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Uncertainty in Social Security's Long-Term Finances: A Stochastic Analysis December 2001

In considering the actuarial aspects of operations in the longer future, the unreliability of any specific estimates is of such degree that only the general course of financial development of the program may be indicated.

--First report of the Board of Trustees of the Federal Old-Age and Survivors Insurance Trust Fund, January 3, 1941

The Social Security Administration (SSA) projects that Social Security's Old-Age and Survivors Insurance and Disability Insurance Trust Funds will be exhausted within a few decades. After that, it predicts, a permanent imbalance will exist between the benefits paid by Social Security and the revenues collected for the program.⁽¹⁾ That projection is based on assumptions about long-term values for the demographic and economic variables (mortality improvement, fertility, immigration, inflation, unemployment, real wage growth, interest rates, and disability patterns) that affect Social Security revenues and benefits. Because a projection of the Social Security system's finances is based on assumptions, it is by nature uncertain.

The Congressional Budget Office (CBO) is one of several organizations that study the financial uncertainty facing Social Security. SSA publishes "high-cost" and "low-cost" scenarios as part of its annual 75-year projections of the program's finances; other analysts have created Social Security models and used them to make stochastic projections.⁽²⁾ CBO has developed a model--called the Long-Term Actuarial Model--that employs a unique combination of modeling detail and an easily managed programming format. That combination allows users to vary numerous inputs to the model and also assign probabilistic interpretations to the range of possible outcomes for the balance of the Social Security trust funds. The model uses inferred uncertainty about each input assumption (based on historical data) to compute the implied uncertainty about Social Security's future finances.
 

GOALS FOR STUDYING TRUST FUND UNCERTAINTY

Each year, SSA reports its long-term estimates of the actuarial status of the Social Security program to the Congress. Those estimates allow policymakers to anticipate imbalances or other structural difficulties with the program and to respond far in advance. However, policy choices should take into account not only expected effects but also how those choices might alter the stability of the Social Security system.

Why Consider Uncertainty?

An important measure of system finances is whether Social Security is in "close actuarial balance"--meaning that the program's revenues will be large enough to pay expected benefits over a 75-year period. According to SSA's baseline (or intermediate) assumptions, that condition is not currently being met.⁽³⁾ Equally important, however, is an understanding of the uncertainty of such projections.

In general, a system with more certainty is preferable because it allows plans to be set in advance. Simply put, uncertainty carries a cost. To make fully informed decisions about Social Security, policymakers should know both the expected path of various indicators--such as the date when the trust funds will be exhausted--and the best available probability distribution of those indicators.

Consider a scenario in which the trust funds are projected to have a positive balance for 50 years but also a 25 percent chance that the balance will turn negative within two decades. Such a system would require more-urgent action than one in which a positive balance was expected to last for just 45 years but there was only a 5 percent chance that the balance would turn negative within 20 years.

Uncertainty and System Structure

Uncertainty about the finances of the Social Security system comes from two factors: uncertainty about inputs and the system's sensitivity to changes in those inputs. The first factor is relatively intractable; despite advances in economic forecasting, accurately predicting national macroeconomic and demographic trends over the long run is impossible. However, the second factor--system sensitivity--can be changed.

Indexing the parameters of the Social Security system to uncertain inputs (so that the system changes along with those inputs) can increase stability. For example, the formula used to compute initial benefits is indexed to the nominal growth of wages, and recipients' current benefits are indexed to inflation. That indexing greatly reduces the system's sensitivity to changes in wage growth and inflation.⁽⁴⁾

The Social Security system is not indexed to demographic characteristics, however. As a result, an unexpectedly low rate of mortality or fertility will increase the system's cost rate (the ratio of benefits to taxable wages). Many analysts have proposed indexing Social Security's retirement age to mortality rates as a way to reduce benefit levels and the system's sensitivity to changes in mortality.

