611 7.8716 7.9836
81:3 7.62 7.6641 7.8113 7.5907 7.7337
81:4 7.73 7.7616 7.8473 7.7236 7.8227
82:1 7.16 7.2538 7.3601 7.2044 7.3177
82:2 6.76 6.869 6.9791 6.8214 6.9391
82:3 6.765 6.8026 6.8664 6.7821 6.864
82:4 6.6 6.6946 6.7147 6.6901 6.7329
83:1 6.32 6.4392 6.4543 6.4432 6.4712
83:2 6.58 6.7414 6.7476 6.7528 6.7627
83:3 6.63 6.729 6.7577 6.7313 6.7597
83:4 6.65 6.8221 6.8454 6.8296 6.8526
84:1 6.58 6.6266 6.6669 6.6225 6.6576
84:2 6.505 6.6396 6.7029 6.6299 6.6913
84:3 6.05 6.1896 6.2647 6.1701 6.236
84:4 5.7 5.856 5.9007 5.854 5.8943
85:1 5.36 5.3599 5.4172 5.3485 5.3999
85:2 5.475 5.6256 5.6502 5.6321 5.6546
85:3 5.695 5.8643 5.8759 5.8767 5.8855
85:4 5.615 5.7464 5.7523 5.7565 5.7593
86:1 5.285 5.4217 5.4161 5.433 5.4277
86:2 5.2533 5.3819 5.3543 5.4002 5.3852
86:3 5.12 5.2036 5.1747 5.2234 5.2067
86:4 5.1067 5.1671 5.1363 5.1855 5.1653
87:1 5.285 5.3375 5.2986 5.359 5.3271
87:2 5.295 5.4082 5.3867 5.4279 5.4088
87:3 5.48 5.5484 5.5331 5.5656 5.5538
87:4 5.14 5.2106 5.212 5.223 5.2209
88:1 5.235 5.2864 5.2713 5.3017 5.2847
88:2 5.045 5.0539 5.0611 5.0593 5.061
88:3 4.92 4.8761 4.8978 4.8704 4.8823
88:4 4.6667 4.7071 4.7352 4.7001 4.7149
89:1 4.69 4.6838 4.7272 4.6655 4.6934
89:2 4.74 4.7499 4.7872 4.7319 4.7532
89:3 4.53 4.6012 4.6251 4.5899 4.6031
89:4 4.305 4.3724 4.3934 4.3623 4.376
90:1 NaN 4.3126 4.3389 4.3094 4.3284
90:2 4.27 4.2037 4.242 4.1864 4.2165
90:3 4.39 4.3852 4.4141 4.3737 4.3961
90:4 4.3 4.3113 4.3293 4.3036 4.3255
91:1 4.315 4.2548 4.2608 4.2539 4.2671
91:2 4.34 4.3667 4.3668 4.3752 4.377
91:3 NaN 4.2097 4.2022 4.2044 4.2002
91:4 4 4.0285 4.0111 4.0458 4.0324
92:1 3.7 3.7068 3.693 3.7257 3.7148
92:2 3.9 3.9067 3.8844 3.9303 3.9096
92:3 3.75 3.7795 3.744 3.8091 3.7754
92:4 3.6 3.59 3.5598 3.6169 3.5923
93:1 3.5 3.4726 3.4355 3.4988 3.4664
93:2 3.7 3.6994 3.6517 3.7303 3.6874
93:3 3.45 3.4548 3.4069 3.4839 3.4397
93:4 3.45 3.4419 3.3964 3.4711 3.4282
94:1 3.45 3.4365 3.3992 3.4627 3.4262
94:2 3.5 3.513 3.4947 3.534 3.5147
94:3 3.5 3.4983 3.487 3.5145 3.4988
94:4 3.5 3.514 3.5178 3.5242 3.5232
95:1 3.3 3.2926 3.3019 3.2949 3.2964
95:2 3.35 3.3836 3.3788 3.3887 3.3763
95:3 3.2 3.2302 3.2264 3.2353 3.2226
95:4 3 2.9972 2.9932 2.9994 2.9858
96:1 3 2.9871 2.9807 2.9913 2.9783
96:2 3 3.0294 3.0342 3.0355 3.0292
96:3 3 2.9981 3.002 3.0024 2.9972
96:4 3 3.0067 3.0043 3.0129 2.9983
97:1 3 2.9945 2.9952 2.9992 2.9902
97:2 2.85 2.8548 2.8655 2.8564 2.854
97:3 3 3.0522 3.0487 3.0596 3.0433
