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| Uncertainty in Social Security's Long-Term Finances: A Stochastic Analysis December 2001 |
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In developing its Long-Term Actuarial Model, the Congressional Budget Office has followed the practices of the Social Security Administration's Office of the Chief Actuary, with certain adaptations. This analysis of the uncertainty of LTAM's projections looks at the same key 75-year assumptions for demographic and economic variables that SSA focuses on in its annual analysis of the solvency of the Social Security trust funds. The demographic variables are
The economic variables are
Each year, the Social Security Board of Trustees makes 75-year projections
for those nine variables. Understanding the challenges it faces in choosing
expected values for those inputs over the projection period is a first
step in understanding the uncertainty inherent in each of the input assumptions.
DEMOGRAPHIC INPUTS AND POPULATION PROJECTIONS
Because Social Security is basically structured as a pay-as-you-go system, its financial status is primarily determined by the ratio of beneficiaries to workers, which in turn depends on the ratio of elderly to working-age people (known as the aged dependency ratio).
Although parameters of the Social Security program vary automatically with changes in wage growth and inflation, no such adjustments occur when the size or structure of the population changes. Thus, estimates of fertility and mortality (and, to a lesser extent, immigration) are very important in projecting the program's future finances.
Fertility
The fertility rate in a specific year is the number of children that
would be born to a woman over her lifetime at the average birth rates for
women of different ages observed in that year. Currently, the fertility
rate is about 2.06 (see Figure 2). SSA's intermediate
assumption is that the rate will fall steadily, but only slightly, over
the next 25 years to 1.95, after which it will stay at that level. Since
1972, fertility rates have remained roughly constant, on average, although
they have been much lower than the very high rates of the baby-boom era
(1946 to 1964).
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FIGURE 2. INTERMEDIATE PROJECTIONS FOR THE OVERALL RATE OF FERTILITY |
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| SOURCE: Social Security Administration, Office of the Chief Actuary. |
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The projection of a 1.95 fertility rate assumes that changing social standards and the availability of oral contraceptives make it very unlikely that fertility rates will return to the levels of more than 3.0 seen during the baby boom. Actuaries at SSA are making a reasonable inference when they suggest that there are no grounds to expect big changes in fertility behavior in the next 75 years.
Nevertheless, the fact that little basis exists for projecting fertility, coupled with the fact that fertility is a chief source of financial instability in Social Security, is a reason to directly consider the uncertainty that surrounds fertility. As shown in later chapters, however, the degree of uncertainty about future fertility depends to some extent on how the historical tea leaves are read.
Mortality Improvement
Mortality projections start with a matrix of current mortality rates,
by age and sex. (The mortality rate is the portion of people of a given
age and sex who die in a given year.) Historically, mortality rates fall
when living conditions and medical care improve; in the absence of a major
new disease or significant social disruption, they are expected to continue
declining. The change in mortality--the rate of mortality improvement--varies
significantly from year to year (see Figure 3).
However, it is negative in most years, indicating a general decline in
mortality rates.
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FIGURE 3. INTERMEDIATE PROJECTIONS FOR THE OVERALL RATE OF MORTALITY IMPROVEMENT |
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| SOURCE: Social Security Administration, Office of the Chief Actuary. |
| NOTE: For this figure, mortality improvements have been aggregated across age and sex groups, resulting in a measure of the change in what demographers refer to as the "central" death rate. |
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The difficulty in making an intermediate projection for mortality improvement lies in determining overall trends in historical variability and anticipating whether the rate of mortality improvement will change in the future. SSA projects age- and sex-specific improvement rates (for 21 age groups for each sex). SSA's model assumes that those rates will rise steadily for the next 25 years and remain constant thereafter. In contrast, it expects the overall rate of improvement, which is adjusted by age and sex, to dip slightly and then gradually return to roughly the current level by 2075 (see Figure 3).
