Working Paper Series

Congressional Budget Office

Washington, D.C.

UNCERTAIN POLICY

FOR AN UNCERTAIN WORLD:

THE CASE OF SOCIAL SECURITY

John Sabelhaus(e-mail: john.sabelhaus@cbo.gov)

Julie Topoleski (e-mail: julie.topoleski@cbo.gov)

Congressional Budget Office

Washington, D.C.

March 2006

2006-05

Working papers in this series are preliminary and are circulated to stimulate discussion

and critical comment. These papers are not subject to CBO’s formal review and editing

processes. The analysis and conclusions expressed in them are those of the authors and

should not be interpreted as those of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series can be obtained at

www.cbo.gov/tech.cfm. 
Abstract

Analysis and discussion of Social Security policy are usually based on expected fiscal and

societal outcomes. However, future demographic and economic trends are uncertain, and thus

ultimate outcomes for aggregate system financial flows and the distribution of taxes and benefits

across generations are uncertain. This paper analyzes a state-dependent approach to policy in

which future Social Security benefit formulas are tied to realized economic and demographic

outcomes over time. The results, based on a microsimulation model with stochastic capabilities,

show the extent to which it is possible to systematically address uncertainty about system

finances and distributional outcomes. 
1

An earlier version of this paper was presented at the Association of Public Policy Analysis and

Management Annual Conference in Washington, D.C. (November 2005). The authors would like to thank Julian

Cristia, Amy Rehder Harris, Noah Meyerson, Michael Simpson, and Reuben Snipper for useful comments and

suggestions.

2

See Social Security Administration Board of Trustees (2005) and Congressional Budget Office (2004). 

3

This argument is consistent with the more general analysis of policymaking under uncertainty discussed by

Popper, Lempert, and Bankes (2005), and the specific example of state budgeting under revenue uncertainty

analyzed by Cornia, Nelson, and Wilko (2004). 

1

1. Introduction1

Although it is widely acknowledged that the U.S. Social Security system is likely to

become insolvent within a few decades, the eventual realized imbalance between inflows and

outflows will ultimately depend on demographic and economic factors whose values are not yet

known.2

 When confronting this type of uncertainty, one approach to policy is to establish rules

for modifying benefit formulas when demographic and economic outcomes are realized, rather

than to try to choose fixed-benefit formulas that are expected to hold for the indefinite future.3

An example, and one of the policy options explored in this paper, is to systematically lower

benefit levels (at a given retirement age) as longevity increases over time. The goal of this paper

is to quantify the effects of tying benefit changes to realized economic and demographic trends,

where the outcomes of interest are the time path of Social Security system finances and the

distribution of taxes and benefits across birth cohorts. 

Consider the effect of a schedule of benefit cuts chosen to achieve expected solvency for

the indefinite future: The expected cost of achieving system solvency would be distributed

across generations depending on the timing of the benefit cuts, and normative judgments would

play a role in deciding how that cost should be allocated. However, system solvency and

distributional outcomes are uncertain. Indeed, if the models and assumptions are correct, there is
4

This abstracts from any interaction between on-budget and off-budget deficits. For example, Smetters

(2004) argues that it cannot be assumed that trust fund surpluses will be saved for future benefit payments, and so

pre-funding the Social Security trust funds does not necessarily reduce the level of debt held by the public.

2

a 50 percent chance that the benefit cuts chosen to achieve solvency would be too large; there is

also a 50 percent chance benefits would be cut too little, which would result in shortfalls. Those

cuts would be larger than needed in good budgetary states of the world, because those good

states of the world would be reflected in a Social Security surplus greater than expected. 

Although this inherent uncertainty cannot be eliminated, it can be quantified, and can be

considered when balancing policy objectives. 

The two sets of policy objectives analyzed here are aggregate system finances and

distributional outcomes across generations. Many would agree that the Social Security system

should be put on a sustainably solvent trajectory, one in which benefits will continue to be paid

without interruption from financing shortfalls. There are many Social Security policy options

that meet the sustainable solvency criteria, but they have very different distributional effects. 

For example, one could impose significant immediate benefit cuts and build up a Social Security

trust fund that is so large the interest on the fund would allow (the now lower) benefits to be paid

indefinitely.4

 At the other extreme, one could schedule future benefit cuts to occur only as

needed to keep benefits payable on a flow basis. Thus, the trust fund would fall to zero, there

would be no interest earnings, and future benefits paid would be limited by taxes collected. This

is functionally equivalent to the current-law policy of allowing trust fund depletion to trigger the

timing of benefit cuts, but, in principle, one could legislate exactly that pattern of cuts, and thus

it serves as a useful benchmark. 

These extreme approaches to putting the system on a solvent trajectory have very
5

The illustrative expected-solvency scenario involves an across-the-board 19 percent cut in new benefit

awards starting in 2012. The year of the benefit cut (which is the same for the two policy experiments) is chosen so

that no one older than age 55 in 2005 would be affected, which reflects recent reform proposals that have been put

forth. The other key assumption of the scenario is that the benefit cut is not reversible; that eliminates situations

3

different distributional implications across birth cohorts because of the timing of benefit

changes. There is of course a middle ground, which is to initiate benefit cuts before the trust fund

is exhausted, but not to cut benefits for near-term retirees so much that they pay a

disproportionate share of the costs. The key insight of this paper is that the middle ground

approach can be taken one step further: Tying the extent and timing of benefit changes to

realized demographic and economic outcomes may be a way to address the competing objectives

of distributional fairness and maintenance of a specific funding strategy. 

Two state-dependent policies are analyzed in which future benefits depend on realized

longevity and productivity trends over time. The first policy change ties future benefit cuts to

longevity increases. As life spans increase for future cohorts, benefits (at any given benefitclaiming age) would be systematically reduced so that lifetime benefits would not increase

relative to lifetime taxes paid. The second policy change modifies growth factors applied to

benefits after benefit claiming begins. Rather than just growing benefits with inflation as in the

current system, benefits would also be tied to productivity, rising faster than inflation when

productivity is above its expected value, and vice versa. Both the longevity-adjusted benefits

and productivity-adjusted cost of living policies shift uncertainty from future taxpayers onto

future beneficiaries. 

