.

Summary of

Social Security Administration

Projections of the OASDI System

Working Paper for the

1999 Technical Panel

on Assumptions and Methods

by Edward W. (Jed) Frees

Social Security Advisory Board

December 1999
.
Preface

In its report issued in November 1999, the Technical Panel on Assumptions and Methods

recommended that the Social Security Administration should devote more resources to the

activity of documenting the modeling done within the Office of the Chief Actuary (OCACT).1

Over the years OCACT has published numerous Actuarial Studies and Notes documenting

various individual parts of these models.2 However, many of those studies are currently out of

date. The OCACT also provides a brief overview of the methodology used each year in the

“Assumptions and Methods” section of the Annual Reports of the Board of Trustees.

A somewhat more comprehensive summary of the entire breadth of OCACT’s models was

attempted by Andrews and Beekman3 in 1987 under the sponsorship of the Actuarial Education

and Research Fund. That treatise, however, is somewhat out of date due to the many

improvements made in OCACT’s models over the last decade. Therefore, Edward W. (Jed) Frees,

a member of the 1999 Technical Panel and an actuary on the faculty of the University of

Wisconsin, initiated an effort to provide an updated overview of OCACT’s methods in the style of

the Andrews and Beekman volume. This publication is the result of Professor Frees’ efforts. It

provides an up-to-date summary of OCACT’s models, as well as a useful starting point for the

type of detailed documentation envisioned by the Technical Panel.

As carefully documented by Professor Frees, extensive details for portions of the methodology

are published by OCACT in various Actuarial Studies. It is the hope of the 1999 Technical Panel

that resources will be provided to OCACT to fully describe those parts of the OCACT models that

do not have current documentation.

1 The 1999 Technical Panel on Assumptions and Methods was the first technical panel established by the Social 

Security Advisory Board since its creation in 1994. The purpose of the Technical Panel was to advise on the 

assumptions and methods used in the Trustees Report on the status of the OASDI Trust Funds.

2 See bibliography of this publication, as well as a complete list of Actuarial Studies and Notes on the internet at 

http://www.ssa.gov/OACT/pubs.html.

3 Andrews, George H. and Beekman, John A., Actuarial Projections For The Old-Age, Survivors, And Disability 

Insurance Program In The United States Of America, 1987.
.
1

Summary of Social Security Administration Projections

 of the OASDI System

by Edward W. (Jed) Frees

University of Wisconsin

Abstract

The projection methods used by the Social Security Administration’s (SSA’s) Office of the Chief

Actuary (OCACT) are important. The resulting projections are cited regularly by policymakers,

academics and others interested in the long-term financial solvency of the OASDI system.

However, a complete description of this projection methodology that is vital for serious policy

discussions is not available to the general public.

This summary was constructed in connection with the Social Security Advisory Board’s 1999

Technical Panel on Methods and Assumptions. A goal of the Methods and Modeling working

group of the Technical Panel was to “work to ensure that the projection methods used by the

Office of the Chief Actuary become more public.” A technical summary can promote fruitful

discussion of SSA projections. Construction of these notes illustrates this point by providing an

initial version of this type of summary. Further, these notes provide a basis for future iterations of

this summary.

Summarizing the projection methods is difficult because the SSA OCACT is constantly

improving, and thus changing, their methodology. Nonetheless, documentation is important for

informed policy discussions; OCACT must acquire the resources to produce this documentation.

Prior advisory panels have also made this recommendation. Below are two quotes from SSA

history underscoring this point.

Quote by the subcommittee for Actuarial Cost Estimates of the 1958 Advisory Council. The quote

appears in Myers (1959), “Methodology Involved in Developing Long-Range Cost Estimates for

the OASDI System” (Actuarial Study Number 49).

“We also recommend that the Actuary adopt the practice of assembling in a single report a detailed

description of the technique used in making cost estimates, the actuarial formulas and factors used

and their bases or derivation and the actual calculations. Such report would be a public document

available to any one for reference or study purposes. It would also simplify the work of future

Advisory Councils.”

