A Stochastic Model
of the Long-Range Financial Status
of the OASDI Program—September 2004
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Three types of financial measures are useful in assessing the actuarial status of the combined OASDI Trust Funds under the financing approach specified in current law: (1) annual balances, income rates, and cost rates, (2) trust fund ratios, and (3) summary measures like actuarial balance and open group unfunded obligation. In assessing the financial condition of the program, particular attention should be paid to the level of the annual balance at the end of the long-range period, and the time at which the annual balance may change from positive to negative values. The ratio of beneficiaries to covered workers on a year-by-year basis (a program ratio rather than a financial ratio), provides a useful comparison to the cost of the OASDI program over the entire 75-year valuation period. Another important measure is the pattern of projected trust fund ratios. The trust fund ratio is the proportion of a year's projected outgo that can be paid with the funds available at the beginning of the year. Particular attention should be paid to the amount and year of maximum trust fund ratio, to the year of exhaustion of the funds, and to stability of the trust fund ratio in cases where the ratio remains positive at the end of the long-range period. The final measures discussed in this appendix summarize the total income and cost over valuation periods that extend through 75 years. These measures indicate whether projected income will be adequate for the period as a whole. The first such measure, actuarial balance, indicates the size of any shortfall as a percentage of the taxable payroll over the period. The second, open group unfunded obligation, indicates the size of any shortfall in present-value discounted dollars.
If the 75-year actuarial balance is zero or positive, then the trust fund ratio at the end of the period, by definition, will be at 100 percent (or greater) and financing for the program is considered to be adequate for the 75-year period as a whole. (Financial adequacy for each year is determined by whether the trust fund is zero or positive throughout the year.) Whether or not financial adequacy is stable in the sense that it is likely to continue for subsequent 75-year periods in succeeding reports is also important when considering the actuarial status of the program. One indication of this stability is the behavior of the trust fund ratio at the end of the projection period. If projected trust fund ratios for the last several years of the long-range period are positive and constant, or rising, then it is likely that subsequent Trustees Reports will also show projections of financial adequacy (assuming no changes in demographic and economic assumptions).
The remaining portion of this appendix discusses these basic measures of assessing the actuarial status of the combined OASDI Trust Funds. Values from the 2004 deterministic model are often given in order to aid in the discussion.
Starting with the dollar level of assets in a given year, the combined OASDI Trust Funds receive income from payroll taxes, income from taxation of benefits, and interest income. In turn, scheduled benefits, administrative expenses, and the net financial interchange to the Railroad Retirement Board, are all paid from the combined OASDI Trust Funds. Hence, the dollar value of assets at the end of a given year is numerically equal to the dollar value of assets at the beginning of the year, plus payroll taxes, plus income from taxation of benefits, plus interest income, less scheduled benefits, less administrative expenses, less net financial interchange to the Railroad Retirement Board.
Basic to the consideration of the long-range actuarial status of the trust funds are the concepts of income rate and cost rate, each of which is expressed as a percentage of taxable payroll. The annual income rate is the ratio of income from revenues (payroll tax contributions and income from the taxation of benefits) to the OASDI taxable payroll for the year. The OASDI taxable payroll consists of the total earnings which are subject to OASDI taxes, with some relatively small adjustments. These adjustments include reflecting that individuals who work for more than one employer and have OASDI covered wages exceeding the contribution and benefit base during the year will be reimbursed for the payroll taxes they paid on wages in excess of the contribution and benefit base for that year. However, each employer pays, on behalf of each employee, payroll taxes on annual wages up to the contribution and benefit base, regardless of the amount of wages an employee receives from other employers. Because the taxable payroll reflects such adjustments as these, the annual income rate can be defined to be the sum of the OASDI combined employee-employer contribution rate (or the payroll-tax rate) scheduled in the law and the rate of income from taxation of benefits (which is, in turn, expressed as a percentage of taxable payroll). As such, it excludes net investment income. The annual cost rate is the ratio of the cost (or outgo, expenditures, or disbursements) of the program to the taxable payroll for the year. In this context, the outgo is defined to include benefit payments, administrative expenses, and net transfers from the trust funds to the Railroad Retirement program under the financial-interchange provisions. For any year, the income rate minus the cost rate is referred to as the annual balance for the year. Considering Social Security's cost as a percentage of the total U.S. economy, GDP provides an additional perspective.
