1

Do Social Security Surpluses Pay Down Publicly Held Debt? 

Evidence from Budget Data 

Randall P. Mariger* 

Staff Economist 

U.S. Department of Treasury, Office of Economic Policy 

Washington, DC 20551 

December 2008 

Abstract 

Being fair to future generations requires that Social Security be reformed in a manner that 

effectively prefunds a significant share of future Social Security benefit payments. All 

serious reform plans have this property. Prefunding is attempted exclusively in the Social 

Security trust fund in some plans, and it is attempted partly in personal retirement 

accounts in others. 

Many analysts believe that Social Security surpluses are offset all or in part by lower 

non-Social Security surpluses. If the offset is 100 percent, then running Social Security 

surpluses does not increase the government’s capacity to pay future Social Security 

benefits. In this case, reforms that rely on trust fund accumulations to make Social 

Security fair to future generations do so at the expense of a non-Social Security policy 

that is less fair to future generations. 

The evidence on whether or not trust fund accumulations pay down federal debt is of two 

general types: formal statistical analyses of historical budget data, and informal 

observations of budget politics. Mariger (2008) reviews the recent history of budget 

politics and concludes that there is a substantial probability that Social Security surpluses 

are in large part offset by smaller non-Social Security surpluses. To complement that 

study, this paper attempts to draw out statistical evidence from budget data. 

It is concluded that the budget data is essentially silent on the question of whether Social 

Security surpluses are truly saved. The reason is that the regression model specification 

is necessarily approximate, Social Security surpluses show little independent year to year 

variation, there are only 37 years of data, and spurious correlations mask the true 

relationships. 

________________________ 

*The analysis and conclusions set forth in this paper are those of the author and do not indicate 

concurrence by other members of the Treasury research staff or Treasury’s senior officials.
2

I. Introduction 

Being fair to future generations requires that Social Security be reformed in a manner that 

effectively prefunds a significant share of future Social Security benefit payments. All 

serious reform plans have this property. Prefunding is attempted exclusively in the Social 

Security trust fund in some plans, and it is attempted partly in personal retirement 

accounts in others. 

The consequences of prefunding Social Security in the trust fund are controversial and 

not well understood. The key question is whether Social Security surpluses are offset by 

smaller non-Social Security surpluses. If Social Security policy does not influence nonSocial Security policy, then the trust fund balance at every date represents the amount by 

which past Social Security cash flows have reduced debt held by the public at that time. 

Reducing a liability in this manner is real saving that increases the government’s capacity 

to pay future Social Security benefits. 

On the other hand, many analysts believe that Social Security surpluses are offset all or in 

part by lower non-Social Security surpluses. If the offset is 100 percent, then running 

Social Security surpluses does not increase the government’s capacity to pay future 

Social Security benefits. In this case, reforms that rely on trust fund accumulations to 

make Social Security fair to future generations do so at the expense of a non-Social 

Security policy that is less fair to future generations (Mariger, 2008). And if political 

constraints dictate that prefunding must be done in the trust fund, then it would be 

rational to compromise on benefit adequacy so as to limit trust fund accumulations in a 

manner that benefits future generations (Mariger, 2008). 

Given that so much rides on the question of whether or not trust fund accumulations pay 

down federal debt, it is important to carefully consider the evidence. That evidence is of 

two general types: formal statistical analyses of historical budget data, and informal 

observations of budget politics. Mariger (2008) reviews the recent history of budget 

politics and concludes that there is a substantial probability that Social Security surpluses 

are in large part offset by smaller non-Social Security surpluses. To complement that 

study, this paper attempts to draw out statistical evidence from budget data. 

The estimates indicate that the offset between Social Security and non-Social Security 

surpluses is significantly greater than the maximum theoretical value of one for one. This 

is taken as evidence that the estimates are biased by left out variables that are correlated 

with Social Security surpluses. Because the standard error on the offset estimate is about 

three-quarters as large as the maximum theoretical offset, and the offset estimate is 

sensitive to the inclusion of time trends in the regression, it is concluded that the evidence 

of a significant offset is weak. 