Quote by the Technical Panel to the 1991 Advisory Council on Social Security, (page 41).

“The panel concludes that: ... The ability of staff to document the continually changing projection

process and to engage in basic research that could enhance the process is severely constrained by

lack of staff and limited computer resources.”
2

1. Introduction

Purposes of the Projection System

The primary purpose of the projection methodology is to provide cost estimates of the current

benefit system, both current and future costs. Long-range projections of costs are used for

calibrating the design of the system, that is, structuring the amount and timing of benefits and

contributions, so that the system is self-supporting. Short-range projections are also used to

calibrate the design as well as to provide budget forecasts for OASDI that are required by all

components of the Federal government.

Increasingly, the projection system is used to value the cost of benefit systems, with alternative

benefit and contribution structures, proposed by policymakers.

The projection system is not directed towards making statements about the adequacy of benefits

to different socioeconomic groups.

How the Projection System Works

The system is split into three main input components; demographic, short-range (10 or fewer

years) and long-range (up to 75 years). Although they follow the same actuarial principles, the

details of the short and long-range projections differ substantially. Short-range projections are

done quarterly whereas the long-range projections are done on an annual basis. On the one hand,

the short-range projections explicitly account for factors such as the timing of tax collections, the

investment (maturity) structure of the Trust Funds and relative growth of sectors of the Gross

Domestic Product that are not as relevant for long-range projections. On the other hand, the longrange projections have more explicit models of trends that are less critical for short-range

projections.

Short-range and long-range projection systems differ, in part, because of the relative knowledge

of the near future compared to the distant future. Further, the budget planning process for the

entire Federal government requires detailed estimates by all components of government. Thus, it

is critical for SSA forecasts to be in congruence with these alternatives.

The demographic component is common to both the short- and long-range projections. The short

and long-range components include economic and programmatic variables. Programmatic

variables are those elements that are directly related to the benefit system whereas the economic

(and demographic) variables are directly related to the population and economy as a whole.

The projection system disaggregates the population into homogeneous demographic cells,

stratified based on age and sex and sometimes additional breakdowns such as marital status or

cause of mortality. 

The system is deterministic; projection uncertainty is portrayed by examining changes in system

output based on small changes in inputs. Table 1 summarizes the key assumption variables that

are inputs into the projections. Table 1 also lists assumption variables where the method of

projection varies by alternative.
3

Some alternative SSA projection systems

Because the system is geared primarily to handle demographic and not economic cohorts, it has

little to say about the adequacy of benefits to different social groups. SSA is developing

alternative models, including the “MINT,” the “CORSIM” and the “Cohorts” models; these

models address the adequacy of benefits under current law and alternative proposals. They are

“micro-simulation” models; as such, they have little to say directly about fiscal implications.

Purpose of these notes

The projection model of the OASDI system is complex and understood by only a few experts

outside of SSA OCACT. 

1. Serious policy discussions are hampered by the fact that so few people understand the

methodology. 

2. Because they do not understand SSA methods, other agencies/groups try to grow alternative

models without the benefit of SSA’s 65 years of experience. Both SSA and these other groups

spend substantial amounts of time comparing and contrasting these competing models.

3. Even well informed consumers do not understand SSA methods. Thus, SSA upper

management spends substantial amounts of time defending their projections to these

individuals.

4. Because of the model’s complexity, there are many places where the development of the

system appears to be uneven. 

This summary was constructed in connection with the Social Security Advisory Board’s 1999

Technical Panel on Methods and Assumptions. This summary does not attempt to suggest

alternatives to the projection system currently in place. A goal of the Methods and Modeling

working group of the Technical Panel was to “work to ensure that the projection methods used by

the Office of the Chief Actuary become more public.” Additional documentation on the

projection methods will be useful for external groups, as described above. Further, it should also

be useful for SSA internal constituencies. In particular, consider:

Table 1. Key Assumption Variables

Demographic Macroeconomics

Total Fertility Rate Productivity Growth Rate (GDP per Hour)

Mortality Decline Rate Inflation Rate (CPI)

Net Flow of Immigration GDP Price Deflator

Labor Economics Nominal Investment Rate

Unemployment Rate Disability

Wage-Share Growth Rate Incidence Rate

Real Wage Growth Rate Recovery Rate

Hours Worked Growth Rate Death-Termination Rate

Methods that Vary by Alternative

Marriage

Divorce
4

1. New hires, who would like an overview of the system.

2. Seasoned veterans, who would like a broad perspective on areas outside of their main area of

interest.

