ACTUARIAL NOTE SOCIAL SECURITY ADMINISTRATION

Number 154

November 2013 Office of the Chief Actuary

Baltimore, Maryland

DIMINISHING EFFECT OF THE SPECIAL MINIMUM PIA

by Craig A. Feinstein, A.S.A.

Background

The Primary Insurance Amount (PIA) is the amount that

a primary beneficiary (that is, a worker) receives if he or

she becomes entitled to Social Security benefits at Normal Retirement Age. The benefit amounts of the

worker’s auxiliaries or survivors are based on specified

percentages of the PIA. There are several formulas for

determining the PIA, but for most beneficiaries it is

determined under a wage-indexed formula (described

later) if the worker attained age 62, became disabled, or

died after 1978.

Enacted in 1972 by Public Law 92-603, the special minimum PIA is an alternative to the wage-indexed PIA to

give people with low earnings over a long working lifetime, along with their auxiliaries and survivors, higher

monthly Social Security benefits than would be generated by the wage-indexed formula. In Actuarial Note

143, we investigated how much gain over the wageindexed PIA a beneficiary could possibly receive from

the special minimum PIA, and we also presented data on

current recipients of the special minimum. In this note,

we update Actuarial Note 143.

The Special Minimum PIA

The special minimum PIA for a worker is a function of

the number of years of coverage, n, before the year of

entitlement and after 1936 in which a specific amount of

earnings are credited. The years of coverage are determined as follows:1

(a) Prior to 1951—one year of coverage for each

$900 of aggregate earnings, not to exceed 14.

(b) After 1950 through 1978—one year of coverage

for any year with earnings no less than 25% of

the contribution and benefit base for that year. 

(c) After 1978 through 1990—one year of coverage

for any year with earnings no less than 25% of

what the contribution and benefit base would

have been for that year had the 1977 Social

Security Amendments not been enacted (in

other words, 25% of the “old-law” contribution

and benefit base).

(d) After 1990 to present—one year of coverage for

any year with earnings no less than 15% of the

“old-law” contribution and benefit base for that

year.

Thus, for a worker with no earnings prior to 1951, the

number of years of coverage, n, is the number of years

in which the earnings of the worker equal or exceed a

specified amount, mj

, for given year j. 

When n  10, the special minimum PIA is zero; otherwise, it is equal to a specific base value, b, times the

minimum of {20, n-10}, times the product of the costof-living adjustments (COLAs), based on increases in

prices, from the year 1979 (if applicable). The specific

base value, b, is determined by the date of entitlement:

(a) For dates of entitlement from January 1973

through February 1974, b = $8.50.

(b) For dates of entitlement from March 1974

through December 1978, b = $9.00.

(c) For dates of entitlement in 1979 or later,

b = $11.50.

For the years 1979 to 1981, after each COLA is applied

the product is rounded up to the next dime. Beginning in

1982, after each COLA is applied the product is rounded

down to the next dime.2

The Wage-Indexed PIA

For a worker born in or after 1930 who lives to attain

age 623 without any pension based on non-covered

employment, the wage-indexed PIA is a function of the

total of the 35 highest indexed annual earnings, with the

indexing based on the growth in national average

wages.4 The total of the indexed annual earnings from

1 http://www.socialsecurity.gov/OACT/COLA/yoc.html

2 http://www.socialsecurity.gov/cola/automatic-cola.htm

3 The age of first eligibility for a retirement benefit.

4 http://www.socialsecurity.gov/OACT/COLA/AWI.html
2

these 35 years is converted to a monthly average by

dividing by 420 (=12×35) and then rounding down to

the next dollar. This amount is called the Average

Indexed Monthly Earnings (AIME). The wage-indexed

PIA at age 62 is then calculated by rounding down to the

next dime the sum of:

(a) 90 percent of the first b1 dollars of the AIME,

plus

(b) 32 percent of the AIME over b1 dollars and

through b2 dollars, plus

(c) 15 percent of the AIME over b2 dollars,

where b1 and b2 are the two bend points for the appropriate year of first eligibility.5

 Beginning in the year of

attainment of age 62, the wage-indexed PIA is increased

by applying COLAs each June before 1983 and each

December after 1982.6

The Maximum Gain of the Special Minimum 

PIA Over the Wage-Indexed PIA

Consider a person born in 1951 who is first eligible for

benefits in 2013 with no earnings before 1973, the year

of attainment of age 22. We want to find the maximum

possible gain that he or she can obtain if his or her PIA

is the special minimum PIA, rather than the wageindexed PIA. This problem can be thought of as the

optimization problem:

Maximize {SPMIN – PIA} over all possible earnings histories,

where we denote by SPMIN the special minimum PIA

and we denote by PIA the wage-indexed PIA.