These findings reflect the inherent difficulty of making inferences when the model 

specification is necessarily approximate, there are only 37 years of data, and Social 

Security surpluses show little independent year to year variation. To drive home these 

points, the paper reports regression estimates utilizing synthetic data generated by a 

plausible model of policymaker behavior that assumes Social Security surpluses are 
3

offset 100 percent by non-Social Security surpluses. It was expected that the offset 

estimate would be insignificant because of lags in the model that generates the synthetic 

data. Surprisingly, the estimated offset turns out to be significant and the wrong sign. 

Only when irrelevant independent variables are excluded from the regression does the 

offset estimate have the right sign. 

II. Estimates 

Smetters (2004) is the most recent analysis of the historical relationship between Social 

Security and non-Social Security budget surpluses and serves as a starting point for the 

current analysis. The basic relationship investigated is: 

(3) 1 / / O S

t tt t S PGDP S PGDP = γ 2 3

S O D D t t + + γ γ 4 / GDP PGDP t t +γ

 5 / WS GDP t t +γ 6 +γ trend 2

7 8 +γ trend + γ

where the γ 's are estimated parameters, O

t S is the non-Social Security primary surplus, 

PGDPt is potential GDP as estimated by the Congressional Budget Office (2007), S

t S is 

the Social Security primary surplus, WSt is wages and salaries, O Dt is debt attributable to 

non-Social Security policy (debt held by the public plus the trust fund balance), S Dt is 

debt attributable to Social Security policy (minus the trust fund balance), and trend is 

time in years beginning with 1 in 1949. The first two parameters are our focus: If trust 

fund accumulations pay down federal debt one for one, then 1 2 γ = γ = 0 , and if they 

enable larger non-Social Security deficits, 1 γ is between -1 and 0 and 2 γ is positive. The 

other explanatory variables in (3) control for the effects of non-Social Security debt 

(expect 3 γ > 0 ), the business cycle (expect 4 γ > 0 ), the effect of GDP makeup on nonSocial Security receipts (expect 5 γ > 0 ), and other unspecified determinants of the nonSocial Security primary surplus captured by the trend variables. 

This specification is the same as Smetters (2004) except for the treatment of wages and 

salaries and debt. Smetters normalizes wages and salaries by potential GDP rather than 

actual GDP, which makes 5 γ hard to interpret because it reflects both business cycle 

effects and GDP composition effects. And instead of including debt variables in his 

specification, Smetters specification subtracts net interest from the dependent variable: 

This would be the same specification as (3) if 2 γ and 3 γ were each time-varying and 

equal to the effective annual government borrowing rate. Because Smetters implicitly 

assumes that 2 3 γ = γ , his specification does not permit the non-Social Security budget to 

be entirely independent of the Social Security budget 2 3 ( . ., 0, 0) i e γ = γ > . 

Estimates of (3) for three different time periods are reported in Table 1. For the 1949-

2006 sample period, the estimates suggest that each $1 or Social Security primary surplus 

causes the non-Social Security primary surplus to be smaller by $3.63, nearly four times 

as large as the maximum offset consistent with theory (see regression (1)). The standard 
4

error on the estimate is rather large relative to its expected range [-1, 0], but because the 

magnitude of the estimate is so large, the one-tailed 95 percent confidence interval shown 

in the last row of the table is 1 γ ≤ −2.579. The coefficient on Social Security debt is also 

quite large and statistically significant. The reported estimate of 2 γˆ = 0.190 constrains 

the coefficient to equal the coefficient on non-Social Security debt ( 3 γˆ ) because the 

unconstrained estimates ( 2 γˆ = 0.489 and 3 γˆ =0.171) violate the theoretical prediction that 

either 2 3 ( 0, 0) γ = > γ or 2 3 γ = γ , which implies 3 2 γ ≥ ≥ γ 0 . 

The second and third columns of Table 1 verify the Smetters finding that the post-1969 

data are responsible for the large estimated negative offset; the estimated one-tailed 95 

percent confidence intervals are 1 γ ≤1.329 for the 1949-69 sample period and 

1 γ ≤ −3.329 for the 1970-2006 sample period. 

The post-1969 data suggest an implausibly large offset between non-Social Security and 

Social Security primary surpluses. Theory suggests that the offset is between in the range 

[-1,0], but the estimates indicate that the probability of 1 γ have an absolute value that 

small is less than one in a ten thousand. It seems likely therefore that the estimates are 

biased by the exclusion of explanatory variables that are correlated with the Social 

Security primary surplus. In that case, the error terms in the regression do not satisfy the 

conditions under which the sampling distributions for the estimated parameters are 

derived, and rigorous statistical analysis is not possible without additional assumptions. 