3. Technical panels. To provide useful advice to the SSA OCACT, a technical panel needs to

have a good grasp on the projection methodology. A technical summary would be an

invaluable addition to the resources of future technical panels.

Outline of the Description

This article summarizes a technical projection system; the exposition is directed towards an

audience that is comfortable with technical expressions. Technical expressions are compact and

readily understood by readers who are actuaries, demographers or economists, the primary

audiences of these notes. In particular, recursive equations are used throughout. Although users

will not be able to replicate the work of the SSA OCACT with this summary (even with access to

the confidential data used in the projections), there is a substantial level of detail involved. 

This summary is meant to provide an overview of the projection system. Many additional details

can be found in Actuarial Studies published by the SSA OCACT. These additional sources are

described, by section, following the main body of the text. Also following the main body of the

text is a list of SSA experts; these individuals provided the information about the projection

system that is not available in public documents.

The summary is organized as follows. We start with the big picture—a description of the inflows

and outgoes from the Trust Fund. This description distinguishes between short- and long-range

projections. Then, we present demographic and population projections. These feed into the shortrange projections of revenues and expenditures. Finally, we consider long-range projections of

revenues and expenditures.

Outline

Section Description Section Description

1 Introduction 6 Short-Range Benefit Projections

2 Trust Fund Projections 6.1 Insured Population

2.1 Introduction 6.2 Disability Beneficiaries

2.2 Income 6.3 Old-Age and Survivor Beneficiaries 

2.3 Outgo 6.4 Benefit Projections

3 Population Projections 7 Long-Range Revenue Projections

3.1 Motivation 7.1 Employment 

3.2 Update Procedure 7.2 Economic Assumptions—GDP

3.3 Projection of Demographic Components 7.3 Earnings

4 Short-Range Employment and Earnings 

Projections 

7.4 Effective Taxable Payroll

4.1 Inflation Rate and GDP 8 Long-Range Benefit Projections

4.2 Employment 8.1 Insured Population

4.3 Earnings 8.2 Disability Beneficiaries

5 Short-Range Revenue Projections 8.3 Old-Age and Survivor Beneficiaries 

5.1 Calendar Year Taxable Wages, by Sector 8.4 Benefit Projections

5.2 Multi-Employer Refund Wages

5.3 Taxable Self-Employment Earnings Sources

5.4 OASDI Tax Collections Acknowledgements
5

2. Trust Fund Projections

2.1 Introduction

Overall fiscal soundness of the OASDI system may be understood by examining an initial level of

the trust fund, denoted by Trust Fund(0), as well as future income and expenditures. Specifically,

the initial level of the trust fund is the end of the year preceding the first projection year. The

index z represents years in the future with respect to year 0. We will consider z = 1, ..., 75 years

when projecting OASDI. For each year, the income minus expenditures, denoted by Income(z) –

Outgo(z), represents the net income to the trust fund in year z. Thus, the fund is incremented by

the expression

Trust Fund(z) = Trust Fund(z–1) + Income(z) – Outgo(z), z = 1, ..., 75. (2.1)

The income and outgo are defined below in Sections 2.2 and 2.3, respectively.

Projections are not made directly based on the system’s income and expenditures for several

reasons.

1. Both are subject to changes in law. As such, these interventions are controllable and are not

readily amenable to forecasting. 

2. They do not directly reflect the changing underlying demographic trends.

3. They only indirectly reflect the changing economic scene.

Broadly speaking, the projection system is decomposed into separate modules. These are (i) the

demographic projections, (ii) the economic and revenue projections and (iii) the benefit

projections. The demographic projections are the most fundamental and feed into the other two

modules. The economic projections are part of the second module yet are also used in the third

module.