This paper quantifies the effects of these two state-dependent policies on system finances

and distributional outcomes. The two policies are compared to a base scenario in which benefits

are cut only once by the amount needed to achieve expected sustainable solvency.5

 The state-
where near-term retirees are forced to accept benefit cuts deeper than those faced by future retirees, which would

also probably violate conditions for political consensus regarding reform. 

4

dependent policies also achieve expected solvency, but the initial benefit cut required is smaller

than in the base case because of subsequent longevity indexing. Because the initial benefit cut is

smaller, and because further cuts are tied to (stochastic) realized economic and demographic

outcomes, the state-dependent policies effectively shift a significant fraction of the upside

potential for future trust funds into upside potential for beneficiaries. Benefit cuts are not

invoked in states of the world when they are not needed, for example, when mortality

improvement is low and productivity growth is high. Further, although there is still a significant

downside risk for trust fund balances, which would lead to benefit cuts for future beneficiaries in

certain states of the world, that downside is moderated when compared with current law

projections in which the trust fund is almost certain to be exhausted. 

Further exploration of the state-dependent policies provides more insights about how one

might incorporate uncertainty into Social Security analysis and policymaking. If variation in

fertility is ignored (that is, the overall fertility rate is always set to the expected value) then all of

the downside risk for future benefits is eliminated relative to the base scenario of expected

solvency after a one-time benefit cut. This is intuitive; the biggest long-run risk facing future

beneficiaries in a partial pay-as-you-go system is that there might not be enough taxpayers to

support them. This is the type of situation that might lead to a more fundamental change in the

structure or scope of Social Security, meaning either higher payroll taxes to maintain the same

benefits, or a reduction in benefits with tax rates held constant. 

The other insights from the stochastic analysis concern which policies would be

consistent with avoiding either explosion or implosion of the Social Security trust fund. Even
5

with longevity indexing and productivity-adjusted COLAs, trust fund balances are very large in

good budgetary states of the world, meaning that benefits have been cut too much at some point

in time. That suggests empirically answering the following question: Assuming that the two

state-dependent policies analyzed here are put into place, what is the most that benefits can be

initially cut to avoid significant chance of an exploding trust fund? The answer is about 5

percent, which is less than half of the 11 percent cut needed to achieve expected solvency. The

fact that trust funds still implode in bad states of the world, however, leads naturally to a second

question: Given that the two state-dependent policies are put into place, what is the least that

benefits can initially be cut to avoid significant chance of an imploding trust fund? That answer

is about 20 percent. 

In discussion of these state-dependent benefit policies, the range between the 5 percent

initial benefit cut that avoids trust fund explosion and the 20 percent initial cut that avoids trust

fund implosion is useful to keep in mind when contemplating cohorts that might support various

proposed Social Security reforms. It is highly unlikely that near-term retirees would agree to the

20 percent cut that virtually guarantees system solvency for future generations, but the criterion

of balanced distributional outcomes across birth cohorts suggests that such a large cut would

probably be inappropriate in any case. The modest 5 percent initial cut for near-term retirees

seems both more acceptable and more distributionally neutral than current law. 
6

The goal of sustainable solvency could in principle be achieved using either benefit cuts or tax increases;

Lee and Yamagata focused on payroll tax increases, but this paper restricts analysis to the benefit side. Benefit

changes are the only policy lever considered here, in order to keep the scope more manageable for addressing the

second policy issue, which is the distribution of the costs of achieving any given aggregate funding target. The

distributional results presented here show how available resources under current law (taxes paid and interest on the

trust fund) will be allocated across generations that are already alive, with the sustainable solvency condition that the

trust fund not be deteriorating at the end of the simulation. The analysis here does not consider the possibility of

imposing taxes on future generations whose lifetime tax and benefit outcomes are not being fully measured, mainly

because that would be the distributional equivalent of a free lunch. This also differentiates the approach in this paper

from the traditional risk-sharing analysis of Social Security as originally described by Gordon and Varian (1988) and

more recently analyzed by Bohn (2001). That literature generally abstracts from trust fund financing, and thus taxes

paid at any point in time equal benefits received.

6

2. The Relationship between Distributional Outcomes and Sustainable Solvency

The analysis of Social Security policy in this paper involves two related criteria: the

implications for annual system financial flows and the ultimate distribution of taxes and benefits

across birth cohorts. Comparing the distributional implications of any two policies on a level

playing field requires holding the conditions for aggregate system financing fixed and requires

working with time-invariant measures for distributional outcomes. In the analysis below, the

condition for aggregate system financing is based on Lee and Yamagata’s (2003) Flat Fund

Ratio sustainable solvency criterion.6

 The distributional outcomes presented here are based on

the ratio of lifetime benefits received to lifetime taxes paid. 

Sustainable Solvency in Social Security

Sustainable solvency means that the Social Security trust fund ratio (trust fund balance

divided by benefits paid) does not rise or fall in the long run. Given steady growth in real wages,

a system in which benefits rise over time in step with real wages, and a steady-state ratio of

beneficiaries to taxpayers, there is a wide range of policies that would all lead to sustainable

solvency. Fundamentally, the larger is the trust fund in any given year, the less payroll tax

revenue is required to pay any given level of current-year benefits and maintain a constant trust
7

fund ratio. Indeed, if the trust fund balance is sufficiently large, the interest alone could be

enough to pay benefits and grow the fund. 

Social Security faces two distinct types of aggregate financing problems. The first is

associated with the aging of the baby-boom generation, which will cause a fundamental shift in

the relationship between revenues and outlays lasting for the next several decades. The second

source of financing problems is more long-run and systematic. If, as expected, mortality rates

continue to fall and the fertility rate stays at recent levels, the ratio of beneficiaries to taxpayers

will continue to rise even after the baby-boom generation has died off. 

The steady-state situation described above is fairly close to what the U.S. is expected to

face after the baby-boom generation has died off, and the only trend divergence between longrun system outlays and revenues is associated with increased longevity. That is, the underlying

projections for fertility, real wage growth, and other factors are such that the system should be on

a steady-state growth path if benefits are simply adjusted for longevity. Abstracting from

longevity increases and holding payroll tax rates fixed, the fraction of scheduled benefits that are

payable in the long run will be fixed and will depend only on how much is left in the Social

Security trust fund after the baby boomers have stopped collecting benefits. 