We can show that the solution to this problem must be a

payment history in which the earnings in any of the 35

years of highest indexed earnings which is a year of

coverage do not exceed the minimum amount required

for a year of coverage in that year. To show this, assume

that we have a solution to the stated maximization

problem, i.e., an earnings history which maximizes the

difference {SPMIN – PIA}. If in this earnings history

there is a year of coverage, j, which is one of the 35

highest indexed annual earnings years and in which the

earnings exceed mj

, we can construct an earnings

history identical to the earnings history of that solution

except that the earnings for year j equal mj

. For this

modified earnings history, SPMIN will stay the same

but the AIME, and hence the PIA, will decrease, so the

difference {SPMIN – PIA} will increase, contradicting

our assumption that the original solution maximizes that

difference. Therefore, for an earnings history to

maximize the difference {SPMIN – PIA}, earnings in

any of the 35 highest indexed earnings years which is a

year of coverage, must not exceed mj

.

Using a similar argument, we can also show that:

(a) the solution to this problem must consist of an

earnings history in which the earnings in the 40

years that are not years of coverage equal zero;

and 

(b) the number of years of coverage in the solution

will not exceed 30.

Combining these results, we see that the 40 earnings

amounts in the earnings history (from the year of attainment of age 22 through the year of attainment of age 61)

that solve our maximization problem must either be mj

or 0, and the number of years that have earnings mj is no

less than 11 and no more than 30. Now, for each

n = 11,..., 30, the amount of the special minimum PIA

does not depend on which of the n years among the 40

are the years with earnings of mj

, but the amount of the

wage-indexed PIA does. In fact, the wage-indexed PIA

will be smallest when the n years are those with the n

smallest values of Mj

, where Mj denotes the wageindexed value of mj

. So to find a solution to our problem, we only need to consider 20 possible solutions,

namely the earnings histories consisting of mj

 for each

year j with one of the n smallest values of Mj

 and zero

for all other years. Once we find the maximum gain

from the special minimum PIA among these 20 possible

solutions, we obtain our answer.

Computational Results

Using the projected values for the national average wage

index, COLAs, bend points, and minimum amounts

required for a year of coverage based on the 2013 Trustees Report,7 we found a solution to the stated problem

by the method described above. In addition, we also

solved the problem for persons born in the years after

1951 and correspondingly first eligible for benefits after

2013. For years of first eligibility after 2012, the following table presents for the earnings histories that solve the

optimization problem the special minimum PIA, the

wage-indexed PIA when government pension receipt is

not involved, and the advantage of the special minimum:

5 http://www.socialsecurity.gov/OACT/COLA/bendpoints.html

6 https://www.socialsecurity.gov/cola/automatic-cola.htm 7 http://www.socialsecurity.gov/oact/tr/2013/
3

This estimate is very sensitive to the assumed path of

assumed future wage and price increases. In order to

give a sense of the scope of this sensitivity, we also replicated the estimation procedure using alternatively the

low-cost and high-cost assumptions in the 2013 Trustees

Report. Based on these assumptions, we found that it

will be impossible for workers with years of first eligibility of 2017 and 2023 respectively to receive a special

minimum PIA instead of a wage-indexed PIA, as indicated in table 1. The reason for the decrease over time of

the maximum gain from the special minimum PIA relative to the wage-indexed PIA is that the special minimum increases from one cohort to the next with COLAs

while the wage-indexed PIA increases from one cohort

to the next with wage growth and prices have generally

grown more slowly than wages in the past, and are projected to continue to do so under the Trustees’ assumptions.

For the person born in 1951, table 2 displays, in order by

the value of Mj

, the rank, n, of Mj, the calendar year j,

the value of mj

, the value of Mj, and the maximum gain

of the special minimum given n years of coverage:

Thus, the minimum number of years of coverage in

order to receive the special minimum upon attainment of

age 62 in the year 2013 is 29. Additional analysis

showed that this number increased to 30 for attainments

in 2017.

