ACTUARIAL NOTE  SOCIAL SECURITY ADMINISTRATION 

Number 100  Office of the Chief Actuary 
February 1980  Baltimore, Maryland 
COMPUTING A SOCIAL SECURITY BENEFIT AFTER THE 1977 AMENDMENTS 

by Steven F. McKay 
The 1977 Amendments to the Social Security Act brought about many changes involving both financing and benefits. In particular, a new "decoupled" or wageindexed method of computing benefits was added for new beneficiaries beginning in 1979, and two existing methods were changed. This Actuarial Note will explain how to use the wageindexed method to compute a Primary Insurance Amount (PIA) and Maximum Family Benefit (MFB), as well as when to use that method and when to use one of the methods carried over from the previous law. Other changes brought about by the amendments, though significant, will not be discussed here.
Since 1979, there have been five basic types of benefit computations:
A potential beneficiary receives the highest benefit yielded by any of the methods which apply in his case. (For people turning 62 in 1975 and later, and for disability and survivor cases where the worker is under age 62, benefit computations do not depend on the sex of the worker. To simplify the exposition, only the male gender will be used in the following discussion.)
One or more of the first three methods may apply to a new beneficiary depending on the type of benefit and year of eligibility. For purposes of computing benefits, "year of eligibility" means (1) for retirement benefits, the year of attaining age 62, (2) for disability benefits, the earlier of the year of onset of disability or the year attaining age 62, and (3) for survivor benefits, the earlier of the year of death or the year attaining age 62.
The applicability of each of the first three methods for retirement benefits will be discussed first. Each method's applicability depends on the year of the worker's attainment of age 62. The PIA table method applies to workers attaining age 62 before 1979, the wageindexed formula applies to workers attaining age 62 in 1979 or later, and the transitional guarantee applies to workers attaining age 62 between the years 1979 and 1983, inclusive.
Next to be discussed is the applicability of each of the first three methods to the computation of disability benefits. The PIA table method applies if the year of eligibility is before 1979, and the wageindexed formula applies if the year of eligibility is 1979 or later. In no case may the transitional guarantee be used.
Problems arise in certain cases when applying the above rules to determine the year of eligibility and the applicability of the transitional guarantee. Consider first the case where a worker attaining age 62 before 1979 is eligible for both a retirement benefit and a disability benefit. Such a worker would have his benefit calculated under the PIA table method, even if he becomes disabled in 1979 or later, because the year of eligibility (for disability) cannot be after the year of attainment of age 62. Next consider the more involved case of someone attaining age 62 in the years 1979 to 1983, inclusive, and becoming disabled in 1979 or later. Applying the above rules, he may use the wageindexed formula, and not the transitional guarantee, for calculating his disability benefit. However, he may elect instead to apply for a retirement benefit, if he is eligible, in which case he may also use the transitional guarantee. The disadvantage in such a procedure is that the retirement benefit is subject to a reduction of 5/9 of one percent per month for retirement before age 65. For instance, for disability at age 62, the disability benefit would be 100 percent of the wageindexed formula PIA, whereas the retirement benefit would be 80 percent of the transitional guarantee PIA (or 80 percent of the wageindexed formula PIA, if that were greater). Possible advantages in selecting the retirement benefit are that the transitional guarantee PIA may be significantly greater than the wageindexed formula PIA, and the fivemonth waiting period which applies in disability cases does not apply in retirement cases.
Next to be considered is the applicability of each of the first three methods to the computation of survivor benefits. The PIA table method and wageindexed formula method apply in a manner analogous to their application to disability benefits, but the transitional guarantee, which cannot be applied to disability benefits, can be applied to the computation of survivor benefits in some cases. The transitional guarantee applies to the benefit computation of the survivors of workers attaining age 62 between the years 1979 and 1983, inclusive, but only if the worker survived to the month of attaining age 62.
Finally, the applicability of the last two methods will be discussed. The oldstart method is not restricted to certain groups of beneficiaries based on year of eligibility alone; however, PIA's based on the oldstart method will become rare beginning in the 1990's because the method requires that there be some earnings before 1951. The special minimum method has no restrictions at all as to who may use it, but in actual practice it yields PIA's higher than the other methods only for workers with many years of relatively low earnings.
