Discount Rate Specification and the Social Security Claiming Decision

by Brian J. Alleva
Social Security Bulletin, Vol. 76 No. 2, 2016
Table equivalent for Chart 1. Death-age boundaries for MCA categories, by discount rate: 1952 birth cohort (either sex)
Discount rate (%) Probability (in percent) that the MCA is—
62:00 63:01–66:00 66:01–69:11 70:00
0.0 76:09 79:08 86:05 120:00
0.1 76:11 79:09 86:06 120:00
0.2 77:00 79:09 86:08 120:00
0.3 77:00 79:11 86:09 120:00
0.4 77:03 80:00 86:11 120:00
0.5 77:03 80:02 87:00 120:00
0.6 77:05 80:03 87:03 120:00
0.7 77:06 80:03 87:05 120:00
0.8 77:08 80:06 87:06 120:00
0.9 77:09 80:06 87:09 120:00
1.0 77:09 80:08 87:11 120:00
1.1 78:00 80:09 88:00 120:00
1.2 78:00 80:11 88:03 120:00
1.3 78:03 81:00 88:05 120:00
1.4 78:03 81:02 88:06 120:00
1.5 78:06 81:03 88:09 120:00
1.6 78:06 81:05 89:00 120:00
1.7 78:09 81:06 89:02 120:00
1.8 78:09 81:08 89:05 120:00
1.9 79:00 81:09 89:06 120:00
2.0 79:02 81:11 89:09 120:00
2.1 79:03 82:00 90:00 120:00
2.2 79:05 82:03 90:03 120:00
2.3 79:06 82:03 90:06 120:00
2.4 79:09 82:06 90:09 120:00
2.5 79:11 82:08 91:00 120:00
2.6 80:00 82:09 91:03 120:00
2.7 80:03 83:00 91:06 120:00
2.8 80:05 83:02 91:09 120:00
2.9 80:06 83:03 92:02 120:00
3.0 80:09 83:06 92:06 120:00
3.1 80:11 83:08 92:09 120:00
3.2 81:00 83:11 93:00 120:00
3.3 81:03 84:00 93:06 120:00
3.4 81:06 84:03 93:09 120:00
3.5 81:09 84:06 94:02 120:00
3.6 81:11 84:08 94:06 120:00
3.7 82:02 84:11 95:00 120:00
3.8 82:05 85:02 95:05 120:00
3.9 82:06 85:03 95:11 120:00
4.0 82:09 85:06 96:03 120:00
4.1 83:00 85:09 96:09 120:00
4.2 83:05 86:00 97:05 120:00
4.3 83:08 86:05 98:00 120:00
4.4 83:11 86:08 98:06 120:00
4.5 84:03 86:11 99:02 120:00
4.6 84:06 87:03 99:11 120:00
4.7 84:09 87:06 100:06 120:00
4.8 85:02 87:11 101:05 120:00
4.9 85:06 88:03 102:03 120:00
5.0 85:09 88:06 103:03 120:00
5.1 86:03 89:00 104:03 120:00
5.2 86:08 89:03 105:05 120:00
5.3 87:00 89:09 106:08 120:00
5.4 87:06 90:03 108:00 120:00
5.5 88:00 90:08 109:08 120:00
5.6 88:05 91:02 111:06 120:00
5.7 89:00 91:08 113:09 120:00
5.8 89:06 92:03 116:06 120:00
5.9 90:02 92:09 120:00 120:00
6.0 90:09 93:06 120:00 120:00
6.1 91:05 94:02 120:00 120:00
6.2 92:02 94:11 120:00 120:00
6.3 93:00 95:08 120:00 120:00
6.4 93:11 96:06 120:00 120:00
6.5 94:09 97:06 120:00 120:00
6.6 95:11 98:08 120:00 120:00
6.7 97:02 99:09 120:00 120:00
6.8 98:06 101:03 120:00 120:00
6.9 100:02 102:09 120:00 120:00
7.0 102:00 104:09 120:00 120:00
7.1 104:03 107:00 120:00 120:00
7.2 107:03 110:00 120:00 120:00
7.3 111:00 114:00 120:00 120:00
7.4 117:00 120:00 120:00 120:00
7.5 120:00 120:00 120:00 120:00
7.6 120:00 120:00 120:00 120:00
7.7 120:00 120:00 120:00 120:00
7.8 120:00 120:00 120:00 120:00
7.9 120:00 120:00 120:00 120:00
8.0 120:00 120:00 120:00 120:00
SOURCE: Author's calculations.
NOTE: Claiming ages from 62:01 through 63:00 do not maximize lifetime benefits for individuals of the 1952 birth cohort, regardless of age at death or discount rate.