97:4 2.65 2.6595 2.6609 2.6614 2.6511
98:1 2.6 2.6632 2.6586 2.6682 2.6531
98:2 2.5 2.5338 2.5334 2.5365 2.5253
98:3 2.5 2.5029 2.5006 2.5038 2.494
98:4 2.5 2.5235 2.5087 2.5312 2.5161
99:1 2.3 2.2743 2.2704 2.2767 2.2698
99:2 2.5 2.485 2.4813 2.4897 2.4829
99:3 2.5 2.5054 2.511 2.5079 2.5099
99:4 2.5 2.4926 2.506 2.4927 2.5002
00:1 2.5 2.4113 2.4323 2.4025 2.4202
00:2 2.5 2.4791 2.504 2.4692 2.4926
00:3 2.5 2.4608 2.4787 2.4487 2.4681
00:4 2.5 2.4809 2.4944 2.4705 2.4863
01:1 2.5 2.4282 2.4273 2.4219 2.4281
01:2 2.5 2.4163 2.4112 2.4179 2.4194
01:3 2.5 2.5003 2.4741 2.5137 2.5001
01:4 2.55 2.5477 2.5044 2.5738 2.5488
02:1 2.5 2.4719 2.4335 2.4984 2.4794
02:2 2.5 2.4514 2.4109 2.4777 2.4587
02:3 2.5 2.4507 2.3977 2.4784 2.4542
02:4 2.45 2.3617 2.3048 2.3889 2.3629
03:1 2.5 2.3821 2.324 2.4096 2.3758
03:2 2.5 2.4827 2.4138 2.5176 2.4657
03:3 2.5 2.4163 2.3603 2.4488 2.4049
03:4 2.5 2.4229 2.3645 2.4559 2.4077
04:1 2.5 2.3437 2.2856 2.3723 2.3232
04:2 2.5 2.3447 2.296 2.3715 2.3322
04:3 2.5 2.3771 2.3262 2.4031 2.3601
04:4 2.5 2.381 2.3323 2.4044 2.3592
05:1 2.45 2.2862 2.249 2.3023 2.2645
05:2 2.5 2.4064 2.3642 2.4234 2.3836
05:3 2.5 2.3237 2.2944 2.3314 2.3013
05:4 2.5 2.3765 2.3529 2.3822 2.3585
06:1 2.5 2.4039 2.3871 2.4074 2.3874
06:2 2.5 2.374 2.368 2.3712 2.363
06:3 2.5 2.4084 2.4 2.405 2.3966
06:4 2.5 2.4803 2.4657 2.4818 2.4655
07:1 2.35 2.1567 2.1571 2.1457 2.1434
07:2 2.4 2.3216 2.3187 2.3171 2.3108
07:3 2.4 2.4077 2.3951 2.41 2.4003
07:4 2.4 2.3649 2.3415 2.3707 2.3565
Return to Figure 3

Figure 4: Estimates of the Term Premium on the 10-yr Treasury Security

Date (YY:Q) Term Premium estimate from Kim-Wright Model Term Premium Estimate from Optimization-based model Term Premium estimate from semi-structural model
64:1 NaN -0.5448 -1.2831
64:2 NaN -0.6305 -1.3506
64:3 NaN -0.6441 -1.4516
64:4 NaN -0.6735 -1.453
65:1 NaN -0.838 -1.8989
65:2 NaN -0.9124 -1.9502
65:3 NaN -0.9888 -2.1354
65:4 NaN -0.9799 -2.1419
66:1 NaN -0.9245 -2.0497
66:2 NaN -1.0569 -2.1274
66:3 NaN -0.8697 -1.8832
66:4 NaN -1.0481 -2.2199
67:1 NaN -1.2145 -2.5324
67:2 NaN -0.8641 -1.9186
67:3 NaN -0.5853 -1.5325
67:4 NaN -0.3681 -1.1839
68:1 NaN -0.6179 -1.6949
68:2 NaN -0.8207 -2.0064
68:3 NaN -1.0404 -2.3167
68:4 NaN -0.9024 -2.0881
69:1 NaN -0.675 -1.8205
69:2 NaN -0.9154 -2.1413
69:3 NaN -0.6378 -1.7418
69:4 NaN -0.1909 -0.9685
70:1 NaN -0.0779 -0.8363
70:2 NaN 0.3364 -0.1962
70:3 NaN 0.4538 -0.0709
70:4 NaN 0.1259 -0.4681
