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SOCIAL SECURITY BENEFIT UNCERTAINTY UNDERINDIVIDUAL ACCOUNTS

AMY REHDER HARRIS. JOHN SABELHAUS, and MICHAEL SIMPSON*

Social Security reforim that include individual accounts change both the expectedhenejlt and the benefit risk. This article uses a lovg-ferm stochastic forecaslingmodel toestimate the distribution of expected benefits under a simple individual accotint,recognizing uncertainties in the current system. Introducing individual aeconntsinereases the overall variability of benefit levels relative to current law: indeed thestandard deviations of expected benefit gains exceed the level of those gains. Theincrease in uncertainty about benefit replacement rates is even larger, however,because individual accotmts partially sever the link between earnings and benefits inthe existing system. (JEL H55)

I. INTRODUCTION

Various Social Security reform proposalsput forth in recent years have included indivi-dual accounts. Two ofthe three reform optionsoffered by the 1994-1996 Advisory Councilon Social Security (1997) incorporatedsuch accounts. One Advisory Council optionincluded mandatory individual accountsrequiring workers to contribute an additional1.6% of payroll, invested in indexed bond orequity funds managed by the federal govem-ment. Another option included a two-tieredsystem with privately held Personal SecurityAccounts (PSAs) that would allow workersto contribute five percentage points of their

*This paper was presented at the Western EconomicAssociation 78"" annual conference. Denver. CO, July 12,2O()3. in a session organized by Nancy Jianakoplos. Theauthors would like lo ihank our discussant. Shawn Knob,and other session participants for helpful comments. Weare grateful to members of the CBO Long-Term ModelingGroup (Josh O'Harra, Kevin Percse. Joel Smith, and JulieTopoieski) for help with the modeling effort and to JoyceManchester and two anonymous referees for comments onan earlier version of this paper. The views expressed in thisarticle are those of Ihe authors and should not he inter-preted as those ofthe Congressional Budget Office.

Harris: Principal Analyst. Congressional Budget Oflice.Washington. D.C. 20515. Phone i-202-226-5669, Fax1-202-225-3149. E-mail amyh(^cbo.gov

!iuhelhmi.-i: Unit Chief. Congressional Budget Office.Washington. D.C. 20515. Phone 1-202-226-5672.Fax 1-202-225-3149, E-mail JohnsaCcJjebo.gcv

Simpson: Pnncipal Analyst, Congressional Budget Offiee,Washington, D.C. 20515. Phone 1-202-226-5668,Fax 1-202-225-3149. E-mail [email protected]

payroll tax to their PSA where it could beinvested in "financial instruments" (AdvisoryCouncil on Social Security. 1997, p.30). TheKolbe-Stenholm 2 r ' Century RetirementSecurity Act (Kolbe and Stenholm. 2002) pro-posal for Social Security reform includes anIndividual Security Account (ISA) to whichworkers would contribute 3 percent of thefirst $10,000 of income plus 2 percent above$10,000, investing the funds in stocks, bonds,or government debt. Most recently, thePresident's Commission to Strengthen SocialSecurity (CSSS) presented three proposals thatall included a version of voluntary individualinvestment accounts; details are discussed inSection II.

These proposals often tout expected ratesof return (based on historical experience)that would lead to higher overall retirementincome for Old-Age Insurance (OAI) worker

ABBREVIATIONS

ARMA; Autoregressive Moving AverageAR: AuloregressiveBLS; Bureau of Labor StatisticsCSSS; Commission to Strengthen Social SecurityDl; Disability InsuranceNIPA: National Income and Product AccountsOAI: Old-Age InsuranceOASDI: Old-Age. Survivors, and Disability

InsuranceSSA: Social Security AdministrationVAR: Vector Autoregression

Contemporary Economic Policy(ISSN 1074-3529)Vol. 23. No. I, January 2005, i-16

doi:tO.I093/cep/byiOOIC'l Western Eeonomic Association International 2005No Claim to Original U.S. Government Works

CONTEMPORARY ECONOMIC POLICY

beneficiaries who participate in the individualaccounts. For example, based on Social Secu-rity Administration (SSA) estimates, the CSSSreport (2001) shows that prototypical workersare expected to be better off under a systemwith individual accounts, even in cases wherethe current-law benefit is reduced in order toeliminate the projected funding gap in SocialSecurity. However, reporting only expectedbenefits under individual accounts using aver-age historical rates of return ignores the riskassociated with investing in private securities,as noted by Feldstein and Rangulova (2001).One approach to controlling for the increasedrisk in evaluations of individual account pro-posals is to use a lower (appropriately risk-adjusted) rate of return. An alternativeapproach, which is used here, is to first generatesequences of future returns for private secu-rities using Monte Carlo simulation, then solvefor benefits under each sequence of futurereturns, and finally analyze the distributionof benefit outcomes across simulations. Thelatter is preferable because it acknowledgesthe higher expected return from investing inprivate securities, but it also produces directmeasures ofthe increased risk (e.g., the prob-abihty that benefits are actually lower underthe proposed alternative).'

The investment risk considered in this articleis modeled on the principle that underlies themost basic CSSS approach to individualaccounts. Participants contribute a fixed frac-tion of their current-law payroll tax to the indi-vidual account and in return they promise togive up a fraction of their existing current-lawscheduled benefit at retirement. The amount bywhich the scheduled benefit is reduced equalsthe tax diverted to the individual account,accrued forward at a designated "offset"rate, usually the government bond rate plusor minus a wedge. Therein lies the investmentrisk—participants are better off if and only iftheir accounts earn more than the designatedoffset rate. The results show that the expectedbenefit gain is positive for a 2 percent individualaccount carve-out with a simple benefit offsetusing the SSA assumptions for the expectedrates of return on stocks and bonds, but thestandard deviation of that gain is much largerthan the gain itself.

I. See Bajtelsmit et al. (2003) for another use of theMonte Carlo technique to measure investment returnvariability for individual accounts-

Although expected gains from individualaccounts are uncertain, it is important tokeep in mind that even without individualaccounts, future current-law benefits areuncertain because key determinants such asfulure real wage growth and inflation areuncertain. For example, higher real wagegrowth increases benefits because the compu-tation of lifetime average earnings, used todetermine benefits, is based on past earningsadjusted by both infiation and real wagegrowth. Therefore introducing individualaccounts does not add uncertainty into a cur-rently riskless system, rather it replaces someofthe risk due to uncertain wage growth withrisk from uncertain financial market returns.Indeed, one result that stands out below isthat benefits under the current system arealready highly uncertain. Under the simple2 percent carve-out proposal, participantswould face an increase in the standard devia-tion of real benefit levels of 25 to 50 percent.