Despite the fact that 1 γˆ in regression (3) is almost certainly biased, one must conclude 

that the data supports values of 1 γ closer to -1 than to 0. As all empirical specifications 

are approximations undoubtedly subject to bias, it would be illogical to dismiss the Table 

1 estimates in their entirety simply because they are too strong. But the bias in 1 γˆ is a 

reminder that there are many untested assumptions underlying regression analysis, and 

that empirical estimates based on aggregative time series data are notoriously unreliable. 

On this score, it is troubling that the offset estimate is insignificantly positive when the 

time trend variables are excluded from the regression (see regression 4). 

The next section further illustrates the unreliability of the estimates. 

III. The Unreliability of Estimates Based on Aggregate Time Series Data 

This section considers this question: If post-1969 non-Social Security primary surpluses 

offset Social Security primary surpluses in precise accordance with a plausible model of 

policymaker behavior that implies the offsets are essentially 100 percent, would time 

series regressions like those in Table 1 give accurate estimates of the offset? Despite the 

fact that the model generating the synthetic data is certainly much simpler than the real 

world, the answer turns out to be an emphatic no. The reason is that the linear regression 

model is an approximate specification, there are only 37 years of data, and spurious 

correlations mask the true relationships. 
5

The Simulation Model for Non-Social Security Primary Surpluses 

The model of policymaker behavior is taken from Mariger (2008). The model was 

developed to help quantify the consequences for intergenerational fairness of not truly 

saving Social Security surpluses. 

The model has at its core a simple model that is modified to incorporate real world 

complexities. The simple core model assumes that the non-Social Security primary 

surplus share of GDP in each year t is set to the level that would be permanently 

sustainable if Social Security primary surplus share of GDP were to equal actual levels 

for the succeeding N years (years t through to year t+N-1), and were to stay constant at 

the year t+N-1 level in all later years. In the simple case were the real government 

borrowing rate and the growth rate of real GDP are forever constant at r and η , 

respectively, the core model is: 

(2) O

t s% 1 1

1 1 ( 1)[ ] t N St i S Nt i tN i t β d ss β β + − − − −

− +− = =− − − ∑ 

 1

O S

t t tt d d ss = −− β − %

where β =+ + (1 ) /(1 ) r η and, for year j, O

j s% is the planned non-Social Security primary 

surplus share of GDP, S

j s is the actual Social Security primary surplus share of GDP, and 

j d is the end-of-year ratio of publicly held debt to GDP. 

The core model is premised on the notion that the optimal non-Social Security fiscal 

policy keeps the non-Social Security primary surplus forever constant as a share of GDP, 

but that the actual non-Social Security surplus share of GDP deviates from that ideal 

because of political constraints that make it difficult to run unified surpluses in 

anticipation of the need to finance future unified deficits. Those constraints are modeled 

as inaccurate forecasts of Social Security primary surpluses beyond N years, but the 

problem is not inaccurate forecasts as much as inability to plan in accordance with those 

forecasts. 

The core model is such that the non-Social Security primary surplus rises or falls in 

accordance with whether the projections on which choices are based worsen 

( 1 2

S S

tN tN s s +− +− < ) or improve ( 2 2

S S

tN tN s s +− +− > ). In a prefunded system, Social Security 

primary surpluses ultimately fall and the news is on balance negative. As a result, nonSocial Security primary surpluses are too low initially and gradually rise over time in 

response to bad news. 

To add realism to the core model, it is assumed that politics precludes full upward 

adjustments to the non-Social Security primary surplus. Specifically, the plan is 

modified to include two regimes given by (2) when (2) calls for an unchanging or 

declining non-Social Security primary surplus share of GDP, 
6

(3a) ˆ

O

t s = Ot s% 1, O Ot t if s s ≤ − %

and which otherwise reverts to a damped version of (2): 

(3b) ˆ

O

t s = 1

O

t s − 1 ( ) O Ot t λ s s + − − % 1, O Ot t if s s > − %

where ˆ

O

t s is the modified plan, Ot s% refers to the core one-regime plan, and λ ∈[0,1] is a 

parameter reflecting resistance to rises in the non-Social Security primary surplus share 

of GDP. The debt to GDP ratio evolves according to: 

(4) 1 ˆ

O S

t t tt d d ss = −− β −

To simulate synthetic post-1969 data for non-Social Security surpluses, the model is 

generalized to allow the real government borrowing rate and the real GDP growth rate to 

accord with actual historical values through to 2006, and values projected in the 2005 

Social Security Trustee Report in later years. (Details are in Mariger (2008).) 