71:1 NaN -0.4705 -1.6963
71:2 NaN -0.3819 -1.3736
71:3 NaN -0.2388 -1.1765
71:4 NaN -0.2894 -1.2454
72:1 NaN -0.2825 -1.3139
72:2 NaN -0.2454 -1.2937
72:3 NaN -0.3108 -1.2862
72:4 NaN -0.5175 -1.6741
73:1 NaN -0.7724 -2.1418
73:2 NaN -1.0176 -2.4342
73:3 NaN -1.2027 -2.6541
73:4 NaN -1.4155 -3.1468
74:1 NaN -1.1326 -2.5651
74:2 NaN -0.9288 -2.3402
74:3 NaN -0.8411 -2.1162
74:4 NaN -0.8125 -2.1311
75:1 NaN -0.1985 -1.0863
75:2 NaN 0.616 0.0857
75:3 NaN 0.6522 0.1017
75:4 NaN 0.7667 0.3308
76:1 NaN 0.6405 0.0583
76:2 NaN 0.6224 0.141
76:3 NaN 0.5525 0.0375
76:4 NaN 0.0808 -0.753
77:1 NaN 0.1845 -0.6126
77:2 NaN 0.0897 -0.8209
77:3 NaN -0.0306 -1.0038
77:4 NaN 0.0462 -0.7611
78:1 NaN 0.381 -0.2707
78:2 NaN 0.2357 -0.7446
78:3 NaN 0.2736 -0.4634
78:4 NaN 0.0481 -0.858
79:1 NaN 0.194 -0.5547
79:2 NaN -0.0565 -0.9667
79:3 NaN -0.4027 -1.5862
79:4 NaN 0.0971 -0.7469
80:1 2.2403 0.8815 0.5239
80:2 2.447 -0.0295 -0.8141
80:3 2.9282 0.6344 0.1476
80:4 2.6305 0.4214 -0.4432
81:1 2.8402 1.2966 0.9238
81:2 3.1944 1.9884 2.1798
81:3 3.7019 3.2749 4.0527
81:4 4.2338 3.595 4.8411
82:1 4.0769 4.111 5.6319
82:2 4.0119 4.1087 5.4073
82:3 4.2856 4.2102 5.6997
82:4 3.4675 2.6588 3.1702
83:1 3.3489 2.9651 3.5929
83:2 3.2143 2.6957 3.1221
83:3 3.6767 3.448 4.3849
83:4 3.7924 3.3852 4.3022
84:1 3.8464 3.4543 4.4392
84:2 4.4592 4.4902 6.1347
84:3 4.113 4.2986 5.8486
84:4 3.8364 3.9727 5.3468
85:1 3.942 4.1319 5.5958
85:2 3.6372 3.5636 4.725
85:3 3.451 2.9704 3.7367
85:4 3.015 2.4834 3.0173
86:1 2.2607 1.6436 1.6292
86:2 1.9604 1.0303 0.6977
86:3 1.9411 1.0702 0.726
86:4 1.8551 0.9609 0.5971
87:1 1.6814 0.6807 0.1507
87:2 2.4046 1.5931 1.5783
87:3 2.6794 1.8872 2.0811
87:4 2.8128 2.2875 2.6451
88:1 2.3842 1.6699 1.7628
88:2 2.5769 2.0685 2.3275
88:3 2.4653 2.1436 2.4936
88:4 2.1869 2.0323 2.2178
89:1 2.201 1.984 2.1546
89:2 1.9595 1.486 1.3566
89:3 1.643 1.1422 0.7888
89:4 1.5855 1.2598 1.0156
90:1 1.9129 1.7197 1.7159
90:2 2.0831 2.0444 2.2872
90:3 2.1297 2.0729 2.3671
90:4 2.0236 2.0561 2.3879
91:1 2.1119 2.0836 2.3961
91:2 2.3325 2.3248 2.6965
91:3 2.2464 2.3465 2.7583
91:4 1.9954 2.1905 2.5023
92:1 2.2695 2.5403 3.0099
92:2 2.3504 2.4675 2.9276
92:3 1.8938 2.0957 2.3411
92:4 2.0425 2.3031 2.6791
93:1 1.7259 1.9566 2.1858
93:2 1.4678 1.5378 1.4774
93:3 1.1998 1.319 1.1116
93:4 1.1795 1.2913 1.0049
94:1 1.4734 1.6634 1.6395
94:2 1.9561 2.3652 2.7398
94:3 1.9759 2.4787 2.9732
94:4 2.1047 2.7638 3.3777
95:1 1.7749 2.472 2.944
