Probability That An Old President Does Not Finish Their Term

Posted on 16-September-2016 by mathscinotes

Quote of the Day

A man always has two reasons for the things he does -- a good one and the real one.

— J.P. Morgan. I have frequently have found this statement to be true.

Introduction

Figure 1: Ronald Reagan, The Oldest US President at Inauguration.

Figure 1: Ronald Reagan, The Oldest
US President at Inauguration (Wikipedia).

Ronald Reagan (Figure 1) was our oldest president at the time of inauguration  – 69 years 349 days old. The 2016 US presidential election is giving us a choice of two candidates that will be relatively old at inauguration: Donald Trump (70 years, 220 days), and Hilary Clinton (69 years, 86 days). Since US presidents often serve 2 terms, it is conceivable they we may have a 77- to 78-year old president in 2024. This fact makes me curious as to what is the likelihood that a 70 year-old's natural life will be long enough for them to serve one or two terms.

We can easily compute this probability using an actuarial life table. In this post, I will compute the probability that a 70-year old male or female will complete one or two 4-year terms.

Background

The basic math behind the life table is well covered in the Wikipedia, and I will refer you there for the details.

Analysis

I have included an actuarial life table in Appendix A. The actual calculations are easily performed using a filtered pivot table version of the life table, which I show in Figure 2.

Figure 2: Calculation of the probability a 70 -year old will not live to be 74 or 78-years old.

Figure 2: Calculation of the probability a 70 -year old will not live to be 74 or 78-years old.

This data is interesting:

  • A 70-year old male has a 10% chance of dying by 74 and a 23% chance of dying by 78.
  • A 70-year old female has a 7% chance of dying by 74 and a 17% chance of dying by 78.

Conclusion

There is a ~23% chance that a 70-year old male president would not be able to complete 2 terms, which is about what I would have expected. There is ~17% chance that a 70-year old female president would not be able to complete 2 terms, which is higher than I would have expected.

 Appendix A: US Social Security Administration Life Table.

Table 1 is the 2013 life table used by the Social Security Administration (SSA). The analysis in this post consists of filtered pivot table version of this date.