Using benefit replacement rates (annualbenefits divided by the average of the last10 years of earnings) as the outcome measure,however, shows individual accounts have amuch larger effect on uncertainty about futureoutcomes. The reason is straightforward—replacement rates are more variable underindividual accounts because the link betweenearnings and benefits that exists in the currentsystem is being partially severed. Undercurrent law, benefits are a direct function ofaverage earnings; under a plan with an indivi-dual account and benefit offset, benefitsare partially a function of average earningsand partially a function of the investmentreturns received on the individual account,"

2. Benefits are computed by first indexing historicalannual earnings for inflation and real wage growth up tothe year the individual reached age 60: earnings after thatage are considered in nominal values. The highest 35 yearsof indexed earnings are then averaged to compute the aver-age indexed monthly earnings (AIME). The primary insu-rance amount (PlA) is computed using the followingprogressive formula;

Pt/t = 0.90 * {min($6I2. AIME)) + 0.32* (max(O, min($3.689 - 612. AIME - $612)))+ 0.15 * (max(O, AIME - $3,689)),

wherethedollar values are applicable for 2004. For workersclaiming at the lull retirement age. benefits equal the PIA,for those claiming earlier (later), benefits are reduced(increased). The full retirement age is increasing overtime, from 65 years for cohorts born before 1938 to67 years for cohorts born in 1960 or later. The exampleworkers considered here claim at age 65 and thus would

HARRIS, SABELHAUS, & SIMPSON; SS BENEFIT UNCERTAINTY

Replacement rates also show how uncertaintywould vary across different types of benefici-aries, even under the simple proposal consid-ered here. Since the existing benefit system isprogressive, the 2 percent carve-out subjects ahigher/racr/on ofthe existing benefit to invest-ment risk for high-earner participants. Low-earner participants may still be more averseto the investment risk because their absolutebenefits are lower.

This article estimates the effect on benefitrisk using a long-term stochastic forecastingmodel containing three components: a SocialSecurity budget model that solves for aggre-gate system fmaneial outcomes based on keydemographic and economic inputs, a stochas-tic macrodemographic model that generatesthose key inputs in a Monte Carlo setting,and a representative micromodel that solvesfor person-level outcomes that are consistentwith the underlying stochastic environmentand policy rules.

In order to limit the scope of the article andmaketheresultsdirectly comparable to those inthe CSSS report, the representative micro-model is based on the same sealed exampleworkers used by the SSA. The key innovationrelative to the CSSS estimates is thereforequantifying the uncertainty about returns onthe individual accounts.^ Because the keydemographic and economic assumptions canall be generated using Monte Carlo simula-tion, it is possible to explicitly consider benefitrisk by solving the model repeatedly and ana-lyzing the distribution of outcomes acrosssimulations.

The individual account alternative consid-ered here is intended to have no impact on theexpected actuarial deficit in the Social Securitysystem in order to distill the pure effect on riskfrom individual accounts. In so doing, this arti-cle does not address the thorny issue of whetherbenefits would be cut or taxes raised in the eventof depletion ofthe Social Security Trust Fund.If one chooses to assume that benefits will becut (as the CSSS did), then one could compareexpected benefit outcomes with benefits pay-able under current law (as the CSSS did) ratherthan current-law scheduled benefits. Choosing

receive just under 100 percent of their PIA for cohortsclaiming in the earliest years. Benefits will decrease to 87percent of the PIA for cohorts claiming in 2025 and later.

3. For a similar exerci.se in the context of investing thetrust funds direetly into corporate bonds and equities, seeHarris etal. (2001).

a baseline for comparison is crucial in evaluat-ing policy alternatives, but for the purpose ofevaluating benefit risk under current law versusan individual account altemative, the issue isappropriately set aside,

11. INDIVIDUAL ACCOUNT PROPOSALS FROMTHE PRESIDENT'S COMMISSION TO

STRENGTHEN SOCIAL SECURITY

Under the direction of the principles estab-lished by President George W. Bush, the CSSSput forward three reform options that includedsome form of a voluntary individual account.The CSSS final report (2001) explains theseoptions in detail, including their recommenda-tions for issues such as investment options andannuitization of balances at retirement.

The first option in the CSSS report wouldallow workers to contribute 2 percent of theircurrent-law payroll tax to the individualaccount. At retirement, participants* current-law scheduled benefit would be offset by atheoretical annuity equal to the stream of(infiation-adjusted) income that would havebeen "purchased" by the 2 percent carve-outaccrued forward using the government bondrate plus 50 basis points. (In this article, theaccumulated balance used to determine thebenefit offset is referred to as a ""notional"account.) Individuals that choose to partici-pate would be betting that they can earnmore on their individual investments than50 basis points above the government bondrate.'' The CSSS benefit offset approach effec-tively charges participants for the interesttheir deferred taxes would have earned hadthey been deposited in the Old-Age, Survivors,and Disability Insurance (OASDI) TrustFund. In that sense, the risk of the individualaccount is completely shifted onto participantsand not onto future taxpayers. The commis-sion noted that this option is a generic indivi-dual account plan which does not containother changes to the existing system, andthus does not purport to bring the systeminto fiscal balance.

The second CSSS option allows participantsto contribute 4 percentage points of their

4. Individual accounts also incur administrative costsin the accrual phase and in the annuitization purchase thaiare not charged against the accrual ofthe notional accountor the notional annuity; thus individtials will actually haveto earn slightly more than the government bond rate plusany offset to increase their benefits under an individualaccount.


payroll tax, up to $1,000 (price indexed) peryear, to an individual account. Upon retire-ment, their scheduled benefit will be offset bythe notional annuity purchased by 4 percentagepoints of payroll, to the cap, accrued forwardusing the government bond rdteminus 100 basispoints. However, the second plan also includesa fairly dramatic change in the scheduled ben-efit computation from wage indexing to priceindexing that would slow benefit growth (rela-tive to scheduled benefits) enough to bring thesystem into balance.

