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, which were presented earlier in this report, illustrate the effects of varying all of the principal assumptions simultaneously, in order to portray a generally more optimistic or pessimistic future. For each sensitivity analysis presented in this appendix, the intermediate alternative II projection is the reference point, and one assumption is varied within that alternative. The variation used for each individual assumption is the same as the level 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. Following each table is a discussion of the estimated changes in cost rates. The change in each of the actuarial balances is approximately equal to the change in the corresponding cost rate, but in the opposite direction. This appendix does not discuss income rates following each table because income rates vary only slightly with changes in assumptions. This stability occurs because the combined rate, which includes payroll taxes and reimbursements from the General Fund of the Treasury, is constant for the entire 75-year valuation period.Table VI.D1 shows OASDI income rates, cost rates, and actuarial balances on the basis of alternative II with various assumptions about the ultimate total fertility rate. The Trustees assume that total fertility will ultimately be 1.7, 2.0, and 2.3 children per woman under alternatives III, II, and I, respectively. The total fertility rate changes gradually from the 2011 level and reaches ultimate values in 2036.

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 reached in 2036.

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 17.12 to 16.27 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 ‑3.05 to -2.29 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. Therefore, program cost increases slightly with higher fertility. For the 75‑year long-range period, however, changes in fertility have a relatively greater effect 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 0.13 percent of taxable payroll.2. Death RatesTable VI.D2 shows 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 2011-86. These assumptions are described in section V.A.2. The Trustees assume that the age-sex-adjusted death rates will decline at average annual rates of 0.39 percent, 0.77 percent, and 1.18 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 age-sex-adjusted death rate decreases from 2011 to 2086 by 26 percent, 44 percent, and 59 percent for alternatives I, II, and III, respectively.

The average annual death-rate reductions used for this analysis are: 0.39 percent from the alternative I assumptions, 0.77 percent from the alternative II assumptions, and 1.18 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 Trustees assume that decreases in death rates will occur gradually. The 25-year cost rate increases from 16.04 percent (for an average annual death-rate reduction of 0.39 percent) to 16.33 percent (for an average annual death-rate reduction of 1.18 percent). The 75-year cost rate increases from 16.20 to 17.19 percent. The actuarial balance decreases from ‑1.07 to ‑1.36 percent for the 25-year period, and from -2.19 to ‑3.16 percent for the 75-year period.Lower death rates raise both the income (through increased taxable payroll) and the cost of the OASDI program. 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). Reductions for people at age 50 to retirement eligibility age result in significant increases to the taxable payroll. However, 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 in death rates do not result in significant increases in the numbers of covered workers or beneficiaries. Consequently, if death rates decline by about the same relative amount for all ages, the cost increases faster than the rate of growth in payroll, which results in higher cost rates and 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 0.12 percent of taxable payroll.3. Net ImmigrationTable VI.D3 shows OASDI income rates, cost rates, and actuarial balances under alternative II with various assumptions about the magnitude of net immigration. The Trustees assume that annual net immigration will average 790,000 persons, 1,080,000 persons, and 1,375,000 persons over the long-range period under alternatives III, II, and I, respectively.

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

Net immigration per year is the 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: 790,000 from the alternative III assumptions, 1,080,000 from the alternative II assumptions, and 1,375,000 from the alternative I assumptions. All other assumptions used for this analysis are from alternative II.

For all three periods, when net immigration increases, the cost rate decreases. For the 25-year period, the cost rate decreases from 16.32 percent of taxable payroll (for average annual net immigration of 790,000 persons) to 16.06 percent (for average annual net immigration of 1,375,000 persons). For the 50-year period, it decreases from 16.74 percent to 16.33 percent, and for the 75-year period, it decreases from 16.95 percent to 16.46 percent. The actuarial balance increases from ‑1.33 to ‑1.11 percent for the 25-year period, from ‑2.47 to -2.12 percent for the 50-year period, and from -2.89 to ‑2.47 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 OASDI income rates, cost rates, and actuarial balances on the basis of alternative II with various assumptions about the real-wage differential. The Trustees assume the ultimate real-wage differential will be 0.51 percentage point, 1.12 percentage points, and 1.71 percentage points under alternatives III, II, and I, respectively. In each case, the ultimate annual increase in the CPI is 2.80 percent (consistent with alternative II). Therefore, the ultimate percentage increases in average annual wages in covered employment are 3.31, 3.92, and 4.51 percent.For the 25-year period, the cost rate decreases from 16.89 percent (for a real-wage differential of 0.51 percentage point) to 15.51 percent (for a differential of 1.71 percentage points). For the 50-year period, it decreases from 17.56 to 15.54 percent, and for the 75-year period it decreases from 17.84 to 15.60 percent. The actuarial balance increases from -1.78 to -0.68 percent for the 25-year period, from ‑3.14 to -1.47 percent for the 50-year period, and from ‑3.61 to ‑1.77 percent for the 75-year period.