Redistribution of Risk

As analysts continually remind policymakers, the balance of the trust funds should not be the only indicator of the condition of Social Security, nor should effects on the trust funds be the only measure for evaluating a policy proposal. Any analysis of proposals to change Social Security must consider the expected benefits, costs, and risks borne by workers, beneficiaries, and other parts of the federal government. For example, although investing trust fund assets in corporate stocks might increase expected returns, it would also increase the riskiness of the system.⁽⁵⁾ In that case, the cost of the increased risk, as valued by financial markets, would exactly equal the expected increase in returns. Thus, the risk-adjusted value of the returns would not change. Individual investment accounts might increase that risk even more, depending on how they were structured, and could also redistribute risk among age and income groups. Finally, as with any program administered by the government, the additional element of political risk (that lawmakers will alter the program) is always present. This paper does not directly address the risk assumed by various parties, but it should be read with that broader context in mind.

Policymakers could eliminate uncertainty about the actuarial balance of the trust funds in a number of simple ways. For instance, after the trust funds were exhausted, the system could move to a pure pay-as-you-go approach--in which revenues equaled outlays each year--by annually cutting benefits, raising taxes, or transferring money from the Treasury. But although those policies would eliminate uncertainty about the actuarial balance, they would also crudely shift risk onto beneficiaries or workers.

Such restructuring of the Social Security system cannot eliminate or even reduce total financial risk. It can only shift that risk, as private insurance systems do. How the risk is redistributed is important, however. The shift should be made in such a way that negative and positive uncertain outcomes are balanced (in other words, risks should be negatively correlated). That result would be one major advantage of indexing the retirement age to mortality--the reduction in benefits would be correlated with increases in life expectancy and corresponding increases in workers' earning capacity.
 

HOW ASSUMPTIONS ABOUT INPUTS DETERMINE SOCIAL SECURITY'S PROJECTED FINANCES

Projecting Social Security's finances decades into the future requires two things: a model that shows how key economic and demographic variables interact with policy rules to determine financial flows, and assumptions about the annual values for those variables. The structure of the model determines how changes in assumptions affect the system's finances and thus how uncertainty about those assumptions results in uncertainty about the financial status of Social Security.

The Overall Structure of CBO's Model

CBO's Long-Term Actuarial Model (LTAM) relies on assumptions about nine primary inputs. Eight of them--rates of fertility, mortality, immigration, unemployment, incidence and termination of claims for Disability Insurance (DI), real wage growth, and inflation--affect intermediate demographic and economic variables that determine the accumulation of money in the Social Security trust funds (see Figure 1). The ninth primary input--the interest rate on Social Security assets--affects the trust funds directly. The final output of the model is the annual change in the trust fund balance, based on a simple accounting formula:
 

Trust fund balance this year =

trust fund balance last year + interest earned on trust fund assets + Social Security payroll taxes and other revenues - benefits paid and other outlays

The higher the interest rate, the faster the trust funds grow (assuming a positive balance).
 

FIGURE 1. HOW INPUTS AFFECT THE BALANCE OF THE SOCIAL SECURITY TRUST FUNDS IN CBO'S LONG-TERM ACTUARIAL MODEL

SOURCE: Congressional Budget Office.

Social Security revenues and outlays equal numbers of people (workers or beneficiaries) multiplied by dollar amounts (average Social Security taxes paid or average benefits). Numbers of people, in turn, are based on population totals, and dollar amounts are based on earnings. Those relationships are explained below.

Projecting Population by Age, Sex, and Marital Status

The equation for projecting total U.S. population is:
 

Current-year population =

population last year + current-year births - current-year deaths + current-year immigration

The details of the calculations are complex. LTAM begins with a huge matrix that includes counts of people by age, sex, and marital status. Once the modeler has selected future annual values for the mortality and fertility rates and the level of immigration, the model applies the mortality rate to the current population to compute the number of deaths by age and sex; it also applies the fertility rate to the female population to determine the number of births by age of the mother. Those figures, along with the assumed net number of immigrants, are added to last year's population to obtain the new population figure (with a new age and sex distribution). After that, the model distributes the new population among four marital-status groups--single, married, divorced, and widowed--according to age and sex. That process is repeated for each year's projection.

Number of Workers. The model applies three factors to the total working-age population (in this analysis, people ages 15 to 74) to obtain a projection of the total number of workers covered by Social Security:

1) Total working-age population x labor force participation rate = labor force

2) Labor force x employment rate = workers

3) Workers x covered-worker rate = covered workers

Labor Force Participation Rate. Over the past 50 years, the labor force participation rate--the fraction of the working-age population that is employed or looking for employment--has changed significantly.⁽⁶⁾ The proportion of women in the labor force has increased steadily and substantially, though the participation rate for women age 65 or older has stayed the same. The rate for older men is substantially lower now than in 1950, but it has remained level since about 1985.