Although they largely follow the same actuarial principles, the details of the short- and long-range

projections differ substantially. Income and outgo for short-range projections are done quarterly

whereas the long-range projections are done on an annual basis. 

The focus of the short-range status is the Trust Fund Ratio, defined to be the trust fund assets at

the beginning of the year divided by the anticipated outgo during the year. That is,

Trust Fund Ratio(z) = . (2.2)

The focus of the long-range status is the Actuarial Balance, defined to be the initial trust fund plus

present value of net contributions minus the present value of the Target Trust Fund, as a

percentage of the present value of future payroll. That is, 

Actuarial Balance

= . (2.3)

TrustFund z( –1)

Outgo z( ) --------------------------------------

Trust Fund( ) 0 {PV(Revenue z( ))−PV(Outgo z( ))} 75 ∑z=1 + −PV( ) T et Trust Fund arg

PV(Effective Taxable Payroll z( )) 75 ∑z=1

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
6

The Target Trust Fund, which is 100 percent of annual expenditures in the 76th year, is considered

to be an adequate reserve for unforeseen contingencies. Sections 2.2 and 2.3 describe revenue and

outgoes in each year. Present values (PV) are done by discounting using forecasts of the nominal

interest rates that appear in Section 2.2.4. Sections 5.4 and 7.4 discuss forecasts of effective

taxable payroll.

This balance is often decomposed into income and outgo portions. Thus, we define the

Summarized Income Rate =

and the

Summarized Cost Rate =.

This yields an alternative expression:

Actuarial Balance = (Summarized Income Rate) – (Summarized Cost Rate).

2.2 Income 

Income can be classified as non-interest income, which we call revenue for brevity, and interest

income. Non-interest income consists of: (1) contributions (payroll taxes and self-employment

taxes), (2) income from taxation of benefits and (3) reimbursements from the general fund of the

Treasury. Thus, we define

Income(z) = Revenue(z) + Trust Fund Interest Earnings(z) (2.4a)

and

Revenue(z) = Contributions(z) + Taxes on Benefits(z) + Treasury Reimbursements(z). (2.4b)

Each component is discussed in turn.

2.2.1 Contributions

The contributions account for about 90% of income. The inputs are the payroll tax rate and

taxable payroll. We may think of contributions as:

Contributions(z) = Employee Taxable Wages(z) × Employee Payroll Tax Rate(z)

+ Employer Taxable Wages(z) × Employer Payroll Tax Rate(z)

+ Self-Employment Taxable Earnings(z) × Self-Employed Tax Rate(z). (2.5)

For 1999 current and anticipated future tax schedules, the employee tax rate equals the employer

tax rate and this is one half of the self-employed tax rate. Thus, we define the Tax Rate(z) to be

simply the self-employed tax rate in year z. With this definition, we may think of the contributions

as:

Contributions(z) = ETP(z) × Tax Rate(z)

Trust Fund( ) 0 PV(Revenue z( )) 75 ∑z=1

+

PV(Effective Taxable Payroll z( )) 75 ∑z=1

-----------------------------------------------------------------------------------------------

PV(Outgo z( )) 75 ∑z=1+ PV( ) T et Trust Fund arg

PV(Effective Taxable Payroll z( )) 75 ∑z=1

-------------------------------------------------------------------------------------------------------------
7

where we define the Effective Taxable Payroll (ETP) as

ETP(z) = Employee Taxable Wages(z)+ Employer Taxable Wages(z) 

+Self-Employment Taxable Earnings(z).

This structure is used for the short-range projections, which are done on a quarterly basis. In

addition, adjustments are made to account for the differences in wages on which tax liabilities are

based (“incurred”) and those on which taxes are collected (“cash”). These adjustments are

outlined in Section 5.