The balance remaining in the Social Security trust fund after the baby-boom generation

dies off is an important connection between system financial and distributional outcomes. The

analysis in this paper captures the effect of trust fund balances over time, because any shortfall in

the trust fund automatically results in benefit cuts that show up in the distributional analysis
7

Although (for convenience) the actual simulations assume all benefits are cut across the board when the

trust fund runs out of money, one could interpret the results as a sequence of cuts in new benefit awards made

several years in advance.

8

The values presented are actually centered five-year averages around single-year birth cohorts. The microsimulation model used to compute the distributional outcomes (see the Appendix for details) is also capable of

computing money’s worth measures within cohort (for example, across lifetime income groups). The policy changes

considered in this paper are restricted to proportional within-cohort benefit changes, in order to isolate the

relationship between aggregate system financing and distribution over time, so all of the within-cohort distributional

outcomes will change proportionally. For a more general analysis of within-cohort distributional outcomes, see, for

example, Gustman and Steinmeier (2001) or Harris and Sabelhaus (2005). 

8

across birth cohorts.7 If the trust fund is allowed to fall to zero, as expected in the middle of te

21st century, benefits payable are assumed to be limited to payroll taxes collected thereafter.

Measuring Distributional Outcomes

The distributional effects of Social Security tax and benefit policy can be characterized

and measured in several ways. The various distributional outcomes are sometimes referred to as

“money’s worth” measures (Geanakoplos, Mitchell, and Zeldes, 1999). The distributional

outcomes shown in this paper are ratios of lifetime benefits to lifetime taxes, where both

numerator and denominator are measured on a present-value basis. The money’s worth

outcomes are calculated for annual birth cohorts from 1950 through 2000.8

There are two basic strategies for measuring money’s worth. The first is to compute the

internal rate of return on Social Security contributions, which is the value for the discount rate

that equates the present values of taxes and benefits. That is the value of r for which:

taxes r benefits r t

t

t

t

t

t

=

−

=

−

∑ ∑ += +

0

100

100

0

100

100 () () 1 1

where taxest and benefitst are taxes paid and benefits received at time t, respectively, and 100 is 

the maximum life span for the calculations. One significant problem with using the internal rate
9

of return is that readers sometimes (mistakenly) compare the outcomes to market rates of return,

and make inappropriate normative judgments about the rate of return to Social Security

(Geanakoplos, et al.).

The second approach to measuring money’s worth is closely related but involves fixing

the value for the real discount rate and taking the ratio of the present value of benefits to the

present value of taxes. That is: 

pvratio

benefits r

taxes r

t

t

t

t

t

t

=

+

+

=

−

=

−

∑

∑

0

100

100

0

100

100

1

1

( )

( )

Given that this equation has the same basic structure as the equation for calculating the internal

rate of return, one would suspect the same basic critique about normative judgments is

applicable. Taking the value for the real discount rate as given, 

 readers may be tempted to view a ratio above 1 as good

and a ratio below 1as bad. In fact, present-value benefit to tax ratios should be compared only to

other ratios that use the same real discount rate (Harris and Sabelhaus, 2005).

The interpretation of and qualifications about present-value ratios are best clarified by

going to the actual data. Figure 1 shows present-value benefit-to-tax ratios for single-year birth

cohorts from 1950 through 2000. The present value ratio for the 1950 cohort is estimated at 72

percent using a real discount rate of 3.3 percent. That is, the present value of all lifetime benefits
9

The calculations include all worker and auxiliary benefits paid under the Old-Age and Survivors Insurance

and Disability Insurance programs, excluding only children’s and young spouse beneficiaries. To underscore the

sensitivity of the estimates to assumptions about real rate of return, Harris and Sabelhaus (2005) observe that setting

the discount rate equal to 2.2 percent generates estimated ratios of around 100 percent. That sensitivity makes sense,

given the differences in timing of taxes and benefits over the life cycle. The same analysis also shows, however, that

the relative estimates of distributional outcomes across groups are not much affected by the discount rate. The value

of 3.3 for the discount rate is used here (and in various Congressional Budget Office publications) in order to

maintain consistency with the assumed rate of return on government bonds. 

10

received (and projected to be received) by the 1950 cohort is about 72 percent of the present

value of all lifetime taxes paid (and projected to be paid).9

There are two sets of projections for present-value ratios across birth cohorts in Figure 1,

computed using two extreme assumptions about Social Security system financing. The higher of

the two, Scheduled Benefits, shows what would be expected of the money’s worth measure

across cohorts if all promised benefits were somehow (unrealistically) paid with just scheduled

tax receipts. The general upward trend (the present-value ratio for the 2000 cohort is about 10

percent higher than the ratio for the 1950 cohort) reflects the fact that future beneficiaries are

expected to live longer and thus receive higher lifetime benefits.

In the alternative Current Law scenario, across-the-board benefit cuts are implemented 

when the Social Security trust fund is exhausted. Figure 2 shows that in the projections

underlying these money’s worth calculations, the Social Security trust fund is exhausted around

the middle of the 21st century, so every cohort for which there are any surviving beneficiaries

after that time will be affected. Of course, the longer a cohort receives benefits post-trust fund

exhaustion, the bigger the lifetime benefit cuts. The projected present-value ratio for the 2000

cohort, expected to receive virtually all of their benefits after trust fund exhaustion, is more than

20 percent lower than the present-value ratio for the 1950 cohort. 
10See the Appendix and references therein for a complete description of the model used here.

11For a detailed discussion of the stochastic model and underlying time series processes, see Congressional

Budget Office (November 2005).

