Marginal returns for Social Security contributions: a simulation approach.
Monte Carlo method
Social security
Rate of return
Counts, R. Wayne
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Name: Review of Business Research Publisher: International Academy of Business and Economics Audience: Academic Format: Magazine/Journal Subject: Business, international Copyright: COPYRIGHT 2008 International Academy of Business and Economics ISSN: 1546-2609
Date: Nov, 2008 Source Volume: 8 Source Issue: 6
Event Code: 830 Sales, profits & dividends Computer Subject: Company earnings/profit; Return on investment
Product Code: 9105310 Social Security NAICS Code: 92313 Administration of Human Resource Programs (except Education, Public Health, and Veterans' Affairs Programs)

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Over the years researchers have performed several "money's worth" studies on Social Security. Calculating a rate of return is complicated by a number of features unique to social insurance. Foremost among the complicating factors is that wages are indexed for inflation. Additionally, some demographic factors also influence the rate of return for Social Security. Race influences the rate of return, as African Americans historically have shorter life expectancies than Caucasians, Hispanics or Asians. Also correlated with race is the longevity of marriage and remarriage rates, both of which affects the availability of spousal and divorced spousal benefits. Caldwell et al. (2004), used a microsimulation technique to calculate the rate of return on Social Security taxes for various cohorts. Their research indicated that on average workers faced a negative rate of return of 5 percent with younger workers facing a negative return of 7 percent.

Prior research has looked at the net tax rates for Social Security but not the marginal rates of return for Social Security taxes (Feldstein and Samwick, 1992) (Cushing, 2005). This study will examine the return various cohorts can expect from contributing an additional dollar to Social Security. This information has policy implications since one proposal to eliminate Social Security's expected deficit is to remove the payroll tax cap, similar to the Health Insurance (Medicare) payroll tax.

This study uses a Monte Carlo simulation in order to ascertain what the marginal rates of return would be for a worker earning one more dollar per month. Using the Panel Study of Income Dynamics, workers will be given one extra dollar per month for historic earnings and future earning will be stochastically generated using demographic and prior earnings histories. Thus workers marginal rates of return for Social Security will be calculated.

Keywords: Social Security, Marginal Return, Monte Carlo Simulation, Money's Worth Study


In there landmark study on Social Security, Caldwell et. al. (2004) found that the overall rate of return for Social Security contributions was 1.8 percent, and that for many in higher income levels the return was actually negative. Since Social Security uses a benefit formula that is progressive, and the benefits are provided in a form of a life annuity for singles and a joint and survivor annuity for married couples, the concept of marginal rates of return are important to judge the equity of the system (Barro and Sahasakul, 1986). This paper uses a Monte Carlo simulation to examine what happens when workers earn one more dollar of income per month and how that marginal increase affects their Social Security benefits.

Using the Panel Study of Income Dynamics (PSID) as a base, each worker in the sample was aged through his/her lifetime. For each worker, historical earnings and marital status reported in the PSID were used through 2004. Prospective earnings, changes in marital status, and death were stochastically determined. Marital status was determined probabilistically using age and number of years in current marital status to determine a likelihood of change in marital status. Death was also determined stochastically using age, gender, race, and income as factors influencing the probability of death. The simulation was run repeatedly. From the simulation, worker's benefits were calculated under current law and compared to the benefits that would be received with one additional dollar of monthly earnings.

Much has been made of Social Security's role in reducing poverty for older Americans (Steuerle and Bakija, 1994) . However, much of the increase in wealth attributed to the system came for early workers. As a pay-as-you-go system, early workers benefited from a rapidly expanding workforce to fund benefits well beyond what they had paid in. The decline in birthrates after the baby boom generation has led to a slowdown in the number of workers who pay into the system as a percentage of retired workers. Also affecting the solvency of the system is the extension of life expectancy over the previous century. While many point to this as the prime cause, it is somewhat overstated as much of the increase in life expectancy has occurred as the decrease in infant mortality. Therefore the change in life expectancy for individuals who attain the age of 21 is not as dramatic as would be intuited from looking at the life expectancy tables alone.

In the most recent trustee's report, the Social Security trust fund was expected to be depleted in 2041 (Social Security Administration, 2007). At that time payments to the system are expected to fund 72-75 percent of the entitled benefits.

