Introduction

This note presents analysis of theoretical internal real rates of return for hypothetical workers with various earnings patterns and levels under the Old-Age, Survivors, and Disability Insurance (OASDI) program.¹ The internal real rate of return (referred to as the internal rate of return) is the real interest rate (effective real annual yield) for which the present value of expected payroll taxes (contributions)² is equal to the present value of expected benefits. Therefore, internal rates of return attempt to answer the question: If a group of workers with selected characteristics were to invest contributions to fund future benefits (including dependents), what real annual yield would be required to finance those future benefits?³

All estimates in this note use the methods and assumptions from the intermediate scenario of the 2011 Trustees Report. Tables 1 through 6 present internal rates of return for hypothetical scaled workers who differ by year of birth, earnings level, and family grouping. Tables 1 and 4 show the internal rates of return for the Present Law Scheduled scenario, which uses contributions and benefits scheduled under present law. Because projected scheduled income would not fully finance scheduled benefits for the OASDI program after 2035, we include the two additional scenarios described below.

Because the OASDI program has operated on a largely pay-as-you-go (PAYGO) basis, the level of contributions for each generation of workers does not directly relate to the benefits these workers will receive. Under a PAYGO plan, benefit levels do not depend on the accumulation of individual contributions, as in a defined contribution plan, nor do annual contributions depend on scheduled future benefits of current workers and beneficiaries, as in an advance-funded defined benefit plan. Rather, the total benefits paid in a year determine the combined amount that workers and employers need to contribute to fund the system for that year.

Thus, internal rates of return for a PAYGO-financed benefit program reflect only theoretical values for contributions on a cohort basis. Payments to beneficiaries each year, in comparison to the total cost of (or resources used by) the program for that year, determine the real value of benefits under a PAYGO social insurance program. On this basis, with current administrative expenses of about 1 percent of total program cost, the real value of OASDI benefits is extraordinarily high.

Internal rates of return do not reflect the value of reducing the risk to individuals for extreme outcomes, such as death or disability at very young ages or survival to very old ages. In addition, OASDI internal rates of return do not compare adequately with similar ratios from private-sector plans, because many features of OASDI benefits are not typically available in private-sector plans. Two such features are annual cost-of-living adjustments and benefits for life in the event of disability. However, internal rate of return analysis does indicate the relative value of benefits that the OASDI program provides across generations and types of workers.

This note presents hypothetical workers with four different levels of scaled pre-retirement earnings patterns.⁴ A worker with a scaled earnings pattern has earnings that vary with age as a percentage of the national average wage index (AWI). The scaled worker enters the labor force at age 21 and retires at age 65. The scaled earnings level at each age reflects both the average earnings level of workers at that age and the percentage of individuals at that age who work. In addition to the scaled workers, this note presents a hypothetical steady maximum worker who has earnings at or above the OASDI contribution and benefit base for each year from age 22 to retirement at age 65.

The Office of the Chief Actuary (OCACT) has been producing theoretical internal rates of return for a number of years, including for recurring Actuarial Note 2009.5⁵ and for the 1994-96 Advisory Council Report on Social Security.⁶ OCACT based the analyses in the 1994-96 Advisory Council report on hypothetical workers with steady earnings patterns, that is, workers with earnings that are a constant percentage of the AWI for each year of work. OCACT first introduced non-steady hypothetical workers, referred to as scaled workers, in Actuarial Note #144 in 2001.⁷ Other authors have addressed alternative approaches to considering non-steady earnings histories, and we recognize that a broader set of earnings patterns may provide additional insights into the distributions of benefits payable and internal rates of return under the OASDI program. However, for the sake of practicality, we limit the number of cases considered in this note.

Methodology and Assumptions

This note presents theoretical internal rates of return for three hypothetical scenarios of the OASDI program: Present Law Scheduled, Increased Payroll Tax, and Payable Benefits. The Present Law Scheduled scenario utilizes the taxes and benefits specified in present law, even though projected program income and assets under present law are inadequate to pay all benefits through the 75-year projection period.