11

3. Uncertainty about System Finances and Distributional Outcomes

Analysis of Social Security policy along the two dimensions described above, aggregate

system finances and distributional outcomes, requires an integrated modeling framework that

generates both macroeconomic and microeconomic results.10 Given the modeling framework,

projections can be deterministic or stochastic. Stochastic simulation explicitly accounts for the

uncertainty underlying the projections by combining many simulations, each based on random

draws for every input assumption in each year of the projection. Any one simulation of this type

has very limited usefulness, it can be thought of only as one possible realization. However, the

collection of multiple simulation results represents a probability distribution for the system

financial and distributional outcomes of interest. That makes it possible to investigate statedependent policy rules such as those being considered here. 

The model used for this paper has 11 stochastic inputs: fertility rate, rate of mortality

improvement, rate of immigration, disability incidence, disability termination, total factor

productivity growth, earnings share of compensation, unemployment rate, inflation rate, gap

between the real interest rate and the marginal product of capital, and gap between the core GDP

deflator and inflation.11 For each input, the underlying equations reflect historical variability and

covariances, and these equations, together with random draws for the equation error terms, are

used to generate annual values.

 The benefit of moving to stochastic simulation is shown in Figure 3, which presents the

uncertainty bands around the expected ratios of lifetime benefits to lifetime taxes for the 1950
12

through 2000 birth cohorts under the same two scenarios (Scheduled Benefits and Current Law)

presented in Figure 1. The upper and lower bands represent the 10th and 90th percentiles of the

estimated probability distribution for the present value ratios. That is, there is a 10 percent

chance that the ratio of lifetime benefit to lifetime taxes will be below the lower band and a 10

percent chance that the ratio will be above the upper band. 

The basic shapes of the ranges for present value ratios are consistent with the

deterministic projections shown in Figure 1, but Figure 3 shows how two different sources of

uncertainty affect the ultimate outcomes. The range for Scheduled Benefits (the cross-hatched

band) reflects the fact that uncertainty in demographic and economic assumptions makes the

ratio of lifetime benefits to taxes uncertain, and that ratio’s uncertainty increases the further

ahead one looks. The range for near-term retirees is narrower than for distant retirees because

lifetime taxes paid are already largely known. Benefits are also very predictable for near-term

retirees because they are based on mostly known earnings histories. There is still uncertainty

about mortality rates, inflation, and other variables, but the range for lifetime benefits to taxes is

much narrower than for retirees in the distant future, who face an entire lifetime of uncertainty.

The range for Current Law (the dark shaded band) includes all of the uncertainty

associated with Scheduled Benefits, but adds uncertainty about trust fund exhaustion. Recall

that when the trust fund is exhausted, scheduled benefits can no longer be paid, and all

beneficiaries experience a benefit cut such that benefits paid are equal to payroll tax revenues in

that year. The fact that the 90th percentile for Current Law benefits is below the 90th percentile

for Scheduled Benefits indicates that the probability of trust fund exhaustion is above 90 percent

at some point during that cohort’s life span. The 10th percentile for Current Law benefits lies
13

well below the 10th percentile for Scheduled Benefits. The trust fund is very likely to become

exhausted and thus force benefit cuts, and there is a potential for those cuts to be quite large. 

The stochastic relationship between system financial and distributional outcomes is

driven home by considering the projected range for trust fund ratios, shown in Figure 4. The

projections clearly show not onlythat the Social Security system is on an expected path to

insolvency, but also that the probability that it maintains solvency over the next 100 years is

negligible. At the 10th percentile, the trust fund is exhausted by 2035, suggesting that there is a

10 percent chance of depletion occurring before 2035. Even at the 90th percentile, the trust fund

is exhausted by 2088 under Current Law, indicating that 90 percent of the time scheduled

benefits are no longer payable by 2088. It is this near-certainty about trust fund exhaustion that

drives such a large wedge between the ranges for distributional outcomes shown in Figure 3. 
14

4. Achieving Sustainable Solvency with a One-Time Benefit Cut

There are many approaches policymakers could take to resolve the expected long-run

financing shortfall in Social Security. This section considers a one-time permanent benefit cut

that is expected to lead to the Flat Fund Ratio sustainable solvency described earlier. The

strategy is to impose a fixed percentage reduction (relative to scheduled benefits) for everyone

55 and younger as of 2005. The benefit cut used in the simulation, 19 percent, was chosen to

meet the sustainable solvency criterion as closely as possible with a single cut in a single year. 

Figure 5 shows that the expected sustainable solvency outcome is achieved by using the

19 percent cut. The dramatic decrease in benefits leads to faster trust fund accumulation starting

in 2012, when the first reductions are implemented. The eventual leveling out of the trust fund

ratio, which occurs after the baby boom generation is expected to have died off, is at a level

nearly twice as high as the peak (around 2020) under current law. Thus, the simulation can be

interpreted as follows: If all retirees claiming benefits after 2012 accept a large cut relative to

current law, that enables the trust fund to stay solvent and reach an equilibrium level where

payroll taxes plus interest earned by the fund are sufficient to pay benefits and maintain a stable

trust fund ratio. 

The effect of this policy on money’s worth ratios across cohorts (shown in Figure 6) is

predictable, causing significant redistribution from near- and medium-term retirees to future

retirees. There are two reinforcing reasons. First, money’s worth ratios in the 19 percent Benefit

Cut scenario show the same pattern (though at a lower level) as seen in the Scheduled Benefit

scenario in Figure 1. That is, relative to near-term retirees, money’s worth ratios rise in the

future because of increased longevity. Second, because the trust fund is not being exhausted
15

benefits do not need to be reduced as under current law. Therefore, relative to current law,

generations born after the early 1980s would find the 19 percent benefit cut to be preferable, but

those born before would be worse off.

The effect of a large one-time benefit cut can also be evaluated using the stochastic

analysis. Figure 7 shows the uncertainty bands for money’s worth ratios under current law

(reproduced from Figure 3) and the 19 percent cut. The inter-generational redistribution

apparent in Figure 6 shows up in Figure 7 through a general downward shift in the uncertainty

bands for near and medium-term retirees. One insight about how stochastic analysis contributes

to understanding of the political aspect of the problem comes from comparing the points where

various lines cross in Figures 6 and 7. In a deterministic world (Figure 6), groups born before

the early 1980s are better off sticking with current law (money’s worth ratios are higher). In a

stochastic world, if people are more concerned about worst-case scenarios (say at the 10th

percentile), then the break-even point shifts back to about the 1970 birth cohort. 