When using this method, a PIA is linked to its corresponding average monthly wage (AMW) and MFB by way of the PIA table. The table is updated every June if the Consumer Price Index (CPI) has risen at least three percent since the measuring period ended for the last increase. If there is an increase in the earnings base (effective at the beginning of a calendar year), the PIA table is extended to a higher range of AMW's (up to an AMW of onetwelfth of the new base).
To calculate a PIA under this method an AMW is first calculated as the monthly average of the highest "n" years of earnings after 1950, where "n" is determined by the year of birth of the individual (and by sex, for workers born before 1913). For retirees, "n" equals the number of years elapsed after 1955 (or year attaining age 26, if later) and before the year attaining age 62, although a slightly different rule applies for males attaining age 62 before 1975. For instance, a retiree reaching age 63 in 1979 has an "n" of 22 (the number of years between 1955 and 1978, exclusive).
Once the AMW is calculated, the corresponding PIA and MFB may be found in the applicable PIA table. Table 1 presents the January 1979 PIA table, which was effective through May 1979.^{1} (The PIA table effective from June 1978 to December 1978 is the same as Table 1, except that it ends at an AMW of $1,475. The JuneDecember 1978 PIA table will be effective for a longer time in the transitional guarantee method, as discussed below.) Table 2 shows the PIA table method benefit calculation for an age 63 retiree in the first half of 1979, assuming he has maximum taxable earnings in every year.
Disability and survivor cases are handled similarly to retirement cases when using this method, with the modification that the AMW is based on an "n" calculated as if the worker turned 62 in the year of disablement or death.
This method introduces a number of complexities into the benefit calculation. The same "n" that would have been used under prior law is used here to compute an average monthly wage, but the average is now of indexed earnings rather than actual dollar amounts of earnings. Indexing attempts to make earnings of different years comparable by adjusting earnings of earlier years for changes in average wages. Table 3 gives the set of average annual wages which is currently used for indexing.
For an example of indexing, consider an age 62 retiree in October of 1979, the first year an age 62 retiree could use the wageindexed formula. Again assume the retiree has maximum earnings in every year. The year to which earnings are indexed (the base year for indexing) is 1977 in this case, since the year to which earnings are indexed is two years before eligibility in all cases. (The twoyear lag is necessary to provide time to collect average earnings data.) Therefore, indexed 1976 earnings equal actual 1976 earnings of $15,300 multiplied by average 1977 earnings (15300 x 9779.44, or 149,625,432.0000), divided by average 1976 earnings, (149,625,432.0000/9226.48), or $16,216.96. Earnings after the base year for indexing are not indexed. Therefore, in this example, earnings in 1978 and later are not indexed. Table 4 completes the calculation of the Average Indexed Monthly Earnings (AIME).
After the AIME is calculated, the PIA is determined. Rather than using the PIA table as in prior law, a threestep formula is used to calculate a PIA based on the AIME (the result is called the AIME PIA). The two dollar amounts in the formula depend on the year of eligibility. For persons becoming eligible in 1979, such as the age 62 retiree in October 1979, the formula to compute the AIME PIA is:
90% of the first $180 of AIME, plusThe result of the formula is rounded up to a multiple of $.10, giving the AIME PIA.
32% of AIME in excess of $180 but less than $1085, plus
15% of AIME in excess of $1085.
The AIME MFB is calculated using a fourstep formula based on the AIME PIA. Again, the dollar amounts in the formula depend on the year of eligibility, with the formula for persons becoming eligible in 1979 being
150% of the first $230 of PIA, plusThe PIA and MFB for the month of retirement are calculated from the AIME PIA and AIME MFB (which are determined for January of the year of eligibility) by applying in sequence all the intervening annual general (CPI) benefit increases rounding up to the next multiple of $.10 each time. Table 4 completes the calculation of the PIA and MFB for the example, applying the June 1979 benefit increase of 9.9 percent. Benefit increases occur in June, so that workers retiring in June or later receive the June general benefit increase in the year of retirement in the initial PIA calculation. Thus, everyone born in one particular calendar year becomes eligible for the same benefit increases, regardless of month of retirement, or month of birth, since a worker retiring before June receives the June general benefit increase by virtue of being a beneficiary on the rolls, and a worker retiring in June or later receives the June general benefit increase in the initial PIA calculation.
