Accessible Version

Unpredictable Recessions, Accessible Data

Figure 1: AUROC of Forward Term Spreads, Unadjusted vs. Adjusted for Term Premium

AUROC

Quarters Forward Term Spread Unadjusted, 95% C.I., Lower Unadjusted Unadjusted, 95% C.I., Upper Adjusted, 95% C.I., Lower Adjusted Adjusted, 95% C.I., Upper
0 0.8177 0.8569 0.8962 0.7594 0.8035 0.8477
1 0.8555 0.8897 0.9239 0.7848 0.8237 0.8627
2 0.8657 0.8971 0.9285 0.7771 0.8154 0.8536
3 0.8447 0.8768 0.9089 0.7439 0.7839 0.8239
4 0.8310 0.8627 0.8945 0.7173 0.7586 0.7998
5 0.7816 0.8165 0.8513 0.6725 0.7160 0.7596
6 0.7379 0.7764 0.8148 0.6365 0.6817 0.7270
7 0.6659 0.7081 0.7504 0.5925 0.6393 0.6862
8 0.6055 0.6517 0.6978 0.5594 0.6077 0.6561
9 0.5505 0.5984 0.6464 0.5235 0.5734 0.6234
10 0.5309 0.5812 0.6316 0.4976 0.5490 0.6003
11 0.5050 0.5555 0.6059 0.4741 0.5259 0.5778
12 0.5006 0.5538 0.6069 0.4602 0.5135 0.5668
13 0.4666 0.5210 0.5755 0.4364 0.4897 0.5430
14 0.4454 0.5020 0.5587 0.4202 0.4743 0.5285
15 0.4399 0.4982 0.5565 0.4119 0.4663 0.5207
16 0.4152 0.4740 0.5328 0.4092 0.4646 0.5201
17 0.4447 0.5075 0.5704 0.4291 0.4859 0.5428
18 0.4255 0.4872 0.5490 0.4318 0.4897 0.5476
19 0.4739 0.5373 0.6007 0.4513 0.5100 0.5687
20 0.4722 0.5351 0.5981 0.4631 0.5230 0.5829

Note: Full sample 1971:M11 to 2019:M01. Dashed lines indicate 95 percent confidence interval.

Source: Author's calculation.

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Figure 2: Median Absolute Prediction Error of Forward Term Spreads

Abs. Error

Quarters Forward Term Spread Unadjusted, 5th quantile, Lower Unadjusted Unadjusted, 95th quantile, Upper Adjusted, 5th quantile, Lower Adjusted Adjusted, 95th quantile, Upper
1 0.0471 0.3917 1.8549 0.0167 0.1864 1.5434
2 0.0582 0.5654 2.0272 0.0203 0.2639 1.8320
3 0.0623 0.7202 2.4034 0.0312 0.3513 1.8139
4 0.0520 0.8173 2.5733 0.0365 0.4345 2.0214
5 0.0955 0.9688 2.8980 0.0636 0.5438 2.2391
6 0.0849 1.1058 3.0587 0.0748 0.7008 2.5235
7 0.1199 1.1763 3.0665 0.0902 0.7928 2.6114
8 0.1078 1.2088 3.1620 0.1066 0.8791 2.7412
9 0.1087 1.2828 3.1514 0.0803 0.8842 2.7668
10 0.0896 1.2512 3.2941 0.1004 0.9688 2.7711
11 0.1406 1.2715 3.3942 0.0859 1.0041 2.7161
12 0.1169 1.2645 3.4002 0.0938 0.9944 2.7389
13 0.1198 1.3131 3.3365 0.0773 0.9923 2.7408
14 0.1025 1.3696 3.3646 0.0744 1.0496 2.8591
15 0.0882 1.3731 3.3430 0.1076 1.0141 2.8456
16 0.1541 1.3493 3.3275 0.1003 1.0498 3.1409
17 0.1374 1.4481 3.3381 0.0910 1.0262 3.1665
18 0.1616 1.4733 3.2144 0.0873 1.0657 3.2882
19 0.1428 1.5555 3.1959 0.0888 1.0846 3.3312
20 0.1555 1.5201 3.1962 0.1300 1.0859 3.3295
21 0.4722 0.5351 0.5981 0.5431 0.6020 0.6609

Note: Full sample 1971:M11 to 2019:M01. Dashed lines indicate 5th and 95th quantiles.