Two model simulations for the non-Social Security primary surplus share of GDP are 

shown in Figure 1 along with actual values. The synthetic data simulation assumes that 

λ = 0.5 and N = 5 . The optimal time profile for the non-Social Security primary surplus 

share of GDP is also shown in the figure; it corresponds to a simulation with N = ∞ and 

λ =1 and implies a non-Social Security surplus share of GDP that is forever flat at 0.26 

percent of GDP. The optimal primary surplus is just sufficient to service outstanding 

debt in 1969 that was attributable to non-Social Security policy, which was 33.8 percent 

of GDP.1

 (Publicly held debt was 30.2 percent of GDP and the trust fund balance was 3.6 

percent of GDP.) The fact that the actual non-Social Security primary surplus share of 

GDP is generally lower than the optimal path implies that publicly held debt attributable 

to non-Social Security policy has grown faster than under the optimal plan; indeed, 

starting from 2006 initial conditions, the optimal path for the non-Social Security primary 

surplus share of GDP is constant at 0.68 percent, a full 0.42 percentage points higher than 

the optimal path starting from 1969 initial conditions. 

 

1 If N = ∞ , λ =1, and the Social Security system abides by its budget constraint, then (3b) and (4) 

reduce to O

t s% 1 1 ( 1)[ ] t t β d f =− + − − , 1

O S

t t tt d d ss = β − − − % , and 1

S

t tt f β f s = − + , where 

1

S ji

j i i j f s β ∞ −

= + = −∑ is the Social Security trust fund balance share of GDP at the end of year j. It is 

easily verified that these equations imply that the optimal non-Social Security surplus share of GDP is 

forever constant at 1 1 ( 1)[ ] t t β d f − + − − . 
7

 Estimates Utilizing Simulated Non-Social Security Primary Surpluses 

Five regressions utilizing simulated data are reported in Table 2. The regressions utilize 

the simulated 1970-2006 time path for non-Social Security surpluses and non-Social 

Security publicly held debt, and actual values for the other independent variables. 

Regression (1) is the most general specification, the same as regression (3) in Table 1 

except that the debt variable coefficients are not forced to be equal. The estimated 

coefficients on the budget variables, the only explanatory variables that are “relevant” in 

the sense that they enter the simulation model generating the dependent variable, are all 

the wrong sign and achieve at least 1 percent statistical significance (one-tailed test). 

Among the other explanatory variables (the “irrelevant” explanatory variables), all but 

the business cycle coefficient achieves at least 5 percent statistical significance. 

Regressions (2)-(4) in Table 2 drop the irrelevant explanatory variables from the 

regression one at a time in the order of lowest to highest statistical significance. Only 

after all irrelevant explanatory variables are purged from the specification do any of the 

coefficients on the relevant explanatory variables become the right sign; in that case 

(regression (4)), the one-tailed 95 percent confidence intervals are (≤ -0.551) for the 

Social Security primary surplus, (≥ -0.005) for non-Social Security debt, and (≥ 0.014) 

for Social Security debt. 

This exercise suggests that including irrelevant variables in a regression can be as 

perilous as leaving out relevant variables when the sample size is small. 

IV. Conclusion 

The budget data is essentially silent on the question of whether Social Security surpluses 

are truly saved. The reason is that the regression model specification is necessarily 

approximate, Social Security surpluses show little independent year to year variation, 

there are only 37 years of data, and spurious correlations mask the true relationships. 