Furthermore, we can see that the gain from the special

minimum for a worker born in 1951 and retiring in 2013

is greatest when the number of years of coverage, n,

equals 30. Again, additional analysis showed that for the

Table 1.—PIAs Based on Earnings Histories

Which Optimize the Effect of the Special Minimum PIA

Computation for Workers in Year of First Eligibility, 

Based on the 2013 Trustees Report

Year of first 

eligibility

Special

minimum

PIA

Wageindexed

PIA

Difference between 

special minimum and 

wage-indexed PIA

2013 $804.00 $762.40 $41.60

Intermediate assumptions (Alternative II)

2014 820.00 773.40 46.60

2015 836.40 788.20 48.20

2016 857.30 818.60 38.70

2017 879.50 857.40 22.10

2018 903.20 898.90 4.30

2019 928.40 940.60 -12.20

Low-cost assumptions (Alternative I)

2014 818.40 773.40 45.00

2015 830.60 798.40 32.20

2016 844.70 835.20 9.50

2017 859.90 872.50 -12.60

High-cost assumptions (Alternative III)

2014 821.60 772.50 49.10

2015 842.10 777.10 65.00

2016 869.80 798.50 71.30

2017 898.50 832.80 65.70

2018 930.80 873.40 57.40

2019 966.10 920.50 45.60

2020 1,002.80 970.00 32.80

2021 1,040.90 1,017.40 23.50

2022 1,080.40 1,071.10 9.30

2023 1,121.40 1,126.20 -4.80

Table 2.—Maximal Effect of the Special Minimum PIA 

Computation for a Worker Born in 1951 and

Retiring at Age 62 in 2013

n

Year of 

earnings

j

Amount required 

for year of 

coverage

mj

mj indexed 

by average 

wages

Mj

Maximum 

gain given

n years of 

coverage

1 1998 $7,605.00 $11,325.14 N/A

2 1999 8,055.00 11,362.08 N/A

3 2000 8,505.00 11,368.17 N/A

4 1997 7,290.00 11,424.25 N/A

5 1996 6,975.00 11,568.42 N/A

6 2007 10,890.00 11,583.77 N/A

7 1992 6,210.00 11,637.17 N/A

8 2006 10,485.00 11,659.11 N/A

9 2005 10,035.00 11,671.61 N/A

10 2001 8,955.00 11,690.76 N/A

11 1991 5,940.00 11,704.73 -$233.00

12 2004 9,765.00 11,773.15 -217.90

13 1995 6,795.00 11,821.03 -202.70

14 2008 11,385.00 11,837.99 -187.80

15 2011 11,880.00 11,880.00 -174.00

16 1993 6,435.00 11,955.98 -158.70

17 2003 9,675.00 12,206.91 -144.60

18 1994 6,750.00 12,213.44 -130.40

19 2002 9,450.00 12,214.49 -116.30

20 2010 11,880.00 12,252.24 -102.00

21 2012 12,285.00 12,285.00 -88.70

22 2009 11,880.00 12,541.82 -74.80

23 1973 2,700.00 15,309.04 -67.20

24 1981 5,550.00 17,319.04 -63.90

25 1980 5,100.00 17,516.82 -61.70

26 1975 3,525.00 17,553.53 -58.60

27 1974 3,300.00 17,661.18 -38.60

28 1979 4,725.00 17,690.61 -11.70

29 1976 3,825.00 17,817.96 15.10

30 1982 6,075.00 17,968.14 41.60
4

years from 2014 to 2018, the gain of the special minimum was also greatest when n equals 30.

Recipients of the Special Minimum PIA Benefit

The Master Beneficiary Record (MBR) is the administrative file of records of benefit entitlement for the OASI

and DI programs. We obtained information from the

MBR regarding the beneficiaries who are receiving the

special minimum PIA in June 2013, including the

amount of the “support PIA”—the PIA which would

have been used if not for the special minimum. For most

of the beneficiaries receiving the special minimum, we

calculated the gain in benefit due to the special minimum PIA as:

GAIN = MBA – MBA

where SUPPIA is the support PIA and MBA is the

Monthly Benefit Amount. The MBA may be less than or

greater than the PIA because the beneficiaries may have

retired earlier or later than the Normal Retirement Age

or because of the family maximum provision. For auxiliaries, the MBA is also based on a specified percentage

of the applicable PIA.

Some beneficiaries are entitled to both a primary and

secondary benefit. For dually-entitled beneficiaries

whose secondary benefit is based on a special minimum

PIA, we modified the formula to: 

GAIN = MBA – MAX { MBA, SAMBA}

to recognize the possibility that the secondary benefit

based on the support PIA might be smaller than the primary’s PIA. SAMBA represents the smaller actuariallyreduced MBA, the primary benefit.