Source: Author's calculation.

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Figure 3: AUROC of Forward Term Spreads vs Term Spread

AUROC

Quarters Forward Term Spread Forward term spreads, 95% C.I., Lower Forward term spreads Forward term spreads, 95% C.I., Upper Term spread, 95% C.I., Lower Term Spread Term spread, 95% C.I., Upper
0 0.8177 0.8569 0.8962 0.8177 0.8569 0.8962
1 0.8555 0.8897 0.9239 0.8402 0.8766 0.9130
2 0.8657 0.8971 0.9285 0.8290 0.8653 0.9015
3 0.8447 0.8768 0.9089 0.8167 0.8541 0.8915
4 0.8310 0.8627 0.8945 0.7928 0.8319 0.8710
5 0.7816 0.8165 0.8513 0.7608 0.8024 0.8440
6 0.7379 0.7764 0.8148 0.7356 0.7776 0.8196
7 0.6659 0.7081 0.7504 0.6861 0.7318 0.7774
8 0.6055 0.6517 0.6978 0.6425 0.6914 0.7402
9 0.5505 0.5984 0.6464 0.6124 0.6641 0.7157
10 0.5309 0.5812 0.6316 0.5717 0.6253 0.6789
11 0.5050 0.5555 0.6059 0.5315 0.5858 0.6400
12 0.5006 0.5538 0.6069 0.4980 0.5517 0.6055
13 0.4666 0.5210 0.5755 0.4682 0.5216 0.5750
14 0.4454 0.5020 0.5587 0.4288 0.4805 0.5322
15 0.4399 0.4982 0.5565 0.5161 0.5663 0.6166
16 0.4152 0.4740 0.5328 0.5374 0.5886 0.6397
17 0.4447 0.5075 0.5704 0.5396 0.5928 0.6459
18 0.4255 0.4872 0.5490 0.5434 0.5996 0.6558
19 0.4739 0.5373 0.6007 0.5373 0.5954 0.6535
20 0.4722 0.5351 0.5981 0.5431 0.6020 0.6609

Note: Full sample 1971:M11 to 2019:M01. Dashed lines indicate 95 percent confidence interval.

Source: Author's calculation.

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Figure 4: AUROC of Forward Term Spreads, Unadjusted vs. Adjusted for Term Premium

