1. Introduction
The Office of the Chief Actuary (OCACT) has traditionally used hypothetical earnings histories to illustrate a range of benefit levels, replacement rates, money's worth measures, and internal rates of return under the Social Security program. OCACT has long used these illustrations to evaluate the program under present law. In addition, in recent years, these hypothetical earnings histories have formed the basis for illustrating possible program changes on benefit levels.^{1}
OCACT developed scaled worker hypothetical earnings patterns starting in 2001. These patterns express earnings at levels relative to the AWI by age. These earnings levels reflect the average patterns of work and earnings of actual insured workers over their careers.
This note presents the three sets of scaled worker factors recently updated for the hypothetical low, medium, and high lifetime earnings examples used in table V.C7 of the 2012 Trustees Report. In addition, this note presents a set of scaled worker factors for a hypothetical worker with "very low" lifetime earnings. Table 6 shows these final scaled factors.
Prior to the development of scaled factors, OCACT generally used hypothetical steady workers, who earn a constant percentage of SSA's national average wage index (AWI)^{2} throughout their careers. These hypothetical steady earnings patterns tended to overrepresent the proportion of actual lifetime earnings received at younger ages and underrepresent the proportion received at prime working ages for most workers. Overrepresenting early earnings tends to bias downward estimates of the internal rate of return of the presentlaw program.
In developing these four sets of factors, we initially developed one set of raw scaled factors using earnings from the Continuous Work History Sample (CWHS). We made a preliminary adjustment to these raw factors for ages 62 and over to account for the select nature of these workers who continue working at such ages. Then, these preliminary adjusted scaled factors are further adjusted so that the resulting careeraverage earnings levels^{3} are 25 percent, 45 percent, 100 percent, and 160 percent of the AWI for the very low, low, medium, and high hypothetical workers, respectively. We selected these careeraverage earnings levels in order to provide both a useful range of examples and continuity with previous estimates for hypothetical workers. This note also includes a final hypothetical "maximum" earner with earnings equal to the OASDI maximum taxable earnings level for each year, in order to provide a fuller range of career taxable earnings levels under the Social Security program.
Table 1 compares overall earnings for these hypothetical workers to those of actual retiring workers. We use the Average Indexed Monthly Earnings^{4} (AIME), which is based on a worker's earnings, as a measure of overall earnings. We develop the distribution of actual workers retiring in 2011, from a 1 percent sample of Social Security administrative records.
Percent with AIME less than AIME for hypothetical case 
Percent with AIME closest to AIME for hypothetical case^{3} 


All males 
All females 
Total, all workers 
All males 
All females 
Total, all workers 

Very Low ($10,413)

7.1

17.6

12.2

11.5

27.0

18.9

Low ($18,744)

15.4

35.7

25.2

15.0

31.1

22.7

Medium ($41,655)

39.4

74.7

56.4

28.7

28.6

28.7

High ($66,648)

69.8

93.8

81.3

29.5

11.5

20.8

Maximum ($97,322)