Although those facts inform projections, many questions remain. For instance, how much further will the labor force participation rate for women increase? Will the long-term trend toward earlier retirement for men continue, or will the rate observed over the past 15 years endure? For the most part, SSA's projections assume that participation rates for various demographic groups will remain at current levels. The 1999 Technical Panel of the Social Security Advisory Board suggested that SSA assume additional increases in women's participation in the workforce and investigate further the effect that changes in pension systems (including Social Security) will have on retirement patterns.⁽⁷⁾ Participation in the labor force is an important source of uncertainty. Still, it is not included as one of the nine input variables in CBO's model, and LTAM does not, at this stage of its development, permit variations of that factor. (Including labor force participation in the quantitative analysis in this paper would be ideal, but it is not possible at this time.)

Currently, LTAM follows SSA's methodology of estimating separate labor force participation rates for 103 age/sex/marital-status groups. Those rates depend on economic factors such as past rates of participation in Social Security, benefit levels, and unemployment rates as well as on social factors such as disability rates, military enrollment, and number of children.

Employment Rate. The employment rate is equal to 1 minus the unemployment rate. The unemployment rate is one of the nine major input variables in CBO's model and is described in more detail in Chapter II.

Covered-Worker Rate. The covered-worker rate is the percentage of employees who work in employment covered by Social Security. Although that rate will increase slightly as older government workers--who are less likely to be covered--retire, it is projected to remain relatively stable over the next 75 years.

Number of Beneficiaries. The Social Security program has about two dozen categories of beneficiaries, including retired workers, disabled workers, widows and widowers, and children. Some of the larger categories are broken down by age and sex, but the major division is between retired workers, their dependents, and the survivors of deceased workers (who receive Old-Age and Survivors Insurance, or OASI, benefits) and disabled workers and their dependents (who receive DI benefits).

The number of OASI beneficiaries is a relatively stable percentage of each age and sex group. As a result, projecting growth in the number of those beneficiaries is fairly easy for a given age- and sex-specific population. Although changes in labor force participation, earnings patterns, and retirement rates affect the number of OASI beneficiaries, the percentage of the elderly in the population has a much greater impact on Social Security's finances.

The number of DI beneficiaries is much less certain. SSA projects disability rates by age and sex. Because those rates increase substantially with age, the gross (overall) disability rate will rise in the future even without changes in age- and sex-specific disability rates. However, the overall rate depends mainly on the projected rates of disability incidence and termination (described in Chapter II).

Projecting Per Capita Revenue and Benefit Levels

Levels of Social Security revenues and benefits per person depend primarily on the growth of wages. That growth in turn can be separated into two sources: real wage growth (which is effectively determined by productivity growth) and inflation.

Average Revenue Levels. By definition, the amount of Social Security payroll taxes paid per capita can be determined by multiplying the average effective taxable payroll by the statutory tax rate. Under current law, the tax rate is constant; thus, the only uncertainty about average revenue levels comes from the taxable payroll.

CBO's model begins with average taxable earnings in the past year, then increases that number by projected nominal wage growth--the sum of inflation and real wage growth (the first two exogenously projected economic variables).

Growth in the average payroll tax paid by a worker tracks average wage growth very closely, but not exactly. Workers pay Social Security taxes only on amounts below the statutory maximum set for taxable earnings--$80,400 in 2001. That maximum is indexed to overall wage growth. If the wage distribution changes, the share of earnings below that level also changes. Currently, about 84 percent of covered wages are taxable; that figure is expected to decline, however, by about 0.1 percent per year in the near term. LTAM does not permit users to vary that assumption. Still, any uncertainty about the effect of distributional changes on the growth of taxable payroll is probably small compared with uncertainty about overall wage growth.

Average Benefits. An average benefit level must be projected for each of Social Security's many beneficiary categories. To analyze the effect of changing the complex benefit formula, CBO, like SSA, employs a microsimulation that projects average benefits for newly retired and newly disabled workers. (Microsimulation involves producing exact calculations of benefits for a simulated sample of the population and aggregating the results from the sample. That type of simulation is necessary because the effects of policy changes on different workers vary widely depending on factors such as those workers' wage levels and years of employment.) LTAM takes a sample of thousands of newly entitled beneficiaries from SSA's Continuous Work History Sample, which includes each worker's entire wage history. Using those wage histories, the model calculates a benefit for each worker and then computes averages for newly retired and newly disabled workers.