Table 1: 2013 Actuarial Life Table from the SSA.
Age Male Prob of Death Males Alive Male Life Exp. Female Prob of Death Female Alive Female Life Exp.
0 0.006519 100000 76.28 0.005377 100000 81.05
1 0.000462 99348 75.78 0.000379 99462 80.49
2 0.000291 99302 74.82 0.000221 99425 79.52
3 0.000209 99273 73.84 0.000162 99403 78.54
4 0.000176 99252 72.85 0.000133 99387 77.55
5 0.000159 99235 71.87 0.000119 99373 76.56
6 0.000146 99219 70.88 0.000109 99361 75.57
7 0.000133 99205 69.89 0.000101 99351 74.58
8 0.000118 99192 68.9 0.000096 99341 73.58
9 0.000102 99180 67.9 0.000093 99331 72.59
10 0.000091 99170 66.91 0.000094 99322 71.60
11 0.000096 99161 65.92 0.0001 99312 70.60
12 0.000128 99151 64.92 0.000112 99303 69.61
13 0.000195 99138 63.93 0.000134 99291 68.62
14 0.000288 99119 62.94 0.000162 99278 67.63
15 0.000389 99091 61.96 0.000194 99262 66.64
16 0.000492 99052 60.99 0.000226 99243 65.65
17 0.000607 99003 60.02 0.000261 99220 64.67
18 0.000735 98943 59.05 0.000297 99194 63.68
19 0.000869 98870 58.09 0.000334 99165 62.70
20 0.001011 98785 57.14 0.000373 99132 61.72
21 0.001145 98685 56.2 0.000412 99095 60.75
22 0.001246 98572 55.27 0.000446 99054 59.77
23 0.001301 98449 54.33 0.000472 99010 58.80
24 0.001321 98321 53.4 0.000493 98963 57.82
25 0.00133 98191 52.47 0.000513 98915 56.85
26 0.001345 98060 51.54 0.000537 98864 55.88
27 0.001363 97928 50.61 0.000563 98811 54.91
28 0.001391 97795 49.68 0.000593 98755 53.94
29 0.001427 97659 48.75 0.000627 98697 52.97
30 0.001467 97519 47.82 0.000664 98635 52.01
31 0.001505 97376 46.89 0.000705 98569 51.04
32 0.001541 97230 45.96 0.000748 98500 50.08
33 0.001573 97080 45.03 0.000794 98426 49.11
34 0.001606 96927 44.1 0.000845 98348 48.15
35 0.001648 96772 43.17 0.000903 98265 47.19
36 0.001704 96612 42.24 0.000968 98176 46.23
37 0.001774 96448 41.31 0.001038 98081 45.28
38 0.001861 96277 40.38 0.001113 97979 44.33
39 0.001967 96097 39.46 0.001196 97870 43.37
40 0.002092 95908 38.53 0.001287 97753 42.43
41 0.00224 95708 37.61 0.001393 97627 41.48
42 0.002418 95493 36.7 0.001517 97491 40.54
43 0.002629 95262 35.78 0.001662 97343 39.60
44 0.002873 95012 34.88 0.001827 97182 38.66
45 0.003146 94739 33.98 0.002005 97004 37.73
46 0.003447 94441 33.08 0.002198 96810 36.81
47 0.003787 94115 32.19 0.002412 96597 35.89
48 0.004167 93759 31.32 0.002648 96364 34.97
49 0.004586 93368 30.44 0.002904 96109 34.06
50 0.005038 92940 29.58 0.003182 95829 33.16
51 0.00552 92472 28.73 0.003473 95524 32.27
52 0.006036 91961 27.89 0.003767 95193 31.38
53 0.006587 91406 27.05 0.004058 94834 30.49
54 0.00717 90804 26.23 0.004352 94449 29.62
55 0.007801 90153 25.41 0.004681 94038 28.74
56 0.008466 89450 24.61 0.00504 93598 27.88
57 0.009133 88693 23.82 0.0054 93126 27.01
58 0.009792 87883 23.03 0.005756 92623 26.16
59 0.010462 87022 22.25 0.006128 92090 25.31
60 0.011197 86112 21.48 0.006545 91526 24.46
61 0.012009 85147 20.72 0.007034 90927 23.62
62 0.012867 84125 19.97 0.007607 90287 22.78
63 0.013772 83042 19.22 0.008281 89600 21.95
64 0.014749 81899 18.48 0.009057 88858 21.13
65 0.015852 80691 17.75 0.009953 88054 20.32
66 0.017097 79412 17.03 0.01095 87177 19.52
67 0.018463 78054 16.32 0.01201 86223 18.73
68 0.019959 76613 15.61 0.013124 85187 17.95
69 0.021616 75084 14.92 0.01433 84069 17.18
70 0.023528 73461 14.24 0.015728 82864 16.43
71 0.025693 71732 13.57 0.017338 81561 15.68
72 0.028041 69889 12.92 0.019108 80147 14.95
73 0.030567 67930 12.27 0.021041 78616 14.23
74 0.033347 65853 11.65 0.023191 76961 13.53
75 0.036572 63657 11.03 0.025713 75177 12.83
76 0.040276 61329 10.43 0.028609 73244 12.16
77 0.044348 58859 9.85 0.03176 71148 11.50
78 0.048797 56249 9.28 0.035157 68888 10.86
79 0.053739 53504 8.73 0.03892 66467 10.24
80 0.059403 50629 8.2 0.043289 63880 9.64
81 0.065873 47621 7.68 0.048356 61114 9.05
82 0.073082 44484 7.19 0.054041 58159 8.48
83 0.08107 41233 6.72 0.060384 55016 7.94
84 0.089947 37890 6.27 0.067498 51694 7.42
85 0.099842 34482 5.84 0.075516 48205 6.92
86 0.110863 31040 5.43 0.084556 44565 6.44
87 0.123088 27598 5.04 0.094703 40796 5.99
88 0.136563 24201 4.68 0.106014 36933 5.57
89 0.151299 20896 4.34 0.118513 33017 5.17
90 0.167291 17735 4.03 0.132206 29104 4.80
91 0.18452 14768 3.74 0.147092 25257 4.45
92 0.202954 12043 3.47 0.163154 21542 4.13
93 0.222555 9599 3.23 0.180371 18027 3.84
94 0.243272 7463 3.01 0.198714 14775 3.57
95 0.263821 5647 2.82 0.217264 11839 3.34
96 0.283833 4157 2.64 0.235735 9267 3.12
97 0.302916 2977 2.49 0.25381 7083 2.93
98 0.320672 2075 2.36 0.271155 5285 2.76
99 0.336706 1410 2.24 0.287424 3852 2.60
100 0.353541 935 2.12 0.30467 2745 2.45
101 0.371218 605 2.01 0.32295 1909 2.30
102 0.389779 380 1.9 0.342327 1292 2.17
103 0.409268 232 1.8 0.362867 850 2.03
104 0.429732 137 1.7 0.384639 541 1.91
105 0.451218 78 1.6 0.407717 333 1.78
106 0.473779 43 1.51 0.43218 197 1.67
107 0.497468 23 1.42 0.458111 112 1.56
108 0.522341 11 1.34 0.485597 61 1.45
109 0.548458 5 1.26 0.514733 31 1.35
110 0.575881 2 1.18 0.545617 15 1.26
111 0.604675 1 1.11 0.578354 7 1.17
112 0.634909 0 1.04 0.613055 3 1.08
113 0.666655 0 0.97 0.649839 1 1.00
114 0.699987 0 0.9 0.688829 0 0.92
115 0.734987 0 0.84 0.730159 0 0.85
116 0.771736 0 0.78 0.771736 0 0.78
117 0.810323 0 0.72 0.810323 0 0.72
118 0.850839 0 0.67 0.850839 0 0.67
119 0.893381 0 0.61 0.893381 0 0.61
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