The Congressional Budget Office (CBO) constructed a model to simulate the mechanics of retirement plans over the long term. The model relies mostly on 1997 tax data--the latest year for which complete data were available--but uses other data where necessary. The model consists of two modules: one for individual retirement accounts (IRAs) and defined-contribution plans, and the other for defined-benefit plans.
 

Data Sources

The model relies primarily on "microdata," that is, information on each individual respondent rather than aggregate amounts. CBO aggregated those microdata into one-year age/sex cohorts.

Whenever possible, CBO used as its source of microdata a stratified random sample of approximately 100,000 individual income tax returns for the year 1997 and their associated information returns provided by the Statistics of Income Division (SOI) of the Internal Revenue Service (IRS). Data from the following tax forms proved particularly useful:

• Forms 1040, 1040A, and 1040EZ, the basic individual income tax return filed by taxpayers: the data from this form were used as a check on the data from the information returns. Also, the form is the only source of data on deductible IRA contributions.
  
  
• Form W-2, an information return sent by employers to employees that reports primarily their taxable wages and the taxes withheld: it is also the only source of data on amounts of deferred compensation (usually 401(k) contributions) and taxpayers' coverage by an employment-based retirement plan.
  
  
• Form 5498, an information return sent by IRA trustees to IRA owners that reports their annual contributions (whether or not they are deductible), the rollovers received, and the end-of-year balances.⁽¹⁾
  
  
• Form 1099-R, an information return sent by IRA trustees or administrators of employment-based retirement plans to recipients of distributions from those plans: it reports the total amount of the distributions, the taxable portion thereof, and the sources of those distributions as either IRAs or an employment-based retirement plan. It does not necessarily indicate whether the employment-based plans are defined-benefit or defined-contribution plans, but the "plan name" field occasionally provides enough information to distinguish between the two types.⁽²⁾

CBO also used a supplemental file provided by SOI containing the age and sex of all taxpayers in a sample between 1987 and 2000.

For data not available from SOI, CBO relied on the 1998 Survey of Consumer Finances (SCF), conducted by the Federal Reserve Board. With the SCF, the Federal Reserve Board collects more complete data on contributions to and balances of retirement plans than the IRS does, but the survey is based on a small sample (of fewer than 7,000 households) and depends largely on the memories and recordkeeping practices of voluntary participants. Nevertheless, the SCF data are considered to be high-quality and are widely used in studies of the distribution of wealth in the United States. For CBO's model, the survey was the source of data on balances in 401(k) plans and provided the information necessary to impute employers' contributions to defined-contribution plans.⁽³⁾

Defined-Contribution Plans and IRAs

The basic structure of the module to project withdrawals from defined-contribution plans and IRAs has been set forth by Sabelhaus.⁽⁴⁾ His model covered IRAs only, but the principles underlying a combined model of IRAs and defined-contribution plans are the same. The module used in this analysis expands upon Sabelhaus's work by utilizing more robust data whenever they are available and by fully integrating information from the two types of plans and from defined-benefit plans.

The starting points for the module are age/sex distributions of the adult population and the assets in defined-contribution plans and IRAs for a base year--in this case, 1997. The population distribution came from the Social Security Administration (SSA), the distribution of IRA assets came from Form 5498 and SOI's age/sex file, and the distribution of assets in defined-contribution plans came from the SCF.⁽⁵⁾

The function of the module is to generate similar distributions for each future year and in the process generate estimates of tax-deferred contributions, investment income, and taxable withdrawals. To accomplish that goal, CBO replaced the population distribution for each year with SSA's middle-series projection. Then, CBO modeled the accumulation of assets in IRAs and defined-contribution plans in each subsequent year in six steps:

• Adding new contributions,
  
  
• Adding internal rollovers received (by IRAs from defined-contribution plans) and subtracting those paid out (by defined-contribution plans to IRAs),
  
  
• Adding external rollovers received (from defined-benefit plans),
  
  
• Adding the return on investments,
  
  
• Subtracting nonrollover withdrawals, and
  
  
• Redistributing assets of deceased participants among beneficiaries.