AUROC

Quarters Forward Term Spread Unadjusted, 95% C.I., Lower Unadjusted Unadjusted, 95% C.I., Upper Adjusted, 95% C.I., Lower Adjusted Adjusted, 95% C.I., Upper
0 0.7869 0.8364 0.8859 0.7138 0.7678 0.8218
1 0.8132 0.8638 0.9144 0.7204 0.7715 0.8227
2 0.8450 0.8904 0.9357 0.7280 0.7770 0.8260
3 0.8337 0.8784 0.9231 0.6905 0.7411 0.7916
4 0.8259 0.8667 0.9076 0.6624 0.7124 0.7623
5 0.7844 0.8249 0.8655 0.6155 0.6668 0.7182
6 0.7465 0.7906 0.8346 0.5923 0.6438 0.6954
7 0.6767 0.7241 0.7715 0.5527 0.6052 0.6578
8 0.6091 0.6620 0.7149 0.5247 0.5777 0.6308
9 0.5275 0.5822 0.6370 0.4773 0.5322 0.5872
10 0.4911 0.5489 0.6067 0.4471 0.5038 0.5606
11 0.4580 0.5169 0.5757 0.4143 0.4730 0.5316
12 0.4466 0.5094 0.5721 0.3963 0.4585 0.5207
13 0.4878 0.5494 0.6111 0.3674 0.4301 0.4927
14 0.5272 0.5905 0.6537 0.3460 0.4114 0.4769
15 0.5452 0.6101 0.6751 0.5262 0.5938 0.6613
16 0.5654 0.6333 0.7011 0.5250 0.5957 0.6664
17 0.5558 0.6272 0.6986 0.5009 0.5742 0.6475
18 0.5692 0.6396 0.7099 0.4998 0.5744 0.6491
19 0.5201 0.5945 0.6689 0.4766 0.5523 0.6280
20 0.5049 0.5820 0.6590 0.4624 0.5406 0.6188
21 0.4459 0.5239 0.6019 0.4380 0.5171 0.5961
22 0.4092 0.4877 0.5661 0.4243 0.5047 0.5852
23 0.4434 0.5176 0.5919 0.4079 0.4870 0.5661
24 0.4513 0.5222 0.5932 0.3953 0.4738 0.5524
25 0.4868 0.5510 0.6153 0.3780 0.4525 0.5270
26 0.4894 0.5531 0.6167 0.4749 0.5495 0.6241
27 0.4927 0.5549 0.6172 0.4868 0.5552 0.6237
28 0.4701 0.5339 0.5977 0.4926 0.5642 0.6359
29 0.4507 0.5128 0.5749 0.5040 0.5713 0.6387
30 0.4292 0.4980 0.5669 0.5114 0.5819 0.6524
31 0.4267 0.4993 0.5719 0.5249 0.5971 0.6692
32 0.4885 0.5635 0.6384 0.5524 0.6279 0.7033
33 0.4717 0.5540 0.6363 0.5494 0.6258 0.7021
34 0.4837 0.5713 0.6589 0.5439 0.6199 0.6958
35 0.4304 0.5268 0.6233 0.5050 0.5863 0.6676
36 0.4130 0.5104 0.6077 0.4806 0.5559 0.6312
37 0.4517 0.5477 0.6438 0.4066 0.4908 0.5750
38 0.4675 0.5640 0.6606 0.4276 0.5026 0.5776
39 0.5590 0.6458 0.7325 0.4993 0.5829 0.6665
40 0.5985 0.6798 0.7611 0.4770 0.5550 0.6329

Note: Full sample 1981:M07 to 2019:M01. Dashed lines indicate 95 percent confidence interval.

Source: Author's calculation.

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Figure 5: Median Absolute Prediction Error of Forward Term Spreads

