Question: What is the expected value of lifetime Social Security benefits for females and for males when benefits are linked to the traditional CPI and when benefits are linked to the chained CPI.
Discuss the reasons why women might prefer a switch to the chained CPI over proposals to partially privatize Social Security.
Short Answer:
Answer is contingent on several assumptions laid out below. I find that changing from the traditional CPI to a chained CPI would reduce the expected value of lifetime Social Security benefits by around $16,000 for males and $21,000 for females.
The actual impact is invariably different from the expected impact. Regardless of gender, people with the longest life span get the most from Social Security.
However, Social Security is really essential for females because private annuities are more expensive. See my previous post on this topic.
http://dailymathproblem.blogspot.com/2014/01/gender-differences-in-life-expectancy.html
Analysis:
Key assumptions:
The key assumptions in this analysis are
- Person retires at age 62 and receives an initial Social Security retirement benefit of $15,000 per year
- Traditional CPI grows at 2.42% per year
- Chained CPI grows at 2.09% per year.
- In year of death person receives ½ year Social Security Benefit
- Probability of surviving from age 62 to age y> 62 is determined by the CDC life tables for females and males.
Readers interested in the discussion of assumptions on difference between traditional and chained CPI might want to look at this post.
http://dailymathproblem.blogspot.com/2014/02/comparing-traditional-and-chained-cpi.html
The expected lifetime Social Security benefit is E(SSB)=Sum(Pyr x CByr) where Pyr is the probability of surviving to a particular year and CByr is the cumulative benefit from the retirement age at 62 to the year of death.
The logic behind the calculation of the probability a retiree survives to a specific date is similar to the logic behind the geometric distribution. The probability of surviving to age y > 62 is the product of the probability of surviving to age y-1 and the probability of dying at age y.
Calculations:
The chart below has data on likelihood of surviving to age y+0.5 for males and females and the cumulative Social Security Benefit to age y+0.5 under both the existing COLA and a chained CPI COLA.
| Survivor Probabilities and Cumulative Benefits | ||||
| Age y | Probability of surviving to exactly age y+0.5 for males | Probability of surviving to exactly age y+0.5 for females | Cumulative Benefit With Existing COLA | Cumulative Benefit With COLA linked to chained CPI |
| 62 | 0.01321 | 0.00831 | $7,500 | $7,500 |
| 63 | 0.01405 | 0.00896 | $22,682 | $22,657 |
| 64 | 0.01496 | 0.00965 | $38,230 | $38,130 |
| 65 | 0.01599 | 0.01044 | $54,156 | $53,927 |
| 66 | 0.01713 | 0.01133 | $70,466 | $70,054 |
| 67 | 0.01830 | 0.01227 | $87,171 | $86,518 |
| 68 | 0.01946 | 0.01322 | $104,281 | $103,327 |
| 69 | 0.02062 | 0.01422 | $121,805 | $120,486 |
| 70 | 0.02178 | 0.01526 | $139,752 | $138,004 |
| 71 | 0.02306 | 0.01647 | $158,134 | $155,889 |
| 72 | 0.02458 | 0.01783 | $176,961 | $174,147 |
| 73 | 0.02620 | 0.01929 | $196,244 | $192,786 |
| 74 | 0.02780 | 0.02077 | $215,993 | $211,816 |
| 75 | 0.02935 | 0.02224 | $236,220 | $231,243 |
| 76 | 0.03079 | 0.02380 | $256,936 | $251,076 |
| 77 | 0.03230 | 0.02547 | $278,154 | $271,323 |
| 78 | 0.03392 | 0.02732 | $299,885 | $291,994 |
| 79 | 0.03557 | 0.02926 | $322,143 | $313,096 |
| 80 | 0.03691 | 0.03112 | $344,938 | $334,640 |
| 81 | 0.03791 | 0.03288 | $368,286 | $356,634 |
| 82 | 0.03876 | 0.03473 | $392,198 | $379,088 |
| 83 | 0.03954 | 0.03677 | $416,690 | $402,011 |
| 84 | 0.03996 | 0.03858 | $441,774 | $425,413 |
| 85 | 0.04032 | 0.04017 | $467,464 | $449,304 |
| 86 | 0.04010 | 0.04170 | $493,777 | $473,694 |
| 87 | 0.03929 | 0.04275 | $520,727 | $498,594 |
| 88 | 0.03787 | 0.04322 | $548,328 | $524,015 |
| 89 | 0.03584 | 0.04302 | $576,598 | $549,967 |
| 90 | 0.03325 | 0.04209 | $605,551 | $576,461 |
| 91 | 0.03021 | 0.04041 | $635,206 | $603,509 |
| 92 | 0.02681 | 0.03798 | $665,578 | $631,123 |
| 93 | 0.02321 | 0.03490 | $696,685 | $659,313 |
| 94 | 0.01957 | 0.03128 | $728,544 | $688,093 |
| 95 | 0.01604 | 0.02730 | $761,175 | $717,474 |
| 96 | 0.01276 | 0.02314 | $794,596 | $747,469 |
| 97 | 0.00984 | 0.01903 | $828,825 | $778,091 |
| 98 | 0.00734 | 0.01513 | $863,882 | $809,353 |
| 99 | 0.00529 | 0.01163 | $899,788 | $841,269 |
| 100 | 0.01012 | 0.02606 | $936,563 | $873,851 |
| 1.00000 | 1.00000 | |||
The expected value of lifetime benefits for males/females under traditional/chained CPI is simply the dot product (the sum product function in EXCEL or NUMBERS) for the relevant probabilities and cumulative benefits.
| Impact of Change in COLA by Gender | |||
| Males | Females | Difference Females- Males | |
| Traditional CPI | $392,077 | $463,804 | $71,727 |
| Chained CPI | $376,005 | $442,772 | $66,767 |
| Difference Traditional-Chained CPI | $16,072 | $21,032 | |
The change in the COLA formula from the traditional CPI to the chained CPI leads to a reduction in expected lifetime benefits of $16,000 for males and $21,000 for females.
Social Security still provides longevity protection under a chained CPI.
http://dailymathproblem.blogspot.com/2014/01/gender-differences-in-life-expectancy.html
This is especially important for females because of their longer life expectancy.
Concluding Thoughts:
The issue of the Social Security COLA is important and complex. I am of the view that a change in the COLA could be part of a package of Social Security and retirement reforms. Social Security reform must also encompass additional revenues and rule changes that eliminate future automatic cuts in Social Security benefits. Pension reform must encompass improvements t0 401(k) plans and additional sources of low-cost annuity income.
Some readers might be interested in my views on the politics of the COLA debate.
http://policymemos.blogspot.com/2014/01/common-ground-on-social-security-colas.html