A Stochastic Model of the Long-Range Financial Status of the OASDI Program—September 2004

III. DOCUMENTATION OF THE COMPUTER PROGRAM

B. MODULES

All of the modules, with the exception of the Assumptions and Summary Results Modules, are adapted from the deterministic computer model used to prepare the 2004 Trustees Report. The modules are written so that the set of nonstochastic inputs required to begin the projections is identical with the input assumptions used when running the deterministic model under the TR04II. Moreover, the mean value for each stochastic variable is assumed to be the same as the value assumed for the variable under the TR04II.

1. Assumptions

The Assumptions Module contains 54 equations, one for each stochastic variable. These equations are described in detail in chapter II, and include ones for the total fertility rate, rates of mortality improvement (21 male age groups and 21 female age groups), immigration level, emigration level, net other immigration level, unemployment rate, inflation rate, real interest rate, percent change in real average covered wages, disability incidence rates (male and female), and disability recovery rates (male and female).

The equations are used to set the annual values for the stochastic variables. In any particular year, the value for a stochastic variable is determined, in part, by the equation's error term. If the error term for an equation is not dependent on the error terms of other equations, then a random number is drawn for each year from a normal distribution with mean zero and standard deviation equal to the estimated standard error for the equation. If the error term for an equation is dependent on the error terms of other equations, then a Cholesky decomposition is used to assign the appropriate level of covariance. See appendix B for more details on this process.

The final step of this module is to use the error terms to calculate the results of each equation. Chapter II provides more details on specific equations.

For the mortality equations, an additional step decomposes the annual rates of decrease in the central death rates by age group into single years of age.

2. Population

The Population Module projects the Social Security area population by sex, single year of age, and marital status. The components of change—fertility, mortality, and immigration—are applied each year throughout the projection period based on levels generated in the Assumptions Module. The population is grouped by marital status using the relative proportions for each age-sex group projected under the TR04II.

The population is projected by starting with the beginning of the year population, adding births and immigration, and subtracting deaths and emigration. The total fertility rate is distributed among women of childbearing age using the relative proportions of age-specific birth rates for each year from the TR04II. The age-specific birth rates are then applied to the midyear population to calculate the number of births. For the mortality projection, central death rates are computed by applying the rates of decrease in the single year of age central death rates to the previous year's central death rates. Death probabilities are derived from the central death rates by assuming a uniform distribution of deaths for each age. The death probabilities are then applied to the beginning of the year population to calculate the number of deaths for each single year of age and sex group. For each type of immigration, the annual levels are distributed among the age-sex groups by using the relative proportions from the TR04II. The resulting population is then distributed by marital status using the relative martial proportions for each age-sex group projected in the TR04II.

3. Economics

The Economics Module receives data from the Assumptions, Population, and DIB Modules. The Assumptions Module passes civilian unemployment, and inflation rates, along with the growth rate in the real average covered wage. The Population Module passes the age-sex levels of the Social Security area population and their life expectancies. The DIB Module passes age-sex levels of disabled-worker beneficiaries in current-payment status.

For employment-related variables, the module projects various measures for the total U.S. economy and then converts them to OASDI covered concepts. For the earnings variables, the module initially projects OASDI covered wages then converts them to a U.S. economy-wide concept. The module estimates levels for most key variables by projecting deviations from values produced for the TR04II.

Labor Force Participation

Future civilian labor force participation rates by age and sex are influenced by projected disability prevalence ratios, business cycles, life expectancies, and Social Security area population. For a given year, the civilian labor force is summed from the products of the age-sex civilian labor force participation rates and civilian noninstitutionalized populations. For each age-sex group, the civilian noninstitutionalized population is the product of the Social Security area population and the ratio of the noninstitutional to Social Security area population from the TR04II.

Total Employment

The civilian unemployment rates by age and sex are projected by distributing the stochastically projected aggregate rate to its age-sex components. Projected total economy-wide employment is summed from age-sex components derived from the corresponding components of the civilian labor force and unemployment rates. The concept of total economy-wide employment is consistent with the Bureau of Labor Statistics' Current Population Survey, and thus represents an "average" level of employment for a particular year. The projected total economy-wide employment by age and sex is then used to estimate the number of workers with employment at-any-time during the year, a concept closer to OASDI covered employment. Total at-any-time employment by age and sex is influenced by the relative number of illegal immigrants in the workforce and by the proportion of the population employed.