Abs. Error

Quarters Forward Term Spread Unadjusted, 5th quantile, Lower Unadjusted Unadjusted, 95th quantile, Upper Adjusted, 5th quantile, Lower Adjusted Adjusted, 95th quantile, Upper
1 0.0494 0.3663 1.1078 0.0147 0.1565 0.8614
2 0.0652 0.5183 1.6628 0.0177 0.2266 0.9912
3 0.0536 0.6742 2.1736 0.0278 0.2840 1.3190
4 0.0456 0.7142 2.4727 0.0317 0.3667 1.5182
5 0.0905 0.8664 2.7842 0.0524 0.4462 1.6474
6 0.0897 0.9996 2.8579 0.0541 0.5963 1.7708
7 0.0951 1.0583 2.9836 0.0845 0.6689 1.9369
8 0.0807 1.0512 3.0281 0.0873 0.7667 2.0248
9 0.0959 1.0831 3.0928 0.0768 0.7968 2.1163
10 0.0869 1.0400 3.1095 0.0843 0.8995 2.1720
11 0.1182 1.1573 3.2892 0.0865 0.9741 2.1642
12 0.0884 1.1406 3.3170 0.0906 0.9680 2.2781
13 0.1052 1.2305 3.2912 0.0767 1.0003 2.3240
14 0.0705 1.1514 3.3158 0.0857 1.0527 2.3877
15 0.0765 1.2250 3.3118 0.1264 1.0384 2.3778
16 0.1275 1.2374 3.3061 0.1016 1.0660 2.3783
17 0.0940 1.3369 3.2884 0.0918 1.0556 2.3220
18 0.1304 1.3523 3.1490 0.0926 1.0725 2.3152
19 0.1259 1.4879 3.0858 0.0898 1.0839 2.3763
20 0.1372 1.4517 3.1433 0.1361 1.0941 2.4126
21 0.1003 1.4759 3.2035 0.0859 1.0780 2.4942
22 0.0594 1.4941 3.2002 0.0867 1.1505 2.4936
23 0.0978 1.5776 3.3907 0.0957 1.1896 2.5280
24 0.1249 1.5627 3.3470 0.1005 1.1841 2.5155
25 0.1569 1.6357 3.4698 0.1011 1.2345 2.6038
26 0.1522 1.5669 3.4220 0.1266 1.2912 2.5747
27 0.1008 1.6028 3.4993 0.0986 1.3730 2.6708
28 0.1927 1.6238 3.4848 0.0892 1.3760 2.6381
29 0.2396 1.7281 3.5780 0.1343 1.4257 2.7559
30 0.2482 1.6806 3.6085 0.1673 1.4585 2.7626
31 0.2116 1.7926 3.7562 0.1612 1.5469 2.8173
32 0.2221 1.7393 3.7089 0.1035 1.5322 2.7734
33 0.2221 1.8411 3.7301 0.0956 1.5941 2.7760
34 0.2406 1.8370 3.6796 0.0811 1.5515 2.7655
35 0.2141 1.8960 3.6202 0.1007 1.6469 2.7947
36 0.2679 1.8950 3.6566 0.1063 1.6089 2.8013
37 0.2488 1.9588 3.6677 0.1397 1.6223 2.8124
38 0.2566 1.9301 3.6741 0.1210 1.5638 2.7866
39 0.2015 1.9465 3.8279 0.1272 1.6688 2.8224
40 0.2136 1.9161 3.8115 0.1015 1.7265 2.7849

Note: Full sample 1981:M07 to 2019:M01. Dashed lines indicate 5th and 95th quantiles.

Source: Author's calculation.

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Figure 6: AUROC of Forward Term Spreads vs Term Spread

AUROC

Quarters Forward Term Spread Forward term spreads, 95% C.I., Lower Forward term spreads Forward term spreads, 95% C.I., Upper Term Spread, 95% C.I., Lower Term Spread Term Spread, 95% C.I., Upper
1 0.7869 0.8364 0.8859 0.7869 0.8364 0.8859
2 0.8132 0.8638 0.9144 0.8422 0.8852 0.9281
3 0.8450 0.8904 0.9357 0.8615 0.8984 0.9353
4 0.8337 0.8784 0.9231 0.8778 0.9106 0.9435
5 0.8259 0.8667 0.9076 0.8505 0.8879 0.9254
6 0.7844 0.8249 0.8655 0.8174 0.8609 0.9045
7 0.7465 0.7906 0.8346 0.7701 0.8218 0.8734
8 0.6767 0.7241 0.7715 0.7217 0.7784 0.8350
9 0.6091 0.6620 0.7149 0.6725 0.7336 0.7948
10 0.5275 0.5822 0.6370 0.6285 0.6938 0.7591
11 0.4911 0.5489 0.6067 0.5811 0.6506 0.7201
12 0.4580 0.5169 0.5757 0.5332 0.6031 0.6731
13 0.4466 0.5094 0.5721 0.4910 0.5605 0.6299
14 0.4878 0.5494 0.6111 0.4608 0.5297 0.5986
15 0.5272 0.5905 0.6537 0.4238 0.4901 0.5564
16 0.5452 0.6101 0.6751 0.3642 0.4284 0.4927
17 0.5654 0.6333 0.7011 0.5507 0.6145 0.6784
18 0.5558 0.6272 0.6986 0.5686 0.6336 0.6986
19 0.5692 0.6396 0.7099 0.5926 0.6599 0.7272
20 0.5201 0.5945 0.6689 0.5975 0.6649 0.7322
21 0.5049 0.5820 0.6590 0.6127 0.6787 0.7447
22 0.4459 0.5239 0.6019 0.5964 0.6609 0.7255
23 0.4092 0.4877 0.5661 0.5811 0.6435 0.7059
24 0.4434 0.5176 0.5919 0.5646 0.6278 0.6910
25 0.4513 0.5222 0.5932 0.5309 0.5980 0.6651
26 0.4868 0.5510 0.6153 0.5145 0.5839 0.6533
27 0.4894 0.5531 0.6167 0.5006 0.5718 0.6430
28 0.4927 0.5549 0.6172 0.5010 0.5759 0.6507
29 0.4701 0.5339 0.5977 0.4624 0.5387 0.6150
30 0.4507 0.5128 0.5749 0.4317 0.5114 0.5911
31 0.4292 0.4980 0.5669 0.4412 0.5236 0.6060
32 0.4267 0.4993 0.5719 0.4538 0.5431 0.6324
33 0.4885 0.5635 0.6384 0.4554 0.5522 0.6491
34 0.4717 0.5540 0.6363 0.4751 0.5719 0.6687
35 0.4837 0.5713 0.6589 0.4829 0.5777 0.6724
36 0.4304 0.5268 0.6233 0.4750 0.5671 0.6593
37 0.4130 0.5104 0.6077 0.4956 0.5845 0.6734
38 0.4517 0.5477 0.6438 0.5254 0.6091 0.6927
39 0.4675 0.5640 0.6606 0.5568 0.6313 0.7058
40 0.5590 0.6458 0.7325 0.6090 0.6744 0.7398
41 0.5985 0.6798 0.7611 0.6474 0.7075 0.7677

