by Ron Lee and Tim Miller
Sudden medical breakthroughs in 2001 could have relatively large impacts on population size this century. For example, a sudden 20 year gain in life expectancy would boost US population size by 21% at mid-century and 23% by 2100 over the baseline forecast. By historical standards, such sudden breakthroughs are unprecedented. The largest single year gain in US life expectancy was 8 years (a rebound following the flu epidemic of 1917). Single year gains in life expectancy exceed 1.0 in 12 of the 98 years in the last century. They exceeded 2.0 only twice.
The achievement of immortality in 2001 would lead to a tripling of the current US population and a more than quadrupling of the current world population by the end of the century. (That is, the world population would twice double in size).
Assumptions about future fertility and immigration levels can have much more dramatic effects on future US population size than can assumptions about mortality. For example, the US Census Bureau's high projection foresees a US population of 1.18 billion by the end of the century -- due to their assumptions of high fertility (TFR=2.6) and high immigration (3 million net immigrants admitted in 2100). In contrast, we project a US population of only 800 million at the end of the century -- even assuming that immortality is achieved next year! This is because our projections assume lower fertility (TFR= 1.9) and lower immigration (900,000 per year) than the Census high forecast.
Looking at the pace of mortality decline in the next century, we find relatively modest effects on population size. At mid-century, US population size in a slow-paced mortality decline and fast-paced decline is 350 vs 382 million or +/- 4% of the midpoint. By 2100, the spread is 380 vs 463 or +/- 10% of the midpoint population.
These modest effects on total US population size translate into very large effects on the elderly population. At mid-century, the elderly US population in a slow-paced versus fast-paced decline is 65 vs 91 million or +/- 17% of the midpoint. By 2100, the spread is 76 vs 146 million or +/- 32% of the midpoint. Sudden breakthroughs would have even more dramatic effects. For example, the achievement of immortality in 2001 would result in an elderly population of 225 million by mid-century and 468 million by 2100.
Based on the pace of mortality decline in the last half of the 20th century, we forecast a gain of +12.5 years in the next century with a 95% probability interval spanning gains of +6.1 years to +17.9 years. We foresee life expectancy increasing from its current level of 76.7 reaching 89.2 by the end of next century with a 95% probability interval ranging from 83.8 to 94.6.
Based on the historical evidence, we would classify the following as unlikely events: (a) extremely slow increase in life expectancy characterized by a gain of less than 6 years over the next century; (b) extremely rapid increase in life expectancy characterized by a gain of more than 18 years over the next century; and (c) very sudden gains in life expectancy or even of the achievement of immortality. Of course, demographers should be among the first to point out that unexpected and improbable events often happen.
We use cohort-component projections of the US population. These assume a long-run TFR of 1.9 children per woman and 900,000 net immigrants per year, consistent with Social Security assumptions.
Experiment 1. We examine the impact of the pace of mortality decline over the next century on US population size and age structure. I consider 5 cases in which 1, 5, 10, 15, or 20 years are gained in life expectancy over the next century. For comparison purposes note that the Census Bureau's low, middle, and high forecasts call for gains of 10, 13, and 17 years.
Experiment 2. We examine the impact of a sudden breakthrough in the year 2001 followed by a resumption of the same pace of mortality decline observed in the late 20th century. I consider 5 cases in which 1, 5, 10, 15, or 20 years are gained in life expectancy in the year 2001. I also consider a sixth case in which immortality is achieved.
Experiment 3. Ansley Coale provides an analytic approximation to determine future population size following the achievement of immortality. I apply this formula to both the US and the World. I can test the accuracy of Coale's approximation by comparison to the figures derived in Experiment 2.
Results from Experiment 1 (Pace of mortality decline in next century)
| Years gained in life expectancy over the next century | 1 | 5 | 10 | 15 | 20 |
| e(0) in the year 2100 | 77.7 | 81.7 | 86.7 | 91.7 | 96.7 |
| US Population Size and (% aged 65+) | |||||
| in the year 2025 | 325 | 328 | 331 | 333 | 335 |
| (18) | (18) | (18) | (19) | (19) | |
| in the year 2050 | 350 | 357 | 366 | 374 | 382 |
| (19) | (20) | (21) | (23) | (24) | |
| in the year 2075 | 367 | 380 | 395 | 409 | 423 |
| (20) | (21) | (24) | (26) | (28) | |
| in the year 2100 | 380 | 399 | 421 | 443 | 463 |
| (20) | (23) | (26) | (29) | (31) |
In 1998 the US population was 271 million with 13% above age 65 and the
life expectancy at birth was 76.7.