The Increased Payroll Tax scenario raises payroll-tax rates, beginning with the year of Trust Fund reserve depletion, to finance scheduled benefits fully in every year. The payroll-tax rate increases from the present law amount of 12.4 percent beginning in 2036. The payroll-tax rate increases to 16.21 percent for 2037 and continues to increase year-by-year, reaching 16.64 percent for 2085. Under this scenario, the payroll tax rate increases further after 2085 due to continuing increases in life expectancy.

Under the third scenario, Payable Benefits, payroll-tax rates hold constant while benefits decrease for each year after Trust Fund reserve depletion so that, for the Trust Funds as a whole, benefits paid equal taxes received. The reductions from scheduled levels apply equally proportionally to all types of benefits paid during the year. The intermediate projections of the 2011 Trustees Report show that program income does not fully pay scheduled benefits in 2036 and later. Thus, for the Payable Benefits scenario, annual benefit reductions begin in 2036 and generally increase each year thereafter. Projected program income, using present-law tax rates, pays 76.5 percent of scheduled benefits in 2037 and 74.4 percent of scheduled benefits in 2085. Under this scenario, annual reductions in benefits continue to grow after 2085 due to continuing increases in life expectancy.

The four earnings patterns for the hypothetical scaled workers reflect very low, low, medium, and high career-average levels of pre-retirement earnings patterns starting at age 21. OCACT sets the career-average level of earnings for these workers at a specified percent of the AWI. For the scaled medium earner, the career-average level of earnings is approximately equal to the AWI. For the scaled very low, low, and high earners, the career-average level of earnings is approximately equal to 25, 45, and 160 percent of the AWI, respectively.

Table A compares overall earnings for these hypothetical workers to those of actual retiring workers. We use the Average Indexed Monthly Earnings⁸ (AIME), which is based on a worker's earnings, as a measure of overall earnings. We develop the distribution of actual workers retiring in 2010, from a 1-percent sample of Social Security administrative records.

This note groups the hypothetical workers into four categories: single males, single females, one-earner couples where only the husband is employed, and two-earner couples. The note presents the single-earner and one-earner couple examples for the four earnings patterns listed above as well as for the hypothetical steady maximum worker. In addition, the note presents the two-earner couples at seven earnings combinations as follows:

(1) Husband high, wife high;

(2) Husband high, wife medium;

(3) Husband medium, wife medium;

(4) Husband medium, wife low;

(5) Husband low, wife low;

(6) Husband low, wife very low; and

(7) Husband very low, wife very low.

We assume that each scaled worker is born on January 2 and starts working on his/her 21st birthday.⁹ The wife and husband of each couple have the same date of birth. Each marriage occurs on the joint 22nd birthday of the wife and husband and continues for life. Assuming that marriages are life-long means that the calculated internal rates of return do not reflect the effects of divorce and of remarriage after death and divorce. However, because each individual may receive a total benefit equal only to the highest of any spouse, widow(er), or worker benefit that may be available, this omission has only a minor consequence. We assume that the couples have two children, one on the joint 27th birthday of the wife and husband, and the other on the joint 29th birthday of the wife and husband. We consider all types of retirement, disability, and survivor benefits, except for benefits to student children, disabled-adult children, and parents based on caring for a disabled-adult child. Omission of these benefits results in a very small understatement of the theoretical internal rate of return.

We assume that all nondisabled, surviving workers retire at age 65. We assume no mortality for children through age 18 in this analysis.

Analysis of Results

The following tables present the theoretical internal rates of return. The tables facilitate comparison of rates of return across different family groups, different years of birth, and different career-average levels of earnings.

Tables 1 through 6 present results for single males, single females, one-earner couples, and two-earner couples under the following three OASDI program scenarios:

For each sex, family grouping, and year-of-birth cohort, the internal rates of return decrease as earnings increase. This decrease occurs because the benefit formula is weighted toward beneficiaries with lower earnings. The advantage for lower earners is partially offset by their lower life expectancy.¹⁰ Females have lower mortality than males, resulting in higher likelihood of surviving to retirement age, longer life after retirement and therefore higher internal rates of return, even when earnings levels are the same. Lower rates of disability for women only partially offset this effect. The one-earner couples have the highest rates of return because of the auxiliary spouse, child, and widow(er) benefits payable based on one earnings record.

