This appendix presents estimates that illustrate the sensitivity of the long-range actuarial status of the OASDI program to changes in selected individual assumptions. The estimates, based on the three alternative sets of assumptions (see sections IV.B, V.A, V.B, andV.C), 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 appendix, the intermediate alternative II projection is used as the reference point, and one assumption at a time is varied within that alternative. The variation used for each individual assumption reflects the levels used for that assumption in the low-cost alternative I and high-cost alternative III projections.Each table in this section shows the effects of changing a particular assumption on the OASDI summarized income rates, summarized cost rates, and actuarial balances for 25-year, 50-year, and 75-year valuation periods. The income rate varies only slightly with changes in assumptions because the annual payroll tax rate is constant for the entire 75-year valuation period. Therefore, the income rate 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.Table VI.D1 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. The ultimate total fertility rate is assumed to be 1.7, 2.0, and 2.3 children per woman, consistent with alternatives III, II, and I, respectively. The total fertility rate is assumed to change gradually from the 2010 level and reach the various ultimate values in 2035.

Table VI.D1.—Sensitivity to Varying Fertility Assumptions

The total fertility rate for any year is the average number of children who would be born to a woman in her lifetime if she were to experience the birth rates by age observed in, or assumed for, the selected year, and if she were to survive the entire childbearing period. The ultimate total fertility rate is assumed to be reached in 2035.

Ultimate total fertility rates used for this analysis are: 1.7 from the alternative III assumptions, 2.0 from the alternative II assumptions, and 2.3 from the alternative I assumptions. All other assumptions used for this analysis are from alternative II.

For the 25-year period, the cost rate for the three fertility assumptions varies by only about 0.05 percent of taxable payroll. In contrast, the 75-year cost rate varies over a wide range, decreasing from 16.67 to 15.84 percent, as the assumed ultimate total fertility rate increases from 1.7 to 2.3. Similarly, while the 25-year actuarial balance varies by only 0.05 percent of taxable payroll, the 75-year actuarial balance varies over a much wider range, from ‑2.60 to -1.86 percent.During the 25-year period, the very slight increases in the working population resulting from increases in fertility are more than offset by decreases in the female labor force and 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 0.12 percent of taxable payroll.2. Death RatesTable VI.D2 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 for the period 2010-85. These assumptions are the same as those used for alternatives I, II, and III, which are described in section V.A.2. The age-sex-adjusted death rates decline at average annual rates of 0.32 percent, 0.78 percent, and 1.31 percent for alternatives I, II, and III, respectively.

Table VI.D2.—Sensitivity to Varying Death-Rate Assumptions

The average annual death-rate reduction is the average annual geometric rate of decline in the age-sex-adjusted death rate between 2010 and 2085. The overall decreases from the age-sex-adjusted death rate in 2010 to the corresponding rate in 2085 are 22 percent, 45 percent, and 63 percent for alternatives I, II, and III, respectively.

The average annual death-rate reductions used for this analysis are: 0.32 percent from the alternative I assumptions, 0.78 percent from the alternative II assumptions, and 1.31 percent from the alternative III assumptions. All other assumptions used for this analysis are from alternative II.

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. The 25-year cost rate increases from 15.38 percent (for an average annual death-rate reduction of 0.32 percent) to 15.78 percent (for an average annual death-rate reduction of 1.31 percent). The 75-year cost rate increases from 15.53 to 16.90 percent. The actuarial balance decreases from ‑0.37 to ‑0.77 percent for the 25-year period, and from -1.54 to ‑2.86 percent for the 75-year period.Lower death rates cause both the income (through increased taxable payroll) and the cost of the OASDI program to be higher. The relative increase in cost, however, exceeds the relative increase in taxable payroll. For any given year, reductions in the death rates for people who are age 62 and over (ages at which 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 at ages 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 at these pre-retirement ages, which are ages of high disability incidence. 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, cost increases at a rate greater than the rate of growth in payroll, which results in higher cost rates and, therefore, lower actuarial balances. Each additional 0.1‑percentage-point increase in the average annual rate of decline in the death rate decreases the long-range actuarial balance by about 0.13 percent of taxable payroll.3. Net ImmigrationTable VI.D3 shows the estimated OASDI income rates, cost rates, and actuarial balances, under alternative II with various assumptions about the magnitude of net immigration. Annual net immigration is assumed to average, over the long-range period, 785,000 persons, 1,075,000 persons, and 1,385,000 persons, consistent with alternatives III, II, and I, respectively.