The third CSSS option calls for 1 percent innew contributions (an "add-on") along with a2.5 percent carve-out of current payroll taxes,with the latter iimited to $ 1,000 (price indexed)annually. In this plan the benefit offset is basedon a notional account accrued forward usingthe government bond rate minus 50 basispoints. To account for increasing life expect-ancy and address fiscal solvency, this plan wouldchange the actuarial adjustments for those whoretire before or after the full retirement age.*̂

The CSSS report also discussed the invest-ments that participants would be able to makewith their individual accounts and how theaccounts would be handled upon retirement,both key determinants of the additional risksintroduced into the system. They recom-mended a two-tier investment structure dic-tated by the size of the individual account.Early in workers' careers, when account bal-ances are low, the funds would be invested in alimited set of broad index funds managed by alow-cost, centralized governing board. Onceaccount balances reach a threshold, indi-viduals would be allowed to shift their balancesinto funds managed by a myriad of private-sector administrators. Account balances,however, must still be invested in broadlydiversified funds. Individuals would not haveaccess to the funds in the accounts prior toretirement.

Upon retirement, account balances must beannuitized or gradually withdrawn, and onlybalances above a minimum threshold could betaken out in a lump sum. Inflation-indexedannuities would be made available (which isessentially what the current Social Security

5. The second and third options include adjustments inbenefit rules for low-income widows/widowers and a largerminimum benellt for all long-time, low-wage workers. Thethird model al.so includes a decrease in the third benefitreplacement factor in the PIA formula from 15 percentto 10 percent.

systetn provides), along with standard annu-ities and annuities that include the option forleaving a bequest. For married retirees, a two-thirds joint and survivor annuity would berequired unless both spouses agree to a differ-ent arrangement.

As noted in the introduction, the goal of thisanalysis is to isolate the issue of uncertaintyabout benefits under individual account alter-natives, so the simplest possible scenario isused. All of the results presented below arebased on a simulation structured to replicatethe CSSS plan 1 approach, a 2 percent carve-out with a benefit offset equal to an accrualof the notional balance at the govertimentbond rate plus a 50 basis point wedge. It isalso assumed that administrative costs aresmoothed across accounts so that a constant30 basis point charge is subtracted from theannual expected portfolio return. Finally,balances are annuitized at retirement for theexample workers analyzed here as single-life,inflation-adjusted annuities using the govern-ment bond rate minus administrative costs andthe SSA unisex life tables.

ill. MODELING SOCIAL SECURITYOUTCOMES

The results presented in this article areprojected using a model that combines threesystems: a budget model, a stochastic macro-demographic model, and an example workermicromodel.

A. Social Security Budget Model

The budget model tracks Social Securityfinances over time given policy rules and valuesfor the demographic and economic inputs, cap-turing the basic features of budgetary projec-tions made by the actuaries at SSA anddescribed by Frees (1999). The crucial test ofthe budget model is that it exhibits responsesto variations in policy parameters (tax ralesand benefit formulas) and input assumptions(mortality improvement, fertihty, immigra-tion, wage growth, infiation, interest rates,unemployment, and disability rates) thatmatch those in the actuaries' estimates.Given these responses, any set of alternativepolicy rules and/or stochastically generatedinput assumptions will lead to simulatedchanges in financial projections that basicallymatch what the Social Security actuarieswould predict.

HARRIS. SABELHAUS, & SIMPSON: SS BENEFIT UNCERTAINTY

The Social Security budget model has twoindependent submodels dealing separatelywith the demographic and financial aspectsof the OASDI system. The demographicmodel tracks population using a "cell-based"approach, projecting person counts by singleyear of age, sex, and marital status groups. Theinputs to the demographic model are annualfertility, total immigration, and rates of mor-tality improvement (by detailed age and sex).Demographic processes are calibrated tomatch Social Security "intermediate" projec-tions when the inputs are set accordingly,and changes in the inputs (jointly or separately)produce changes in population counts that arealso consistent with the sensitivity analysisreported by the SSA actuaries in the annualreport to the OASDI Board of Trustees(2003). The finaticial part ofthe Social Securitybudget model is also generally "cell-based" innature. The approach in the model is to trackvariables like labor force participation, averagebenefits, and beneficiary counts by age and sex.then multiply by the population counts fromthe demographic modules to solve for deter-minants of aggregate system financial flows.

B. Stochastic Macrodemographic Model

The goal of the stochastic macrodemo-graphic model is to generate values for the eco-nomic and demographic inputs to the SocialSecurity budget model in a Monte Carlo set-ting. The basic approach involves using stan-dard time-series techniques applied to thestochastic inputs, as in Frees et al. (1997) andChang and Cheng (2002). The demographicinputs are the rate of mortality improvementacross detailed age and sex groups, the overallfertility rate, and the level of immigration. Theeconomic inputs for the budget model are realwage growth, infiation. the unemploymentrate, interest rates, and rates of disabilityincidence and termination. For simulationsinvolving investment in private securities, thestochastic simulator also generates values forequity and corporate bond returns. The goal ofthe macrodemographic model is to create real-istic stochastic variation in the annual valuesfor each input, including correlations betweenthose variables.

The stochastic macrodemographic modelstarts with SSA intermediate projections toset central tendencies for each of the nineinputs. The SSA intermediate values are

based on extrapolating historical averagesfor (generally) stationary processes such aswage and price growth rates, and in thatsense are consistent with the underlying time-series analysis used to build the macrodemo-graphic model. Most of the stochastic inputsare treated as independent time-series pro-cesses, although infiation. unemployment,and interest rates are modeled together in avector autoregression (VAR) and short-runwage growth dynamics are affected by theother three economic variables. In all casesthe specifications were chosen using standardtime-series techniques (Congressional BudgetOffice. 2001).

The three demographic models are all esti-mated using data from the SSA (see Table 1).Mortality improvement is modeled as anAR(1) process for each of 42 separate age-sex groups. The data are available back to1900. Although the equations are estimatedseparately, the rates of mortality improvementacross age groups are correlated because thevector of innovations is drawn from a multi-variate normal distribution estimated using thehistorical error terms, which are correlated.The overall fertility process is characterizedas an ARMA(4,i) model estimated on databack to 1917. Identifying a stationary charac-terization for the fertility proces.s is somewhatcomplicated by distinct breaks in the series atvarious points in history, notably at the end olthe baby boom. Experiments with an alter-native to the ARMA representation (a first-difference model) did change implied fertilitydynamics, but the effect on variability in systemfinances was modest (Congressional BudgetOffice, 2001). Finally, the immigration processis also dominated by distinct breaks in the time-series at various points in history, but in Ihiscase, because of changes in policy. Again, theARMA(4,1) representation is most approp-riate for immigration.

