Life
Expectancyã
Draft
By
William Larsen
8-2-2004
Increased life expectancy has been identified as one of the key variables impacting Social Security. Is it fact or myth that increased life expectancy is a creating a large problem for Social Security. Insurance companies have used life tables for a very long time do ascertain the risk or cost in issuing life insurance policies. Therefore, life tables would be a very important reference to use to understanding how changes in life expectancy can affect Social Security.
Life expectancy can mean many things and is dependent upon the age at which it is referenced. There are two types of Life Tables: Period Life Table and a Cohort or Generation life Table.
· Period Life Tables are based on an entire population over a short span of years. They are beneficial in analyzing changes in mortality by a population over time.
· The Cohort or Generation Life Table represents those born in a particular year. They are useful in projecting populations into the future and evaluating changes in life expectancy over time.
The following Cohort Life Period Tables were used as references in this analysis.
7
- Cohort Life Tables for U. S. Social Security Area by Year of Birth and Sex
These tables are easily copied into a spreadsheet such as Lotus 123 or Excel. Heading definitions are listed below.
|
Heading |
Description |
|
x |
This is the beginning age |
qx |
This is the death probability for that year. Multiplying this probability by the number of individuals alive at the start of this age (lx) yields the number of individuals who will die prior to the next age (dx). |
|
lx |
This is the number of individuals who live to age x. |
|
dx |
Number of individuals in this age group who will die prior to the next age. |
|
Lx |
The number of person years lived between age x and x+1 |
|
Tx |
The sum of lx starting in year xn+1 to year x119 + xn x ½. Social Security assumes a linear uniform distribution of deaths during the year. |
|
ex |
Life expectancy at
this age. The average number of years
left to live at this age. Tx divided by lx. The total years left to live by group
divided by the number of individuals alive at beginning of year. |
Definitions of Life Table Functions
Life expectancy at any given age is calculated by summing the number of individuals living at the beginning of each age beyond the year in question divided by the number living in the year questioned.
For example in 1900 for males, we wish to determine the life expectancy at birth. We would add the total number of people living at each age starting at age 1 and ending at age 119. Summing lx from age 1 to 119 we obtain 5,104,202. Add in half those alive at the start of age zero, 50,000 and we total 5,144,202 life-years remaining for the 1900 cohort. Since there were 100,000 living at the start of the year when these babies were zero, we divide the 5,144,202 by 100,000 to obtain a life expectancy at birth of 51.44 years.
To obtain a combined life expectancy for males and females, the same methodology applies. Simple add the total male and female years lived and divide it by the number of males and females alive at the beginning of the year in question. For those born in 1900 the combine life expectancy at age 65 is 15.99 years.
Three tables were created listing life expectancy by age and cohort for males, females and both combined. At age zero life expectancy in 1900 was 51.52 years and had increased to 79.68 years for those born in 2000. This would indicate we are living longer, but is the rate of living longer increasing or decreasing?
Three tables were created listing the increased in life expectancy on a yearly basis in days for males, females and combined males and females. It is clear the rate of change in life expectancy was increasing each year up till 1940, but the rate of change is now slowing. At age 65, increased life expectancy is increasing at about 20 days more for each new cohort born.
“Life expectancy at birth in 1930 was indeed only 58 for men and 62 for women. But life expectancy at birth in the early decades of the 20th century was low due to high infant mortality, and someone who died as a child would never have worked and paid into Social Security. A more appropriate measure is probably life expectancy after attainment of adulthood.
Since average life expectancy at birth is now about 76, this is interpreted as implying that people collect benefits for 14 to 18 years longer than they used to. However, as Table 1 indicates, the average life expectancy at age 65 (i.e., the number of years a person could be expected to receive unreduced Social Security retirement benefits) has only increased a modest 5 years (on average) since 1940. So, for example, men attaining 65 in 1990 can expect to live for 15.3 years compared to 12.7 years for men attaining 65 back in 1940. So the actual increase in time that males can anticipate receiving Social Security is closer to 3 years than to 14.” [1]
Life tables are critical in determining what the cost is of life insurance. It can also be used to calculate what the cost is for Social Security. In this analysis, the male cohort table was used. Ages 21 through 64 were considered to be working years while 65 and over were retired. The assumption was a 6% rate of return, wages increasing at 3.5% a year and inflation of 2%. The premium paid by each worker to pay a 42% life time indexed wage benefit at age 65 and adjust this benefit by inflation yearly was calculated using an iterative routine. When the premium incremental rate was <.0000000000001, the routine was stopped.
Three tables were created showing the tax rates needed to pay the equivalent Social Security Old Age Benefit at age 65 for males, females and both combined for cohort years 1900 through 2000. These tables list the age the worker begins work and its corresponding premium needed to pay the defined benefit. Some workers would pay the tax and die before collecting anything while others would live far longer than the average life expectancy collecting more than the average. The concept of insurance is to provide coverage for a high cost loss that has a low risk of occurring. The greater the potential of a loss occurring the higher the premium required to cover the potential loss.
An individual born in 1900 would be 37 when Social Security began. At age 37, the tax rate would be 7.45% to cover this cohort’s cost. A person who was age 21 would have to pay a tax of 3.47%. The initial OASI tax was 2%, which was actuarial unsound even for the youngest of workers. In addition, the analysis assumes the worker is continually working each year from age 21 to age 65 without layoff. It also assumes no benefit for survivors. To cover intermittent layoffs would increase the cost.
Prior to 1937, no one had paid into Social Security. These three tables identify the tax rate needed based on age when Social Security began in order to fund the defined Social Security benefit. At age 50 the tax would have had to been 18.23%. Social Security was setup to pay benefits starting three years after the program began collecting taxes. The average tax rate for those age 37 and over in 1937 would have needed to been 41.6%. The tax rate would have had to been 26.8% for those age 21 and over the next 44 years to pay the Social Security benefits that were promised.
Adding a benefit where by a surviving spouse would be paid the workers benefit increases the cost considerably. This benefit no longer fits the shared risk pool. The funds paid by those who died early are no longer there to pay benefits to those who live longer. Those funds are now paid to survivors, which change the risk assessment.
The retirement age has been increased for those born after 1938. For those born in the mid 1960’s the retirement age will be 67. The tax rate for this cohort at age 21 is 4.53%. This table lists the tax actuarial tax rates required to pay the scheduled Social Security Benefit based on a retirement age of 67.
Increased life expectancy is not the main reason behind Social Security’s problem. The root cause is one of design. A paper on ACTUARIAL TABLES BASED ON THE U.S. LIFE TABLES: 1989-91 clearly identifies the proper method of calculating the cost associated with annuities.