Covered Employment

Total OASDI covered employment by age and sex is projected by removing noncovered workers, including those assumed illegal, from the total at-any-time employment. Total OASDI covered employment is then distributed to those with wages and to those with self-employed net income only.

Covered Wages

Total OASDI covered wages are the product of the number of covered wage workers and their average nominal covered wage. The average nominal covered wage is determined using the annual inflation rate and the real average OASDI covered wage from the Assumptions Module. Total U.S. economy-wide wages are projected as a ratio to OASDI covered wages, adjusted for relative differences in illegal immigration. Total compensation for wage workers, total and covered self-employed income, taxable wages, and taxable self-employed net income are all derived from assumed relationships from the TR04II. Multi-employer refund wages are projected as a ratio to OASDI covered wages, adjusted for relative differences in the unemployment rate.

Taxable Payroll, Average Wage Index, and COLA

The OASDI taxable payroll is the sum of taxable wages and self-employed income, less one-half of multi-employer refund wages. The average wage index is determined using the annual growth rate in the economy-wide average wage, defined as the ratio of total U.S. economy-wide wages to total at-any-time wage employment. The COLA is determined by the inflation rate.

4. Insured (Fully Insured and Disability Insured)

Fully insured status is required to receive worker benefits and is determined by a worker's accumulation of quarters of coverage (QCs). Prior to 1978, one QC was credited for each calendar quarter in which at least \$50 was earned. Quarterly reporting was replaced by annual reporting in 1978. The minimum annual required amount, starting with \$250 for each QC in 1978, is adjusted each year according to the average wage index. This value for 2004 is \$900. Thus, if a worker earns at least \$3,600 in covered employment anytime during 2004, then the worker receives credit for four quarters of coverage.

Fully insured status is determined by the number of earned QCs and the worker's age. To be fully insured, a worker must have a total number of QCs greater than or equal to the number of years elapsed after attaining age 21 (with a minimum of six QCs required). Once reaching 40 QCs, the worker remains permanently fully insured. Disability insured status is acquired by any fully insured worker over age 30 who has accumulated 20 QCs during the 40-quarter period ending with the quarter in which the disability began. A fully insured worker aged 24-30 needs to accumulate at least one-half of the quarters elapsed after attaining age 21. A fully insured worker under age 24 needs to have accumulated six QCs during the 12-quarter period immediately before becoming disabled.

In the TR04II, projections of the fully insured population, as a percentage of the Social Security area population, are made by age and sex for each birth cohort beginning with 1900. These percentages are based on 30,000 simulated work histories for each sex and birth cohort. The simulated work histories are constructed to reproduce fairly closely the historical insured percentages from 1990 to date, using the historical portions of the following data:

• Median earnings, by age and sex,
• Covered workers and Social Security area population, by age and sex, and
• Net legal immigrants and other immigrants, by age and sex.

The projected portions of the above data are then used in order to continue the simulation process of work histories of the Social Security area population throughout the projection period. Projected fully insured percentages for each sex and birth cohort are then determined by identifying all simulated work histories that meet the QC requirement for fully insured status as a percentage of the 30,000 simulated cases which represent the Social Security area population. A similar process is applied to produce the disability insured percentages.

In the OSM, the Insured Module projects the percentages of the population that will be fully insured and disability insured for each birth-sex cohort. Projections of fully insured percentages are based on the baseline projection in the TR04II and an adjustment that accounts for the difference between the 10-year moving averages of the covered worker rates1 from the Economics Module and the TR04II. Projections of the disability insured percentages are modeled in a similar manner. Finally, these percentages are multiplied by the Social Security area population from the Population Module to produce the numbers of insured.

5. Disability Insurance Beneficiaries (DIB)

The DIB Module begins with projections of the disabled-worker beneficiaries in current-payment status. The projections are based on the age-sex specific disability insured population received from the Insured Module and the age-adjusted male and female incidence and recovery rates passed from the Assumptions Module. Additionally, the module uses an estimate2 of those currently entitled (as of the beginning of the projection period) to a disabled-worker benefit as a starting value.

