Monday, February 24, 2014

Expected Life Time Social Security Benefits and the COLA

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.



Analysis:

Key assumptions:

The key assumptions in this analysis are


  1. Person retires at age 62 and receives an initial Social Security retirement benefit of $15,000 per year
  2. Traditional CPI grows at 2.42% per year 
  3. Chained CPI grows at 2.09% per year.
  4. In year of death person receives ½ year Social Security Benefit
  5. 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.



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.



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.





















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