272% of PIA in excess of $230 but less than $332, plus
134% of PIA in excess of $332 but less than $433, plus
175% of PIA in excess of $433.
For persons becoming eligible for benefits in years after 1979, the PIA formula dollar amounts ($180 and $1085 in 1979) and MFB formula dollar amounts ($230, $332, and $433 in 1979) are adjusted by the change in average earnings, with a twoyear lag. For instance, the 1980 PIA formula dollar amounts (bend points) equal the $180 and $1085 amounts increased by the growth in average wages from 1977 to 1978 ($10,556.03/9,779.44), resulting in $194.29 and $1,171.16. Those amounts are rounded to the nearest whole dollars, $194 and $1171. Similarly, the 1980 MFB formula bend points are calculated to be $248, $358, and $467.
As a further example, Table 5 shows the PIA calculation for a retiree aged 62 (born in January 1918) and retiring in January of 1980 with maximum earnings in all previous years. The year of eligibility for benefits is 1980; therefore, the 1980 PIA and MFB formula bend points are used. The final result in this case is that the PIA and MFB are $492.80 and $862.50, respectively.
A final test in the wageindexed method, in whatever year is being considered, is that if the calculated PIA is less than the minimum PIA of $122, the PIA will be that minimum. (The $122 minimum PIA applies only to the decoupled formula method. The PIA table method and transitional guarantee method have different minimums.) General benefit increases do not apply from the year attaining age 62 for the minimum benefit, but only since first receipt of benefits, or from the year attaining age 65 if the worker has not retired by that time.
The transitional guarantee method may be used by persons turning 62 in the fiveyear period beginning in 1979 (born in the years 1917 to 1921, inclusive), regardless of the year of retirement. This method is a mixture of a method 1 and a method 2 calculation, in that the PIA is found from a PIA table after which the MFB is found from the wageindexed method MFB formula.
When finding a PIA, the PIA table used is "frozen" in two ways. First, no earnings in the year of attainment of age 62 or later may be used to compute an AMW. Second, the JuneDecember 1978 PIA table, with general benefit increases applied to the PIA so determined only for the year attaining age 62 and later, is used. (As noted earlier, the JuneDecember 1978 PIA table is the same as the one for JanuaryMay 1979, Table 1, for AMW's up to $1475.) By comparing the decoupled method with the transitional guarantee, one can see that the same benefit increases apply to the initially calculated PIA, whether it is the AIME PIA of the decoupled method or the December 1978 PIA of the transitional guarantee. In both cases, benefit increases apply in the year the worker attains age 62, whether or not he is retired, and regardless of the month of birth or the month of retirement, and in every year thereafter.
Table 6 represents the computation of a transitional guarantee PIA and MFB for the age 62 retiree in October 1979 (the same retiree as in Table 4).
After comparing the resulting PIA in Table 6 to that in Table 4, the age 62 retiree in October 1979 would receive the transitional guarantee PIA of $534.30, since it is greater than the wageindexed formula PIA of $498.00. To further illustrate the transitional guarantee and wageindexed formula methods, suppose that this same retiree continued to work in 1979, earned the maximum of $22,900, and retired in January 1980. Then, after substituting $22,900 in the AIME calculation in Table 4 for the lowest year of indexed earnings ($11,180.15 in 1958), his AIME would be increased to $1,138, and his January 1980 wageindexed formula PIA and MFB would be $505.20 and $884.10, respectively. His transitional guarantee PIA and MFB in Table 6 would not change, since the $22,900 was earned in the year of attaining age 62 and would therefore not be available for a transitional guarantee calculation. As a result, the retiree in January 1980 would still receive the transitional guarantee PIA of $534.30.
Table 7 presents the computation of a transitional guarantee PIA and MFB for the age 62 retiree in January 1980 (the same retiree as in Table 5). Again this retiree gets the transitional guarantee PIA of $503.40, since it is greater than the decoupled formula PIA of $492.80.
One of the three methods discussed above (the PIA table, the wageindexed formula, and the transitional guarantee) will be the applicable method (giving the largest PIA) for the large majority of future beneficiaries. However, for completeness, the last two methods will now be briefly described.