Disabled Workers

The number of disabled-worker beneficiaries at the end of a year is calculated by adding those newly entitled to a disabled-worker benefit during the year to those currently entitled at the beginning of the year and subtracting those who recover, die, or convert to a retirement benefit upon reaching normal retirement age during the year. New entitlements are calculated by multiplying the incidence rate by the exposed population (disability insured less those currently entitled). For each sex, the future age-specific incidence rates are assumed to grow at the same rate as the growth in the age-adjusted incidence rate.3

Deaths and recoveries are calculated by applying the death and recovery rates to the number of people who are currently entitled at the beginning of the year and to the number of people who are newly entitled during the year. Death rates4 by age, sex, and duration since entitlement are projected to improve at the same rate as the general population aged 19 through 64. For each sex, the future age-specific recovery rates are assumed to grow at the same rate as growth in the age-adjusted recovery rate.4 The number of disabled-worker beneficiaries in current-payment status is then estimated by reducing those currently entitled by those for whom payment has not yet begun.

Dependents of Disabled Workers

The projected number of auxiliary beneficiaries of disabled workers basically depends on the projections of disabled workers and the Social Security area population. Minor child beneficiaries of disabled workers are projected as the product of the child population, and factors which represent the probabilities that a worker is under normal retirement age, is disability insured, and is disabled, and a statistical residual factor. Student and disabled-adult-child beneficiaries are calculated similarly. Married aged-spouse beneficiaries of disabled workers are projected as a percentage of disabled-worker beneficiaries. This percentage is set as in the TR04II and a factor that adjusts for differences between the OSM and the TR04II projected distributions of the age 62 or older married population. Young-spouse and divorced aged-spouse beneficiaries are calculated similarly, but with their respective populations.

6. Old-Age and Survivors Insurance Beneficiaries (OASIB)

The OASIB module receives variables passed from the Population, Insured, and DIB Modules. The Population Module passes the Social Security area population by age, sex, and marital status. The Insured Module passes the number of fully insured persons, also by age, sex, and marital status. The DIB Module passes disability prevalence rates,5 and the numbers of disabled-worker and converted disabled-worker beneficiaries, by age and sex. Using the data received, the OASIB Module estimates the number of retired-worker beneficiaries, along with five categories of auxiliary and survivor beneficiaries who are eligible to receive benefits based on the earnings of a retired or deceased worker (also referred to as the primary account holder). These categories are aged-widow(er), aged-spouse, disabled-widow(er), children (minor, student, and disabled adult), and young-spouse beneficiaries.

Aged Widow(er)s

Aged widow(er)s are divided into two subcategories: insured and uninsured. The number of insured aged-widow(er) beneficiaries is projected as the product of the widowed and divorced population aged 60 or older, and the probability that:

• The primary account holder is deceased,
• The primary account holder was fully insured at death, and
• The aged-widow(er) is fully insured but, if at least age 62, did not apply for a retired-worker benefit based on his/her own earnings (assuming that his/her own retired-worker benefit is less than his/her widow(er) benefit).

The number of uninsured aged-widow(er) beneficiaries is projected as the product of the widowed and divorced population aged 60 or older, and the probability that:

• The primary account holder is deceased,
• The primary account holder was fully insured at death,
• The aged widow(er) is not fully insured,
• The aged widow(er) is not receiving a young-spouse benefit for the care of a child, and
• The aged-widow(er)'s benefits are not withheld because of receipt of a significant government pension based on earnings in noncovered employment.

For both the insured and uninsured categories, an additional probability is applied which accounts for other conditions not previously mentioned. For example, in the case of an aged widow(er), the additional factor includes the probability that the widow(er) did not remarry before age 60. In the case of a divorced widow(er), the factor includes the probability that the marriage to the primary account holder lasted at least 10 years.

Retired Workers

To calculate the number of retired-worker beneficiaries, the population aged 62 or older is multiplied by the probability that:

• The worker is fully insured,
• The worker is not receiving disability benefits, and
• The worker is not an insured aged widow(er).6

Retirement prevalence rates7 used in the TR04II are then applied to calculate the number of retired-worker beneficiaries.