But the budget data is not the only source of information. Observations of recent budget 

politics do not submit to formal statistical tests, but they do nevertheless provide 

compelling evidence. Mariger (2008) reviews that evidence and concludes that there is a 

substantial probability that Social Security surpluses are in large part offset by smaller 

non-Social Security surpluses. 
8

(1) (2) (3) (4)

1949-2006 1949-1969 1970-2006 1970-2006

-3.652 -0.36 -4.632 0.159

(0.64) (0.954) (0.768) (0.736)

0.264

0.190** (0.715) 0.126** 0.085

(0.026) 0.672 (0.029) (0.034)

(0.125)

0.277 0.107 0.465 0.434

(0.061) (0.081) (0.085) (0.123)

1.214 0.658 1.615 0.301

(0.169) (0.358) (0.169) (0.119)

0.003 0.028 0.009 --------

(0.001) (0.006) (0.002)

-0.00001 -0.001 -0.0001 --------

(0.00001) (0.0002) (0.00002)

-1.018 -1.011 -1.51 -0.61

(0.108) (0.264) (0.132) (0.112)

Other Statistics

R2 0.669 0.715 0.856 0.56009

95% Confident SS 

Coefficient is less than: -2.579 1.329 -3.329 1.408

Estimated Coefficient and 

Standard Error for:

SS Primary Surplus

/Pot. GDP

Table 1

Regression Equations Explaining the On-Budget Primary Surplus 

Share of Potential GDP*

Regresssion Number And Estimation Period 

Time

Time Squared

Constant

*The dependent variable and all independent variables other than the constant and time 

variables are normalized by potential GDP. Robust standard errors are reported in 

parentheses.

**Coefficients on debt due to SS and due to Non-SS constrained to be equal. For regressions 

1 and 3, the reason is that the unconstrained estimates violate the theoretical prediction that 

that the SS coefficient is no larger than the non-SS coefficient. Regression 5 is constrained to 

be consistent with myopic unified budget planning.

Lagged Debt Due to SS/ 

Pot. GDP

Lagged Debt Due to NonSS/ Pot. GDP

GDP/Pot. GDP

Wages and Salaries

/GDP
9

(1) (2) (3) (4)

0.646 0.664 0.451 -0.812

(0.144) (0.135) (0.12) (0.135)

-0.314 -0.313 -0.275 0.023

(0.039) (0.039) (0.037) (0.017)

-0.085 -0.084 -0.075 0.04

(0.011) (0.012) (0.011) (0.015)

0.008

(0.01)

-0.063 -0.062

(0.017) (0.017)

0.001 0.001 0.001

(0.0004) (0.0004) (0.0005)

-0.00003 -0.00003 -0.00003

(0.00001) (0.00001) (0.00001)

0.035 0.042 0.006 -0.009

(0.017) (0.014) (0.009) (0.004)

Other Statistics

R2 0.942 0.941 0.931 0.557

95% Confident SS 

Coefficient is less than: 0.891 0.893 0.655 -0.584

Lagged Debt Due to SS/ 

Pot. GDP

Lagged Debt Due to NonSS/ Pot. GDP

Table 2

Regression Equations Explaining the Simulated Suboptimal 1970-2006 

On-Budget Primary Surplus Share of GDP Shown in Figure 2*

Estimated Coefficient and 

Standard Error for:

Regresssion Number

SS Primary Surplus

/Pot. GDP

Time

Time Squared

Wages and Salaries

/GDP -- --

GDP/Pot. GDP

--

Constant

* Robust standard errors are reported in parentheses. If noise orthogonol to the right-handside variables is added to the dependent variable so as to lower the regression (1) R2 to the 

same level as for a regression using actual data (0.876), all standard errors in all regressions 

would be higher by 82 percent.

-- -- --

--
Figure 1

Simulated Non-Social Security Primary Surplus Share of GDP Starting 

From 1969 Initial Conditions

-4-2

024

1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 

Year

Percent

Synthetic data simulatioN=5, Lambda = 0.5

Actual

Optimal simulation, N=∞, Lambda = 1
11

References 

Congressional Budget Office. 2007. The Cyclically Adjusted and Standardized 

Budget Measures. February. 

Mariger, Randall. 2008. Prefunding Social Security Benefits to Achieve 

Intergenerational Fairness: Can It Be Done in the Social Security Trust Fund?, mimeo, 

December. 

Smetters, Kent. 2004. “Is the Social Security trust fund a Store of Value?” American 

Economic Review 94(2): 176-181. 

Social Security Trustees. 2005. The 2005 OASDI Trustees Report. Washington D.C.: 

U.S. Social Security Administration.