For the long-range projections, we include a specific allowance for military wage credits. (For

short-range projections, military wages are treated in the same fashion as other wages.) Thus, we

have:

ETP(z) = Employee Taxable Wages(z)+ Employer Taxable Wages(z) 

+Self-Employment Taxable Earnings(z)+Military Wage Credit(z)

and use

Contributions(z) = Lag Factor × ETP(z–1) × Tax Rate(z–1)

+ (1–Lag Factor)×ETP(z) × Tax Rate(z)

where

Lag Factor = .

The purpose of the Lag Factor is to convert taxable payroll from an incurred basis to a cash basis.

Essentially, for long-range projections, tax liabilities are forecast directly and then converted to a

collection, or cash, basis.

Because future tax rate schedules are known, an important goal of Sections 5 and 7 will be to

provide forecasts of taxable earnings for short- and long-range projections, respectively.

2.2.2 Taxes on Benefits

Beginning in 1994, up to 85% of Social Security benefits are subject to income tax. The OASI

and DI Trust Funds receive this tax from Treasury (IRS), up to the first 50%. (The remainder of

the taxes are credited to the HI Trust Fund.)

Historical data on income taxation of benefits comes from the Office of Tax Analysis in the

Department of the Treasury. These data allow one to project the percentage of benefits taxable.

This percentage, together with projected benefit payments (that will be described in Sections 6

and 8), yields projected taxes on benefits. That is, from the Office of Tax Analysis, we get %

Benefits Taxable(z). This yields

Taxes on Benefits(z) 

= Annuity Benefits(z) × % Benefits Taxable(z) × Average Marginal Tax Rate. (2.6)

For the short-range projections, additional adjustments are made for taxes on benefits paid to nonresident aliens. These adjustments are described in Barrick and Zayatz (1996, Section IV.C,

page 180).

1⁄2 1⁄2

1⁄

2 1⁄2

Tax Rate( ) 10 ×ETP( ) 10 –Contributions( ) 10

Tax Rate( ) 10 ×ETP( ) 10 –Tax Rate( ) 9 ×ETP( ) 9 ---------------------------------------------------------------------------------------------------------------
8

2.2.3 Treasury Reimbursements

Reimbursements from Treasury to the trust funds are made for military service transfers and for

benefits to uninsured persons.

Annual payments are made from the general fund of the Treasury to the trust fund for military

service payments; payments representing employee and employer contributions for military

service credit. For years after 1956, the basic pay of the military personnel is covered under

OASDI. In addition, credits are granted to recognize that military personnel receive wages in kind

(such as food and shelter) in addition to cash payments. In years after 1977, noncontributory wage

credits of $100 are granted for each $300 of military wages, up to a maximum credit of $1,200 per

calendar year. For the short-range projections, these are part of contributions. As we have seen in

Section 2.2.1, the long-range projections make a specific allowance for military wage credits.

Additional adjustments are made for service credits prior to 1957. The short-range projections

project future transfers for 2000 that fall under this category. Further discussion of this may be

found in Barrick and Zayatz (1996, Section IV.B, page 179). The long-range projections

incorporate the short-range estimate for this special category.

The other type of special transfer from Treasury to the Trust Funds is for benefits to uninsured

persons. The law provides for special monthly cash payments to certain uninsured persons who

attained age 72 before 1968 or who have 3 quarters of coverage for each year after 1966 and

before the year of attaining age 72. The number of such persons is based on extrapolation of

historical survival rates. The average benefit is increased by the same percentage as regular

OASDI benefits; see Sections 6.4.3 and 8.4.2. 

2.2.4 Trust Fund Interest Earnings

For the short-range projections, the SSA OCACT uses a complex “simulation” model that tracks

starting period assets of trust funds by amount, coupon rate and due date. It specifies monthly new

issue rates, monthly payments and float factors. This model provides a detailed picture of the

monthly performance of Treasury invested funds.