Three of the four economic variables (infia-tion, unemployment, and the real interest rate)passed the test for inclusion in a VAR. while thefourth (real wage growth) was rejected. TheVAR model uses two annual lags for each ofthe three variables and is estimated usingdata from the Bureau of Labor Statistics(unemployment and Consumer Price Indexfor Urban Wage Earners and Clerical Workers[CPI-Wl infiation) and SSA (real interest rateson new issues of OASDI Trust Fund assets) forthe period 1954-1999. Unemployment rates


TABLE IEquations in Stochastic Macrodemographic Model

Variable Description of Stochastic Proecss

Mortality Improvement

FertilityImmigration

Llnemplo) mcnt

ifiHatlon (CPI-W)

Real Wage Growth

Real Interest Rate

Dl IncidenceDl TerminationEquity Returns

Corporate Bond Returns

Separate ARU) equations for each of 21 age and two sex groups estimated usingSSA data for 1900-1995. Model draws two sets of 21 correlated errors usingmultivariate normal distribution."

ARMA(4,1) equation for overall fertility rate estimated using SSA data for 1917-1997,"ARMA(4,1) equation for total immigration estimated using SSA data for 1901-1995."VAR modei with two lags each on unemployment, inflation, and real interest rateestimated using BLS and SSA data for I954-1999.''

VAR model with two lags each on unemployment, inflation, and real interest rateestimated using BLS and SSA data for 1954-1999."

Level of nominal wage growth as a function of the three economic variables, equationestimated using NIPA, BLS. and SSA data for 1954-1999; real wage (comparableto SSA's "dilTerential") is nominal wage less inflation.^

VAR model with iwo lags each on unemployment, inflation, and real interest rateestimated using BLS and SSA data for 1954-1999."

AR( 1) model for overall Dl incidenee rale estimated using SSA data for 1975-1999.'AR( I) model for overall Dl termination rate estimated using SSA data for 1975-1999."Total returns a white-noise process estimated using Ibbotson Associates (2001)large-cap data for the period 1954-1999.^Level of large-cap bond returns as a function of inflation, unemployment, andinterest rate estimated using Ibbotson Associates (2001), SSA, and BLSdata for the period 1954-1999.^

"For details on Ihe parameter estimates and the associated statistics see Congressional Budget Office (2001,pp. 35-55). Available at www.cbo.gov.

''For details on the parameter estimates and the associated statistics see Smith and Sabelhaus (2003, pp.15-17).Available at www.cbo.gov.

are transformed using a log-odds ratio prior toestimation, so the predicted values are con-strained to the zero-one range in all cases.Although real wage growth does not lead theother three variables, it is strongly correlatedwith contemporaneous values. After control-ling for current values of inflation, unemploy-ment, and interest rates, the real wage growthresiduals are white noise, which suggests theinteresting dynamics occur through the othervariables, because real wage growth (by itself)is highly autocorrelated.

The last two inputs to the Social Securitybudget model are disability incidence andtermination. Finding reasonable equationsfor variations in disability incidence and termi-nation rates is made difTicult because consistentdata only exist back to 1975, and is furthercomplicated because of changes in policy(stated and implicit) with respect to eligibilityfor the program. The problem is similar tothe fertility model; there are clear breaks inthe data that are (ex post) explainable, butit is not clear how to use that informationwhen predicting future variability. Becausethere is no clear signal from the data,

both models are specified as simple AR(1)processes.

In policy experiments involving trust fundinvestment in private securities or individualaccounts, the stochastic model generates valuesfor equity and corporate bond returns using arandom returns or "white noise" process. Thealternative to white noise is to introduce somesort of mean-reverting process, for example,one based on the dividend-to-price ratio.Annual stock yields are not correlated overtime, but there is some evidence that the currentlevel of the stock market is correlated withfuture returns, and therefore future yieldsare, in a sense, "predictable" (see. e.g., Campbellet al.. 1997; Campbell and Shiller, 1998). Theevidence of mean reversion is statisticallyweak, however, so (following Feldstein andRangulova, 2001) the random returns processis adopted.

Given the choice of a white-noise process forequity returns, one still has to select values forexpiected returns and the standard deviation ofreturns in the simulations. Published data onequity yields are available from IbbotsonAssociates (2001) back to 1926, and the exact

HARRIS, SABELHAUS. & SIMPSON: SS BENEFIT UNCERTAINTY

time period used to measure the average andvariance for yields matters a lot. In the simula-tions involving equity investment, the modelassumes a white-noise process with expectedreturns of 6.5 percent (the value used bySSA actuaries in their analysis of the CSSSplans (2002)) and a standard deviation of19.795 percent, which should, if atiything,bias the answers toward generating less posi-tive gains from equity investments.

Although equity returns are an independentwhite-noise process, real corporate bond yieldsare integrated with the rest ofthe macro model.The equation for corporate bond returns usesthe three variables in the VAR: unemployment,inflation, and the real interest rate on govern-ment bonds. Thus the equation captures boththe overall variability in corporate bond yieldsand the short-run macrodynamics in the rest ofthe model. As noted above, although Ibbotsondata on corporate bond yields are availableback to 1926, the range for the other variables(in a consistent format) is limited to 1954and later, so the equation is estimated forthat period.^

C Example Worker Micromodel

The micromodel is based on the same"scaled example" workers used by SSA(Goss and Wade, 2001; Nichols et al., 2002)in their distributional analysis of current lawand alternative policies. Outcomes for exampleworkers are tied to the economic/demographicenvironment and the Social Security budgetmodel, thus alternative policies will impactthe example worker outcomes.

