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## Trustees Reports- 1995 |

## G. LONG-RANGE SENSITIVITY ANALYSISThis section presents estimates which illustrate the sensitivity of the long-range actuarial balance of the OASDI program to changes in selected individual assumptions. The estimates based on the three alternative sets of assumptions (see sections II.D and II.F2) illustrate the effects of varying all of the principal assumptions simultaneously in order to portray a generally more optimistic or pessimistic future, in terms of the financial status of the OASDI program. In the sensitivity analysis presented in this section, the intermediate alternative II is used as the reference point, and one assumption at a time is varied within that alternative. Similar variations in the selected assumptions within the other alternatives would result in similar relative variations in the long-range estimates. Each table that follows shows the effects of changing a particular assumption on the OASDI summarized income rates, summarized cost rates, and actuarial balances (as defined earlier in this report) for 25-year, 50-year, and 75-year valuation periods. Because the income rate varies only slightly with changes in assumptions, it is not considered in the discussion of the tables. The change in each of the actuarial balances is approximately equal to the change in the corresponding cost rate, but in the opposite direction.
## 1. Total Fertility RateTable II.G1 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about the ultimate total fertility rate. These assumptions are that the ultimate total fertility rate will be 1.6 children per woman (as assumed for alternative III), 1.9 (as assumed for alternative II), and 2.2 (as assumed for alternative I). The rate is assumed to change gradually from its current level and to reach the various ultimate values in 2019. For the 25-year period, the cost rate for the three fertility assumptions varies by only about 0.07 percent of taxable payroll. In contrast, the 75-year cost rate varies over a wide range, decreasing from 15.92 to 14.99 percent, as the assumed ultimate total fertility rate increases from 1.6 to 2.2. Similarly, while the 25-year actuarial balance varies by only 0.06 percent of taxable payroll, the 75-year actuarial balance varies over a much wider range, from -2.62 to -1.75 percent. During the 25-year period, the very slight effect of changes in fertility on the working population is more than offset by increases in the number of child beneficiaries. Hence, the program cost slightly increases with higher fertility. For the 75-year long-range period, however, changes in fertility have a relatively greater impact on the labor force than on the beneficiary population. As a result, an increase in fertility significantly reduces the cost rate. Each increase of 0.1 in the ultimate total fertility rate increases the long-range actuarial balance by about 0.15 percent of taxable payroll.
## 2. Death RatesTable II.G2 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about future reductions in death rates. The analysis was developed by varying the percentage decrease assumed to occur during 1994-2069 in the death rates by age, sex, and cause of death. The decreases assumed for this period, summarized as changes in the age-sex-adjusted death rate, are about 16 percent (as assumed for alternative I), 35 percent (as assumed for alternative II), and 54 percent (as assumed for alternative III). It should be noted that these reductions do not apply uniformly to all ages, as some variation by age was assumed (see section II.H1) consistent with the objective of selecting assumptions for alternatives I and III that are relatively more optimistic and more pessimistic, respectively, in terms of the financing of the OASDI program. The variation in cost for the 25-year period is less pronounced than the variation for the 75-year period because the decreases in death rates are assumed to occur gradually and because of the specific changes in the age composition of the population that are projected to occur. The 25-year cost rate increases from 12.68 percent (for 16-percent lower ultimate death rates) to 13.12 percent (for 54-percent lower ultimate rates). The 75-year cost rate increases from 14.71 to 16.27 percent. The actuarial balance decreases from +0.75 to +0.33 percent for the 25-year period, and from -1.48 to -2.96 percent for the 75-year period. Lower death rates cause both the income (as well as taxable payroll) and the outgo of the OASDI program to be higher than they would otherwise be. The relative increase in outgo, however, exceeds the relative increase in taxable payroll. For any given year, reductions in the death rates for people who have attained the retirement eligibility age of 62 (people whose death rates are the highest) increase the number of retired-worker beneficiaries (and, therefore, the amount of retirement benefits paid) without adding significantly to the number of covered workers (and, therefore, to the taxable payroll). Although reductions for people aged 50 to retirement eligibility age do result in significant increases to the taxable payroll, those increases are not large enough to offset the sum of the additional retirement benefits mentioned above and the disability benefits paid to additional beneficiaries in this pre-retirement age group. At ages under 50, death rates are so low that even substantial reductions would not result in significant increases in the numbers of covered workers or beneficiaries. Consequently, if death rates for all ages are lowered by about the same relative amount, outgo increases at a rate greater than the rate of growth in payroll, thereby resulting in higher cost rates. Each additional 10-percentage-point reduction in the age-sex-adjusted death rate assumed to occur in 1994-2069, relative to the 35-percent reduction assumed for alternative II, decreases the long-range actuarial balance by about 0.39 percent of taxable payroll.