Aged Spouses

The number of aged spouses of retired workers is projected as the product of the married and divorced population aged 62 or older, and the probability that:

• The primary account holder is alive and fully insured,
• The primary account holder is receiving a retirement benefit (not required for divorced spouses),
• The aged spouse is not receiving a young-spouse benefit for the care of a child,8
• The aged-spouse is not insured, and
• The aged-spouse's benefits are not withheld because of receipt of a significant government pension based on earnings in noncovered employment.

In addition to the stated conditions, an adjustment is made for other requirements. One such requirement is that the aged spouse has been married to the primary account holder for at least 1 year. In the case of a divorced aged spouse, the requirement is that their marriage had lasted at least 10 years. As is the case with many of the listed requirements, there are exceptions to this requirement.

Disabled Widow(er)s

To calculate the number of disabled-widow(er) beneficiaries, the widowed and divorced population ages 50 through 64 is multiplied by the probability that:

• The primary account holder is deceased,
• The primary account holder was fully insured at time of death,
• The surviving spouse is disabled, and
• The disabled widow(er) is not receiving another type of benefit.

Finally, an additional factor is applied to account for other eligibility requirements. For example, there is a 7 year deadline for surviving spouses to qualify for benefits on the basis of disability.

Children

The OASIB Module calculates the number of child beneficiaries for three different child categories: minor, student, and disabled adult. Child beneficiaries are estimated separately for retired and deceased primary account holders. The population of potential beneficiaries for minor children includes children under age 18, while student status includes children of age 18 (and occasionally also age 19). Disabled adult status includes all persons over age 17 who were disabled prior to age 22.

To calculate the number of minor children of retired workers, the population of children under age 18 is multiplied by the probability that:

• The parent is fully insured,
• The parent is indeed receiving a retired-worker benefit, and
• The child is not receiving a benefit based on his/her other parent's earnings.

For minor children of deceased workers, the same population is multiplied by the probability that:

• The parent is deceased,
• The parent was fully or currently insured at time of death, and
• The child is not receiving a benefit based on his/her other parent's earnings.

Student and disabled adult children of retired and deceased workers are calculated similarly using their respective age-specific populations.

For each child category, an adjustment is made for other conditions, such as the marital status of the child (more common in the case of a disabled adult child) or the dependency status of the child. For example, if a child marries, he/she is no longer entitled to a benefit. Also, if it is determined that the child is not dependent upon the parent (or was not at the time of the parent's death) then he/she is not entitled to receive benefits.

Young Spouses

Young-spouse beneficiaries are broken into two categories, young spouses of retired workers and young spouses of deceased workers (also referred to as mother-survivor and father-survivor beneficiaries). In order to estimate the number of young spouses of retired workers, the married population under age 65 is multiplied by the probability that:

• The primary account holder is age 62 or older,
• The young spouse has a child (under age 16 or a disabled adult) in his/her care, and
• The child is entitled to a child benefit.

To estimate the number of young spouses of deceased workers, the population of widowed and divorced spouses under age 65 is multiplied by the probability that:

• The primary account holder is deceased,
• The young spouse has a child in his/her care (under age 16 or a disabled adult),
• The child is entitled to a child benefit, and
• The young spouse has not remarried.

As with all categories, an additional factor is applied to account for other eligibility requirements, such as ensuring that the young spouse is not entitled to a widow(er) benefit, or is not receiving a retired-worker benefit based on his/her own earnings.9

7. Awards

The Awards Module uses a stratified sample of newly entitled worker beneficiaries. A one-percent sample is used for OASI accounts and a five-percent sample is used for DI accounts. In addition, the Awards Module is passed historical and projected covered workers and population from the Economics and Population Modules, respectively. The module also utilizes historical and projected data from the Economics Module such as average wage, and average taxable earnings in order to produce the modified earnings levels and the earnings history of the sample for the representation of future awards. The module ultimately produces projected levels of benefits, in terms of Average Indexed Monthly Earnings (AIME), for those beneficiaries newly awarded by age, sex, and trust fund. These projected levels are passed to the Cost Module.

