MEMORANDUM

From: Steve Goss, Deputy Chief Actuary
      Social Security Administration

Subject: Problems with "Social Security's Rate of Return" A Report of the Heritage Center for Data Analysis

The analysis by William M. Beach and Gareth G. Davis of the Heritage Foundation attempts to provide an answer to the question "What can Americans expect in future Social Security retirement benefits?" The paper suggests that expected rates of return will decrease substantially in the future and that African Americans do now and will in the future have substantially lower expected rates of return that for the general population. However, the conclusions are highly misleading due to two major errors in the methodology, plus a number of incorrect or inappropriate assumptions.

Due to these errors, rates of return for the general population in this study are at a substantial variance with those produced for the 1994-6 Advisory Council on Social Security (See Appendix 2 of Volume 1 of the report, pages 219-22). For example, for single men (all races combined) born in 1970 with average earnings, real rates of return are estimated at only 0.47 percent by Heritage, compared with 1.28 percent in the Advisory Council Report.

More importantly, the methods utilized by the authors bias expected rates of return downward to a far greater degree for African Americans than for the general population. This study thus erroneously indicates differences in rates of return by race that are greatly exaggerated. In fact, results from more careful research reflecting actual work histories for workers by race indicate that the non-white population actually enjoys the same or better expected rates of return from Social Security that for the white population. (See Duggan, et. al., "The Returns Paid to Early Social Security Cohorts," Contemporary Policy Issues, (October), pp. 1-13.)

Error in Method of Computing Expectation

Expected values indicate the average of all possible outcomes for individuals at a point in time with an uncertain future. Instead, the Heritage study erroneously analyzes a single outcome where an individual is assumed to know how long he or she will live. For persons at each age 22 through 66 in 1997, the authors estimated the remaining life expectancy, i.e., the average number of years of life remaining after 1997. Individuals at each age were then assumed to live for precisely the number of years indicated by this average life expectancy. This approach consistently overestimates the expected number of years of work and consistently underestimates the expected number of years after reaching retirement age. As a result, it grossly underestimates the expected rates of return from Social Security retirement benefits. Moreover, the extent of this bias is greater for workers with lower life expectancy, in particular African Americans. The error is also greater for younger workers who are far from retirement age in 1997.

To illustrate this error, consider the expected years of work and retirement under the Heritage method in comparison with the true expected years for white and black men based on the 1992 United States Life Tables. Life expectancy at age 20 was 54.3 years for white men and 47.2 years for black men. Assuming both planned to work until retirement age at 65, the Heritage approach would assume 45 work years for each, and 9.3 retirement years for white men but only 2.2 years of retirement for black men.

However, the true expected number of work years for both black and white men must be less that 45, because some will die before reaching age 65. In fact, the true expected number of work years (reflecting deaths before 65) is 42.2 years for white men and 39.1 years for black men. Computing, for 20-year-old men the expected number of retirement years after 65 requires both the probability of surviving to 65 and the life expectancy at 65 for those who do survive. For white men age 20, 78.1 percent would expect to survive to 65 at which point they would average an additional 15.5 years of life after 65. Thus, the expected years of life for a 20-year-old white male after reaching 65 would be 12.1 years (= 15.5 x .781). For black men age 20, 60.3 percent would average an additional 13.5 years of life. Their expected retirement years would thus be 8.1 (= 13.5 x .603).

Clearly, computed rates of return for retirement benefits using true expectation will be much higher for all men, and, moreover, the difference between rates of return for black and white men will be dramatically smaller, than if the erroneous Heritage method is used. While this is the largest and most fundamental error in the Heritage analysis, an number of additional errors further bias the results.

Error in Not Reflecting Relationship Between Mortality and Income

The authors acknowledge the fact that life expectancy is highly correlated with income, and that their estimates do not reflect this fact. Estimates made by the Office of the Chief Actuary, Social Security Administration indicate that for the general population, about 20 percent of the difference in the rates of return between low- and high-income workers is removed by properly reflecting mortality differences by income. However, this correlation would be far more important in comparing rates of return between African Americans and the general population.

The authors note that rates of return would be lower for low-income and higher for high-income workers if adjusted appropriately for mortality at the indicated level of income. Average-income workers would presumably have mortality at about the level of the average population, and thus be unaffected by the adjustment. While this is all true for the general population, the African American rates of return would be increased much more for high-income workers, would also increase for average-income workers, and would decline much less for low-income workers. This is true because average income for African Americans is substantially lower than for the general population at this time.