For the long-range projections, we use:

Trust Fund Interest Earnings(z) = Trust Fund(z–1) × nominal interest rate(z)

+ ( ×Contributions(z) + ×Taxes on Benefits(z) – × Benefits(z)

– ×Expenses(z) – ×RRI(z)) × nominal interest rate(z). (2.7)

Each coefficient in equation (2.7) represents the SSA OCACT’s estimate of the midpoint of the

annual flow of the associated variable. To illustrate, for the Expenses variable, Trust Fund

expenses are assumed to occur uniformly throughout the year. Thus, approximately 1⁄2 year of

interest is lost in the total amount of monies paid out due to expenses. Forecasts of contributions

and taxes on benefits were given in equations (2.5) and (2.6), respectively. Forecasts of the outgo,

including benefits, expenses and Railroad Retirement Interchange (RRI) are outlined in Section

2.3.

Assets of OASDI Trust Funds are invested in special non-negotiable US government securities.

6.3⁄

12 1⁄2 1⁄2

1⁄

2 7 12 ⁄
9

For the intermediate assumptions of the 1999 Trustees Report, the 1999 nominal interest rate

payable semiannually is 4.7% and reaches its ultimate value of 6.3% in 2008. The ultimate lowcost assumption is 6.0% and the high-cost assumption is 6.5%. These reflect assumed ultimate

real interest rates of 3.0% for intermediate, 3.7% for low cost and 2.2% for high cost. The ultimate

values are based on the opinions of the Trustees. Near term results from the simulation model are

modified, based on the judgment of the SSA OCACT, to approach the ultimate values smoothly.

2.3 Outgo

Outgo from the OASI and DI Trust Funds can be classified into miscellaneous expenditures and

(annuity) benefit payments. The annuity benefit payments are periodic benefits paid to qualified

disabled and retired workers and their auxiliaries and to qualified survivors; they account for

about 98% of outgo. Thus, we consider

Outgo(z) = Misc Outgo(z) + Annuity Benefits(z). (2.8)

Sections 6 and 8 provide details on forecasts of annuity benefits for short- and long-range

projections, respectively.

The miscellaneous benefits and expenses consist of (1) lump-sum death benefits, (2) net transfers

to the Railroad Retirement program, (3) administrative expenses, and (4) other miscellaneous

expenses. Thus, we have

Misc Outgo(z) = Death Benefits(z) + RRI(z) + Expenses(z) + Other Misc Expenses(z). (2.9)

2.3.1 Death Benefits

We compute death benefits as $255 times the projected number of insured deaths. The projected

number of insured deaths is computed as follows:

1. Section 3 describes projections of the population and number of deaths by age, sex, marital

status, for each year z. These are denoted as P(age, sex, marital status, z) and D(age, sex,

marital status, z), respectively. Section 8.1.1 describes projections of the fully insured

population; we will denote this as PFI (age, sex, marital status, z). Thus, form a preliminary

estimate of the number of insured deaths:

.

Here, the second sum is over marital status = married and widowed, where the deaths for the

widowed insured population is that portion which is estimated to have eligible children.

2. Using historical data, we may compute a preliminary estimate of the death benefit payments as

Deaths0(z) × 255. An adjustment Factor is computed as the ratio of actual death benefit

payments to this preliminary estimate for historical values. The final projected death benefit is:

Death Benefits(z) = $255 × Deaths0(z) × Factor. (2.10)

Deaths z( ) 0

age sex ,

∑

ms married = , widow er ( )

∑ D( ) age sex marital , , status z,

P( ) age sex marital , , status z, = P ------------------------------------------------------------------ ( ) age sex marital , , status z, FI
10

2.3.2 Railroad Retirement Interchange

An annual exchange of funds between OASDI and the Railroad Retirement program. It is

designed to place each trust fund in the same position in which it would have been if railroad

employment had always been covered under Social Security.

This is evaluated on the basis of trends similar to those used above. The inputs consist of data

from the Railroad Retirement Board, average wage index and average benefits for the Old-Age

Insurance beneficiaries. The resulting effect is a long-range loss to the OASDI program of about

0.05 percent of taxable payroll.

2.3.3 Administrative Expenses

For the short-range projections, expenses are projected by a time series regression model, taking

account of historical experience of the expected growth in average wages in the economy. Further,

estimates for the first 2 years reflect the latest available estimates prepared by SSA Office of

Budget.