Table equivalent for Chart 2. Relative probabilities that the MCA falls within specified ranges for men born in 1952, by discount rate
Discount rate (%) Probability (in percent) that the MCA is—
62:00 63:01–66:00 66:01–69:11 70:00
0.0 25.25 7.81 23.48 43.46
0.1 25.46 7.85 23.57 43.13
0.2 25.68 7.87 23.99 42.46
0.3 25.90 7.89 24.42 41.79
0.4 26.34 7.70 24.50 41.46
0.5 26.56 7.99 24.68 40.77
0.6 26.78 8.02 25.11 40.09
0.7 27.00 8.06 25.54 39.41
0.8 27.44 8.12 25.71 38.72
0.9 27.66 8.16 26.14 38.04
1.0 27.88 8.19 26.57 37.36
1.1 28.33 8.25 26.75 36.67
1.2 28.56 8.27 27.19 35.98
1.3 29.03 8.07 27.61 35.29
1.4 29.26 8.37 27.76 34.60
1.5 29.72 8.18 28.53 33.57
1.6 29.95 8.48 28.68 32.89
1.7 30.42 8.28 29.09 32.21
1.8 30.65 8.58 29.58 31.19
1.9 31.12 8.64 29.73 30.51
2.0 31.61 8.42 30.48 29.48
2.1 31.85 8.74 30.93 28.48
2.2 32.33 8.82 31.36 27.49
2.3 32.82 8.61 31.74 26.82
2.4 33.30 8.69 32.18 25.83
2.5 33.79 8.77 32.60 24.85
2.6 34.30 8.82 33.30 23.58
2.7 34.80 8.89 33.68 22.63
2.8 35.31 8.97 34.04 21.68
2.9 35.82 9.05 34.65 20.48
3.0 36.33 9.13 35.25 19.29
3.1 36.83 9.22 35.55 18.40
3.2 37.37 9.57 35.80 17.27
3.3 38.17 9.39 36.54 15.91
3.4 38.70 9.47 37.01 14.82
3.5 39.50 9.60 37.08 13.82
3.6 40.03 9.69 37.68 12.60
3.7 40.87 9.78 37.94 11.41
3.8 41.71 9.91 38.03 10.35
3.9 42.27 9.99 38.65 9.08
4.0 43.12 10.12 38.57 8.19
4.1 43.99 10.22 38.67 7.12
4.2 45.16 10.03 38.73 6.07
4.3 46.05 10.49 38.38 5.09
4.4 46.93 10.61 38.18 4.28
4.5 48.17 10.37 37.90 3.56
4.6 49.10 10.81 37.32 2.77
4.7 50.34 10.94 36.49 2.23
4.8 51.62 11.02 35.69 1.67
4.9 52.91 11.11 34.75 1.23
5.0 54.21 11.19 33.77 0.84
5.1 55.87 11.24 32.33 0.56
5.2 57.54 10.93 31.19 0.34
5.3 59.23 10.95 29.63 0.19
5.4 60.94 11.25 27.72 0.09
5.5 62.99 10.85 26.12 0.04
5.6 64.71 11.08 24.20 0.01
5.7 67.11 10.57 22.32 a
5.8 69.15 10.66 20.18 a
5.9 71.85 10.04 18.11 . . .
6.0 74.17 9.92 15.91 . . .
6.1 76.73 9.45 13.82 . . .
6.2 79.52 8.86 11.62 . . .
6.3 82.46 7.82 9.72 . . .
6.4 85.45 6.89 7.66 . . .
6.5 88.14 6.08 5.78 . . .
6.6 90.92 4.91 4.17 . . .
6.7 93.49 3.65 2.85 . . .
6.8 95.60 2.63 1.77 . . .
6.9 97.43 1.59 0.98 . . .
7.0 98.66 0.89 0.45 . . .
7.1 99.46 0.39 0.15 . . .
7.2 99.86 0.11 0.03 . . .
7.3 99.98 0.01 a  
7.4 100.00 a . . . . . .
7.5 100.00 . . . . . . . . .
7.6 100.00 . . . . . . . . .
7.7 100.00 . . . . . . . . .
7.8 100.00 . . . . . . . . .
7.9 100.00 . . . . . . . . .
8.0 100.00 . . . . . . . . .
SOURCE: Author's calculations.
NOTES: Probabilities are based on the survival function of men currently aged 62.
Claiming ages from 62:01 through 63:00 do not maximize lifetime benefits for individuals of the 1952 birth cohort, regardless of age at death or discount rate.
. . . = not applicable.
a. Less than 0.005 percent.