In addition to the expected shift in resources across generations, the range of money’s

worth ratios for the 19 percent cut is much narrower in the long run, which is consistent with the

stochastic projections for Social Security trust fund ratios shown in Figure 8. The upside

potential for money’s worth is mitigated because everyone faces the 19 percent benefit cut in all

states of the world. This is worse than the best possible outcome under Current Law, because

achieving expected solvency means that sometimes benefits will have been cut too much, as

reflected in an exploding trust fund ratio at the 90th percentile (Figure 8). The downside potential

for money’s worth is mitigated because the risk of trust fund exhaustion is greatly reduced.
12It is worth noting that other distributional objectives would not necessarily be consistent with the strategy

of putting the system on “auto-pilot” using state-dependent policy rules. One example is the objective of making

sure that benefit levels for the lowest earning retirees are generally sufficient to alleviate elderly poverty. 

16

5. Stochastic Outcomes Using State-Dependent Policy Rules 

The 19 percent one-time Benefit Cut scenario analyzed in the previous section achieves

expected Social Security system solvency, but the distributional consequences are rather

extreme, especially for near-term retirees. It is not obvious what normative reasoning could

justify a policy that lowers expected money’s worth ratios more for near-term retirees than it

does for future retirees. One could argue the opposite that, because future retirees are expected

to enjoy higher real living standards, giving them a lower rate of return on their taxes paid might

be appropriate. In any case, the policy leaves a lot of money on the table in a stochastic sense. 

The exploding 90th percentile for the Social Security trust fund ratio in Figure 8 shows that there

is a good chance that benefits will have been cut more than needed to maintain a stable trust fund

ratio in the long run. 

The analysis in this paper suggests that introducing state-dependent policies could help

balance the goals of achieving certain distributional objectives and maintaining system

solvency.12 In particular, if future benefit cuts are tied to realized demographic and economic

outcomes, one could start with smaller initial benefit cuts for near-term retirees, tie benefits to

economic and demographic outcomes in a way that directly affects money’s worth calculations,

and recapture the upside potential for future retirees in good states of the world by deferring

benefit cuts when they are not needed. Although the underlying uncertainty about demographic

and economic outcomes cannot be changed, that uncertainty can be systematically incorporated

into policymaking. 
13The version of longevity indexing used here is the same as that proposed in The Bipartisan Retirement

Security Act of 2004 (H.R. 3821), better known as the Kolbe-Stenholm reform plan. 

14The analysis here abstracts from normative judgment about how benefits should change after claiming

begins. Feldstein (1990) considers arguments for whether benefits should be tied to inflation or grow with

productivity. Also, an interesting aspect of the Diamond and Orszag (2004) Social Security reform plan is the

17

Longevity Indexing and Productivity-Adjusted COLAs

There are two state-dependent policies analyzed here. The first ties future benefit cuts to

changes in longevity outcomes over time. That would shift a larger portion of the long-term

funding burden onto future retirees, easing the burden on near-term retirees, but in such a way as

to automatically flatten the money’s worth ratios across cohorts. In a deterministic simulation,

the sustainable solvency outcome is achieved using an 11 percent initial benefit cut in 2012 plus

longevity indexing.13 

The second state-dependent rule analyzed here ties post-retirement benefit adjustments

(also known as COLAs) to productivity and Consumer Price Index (CPI) inflation, rather than

just to CPI inflation as under current law. If productivity growth is strong, the Social Security

system becomes more solvent because payroll taxes rise immediately but benefits increase only

after a lag. Indeed, a large part of the upside potential for the trust fund ratio shown in Figure 8

is because of the upside potential for productivity growth. With productivity-adjusted COLAs,

benefits paid would be immediately higher when productivity growth is strong, which shifts

some of that upside potential for the trust fund to higher money’s worth for retirees. However, in

order to avoid expected benefit increases, the proposal simulated here involves starting with CPI

inflation, then adding the deviation in productivity from its average (1.2 percent per year) to

determine the overall COLA. In that sense, below-average productivity outcomes would lead to

a decline in benefits relative to the inflation-only COLA.14
“super-COLA” for disabled worker beneficiaries, which would grow benefits at a rate above CPI inflation in order to

avoid the lifetime (relative) deterioration that occurs under current law. 

18

Figure 9 compares money’s worth ratios under the one-time 19 percent benefit cut

(reproduced from Figure 5) to the results from the 11 percent cut along with the two statedependent policy rules. Again, both of these policy packages exhibit expected sustainable

solvency, so they are comparable. The comparison clearly shows a stochastic improvement in

the upside potential for money’s worth outcomes for both near-term and future retirees, because

the initial benefit cut is lower and future benefit changes are tied to longevity and productivity

outcomes. Indeed, the 90th percentile for money’s worth ratios is nearly flat across birth cohorts. 

As before, the pattern of money’s worth outcomes is tied directly to trust fund outcomes, as

shown in Figure 10. The upside potential for money’s worth ratios is higher under the statedependent policy rules because the top of the range for trust fund ratios is much lower.

Figure 9 also shows that there is some deterioration relative to the 19 percent cut at the

low end (10th percentile) for future retirees. That occurs because the probability of trust fund

exhaustion is somewhat higher under the state-dependent policies than it is under the 19 percent

benefit cut, as shown in Figure 10. Still, the difference in downside potential is fairly modest

relative to the overall range for money’s worth outcomes. Also, the 10th percentile of money’s

worth outcomes for future retirees is still well above the downside outcome under current law

(Figure 7). 
15This observation is based on the decomposition of overall uncertainty about trust fund outcomes into its

component sources, as shown in Congressional Budget Office (November 2005).

19

The Role of Uncertain Fertility

Although Figure 10 exhibits considerably less upside potential for the trust fund ratio

under the state-dependent policy rules plus the 11 percent cut than under the 19 percent cut,

other uncertain inputs still affect trust fund outcomes. The 90th percentile for the state-dependent

policy rules plus the 11 percent cut shows the same upward trend as the 90th percentile for the 19

percent cut (an exploding trust fund) although at a somewhat slower pace. Also, the downside

risk for system solvency is now somewhat worse, because starting with only an 11 percent initial

benefit cut increases the probability of exhaustion relative to the 19 percent cut. Adjusting

future benefits for longevity and productivity are not powerful enough to reverse that effect. 