The oldstart method has evolved from the original 1939 Act formula which related an AMW to a Primary Insurance Benefit (PIB). This method became "oldstart" when the 1950 Act introduced the "newstart" formula (the current PIA table method), which involved only earnings after 1950. At that time, the oldstart method was allowed as an alternative for people with substantial earnings before 1951, and required the tabulation of yearbyyear earnings from 19371950.
The 1967 Amendments simplified the procedure by requiring only the sum of an individual's pre1951 earnings and an assumption as to their yearly distribution. The 1967 oldstart formula was to be effective for people becoming eligible before 1978. Therefore, had there been no 1977 Amendments, it would have been necessary, beginning in 1978, to return to the pre1967 oldstart formula.
The 1977 Amendments avoided this complication by introducing a new simplified oldstart formula for people becoming eligible in 1978 and later. The formula relates a calculated oldstart AMW to a PIB (Primary Insurance Benefit), which in turn is linked via the PIA table to a PIA. For instance, a PIB of $45.60 (the maximum possible) was linked to a PIA of $251.80 and an MFB of $384.90 in the JuneDecember 1978 PIA table.
Since 1979, the oldstart method has been similar to the transitional guarantee method in two ways. First, the PIB's are permanently related to corresponding PIA's by the JuneDecember 1978 PIA table, whereas in the past the PIB's and PIA's were related by the latest updated PIA table. Second, for people becoming eligible in 1979 and later, earnings in and after the year of eligibility cannot be used in an oldstart calculation. Such earnings can be used only under the wageindexed formula. Unlike the transitional guarantee, however, there is no fiveyear limit on use of the oldstart method; anyone with earnings prior to 1951, including those disabled, may use it if it results in a higher PIA than other applicable methods.
This method is useful for workers with long periods of relatively low earnings. The benefit equals the number of years of coverage in excess of ten but not more than thirty (maximum twenty) times a dollar amount. A year of coverage for this purpose is a year in which earnings were at least one quarter of the earnings base, for years up to 1978. Because of the large ad hoc increases in the base in 1979, 1980, and 1981, years of coverage in 1979 and later are years in which earnings are at least one quarter of what the earnings base would have been without the ad hoc increases ($18,900 in 1979 and $20,400 in 1980). The dollar amount in the special minimum was $8.50 in 1973 and $9.00 from 1974 to 1978, but the 1977 Amendments increased the amount to $11.50 effective in January 1979, and provided for automatic increases thereafter. Special minimum PIA's are increased each June by the same general benefit increase as are all other nonfrozen PIA's. Because the minimum PIA under the decoupled method is frozen, and because the PIA's under the oldstart method are frozen, the special minimum PIA could become the applicable PIA for an increasing proportion of beneficiaries.
When the dollar amount in the special minimum formula increased to $11.50, the MFB's corresponding to the special minimum PIA's were determined by applying the thencurrent wageindexed method MFB formula. Since the maximum PIA under the special minimum provision in 1979 was $230, which equaled the first dollar amount in the MFB formula, all special minimum MFB's were $150 percent of the corresponding PIA's, rounded up to the next multiple of $.10, in the first half of 1979.
The above illustrations have presented the calculation of PIA's and MFB's. The actual benefit payable to a beneficiary would be related to the PIA or MFB where the relationship could depend on the type of benefit, the age of the beneficiary, and the total number of beneficiaries. For instance, a retiree's benefit would be the PIA reduced by 5/9 percent for each month retirement preceded the month of attaining age 65. For the age 62 retiree in January 1980, whose PIA was calculated in Tables 5 and 7, the reduction would be 36 times 5/9 percent, or 20 percent, of his PIA of $503.40. The reduction would therefore be $100.68, rounded down to $100.60, so the benefit payable wold be $402.80.