In every birth cohort there are three exam-ple workers: low, medium, and high earners.The example workers have hump-shaped age-earnings profiles over the interval from 22 to 64years which are derived from actual earningspatterns in SSA data files. The workers areunisex and have no specified marital status.In all cases, earnings for any given cohort ata given age are expressed relative to the average

6. Another possible correlation exists between assetreturns and real wage growth. The maerodemographicmodel used here is intentionally restricted to mimic theSocial Security actuaries modeling approach so that themedian outcomes are directly comparable, thus it is notfeasible to address this correlation direetly. However, in amodified version of this model with a Cobb-Douglas pro-duction function, standard first-order conditions, and exo-genous total factor produetivity. Smith and Sabelhatis(2003) show that the effect of introdueing that correlationdoes not significantly change the results shown here.

wage index, so earnings for example workersare tied to average wages (which are deter-mined by the macrodemographie model) inevery simulation. Averaged over each worker'slifetime, earnings are roughly 45 percent ofeconomy-wide average wages for the lowearner, 100 percent for the medium earner,and 160 percent for the high earner.

The connection between the policy rules inthe budget and micromodels is also direct.Example workers pay payroll taxes or receivebenefits according to the rules in place eachyear. In addition, example workers contributeto individual accounts based on contributionrates and designated sources of contributions.For each year that the workers contribute,balances in the individual account and thenotional account are tracked. At age 65, thecurrent-law scheduled benefit, the single annu-ity purchased with the accrued individualaccount, and the offset annuity that thenotional account could '"purchase" are com-puted. The benefit with the individual accountis the current-law benefit plus the purchasedannuity minus the offset annuity. The expectedgain equals the purchased annuity minus theoffset annuity.

IV. SOCIAL SECURITY BENEFITUNCERTAINTY

This section analyzes how expected SocialSecurity benefits and uncertainty about thosebenefits would be affected by the introductionof individual accounts. The starting point forthe analysis is measuring uncertainty aboutbenefits under current law. It is important torecognize that future benefit levels are highlyvariable because real wage growth and infla-tion (which determine benefits) are themselveshighly variable. This current-law variabilityexplains why, even though the model suggeststhat the standard deviation of benefit gainsfrom individual accounts is generally largerthan the level of expected gains, participantswould not face an overwhelming increase inthe overall variability of real benefit levelsunder the introduction of an individualaccount.

The conclusion that overall benefit uncer-tainty does not explode when individualaccounts are added to the system is in partattributable to a focus on benefit levels. Indi-vidual accounts do substantially increase thevariability of benefit replacement rates because

8 CONTEMPORARY ECONOMIC POLICY

they partially sever the link between earningsand benefits in the existing system. Thus, tosome extent, conclusions about benefit vari-ability depend on the benefit outcome of inter-est. The benefit replacement rate measure alsoshows an important difference across earningsgroups; because high-earner participants havelower replacement rates under the currentsystem, their expected gains from individualaccounts (relative to current benefits) arehigher, but the relative variability in theirreplacement rates is also higher.

A. Benefit Uncertainty Under Current Law

One aspect of Social Security often over-looked in reform debates is that benefitsunder current law are highly uncertain. Fluc-tuations in real wage growth and inflation workthrough the existing benefit formula to causevariations in projected benefit outcomes. Thusintroducing individual accounts does not adduncertainty into a currently riskless system,rather it replaces some ofthe risk due to uncer-tain wage growth with risk from uncertainfinancial market returns. Before the variability

of outcomes under an individual account isconsidered, it is important to quantify theuncertainty that exists in the current system.

The solid line in Figure I shows expectedbenefits (in 2003 dollars) under current lawfor SSA exampie medium-earner workersclaiming in each of the next 75 years at age65. In addition, the estimated 5th and 95thpercentiles of benefits are shown as dottedlines. The variability of benefit levels is drivenby variability in wage growth and inflation thatchange individual earnings for the exampleworker and thus alter future benefits. Wagegrowth and inflation also affect the aggregateindexing formula for benefit computations.Since this aggregate indexing formula is onlyapplied to earnings up to age 60, the variabilitypicks up dramatically for example workerswho reach age 60 in 2003 or later, those claim-ing in 2008 or later. The uncertainty about ben-efit levels for future beneficiaries is sizeable.Although benefits are expected to roughly dou-ble over the 75-year projection period as wagescontinue to rise, the range between the 5th and95th percentiles spans 14 percent real growth inthe benefit level to over 300 percent.

FIGURE 1Benefit Variability Under Current Law: SSA Example Medium-Earner Worker Claiming at

65. 2003-2077

S50.000

S45.0O0-

S40.000 -

95th Perccntile

5th Percentilc

2tK)3 200K 2013 2018 202.? 202B 2033 2038 2043 2048 2053 2O5R 206.) 206S 2073

Yesr

Source: Authors' calculations based on 500 Monte Carlo simulatiotis. The medium-earner worker earns approximately100 percent of the average wage.

HARRIS, SABELHAUS, & SIMPSON: SS BENEFIT UNCERTAINTY

The conclusion that benefits in the currentsystem are uncertain holds true even if themetric is benefit replacement rates (annual ben-efits divided by the average of the last 10 yearsof earnings adjusted for inflation). Figure 2shows benefit replacement rates for the sameexample medium-earning workers claimingat age 65. The expected replacement rate fallsbetween 2003 and 2025 because scheduledincreases in the full retirement age will lowerbenefits (at age 65) relative to earnings. Afterthe full retirement age increases are phased in,the example medium-earning worker claimingat age 65 expects a replacement rate of approxi-mately 45 percent of the average of the last10 years of earnings with a 90 percent confi-dence interval spanning 42 to 49 percent of finalaverage earnings. The strong link betweenearnings and benefits limits the uncertainty inreplacement rates. Some uncertainty remainsunder current law because of how the replace-ment rate is defined here and how infiation istreated in the benefit computation. The replace-ment rate is benefits divided by the average of

the last 10 years of earnings adjusted only forinflation, where benefits are a linear functionof the average of the top 35 years of earningsindexed for inflation and real wage growth(see note 2). Also, when benefits are computed,only earnings up to age 60 are indexed for realwage growth and infiation. Thus real wagegrowth and infiation that occurs between age60 and 64 for these example workers will alterthe denominator but not the numerator.

Current-law benefit variability is alsoapparent across the three SSA example work-ers. Tables 2 and 3 are divided into three panelsof rows corresponding to the projection years2020, 2035, and 2075. Each panel includesbenefit outcomes for the example low-, med-ium-, and high-earning workers retiring atage 65 in each year. The first rows of eachpanel show the mean, standard deviation,and coefficient of variation for scheduledbenefits, in 2003 dollars (Table 2). or benefitreplacement rates (Table 3) under current law.