Table equivalent for Chart 3. Relative probabilities that the MCA falls within specified ranges for women born in 1952, by discount rate
Discount rate (%) Probability (in percent) that the MCA is—
62:00 63:01–66:00 66:01–69:11 70:00
0.0 18.54 6.51 21.13 53.82
0.1 18.71 6.54 21.26 53.49
0.2 18.89 6.56 21.70 52.84
0.3 19.07 6.59 22.15 52.19
0.4 19.44 6.44 22.26 51.87
0.5 19.62 6.69 22.51 51.19
0.6 19.80 6.72 22.97 50.50
0.7 19.99 6.75 23.44 49.82
0.8 20.35 6.82 23.69 49.14
0.9 20.53 6.85 24.16 48.46
1.0 20.71 6.89 24.62 47.78
1.1 21.09 6.94 24.90 47.07
1.2 21.28 6.96 25.39 46.37
1.3 21.67 6.81 25.86 45.66
1.4 21.86 7.07 26.11 44.96
1.5 22.25 6.92 26.94 43.90
1.6 22.44 7.18 27.19 43.19
1.7 22.83 7.03 27.68 42.47
1.8 23.02 7.29 28.30 41.39
1.9 23.42 7.35 28.56 40.67
2.0 23.83 7.18 29.41 39.59
2.1 24.03 7.47 29.99 38.51
2.2 24.44 7.55 30.58 37.43
2.3 24.84 7.39 31.06 36.71
2.4 25.25 7.47 31.65 35.62
2.5 25.66 7.56 32.24 34.55
2.6 26.09 7.62 33.17 33.12
2.7 26.52 7.70 33.73 32.05
2.8 26.95 7.80 34.27 30.98
2.9 27.38 7.90 35.14 29.58
3.0 27.82 7.99 36.00 28.19
3.1 28.25 8.09 36.51 27.15
3.2 28.71 8.43 37.07 25.80
3.3 29.40 8.31 38.15 24.14
3.4 29.85 8.42 38.91 22.82
3.5 30.54 8.59 39.31 21.55
3.6 31.00 8.70 40.30 20.00
3.7 31.74 8.82 40.96 18.47
3.8 32.48 9.00 41.46 17.06
3.9 32.97 9.12 42.55 15.36
4.0 33.71 9.30 42.89 14.10
4.1 34.49 9.44 43.48 12.59
4.2 35.54 9.34 44.08 11.04
4.3 36.34 9.84 44.26 9.55
4.4 37.13 10.02 44.57 8.28
4.5 38.28 9.86 44.77 7.10
4.6 39.13 10.36 44.75 5.76
4.7 40.27 10.59 44.34 4.80
4.8 41.48 10.75 44.03 3.75
4.9 42.70 10.93 43.48 2.88
5.0 43.93 11.12 42.89 2.07
5.1 45.53 11.28 41.73 1.45
5.2 47.16 11.09 40.81 0.94
5.3 48.81 11.23 39.39 0.56
5.4 50.52 11.69 37.49 0.29
5.5 52.58 11.44 35.85 0.13
5.6 54.34 11.83 33.79 0.05
5.7 56.81 11.49 31.68 0.01
5.8 58.97 11.79 29.23 a
5.9 61.85 11.34 26.81 . . .
6.0 64.38 11.48 24.14 . . .
6.1 67.24 11.21 21.55 . . .
6.2 70.42 10.82 18.76 . . .
6.3 73.87 9.92 16.21 . . .
6.4 77.51 9.14 13.35 . . .
6.5 80.93 8.47 10.60 . . .
6.6 84.64 7.26 8.09 . . .
6.7 88.31 5.78 5.91 . . .
6.8 91.54 4.52 3.94 . . .
6.9 94.60 3.03 2.37 . . .
7.0 96.89 1.90 1.20 . . .
7.1 98.59 0.95 0.46 . . .
7.2 99.57 0.32 0.11 . . .
7.3 99.94 0.05 0.01  
7.4 100.00 a . . . . . .
7.5 100.00 . . . . . . . . .
7.6 100.00 . . . . . . . . .
7.7 100.00 . . . . . . . . .
7.8 100.00 . . . . . . . . .
7.9 100.00 . . . . . . . . .
8.0 100.00 . . . . . . . . .
SOURCE: Author's calculations.
NOTES: Probabilities are based on the survival function of women currently aged 62.
Claiming ages from 62:01 through 63:00 do not maximize lifetime benefits for individuals of the 1952 birth cohort, regardless of age at death or discount rate.
. . . = not applicable.
a. Less than 0.005 percent.