This paper examines how the marginal rates of return vary among cohorts and household earning status in light of a number of changes that have occurred and are expected to occur demographically, statutorily and economically. One obvious demographic change is survival rates. As life expectancies increase workers will draw benefits for longer periods of time. This increase in life expectancy, the majority of which occurs during the "benefit period" serves to increase both the overall return and the marginal return to the individual (Geanakopolos, Mitchel and Zeldes, 1999). Statutorily the normal retirement age is increasing. Normal retirement age is defined as the age workers must attain in order to receive "full" benefits under Social Security regulations. Workers may retire early but receive a reduced benefit, while delaying the receipt of benefits will allow the worker to receive higher benefits. For workers born prior to 1937, 65 is the normal retirement age. For workers born after 1937, the normal retirement age increases two months for each year of birth after 1937 until birth year 1943 where it levels off for 11 years. From 1943 until 1954 the normal retirement age is 66 years and again for birth years following 1954 it increases two months for every year until the normal retirement age becomes 67 for all workers born in 1960 or later. It is because of this change in normal retirement age that the specific cohorts were selected. Economically the growth rate in wages has slowed from the early years of the program which limits the amount of indexing of wages which also reduces the rate of return.

Perhaps one of the greatest workforce demographics which has occurred in the last 30 years is the rise in the number of women in the workplace. One of the results of that trend is the rise in dual earner families. For this paper the primary worker is the worker who has the highest Average Indexed Monthly Earning (AIME), a dual earner family is one where the spouse has benefits from Social Security based on their own work record that is greater than one-half of the primary earners benefit. This means that any spousal benefit accruing to the primary worker is greatly reduced. A dependant spouse is defined a one who's work record would not generate a benefit equal to one half of the primary worker's benefit.

Perhaps the most significant finding of this study is the returns for dual income workers much more closely approach that of single workers than for married workers. It is anticipated that the percentage of dual income families will continue to increase for several years to come. Those families will receive considerably lower rates of return than traditional families do.

The first section of the paper reviews the tax and benefit rules for the OASI program. The second section discusses the methodology in arriving at the marginal rates of return for the program. The third section discusses the results of the calculations and the fourth section is the conclusion.


This paper looks at six distinct types of workers: male workers with no dependants, female workers without any dependants, male workers with a dependant spouse, female workers with a dependant spouse, male workers with a spouse who draws benefits based on her own record, and female workers with a spouse who draws benefits based on his own record. Benefits that are afforded to divorced spouses are ignored in this paper.

The full amount of statutory tax is 15.3 percent. While the withholding is 7.65 percent of the workers earnings up to a maximum level which is determined each year. For 2008 the maximum is $102,000. The workers contribution is matched by the employer. While the employer pays one half of the tax, it is widely regarded that the full incidence of the tax is on the employee. Of the 15.3 percent, 10.6 percent is credited to the Old-Age and Survivors trust fund. The remainder is put in trust for Medicare and Disability insurance.

The discussion of Social Security benefits is simplified for the purposes of this paper. First off the minimum benefit is not discussed as I focus on only those benefits that are tied to contributions. Second the retirement benefit that can be received by a divorced spouse is also ignored.

Social Security rules for married workers allow the spouse to collect a benefit equal to one-half of the workers benefit or benefits based on their own work record, whichever is greater. For primary earners with a dependant spouse, one half or the primary wage earner's benefit is greater than any benefit that would be received on their own work record. For dual income families, the spouse has a benefit on their own work record that is greater than one-half of the primary earner's but less than the primary earner's benefit. This means that the only time a spousal benefit applies is when the primary earner predeceases the spouse so that the spouse then receives the primary worker's benefit in place of their own. For a couple with a dependant spouse this makes the Social Security benefit the equivalent of a joint and two-thirds life annuity. While for a dual income family the benefit becomes a joint annuity at two-thirds the rate of the family that has a dependant spouse.

Benefits are based on the worker's earnings history. Each year the earnings are indexed to reflect changes in the general wage levels up through the year the worker attains age 60. After age 60 no indexing occurs. In calculating benefits the highest 35 earning years, after indexing, are used. Only years after the worker reaches the age of 21 are included. Once the indexed earnings for the worker are summed, the amount is divided by the number of months (420 in most cases) the result is then rounded down to the next whole dollar to arrive at the Average Indexed Monthly Earnings (AIME). After the calculation of the AIME the primary insurance amount (PIA) is calculated. The formula applies a statutory percentage to the AIME based on breakpoints. For 2008 the first breakpoint is $711 for which the percentage is 90 percent, for the amounts between $711 and $4,288 the percentage is 32 percent and for all amounts of the AIME above $4,288 the amount is 15 percent. After the application of the PIA formula the amount is rounded down to the next 10 cents.