Awards Sample

The sample of worker beneficiaries who are newly awarded in 2003 is the foundation of the Awards Module. The sample contains a total of 29,002 newly awarded beneficiaries, 14,412 retired-worker beneficiaries and 14,590 disabled-worker beneficiaries. This sample is a subset of the 10-percent sample used for the TR04II.

Each record in the sample includes the worker's history of taxable earnings under the OASDI program as well as additional information such as birth date, sex, type of benefit, and month of entitlement of the worker. This information allows us to compute the benefits and classify each beneficiary in the sample. Some preliminary calculations made on the sample are utilized within the model. These include the sample's covered worker rates calculated separately for retired-worker and disabled-worker beneficiaries. These rates are determined using the sample's earnings histories for 1951 through 2002. The rates are defined for each age group and sex as the ratio of (1) the number of beneficiaries with earnings to (2) the total number of beneficiaries.

Breakdown of the Awards Module

A goal of the Awards Module is to adjust earnings histories and earnings levels in the sample to represent those of future awards. The Awards Module is composed of three distinct components:

• The Coverage Loads component applies an adjustment to the earnings histories to reflect the projected changes in covered worker rates.
• The Base Loads component adjusts the earnings levels to incorporate earnings above the historical maximum taxable earnings, or wage base.
• The AIME component computes an AIME level for each beneficiary in the sample. A distribution of these AIME levels is the basic input for determining average benefits by the Cost Module.

In order to estimate future benefit levels, the earnings histories in the sample are modified to represent those of the sample in a given projection year. First, the covered worker rates of current and future sample cohorts are calculated based on sex and age group using data provided by both the Economics Module and the Population Module. The percentage changes from these rates10 are then applied to the corresponding sample's covered worker rates by randomly removing or adding earnings in such a way as to maintain the levels in the sample's average taxable earnings for each year by sex.

The earnings posted for beneficiaries in the sample are limited by the historical wage base. Prior to 1975, the maximum annual amount of earnings on which OASDI taxes were paid was determined by ad hoc legislation. After 1974, however, the annual maximum level was legislated to be determined automatically, based on the increases in the Social Security Average Wage Index (AWI). Prior to these automatic wage base increases, a larger portion of workers earned income at or above the base. Additional ad hoc legislation raising the annual maximum taxable level occurred in 1979, 1980, and 1981. In addition, the AWI used in the automatic calculation of the annual taxable maximum was modified in the early 1990s to include deferred compensation amounts. Hence, an adjustment must be made to incorporate earnings above the historical wage base in the sample to reflect the earnings levels for future samples.

AIME

Average taxable earnings may grow at a different rate than the AWI. Therefore, in the AIME component, all earnings levels in the sample are adjusted to reflect the overall increase in the average taxable earnings of future cohorts, relative to that in the AWI, as projected by the Economics Module.

Based on the modified earnings levels and earnings histories, the new AIMEs can be obtained for the future samples. The module then calculates the distribution of the AIME levels.

8. Cost

The Cost Module serves two broad purposes. The first is to compute the year-by-year progress of the combined OASDI Trust Funds for a 75-year projection period.11 The second is to produce the summary measures used to assess the long-range financial status of the OASDI program for the 75-year projection period.

Progress of Trust Funds

In order to determine the progress of the trust funds, the dollar amounts of income and outgo are computed for each year. Income includes payroll taxes, the taxation of benefits, and interest. Outgo consists of scheduled benefits, administrative expenses, and the railroad retirement interchange. Once the values of income and outgo have been determined for a given year, the amount of end-of-year assets is determined by starting with beginning-of-year assets, adding income and subtracting outgo. Each simulation of the model projects the progress of the trust funds for 75 years. For any simulation, full scheduled benefits are assumed to be paid from the trust funds, even if the assets of the trust funds become exhausted at some point in the projection period.

Payroll Tax Revenue

The OASDI payroll tax rate for the employer and employee, each, is currently specified as 6.2 percent, resulting in a combined employer/employee tax rate of 12.4 percent. Income to the trust funds from payroll taxes is first computed by multiplying the combined payroll tax rate by the effective taxable payroll from the Economics Module. Because there is a time lag between incurring and collecting payroll taxes, an adjustment is made when computing the annual revenue from payroll taxes.