SSA's projected overall rate of mortality improvement is approximately equal to the average of recent annual rates. Examining data since 1940 shows huge short-term variation as well as longer-term changes in mortality rates, with relatively large declines from 1940 to the mid-1950s that were repeated in the 1970s, and a stable rate of decline during the 1960s. From 1960 to 1968, the overall mortality rate decreased by an average of 0.2 percent a year. Over the next 14 years, however, the average drop was 1.9 percent. Since 1983, the mortality rate has fallen by an average of 0.8 percent a year.
Immigration
SSA's intermediate assumption for the level of immigration is 900,000
people in each of the projection years. At first glance, the clear trend
of growth in immigration over the past 50 years makes that flat level appear
unlikely (see Figure 4). Moreover, it may seem natural
to think that immigration will increase with the total population. However,
unlike fertility and mortality rates, the number of immigrants to the United
States is governed partly by law, and Social Security's baseline is calculated
on the basis of current law.
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FIGURE 4. INTERMEDIATE PROJECTIONS FOR THE LEVEL OF IMMIGRATION |
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| SOURCE: Social Security Administration, Office of the Chief Actuary. |
| NOTE: Recent historical data for the level of immigration are unavailable. |
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ECONOMIC INPUTS
The six economic inputs that go into financial projections for Social Security can be classified in three categories: variables that affect how much workers earn and receive in benefits (wage growth, inflation, and unemployment); variables that affect the growth of the trust funds over time (the interest rate on Social Security assets); and variables that affect the ratio of beneficiaries to workers (disability incidence and termination rates).
Real Wage Growth
The nominal rate of wage growth used to compute taxable wages and determine benefits in Social Security projections is the sum of the inflation rate and real wage growth. Although real wage growth depends mainly on productivity growth, factors such as the average number of hours worked and the level of nonwage compensation also matter. SSA analyzes and projects each component of wage growth separately.
Real wage growth varies significantly both from year to year and over
longer time periods (see Figure 5). Most of that
variability is attributable to changes in productivity growth. (Other factors,
such as average hours worked and the ratio of taxable wages to total compensation,
are more stable.) Because productivity growth is one of the great unexplained
variables in economics, real wages are hard to project with precision.
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FIGURE 5. INTERMEDIATE PROJECTIONS FOR THE RATE OF REAL WAGE GROWTH |
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| SOURCES: Department of Commerce, Bureau of Economic Analysis; Social Security Administration, Office of the Chief Actuary. |
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The most difficult part of forecasting real wage growth is guessing whether future growth will be consistent with that of the previous few years, the past few decades, or the entire postwar period--all of which are very different. The past few years have been characterized by a boom in real wage growth and productivity, with sustained rates of increase not seen since the early 1960s. But is that recent boom an indication that the United States is returning to an era of strong growth or simply an aberration from the lower level of average growth that appears to have been in place from the early 1970s through the mid-1990s?
SSA has taken a fairly conservative view of recent productivity gains. Thus, its intermediate projection of average real wage growth over the next 75 years--about 1.0 percent per year--is consistent with the idea that the United States will return to the lower rates of growth seen since the 1970s.
The assumption about real wage growth is crucial because, in the short term, high real wage growth causes Social Security revenues to rise but has little impact on benefits. Thus, it improves the program's financial balance. Long-term finances are not quite as sensitive to changes in the rate of real wage growth because initial Social Security benefits are indexed to such growth. Nevertheless, higher wage growth promotes long-term solvency because it causes an immediate rise in payroll tax revenues but a delayed increase in benefits, since only new benefits are indexed to wages. (After a Social Security recipient begins collecting benefits, those payments rise each year with prices.)
Inflation
Prices, as measured by the consumer price index for wage earners (CPI-W),
increased at an average rate of 4.4 percent a year during the four decades
between 1959 and 1998, but by only 3.2 percent a year during the decade
from 1989 to 1998. In projecting that inflation will rise to only 3.3 percent
by 2005 and remain at that level thereafter, SSA may be giving too much
weight to recent experience (see Figure 6). However,
the inflation booms of the 1940s and 1970s were clearly linked to events--such as World War II and the OPEC oil embargo--that are unlikely to recur,
which makes SSA's assumption seem more reasonable.