After executing those steps, CBO shifted the asset balance up to the next age group and repeated the steps for another year (see Box A-1).
 

Box A-1. Illustration of the Defined-Contribution Module for a Sample Cohort Consider the cohort of 915,128 females born in 1937. According to the data, women in that cohort held $13,553.6 million in assets in defined-contribution plans at the end of 1997 when they were 60 (see line 1, below). To that amount, the model adds contributions in 1998 (line 2), which are calculated by increasing the average contribution of 61-year olds in 1997 of $3,245 by 6.25 percent to account for wage growth and assigning that amount to the 13 percent of the cohort who actively participated in such plans. The model also adds rollovers from defined-benefit plans (line 3) and assets from deceased parents and husbands (line 5). Investment income accrues on the original balance plus half of contributions and other income (under the assumption that they are deposited regularly throughout the year) at a rate of approximately 14 percent (line 4). The model then assigns approximately 6 percent of assets (after the full year's income is added) to be rolled over to an IRA (line 6). Of the remaining balance, the model assigns just over 2 percent to be withdrawn (line 7). That leaves a balance of $14,918.7 million (line 8) with which to start the process over in 1999.         Accumulation of Assets Held in Defined-Contribution Plans in 1998 by Females Born in 1937 (Millions of Dollars)     Key Parameters Amount (1) Beginning-of-Year Assets   $13,553.6   Plus     (2) Contributions 13% of participants x $3,450 409.1 (3) Rollovers from Defined-Benefit Plans   18.2 (4) Investment Income 14% of balance after half year's contributions and other income (reflecting rate of return in 1998) 1,928.9 (5) Net Redistributions Due to Deaths   340.4   Minus     (6) Rollovers to IRAs 6% of balance after full year's income 1,019.7 (7) Withdrawals 2% of balance after full year's income and rollovers 11.8 (8) End-of-Year Assets   14,918.7

Contributions. Data on contributions to IRAs are available from Form 5498, and the deductible portion can be identified on Form 1040. Data on employees' contributions to defined-contribution plans are available from Form W-2. CBO assumed that any contributions not associated with 401(k) or 403(b) plans were made after tax. CBO imputed employers' contributions on the basis of the ratio of employers' to employees' contributions in the SCF. Using those data, CBO calculated the following parameters by age/sex class: the percentage of the population making contributions, the average contribution amount, and the deductible share of the contributions. In the model, the average contribution amount increases over time at the same rate as the growth in average wages, and contributions are added to assets each year.

Internal Rollovers. Rollovers from one IRA to another do not affect the accumulation of IRA assets, so the model ignores them. However, it keeps track of rollovers from defined-contribution plans to IRAs so that different rates of return can be applied as appropriate. Data on direct rollovers (that is, those that go directly from qualified plans to IRAs) are available from Form 1099-R. Data on indirect rollovers (that is, those paid by qualified plans to participants and then later deposited in IRAs) can be inferred from the difference between total rollovers received (as reported on Form 5498) and direct rollovers. CBO used those data to calculate the percentage of assets in defined-contribution plans rolled over to IRAs.⁽⁶⁾

External Rollovers. CBO calculated rollovers from defined-benefit plans as part of the defined-benefit module (described below) and split the amounts generated between the assets held in both IRAs and defined-contribution plans in each year.

Return on Investments. In the model, the rate of return on investments is the only major parameter that does not vary by age. CBO expressed nominal rates of return as markups above nominal GDP growth, with the defaults set at 5.0 percent for stocks and 1.0 percent for bonds.⁽⁷⁾ Under CBO's assumptions, IRA portfolios consisted of 78 percent stocks and 22 percent bonds, and portfolios for defined-contribution plans, 56 percent stocks and 44 percent bonds.⁽⁸⁾ To account for management fees, CBO subtracted 50 basis points. The weighted average rate of return in excess of GDP growth was thus 3.62 percent for IRAs and 2.74 percent for defined-contribution plans. see Table A-1 shows the actual rates of return used at 15-year intervals.