Fertility rates rank among the most important of the other determinants of uncertainty

about trust fund balances.15 It is not immediately obvious how one could tie benefit changes to

fertility rates, but a simple experiment shows how important fertility variation is for future

system solvency and money’s worth outcomes. Figures 11 and 12 show two versions of

money’s worth ratios and trust fund outcomes under the 11 percent benefit cut plus statedependent policy option. The first set is reproduced from Figures 9 and 10, with all sources of

uncertainty considered. The second set of outcomes are for the same policy simulations, but

with the stochastic variation in fertility turned off.

The most noticeable effect of shutting down the variation in fertility rates is that the

downside risk for money’s worth outcomes for future retirees is greatly mitigated. Indeed, the

10th percentile for future retirees is now roughly equal to that for the 19 percent benefit cuts. A

major risk facing future retirees in a partially pay-as-you-go system is that there will not be
20

enough future taxpayers to fund their benefits. The upside potential for money’s worth ratios is

not affected by shutting down the fertility variation, because having more than enough taxpayers

to fund benefits does not lead to an increase in benefits. It leads instead to an increase in trust

fund balances. 

This powerful relationship between fertility, trust fund ratios, and money’s worth

outcomes suggests that there is a higher level of state-dependent policymaking that could come

into play in certain scenarios. In particular, Sheshinski and Weiss (1981) show that, in an

overlapping-generations model with uncertain life span, the optimal level of Social Security rises

if fertility rates fall. That suggests future retirees might decide, if they choose to have fewer

children than currently projected, to pay more in taxes while working in order to fund their own

benefits. The alternative to paying the higher taxes is to receive lower benefits. 

Avoiding Exploding and Imploding Trust Funds

Adopting state-dependent policy rules for determining Social Security benefit changes

over time is an important step toward balancing the objectives of stable system finances and

fairness in distributional outcomes. The two state-dependent rules considered here move only

part of the way towards a system that is robust with respect to demographic and economic

outcomes, and there are no other obvious trigger mechanisms that could be used to offset

variation in the other inputs. It is useful to explore the issue from another point of view,

however: to consider what range of initial benefit changes, when combined with the statedependent policies, is consistent with trust fund ratios that neither explode nor implode. 

Even with longevity indexing and productivity-adjusted COLAs, trust fund balances are

very large in good budgetary states of the world, meaning that benefits have been cut too much
21

at some point in time. The trust fund explodes in good states of the world because the benefit

cuts put in place into 2012 are (ex post) too deep if outcomes are favorable to system finances. 

So, the first question to ask is this: Assuming that (1) any benefit cuts put in place will never be

reversed and (2) benefits will be adjusted for longevity and the COLA will be adjusted for

productivity, what is the most that benefits could be reduced in 2012 without introducing the

possibility of exploding trust fund ratios? 

There is no direct way to solve for the maximum initial cut that rules out an exploding

trust fund. The only feasible approach is to choose a value, use the stochastic simulation

capability, and observe what happens to the 90th percentile of the trust fund ratios. The answer

generated by this search algorithm is 5 percent. If benefits are initially cut by 5 percent in 2012

and then are indexed to longevity and adjusted for productivity, the 90th percentile of the trust

fund ratio is basically stable after the middle of the century. Thus, it can be argued that an initial

cut of 5 percent, when combined with the state-dependent policy rules, would rarely lead to a

situation in which, in review, benefits had been cut too much for near-term retirees. 

The 5 percent cut that avoids trust fund explosion is less than half the 11 percent cut

needed to achieve expected solvency, and thus the probability of an imploding trust fund is

higher. That leads naturally to a second question: Given that the two state-dependent policies

are put into place, what is the least that benefits can be cut initially while still avoiding a high

probability of an imploding trust fund? That is, is there a policy such that the 10th percentile of

the trust fund ratio range flattens out and stays parallel with the 90th percentile into the indefinite

future? This answer, also solved for by searching over possible values for the initial cut, is an

initial benefit cut (in 2012) of about 20 percent. The wide range between the initial changes that
22

prevent trust fund explosion or implosion arises in part because of inherent uncertainty, but also

because of the underlying demographics expected to drive trust fund balances. Basically, only a

huge cut for near-term retirees could guarantee a solvent system for the indefinite future.

6. Conclusions

The Social Security system is expected to experience financing problems sometime in the

next few decades, but the exact timing and magnitude of those problems are uncertain. In such a

situation, systematically tying policy rules to realized economic and demographic trends could

help balance the objectives of maintaining system solvency and targeting distributional

outcomes. Although uncertainty about economic and demographic trends cannot be eliminated,

it can be addressed, as reflected in a general narrowing of the size and change in the shape of

uncertainty bands around trust fund ratios over time and money’s worth outcomes across

cohorts. 

One of the implications of this analysis has to do with the impetus for changing Social

Security. Near-term retirees may have little interest in participating in a reform discussion,

because the system is not expected to experience funding shortfalls for several decades. Future

retirees, on the other hand, may begin to realize that failure to implement any benefit changes for

near-term retirees means they will be bearing all the costs of shortfalls under current law because

their benefits will be reduced after the Social Security trust fund is exhausted. Their support for

the existing system could wane. 

If the system’s goals are sustainable solvency and reasonably stable money’s worth

ratios, then a conditional approach to policy, a combination of longevity indexing and
23

productivity-adjusted benefits, could alter the prospects for change. The analysis here shows

how a fairly modest initial benefit cut followed by further changes tied to economic and

demographic outcomes would lower the chance of future system insolvency while maintaining a

relative narrow range for distributional outcomes. 
24

Appendix: The CBOLT Micro-Simulation Model

The Congressional Budget Office Long-Term (CBOLT) policy analysis tool integrates

microsimulation with a long-run macroeconomic and federal budget simulation model. The

microsimulation component of CBOLT has two phases. The first phase involves generating

realistic demographic and economic outcomes for a large representative sample of the

population. The second phase involves applying Social Security program rules to determine

individual taxes and benefits. The taxes and benefits solved for in the microsimulation are

aggregated to solve for overall system financial outcomes, and are also used for comparative

analysis of outcomes across various demographic and socioeconomic groups. One feature of the

CBOLT macroeconomic framework also plays an important role in the analysis here: The model

can be solved repeatedly, using random draws for key economic and demographic assumptions,

which allows presentation of outcomes in terms of probability distributions, rather than just in

expected values. 