Note: Full sample 1981:M07 to 2019:M01. Dashed lines indicate 95 percent confidence interval.

Source: Author's calculation.

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Figure 7: April 2021 Forward Term Spreads Recession Probability Curve

Probability

Quarters Forward Term Spread 95% C.I., Lower Probability of recession within year after forward 95% C.I., Upper
0 0.1508 0.1863 0.2265
1 0.0977 0.1294 0.1676
2 0.0322 0.0563 0.0927
3 0.0099 0.0243 0.0532
4 0.0029 0.0105 0.0315
5 0.0026 0.0100 0.0321
6 0.0049 0.0159 0.0436
7 0.0080 0.0230 0.0568
8 0.0486 0.0780 0.1192
9 0.0625 0.0945 0.1373
10 0.1181 0.1506 0.1886
11 0.1198 0.1525 0.1905
12 0.1340 0.1696 0.2107
13 0.1317 0.1668 0.2075
14 0.1134 0.1524 0.1996
15 0.0988 0.1368 0.1837
16 0.0701 0.1067 0.1555
17 0.0630 0.1003 0.1516
18 0.0477 0.0825 0.1335
19 0.0565 0.0995 0.1625
20 0.0483 0.0891 0.1511
21 0.0711 0.1297 0.2153
22 0.0769 0.1373 0.2239
23 0.1002 0.1749 0.2776
24 0.0930 0.1613 0.2559
25 0.0967 0.1680 0.2663
26 0.0970 0.1635 0.2542
27 0.0950 0.1608 0.2508
28 0.0965 0.1581 0.2410
29 0.0849 0.1438 0.2255
30 0.0839 0.1396 0.2164
31 0.0743 0.1292 0.2073
32 0.1001 0.1554 0.2279
33 0.1047 0.1609 0.2339
34 0.1231 0.1764 0.2424
35 0.1092 0.1621 0.2294
36 0.1159 0.1646 0.2249
37 0.0911 0.1390 0.2016
38 0.0900 0.1335 0.1897
39 0.0727 0.1163 0.1759
40 0.0680 0.1079 0.1625

Note: Probability for 2021:M04. Full sample 1981:M07 to 2019:M01. Dashed lines indicate 95 percent confidence interval.

Source: Author's calculation.

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Last Update: July 02, 2021