The following table shows the number of entitled beneficiaries and the average gain due to the special minimum PIA by year of current entitlement and beneficiary

type as of June 2013, for those beneficiaries entitled in

December 2012 or earlier. We have not included beneficiaries who are receiving a primary benefit based on the

special minimum but are dually entitled to a larger secondary benefit not based on the special minimum, and

hence are not really gaining from the special minimum

calculation.

We see that the number of entitlements has dropped

since the late 1990’s, while the average gain of the special minimum over the support PIA has dropped for

entitlements in 2000 and later.

In the above table, the child category is the aggregated

result of children of three different categories of insured

workers. An eligible child beneficiary8

 has a parent who

is either a retired worker beneficiary, a disabled worker

beneficiary, or a deceased insured worker. Children of

retired and disabled workers are eligible for a monthly

benefit of one-half of the PIA, and children of deceased





 





SPMIN

SUPPIA





 





SPMIN

SUPPIA

Table 3.—Number of Entitled Beneficiaries and Average Gain in Monthly Benefit Amount Due to the

Special Minimum PIA by Year of Current Entitlement and Beneficiary Type, as of June 2013

Entitlement 

Year

Worker Spouse Child Widow All beneficiary types

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

1965-1969 1 $94.15 — — 24 $23.56 — — 25 $26.38

1970-1974 29 37.01 — — 83 22.80 8 $34.95 120 27.04

1975-1979 159 37.96 1 $22.57 117 26.66 58 25.28 335 31.77

1980-1984 2,638 45.89 33 26.92 263 31.52 226 33.49 3,160 43.61

1985-1989 7,213 44.70 218 21.00 305 33.09 672 34.48 8,408 42.84

1990-1994 6,807 51.99 377 22.49 159 31.06 1,079 35.87 8,422 48.21

1995-1999 3,389 61.53 305 26.19 88 31.57 1,250 37.80 5,032 52.97

2000-2004 2,180 59.24 261 28.62 74 28.62 1,292 34.28 3,807 48.07

2005-2009 1,802 53.11 210 26.02 38 23.89 1,294 36.38 3,344 44.60

2010-2013 1,115 54.91 121 27.44 48 18.16 794 38.58 2,078 46.22

Total 25,333 51.28 1,526 25.04 1,199 29.67 6,673 36.03 34,731 46.45

8 Children are eligible if they are in one of three categories: a minor

child under age 18, a student child aged 18 or19, or a disabled adult

child age 18 or older whose disability began before age 18. 
5

workers are eligible for a monthly benefit of threefourths of the PIA. 

Widows, including widowers, may be aged widow(er)s,

disabled widow(er)s, or young widow(er)s. Aged and

disabled widow(er)s are eligible for monthly benefits

equal to the full applicable PIA, with appropriate reductions for entitlement prior to Normal Retirement Age.

Young widow(er)s must be caring for a dependent child

under age 16 and are paid at the rate of three-fourths of

the PIA. Table 4 presents data for children and widows

by type of child and widow.

The following table provides information on the eligibility year of the worker and the basis for the support PIA,for families receiving the special minimum PIA entitled

in December 2012 or earlier:

Table 4.—Number of Entitled Child and Widow(er) Beneficiaries and Average Gain in Monthly Benefit Amount Due to 

the Special Minimum PIA by Year of Current Entitlement and Beneficiary Type, as of June 2013

Entitlement

Year

Children of... Widow(er)s

Retired or disabled 

workers Deceased workers Aged Disabled Young

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

Number of 

beneficiaries

Average

gain

1965-1969 — — 24 $23.56 — — — — — —

1970-1974 1 $25.70 82 22.76 8 $34.95 — — — —

1975-1979 — — 117 26.66 58 25.28 — — — —

1980-1984 11 24.33 252 31.83 226 33.49 — — — —

1985-1989 30 21.11 275 34.40 671 34.48 — — 1 $30.82

1990-1994 23 25.56 136 31.99 1,077 35.89 — — 2 23.70

1995-1999 17 26.90 71 32.69 1,242 37.85 8 $29.34 — —

2000-2004 32 29.51 42 27.93 1,273 34.39 16 29.22 3 13.22

2005-2009 26 21.01 12 30.12 1,269 36.56 25 27.00 — —

2010-2013 40 19.11 8 13.42 784 38.84 9 18.28 1 16.50

Total 180 23.48 1,019 30.76 6,608 36.13 58 26.58 7 19.20

Table 5.—Number of Families with Benefit Entitlements Receiving the Special Minimum PIA, by the Eligibility Year of the 