95:2 1.1775 1.5874 1.4947
95:3 1.0766 1.4936 1.2741
95:4 0.7899 1.2071 0.81
96:1 0.8907 1.3243 1.0075
96:2 1.4662 2.0618 2.1279
96:3 1.4546 2.0516 2.1941
96:4 1.1858 1.6543 1.5382
97:1 1.3393 1.8532 1.8894
97:2 1.4339 2.0165 2.0878
97:3 1.1521 1.4949 1.2825
97:4 0.9086 1.4184 1.1796
98:1 0.7085 1.181 0.7778
98:2 0.7353 1.2726 0.9258
98:3 0.4973 0.8481 0.2105
98:4 0.2859 0.5401 -0.2921
99:1 0.5794 1.0626 0.6265
99:2 0.9108 1.4053 1.2084
99:3 1.135 1.6838 1.6177
99:4 1.1624 1.8111 1.7906
00:1 1.2642 1.9115 2.0757
00:2 1.0211 1.4809 1.233
00:3 0.7182 1.1666 0.8735
00:4 0.4109 0.8556 0.3132
01:1 0.4202 0.6468 0.0533
01:2 0.8808 1.1036 0.7258
01:3 0.8146 1.1409 0.8768
01:4 1.0257 1.2852 1.0792
02:1 1.3495 1.7134 1.7401
02:2 1.3149 1.7184 1.7835
02:3 0.6065 0.9716 0.5748
02:4 0.4593 0.8618 0.4281
03:1 0.4159 0.7381 0.193
03:2 0.1772 0.429 -0.3433
03:3 0.6506 0.9944 0.5198
03:4 0.714 1.0155 0.6274
04:1 0.4989 0.7156 0.1658
04:2 0.9427 1.2862 1.0894
04:3 0.5879 0.9096 0.4629
04:4 0.3453 0.673 0.062
05:1 0.3578 0.6502 -0.0066
05:2 0.1907 0.3931 -0.3856
05:3 0.1049 0.3001 -0.5831
05:4 0.1762 0.4968 -0.2585
06:1 0.1281 0.436 -0.4311
06:2 0.3351 0.8085 0.2292
06:3 0.1523 0.6017 -0.0963
06:4 -0.0261 0.3772 -0.5298
07:1 0.0038 0.5173 -0.2775
07:2 0.1618 0.647 -0.1314
07:3 0.1711 0.649 -0.1112
07:4 0.0266 0.3956 -0.4911
Return to Figure 4

Figure 5: Differential Impact of Expected Short-term Interest Rates and Term Premiums (Blue-Optimization-based; Red-Semi-structural; Solid-Short-term Policy Rate; Dashed-Term Premiums)

X-axis periods since shock Panel a policy rate at annual rate optimization-based model change in policy rate Panel a policy rate at annual rate semi-structural model change in policy rate Panel a policy rate at annual rate optimization-based model change in term premium Panel a policy rate at annual rate semi-structural model change in term premium Panel b long-term interest rate at annual rate optimization-based model change in policy rate Panel b long-term interest rate at annual rate semi-structural model change in policy rate Panel b long-term interest rate at annual rate optimization-based model change in term premium Panel b long-term interest rate at annual rate semi-structural model change in term premium Panel c output (percent) optimization-based model change in policy rate Panel c output (percent) semi-structural model change in policy rate Panel c output (percent) optimization-based model