Workers are eligible to first draw retirement benefits at age 62. However, the normal retirement age varies between age 65 and 67 depending on the workers year of birth. Workers who draw benefits prior to the normal retirement age have their benefits reduced. This reduction in benefits is intended to be actuarially equivalent; however there is some question as to the efficacy of the equivalence due to adverse selection (Spitzer, 2004). If a worker retires before the normal retirement age, then the benefit is reduced by 5/9ths of one percent for each month that retirement is begun before the normal retirement age for the first 36 months. For each month in excess of 36 months, the benefit is reduced by 5/12ths of one percent. Spousal benefits are reduced by a slightly different formula. The benefit reduction for collecting prior to the normal retirement age for spouses is 25/32ds of one percent for the first 36 months 5/12ths of one percent for each month in excess of 36 months. For workers who choose to delay benefits beyond the normal retirement age a credit of eight percent per year is give for each year up to age 70. No credit is given for delaying spousal benefits.


Much has been made of the pending shortfall in Social Security. President Bush tried to make it a centerpiece of his second term, however, his efforts failed to reach a consensus in Congress. There are several demographic factors that contribute to the Social Security shortfall. Prime among these is the longer life expectancies of Americans from when the program was first adopted. Some additional factors that contribute to the overall return and the marginal return are the age differences between spouses and the marital status at retirement age. In 1960 the average age difference in spouses was four years; the most recent information is that the difference has shrunk to a current average of the husband being only two years older than the wife. Many of the issues that affect the program overall, do not affect the individual and his/her return from the program.


This study takes historical data from 1968 through 2004 using the PSID. The data is stochastically generated data from 2005 through 2078. For wages, the wage is multiplied time the average wage increase, an increase factor for age and then a random factor. Mortality is determined stochastically also. First a tentative PIA will be calculated. Then the worker's mortality is adjusted for race and income level. Once the worker's year of death is determined for the simulation, the PIA is recalculated.

Following the calculation for PIA, the observations are simulated to go through a probabilistic change in marital status. Each person in the sample is "allowed" to divorce, remarry, or experience no change for each year in the analysis based on the relative probabilities of each event occurring in the population. The portfolio accounts, in the case of divorce, are divided for the change in value during the duration of the marriage.

The Office of the Actuary makes the simplifying assumption when calculating the money's worth of Social Security that the husband and wife are of the same age. While this simplifies the study, it could lead to a substantial understatement of the PV of benefits currently and an increasing understatement in the future (Motsiopoulos and Zayatz, 2001). The majority of wives are younger than husbands. With the increased participation of married women in the workforce, fewer women will draw the spousal benefit, but since men still tend to spend longer in the workforce and earn higher wages, a wife is still likely to receive higher widow benefits than her own work history would provide. Since the wife is generally younger, in actuality she will receive benefits longer than the simplifying assumption would suggest. The simplifying assumption thus serves to understate the true money's worth of the benefits under the current plan. This study seeks to improve on that assumption, by including the actual ages from the data sample in calculating widow(er) benefits.

Money's worth studies are invariably a mix of historical and forecasted data (Geanakopolos, Mitchell and Zeldes, 1999). This study uses stochastic simulation, based on historical data for economic growth rates, employment figures, wage growth and individual wage histories.

Persons are aged and their survival or death in a given year determined probabilistically. All persons who die in a given year are assumed to die mid-year. In order to more accurately depict life expectancies, I follow the procedure used by Steuerle et al. (1994) who adjusted life expectancies up 7 percent for high-income males and down 7 percent for low-income males. The adjustment for females is 4 percent in the same direction as for males. Following Caldwell et. al. (2004), several adjustments are made to the data and the sample is grown and aged in various ways. Demographic growth includes death, marriage, divorce and educational attainment. Economic growth includes working/not-working, number of weeks worked and labor earnings. This is the same procedure that is done in the CORSIM database. Random drawings are used in the simulation, so that the simulation provides a range with a mean and standard deviation for each observation. The average of multiple runs is used to arrive at the predicted value.

In order to calculate the marginal return workers incomes are calculated by the use of the simulation. A second calculation is made by increasing the monthly earnings by one dollar for each month of earnings.

Workers are then divided into three cohorts. The 1933 cohort consists of workers born between 1933 and 1937; the 1946 cohort represents workers born between 1946 and 1950; the final cohort of this study is for workers born between 1960 and 1964. In the calculation of Social Security benefits, the highest indexed 35 years are used. Since only wages after attainment of age 21 are used there is a potential for 45 years to be selected from. For the purposes of this study the indexing of a cohort includes the final 25 years and an average of the first 20 years. This corresponds with most workers hitting their peak earning years in their 40's and 50's. After the calculation of the marginal AIME, the marginal PIA for each class of workers is calculated. For 2008 the breakpoints are at $711 and $4,288. For low income workers the PIA amount will 90 percent of the indexed AIME, 32 percent for middle income earners and 15 percent for high income earners. This benefit is then calculated for life expectancy. For workers in the 1933 cohort the life expectancy for those reaching age 65 is 15.3 years for males and 1.6 years for females. The life expectancy is then adjusted upwards one month for each subsequent year of birth so that the 1946 cohort has an adjusted life expectancy of 16.4 years for males and 20.7 years for females. The 1960 cohort has adjusted life expectancies of 18.4 years for males and 22.7 years for females.