Nonrollover Withdrawals. Data on withdrawals that were not rolled over and the taxable portion thereof are available from Form 1099-R. CBO used those data to calculate the percentage of assets withdrawn and the percentage of those withdrawals that were taxable by age/sex class.⁽⁹⁾ CBO then subtracted the withdrawals from assets in each year.

Redistribution of Assets at Death. For each year, CBO applied a survival rate and then redistributed the assets held by people assumed to have died. On the basis of 1997 data, CBO assumed that a certain percentage of people in each age/sex class who died were married; their assets were redistributed to members of the opposite sex on the basis of the average age difference between spouses: three years younger if the decedent was male or three years older if female. The assets attributable to unmarried decedents were redistributed on the basis of the average age difference between parents and children: 29 years younger if the decedent was male or 26 years younger if female. The redistributed assets of single decedents were then subjected to mandatory withdrawal and taxation over a five-year period.

Defined-Benefit Plans

The nature of traditional defined-benefit plans makes it unnecessary to link benefits to asset levels; benefits are instead set by formula. Instead of assets, the starting point of the defined-benefit module is a distribution of plan participants, both those accumulating the right to future benefits during their careers ("active") and those receiving benefits after their retirement ("retired"). The model maintains the average benefits of participants retired as of 1997 until they die (indexing, when appropriate, for inflation), then identifies new retirees in each year and assigns them an appropriate average benefit, which they likewise receive until they die (see Box A-2). Asset levels are, however, needed to estimate investment income and contributions. Beginning with 1997 assets, the model estimates investment income on the basis of the same rates of return on stocks and bonds used in the defined-contribution/IRA module. Then, it estimates the level of contributions in each year that would be required to fully fund the benefits previously calculated. Three different types of plans are modeled separately: state and local government plans, private qualified plans, and nonqualified annuities.
 

Box A-2. Illustration of the Defined-Benefit Module for a Sample Cohort Consider the cohort of males born in 1934. According to the data, 288,900 men in that cohort participated in a private defined-benefit plan in 1997 when they were 63 years old. Of those, 24 percent (or 67,800) were active participants; the remaining 76 percent (or 221,100) were retirees receiving benefits averaging $10,000. The total amount of benefits received in that year, therefore, was $2.211 billion. According to population growth rates from the Social Security Administration, the total number of 64-year-old participants in 1998 would have been 287,300--an decrease of 0.6 percent. For that age group, however, the model assumes that a higher percentage of participants, or 80 percent, received benefits than was the case for 63-year-olds. That assumption yields 58,000 64-year-old males who were active participants and 229,300 who were retired and receiving benefits from a private defined-benefit plan in 1998. However, only 98.14 percent of 63-year-old recipients in 1997 would have survived to 1998. Hence, the number of original retirees (that is, those receiving an average benefit of $10,000) would be 217,000. The remaining 12,300 recipients would be new retirees who would receive higher benefits. That benefit is calculated by multiplying the average benefit received by 64-year-olds in 1998 ($9,787) by the change in five-year average wages between the year in which the typical recipient in 1997 retired and 1998 (1.049) for a total of $10,270. All together, the benefits received in 1998 would be $2.296 billion.               Benefits from Private Defined-Benefit Plans Received by Males Born in 1934     Original Retirees New Retirees Total Benefits (Billions of dollars)   Workers (Thousands) Number (Thousands) Average Benefit Number (Thousands) Average Benefit 1997 67.8 221.1 $10,000 n.a. n.a. $2.211 1998 58.0 217.0 $10,000 12.3 $10,270 $2.296

Active Participants. Active participants in qualified plans in the base year can be identified using Form W-2. The model keeps track of the number of active participants in each age/sex class primarily so that it can "retire" some of them as they age and thereby know when to begin counting the distributions they receive. Also, the model simulates death prior to retirement, as well as the entry of some older workers into the labor force.