Table equivalent for Chart 4. OCA and EOL for men born in 1952, by discount rate
Discount rate (%) Prospective—
OCA EOL ($)
0.0 69:07 12.95
0.1 69:06 12.92
0.2 69:05 12.88
0.3 69:04 12.83
0.4 69:03 12.77
0.5 69:02 12.70
0.6 69:01 12.63
0.7 68:11 12.54
0.8 68:10 12.45
0.9 68:09 12.36
1.0 68:08 12.26
1.1 68:07 12.15
1.2 68:06 12.04
1.3 68:05 11.92
1.4 68:04 11.80
1.5 68:03 11.68
1.6 68:01 11.55
1.7 68:00 11.42
1.8 67:11 11.28
1.9 67:10 11.15
2.0 67:09 11.01
2.1 67:08 10.87
2.2 67:07 10.72
2.3 67:06 10.58
2.4 67:05 10.44
2.5 67:04 10.29
2.6 67:02 10.15
2.7 67:01 10.00
2.8 67:00 9.86
2.9 66:11 9.71
3.0 65:01 9.56
3.1 65:00 9.24
3.2 64:10 8.93
3.3 64:09 8.63
3.4 64:08 8.33
3.5 64:07 8.04
3.6 64:06 7.75
3.7 64:05 7.46
3.8 62:00 7.07
3.9 62:00 6.60
4.0 62:00 6.15
4.1 62:00 5.71
4.2 62:00 5.29
4.3 62:00 4.89
4.4 62:00 4.50
4.5 62:00 4.13
4.6 62:00 3.78
4.7 62:00 3.44
4.8 62:00 3.12
4.9 62:00 2.82
5.0 62:00 2.53
5.1 62:00 2.26
5.2 62:00 2.01
5.3 62:00 1.77
5.4 62:00 1.55
5.5 62:00 1.34
5.6 62:00 1.15
5.7 62:00 0.97
5.8 62:00 0.81
5.9 62:00 0.67
6.0 62:00 0.54
6.1 62:00 0.43
6.2 62:00 0.33
6.3 62:00 0.24
6.4 62:00 0.18
6.5 62:00 0.12
6.6 62:00 0.08
6.7 62:00 0.05
6.8 62:00 0.02
6.9 62:00 0.01
7.0 62:00 a
7.1 62:00 a
7.2 62:00 a
7.3 62:00 a
7.4 62:00 a
7.5 62:00 0.00
7.6 62:00 0.00
7.7 62:00 0.00
7.8 62:00 0.00
7.9 62:00 0.00
8.0 62:00 0.00
SOURCE: Author's calculations.
a. Less than $0.005.
Table equivalent for Chart 5. OCA and EOL for women born in 1952, by discount rate
Discount rate (%) Prospective—
OCA EOL ($)
0.0 70:00 9.90
0.1 70:00 9.93
0.2 70:00 9.96
0.3 70:00 9.98
0.4 70:00 10.01
0.5 70:00 10.04
0.6 70:00 10.07
0.7 70:00 10.11
0.8 69:11 10.13
0.9 69:10 10.15
1.0 69:08 10.15
1.1 69:07 10.14
1.2 69:06 10.12
1.3 69:05 10.09
1.4 69:03 10.05
1.5 69:02 10.00
1.6 69:01 9.94
1.7 69:00 9.87
1.8 68:11 9.80
1.9 68:09 9.72
2.0 68:08 9.64
2.1 68:07 9.55
2.2 68:06 9.45
2.3 68:05 9.35
2.4 68:03 9.25
2.5 68:02 9.14
2.6 68:01 9.03
2.7 68:00 8.91
2.8 67:11 8.80
2.9 67:10 8.68
3.0 67:08 8.56
3.1 67:07 8.43
3.2 67:06 8.31
3.3 67:05 8.19
3.4 67:04 8.07
3.5 67:03 7.94
3.6 67:02 7.82
3.7 67:00 7.70
3.8 66:11 7.58
3.9 65:00 7.40
4.0 64:11 7.11
4.1 64:10 6.83
4.2 64:08 6.55
4.3 64:07 6.27
4.4 64:06 6.01
4.5 64:05 5.75
4.6 62:00 5.32
4.7 62:00 4.88
4.8 62:00 4.45
4.9 62:00 4.05
5.0 62:00 3.66
5.1 62:00 3.30
5.2 62:00 2.95
5.3 62:00 2.63
5.4 62:00 2.32
5.5 62:00 2.03
5.6 62:00 1.77
5.7 62:00 1.52
5.8 62:00 1.29
5.9 62:00 1.08
6.0 62:00 0.89
6.1 62:00 0.72
6.2 62:00 0.57
6.3 62:00 0.44
6.4 62:00 0.32
6.5 62:00 0.23
6.6 62:00 0.16
6.7 62:00 0.10
6.8 62:00 0.06
6.9 62:00 0.03
7.0 62:00 0.01
7.1 62:00 a
7.2 62:00 a
7.3 62:00 a
7.4 62:00 a
7.5 62:00 0.00
7.6 62:00 0.00
7.7 62:00 0.00
7.8 62:00 0.00
7.9 62:00 0.00
8.0 62:00 0.00
SOURCE: Author's calculations.
a. Less than $0.005.