The variability of annual benefit outcomesis quite large relative to the level of annual

FIGURE 2Replacement Rate Variability Under Current Law: SSA Example Medium-Earner Worker

Claiming at 65, 2003-2077

60 •

50-

95th PercentileExpceted Replacement Rale

75 th Pereenllle

201)3 2008 2013 2018 2023 2028 2033 2038 2043

VMf

2048 2053 2058 2063 2068 2073

Source: Authors' calculations based on 500 Monte Carlo simulations. The replacement rate equals the annual benefitdivided by the average of inflation-adjusted earnings over ages 55-64. The medium-earner worker earns approximately 100percent of the average wage.


TABLE 2Benefit Uncertainty Under Current Law and a 2 Percent Carve-Out with Offset

2020Scheduled benefit(Standard deviation)

Coefficient of variationBenefit with individual account

(Standard deviation)CoeiTieient of variationExpected gain(Standard deviation)

Coefficient of variationOdds of negative gain

2035Scheduled benefit

(Standard deviation)

Coefficient of variationBenefit witb individual account

(Standard deviation)Coefficient of variationExpected gain



2075Scheduled benefit(Standard deviation)

Coefficient of variationBenefit with individual account

(Standard deviation)Coefficient of variation "Expeeted gain



Scaled Low Earner

$9,264

(1.092)0.12

$9,297

(1,153)0.12

$33(183)

5.5550%

- - •

$10,273(1,924)

0.19

$10,611(2.175)

0.20

$339(733)2.1638%

$15,658(4,861)

0.31$17,007

(6,053)

0.36$U30(2,323)

1.7228%

Example Worker Benefits at Age 65

Scaled Medium Earner

$15,311(1,803)

0.12$15,385(1,947)

0.13S73

(407)

5.58' 50%

, ,' $16,976(3.176)

0.19

$17,728(3.814)

0.22

$752(1,629)

2.17

38%

$25,868(8,027)

0.31$28,876

(10.920)0.38

$3,008(5.177)

: 1.72

28%

Scaled High Earner

$20,220

(2,383)0.12

520,337(2,624)

0.13$118

(651)5.5250%

$22,416

(4,196)0.19

$23,620(5.312)

0.22$1,204(2,606)

2.1638%

$34,155(10.603)

0.31$38,969

(15,500)

0.40$4,814

(8,285)1.7228%

Source: Authors' calculations based on 500 Monte Carlo simulations. Example workers are assumed to contribute2 percent of payroll starting in 2004 into an individual account, investing 50*%! in equities with a 6.5% mean return, 30%in corporate bonds with a 3.5% mean return, 20% in government bonds with a .^.0% mean return, and 30 basis points inadministrative cost. At retirement, the annuity purchased with the individual account is ofTset by a reduction in thescheduled benefit equal to the notional balance accrued at the government bond rate plus 50 basis points. All numbersare in 2003 dollars.

benefits. The coefficient of variation (standarddeviation divided by the level of benefits) is 0.12for each example worker claiming at age 65 in2020, despite the fact that most of their earn-ings histories are already known with certainty.For retirees in the distant future, the coefficientof variation rises to 0.31. The variability ofbenefit replacement rates (Table 3) does notgrow over time because the uncertainty causedby wage growth and inflation affects both

the numerator and denominator. Still, thevariability of benefit replacement rates sug-gests uncertainty about benefit outcomes forany given cohort of future retirees does exist.

B. Benefit Uncertainty Under a 2 PercentCarve-Out with a Simple Benefit Offset

Given this background of uncertainty undercurrent law, the next step is to consider how

HARRIS, SABELHAUS. & SIMPSON: SS BENEFIT UNCERTAINTY 11

TABLE 3Uncertainty in Replacement Rates Under Current Law and a 2 Percent

Carve-Out with Offset

2020

Replacement rate with scheduled benefit(Standard deviation)CoelFieient of variationReplacement rate with individual account(Standard deviation)Coefficient of variation

Expeeted gain(Standard deviation)Coelllcient of Variation

2035

Replacement rate with scheduled benefit(Standard deviation)Coefficient of variation

Replacement rate with individtial accotmt(Standard deviation)

Coefficient of variation r^Expected gain(Standard deviation)

Coefficient of variation2075

Replacement rate with scheduled benefit(Standard deviation)

Coefficient of variationReplacement rate with individual account

(Standard deviation)Coefficient of variationExpected gain(Standard deviation)

Coefiieient of variation

Example Worker Replacement Rates at Age 65

Scaled LowEarner

63.9

(3.0)0.05

64.1(3.2)

0.050.2

(1-2)6.00

60.4(2.9)0.05

62.3

(5.1)0.081.9

(4.2)

2.21

60.3(2.9)

0.0565.1(8.4)

0.134.8

(7.8)1.63

Scaled MediumEamn*

47.5

(2^)0.05

47.7

(2.5)0.050.2

(1.2)6.00

44.9

(2.1)0.05

46.8(4.7)0.10

L9(4.2)

2.21

44.8(2.2)0.05

49.6(8.2)0.174.8

(7.8)1 .(l^

Scaled HighEarner

39.2

(1.8)0.05

39.4(2.2)0.06

0.2

(1.2)6.00

37.0

(1.8)0.05

38.9(4.5)0.121.9

(4.2)2.21

37.0(1.8)

0.05

41.8(8.1)0.194.8

(7.8)1.63

Source: Authors' calculations based on 500 Monte Carlo simulations. Example workers are assumed to contribute2 pereent of payroll starting in 2004 into an individual account, investing 50"/.i in equities with a 6.5% mean return, 30"^in corporate bonds with a 3.5% mean retum, 20'^ in government bonds with a 3.0'>ii mean return, and 30 basis points inadministrative cost. Replacement rates equal the annual benefit at claim divided by the average of infiation-adjustedannual earnings over ages 55 to 64.

that variability would change under a simpleindividual account alternative. The second andthird set of rows in each panel of Table 2 showthe effect on individual benefits for the exampleworkers under a 2 percent carve-out with asimple benefit offset. Table 3 shows the sameexperiment using benefit repiacement rates asthe outcome of interest.