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

The first value in each pair is the ultimate annual percentage increase in average wages in covered employment. The second value is the 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 0.51, 1.12, and 1.71 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. Higher wages increase taxable payroll immediately, but they 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 real-wage differential increases the long-range actuarial balance by about 0.77 percent of taxable payroll.Table VI.D5 shows 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 Trustees assume the annual increase in the CPI will be 1.80 percent, 2.80 percent, and 3.80 percent under alternatives I, II, and III, respectively. In each case, the ultimate real-wage differential is 1.12 percentage points (consistent with alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 2.92, 3.92, and 4.92 percent.

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

The first value in each pair is the ultimate annual percentage increase in average wages in covered employment. The second value is the 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 1.80, 2.80, and 3.80 percent are the same as in alternatives I, II, and III, respectively. The ultimate real-wage differential of 1.12 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 when the assumed rates of increase in the CPI are greater. For the 25-year period, the cost rate decreases from 16.36 (for CPI increases of 1.80 percent) to 16.01 percent (for CPI increases of 3.80 percent). For the 50-year period, it decreases from 16.75 to 16.29 percent, and for the 75-year period, it decreases from 16.94 to 16.44 percent. The actuarial balance increases from -1.35 to -1.08 percent for the 25-year period, from ‑2.48 to -2.09 percent for the 50-year period, and from ‑2.88 to ‑2.45 percent for the 75-year period.The time lag between the effects of the CPI changes on taxable payroll and on benefit payments explains these patterns. When the rate of increase in the CPI is greater and the real-wage differential is constant, then: (1) the effect on taxable payroll due to a greater rate of increase in average wages occurs immediately; and (2) the effect on benefits due to a larger COLA occurs with a lag of about 1 year. As a result of these effects, 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 the change in the CPI increases the long-range actuarial balance by about 0.22 percent of taxable payroll.Table VI.D6 shows OASDI income rates, cost rates, and actuarial balances under alternative II with various assumptions about the annual real interest rate (compounded semiannually) for special public-debt obligations issuable to the trust funds. The Trustees assume that the ultimate annual real interest rate will be 2.4 percent, 2.9 percent, and 3.4 percent under alternatives III, II, and I, respectively. In each case, the ultimate annual increase in the CPI is 2.80 percent, which is consistent with alternative II. Therefore, the ultimate annual yields are 5.3, 5.8, and 6.3 percent, respectively.

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

The ultimate real interest rate is 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: 2.4 percent from the alternative III assumptions, 2.9 percent from the alternative II assumptions, and 3.4 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 16.26 percent (for an ultimate real interest rate of 2.4 percent) to 16.10 percent (for an ultimate real interest rate of 3.4 percent). For the 50-year period, it decreases from 16.62 to 16.42 percent and, for the 75‑year period, it decreases from 16.81 to 16.56 percent. The actuarial balance increases from -1.36 to ‑1.07 percent for the 25-year period, from ‑2.47 to ‑2.09 percent for the 50-year period, and from -2.89 to -2.44 percent for the 75-year period. Each 0.5-percentage-point increase in the real interest rate increases the long-range actuarial balance by about 0.22 percent of taxable payroll.7. Disability Incidence RatesTable VI.D7 shows 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, the Trustees assume that incidence rates by age and sex will vary during the early years of the projection period before attaining ultimate levels in 2031. In comparison to the historical period 1970 through 2011, the ultimate age-sex-adjusted incidence rate is about 4 percent higher for alternative II, 15 percent lower for alternative I, and 25 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 15.96 percent (for the relatively low rates assumed for alternative I) to 16.41 percent (for the relatively high rates assumed for alternative III). For the 50-year period, it increases from 16.24 to 16.79 percent, and for the 75-year period, it increases from 16.40 to 16.97 percent. The actuarial balance decreases from ‑1.00 to -1.44 percent for the 25-year period, from -2.01 to -2.55 percent for the 50-year period, and from -2.38 to ‑2.95 percent for the 75-year period.Table VI.D8 shows 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, the Trustees assume that death rates will decline throughout the long-range period. For alternative II, the age-sex-adjusted^{1}death rate declines to a level in 2086 that is about 58 percent lower than the level in 2011. For alternative I, the age-sex-adjusted death rate declines to a level in 2086 that is about 32 percent lower than the level in 2011. For alternative III, the age-sex-adjusted death rate declines to a level in 2086 that is about 75 percent lower than the level in 2011.For all three alternatives, ultimate recovery-termination rates by age, sex, and duration are attained in the twentieth year of the projection period. For alternative II, the age-sex-adjusted1 recovery rate in 2031 is about 10 recoveries per thousand disabled-worker beneficiaries. For alternative I, the age-sex-adjusted recovery rate in 2031 is about 12 recoveries per thousand disabled-worker beneficiaries. For alternative III, the age-sex-adjusted recovery rate in 2031 is about 8 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 16.14 percent (for the relatively high termination rates assumed for alternative I) to 16.22 percent (for the relatively low termination rates assumed for alternative III). For the 50-year period, it increases from 16.47 to 16.57 percent, and for the 75-year period, it increases from 16.64 to 16.73 percent. The actuarial balance decreases from -1.18 to -1.25 percent for the 25-year period, from -2.23 to -2.33 percent for the 50-year period, and from -2.62 to ‑2.71 percent for the 75-year period.

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