Table VI.D3.—Sensitivity to Varying Net-Immigration Assumptions

Net immigration per year is the assumed annual net immigration to the Social Security area, including both legal and other immigration, averaged over the 75-year projection period.

The average annual net immigration assumptions used for this analysis are: 785,000 from the alternative III assumptions, 1,075,000 from the alternative II assumptions, and 1,385,000 from the alternative I assumptions. All other assumptions used for this analysis are from alternative II.

For all three periods, the cost rate decreases with increasing rates of net immigration. For the 25-year period, the cost rate decreases from 15.74 percent of taxable payroll (for average annual net immigration of 785,000 persons) to 15.47 percent (for average annual net immigration of 1,385,000 persons). For the 50-year period, it decreases from 16.25 percent to 15.82 percent, and for the 75-year period, it decreases from 16.50 percent to 16.00 percent. The actuarial balance increases from ‑0.70 to ‑0.49 percent for the 25-year period, from ‑1.97 to -1.60 percent for the 50-year period, and from -2.44 to ‑2.01 percent for the 75-year period.The cost rate decreases with an increase in net immigration because immigration occurs at relatively young ages, thereby increasing the numbers of covered workers earlier than the numbers of beneficiaries. Increasing average annual net immigration by 100,000 persons improves the long-range actuarial balance by about 0.07 percent of taxable payroll.Table VI.D4 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. The ultimate real-wage differential is assumed to be 0.6 percentage point, 1.2 percentage points, and 1.8 percentage points, consistent with alternatives III, II, and I, respectively. In each case, the ultimate annual increase in the CPI is assumed to be 2.8 percent (consistent with alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 3.4, 4.0, and 4.6 percent.For the 25-year period, the cost rate decreases from 16.27 percent (for a real-wage differential of 0.6 percentage point) to 14.96 percent (for a differential of 1.8 percentage points). For the 50-year period, it decreases from 17.02 to 15.09 percent, and for the 75-year period it decreases from 17.33 to 15.19 percent. The actuarial balance increases from -1.11 to -0.09 percent for the 25-year period, from ‑2.58 to -1.01 percent for the 50-year period, and from ‑3.10 to ‑1.36 percent for the 75-year period.

Table VI.D4.—Sensitivity to Varying Real-Wage Assumptions

The first value in each pair is the assumed ultimate annual percentage increase in average wages in covered employment. The second value is the assumed ultimate annual percentage increase in the Consumer Price Index. The difference between the two values is the ultimate real-wage differential.

The ultimate real-wage differentials of 0.6, 1.2, and 1.8 percentage points are the same as in alternatives III, II, and I, respectively. All other assumptions used for this analysis are from alternative II.

The cost rate decreases with increasing real-wage differentials. This is because higher wages increase taxable payroll immediately, but increase benefit levels only gradually as new beneficiaries become entitled. In addition, cost-of-living adjustments (COLAs) to benefits depend not on changes in wages, but on changes in prices. Each 0.5-percentage-point increase in the assumed real-wage differential increases the long-range actuarial balance by about 0.72 percent of taxable payroll.Table VI.D5 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). The ultimate annual increase in the CPI is assumed to be 1.8 percent, 2.8 percent, and 3.8 percent, consistent with alternatives I, II, and III, respectively. In each case, the ultimate real-wage differential is assumed to be 1.2 percentage points (consistent with alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 3.0, 4.0, and 5.0 percent.

Table VI.D5.—Sensitivity to Varying CPI-Increase Assumptions

The first value in each pair is the assumed ultimate annual percentage increase in average wages in covered employment. The second value is the assumed ultimate annual percentage increase in the Consumer Price Index. The difference between the two values is the ultimate real-wage differential.

The ultimate CPI increases of 1.8, 2.8, and 3.8 percent are the same as in alternatives I, II, and III, respectively. The ultimate real-wage differential of 1.2 percentage points is the same as in alternative II. All other assumptions used for this analysis are also from alternative II.