The individual account alternative shownin Tables 2 and 3 is structured to replicate

the CSSS plan I. Example workers age 55and younger in 2002 contribute 2 percent oftheir current-law payroll tax to an individualaccount starting in 2004. The assumed annualexpected return for the individual investmentaccount is 4.6 percent, reflecting a portfolioassumption of 50 percent in equities with a6.5 percent expected return, 30 percent incorporate bonds with a 3.5 percent expectedreturn, and 20 percent in govemment bonds

12 CONTEMPORARY ECONOMIC POUCY

with a 3.0 percent expected return, minus a 30basis point administrative cost. For simplicity,it is assumed the individual account is balancedeach year to maintain this allocation. Thenotional account is also tracked with a 2 per-cent contribution each year and annualexpected return of the govemment bond rateplus 50 basis points.

Al retirement, the annual current-lawscheduled benefit for each example worker iscomputed along with the annuity values ofthe individual account and the notionalaccount. The annuity values are computed asa single-life, inflation-indexed annuity usingunisex life tables where the sum of expectedpayments equals the balance of the individualor notional account, given the age of theworker (and his future probability of beingalive), and the effective interest rate {equal tothe long-term real interest rate, and for theindividual account annuity, minus an assumedadministrative cost of 30 basis points).^ Thebenefit with the individual account equalsthe scheduled benefit minus the notionalannuity plus the individual account annuity.That is.

Annual Income= Scheduled benefit - Notional annuity

+ Individual account annuity.

Thus the expected gain equals the indiv-idual account annuity minus the notionalannuity.

For example, a medium earner participatingin the individual account during a full workingcareer is expected to have an individual accountbalance of $120,000 and a notional accountbalance of $94,000 upon reaching age 65 (alldollar amounts are presented in 2003 dollars).The scheduled annual benefit for this workerwould be $24,700. The individual accountbalance could purchase a real annuity of$7,700.The benefit offset iscomputed as the real

7. The formula for the annuity calculation is thefollowing:

Individual account balance

= > , ,„ Annuity payment^^Acclaim agf, 100 ^ f J

* P(alive ai A\a/ive at Claim age)

* [1/(1 + Effeclive rale)]"-'^'''^'"'.

annuity value ofthe notional account balance,and would be $6,500. The actual benefit paidby the Social Security system would be thedifference ofthe scheduled benefit and the off-set, $24,700 - $6,500 = $ 18.200. The worker'sfull retirement benefit would include the actualbenefit paid by Social Security plus the indivi-dual account annuity, $18,200+ $7,700 =$25,900. The gain from the individual accountis the increase above the scheduled benefit.$25.900-$24,700 = $1,200, or the differencebetween the individual account and thenotional account annuities. $7,700 - $6,500 =$1,200.

The first result that stands out in Tables 2and 3 is that expected gains for the individualaccounts are positive for each type of worker inevery year; however, the gains are not statisti-cally different from zero given the magnitudeofthe standard deviation of those gains. Overtime, the ratio ofthe standard deviation to theexpected gain in benefit levels-the coefficientof variation—falls from more then five to lessthan two (Table 2). This decline reflects theadditional years workers are able to contributeto the individual account. Since contributionsto the accounts cannot start until 2004. theworkers claiming in 2020 are only able to con-tribute to an individual account for 15 years.However, the uncertainty surrounding benefitgains drops by more than half for workersclaiming in 2035. With 30 years to contributeto individual accounts, workers have moreyears to average across good and bad marketreturns.

Another measure ofthe potential for gainsor losses under an individual account is theodds that the individual will have a negativegain, that is. where the benefit with the indivi-dual account is actually less than the scheduledbenefit. In 2020. 50 percent of the simulationsreturn a negative gain; however, gains andlosses at this point arc small given smallindividtial account balances. The odds dropto 38 percent by 2035. as the additional yearsfor participating in the individual accountand the benefits of compounding reduce theshare of bad outcomes for future retirees.By 2075, the share of negative outcomes is28 percent, which is still a significant probabil-ity that full-career participants will end upwith a smaller benefit than what is promisedunder current law. It is important to keep inmind that the strong possibility of negative out-comes in this particular experiment is directly

HARRIS, SABELHAUS, & SIMPSON: SS BENEFrr UNCERTAINTY 13

attributable to the specified benefit ofTsetmechanism. In order to be better off with anindividual account, participants must do morethan receive positive investment returns, theymust receive returns in excess of the govern-ment bond rate plus 50 basis points andthe costs of account administration andannuitization.

Figures 3 through 5 show expected gainsin Social Security benefits along with the 5thand 95th percentiles for each cohort ofthe threeSSA example workers over the next 75 years.Although the odds of negative gains seen inTable 2 are the same across the three types ofearners, these figures show that the magnitudesof the potential gains and losses are quitedifferent. This is not surprising given themuch higher contributions that high earnersmake relative to low earners in this simpleplan with no contribution cap.

Even though the variability of gains fromthe individual accounts is large. Table 2shows that the overall variability of postreformbenefits (the reduced scheduled benefit plusthe annuity from the individual account) is

not dramatically larger than the variability ofthe scheduled benefit itself. The standarddeviations are about the same in the earlyyears when individual account balances aresmall; the coefficient of variation is onlyslightly higher for the medium and highearners. By 2075. the coefficient of variationof the benefit with the individual account ishigher for each of the types of workers,although the magnitude of the increase is notlarge, from 16 percent to 33 percent.

The result that individual accounts onlyincrease uncertainty about future Social Secur-ity outcomes by no more than one-third is afunction of looking at benefit levels. The con-clusion changes when looking at benefit repla-cement rates. Table 3 shows that the coefficientof variation for the benefit replacement ratewith the individual account more than doublesfor workers claiming in 2075. Again, the starkincrease in uncertainty due to the introductionof individual accounts reflects the partial sever-ing of the link between earnings and benefitsthat reduced uncertainty about replacementrates under current law.

FIGURE 3Variability of Expected Gains from 2 Percent Carve-Out with Offset: SSA Example

Low-Earner Worker Claiming at 65. 2003-2077

825,000

S20.000-

S 15.000 •

S 10.000

S5,000-

SO-

-S5.000

95th Perccniile

Expecicd Gain

5lh Pcrcentile

2003 2IJI3 2018 2023 2028 2033 2043 204B 2053 2O5H 2063 2O6K 2073

Vemr

Source: Aulhors' calculations based on 500 Monle Carlo simulations. The expected gain equals the annuity purchasedwith the individual account minus the national annuity, or the change in the worker's benefit with the individual account andoffset relative to current law. The low-earner worker earns approximately 45 percent of the average wage.