Benefit Outgo

A key component in projecting the amount of benefit payments for a given year is the projection of average benefits of worker beneficiaries who are newly awarded and those who are in current-payment status. The primary insurance amount (PIA) formula factors are as specified in current law. The two bend points for 2003 are indexed by the increase in the average wage supplied by the Economics Module.

The Cost Module uses a starting average benefit matrix for worker beneficiaries in current-payment status based on a one-percent sample of the Master Beneficiary Record (MBR) as of December 31, 2003. This starting matrix is read in once by the Cost Module in its initialization subroutine. For each sex, the starting matrix of retired-worker average benefits is broken out by age of entitlement to benefits (62 through 70+) and by current age (62 through 95+). The average benefits of retired workers who have converted from disability status are classified in a separate age of entitlement category. Similarly, for each sex, the starting matrix of disabled-worker average benefits is broken out by benefit duration (0 through 9+) and by current age (20 through 66).

The Cost Module updates this starting matrix each year of the projection. First, average benefits are computed for worker beneficiaries who are newly awarded during the year. To compute these amounts, the distributions of AIME levels by age and sex for OASI and DI are obtained from the Awards Module. The average benefit for each age and sex is computed by applying this distribution to the intervals of potential AIME dollars, and then converting to the average PIA. Benefit amounts are determined by applying adjustment factors necessitated by provisions in current law (e.g., actuarial reduction factors and delayed retirement credits). To complete the update of the matrix, two adjustments are made to the benefit levels of those who were awarded benefits in a previous year. The first is increasing benefit levels due to the COLA received from the Economics Module. The other adjustment is to reflect earnings after entitlement and mortality being higher for beneficiaries with lower benefits. Average benefits for worker beneficiaries are determined using the updated benefit matrix and the beneficiary matrix from the OASIB and DIB Modules.

Average benefits of auxiliary beneficiaries are computed by using the historical trend of the level of these benefits, as a percentage of either the average PIA or monthly benefit amount (MBA) of the primary worker beneficiary. The dollar amounts of these average benefits are computed by applying these factors to the appropriate average PIA or MBA projection. Computations are made by sex and type of auxiliary beneficiary.

Finally, the aggregate value of benefits scheduled to be paid is the sum of the products of average benefits and the numbers of beneficiaries by type of benefit. The numbers of beneficiaries by type of benefit are from the OASIB and DIB Modules.

Income from taxation of benefits in a given year is computed by applying a ratio to the projected benefit payments scheduled for that year. This ratio is the same as in the TR04II. The projection of administrative expenses and railroad retirement interchange uses the same methodology as in the TR04II.

Interest

The nominal yield on the combined OASDI Trust Funds is computed by multiplying the increase in the Consumer Price Index by the increase in the real interest rate assumed for the special public-debt obligations held by the trusts funds. Both of these values are allowed to vary and are obtained from the Assumptions Module.12

The amount of interest on trust fund assets at the beginning of the year is calculated by multiplying the nominal yield by the amount of these assets. Additionally, interest is calculated for amounts that enter and leave the trust funds during the year. Dollar amounts of tax income, taxation of benefits, scheduled benefits, railroad retirement interchange, and administrative expenses are exposed to, or from, the point in the year at which, on average, they are received or paid out. The amount of interest on the trust funds is then obtained by multiplying the net exposed amounts by the nominal yield for the appropriate fund.

Year-by-Year Actuarial Measures

Once the various components of income and outgo have been computed for a given year, the Cost Module computes the annual cash-flow measures and the trust fund ratio for that year. The annual cash-flow measures include income rate, cost rate, and annual balance (all as a percentage of payroll).

Long-Range Actuarial Measures

The Cost Module computes various summary measures that are used to assess the financial status of the OASDI program during the projection period. These measures summarize, on a present-value basis, the projected annual income and outgo components of the combined OASDI Trust Funds over the 75-year period. The assumed nominal yield on trust fund assets is used to discount the annual income and outgo components. The summary measures include the summarized income rate, summarized cost rate, and actuarial balance, all as a percentage of taxable payroll and as a percentage of gross domestic product (GDP). An additional important summary measure is the 75-year open group unfunded obligation. All of these summary measures are stored for each simulation of the trust funds. Additional details concerning the calculations of these measures are given in appendix A.