The benefits are then discounted at the average of the 5 year Treasury Inflation Protected Securities (TIPS) rate which is 2.635 percent. This rate was chosen since the benefits from Social Security are indexed to inflation (Nichols, Clingman, and Glanz, 2001). The present value of the benefits is then used to find the interest rate required to achieve those benefits. This then becomes the marginal rate of return on average for workers in each cohort and in each income level.


For the most part the results from the calculations are not surprising. Women receive generally higher marginal returns than men, based on their longer life expectancy. Lower income workers obtain higher marginal returns than higher income workers as would be expected since the benefit formula is structured to be progressive.

For single male workers the average marginal rate of return is between 6.06 percent for the 1933 cohort and 4.74 percent for the 1960 cohort. For single female workers the marginal rates of return are between 7.13 percent for the 1933 cohort and 6.14 percent for the 1960 cohort. Compare this to the high income workers and for single males the marginal rate of return varies between -0.86 percent for the 1933 cohort and -2.72 for the 1960 cohort.

Married workers fair somewhat better with families with dependant workers fairing the best. For male primary earners with dependant spouses the marginal rate of return is between 7.80 percent for low wage earners in the 1933 cohort and -0.05 percent for high wage earners in the 1960 cohort. Primary workers who are female fare somewhat better due to the decreased mortality between 21 and 65. For low female wage earners in the 1933 cohort the marginal rate of return 8.27 percent and for high wage earners in the 1960 cohort the marginal rate of return is 0.59 percent.

For dual income families the return is very close to the return for singles. This is due to the fact that the spousal benefit is on average only one-fourth of the primary wage earners benefit and the it only occurs after the death of the primary wage earner, therefore it is available for a much shorter period of time and is discounted significantly due to time.


For all but low wage earners, the marginal rate of return on OASI contributions is very low. As the average increase in wages has slowed since the 1950's the rate of return continues to decrease. The trend of more dual income families also tends to decrease the marginal returns for Social Security since the spousal benefit is decreased over what the traditional family receives.


Barro, Robert J. and Chiapat Sahasakul "Average Marginal Tax Rates on Social Security and the Individual Income Tax" Journal of Business 59 No. 4 Oct, 1986 pp. 555-66

Caldwell, Steven, Melissa Favrealt, Alla Gantman,Jagadeesh Gokhale, Thomas Johnson, and Laurence J. Kotlikoff, "Social Security's Treatment of Postwar Americans" National Tax Journal Jun 2004 Cushing, Mathew J. "Net Marginal Social Security Tax Rates over the Life Cycle" National Tax Journal; Jun 2005 pp 227-245

Feldstein, Martin S. and Andrew A. Samwick "Social Security Rules and Marginal Tax Rates" National Tax Journal 45 No. 1 Mar 1992 pp. 1-22

Geanakopolos, John, Olivia S. Mitchell, and Stephen P. Zeldes; "Would a Privatized Social Security System Really Pay a Higher Rate of Return?" In Douglas Arnold, M. Graetz and Alicia Munnell, eds. Framing the Social Security Debate; Washington, D.C.: National Academy on Social Insurance and the Brookings Institution 1999.

Motsiopoulos, Chris, and Tim Zayatz "Short-Range Actuarial Projections of the Old-Age, Survivors, and Disability Insurance Program" Actuarial Study No. 115 Social Security Administration, July 2001

Nichols, Orlo R., Michael D. Clingman , and Milton P. Glanz "Internal Real Rates of Return under the OASDI Program for Hypothetical Workers" Actuarial Notes No. 144 Social Security Administration, June 2001

Social Security Administration The 2007 Annual Report of the board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds. Washington D.C. 2007

Spitzer, John J. "Delaying Social Security Payments: a bootstrap" Financial Services Review; Fall 2006 pp 223-245

Steuerle, C. Eugene and Jon M. Bakija, Retooling Social Security for the 21st Century. Washington, D.C.: (The Urban Institute Press, 1994).

R. Wayne Counts, University of Texas of the Permian Basin, Odessa TX, USA


Dr. R. Wayne Counts earned his Ph.D. at Texas Tech University in 2005. Currently he is an assistant professor of accountancy at the University of Texas of the Permian Basin
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