100.0

100.0

100.0

15.4

1.9

8.9

^{1}See text for definition of hypothetical workers. ^{2} Careeraverage earnings of hypothetical scaled workers retiring at age 62 in 2011. Earnings are wage indexed to 2010 in this calculation. ^{3}Rounded values do not necessarily sum to 100 percent. The percentage of workers with AIME values closest to that of the hypothetical maximum worker is expected to decline in future years. This is due to a significant increase in the OASDI maximum taxable earnings, relative to the AWI, in 1981 and a smaller increase in 1990. Note: Worker distributions include individuals who are dually entitled, or may become dually entitled to a higher benefit in the future, based on another worker's account. A significant proportion of entitled female workers, especially those with lower earnings, will receive higher benefits as aged spouse or aged widow beneficiaries. If such dually entitled workers were excluded from this analysis the distributions would skew more toward the higherlevel hypothetical workers. 
Table 1 shows that 35.7 percent of female workers retiring in 2011 have AIMEs below that of a hypothetical low wage scaled worker and that about 42 percent of all workers retiring in 2011 have AIMEs closest to that of hypothetical low or very low wage scaled workers. OCACT first included the level of earnings corresponding to the very low scaled factors in 2004 and chose this level of earnings so that approximately half the retirees who were previously bestrepresented by the hypothetical low scaled worker would now be bestrepresented by the hypothetical very low scaled worker.
Dually entitled workers, though still insured for worker benefits, receive a larger benefit as a dependent on another worker's account (generally as a spouse or widow(er)) than they would as a worker beneficiary only. A significant proportion of entitled female workers, especially those with lower earnings, will receive higher benefits as aged spouse or aged widow beneficiaries. If we excluded such dually entitled workers from this analysis, a higher percentage of the remaining workers would have earnings closer to the higherlevel hypothetical workers.
2. Developing Raw Scaled Factors from Earnings in the CWHS
Development of the raw scaled factors occurs in three steps:
a. Select workers in the CWHS for computing the factors;
b. Tabulate the earnings for these workers; and
c. Develop the raw scaled factors from the tabulated earnings.
a. Select Workers in the CWHS for Computing the Factors
The CWHS is a 1percent sample of workers with some OASDI taxable earnings during their lifetime. The Office of Systems updates it annually based on specifications from the Office of Research, Evaluation, and Statistics. We develop the factors in this actuarial note using the CWHS containing earnings data through 2009. The CWHS contains earnings for all the workers in the sample. It is important to limit analysis only to workers who are likely either to be eligible for retirement or disability benefits, or to have dependents eligible for survivors benefits. To include only those workers, we used the status of fully insured. A worker is considered fully insured if he or she has a total number of quarters of coverage (QCs)^{5} at least equal to the number of years after attainment of age 21 through the last year considered in the analysis (in this case 2008). A further requirement is that the worker must have a minimum of 6 QCs. Since a worker achieves permanent insured status with 40 QCs, any worker with 40 QCs is fully insured no matter how many years have elapsed since age 21. Any fully insured worker is likely to become eligible for a Social Security retirement benefit if he or she survives to eligibility age.
b. Tabulate Earnings for These Workers
The updated CWHS file contains taxable earnings for years 1951 through 2009. Due to posting delays, the earnings for 2009 in this file are less complete than for earlier years and were not used in our analysis. For each of the workers classified as fully insured as of 2008 (based on all earnings after 1950), our analysis includes earnings for the most recent 18year period (1991 through 2008) for ages 21 and over. We classify earnings by age of worker, and express earnings as their ratio to the AWI for the specific year.
OCACT developed scaled factors taking into account both the variations in earnings by age and the probabilities that workers may have years with zero earnings. The earnings records selected include years with zero earnings, but not years in which the worker was deceased^{6} or receiving a retired worker or disabled worker Social Security benefit.
c. Develop Raw Scaled Factors from the Tabulated Earnings
To normalize earnings from different years, annual earnings amounts for each year are divided by the AWI for that year. For each fully insured worker, normalized earnings are tabulated by age for each age 21 and over for years 19912008, as described in the preceding paragraph. The normalized earnings are summed by age and a corresponding worker count is kept. The raw scaled factors are determined by dividing the tabulated sum for each age, including years at zero earnings, by the corresponding numbers of workers. Table 2 displays the results.
3. Adjust Raw Scaled Factors to Match Selected CareerAverage Earnings Levels
Adjustment of the raw scaled factors occurs in three steps:
a. Calculate preliminary adjusted scaled factors from the raw scaled factors by overriding the scaled factors at ages 6264;
b. Construct the earnings pattern and calculate the careeraverage earnings for a hypothetical scaled worker using the preliminary adjusted scaled factors; and
c. Calculate very low, low, medium, and high final scaled factors from the preliminary adjusted scaled factors such that the careeraverage earnings for these hypothetical workers match the selected percentages of the AWI in the year prior to entitlement (25, 45, 100 and 160 percent) .
a. Calculate Preliminary Adjusted Scaled Factors from Raw Scaled Factors
The following values, based on table 2, show that there is an accelerating decline in raw factors at ages 60 and 61, followed by increases at ages 62 and 63:
Age

