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 significantly 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 reaches ultimate values in 2038.

For the 25-year period, the cost rate for the three fertility assumptions varies by only about 0.06 percent of taxable payroll. In contrast, the 75-year cost rate varies over a wide range, decreasing from 17.20 to 16.36 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 ‑3.27 to -2.51 percent.During the 25-year period, the very slight increases in the working population resulting from higher fertility (than that experienced in an alternative scenario) 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 2013-88. 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 0.41 percent, 0.79 percent, and 1.20 percent for alternatives I, II, and III, respectively.

The average annual death-rate reduction is the average annual geometric rate of decline in the age-sex-adjusted death rate between 2013 and 2088. The overall age-sex-adjusted death rate decreases from 2013 to 2088 by 27 percent, 45 percent, and 60 percent for alternatives I, II, and III, respectively.

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.Table 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 830,000 persons, 1,125,000 persons, and 1,430,000 persons over the long-range period under alternatives III, II, and I, respectively.

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.

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, 1.13 percentage points, and 1.76 percentage points under alternatives III, II, and I, respectively. In each case, the ultimate annual increase in the CPI is 2.70 percent (consistent with alternative II). Therefore, the ultimate percentage increases in average annual wages in covered employment are 3.21, 3.83, and 4.46 percent.

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 3.40 percent, 2.70 percent, and 2.00 percent under alternatives I, II, and III, respectively.^{1}In each case, the ultimate real-wage differential is 1.13 percentage points (consistent with alternative II), yielding ultimate percentage increases in average annual wages in covered employment of 4.53, 3.83, and 3.13 percent.

The time lag between the effects of the CPI changes on taxable payroll and on scheduled benefits 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 decrease in the rate of the change in the CPI decreases 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 2.70 percent, which is consistent with alternative II. Therefore, the ultimate annual yields are 5.2, 5.7, and 6.2 percent, respectively.

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 comparison to the historical period 1970 through 2013, the ultimate age-sex-adjusted incidence rate is about 4 percent higher for alternative II, 17 percent lower for alternative I, and 25 percent higher for alternative III.

8. Disability Termination RatesTable 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, including deaths and recoveries up to the age at which disabled-worker beneficiaries convert to retired-worker status.For all three alternatives, the Trustees assume that death rates for disabled-worker beneficiaries will decline throughout the long-range period. For alternative II, the age-sex-adjusted^{2}disability death rate declines to a level in 2088 that is about 56 percent lower than the level in 2013. For alternative I, the age-sex-adjusted disability death rate declines to a level in 2088 that is about 29 percent lower than the level in 2013. For alternative III, the age-sex-adjusted disability death rate declines to a level in 2088 that is about 74 percent lower than the level in 2013.For all three alternatives, ultimate recovery 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 2033 is about 11 recoveries per thousand disabled-worker beneficiaries. For alternative I, the age-sex-adjusted recovery rate in 2033 is about 13 recoveries per thousand disabled-worker beneficiaries. For alternative III, the age-sex-adjusted recovery rate in 2033 is about 8 recoveries per thousand disabled-worker beneficiaries.

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