The year-by-year relationship of the income and cost rates illustrates the expected pattern of cash flow for the OASDI program over the full 75-year period. The pattern of the OASDI program's estimated cost rate is generally much different than that of the income rate. The income rate generally increases only slightly during the next 75 years, from just under to just over 13 percent as income from taxation of benefits increases. There is only a very small difference in the income rate among the TR04I, TR04II, and TR04III. Under the TR04II, the OASDI cost rate is estimated to remain fairly stable and well below the income rate for the next several years, until about 2010. It then begins to increase rapidly and first exceeds the income rate for 2018, producing cash-flow deficits thereafter. The cost rate continues rising through about 2030 as the baby-boom generation reaches retirement age. By 2078, the projected continued reductions in death rates and relatively low birth rates will cause a significant upward shift in the average age of the population and will push the cost rate to over 19 percent of taxable payroll under the TR04II. Annual deficits generally increase throughout the remainder of the 75-year projection period, reaching nearly 6 percent of taxable payroll by 2078. The OASDI cost rates for the TR04I and TR04III follow generally similar patterns, but differ significantly in magnitude from those projected for the TR04II.
The primary reason that the estimated OASDI cost rate generally increases rapidly after 2010 is that the number of beneficiaries is projected to increase more rapidly than the number of covered workers. This generally occurs because the relatively large number of persons born during the baby-boom generation will reach retirement age, and begin to receive benefits, while the relatively small number of persons born during the subsequent period of low fertility rates will comprise the labor force.
Based on the TR04II, the number of covered workers per OASDI beneficiary declines to 2.1 by 2031, and to 1.9 by 2062. Under the TR04I, for which high fertility rates and small reductions in death rates are assumed, this ratio declines to 2.3 by 2032, and then rises back to a level of 2.4 by 2044. Under the TR04III, for which low fertility rates and large reductions in death rates are assumed, the decline in this ratio is much greater, reaching 1.8 by 2037, and 1.4 by 2074.
The impact of the demographic shifts under the TR04I, TR04II, and TR04III on the OASDI cost rates is better understood by considering the projected number of beneficiaries per 100 workers. As compared to the 2003 level of 30 beneficiaries per 100 covered workers, this ratio is estimated to rise significantly by 2080 to 54, 41, and 71 under the TR04II, TR04I, and TR04III, respectively. The significance of these numbers can be seen by noting that the trend of the OASDI cost rates is essentially the same as the trend of the number of beneficiaries per 100 covered workers over the 75-year projection period. This emphasizes the extent to which the cost of the OASDI program as a percentage of taxable payroll is determined by the age distribution of the population. Because the cost rate is basically the product of the number of beneficiaries and their average benefit, divided by the product of the number of covered workers and their average taxable earnings (and because average benefits rise at about the same rate as average earnings), it is to be expected that the pattern of the annual cost rates is similar to that of the annual ratios of beneficiaries to workers.
The trust fund ratio is a useful indicator of the adequacy of the financial resources of the Social Security program at any point in time. The combined OASDI Trust Fund ratio for a given year is, by definition, the ratio of the assets at the beginning of the year in the combined OASDI Trust Funds to the total outgo during that year, expressed as a percentage. In general, a yearly trust fund ratio of 100 percent or greater is desired. For any year in which the projected trust fund ratio is positive (i.e., the trust fund holds assets at the beginning of the year), but is not positive for the following year, the trust fund is projected to become exhausted during the year. Under present law, the combined OASDI Trust Funds do not currently have the authority to borrow. Therefore, exhaustion of the assets in either fund during a year would mean that there are no longer sufficient funds to cover the full amount of benefits scheduled under present law.
The trust fund ratio also serves an additional important purpose in assessing the actuarial status of the OASDI program. When the financing is adequate for the timely payment of full benefits throughout the long-range period, the stability of the trust fund ratio toward the end of the period indicates the likelihood that this projected adequacy will continue for subsequent Trustees Reports. If the trust fund ratio toward the end of the period is level or increasing, then projected adequacy for the long-range period is likely to continue for subsequent reports.