The starting point in any microsimulation model is the base data file. CBOLT uses the

Social Security Administration (SSA) Continuous Work History Sample (CWHS), which is a 1-

in-100 sample covering every Social Security number ever issued. For each observation in the

data file, the CWHS reports a comprehensive earnings and worker benefit history along with

basic demographics. The primary advantages of the CWHS are that the sample is very large

(indeed, CBOLT uses only one-tenth of the CWHS, so the model itself is a 1-in-1000 sample),

the data are from high-quality administrative records (as opposed to limited and sometimes

biased self-reported data), and the data set is updated annually (so CBOLT can be re-based every

year). The primary disadvantage of the CWHS is the lack of comprehensive demographics and
25

other information that is available from public surveys, but that shortcoming is resolved in the

microcalibration process discussed below. 

Given a micro database file, the next step in any microsimulation is to specify transition

equations, the processes by which demographic and economic outcomes for individuals in the

microsample evolve over time. CBOLT operates on the basic processes (birth, education, labor

supply, earnings, first marriage, divorce, remarriage, mate matching, benefit claiming, benefit

awards, and death) needed to calculate Social Security taxes and benefits and to integrate the

microeconomic outcomes with the macroeconomic growth model and unified budget framework. 

The micro transition processes are described in detail in a series of technical papers available on

the Congressional Budget Office web site. For a more detailed overview of the micro-modules,

see O’Harra, Sabelhaus, and Simpson (2004). 

In general, the CBOLT microtransitions equations are not designed to incorporate

dynamic optimizing behavior. Rather, the focus is on identifying and replicating real-world

microheterogeneity in the simulated sample. However, even this limited-behavior version of the

microsimulation-based approach leads to important insights about Social Security that do not

come through in other analyses. First, all else equal, the microsimulation generates projected

benefit awards for male OAI workers below those based on standard actuarial techniques,

because CBOLT properly captures observed shifts in the historical relative earnings profiles

(Congressional Budget Office, 2004). Second, direct analysis of the micro-level outcomes

suggests there are serious problems with using hypothetical-example workers to analyze the

impact of proposed reforms.
26

The microtransition processes developed for projecting future individual outcomes are

also used to assign information that is not available in the base (CWHS) data file. CBOLT uses

a historical-simulation approach to assign the demographic characteristics that are not present on

the micro-database file. Although this type of imputation-based assignment is used in all major

microsimulation projects, it is quite extensive in CBOLT and deserves special mention. The

basic idea is to assign missing characteristics in history by using the same methods used for

projecting forward, then to test and calibrate the processes by using external data sources

available in history.

The initial CBOLT microsample is actually drawn to be representative of the U.S. 

population for the period 1984 through 2003. Social Security coverage rates were much lower

for working-age cohorts before then; also, the availability of earnings data above the taxable

maximum did not occur until the 1980s. The historical simulation begins in 1984, when each

individual is assigned initial unobserved characteristics based on observed characteristics (a

standard imputation). Next, each micro-process is applied and then calibrated so that it generates

the actual observed distributions (say, population by marital status) that are known from some

external data sources. The model is also carefully tested for its ability to reproduce empirical

covariances (say, between husband and wife ages). Perhaps the most important test of the model

is that it matches Social Security system outcomes (numbers of beneficiaries and average

benefits by type of benefit award) in the historical period. 

Uncertainty is explicitly accounted for in CBOLT by using a stochastic

macrodemographic model that generates values for certain demographic and economic inputs. 

The stochastic modules in CBOLT are related to other models of this type, including Holmer
27

(1999), Lee and Tuljapurkar (1998), and Lee and Edwards (2002). The key demographic input

assumptions varied stochastically in the Monte Carlo simulations are fertility, mortality, net

immigration, and rates of disability incidence and termination. The key economic inputs varied

stochastically are total factor productivity growth, inflation, unemployment, the relationship

between interest rates and the return to capital, the share of compensation that shows up as

taxable earnings, and the gap between the core GDP deflator and growth in the consumer price

index for urban wage earners and clerical workers (CPI-W). These factors together determine

the individual and aggregate outcomes of interest in any simulation (for further details see

Congressional Budget Office, November 2005). In this paper, all stochastic results are based on

500 simulations. 
28

References

Bohn, Henning (2001). “Retirement Saving in an Aging Society: A Case for Innovative

Government Debt Management.” University of California, Santa Barbara, Economics

Working Paper Series, Number 1056.

Congressional Budget Office (June 2004). The Outlook for Social Security. Washington, D.C. 

Congressional Budget Office (November 2005). Uncertainty in the Analysis of Long-Term

Social Security Projections. Washington, D.C. 

Congressional Budget Office (March 2005). Updated Long-Term Projections for Social Security. 

Washington, D.C. 

Cornia, Gary C., Ray D. Nelson, and Andrea Wilko (2004). “Fiscal Planning, Budgeting, and

Rebudgeting Using Revenue Semaphores.” Public Administration Review, Vol. 64, No.

2 (March/April), pp. 164-179.

Diamond, Peter A. and Peter R. Orszag (2004). Saving Social Security. Washington, D.C.:

Brookings Institution Press.

Feldstein, Martin (1990). “Imperfect Annuity Markets, Unintended Bequests, and the Optimal

Age Structure of Social Security Benefits.” Journal of Public Economics, 41:1, 31-43

(February). 

Geanakoplos, John, Olivia S. Mitchell, and Stephen P. Zeldes (1999). “Social Security Money’s

Worth.” Prospects of Social Security Reform, eds. Olivia S. Mitchell, Robert J. Meyers,

and Howard Young. Philadelphia: Pension Research Council, Wharton School of the

University of Pennsylvania.