Raw Scaled Factor

Difference

55 
0.874 
 
56 
0.846 
0.028 
57 
0.817 
0.029 
58 
0.787 
0.030 
59 
0.755 
0.032 
60 
0.715 
0.040 
61 
0.665 
0.050 
62 
0.842 
+0.177 
63 
0.864 
+0.022 
64 
0.846 
0.018 
We do not have definitive information on the reasons for these changes after age 59. However, it seems reasonable to assume that some of the decline in the raw factors at ages 60 and 61 is due to the retirement (total or partial) of some workers before they became entitled to their OASDI retirement benefits at age 62. The increases in the raw factors at ages 62 and 63 may well occur because healthier, higherwage workers, and workers who have maintained consistent employment at older ages, are more likely to delay entitlement to OASDI benefits until after age 62. Our methodology removed the earnings of many nonworkers, lowwage workers, or lesshealthy workers from the tabulated group starting at age 62 because they started to receive Social Security retirement benefits.
Due to the differences between the groups of workers represented in data for ages justbefore versus justafter reaching age 62, we develop a smoother set of "adjusted" raw factors for ages 6264. Here we assume that earnings for workers over age 61 will stay constant in nominal dollars, thus decreasing relative to the AWI.
The preliminary adjusted scaled factors equal the raw scaled factors for ages up to 61. Table 3 calculates factors for ages 62 and over so that earnings in nominal dollars stay constant at the level for age 61. For example, we calculate the preliminary adjusted factor for age 62 by dividing the factor for age 61 by the ultimate assumed annual increase in average wages under the intermediate assumptions of the 2012 Trustees Report. Table 3 shows the calculation of the preliminary adjusted scaled factors for ages 6264.
Though it provides an imperfect approximation for all types of workers, we adopted this approach in order to avoid having different scaled factors for workers who become entitled to OASDI benefits at different ages.
b. Construct the Earnings Pattern and Calculate the CareerAverage Earnings for a Selected Hypothetical Scaled Worker Using the Preliminary Adjusted Scaled Factors
The selected hypothetical scaled worker (referred to as the 1960born preliminary scaled worker) was born on January 2, 1960, has earnings from age 21 through 64, and retires at age 65. We calculate earnings for each year by multiplying the preliminary adjusted scaled factor for that age by the AWI value for the corresponding year. This worker turns age 22 in 1982, so the age 22 preliminary adjusted factor of 0.325 is multiplied by the 1982 AWI of $14,531.34 to obtain annual earnings of $4,722.69. Table 4 shows the preliminary adjusted scaled factors, AWI amounts, and corresponding hypothetical earnings for the 1960born preliminary scaled worker.
The last line of table 4 shows careeraverage earnings of $61,929 (wage indexed to 2024) for the 1960born preliminary scaled worker. This is a slightly different calculation than the AIME because (1) earnings are indexed to the year prior to entitlement rather than to two years prior to eligibility, and (2) earnings are averaged on an annual basis instead of a monthly one. For the 1960born preliminary scaled worker, who retires at age 65 in 2025, the indexing year used to compute careeraverage earnings is 2024.
Note: We base careeraverage earnings on the highest 35 years of indexed earnings (column 4). Years 198187 and 20232024 are excluded because they are not among the highest 35 years of indexed earnings.
c. Calculate Very Low, Low, Medium, and High Final Scaled Factors from the Preliminary Adjusted Scaled Factors such that Selected Hypothetical Scaled Workers with Earnings Based on These Factors Would Have CareerAverage Earnings Equal to Selected Percentages of the AWI in the Year Prior to Entitlement
The selected careeraverage earnings level for the medium scaled worker is the AWI in the year prior to entitlement. Similarly, the selected careeraverage earnings levels for the very low, low, and high scaled workers are 25 percent, 45 percent and 160 percent of the AWI in the year prior to entitlement, respectively. As noted earlier, the careeraverage earnings for the 1960born preliminary scaled worker equals $61,929, wage indexed to 2024 (see table 4). By comparison, the average wage index for 2024 is $73,998.19^{7}. Corresponding careeraverage earnings levels for a very low, low, and high earner are $18,500, $33,299, and $118,397, respectively. Table 5 summarizes this information, and provides the ratio of the selected careeraverage earnings levels to the careeraverage earnings for the 1960born preliminary scaled worker.