CBO applied employment growth rates to each class of active participants to get the size of the class in the next year.⁽¹⁰⁾ CBO then applied a survival rate to the active participants in each age/sex class and if the size of a class exceeded the number of survivors from the previous year, attributed the difference to new participants.

Retired Participants. The model tracks not just the number of retired participants by age/sex class but also keeps track of when they retired because that affects the size of their pension. CBO identified the retired participants in the base year from Form 1099-R and applied population growth rates and survival rates, just as it did for active participants. Then, CBO adjusted the number of retired participants in each age/sex class to maintain the same ratio of retired participants to total participants in that class over time. Because the percentage retired increases with age, that adjustment typically involved reclassifying as "retired" some participants who had been active in the previous year.

Distribution Amounts. For people who were retired in the base year, CBO assigned the same average taxable distribution (fully or partially indexed for inflation if they were in a government plan) until they died (at no later than age 89). For people who retired in later years, it assigned a higher average pension, based on the growth in average wages between the year in which the average recipient in 1997 retired (estimated to be 1990) and the year the later retirees left the workforce.⁽¹¹⁾

CBO calculated amounts rolled over to IRAs and 401(k)s (and used by that module as "external rollovers") in each year as a percentage of taxable distributions, after initially estimating those percentages by age/sex class in the base year.

Contributions and Investment Earnings. Although they are not needed to project taxable distributions, deductible contributions and tax-exempt investment earnings both affect revenues and therefore must be projected. The fundamental principle followed in projecting those amounts was to ensure that all of the projected benefits would be fully funded. Hence, the model estimates the additional liability incurred by plans in each year and sets the sum of contributions and investment income equal to that amount. The most straightforward method of estimating the liability increment for a particular year is to calculate the lifetime benefits that would be collected by participants projected to retire in that year.⁽¹²⁾ All benefits to be paid through 2078 were available from the model's projections of distributions. For people whose retirement would extend beyond 2078, benefits were projected to continue at the same level (partially adjusted for inflation in the case of participants in state and local government plans) until age 89.

CBO estimated investment income as a certain percentage of total assets depending on the typical split between stocks and bonds for each type of plan. In the model, stocks constitute 64 percent of the assets in private plans, 38 percent of the assets in state and local plans, and 20 percent of the assets in nonqualified annuities.⁽¹³⁾ Using the markups over GDP growth and management fees described above for defined-contribution plans, CBO then determined these weighted average rates of return in excess of GDP growth: for private plans, 3.06 percentage points; for state and local plans, 2.02 percentage points; and for nonqualified annuities, 1.30 percentage points. Table A-2 shows the actual rates of return used at 15-year intervals.

For all types of plans, CBO generally calculated contributions as the difference between the annual liability increment and total investment income. For 2004 through 2013, however, the model assumes additional contributions equal to 10 percent of the amount by which plans were underfunded in 2003. Alternative time periods for the restoration of full funding are presented in the body of this paper and Appendix B.

Federally Administered Plans. The assumption that employment growth in each age/sex class is proportional to population growth in that class works well for private-sector and state and local plans. Using that assumption for the federal government, however, would greatly overstate the growth in federal employment and would also skew the age distribution--particularly for the military. Rather than construct a separate set of age/sex-specific growth rates for federally administered plans, CBO based its projections for those plans on ones provided by the administering agencies.⁽¹⁴⁾ Each agency has its own long-term forecasting model with at least a 75-year horizon and uses its own assumptions concerning employment levels, average wage growth, rates of return, and inflation. CBO retained the agencies' assumptions for employment, average wage growth, and rates of return but adjusted their projections to be consistent with benefits indexed to CBO's forecast of the consumer price index rather than the agencies' forecasts.