## 3. Net ImmigrationTable II.G3 shows the estimated OASDI income rates, cost rates, and actuarial balances, under alternative II with various assumptions about the magnitude of net immigration. These assumptions are that the annual net immigration will be 750,000 persons (as assumed for alternative III), 900,000 persons (as assumed for alternative II), and 1,150,000 persons (as assumed for alternative I). For all three periods, the cost rate decreases with increasing rates of net immigration. For the 25-year period, the cost rate decreases from 12.95 percent of taxable payroll (for annual net immigration of 750,000 persons) to 12.83 percent (for annual net immigration of 1,150,000 persons). For the 50-year period, it decreases from 14.70 percent to 14.46 percent, and for the 75-year period, it decreases from 15.55 percent to 15.27 percent. The actuarial balance increases from +0.50 to +0.61 percent for the 25-year period, from -1.41 to -1.20 for the 50-year period, and from -2.28 to -2.02 percent for the 75-year period. The cost rate decreases with increasing rates of net immigration because immigration occurs at relatively young ages, thereby increasing the numbers of covered workers earlier than the numbers of beneficiaries. Each additional group of 100,000 immigrants relative to the 900,000 net immigration assumed for alternative II, increases the long-range actuarial balance by about 0.06 percent of taxable payroll.
## 4. Real-Wage DifferentialTable II.G4 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about the real-wage differential. These assumptions are that the ultimate real-wage differential will be 0.5 percentage point (as assumed for alternative III), 1.0 percentage points (as assumed for alternative II), and 1.5 percentage points (as assumed for alternative I). In each case, the ultimate annual increase in the CPI is assumed to be 4.0 percent (as assumed for alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 4.5, 5.0, and 5.5 percent under alternatives III, II, and I, respectively. For the 25-year period, the cost rate decreases from 13.30 percent (for a real-wage differential of 0.5 percentage point) to 12.52 percent (for a differential of 1.5 percentage points). For the 50-year period, it decreases from 15.16 to 14.05 percent, and for the 75-year period it decreases from 16.04 to 14.84 percent. The actuarial balance increases from +0.19 to +0.88 percent for the 25-year period, from 1.83 to -0.83 for the 50-year period, and from -2.71 to -1.63 percent for the 75-year period. The cost rate decreases with increasing real-wage differentials, because the higher real-wage levels increase the taxable payroll, while benefit increases are not affected. Although the initial benefit levels are higher because of the higher wages, these increases are more than offset by the increases in the taxable payroll of future workers. Each 0.5-percentage-point increase in the assumed real-wage differential increases the long-range actuarial balance by about 0.54 percent of taxable payroll.
## 5. Consumer Price IndexTable II.G5 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about the rate of increase for the Consumer Price Index (CPI). These assumptions are that the ultimate annual increase in the CPI will be 3.0 percent (as assumed for alternative I), 4.0 percent (as assumed for alternative II), and 5.0 percent (as assumed for alternative III). In each case, the ultimate real-wage differential is assumed to be 1.0 percentage points (as assumed for alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 4.0, 5.0, and 6.0 percent under alternatives I, II, and III, respectively. For all three periods, the cost rate decreases with greater assumed rates of increase in the CPI. For the 25-year period, the cost rate decreases from 13.05 (for CPI increases of 3.0 percent) to 12.77 percent (for CPI increases of 5.0 percent). For the 50-year period, it decreases from 14.81 to 14.40 percent, and for the 75-year period, it decreases from 15.68 to 15.21 percent. The actuarial balance increases from +0.42 to +0.66 percent for the 25-year period, from 1.52 to -1.14 for the 50-year period, and from -2.39 to -1.96 percent for the 75-year period. The patterns described above result primarily from the time lag between the effects of the CPI changes on taxable payroll and on benefit payments. When assuming a greater rate of increase in the CPI (in conjunction with a constant real-wage differential), the effect on taxable payroll of the implied greater rate of increase in average wages is experienced immediately, while the effect on benefits of the greater rate of increase in the CPI is experienced with a lag of about 1 year. In addition, the effect on benefits of the greater rate of increase in average wages is experienced no sooner than 2 years later. Thus, the higher taxable payrolls have a stronger effect than the higher benefits, thereby resulting in lower cost rates. The effect of each 1.0-percentage-point increase in the rate of change assumed for the CPI is an increase in the long-range actuarial balance of about 0.21 percent of taxable payroll.