change in term premium Panel c output (percent) semi-structural model change in term premium Panel d inflation rate at annual rate optimization-based model change in policy rate Panel d inflation rate at annual rate semi-structural model change in policy rate Panel d inflation rate at annual rate optimization-based model change in term premium Panel d inflation rate at annual rate semi-structural model change in term premium
1 -0.5 -0.5 0 0 -1.0072 -1.0072 -1.0072 -1.0072 0.3441 0.2434 0.1501 0.1499 0.0045 0.0279 0.0019 0.0172
2 -1 -1 0 0 -1.0196 -1.0196 -1.0196 -1.0196 0.6534 0.5296 0.285 0.3261 0.0076 0.0475 0.0033 0.0293
3 -1.5 -1.5 0 0 -1.0194 -1.0194 -1.0194 -1.0194 0.9279 0.7927 0.4047 0.4881 0.0097 0.061 0.0043 0.0376
4 -2 -2 0 0 -1.0065 -1.0065 -1.0065 -1.0065 1.1677 1.0137 0.5093 0.6241 0.0112 0.0699 0.0049 0.043
5 -2.5 -2.5 0 0 -0.9804 -0.9804 -0.9804 -0.9804 1.3726 1.1889 0.5987 0.732 0.0121 0.0753 0.0053 0.0463
6 -3 -3 0 0 -0.9409 -0.9409 -0.9409 -0.9409 1.5429 1.32 0.673 0.8127 0.0127 0.078 0.0055 0.048
7 -3.5 -3.5 0 0 -0.8875 -0.8875 -0.8875 -0.8875 1.6784 1.4094 0.7321 0.8677 0.0129 0.0786 0.0056 0.0484
8 -4 -4 0 0 -0.82 -0.82 -0.82 -0.82 1.7793 1.4596 0.7761 0.8986 0.013 0.0778 0.0057 0.0479
9 -3.6 -3.6 0 0 -0.738 -0.738 -0.738 -0.738 1.8454 1.4728 0.8049 0.9067 0.0128 0.0758 0.0056 0.0467
10 -3.24 -3.24 0 0 -0.6642 -0.6642 -0.6642 -0.6642 1.8826 1.456 0.8211 0.8964 0.0126 0.073 0.0055 0.045
11 -2.916 -2.916 0 0 -0.5978 -0.5978 -0.5978 -0.5978 1.8958 1.4167 0.8269 0.8722 0.0123 0.0697 0.0053 0.0429
12 -2.6244 -2.6244 0 0 -0.538 -0.538 -0.538 -0.538 1.8892 1.3614 0.824 0.8381 0.0119 0.0659 0.0052 0.0406
13 -2.362 -2.362 0 0 -0.4842 -0.4842 -0.4842 -0.4842 1.8665 1.2953 0.8141 0.7975 0.0114 0.062 0.005 0.0382
14 -2.1258 -2.1258 0 0 -0.4358 -0.4358 -0.4358 -0.4358 1.8309 1.2227 0.7986 0.7527 0.0109 0.058 0.0048 0.0357
15 -1.9132 -1.9132 0 0 -0.3922 -0.3922 -0.3922 -0.3922 1.785 1.1465 0.7786 0.7058 0.0104 0.054 0.0046 0.0332
16 -1.7219 -1.7219 0 0 -0.353 -0.353 -0.353 -0.353 1.7311 1.0692 0.7551 0.6583 0.0099 0.05 0.0043 0.0308
17 -1.5497 -1.5497 0 0 -0.3177 -0.3177 -0.3177 -0.3177 1.6712 0.9926 0.7289 0.6111 0.0094 0.0462 0.0041 0.0284
18 -1.3947 -1.3947 0 0 -0.2859 -0.2859 -0.2859 -0.2859 1.6069 0.9179 0.7009 0.5651 0.0089 0.0425 0.0039 0.0262
19 -1.2552 -1.2552 0 0 -0.2573 -0.2573 -0.2573 -0.2573 1.5397 0.8461 0.6716 0.5209 0.0084 0.0391 0.0037 0.0241