Medium-Earner Worker Claiming at 65, 2003-2077

S25.000

$20,000-

515.000

S10.00(t -

S5,000-

-S5.001)

95th Pcrcentile

Gain

Sth Percentile

2003 2008 2013 2018 2023 2028 2033 2038 204J 2048 2053 20S8 2063 206K 207.1

Year

Source: Authors' calculations based on 500 Monte Carlo simulations. The expected gain equals the annuity purchasedwith the individual account minus the notional annuity, or the change in the worker's benefit with the individual account andoffset relative to current law. The medium-earner worker earns approximately 100 percent ofthe average wage.


High-Earner Worker Claiming at 65, 2003 2077

S25.OO0

$20,000 -

s sio.o

SO-

•SS,000

• * .

95th Percentiie

' 4 '

Expected Gain

\ ^ ^ —

5jh Percentile

2003 2008 2013 2018 2023 2028 2033 2038 2043 2048 2053 2058 2063 2068 2073

Ye«r

Source: Authors' calculations based on 500 Monte Carlo simulations. The expected gain equals the annuity purchasedwith the individual account minus the notional annuity, or the change in the worker's benefit with the individual account andofFset relative to current law. The high-earner worker earns approximately 160 percent ofthe average wage.

HARRIS, SABELHAUS, & SIMPSON; SS BENEFIT UNCERTAINTY

There is also an important distributionaleffect on risk and returns. When consideringbenefit levels (Table 2). the relative uncertaintyintroduced with individual accounts is similaracross the low, medium, and high earners.However, a different story emerges when repla-cement rates are considered in Table 3. Sincethe current-law benefit formula is progressive,that is, replacement rates fall as earningsrise, the 2 percent carve-out subjects a higherfraction of the existing benefit to investmentrisk for high-earner participants. The increasein the replacement rate coefficient of variationbetween the scheduled benefit and the benefitwith the individual account is much largeras earnings increase. For example, in 2075 thelow-earner coetTicient of variation with theindividual account is more than 2.5 times largerthan for the scheduled benefit, while the high-earner coefficient of variation is almost 4 timeslarger. The introduction of individual accountsinteracts with the progressive structure ofthecurrent system and thus makes benefits of highearners more uncertain. However, low earnersmay still be more averse to increasing realbenefit variability because their absolutebenefit levels are lower.

A final question to consider is how thechange in expected benefits and benefit varia-bility under the refbrm plans might be expectedto affect individual well-being. In particular,Smetters (2001) has criticized simply relyingon estimating ranges for potential outcomes,arguing that a Black and Scholes (1973) option-pricing approach may capture the utility impli-cations of severe negative outcomes, and isthus more appropriate for valuing the changein risk and returns." In their article, Feldsteinand Rangulova (2001) complemented the esti-mated ranges for benefit outcomes with explicitutility valuation of the alternative policy, whichaddresses this question directly. They foundthat, although the exact value depends on theassumed coefficient of relative risk aversion,the general conclusion that the change inrisk is not particularly onerous does hold upwell. The same conclusion applies to the esti-mates here, and perhaps even more so, becauseour stochastic benchmark is not simply afixed scheduled benefit as in Feldstein andRangulova (2001).

8. See also Lachance et al. (2003) for an applicationof this approach to the valuation of defined contributionversus defmed benefit income streams.

C Comparing Stochastic Results to SSALow- and High- Yield Scenarios

Similar to the low- and high-cost scenariosused in the annual OASDI Trustees Report(2003), the SSA's analysis of the CSSS plans(2002) includes a low-and high-yield assump-tion for the individual account to provide somebounds on their estimated outcomes. For a lowyield, the SSA assumes a conservative indivi-dual account portfolio of 100 percent govem-ment bonds (or similarly, a lower overallportfolio yield of 2.7 pereent, in contrast tothe intermediate scenario yield of 4.6 percent).For a high yield, the SSA assumes a more riskyindividual account portfolio of 60 percentequities. 24 percent corporate bonds, and16 percent government bonds (or similarly, ahigher overall portfolio yield of 4.92 percent).

Under these low- and high-yield assump-tions, the SSA projects a range of expectedannual benefits between 95 percent and 101pereent of the benefit for the medium earnerin 2032 under the intermediate portfolioassumptions. This is a much narrower rangethan that suggested by the stochastic resultspresented here. For the medium earner in2032, one standard deviation around theexpected scheduled benefit gives a range of82 percent to 118 percent of the expeetedbenefit, while one standard deviation aroundthe benefit with the individual account givesa slightly broader range of 80 percent to120 percent. These results suggest that thelow- and high-yield scenarios used by theSSA do not capture a reasonable range ofuncertainty for the system with individualaccounts, due mostly to the fact that theirmeasurements do not capture the uncertaintyof the system under current law.

V. CONCLUSION

Adding a 2 percent individual accountcarve-out to the existing Social Security systemwould increase the expected benefits for parti-cipants under reasonable assumptions aboutexpected asset returns, but those gains—atleast under the simple offset method usedhere—^would be highly uncertain. However,the extent to which these uncertain returnsare deemed to affect worker's retirementsecurity is driven by the choice oi^ outcomemeasure. The introduction of a simple indivi-dual account would increase the overall var-iability of outcomes as measured by benefit


replacement rates far more than as measuredby benefit levels.

The introduction of an individual accountwould only increase the coefficient of variationof benefit levels by 16 percent to 33 percentbecause uncertainty about real wage growthand inflation already cause significant uncer-tainty about future benefits under current law.The additional uncertainty of asset returnsadds only a marginal amount of risk to analready risky benefit. The standard deviationof a worker's benefit in 2075 is already 31percent of his benefit; adding the individualaccount raises it only by between 5 and 9percentage points, to a maximum of 40 percentfor a high-earning worker.

The variability of benefit replacement rates(annual benefits divided by the average ofthelast 10 years of earnings) is much more sensitiveto the introduction of individual accountsbecause the connection between earnings andbenefits under existing rules would be partiallysevered under the individual account alterna-tive. The introduction of an individual accountwould increase the coefficient of variation ofreplacement rates by 260 percent to 380 per-cent. Using replacement rates to analyzeoutcomes also highlights other aspects ofindividual accounts. For example, becausehigh-earner participants have lower benefitreplacement rates in the existing system, theadded variance for high-earner participantsrelative to low-earner participants is muchlarger (46 percent greater) than when measuredin benefit levels (14 percent greater).

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