Two primary reasons for choosing the year prior to entitlement as the indexing year in computing the careeraverage earnings are:
Furthermore, careeraverage earnings provide a reasonable denominator for replacement rate calculations that allow hypothetical scaled worker replacement rates to maintain consistency with the prior hypothetical steady worker replacement rates.
The last step is to apply the ratios from table 5 to the preliminary adjusted scaled factors. This step requires four separate calculations, one each for the very low, low, medium, and high scaled worker cases. For example, we determine the scaled factors for the hypothetical medium scaled worker by multiplying:
Table 6 shows the calculation of the final scaled factors, combining the preliminary adjusted scaled factors with the adjustment factors.
4. Developing Hypothetical Worker Earnings from Factors
Given a year of birth, and an earnings level for scaled workers, classified as either very low, low, medium, or high, one can obtain annual earnings by multiplying the relevant set of scaled factors by the AWIs in the corresponding years. Consider as an example a low earnings worker born in 1970. To determine earnings for this worker at age 22, multiply the scaled factor for the low scaled worker at age 22 by the AWI in 1992, the year in which the worker turns 22. Because the hypothetical workers are born in January, a year of age corresponds to a calendar year. Therefore, a worker born on January 2, 1970 would be age 22 throughout 1992. In this way, one can develop a series of very low, low, medium, and high scaled earnings for any age and hypothetical year of birth. Table 7 carries out the calculation of hypothetical scaled worker earnings for high earnings workers for the selected years of birth 1930, 1949, and 1997.
^{1}
Refer to the February 2, 2011 letter from Stephen C. Goss for an example of this
illustrative benefits analysis. This letter is located at:
http://www.socialsecurity.gov/OACT/solvency/BowlesSimpsonRivlinDomenici_20110202.pdf
^{2}
For more information on the national average wage index, including
historical values, see:
http://www.socialsecurity.gov/OACT/COLA/AWI.html.
^{3} We define careeraverage earnings as the average of the highest 35 years of earnings, indexed for growth in average wages to the year prior to benefit entitlement. See further discussion under subsection 3.b. We introduced this revision with the 2003 Trustees Report.
^{4} See http://www.socialsecurity.gov/OACT/COLA/Benefits.html#aime for more details on how to calculate the AIME.
^{5}
The QC is the basic unit for determining whether a worker is insured for
Social Security benefits. In 2012, for example, a worker needed to have
$1,130 in covered earnings to obtain a QC. Workers can earn up to 4 QCs
per calendar year. Since 1978 the amount of covered earnings required to
obtain a QC has been automatically indexed each year with the growth in
SSA's national average wage index.
See
http://www.socialsecurity.gov/OACT/COLA/QC.html
for more information, including a list of historical QC amounts.
^{6} Data concerning worker deaths appears in the CWHS. However, death data in the CWHS does not include all statereported death data. Therefore, we also used Social Security's NUMIDENT file to identify deaths of individuals in the CWHS. The NUMIDENT file contains, among other things, death data including statereported deaths.
^{7}
The projected AWI value for 2024 is taken from the 2012 Trustees Report.
See
http://www.socialsecurity.gov/OACT/TR/2012/lr6f6.html.
^{8} Prior to 2001, the hypothetical workers used were all "steady" workers. Today, we retain only the "steady maximum" worker. "Steady" workers were assumed to work beginning at age 22 until retirement, death, or disability, and to have a steady amount of earnings relative to the AWI each year. For example, the "steady average" worker earns the AWI for every working year. Similarly, the "steady low" worker earns 45 percent of the AWI for every working year, and the "steady high" worker earns 160 percent of the AWI for every working year.