20 -1.1297 -1.1297 0 0 -0.2316 -0.2316 -0.2316 -0.2316 1.4706 0.7776 0.6414 0.4787 0.008 0.0358 0.0035 0.022
21 -1.0167 -1.0167 0 0 -0.2084 -0.2084 -0.2084 -0.2084 1.4006 0.713 0.6109 0.4389 0.0075 0.0328 0.0033 0.0202
22 -0.9151 -0.9151 0 0 -0.1876 -0.1876 -0.1876 -0.1876 1.3306 0.6523 0.5804 0.4016 0.007 0.0299 0.0031 0.0184
23 -0.8236 -0.8236 0 0 -0.1688 -0.1688 -0.1688 -0.1688 1.2612 0.5957 0.5501 0.3667 0.0066 0.0273 0.0029 0.0168
24 -0.7412 -0.7412 0 0 -0.1519 -0.1519 -0.1519 -0.1519 1.1929 0.5431 0.5203 0.3344 0.0062 0.0248 0.0027 0.0153
25 -0.6671 -0.6671 0 0 -0.1368 -0.1368 -0.1368 -0.1368 1.1261 0.4944 0.4912 0.3044 0.0058 0.0226 0.0025 0.0139
26 -0.6004 -0.6004 0 0 -0.1231 -0.1231 -0.1231 -0.1231 1.0612 0.4496 0.4629 0.2768 0.0054 0.0205 0.0024 0.0126
27 -0.5403 -0.5403 0 0 -0.1108 -0.1108 -0.1108 -0.1108 0.9984 0.4084 0.4355 0.2514 0.0051 0.0186 0.0022 0.0114
28 -0.4863 -0.4863 0 0 -0.0997 -0.0997 -0.0997 -0.0997 0.938 0.3705 0.4091 0.2281 0.0047 0.0169 0.0021 0.0104
29 -0.4377 -0.4377 0 0 -0.0897 -0.0897 -0.0897 -0.0897 0.8799 0.3359 0.3838 0.2068 0.0044 0.0153 0.0019 0.0094
30 -0.3939 -0.3939 0 0 -0.0808 -0.0808 -0.0808 -0.0808 0.8244 0.3043 0.3596 0.1874 0.0041 0.0138 0.0018 0.0085
31 -0.3545 -0.3545 0 0 -0.0727 -0.0727 -0.0727 -0.0727 0.7715 0.2755 0.3365 0.1696 0.0038 0.0125 0.0017 0.0077
32 -0.3191 -0.3191 0 0 -0.0654 -0.0654 -0.0654 -0.0654 0.7212 0.2493 0.3146 0.1535 0.0036 0.0113 0.0016 0.007
33 -0.2872 -0.2872 0 0 -0.0589 -0.0589 -0.0589 -0.0589 0.6734 0.2254 0.2937 0.1388 0.0033 0.0102 0.0014 0.0063
34 -0.2584 -0.2584 0 0 -0.053 -0.053 -0.053 -0.053 0.6282 0.2037 0.274 0.1254 0.0031 0.0092 0.0013 0.0057
35 -0.2326 -0.2326 0 0 -0.0477 -0.0477 -0.0477 -0.0477 0.5855 0.184 0.2554 0.1133 0.0028 0.0083 0.0012 0.0051
36 -0.2093 -0.2093 0 0 -0.0429 -0.0429 -0.0429 -0.0429 0.5452 0.1662 0.2378 0.1023 0.0026 0.0075 0.0012 0.0046
37 -0.1884 -0.1884 0 0 -0.0386 -0.0386 -0.0386 -0.0386 0.5073 0.15 0.2213 0.0924 0.0024 0.0068 0.0011 0.0042
38 -0.1696 -0.1696 0 0 -0.0348 -0.0348 -0.0348 -0.0348 0.4716 0.1354 0.2057 0.0834 0.0023 0.0061 0.001 0.0038
39 -0.1526 -0.1526 0 0 -0.0313 -0.0313 -0.0313 -0.0313 0.4381 0.1222 0.1911 0.0752 0.0021 0.0055 0.0009 0.0034
40 -0.1373 -0.1373 0 0 -0.0282 -0.0282 -0.0282 -0.0282 0.4068 0.1102 0.1774 0.0678 0.0019 0.005 0.0008 0.0031
Return to Figure 5
♣ This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Text
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Last update: November 5, 2012