The Cost Module also stores the years during the 75-year projection period that relate to certain trust fund events. For each simulation of the trust funds, the following special years are determined, if possible: (1) the first year trust funds are exhausted, (2) the first year trust funds are exhausted and remain exhausted, (3) the first year that outgo exceeds income excluding interest, and (4) the first year that outgo exceeds total income.

9. Summary Results

The Summary Results Module receives data from the Assumptions, Population, and Cost Modules for each of the stochastic simulations. It then computes the estimated probability distributions of two different types of data: annual data and summarized data.

Annual Data

The Summary Results Module produces the estimated distributions of projected data available on an annual, or year-by-year, basis. Such data include the annual variables that are projected in the Assumptions Module using standard time-series modeling. These variables are the total fertility rate, legal immigration, legal emigration, net other immigration, mortality changes by five-year age groups, unemployment rate, inflation rate, real interest rate, change in average wages, and disability incidence and recovery rates. In the Population Module, life expectancy data are computed and sent to the Summary Results Module for analysis. In addition, annual data projected in the Cost Module and sent to the Summary Results Module for analysis include trust fund ratio, income and cost rates, and covered workers per beneficiary. The Summary Results Module processes the data, most of which is stored in arrays dimensioned by valuation year and stochastic iteration. For each of the stochastic simulations, the data for a given year is sorted using Heapsort (Press, et al., 2001). The probability distributions of the year may then be computed. For each piece of data (e.g., the total fertility rate) the Summary Results Module computes the smoothed empirical estimates (Klugman, et al., 1998) of the 2.5th, 5th, 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th, 95th, and 97.5th percentiles. These percentiles are stored in new arrays and are written to disk, where they are accessible to post-processing steps used to create graphs and other printed output. The Summary Results Module also computes various 75-year and final 50-year averages (arithmetic or geometric, as appropriate) for each piece of annual data.

Summarized Data

Some data are only available as a summary measure for each of the stochastic simulations. Examples are actuarial balance, summarized income and cost rates, open group unfunded obligation, and the exhaustion year of the combined OASDI Trust Funds. The Summary Results Module processes these data, most of which are passed to the module run by run. At the end of the stochastic simulations, the module computes the estimated frequency distributions for each piece of data. It computes the mean, median, and bounds for 95-, 90-, 80-, 60-, 40-, and 20-percent confidence intervals.

Footnotes—

1Covered worker rates are defined as the number of covered workers, expressed as a percentage of the Social Security area population.

2The current number of entitled disabled-worker beneficiaries is not completely known because of the time lag between entitlement to and receipt of benefits.

3Growth is determined from a 1994-96 base period.

4Growth is determined from a 1991-95 base period.

5A disability prevalence rate is the ratio of the number of disabled workers to the number of disability insured workers.

6In this case, the worker is fully insured and, therefore, eligible to receive his/her own retired-worker benefit. Instead, he/she has decided not to apply for a retired-worker benefit, and is receiving only an aged-widow(er) benefit.

7A retirement prevalence rate is the ratio of the number of retired workers to the number of fully insured workers (not receiving disability or widow(er)'s benefits).

8The upper age limit to be eligible for a young-spouse benefit is 69, as long as there is a dependent child under 16 or disabled. Since the minimum age to receive an aged-spouse benefit is 62, there is a chance that some spouses between the ages of 62 and 69 are still receiving young-spouse benefits.

9The eligible age requirement to receive a young-spouse benefit is 69 or younger. Therefore it is necessary to exclude those who are of age to receive a young-spouse benefit, but are receiving their own retired-worker benefit and are counted in the retired-worker calculation.

10Changes in rates are determined as the ratio of the absolute difference in the rates to the potential difference in the rates.

11A projection for the 76th year is required to estimate the target fund, equal to the present value of the outgo in the 76th year. See appendix A.5 for more information.

12The simulated nominal yield on new issues is converted to a nominal yield on the combined OASDI Trust Funds in the Assumptions Module.