For the long range, the inputs consist of estimated 10th-year administrative expenses, total

beneficiary population, average wage index and assumed increases in productivity. The longrange projected expenses are:

Expenses(z) = Expenses(z–1) × (1 + %Wage increase(z–1)) z > 10

× (1 + % increase in the Number of Beneficiaries(z–1))

× (1 + % increase in productivity(z–1))

2.3.4 Other Miscellaneous Expenses

There are two other sources of miscellaneous expenses that are itemized in the short-range,

although not the long-range, projections. These are vocational rehabilitation expenses and

unnegotiated check reimbursements.

Vocational rehabilitation expenses are for services designed to contribute to the successful

rehabilitation of disabled persons receiving cash benefits because of their disabilities. These costs

are paid from the DI Trust Fund.

The OASI and DI Trust Funds are debited the amount of a benefit check at the time the check is

issued. Treasury checks issued in October, 1989 or later are negotiable for 1 year; if uncashed

after such time, action to reimburse the trust funds is instituted.

Barrick and Zayatz (1996) documents these expenses sources in greater detail; see Sections IV.E

and IV.F. 
11

3. Population Projections

3.1 Motivation 

The contributions depend on the projected number of workers. The benefits depend on the future

population through age, sex and marital status.

Population projections begin with the initial population, by age, sex and marital status. They are

updated through birth, death, marriage, divorce, widowing and net immigration.

Input data include: National Center for Health Statistics (NCHS) birth rates, number of marriages

and divorces, number of deaths, Medicare deaths and population, Census population and INS

immigration.

The key assumption variables are total fertility rate, mortality decline rates and net flow of

immigration. These are given as low-cost, intermediate and high-cost alternatives. Further, certain

methods also vary by alternative. These include marriage and divorce.

3.2 Update Procedure

Use P to denote the SSA population as a function of age, sex, marital status and valuation date.

That is, P(age, sex, marital status, valuation date). SSA population is composed of all civilian

residents of the US, Puerto Rico, Virgin Islands, Guam, American Samoa, Northern Mariana

Islands and all members of the Armed Forces both at home and abroad.

The population is updated through:

We use the notation x for the age of a male last birthday,

y for the age of a female last birthday and ms for marital status, where .

The valuation date is denoted by z and taken at January 1, z; z = 0, 1, ..., 75. With this notation,

projected populations are updated through:

Function Name Description Level of Detail

B Births sex

D Deaths age, sex and marital status

C Marriages age, sex and prior marital status

S Divorce age and sex

W Widowings age and sex

I Net immigrants age, sex and marital status.

single P(age+1,sex,1,z+1) = P(age, sex,1,z) – D(age, sex,1,z) – C(age, sex,1,z) 

+ I(age, sex,1,z)

married P(age+1,sex,2,z+1) = P(age, sex,2,z) – D(age, sex,2,z) + C(age, sex,1,z) + C(age, sex,3,z) 

+ C(age, sex,4,z) – W(age, sex,z) – S(age, sex,z) + I(age, sex,2,z)

widowed P(age+1,sex,3,z+1) = P(age, sex,3,z) – D(age, sex,3,z) – C(age, sex,3,z) + W(age, sex,z) 

+ I(age, sex,3,z)

divorced P(age+1,sex,4,z+1) = P(age, sex,4,z) – D(age, sex,4,z) – C(age, sex,4,z) + S(age, sex,z) 

+ I(age, sex,4,z)

ms

1 single

2 married

3 widowed

4 divorced 













=
12

The initial (SS Area) population P(age, sex, marital status, 0) is estimated from Census Bureau

reports. Typically, each Trustees Report uses Census Bureau estimates from the previous two

years.

Joint lives (xy) of married couples are projected via the equation:

PJL(x+1, y+1, z+1) = PJL(x, y, z) – DJL(x, y, z) + CJL(x, y, z) – SJL(x, y, z) + IJL(x, y, z).