Year  Earnings  High n Years of Earnings 

1951  $3,600  
1952  3,600  
1953  3,600  
1954  3,600  
1955  4,200  
1956  4,200  
1957  4,200  $4,200 
1958  4,200  4,200 
1959  4,800  4,800 
1960  4,800  4,800 
1961  4,800  4,800 
1962  4,800  4,800 
1963  4,800  4,800 
1964  4,800  4,800 
1965  4,800  4,800 
1966  6,600  6,600 
1967  6,600  6,600 
1968  7,800  7,800 
1969  7,800  7,800 
1970  7,800  7,800 
1971  7,800  7,800 
1972  9,000  9,000 
1973  10,800  10,800 
1974  13,200  13,200 
1975  14,100  14,100 
1976  15,300  15,300 
1977  16,500  16,500 
1978  17,700  17,700 
Total  183,000  
AMW = $183,000/(22x12) = $693.18, rounded down to $693
From January 1979 PIA table (Table 1): 
Year  Average Annual Wages 

1951  $2,799.16 
1952  2,973.32 
1953  3,139.44 
1954  3,155.64 
1955  3,301.44 
1956  3,532.36 
1957  3,641.72 
1958  3,673.80 
1959  3,855.80 
1960  4,007.12 
1961  4,086.76 
1962  4,291.40 
1963  4,396.64 
1964  4,576.32 
1965  4,658.72 
1966  4,938.36 
1967  5,213.44 
1968  5,571.76 
1969  5,893.76 
1970  6,186.24 
1971  6,497.08 
1972  7,133.80 
1973  7,580.16 
1974  8,030.76 
1975  8,630.92 
1976  9,226.48 
1977  9,779.44 
1978  10,556.03 
Year  Earnings  Earnings x $9779.44 
Indexed Earnings 
High n Years of Indexed Earnings 


1951  $3,600  $35,205,984.00  $12,577.34  $12,577.34  
1952  3,600  35,205,984.00  11,840.63  11,840.63  
1953  3,600  35,205,984.00  11,214.10  11,214.10  
1954  3,600  35,205,984.00  11,156.53  
1955  4,200  41,073,648.00  12,441.13  12,441.13  
1956  4,200  41,073,648.00  11,627.82  11,627.82  
1957  4,200  41,073,648.00  11,278.64  11,278.64  
1958  4,200  41,073,648.00  11,180.15  11,180.15  
1959  4,800  46,941,312.00  12,174.21  12,174.21  
1960  4,800  46,941,312.00  11,714.48  11,714.48  
1961  4,800  46,941,312.00  11,486.19  11,486.19  
1962  4,800  46,941,312.00  10,938.46  
1963  4,800  46,941,312.00  10,676.63  
1964  4,800  46,941,312.00  10,257.44  
1965  4,800  46,941,312.00  10,076.01  
1966  6,600  64,544,304.00  13,069.99  13,069.99  
1967  6,600  64,544,304.00  12,380.37  12,380.37  
1968  7,800  76,279,632.00  13,690.40  13,690.40  
1969  7,800  76,279,632.00  12,942.44  12,942.44  
1970  7,800  76,279,632.00  12,330.53  12,330.53  
1971  7,800  76,279,632.00  11,740.60  11,740.60  
1972  9,000  88,014,960.00  12,337.74  12,337.74  
1973  10,800  105,617,952.00  13,933.47  13,933.47  
1974  13,200  129,088,608.00  16,074.27  16,074.27  
1975  14,100  137,890,104.00  15,976.29  15,976.29  
1976  15,300  149,625,432.00  16,216.96  16,216.96  
1977  16,500  161,360,760.00  16,500.00  16,500.00  
1978  17,700  —  17,700.00  17,700.00  
Total  302,427.75  
AIME = $302,427.75/(23x12) = $1,095.75, rounded down to $1,095.
AIME PIA = 90% of $180 + 32% of $905 + 15% of ($1,095  $1,085) = $453.10. AIME MFB = 150% of $230 + 272% of $102 + 134% of $101 + 175% of ($453.10  $433) = $792.955, rounded up to $793.00.