Results from Experiment 2 (A breakthrough in 2001).
| Sudden gain in life expectancy in 2001 | 1 | 5 | 10 | 15 | 20 | Immortal |
| e(0) in the year 2100 | 89.8 | 93.7 | 99.3 | 104.7 | 108.7 | (220) |
| US Population Size and (% aged 65+) | ||||||
| in the year 2025 | 334 | 344 | 356 | 365 | 373 | 396 |
| (19) | (21) | (23) | (25) | (26) | (30) | |
| in the year 2050 | 374 | 390 | 411 | 430 | 446 | 524 |
| (23) | (25) | (28) | (31) | (34) | (43) | |
| in the year 2075 | 406 | 424 | 448 | 472 | 492 | 657 |
| (25) | (28) | (31) | (34) | (37) | (52) | |
| in the year 2100 | 436 | 457 | 483 | 509 | 529 | 794 |
| (28) | (30) | (34) | (37) | (39) | (59) |
In 1998 the US population was 271 million with 13% above age 65 and the life expectancy at birth was 76.7.
Results from Experiment 3 (Immortality: Coale's approximation)
Ansley Coale derived the formula for calculating future population size following the achievement of immortality ("Age Composition in the Absence of Mortality and in Other Odd Circumstances").
To apply the formula to the US population (which is nearly at replacement-level fertility with very little pre-reproduction mortality), I use a starting population of 271 million in 1998 and 4 million births per year and 1 million immigrants. Hence, P(t) = 271 + 5*t.
The following table shows that this approximation works quite well in the case of the US.
| Population Size (millions) | Coale | Cohort-Component (from Experiment 2) |
| 2025 | 411 | 396 |
| 2050 | 536 | 524 |
| 2075 | 661 | 657 |
| 2100 | 786 | 794 |
For the World, we can use Coale's formula (but unlike the US case we must now account for above-replacement fertility and forpre-reproduction mortality).
P(t) = P(0) + (B(0)/r)(exp(rt)-1)
P(0) is 6,038 million.
B(0) is 131 million.
Lotka's r for the world in a zero mortality regime is a bit tricky to calculate. But we can crudely approximate it. The Census Bureau reports world population growth in 2000 as 1.25% declining to 0.50% in 2050. I'll assume it is 0 in 2100. In the initial year of a zero-mortality regime, the birth rate would jump even with no change in fertility behavior since women who were formerly exposed to the risk of mortality now survive to bear children. In demographic terms, the NRR becomes the GRR. Assuming 2.4 as replacement level (meaning l(u) ~= .85), this means the NRR in a zero-mortality regime would about 1.17 (= 2.4/2) times greater. So, we can assume the intrinsic growth rate would increase by approximately 0.56% (= log(1.17)/28) in 2000. However, by 2050 this adjustment would be much smaller since mortality is projected to decline. Let's assume l(u) = .95, so the adjustment to the growth rate is a modest 0.18%. By 2100, the effect can be ignored. So, we calculate the intrinsic growth rate, r, in a zero-mortality world as follows:
2000 1.25 + .56 = 1.81%
2050 0.50 + .18 = 0.68%
2100 0
average 2000-2050 1.245%
average 2000-2100 0.905%
Note that we are ignoring the fact that the regions of the world with the highest fertility levels are the same regions with the highest pre-reproductive mortality, so our aggregate treatment underestimates the probable effect on growth. So, let's consider our estimates as lower bounds and forge ahead.
Coale's formula yields world population estimates of
P(2050) = 6,038 + 131*(exp(.01245*50)-1)/.01245 = 15,124
P(2100) = 6,038 + 131*(exp(.00905*100)-1)/.00905 = 27,344
So, world population at the end of the century would undergo 2 more doublings in size.
Thus, achievement of immortality would imply a tripling of the US population and a more than quadrupling of the World population by the end of this century. These assume that future fertility rates are unchanged following the achievement of immortality.
END
Population projection figures in pdf format.