Worker and the Basis for the Support PIA, as of June 2013

Year of

worker’s

eligibility

Basis for the support PIA

Total

Average

monthly

wage

(Eligibility

before

1979)

Average

indexed

monthly

earnings

(AIME)

AIME

with

windfall

elimination 

provision Others1

Pre-1979 1,530 16 1 108 1,655

1979 — 107 — 39 146

1980 — 277 2 36 315

1981 — 937 3 39 979

1982 — 1,780 7 43 1,830

1983 — 1,924 6 68 1,998

1984 — 1,873 19 65 1,957

1985 — 2,037 19 99 2,155

1986 — 1,805 70 142 2,017

1987 — 1,332 146 107 1,585

1988 — 1,723 643 130 2,496

1989 — 1,171 882 111 2,164

1990 — 874 1,158 57 2,089
6

The diminishing effect of the special minimum is even

more obvious from table 5; in later eligibility years the

special minimum never exceeds the regular AIME PIA

and exceeds the WEP PIA relatively infrequently. Even

though it was theoretically possible for first eligibilities

from 1999 to 2012 for a family with a PIA based on the

AIME to receive a special minimum PIA, the probability of such a family receiving a special minimum PIA

was very small. The worker in such a family would have

to have had earnings for at least 27 years that were no

lower than but not much higher than 25% of the “old

law” contribution and benefit base for years 1950 to

1990 and 15% of the “old law” contribution and benefit

base for years after 1990.

The only recipients of the special minimum in recent

years are workers who are also receiving a pension

based on work not covered by the Social Security program and their dependents and would have otherwise

received the Windfall Elimination Provision PIA, which

is also based on indexed earnings but pays a less generous PIA than the regular formula.

The following table provides information on the number

of years of coverage for families receiving the special

minimum PIA in June 2013:

1991 — 896 1,106 1 2,003

1992 — 369 748 — 1,117

1993 — 137 753 — 890

1994 — 38 518 — 556

1995 — 67 522 — 589

1996 — 75 558 — 633

1997 — 47 595 — 642

1998 — 10 573 — 583

1999 — — 437 — 437

2000 — — 405 — 405

2001 — — 411 — 411

2002 — — 340 — 340

2003 — — 300 — 300

2004 — — 400 — 400

2005 — — 383 — 383

2006 — — 367 — 367

2007 — — 311 — 311

2008 — — 367 — 367

2009 — — 260 — 260

2010 — — 171 — 171

2011 — — 151 — 151

2012 — — 104 — 104

Total 1,530 17,495 12,736 1,045 32,806

1 Includes 1990 Old-start PIAs, 1990 New-start PIAs, Old-start guarantee PIAs, New-start guarantee PIAs, and Frozen minimum PIAs.

Table 5.—Number of Families with Benefit Entitlements Receiving the Special Minimum PIA, by the Eligibility Year of the 

Worker and the Basis for the Support PIA, as of June 2013 (Cont.)

Table 6.—Number of Families Receiving the Special 

Minimum PIA, by Number of Years of Coverage and June 

2013 Special Minimum PIA, as of June 2013

Years of 

coverage

June 2013 Special 

Minium PIA Number of Families

11 $38.80 —

12 79.10 3

13 119.50 34

14 159.60 149

15 199.50 227

16 240.00 285

17 280.20 459

18 320.50 780

19 360.70 929

20 401.10 1,175

21 441.40 1,119

22 481.40 1,167

23 522.30 1,316

24 562.50 1,367

25 602.50 1,418

26 643.40 1,494

27 683.20 1,783

28 723.50 2,316

29 763.80 3,091

30 804.00 13,694

Total 668.141

1 Weighted average.

32,806
7

Conclusion

For first eligible beneficiaries in recent years, the probability is very small that an earnings record will yield a

higher special minimum PIA than a regular wageindexed PIA, and, in fact, there are no recent eligible

beneficiaries with a special minimum PIA except those

affected by the WEP - and relatively few of them. Projections indicate that only under very limited circumstances will one be able to benefit from the special

minimum now and in the future.

The minimum earnings that qualify for a year of coverage were dropped in 1991 from 25% to 15% of the “oldlaw” contribution and benefit base to give more people

the opportunity to receive the special minimum. However, as we observed from the MBR records, the number

of people who received the special minimum continued

to drop even for people with eligibility years after 1990.