Social Security is a social insurance program that provides benefits to offset earnings losses associated with disability, death, and retirement. Although this is widely understood, policy analysts typically compare current-law policies with reforms using "money's worth" measures (e.g., the difference between lifetime benefits and lifetime contributions) that ignore the role social security benefits play in reducing risk to the individual by cushioning income and consumption against earnings declines caused by these events. As a consequence, the value of social security to the individual has been underestimated, and the value of the program under different kinds of reforms has also been estimated incompletely.
This report by Martin Holmer develops a general method of estimating the insurance value of social security, where insurance value is defined as what people are willing to pay for social security benefits and is expressed as a percentage of taxable earnings. The report then uses this method to estimate the insurance value of disability insurance (DI) benefits, and to compare their insurance value to their actuarial value, which is the cost of providing the DI benefits, also expressed as a percent of taxable earnings. An individual may be willing to pay more for DI benefits than the actuarial cost of providing these benefits, because the individual may be risk-averse, and because he or she cannot average out life uncertainties in the same way an insurance company can average claim experiences over a broad group of people.
Findings: Individuals Are Willing to Pay More For the Social Security Disability Insurance Program Than the Actuarial Cost of Providing the Disability Benefits
This analysis finds that, for men and women who (1) are risk averse, (2) have average chances of becoming disabled, and (3) have average earnings for people their age and gender, the insurance value of DI benefits (i.e., the amount they are willing to pay for DI insurance) substantially exceeds their actuarial value (i.e., the cost of providing the benefits). In addition, the insurance value of DI benefits always exceeds the current-law DI payroll tax rate of 1.8 percent. This result is true for a range of assumptions about the extent of their aversion to risk. Furthermore, under several reasonable assumptions about risk aversion, willingness to pay for DI would, if incorporated into the FICA tax rate, more than pay for the achievement of solvency for the entire OASDI program.
In particular, the method developed in this report combines the use of Monte Carlo simulation, used to represent the risks that cause uncertainty in lifetime earnings and benefits, with two leading theories of how individuals choose under risk. The analysis focuses on a man and a woman, both born in 1978, who are considered as a married individual, an unmarried individual, and a couple. At each age, the man and the woman are assumed to have the average earnings, average mortality rates, and average movement on to and off of the DI program for someone of their gender and age. For each individual and couple, the Monte Carlo simulation generates 10,000 possible lifetime outcomes for the present value of earnings and the present value of DI benefits. This simulated distribution represents the uncertainty facing an individual, with each value in the distribution representing a different possible life outcome.
Table 1 presents a range of estimates of the value of the Social Security disability program to individuals and couples, presented as a percent of taxable earnings, so that they can be compared easily to the current law disability tax rate of 1.8 percent of taxable earnings.
The actuarial value of disability benefits in Table 1 was calculated as the mean present value of disability benefits received by the individual or couple over 10,000 simulated lifetime outcomes, expressed as a percent of taxable earnings. The actuarial value is higher for the married man and the married woman, because they are eligible for spousal and child DI benefits. The lifetime actuarial value for the couple is not as high as the sum of those for the individuals because there is a small chance of both individuals becoming disabled during their lifetimes. In conventional money's worth analyses, the actuarial value is compared to the current DI tax rate of 1.8 percent of taxable earnings.
The money's worth methodology is valid, however, only if one assumes that individuals have no aversion to risk. If individuals are averse to risk, then the DI program provides an "insurance" value to the individual or couple. This insurance value represents the amount that the individual (or couple) would be willing to pay to insure against the loss of income due to disability. An individual's insurance value is generally higher than the actuarial value of providing the insurance, which is the cost to the insurer of insuring many people with offsetting risks of disability. The methodology developed in this report calculates the insurance value of disability benefits using two leading theories of individual choice under risk: expected utility theory and cumulative prospect theory. Cumulative prospect theory is used because there is substantial empirical literature showing that expected utility theory often fails to predict accurately how people make decisions among risky prospects.
In Table 1, the results for expected utility theory are reported using three different assumptions about an individual's degree of risk aversion, which is denoted in the literature by the coefficient. In this analysis, is assumed to take on values from 0.9 to 2.7. Results from empirical studies have often found evidence for much higher values, indicating that the values assumed here may be on the low side. For cumulative prospect theory, a mathematical representation of the theory is used that is based on numerous empirical studies.
Thus, for a man with average male earnings at every age, and an average chance of becoming disabled, the actuarial value of DI benefits is about 1.7 percent of taxable earnings. This is less than the current DI tax rate of 1.8 percent of taxable earnings. Yet when risk aversion is taken into account, this man would be willing to pay up to 2.6 percent of his taxable earnings in order to insure himself against the possibility of income loss due to disability, under the assumption that he has a low level of risk aversion ( = 0.9) using expected utility theory. In other cases that involve single individuals with a higher assumed degree of risk aversion, or using cumulative prospect theory, the insurance value is typically at least twice the actuarial value of DI benefits.
Of the cases considered in this paper, the smallest understatement of insurance value is for the couple with the lowest level of risk aversion. The insurance value for the couple is lower than that for the married individuals considered alone, because it is unlikely that both members of the couple will experience, at the same time, earnings reductions because of disability. For the couple, the insurance value of the DI program is equivalent to about 2.3 percent of combined taxable earnings, which is 0.3 percent higher than the actuarial value of the benefits, and 0.5 higher than the 1.8 percent tax that the couple pays on its combined earnings.
These results indicate that use of conventional measures of "money's worth" lead to a substantial underestimation of the value of insurance protection provided by the DI program. Conventional "money's worth" analysis compares only the actuarial value of benefits to DI payroll taxes. Yet this approach is valid only under the extreme assumption that individuals have no aversion to risk. The analysis here shows that, when risk is considered, many individuals and couples would be willing to pay twice the current law DI tax rate, or more, in order to avoid elimination of the DI program.
Written by Martin R. Holmer
John Gist and Alison Shelton, Project Managers, AARP Public Policy Institute
May be copied only for noncommercial purposes and with attribution; permission required for all other purposes.
Public Policy Institute, AARP, 601 E Street, NW, Washington, DC 20049