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FIGURE 6. INTERMEDIATE PROJECTIONS FOR THE INFLATION RATE |
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| SOURCES: Department of Labor, Bureau of Labor Statistics; Social Security Administration, Office of the Chief Actuary. |
| NOTE: In this figure, inflation is measured as the change in the consumer price index for wage earners (CPI-W). |
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Assumptions about inflation have an important impact on Social Security's finances, but not in the way that most people would think. Social Security benefits are indexed by law to inflation in the previous year, but wages are indexed implicitly to current inflation (because nominal wage growth includes inflation). Thus, a rise in inflation increases revenues immediately but raises benefits only in the future. Although high inflation is generally considered harmful--especially for the elderly, who often receive pensions that are not indexed to prices--inflation actually improves the actuarial status of Social Security.
Unemployment
The unemployment rate is the percentage of the labor force that is not
employed but is actively looking for work. As with any volatile macroeconomic
variable, projecting unemployment in the short run is very difficult, although
a long-run tendency around fairly stable averages seems to exist (see Figure
7). The positive experience of the past few years has been atypical,
and it would be optimistic to assume that unemployment will remain at such
a historically low level. Still, recent history prompted SSA to reduce
its long-term projection of unemployment from 6.0 percent in its 1998 report
to 5.5 percent in its 1999 report. Currently, SSA assumes that the unemployment
rate will rise smoothly from 4.1 percent in 2000 to 5.5 percent in 2009
and remain at that level thereafter.
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FIGURE 7. INTERMEDIATE PROJECTIONS FOR THE UNEMPLOYMENT RATE |
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| SOURCES: Department of Labor, Bureau of Labor Statistics; Social Security Administration, Office of the Chief Actuary. |
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Interest Rate
SSA lists as one of its key inputs the nominal interest rate on assets held in the Social Security trust funds. Under standard economic theory, nominal interest rates are the sum of inflation and the real interest rate--the return investors would receive if inflation were zero. Because inflation is a separate input, it is appropriate to describe returns on trust fund assets in terms of the real interest rate and to sum the two assumptions to compute nominal returns on those assets.
SSA projects a real interest rate for the trust funds of 3.0 percent
per year over the next 75 years (see Figure 8).
Although that rate is significantly higher than the historical average
(about 2.4 percent since 1926), it is much lower than the average over
the past few decades (4.2 percent since 1980 and 3.4 percent since 1990).
SSA's assumption is consistent with two offsetting observations: first,
real interest rates were negative during the 1970s because the high inflation
of that period surprised investors, and second, nominal interest rates
take time to reflect new information about inflation. The spike in real
interest rates during the early 1980s was associated with the extremely
tight monetary policy of that time (which was put in place to rein in inflation,
which had galloped out of control). Thus, unless inflationary shocks and
tight monetary policy recur, there is no reason to suspect that the real
interest rate will diverge from that experienced during more normal times--about
3.0 percent.
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FIGURE 8. INTERMEDIATE PROJECTIONS FOR THE REAL INTEREST RATE ON ASSETS IN THE SOCIAL SECURITY TRUST FUNDS |
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| SOURCE: Social Security Administration, Office of the Chief Actuary. |
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Disability Incidence and Termination
SSA projects separate rates for the onset and ending of disability. The onset (or incidence) rate is the percentage of nondisabled workers covered by Disability Insurance who become disabled in a given year. The termination rate is the percentage of disabled workers who leave the DI rolls in a given year--because they either recover, die, or begin receiving retired-worker benefits instead (which occurs automatically when they reach Social Security's normal retirement age).
To project the prevalence of disability, SSA starts by projecting future trends in morbidity (the incidence of disease). Like mortality rates, morbidity rates are expected to continue to fall.(1) Still, projecting disability status is more complicated than that because it involves not only morbidity but, perhaps more important, government policy (which varies even in the absence of legislation), changes in the labor market's demand for certain skills, and social definitions of disability.
Thus, although rates of morbidity are improving, rates of disability
incidence have not changed steadily over time (see Figure
9). The overall rate of incidence has declined in the past several
years; however, SSA expects it to rise over the next few decades and then
level out.