Gordon, Roger H. and Hal R. Varian (1988). “Intergenerational Risk Sharing.” Journal of

Public Economics, Vol. 37, pp. 185-202.

Gustman, Alan L. and Thomas L. Steinmeier (2001). “How Effective is Redistribution under the

Social Security Benefit Formula?” Journal of Public Economics, 82:1, 1-28 (October). 

Harris, Amy Rehder and John Sabelhaus (May 2005) “How Does Differential Mortality Affect

Social Security Progressivity and Finances?” Technical Paper 2005-5. Congressional

Budget Office, Washington, D.C.

Harris, Amy Rehder and Michael Simpson (2005) “Winners and Losers Under Various

Approaches to Slowing Social Security Benefit Growth,” National Tax Journal, Vol. 58,

No. 3 (September), pp. 523-544.
29

Holmer, Martin R. (1999). “Stochastic Simulation of Economic Growth Effects of Social

Security Reform.” Prospects of Social Security Reform, eds. Olivia S. Mitchell, Robert J.

Meyers, and Howard Young. Philadelphia: Pension Research Council, Wharton School

of the University of Pennsylvania.

Lee, Ronald and Ryan Edwards (2002). “The Fiscal Impact of Population Aging in the U.S.:

Assessing the Uncertainties.” Center for Economics and Demography of Aging,

University of California, Berkeley. 

Lee, Ronald and Shripad Tuljapurkar (1998). “Stochastic Forecasts for Social Security.” in

Frontiers in the Economic of Aging, ed. David A. Wise, Chicago and London: University

of Chicago Press. 

Lee, Ronald and Hisashi Yamagata (2003). “Sustainable Social Security: What Would It Cost?”

National Tax Journal, Vol. 57, No.1, Part 1 (March) pp. 27-43.

O’Harra, Josh, John Sabelhaus, and Michael Simpson (January 2004) “Overview of the

Congressional Budget Office Long-Term (CBOLT) Policy Simulation Model,” Technical

Paper 2004-1. Congressional Budget Office, Washington, D.C. 

Popper, Steven W., Robert J. Lempert and Steven C. Bankes (2005). “Shaping the Future:

Overview/Dealing with Uncertainty.” Science, March 28. 

Sheshinski, Eytan, and Yoram Weiss (1981). “Uncertainty and Optimal Social Security

Systems.” Quarterly Journal of Economics, 96:2, 189-206 (May).

Smetters, Kent (2004). “Solvency and Reform of Social Security: Is the Social Security Trust

Fund a Store of Value?” American Economic Review, Vol. 94, No. 2 (May), pp. 176-

181. 

Social Security Administration Board of Trustees (April 2005). “The 2005 Annual Report of the

Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability

Insurance Trust Funds.” Available at www.ssa.gov/OACT/TR/TR05/tr05.pdf.
Figure 1. Social Security Benefit-to-Tax Ratios by Single-Year Birth Cohorts

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Benefit-to-Tax Ratio

Current Law

Scheduled Be
Figure 2. Expected Social Security Trust Fund Ratio 

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 

Current Law
Figure 3. Potential Ranges for Ratios of Lifetime Benefits to Lifetime Taxes

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Ratio of Present Value of Lifetime Benefits to Lifetime Taxes 

(in percent)

Current LawScheduled Benefits
Figure 4. Potential Range for Social Security Trust Fund Ratios under Current L

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 208

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 
Figure 5. Social Security Trust Fund Ratios 

(Current Law and One-Time Sustainably Solvent Benefit Cut)

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 208

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 

Current Law

19% Bene
Figure 6. Ratios of Lifetime Benefits to Lifetime Taxes

(Current Law and One-Time Sustainably Solvent Benefit Cut)

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Benefit-to-Tax Ratio

Current Law

19% Benefit Cut in 2012
Figure 7. Potential Ranges for Ratios of Lifetime Benefits to Lifetime Taxes 

(Current Law and One-Time Sustainably Solvent Benefit Cut)

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Ratio of Present Value of Lifetime Benefits to Lifetime Taxes 

(in percent)

Current Law19% Benefit Cut in 2012
Figure 8. Potential Ranges for Social Security Trust Fund Ratios

(Current Law and One-Time Sustainably Solvent Benefit Cut)

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 208

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 

Current Law19% Benefit Cut in 2012
Figure 9. Potential Ranges for Ratio of Lifetime Benefits to Lifetime Taxes

(Sustainably Solvent Benefit Cuts with and without State-Dependent Policy Rul

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Ratio of Present Value of Lifetime Benefits to Lifetime Taxes 

(in percent)

19% Benefit Cut in 201211% Benefit Cut in 2012 Plus Longevity Indexing and Productivity-Adjusted COLA
Figure 10. Potential Ranges for Social Security Trust Fund Ratios

(Sustainably Solvent Benefit Cuts with and without State-Dependent Policy Rul

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 20

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 

19% Benefit Cut in 201211% Benefit Cut in 2012 Plus Longevity Indexing and Productivity-Adjusted COLA 
Figure 11. Potential Ranges for Ratios of Lifetime Benefits to Lifetime Taxes

(State-Dependent Policy Rules with and without Fertility Variation)

0

102030405060708090

100

1950 1955 1960 1965 1970 1975 1980 1985 1990 

Cohort Birth Year

Ratio of Present Value of Lifetime Benefits to Lifetime Taxes 

(in percent)

11% Benefit Cut Plus Longevity Indexing and Productivity-Adjusted COLA11% Benefit Cut Plus Longevity Indexing and Productivity-Adjusted COLA: No Fertility Variation
Figure 12. Potental Ranges for Social Security Trust Fund Ratios 

(State-Dependent Policy Rules with and without Variation in Fertility)

05

10152025

2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075 2080 208

Calendar Year

Ratio of Trust Fund Balance to Trust Fund Outlays 

11% Benefit Cut in 2012 Plus Longevity Indexing and Productivity-Adjusted COLA 11% Benefit Cut in 2012 Plus Longevity Indexing and Productivity-Adjusted COLA: No Fertility Variation