Under the TR04II, the trust fund ratio for the combined OASDI Trust Funds rises from 306 percent at the beginning of 2004 to a peak of 448 percent at the beginning of 2015. Thereafter, the ratio declines, with the combined funds becoming exhausted in 2042. The trust fund ratio first declines in 2016, about 2 years before annual expenditures begin to exceed noninterest income. After 2015, the dollar amount of assets is projected to continue to rise through the beginning of 2028, because interest income more than offsets the shortfall in noninterest income. Beginning in 2018, the OASDI program is projected to experience increasingly large cash-flow shortfalls that will require the trust funds to redeem special public-debt obligations of the General Fund of the Treasury. The pattern of the trust fund ratios under the TR04III is similar to that under the TR04II, with a lower maximum value and an earlier exhaustion year (2031). While the pattern of the trust fund ratios under the TR04I seems similar to that under the TR04II, the trust fund ratios under the TR04I stabilize generally and remain over 480 percent for most of the second half of the 75-year long-range period.
The deterministic model projects nominal dollar levels of trust fund assets over a 75-year period. In order to assess the financial status of the OASDI program quantitatively, in particular, to view the program as a whole at a specified point in time, the notion of present value, or time-value of money, is required. An essential ingredient in computing present values is the interest rate. Under the TR04II, the ultimate value of the annual nominal yield on the combined OASDI Trust Funds is 5.88 percent, achieved in 2018. The ultimate value of the annual nominal yield rate is 5.57 and 6.08 under the TR04I and TR04III respectively. In the short-range period, interest earned by these new issues, along with interest earned on the existing assets of the trust funds, determine implicitly the nominal yield earned by the combined OASDI Trust Funds in the short-range period 2004-13. In a five-year blending period, 2014-18, the annual yield rate on the combined OASDI Trust Funds is linearly interpolated between the yield rate in 2013 and the ultimate value achieved in 2018 to obtain the nominal yield on the combined funds in those years.
The 75-year long-range actuarial balance (henceforth referred to as the actuarial balance) is a measure, as a single number, of the program's financial status for the 75-year valuation period as a whole. It is essentially the difference between income and cost of the program expressed as a percentage of taxable payroll summarized over the valuation period. When the actuarial balance is negative, the magnitude of the negative actuarial balance, the actuarial deficit, can be interpreted as the percentage that would have to be added to the current law income rate in each of the next 75 years, or subtracted from the cost rate in each year, to bring the funds into actuarial balance. Under the TR04II, there is an actuarial deficit of 1.89 percent of taxable payroll for the combined OASDI Trust Funds. Under the TR04I, the actuarial balance is 0.41 percent of taxable payroll while under the TR04III, the actuarial deficit is 4.96 percent of taxable payroll.
Summarized values for the full 75-year period are useful in analyzing the long-range adequacy of financing for the program over the period as a whole under present law. The summarized income rate for the 75-year valuation period is equal to the present value of tax income, plus the beginning-of-year 2004 assets, expressed as a percentage of the present value of taxable payroll. Similarly, the summarized cost rate for the 75-year valuation period is equal to the present value of the cost for the 75-year period, plus the present value of the 76th year's outgo (the so-called "target fund"), expressed as a percentage of the present value of taxable payroll. These summarized rates are useful for comparing the total cash flows of tax income and expenditures as an indicator of the degree to which accumulated assets and tax income during the period are sufficient to meet the outgo estimated for the long-range period. The OASDI long-range actuarial balance is defined to be the difference between the summarized 75-year income rate and the summarized 75-year cost rate.
The summarized income rate and summarized cost rate, as described above, are expressed as a percentage of the present value of taxable payroll. However, it is also useful to provide summary measures expressed in terms of the total economy of the United States. The income and cost of the OASDI program may also be expressed in terms of GDP. In this case, summary values for the OASDI program are expressed as a percentage of the present value of GDP (instead of payroll). The summarized long-range (75-year) balance as a percentage of GDP for the OASDI program is estimated to be -0.70 percent of GDP under the TR04II.
Conceptually, the open group unfunded obligation is the present value of the cash deficits observed over the 75-year period less the accumulated trust fund assets at the beginning of the period. In particular, it is the present value of the cost of the program, less the sum of the present value of tax income and the assets on hand at the beginning of the 75-year valuation period. Under the TR04II, the open group unfunded obligation was estimated to be $3.7 trillion. It is -$1.1 trillion and $10.3 trillion under the TR04I and TR04III, respectively. A negative estimate of the open group unfunded obligation, as observed for the TR04I, indicates that over the 75-year period the OASDI program runs a net surplus (in present-value terms), i.e., the sum of accumulated trust fund assets and the present value of tax income is strictly greater than the present value of outgo over the 75-year period.