The Social Security system and the Old Age, Survivors, and Disability Insurance program (OASDI) were created by the Social Security Act of 1935. Social Security is the key part of a set of public social insurance programs in the United States because of its near-universal coverage of Federal and private sector employees. The program is immensely popular with the American public, but its size resulting from the scope of its coverage also makes it a symbol of excessive government to that portion of the public that wishes to shrink the central government. It is politically difficult to attack the program outright, even though the program might benefit from some reform. A different strategy is to reduce Americans’ dependence on the program by keeping the benefit payments small. This has been justified by claiming that when the program was started, life expectancy was equal to the retirement age; the average contributor wasn’t expected to live long enough to collect. The data presented here argue that this claim is false. In examining this claim, it may be possible to address some other issues in actuarial estimates of life expectancy and see what factors are impacting the age composition of American society.
At any moment, each person is faced with a probability of dying. The probability varies across one’s life, but toward one’s later years its central tendency is to increase; death is certain at some point. For any individual, the exact probability is likely unknowable. Actuaries have constructed functions or life tables that approximate for a model population, the probability of death for each surviving individual within the year. The model is a count of the number surviving out of a population of, say, one hundred thousand individuals starting at the same time. The reduction in the number of survivors by the end of any year divided by the number at the beginning of the year estimates the probability of death within that year. Life tables have been produced since the 17th century. The rates of mortality will vary with the population and its age as advances in medicine and public health change the odds.
For the purpose of this narrow question, however, let us use the Commissioners 1941 Standard Ordinary Mortality Table from the Actuarial Society of America because it is close to the data available to Congress when the Social Security Act became law. The table is based on the experience of white males. A table for white females would have longer lives and tables for non-whites would have shorter ones. This table was selected because it would be the model of who was in the workforce in 1935. (This table is also attached below.) The table lists five variables:
- x = age at beginning of the year
- l(x) = the number living at the beginning of the year
- d(x) = the number dying during the year
- p(x) = the probability of surviving the year, or (1 – d(x)/l(x))
- e(x) = the number of years left that an individual of age x can expect to live.
Manipulation of these values in the table allows one to calculate such things as the chance of dying between any two ages or similar questions.
Consider some key points:
- At age 0, e(x) is 62.3 years. That means life expectancy at birth in this table is about 62 years and 4 months. That would seem to match the claim that Social Security was designed so that workers could not expect to collect the benefits . Note, however, that p(x) is 97.74% which means that newborns had about a 2% chance of dying within that first year. As will be discussed later, childhood mortality exerts a major impact on life expectancy at birth. By the same table, those aged 5 will number 983,817 out of 1,023,102 born five years earlier. This suggest a 3.8% chance of dying within the first five years for this population. It should be noted that for those who survive to age 5, total life expectancy is 59.8 additional years for a total life of 64.8 years.
- Newborns do not work. Given child labor laws, even in 1941, one did not expect to work before age 16 at a minimum. The population that reached at least 16 is 960,201 out of the original population for a 93.8% survival rate from birth. At this point, many hazards have been met. The remaining life expectancy at age 16 is 50.1 years for a total life expectation from the start of participation in the workforce of 66.1 years. At this point, the claim loses validity: anyone entering the workforce has, on average, an expectation of living 13 months into retirement.
- At age 40, one is about halfway through one’s working years as that is halfway between entering the labor force at 16 and retiring at 65. Although the risk of mortality within the year is slightly greater than it was at age 16, it has increased at a slower pace than life expectancy. If one survived to 40, one had the expectation of living to 69.3. At that point, 25 years before retiring, one could expect to enjoy Social Security benefits for at least four years.
- At age 65, upon retirement, e(x) is 11.6 years. That is, total life expectancy for new retirees would be 76 years and 6 months. The total population that started working at 16 has been reduced by almost 40%, but more than 60% of that group will reach retirement age. But half of that loss has occurred since age 53, or within a dozen years of retirement. Clearly, the claim that Social Security was designed such that retirees were never intended to collect the benefits (because life expectancy was less than 65 years) is absolutely false.
The underlying issue this exercise points to is how to interpret life expectancy and interpret what affects its value. Looking at single values such as expectation at a specific age does not give sufficient information to draw conclusions about the dynamics involved. Consider four life tables: English Life Tables No. 8 for Males 1910-1912; Commissioners 1941 Standard Ordinary Mortality Table; Commissioners Standard Ordinary (1958 CSO) Mortality Table for Male Lives; and the Social Security mortality table for males of 2010. There are some methodological differences among them and they address somewhat different populations. Nonetheless, they tell a consistent story about changes in life expectancy across the past century.
Across these four tables, life expectancy at birth was 51.50 years, 62.33 years, 67.55 years, and 75.96 years respectively. This would indicate that across the past century, an expected male lifespan had increased by approximately 24 years! Does this represent advances in gerontology that increase the chances of living well into old age? Look instead at the life expectancy of someone attaining age 21. For the four tables the values are 64.37 years, 66.66 years, 70.33 years, and 76.96 years. The spread in lifespan across the tables has decreased from 24 years to 12 years. At age 65, the values are 75.99 years, 76.55 years, 77.97 years, and 82.61 years. The range has dropped to seven years, but only the 2010 table shows a major improvement in life span.
What has happened is seen in graphs that compare the annual mortality probabilities and the life expectancy by age among the four tables as shown in the two attached graphs. The key problem is that is one does not have a good chance of reaching 5 years or 16 years or 21 years, then one has a much lower probability of reaching old age; life expectancy at birth is lower. Across the four tables, the greatest spread of estimated lifespan occurs at birth. The English curve shows a steep climb during the first year. That is, life expectancy climbs very quickly during that year for those who survive it. What is at play is a significant reduction in childhood mortality and a general improvement in survival probabilities for the rest of one’s life.
This is more clearly seen in the second graph, Annual Mortality Probability. The lower a curve sits in the graphed space, the lower is the probability of death at any year. Mortality tables from later years – 1941, 1959, and 2010 – show a lower probability of death at every age. The major area of improvement in terms of lower mortality rates is particularly in the area between birth and age 20. In general, the more recent the life table, the lower the mortality rates. This even holds up to age 40. Beyond that, three of the curves lie fairly close together; there was only marginal improvements in mortality over the years from 1910 to 1960.
Note that for the English Males data, mortality in the first year of life is approximately 12%. Approximately one in eight infant boys would not live through their first year. In calculating a weighted average – life expectancy is just that: an average of ages weighted by the share of the population that achieves it – adding a large zero for twelve percent of the population will pull down the average. This explains why the spread among the four estimates of life expectancy at birth was so wide and then narrowed for later ages. For males who survived to age 20, the probabilities of death were fairly similar for each year thereafter under three of the tables. Their expected life span from that point forward would be about the same. Only the 2010 model shows a consistently lower mortality rate for all ages. This probably reflects a general improvement in health across the whole of life, not just the improvement of childhood experience.
In summary, using life expectancy as a measure of life quality or such requires care in stating the proposition. We have shown how it was misapplied in the case of Social Security. A review of these life tables then highlights what has been the real impact of better medicine and healthier lives over the past 100 years. The improvements have had their greatest impact in childhood mortality. If we have more old people alive in our society today, the reason may be less one of over-investment in gerontology as much as success in childhood health.
Table: 1941 Commissioners Standard Ordinary Life Table
Graph: expected total lifespan by age attained
Graph: annual mortality probability