For example, African Americans with earnings equal to the general population average have much higher-than-average earnings within the African American population. As a result, they must be assumed to have much better mortality than the average for all African Americans. Thus, with proper adjustment with mortality by income level, race differentials in life expectancy would diminish greatly, for individuals at the same income levels.

Without appropriate adjustment of mortality by income, race-differentials in rates of return are highly misleading. This is the reason that the Office of the Chief Actuary, Social Security Administration has not as yet developed race-specific money's worth ratios or rates of return.

Additional Errors

The authors of the Heritage study exclude disability benefits and taxes from the analysis, even though the Disability Insurance program represents nearly 15 percent of the Social Security. While including disability would not substantially change the expected rate of return for the general population, it would considerably narrow the rate of return for African Americans versus the general population. This follows from the fact that disability benefits are significantly more likely for African Americans than for the population as a whole.

Because Social Security provides survivor benefits when a worker dies before retirement age, and Heritage omits these benefits, the authors also deducted from taxes a premium intended to cover these benefits. The premium appears to exclude those survivor benefits for a spouse that are payable after the youngest child reaches age 16, i.e., widow(er)s benefits that are payable from age 60 to the end of life. Premiums are also likely to be too low if Heritage used premiums for commercially-available life insurance. Life insurance is sold largely to healthy, higher-income persons who can afford the premium and can qualify as insurable. Including lower-income and uninsurable individuals would boost the premium substantially. Making these changes would increase rates of return from Social Security.

The authors raised tax rates for Social Security starting 2015 by enough to cover future benefit costs, ignoring the fact that the Trust Fund balance projected for that time, 300 percent of annual benefits, would continue to grow as a percent of annual benefits under these conditions. In order to produce a pay-as-you-go financed Social Security program, tax rates would not need to be raised until around 2025, and by less than the authors assumed. The early, too-large increase in tax rates results in rates of return that are estimated to be too low for Social Security.

The authors included a "high-income" worker with earnings at 300 percent of the average wage. In fact, the maximum level of earnings that is taxable and creditable for Social Security benefits is now and will be in the future 240 percent of the average wage (less than 240 percent in years before 1978). It is not clear whether the authors included taxes above this maximum benefit level. If they did, then rates of return for Social Security are estimated to be too low for high-income workers.

MEMORANDUM

Date:    April 2, 1998

To:      Harry C. Ballantyne
         Chief Actuary

From:    Stephen Goss
         Deputy Chief Actuary

Subject: Comments on Heritage Rates of Return for Hispanic Americans

In an analysis from the Heritage Foundation dated January 15, 1998, the authors Bill Beach and Gareth Davis, suggested that African Americans can expect to get a lower rate of return, and Hispanic Americans a higher rate of return from Social Security, than the general population. My memorandum on February 4, 1998 addressed a number of technical shortcomings in the methods used in this analysis. These shortcomings resulted in an understatement of the expected rates of return for all groups. The understatement was largest for African Americans, and smallest for Hispanic Americans. There correct expected rates of return would be higher, and closer together than presented by Heritage.

In a subsequent statement by Heritage in early March, referring to the results of he January 15 analysis, it was suggested that Hispanic Americans could expect far lower rates of return from Social Security than would be possible from individual accounts. The statement compared the (erroneously) computed expected rates of return from Social Security to the expected rate of return for an individual account invested either all in bonds or partly in stocks. But the comparison ignores both the cost of transition to an individual-account program, and the administrative expenses associated with individual accounts. Transition costs associated with the continuation of benefit payments for current OASDI beneficiaries and today's older workers would be substantial. Adding in these costs, which are excluded from the Heritage analysis, would greatly reduce the overall rate of return for the combination of individual accounts and the OASDI program under the Heritage proposal.

Finally, the authors fail to note in the March statement that, by their own calculations, see page 7 of January 15 report, Hispanic Americans would be expected to receive a substantially higher rate of return for Social Security that would the general population, on average. A somewhat higher rate of return for Hispanic Americans is to be expected, based on the higher life expectancy for Hispanic Americans, and the fact that Hispanic Americans have lower than average earnings. However, the extent to which Heritage shows higher returns for Hispanic Americans is overstated, just as the extent to which African Americans are show to have lower rates of return (Heritage January 15) is overstated.

Stephen C. Goss

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