Because beneficiaries who retire in 2010 or 2050 will have different earnings patterns from today's retirees, the model adjusts the data to account for changing labor force participation patterns. Other changes that might occur between now and then are not simulated.⁽⁸⁾ The input variables in LTAM that affect benefit levels are wage growth, unemployment, inflation, and, to a lesser extent, disability rates.
 

WHAT TYPES OF UNCERTAINTY ARE NOT BEING CAPTURED?

This paper quantifies the uncertainty in actuarial projections that results from uncertainty in the nine major input assumptions. However, other sources of uncertainty not included in this analysis will also affect Social Security's finances. Thus, the measures of uncertainty described in Chapter V should be considered lower bounds.

Every model is, by necessity, a simplification of events that are likely to occur in the real world. That simplification is particularly true of macroeconomic models, which employ a few variables to represent an entire national economy. Models for Social Security are simpler because explicit rules can be employed to model a specific person's experience. Still, LTAM is only an actuarial model, which generally substitutes averages for actual person-by-person calculations. (CBO is working on a comprehensive microsimulation model that will generate individual-level calculations for benefits and other information.) For the model to function, assumptions about the actuarial processes must be made.

For some factors, CBO assumes that current ratios will remain constant. For example, like SSA, it assumes that the current relationship between average auxiliary benefits (those based on another person's work history) and average worker benefits (those based on one's own work history) will stay the same. (Each type of auxiliary benefit is tracked separately.) That assumption is only an approximation. To the extent that the relationship changes over the next 75 years--and it will--LTAM's projections will be in error. However, CBO expects that error to be small, for two reasons. First, auxiliary benefits represent a minority (about one-quarter) of total Social Security benefits. Second, the ratios used to project auxiliary benefits are bounded between zero and one and are unlikely to be near those bounds. Thus, the magnitude of possible errors is limited.

Other required factors that are held constant in CBO's model include the labor force participation rate, the fraction of workers eligible for benefits, and the rate of retirement. In addition, because Social Security's benefit formulas are progressive (an extra dollar of earnings increases a low-income person's benefit more than it would increase a high-income person's benefit), shifts in the distribution of income would change average benefit levels and, to a lesser extent, the effective payroll tax base. LTAM assumes, however, that the distribution of wages and benefits will stay relatively constant. That assumption should be suitable for CBO's purposes because any variation is likely to be small, and the Social Security system should not be particularly sensitive to the variation that will arise.

1. Social Security Administration, The 2000 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (March 30, 2000).

2. See, for example, Ronald Lee and Shripad Tuljapurkar, "Stochastic Forecasts for Social Security," in David Wise, ed., Frontiers in the Economics of Aging (Chicago: University of Chicago Press, 1998), pp. 393-420; and Craig Copeland, Jack VanDerhei, and Dallas L. Salisbury, Social Security Reform: Evaluating Current Proposals, Issue Brief No. 210 (Washington, D.C.: Employee Benefit Research Institute, June 1999). In a stochastic model, every input variable is assigned a range of possible values; the model is run many times (each time drawing values for the inputs from their respective ranges) and yields a set of results with varying probabilities. In a deterministic model, such as the one used by SSA, each input is assigned a single value for each year, and the model produces a single result.

3. Social Security Administration, The 2000 Annual Report of the Board of Trustees, Section II.F.

4. The Social Security system remains somewhat sensitive to changes in wage growth and inflation because of timing lags between when those changes occur and when they are reflected in recipients' benefits.

5. See Amy Rehder Harris, Noah Meyerson, and Joel Smith, "Social Insecurity? The Effects of Equity Investments on Social Security Finances," National Tax Journal (September 2001).

6. Howard Fullerton Jr., "Labor Force Participation: 75 Years of Change, 1950-98 and 1998-2025," Monthly Labor Review (December 1999).

7. 1999 Technical Panel on Assumptions and Methods, Report to the Social Security Advisory Board (November 1999).

8. LTAM uses data on the cohort that claimed benefits in 1997. Those data are adjusted for changes in 1998 through 2075.

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