October 1979 PIA = $498.00 
Year  Earnings  Earnings x $10,556.03 
Indexed Earnings 
High n Years of Indexed Earnings 

1951  $3,600  $38,001,708.00  $13,576.11  $13,576.11 
1952  3,600  38,001,708.00  12,780.90  12,780.90 
1953  3,600  38,001,708.00  12,104.61  12,104.61 
1954  3,600  38,001,708.00  12,042.47  
1955  4,200  44,335,326.00  13,429.09  13,429.09 
1956  4,200  44,335,326.00  12,551.19  12,551.19 
1957  4,200  44,335,326.00  12,174.28  12,174.28 
1958  4,200  44,335,326.00  12,067.97  12,067.97 
1959  4,800  50,668,944.00  13,140.97  13,140.97 
1960  4,800  50,668,944.00  12,644.73  12,644.73 
1961  4,800  50,668,944.00  12,398.32  12,398.32 
1962  4,800  50,668,944.00  11,807.09  
1963  4,800  50,668,944.00  11,524.47  
1964  4,800  50,668,944.00  11,071.98  
1965  4,800  50,668,944.00  10,876.15  
1966  6,600  69,669,798.00  14,107.88  14,107.88 
1967  6,600  69,669,798.00  13,363.50  13,363.50 
1968  7,800  82,337,034.00  14,777.56  14,777.56 
1969  7,800  82,337,034.00  13,970.20  13,970.20 
1970  7,800  82,337,034.00  13,309.71  13,309.71 
1971  7,800  82,337,034.00  12,672.93  12,672.93 
1972  9,000  95,004,270.00  13,317.48  13,317.48 
1973  10,800  114,005,124.00  15,039.94  15,039.94 
1974  13,200  139,339,596.00  17,350.74  17,350.74 
1975  14,100  148,840,023.00  17,244.98  17,244.98 
1976  15,300  161,507,259.00  17,504.75  17,504.75 
1977  16,500  174,174,495.00  17,810.27  17,810.27 
1978  17,700  186,841,731.00  17,700.00  17,700.00 
1979  22,900  —  22,900.00  22,900.00 
Total  347,938.11  
AIME = $347,938.11/(24x12) = $1,208.12, rounded down to $1,208.
AIME PIA = 90% of $194 + 32% of $977 + 15% of ($1,208  $1,171) = $492.79, rounded up to $492.80. AIME MFB = 150% of $248 + 272% of $110 + 134% of $109 + 175% of ($492.80  $467) = $862.41, rounded up to $862.50.
January 1980 PIA = $492.80 
Year  Earnings  High n Years of Earnings Before Age 62  

1951  $3,600  
1952  3,600  
1953  3,600  
1954  3,600  
1955  4,200  
1956  4,200  $4,200  
1957  4,200  4,200  
1958  4,200  4,200  
1959  4,800  4,800  
1960  4,800  4,800  
1961  4,800  4,800  
1962  4,800  4,800  
1963  4,800  4,800  
1964  4,800  4,800  
1965  4,800  4,800  
1966  6,600  6,600  
1967  6,600  6,600  
1968  7,800  7,800  
1969  7,800  7,800  
1970  7,800  7,800  
1971  7,800  7,800  
1972  9,000  9,000  
1973  10,800  10,800  
1974  13,200  13,200  
1975  14,100  14,100  
1976  15,300  15,300  
1977  16,500  16,500  
1978  17,700  17,700  
Total  187,200  
AMW = $187,200/(23x12) = $678.26, rounded down to $678.
December 1978 PIA = $486.10 from Table 1.
October 1979 PIA = $534.30 
Year  Earnings  High n Years of Earnings Before Age 62 

1951  $3,600  
1952  3,600  
1953  3,600  
1954  3,600  
1955  4,200  
1956  4,200  $4,200 
1957  4,200  4,200 
1958  4,200  4,200 
1959  4,800  4,800 
1960  4,800  4,800 
1961  4,800  4,800 
1962  4,800  4,800 
1963  4,800  4,800 
1964  4,800  4,800 
1965  4,800  4,800 
1966  6,600  6,600 
1967  6,600  6,600 
1968  7,800  7,800 
1969  7,800  7,800 
1970  7,800  7,800 
1971  7,800  7,800 
1972  9,000  9,000 
1973  10,800  10,800 
1974  13,200  13,200 
1975  14,100  14,100 
1976  15,300  15,300 
1977  16,500  16,500 
1978  17,700  17,700 
1979  22,900  22,900 
Total  210,100  
AMW = $210,100/(24x12) = $729.51, rounded down to $729.
December 1978 PIA = 1980 PIA = $503.40 from Table 1
January 1980 PIA = $503.40 