For two-earner couples at higher earnings levels, the internal rates of return often fall between the corresponding rates for single male workers and single female workers. In tables 1, 2, and 3, where both spouses have the same earnings, the rate of return for the two-earner couples is closer to the higher (female) single rate of return because of the inclusion of child benefits not reflected for single cases. In tables 4, 5, and 6, where spouses have different earnings levels, the two-earner rate of return is generally closer to the single female rate of return, at the female's earnings level, because of the inclusion of child and surviving spouse benefits. For the cases presented in this note, the lower earner's (wife's) retired worker benefit is always more than half of her husband's, so no aged spouse's benefit is payable.

This note does not include cases where a single individual has children, an increasingly common occurrence. Future analyses may address these cases. We believe that the internal rate of return for such cases will fall between those for the single worker and one-earner couple.

Based on the rising tax rates for the OASDI program (combined employer and employee tax went from 2 percent in 1941 to 12.4 percent starting in 1990), and the declining relative value of benefits due to an increase in the normal retirement age, one might expect that internal rates of return would decline steadily as the year of birth advances. In fact, every one of the combinations of sex, family groupings and earnings levels shows substantial decreases in real rates of return from the first to the fourth year-of-birth cohorts (1920, 1930, 1937, and 1943). However, increasing life expectancies, the start of disability benefits in 1957, and generally increasing disability rates since then, contribute toward higher internal rates of return after the 1943 birth cohort.

For the Present Law Scheduled scenario (tables 1 and 4), the internal rates of return generally increase from the 1943 to the 1955 birth cohort, except for maximum earners, for which they generally decrease. Improved mortality causes an increase in rates of return for most categories. Rates for maximum workers decrease because of the increasing relative level of the taxable maximum through 1982. Rates for one-earner couples decrease, or increase less rapidly than for other family groups, because of: (1) reductions in survivor and disability auxiliary benefits caused by mortality improvements; and (2) a reduction in the disability family maximum. Rates of return then decrease from the 1955 to the 1964 birth cohort for all family groupings due to increases in the normal retirement age. After the 1964 cohort, internal rates of return increase in almost all categories due to improving mortality rates, a fixed normal retirement age, and a fixed payroll tax rate. However, for one-earner couples, mortality improvements lead to reduced benefits for survivor beneficiaries and either decreases or smaller increases from cohort to cohort.

For the Increased Payroll Tax scenario (tables 2 and 5) payroll tax rates increase from those scheduled in present law beginning in 2036. Internal rates of return for the first seven year-of-birth cohorts (from 1920 to 1964) are the same as for the Present Law Scheduled scenario for all family groupings and earnings levels, since each of these year-of-birth cohorts reaches age 65 prior to 2036 and are not affected by the tax increase. Internal rates of return decrease for the 1973 cohort relative to the Present Law Scheduled scenario. After the 1973 birth cohort, rates of return decrease for all family groupings due to the increasing tax rates under this scenario.

For the Payable Benefits scenario (tables 3 and 6), benefits decrease from those scheduled in present law beginning in 2036. For the 1920 through 1937 birth cohorts, only retired beneficiaries age 99 or over are affected and there is little significant change from the Present Law Scheduled scenario. Beginning with the 1943 cohort, internal rates of return decrease relative to the Present Law Scheduled scenario. Within the Payable Benefits scenario, for the 1949 and 1955 cohorts, rates of return fluctuate, with improvements due to improved mortality being partially or fully offset by benefit reductions. For maximum wage workers in these cohorts, rates continue to decrease due to the increasing relative level of the taxable maximum. From the 1955 through the 1973 birth cohorts, rates of return decrease across-the-board as the benefit reductions have more effect. By the 1985 cohort, the benefit reductions are largely phased in and improved mortality offsets further reductions in later years, causing rates to fluctuate.