## 6. Real Interest RateTable II.G6 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about the annual nominal real interest rate for special public-debt obligations issuable to the trust funds, which are compounded semiannually. These assumptions are that the ultimate annual real interest rate will be 1.5 percent (as assumed for alternative III), 2.3 percent (as assumed for alternative II), and 3.0 percent (as assumed for alternative I). In each case, the ultimate annual increase in the CPI is assumed to be 4.0 percent (as assumed for alternative II), resulting in ultimate annual yields of 5.6, 6.4, and 7.1 percent under alternatives III, II, and I, respectively. For the 25-year period, the cost rate decreases slightly with increasing real interest rates from 13.00 percent (for an ultimate real interest rate of 1.5 percent) to 12.83 percent (for an ultimate real interest rate of 3.0 percent). For the 50-year period, it decreases from 14.92 to 14.35 percent, and for the 75-year period, it decreases from 15.92 to 15.05 percent. The actuarial balance increases from +0.40 to +0.65 percent for the 25-year period, from -1.68 to -1.03 percent for the 50-year period, and from -2.68 to -1.75 percent for the 75-year period. Each 0.5-percentage-point increase in the assumed real interest rate increases the long-range actuarial balance by about 0.31 percent of taxable payroll.
## 7. Disability Incidence RatesTable II.G7 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions concerning future disability incidence rates. For all three alternatives, incidence rates by age and sex are assumed to increase during the early years of the projection period before declining to ultimate levels, which are attained in 2009. At that time they reach levels that, in comparison to the corresponding annual rates experienced during the base period 1984-86, are higher by about 8 percent for alternative I, 35 percent for alternative II, and 62 percent for alternative III. For the 25-year period, the cost rate increases with increasing disability incidence rates from 12.70 percent (for the relatively low rates assumed for alternative I) to 13.11 percent (for the relatively high rates assumed for alternative III). For the 50-year period, it increases from 14.34 to 14.87 percent, and for the 75-year period, it increases from 15.16 to 15.73 percent. The actuarial balance decreases from +0.74 to +0.33 percent for the 25-year period, from -1.06 to -1.59 percent for the 50-year period, and from -1.89 to -2.45 percent for the 75-year period. Each 10-percentage point increase from the base period in the ultimate assumed gross incidence rate decreases the long-range OASDI actuarial balance by about 0.10 percent of taxable payroll.
## 8. Disability Termination RatesTable II.G8 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about future disability termination rates. For alternative II, death-termination rates by age and sex are assumed to decline until they reach levels by the end of the 75-year period that, in comparison to the corresponding annual rates experienced during the base period 1977-80, are lower by about 33 percent for men and 26 percent for women. For the other alternatives, the rates are assumed to spread gradually from the rates for alternative II. By the end of the projection period, for men the rates are 16 percent lower for alternative I and 48 percent lower for alternative III, and for women they are 6 percent lower for alternative I and 46 percent lower for alternative III. For alternative II, ultimate recovery-termination rates by age and sex are assumed to be attained in 2009; such rates are assumed to be about 50 percent lower than those experienced in the base period, 1977-80. For the other alternatives, the rates are assumed to spread gradually from the rates for alternative II; from that year until the end of the projection period the rates under alternative I and III are 20 percent higher and lower, respectively, than the rates for alternative II. For the 25-year period, the cost rate increases with decreasing disability termination rates from 12.87 percent (for the relatively high rates assumed for alternative I) to 12.93 percent (for the relatively low rates assumed for alternative III). For the 50-year period, it increases from 14.56 to 14.66 percent, and for the 75-year period, it increases from 15.38 to 15.50 percent. The actuarial balance decreases from +0.57 to +0.51 percent for the 25-year period, from -1.28 to -1.38 percent for the 50-year period, and from -2.11 to -2.23 percent for the 75-year period. |
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