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FIGURE 9. INTERMEDIATE PROJECTIONS FOR THE RATE OF DISABILITY INCIDENCE |
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| SOURCES: Congressional Budget Office; Social Security Administration, Office of the Chief Actuary. |
| NOTE: Recent historical data for the rate of disability incidence are unavailable. |
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Rates of disability termination are also affected by underlying changes
in demographics, because death rates play a part in determining how many
people leave the disability rolls each year. The termination rate has fallen
in the past few years, but that change was influenced by policy and social
norms as well as by underlying demographics (see Figure
10). SSA expects that the termination rate will rise in the short term
and thereafter be influenced mainly by demographics.
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FIGURE 10. INTERMEDIATE PROJECTIONS FOR THE RATE OF DISABILITY TERMINATION |
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| SOURCES: Congressional Budget Office; Social Security Administration, Office of the Chief Actuary. |
| NOTE: Recent historical data for the rate of disability termination are unavailable. |
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PROJECTING SOCIAL SECURITY'S FINANCES USING THE LONG-TERM ACTUARIAL MODEL
A number of questions arise about the choice of input assumptions used to project the Social Security system's finances. Indeed, much of the focus of every year's trustees' report is on how the values for the inputs are determined. As noted above, historical data can be interpreted in many ways, and inferences about future values that are based on those data can also vary. In this analysis, CBO does not question the underlying choices of intermediate assumptions made by the trustees. Rather, it employs a model of trust fund accumulation to measure how uncertainty about those inputs leads to uncertainty about Social Security's finances.
CBO's new analytical tool, LTAM, is capable of generating estimates that basically match SSA's projections for a particular set of inputs. In other words, given values for fertility, mortality improvement, immigration, real wage growth, inflation, unemployment, the real interest rate, disability incidence, and disability termination, LTAM can generate projections of the trust fund balance that generally match those produced by SSA.
Moreover, the LTAM approach allows uncertainty to be studied in a way that is not possible with SSA's models. At SSA, the various pieces that go into a trust fund projection--population by demographic group, average wages, benefits, and other variables--are studied separately using analytical tools developed with different software and sometimes different computer systems. Results from each step are combined only at the end when trust fund calculations are made. In contrast, LTAM pulls all sectors together in one compiled model, which can be solved repeatedly (and very quickly) using any combination of input assumptions. That feature makes possible the uncertainty analysis described in the rest of this paper.
The cost of pulling projection techniques together into one model is a certain amount of simplification relative to SSA's projection techniques--LTAM lacks some of the detail of SSA's models. Still, it can simulate how the Social Security system will respond to changes both in assumptions and in most policy parameters. For key calculations--computing the number of deaths using a given mortality rate, or solving for average worker benefits using the microsimulation approach--LTAM attempts to follow the same modeling strategy used by SSA. The criterion for successful model development at CBO was ensuring that the answers for the baseline values were about the same as those produced by SSA's models. Given inputs and outputs from SSA, the model developed at CBO does a good job of mimicking those answers.(2)
Some elements of the LTAM projections, however, do not reproduce SSA's methods. Rather, they use SSA outputs as inputs to the model. For example, the ratio of auxiliary benefits to worker benefits is held fixed at ratios computed directly from Social Security output files. That practice is necessarily limited to parts of the model that would not vary (or would have a negligible change) with new policies or new inputs, because LTAM is primarily designed to capture changes in the Social Security system's finances that occur with changes in input assumptions or policy parameters.
Conclusions about whether an approximating model such as LTAM can show
how system finances will change when inputs change--a prerequisite for
the type of uncertainty analysis conducted here--should be based on evidence,
not assertions. Such a basis is possible because results from LTAM can
be compared with the results that SSA publishes in its "high-" and "low-cost"
scenario analysis, which is discussed in the next chapter.
1. See, for example, E. Crimmins, Y. Saito, and D. Ingegneri, "Trends in Disability-Free Life Expectancy in the United States, 1970-1990," Population and Development Review, vol. 23 (1997), pp. 555-572.
2. To the extent that minor differences remain, CBO uses "calibration" factors in various parts of the model to produce exact matches of SSA's baseline projections.