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 15.79 (for CPI increases of 1.8 percent) to 15.44 percent (for CPI increases of 3.8 percent). For the 50-year period, it decreases from 16.27 to 15.83 percent, and for the 75-year period, it decreases from 16.50 to 16.02 percent. The actuarial balance increases from -0.73 to -0.48 percent for the 25-year period, from ‑1.98 to -1.61 percent for the 50-year period, and from ‑2.44 to ‑2.02 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 combination with a constant real-wage differential), the effect on taxable payroll due to a greater rate of increase in average wages is experienced immediately, while the effect on benefits due to a larger COLA is experienced with a lag of about 1 year. Thus, the higher taxable payrolls have a stronger effect than the higher benefits, which results in lower cost rates. Each 1.0‑percentage-point increase in the rate of change assumed for the CPI increases the long-range actuarial balance by about 0.21 percent of taxable payroll.Table VI.D6 shows the estimated OASDI income rates, cost rates, and actuarial balances, on the basis of alternative II with various assumptions about the annual real interest rate for special public-debt obligations issuable to the trust funds, which are compounded semiannually. The ultimate annual real interest rate is assumed to be 2.1 percent, 2.9 percent, and 3.6 percent, consistent with alternatives III, II, and I, respectively. In each case, the ultimate annual increase in the CPI is assumed to be 2.8 percent (consistent with alternative II), which results in ultimate annual yields of 5.0, 5.8, and 6.5 percent.

Table VI.D6.—Sensitivity to Varying Real-Interest Assumptions

The ultimate real interest rate is defined as the effective annual yield on assets held by the trust funds divided by the annual rate of growth in the CPI.

The ultimate annual real interest rates used for this analysis are: 2.1 percent from the alternative III assumptions, 2.9 percent from the alternative II assumptions, and 3.6 percent from the alternative I assumptions. All other assumptions used for this analysis are from alternative II.

For the 25-year period, the cost rate decreases with increasing real interest rates, from 15.74 percent (for an ultimate real interest rate of 2.1 percent) to 15.50 percent (for an ultimate real interest rate of 3.6 percent). For the 50-year period, it decreases from 16.21 to 15.89 percent, and for the 75‑year period, it decreases from 16.47 to 16.06 percent. The actuarial balance increases from -0.84 to ‑0.39 percent for the 25-year period, from ‑2.10 to ‑1.50 percent for the 50-year period, and from -2.60 to -1.89 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 0.24 percent of taxable payroll.7. Disability Incidence RatesTable VI.D7 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 vary during the early years of the projection period before attaining ultimate levels in 2030. In comparison to the historical period 1970 through 2010, the ultimate age-sex-adjusted incidence rate is about the same for alternative II, 19 percent lower for alternative I, and 21 percent higher for alternative III.

Disability incidence rates

based on alternative— For the 25-year period, the cost rate increases with increasing disability incidence rates, from 15.39 percent (for the relatively low rates assumed for alternative I) to 15.82 percent (for the relatively high rates assumed for alternative III). For the 50-year period, it increases from 15.77 to 16.29 percent, and for the 75-year period, it increases from 15.96 to 16.52 percent. The actuarial balance decreases from ‑0.38 to -0.80 percent for the 25-year period, from -1.52 to -2.04 percent for the 50-year period, and from -1.95 to ‑2.49 percent for the 75-year period.8. Disability Termination RatesTable VI.D8 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 all three alternatives, death rates are assumed to decline throughout the long-range period. For alternative II, the age-sex-adjusted^{1}death rate is assumed to decline to a level in 2085 that is about 57 percent lower than the level in 2010. For alternative I, the age-sex-adjusted death rate is assumed to decline to a level in 2085 that is about 25 percent lower than the level in 2010. For alternative III, the age-sex-adjusted death rate is assumed to decline to a level in 2085 that is about 72 percent lower than the level in 2010.For all three alternatives, ultimate recovery-termination rates by age, sex, and duration are assumed to be attained in the twentieth year of the projection period. For alternative II, the age-sex-adjusted1 recovery rate in 2030 is about 11 recoveries per thousand disabled-worker beneficiaries. For alternative I, the age-sex-adjusted recovery rate in 2030 is about 13 recoveries per thousand disabled-worker beneficiaries. For alternative III, the age-sex-adjusted recovery rate in 2030 is about 9 recoveries per thousand disabled-worker beneficiaries.

Disability termination rates

based on alternative— For the 25-year period, the cost rate increases with decreasing disability termination rates, from 15.57 percent (for the relatively high termination rates assumed for alternative I) to 15.64 percent (for the relatively low termination rates assumed for alternative III). For the 50-year period, it increases from 15.99 to 16.08 percent, and for the 75-year period, it increases from 16.19 to 16.29 percent. The actuarial balance decreases from -0.56 to -0.63 percent for the 25-year period, from -1.73 to -1.82 percent for the 50-year period, and from -2.17 to ‑2.26 percent for the 75-year period.

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