Conclusion

This note presents theoretical internal rates of return over time for various illustrative demographic groups and earnings levels. We could have used a variety of other approaches, methods and assumptions in this type of analysis. However, these hypothetical examples provide useful insight into how individual and cohort internal rates of return vary across generations, and within generations by sex, earnings level and pattern, and family grouping.

It is important to keep the significance of the internal rate of return in proper perspective. A higher internal rate of return does not necessarily mean a higher monthly benefit, even for two individuals with the same earnings. As one example, consider a man and a woman with the same earnings. A woman born in 1975 may expect to live 22.6 years on average after reaching age 65. Her male counterpart born in 1975 may expect to live 20.6 years on average after reaching age 65.¹¹ Her expected number of years of life after age 65 exceeds his by 10 percent, and, as a result, her internal rate of return is considerably higher than his. However, the monthly benefit she receives is exactly the same as he receives. Her higher internal rate of return derives solely from her longer expected lifetime.

Based on the provisions for benefits in the Social Security Act that have evolved since 1935, a primary goal of the OASDI program is to provide monthly benefit levels with a mix of equity (higher benefits for higher earners/ contributors) and adequacy (replacement of a larger portion of pre-retirement earnings for lower earners). The program's goal is not to provide similar lifetime benefits or internal rates of return across earnings levels and family groupings.

Internal rates of return for a PAYGO-financed benefit program reflect only theoretical values for contributions on a cohort basis. Payments to beneficiaries each year, in comparison to the total cost of (or resources used by) the program for that year, determine the real value of benefits under a PAYGO social insurance program. On this basis, with current administrative expenses of about 1 percent of total program cost, the real value of OASDI benefits is extraordinarily high.

Note: 2011 Trustees Report Intermediate Assumptions

Actuarial Note No. 2011.5
Office of the Chief Actuary,
Social Security Administration
July 2012

Note: 2011 Trustees Report Intermediate Assumptions

Actuarial Note No. 2011.5
Office of the Chief Actuary,
Social Security Administration
July 2012

Note: 2011 Trustees Report Intermediate Assumptions

Actuarial Note No. 2011.5
Office of the Chief Actuary,
Social Security Administration
July 2012

Note: 2011 Trustees Report Intermediate Assumptions

Note: 2011 Trustees Report Intermediate Assumptions

Note: 2011 Trustees Report Intermediate Assumptions

Actuarial Note No. 2011.5
Office of the Chief Actuary,
Social Security Administration
July 2012

¹ Internal rates of return are highly theoretical measures that in fact are not directly related to a pay-as-you-go financed benefit program, as discussed later in this section.

² Payroll taxes include any amounts transferred from the General Fund of the Treasury to substitute for employee/employer contributions, such as the 2 percent employee payroll tax reduction in 2011 under Public Law 11-312.

³ Because the OASDI Trust Funds receive transfers from the General Fund of the Treasury equal to a portion of taxes on benefits, internal rates of return that ignore these transfers may arguably overstate the ratio. Due to the difficulty of determining the level of income tax on benefits, this factor is not addressed in this note.

⁴ Additional details on developing scaled earnings patterns appear in the recurring Actuarial Note 2011.3, at: http://www.socialsecurity.gov/OACT/NOTES/ran3/an2011-3.html.

⁵ This note appears at the following internet address: http://www.socialsecurity.gov/OACT/NOTES/ran5/an2009-5.html.

⁶ The final report is located at the following internet address: http://www.socialsecurity.gov/history/reports/adcouncil/report/toc.htm.

⁷ This note appears at the following internet address: http://www.socialsecurity.gov/OACT/NOTES/note2000s/note144.html.

⁸ See http://www.socialsecurity.gov/OACT/COLA/Benefits.html#aime for more details on how to calculate the AIME.

⁹ The maximum steady worker is assumed to be born on January 2 and to start working on his/her 22nd birthday.

¹⁰ While the rates in this note do not reflect any differences in mortality by earnings level, we recognize the tendency for higher paid earners to have greater life expectancy, which would offset, to some degree, the progressive nature of benefits on a lifetime basis.

¹¹ Based on 2011 Trustees Report intermediate mortality assumptions.