The initial joint distribution is from a 1980 Census Bureau report. This distribution is applied to the

SS Area Population, P(age,sex,ms,z), using “iterative prorationing” techniques to yield PJL(x, y, z).

3.3 Projection of Demographic Components

3.3.1 Mortality

Mortality is disaggregated by age, sex, and cause. Here, cause is broken down by 10 causes.

These are: 

In addition, separate analyses are done for AIDS.

1. Calculate historical central death rates.

The historical central death rates, for ages under 65, come from the number of deaths by age,

sex and cause tabulated by NCHS and the Census Bureau’s estimates of US resident

population. For ages 65 and over, Medicare records were used to determine rates by age and

sex. Number of deaths by age, sex and cause tabulated by NCHS were used to decompose the

Medicare age/sex rate by cause. The basic data are not by joint life.

The central death rates are broken down into 21 age groups, primarily five year age groupings.

The central death rates are calculated as the number of deaths divided by the number of person

years in each age group. 

2. Calculate starting year central death rates.

By age, sex and cause cell, examine the trend over the last 12 years. Use this to establish an

initial set of central death rates.

3. Calculate average annual percentage reductions in central death rates.

By age, sex and cause cell, calculate the average percentage decline since 1968. Use this

average to project central death rates for 24 years.

Heart Disease Congenital Malformations and Diseases of Early Infancy

Malignant Neoplasms (Cancer) Diseases of the Digestive System

Vascular Diseases Diabetes Mellitus

Accidents, Suicide and Homicide Cirrhosis of the Liver

Diseases of the Respiratory System Other Causes Excluding AIDS
13

4. Blend ultimate level average annual percentage reductions in central death rates.

Beginning in the 24th year after the Trustees Report, use the ultimate levels from the Trustees.

For the 1999 Trustees Report, these begin in 2023. These are separated only into five age

groups. Use this to project central death rates for the remainder of the projection period.

For the first 24 years, use a function of the average annual reduction calculated in Step 3 and

the ultimate levels. The function is a logarithmic one, designed to gradually transform the

empirical annual reduction to the ultimate one.

5. Convert central death rates by cause to individual age, grouped death rates.

Define q(age, sex, z) to be the projected death rates for z =1, ..., 75.

6. Calculate the total projected number of deaths.

The total is the sum over four marital status categories. We have:

D(age, sex, ms, z) = q(age, sex, z) × ( P(age, sex, ms, z)).

Future relative differences in death rates by marital status are assumed to be the same as those

determined using 1980 and 1981 data. This yields D(age, sex, ms, z) by age, sex and marital status

cohort.

The Trustees select the low-cost and high-cost ultimate level of average annual percentage

reductions in the central death rates. Special techniques are used to blend actual experience and

assumed ultimate rates for the first 24 years of the projection (prior to 2023 for the 1999 report).

3.3.2 Widowings 

Calculate the probability that a marriage dissolves through death by assuming independence of

male and female lives. Specifically, this probability is expressed as:

2

qxy = Prob (xy fails) = 1 – (1–2qx)(1– 2qy).

Here, 2qx is the probability that a male age x dies and 2qy is the probability that a female age y

dies. Projections of these probabilities, say 2qxy,z, are based on projections of mortality projections

described above.

Thus, we have:

q(age, sex, ms=2, z) = D(age, sex, ms=2, z) / P(age, sex, ms=2, z)

2

qxy,z= 1 – (1– q(x, male, ms=2, z))(1– q(y, female, ms=2, z))

DJL(x, y, z+1) = PJL(x, y, z) × 2qxy,z

W(age, sex,z) = DJL(x, y, z) – D(age, sex, ms=2, z).

Here, if sex = male, then age = x and if sex = female, then age = y.

4

∑ms=1

4

∑ms=1
14

3.3.3 Fertility

Define the central birth rate to a female age y in valuation year z as

.

The total (period) fertility rate in valuation year z is TFR(z) = Σy by,z.

1. Calculate by,z for historical years.

2. Calculate an average fertility distribution.

Use the last 31 years of completed cohort rates to calculate an average age-specific

fertility distribution. The most recent completed cohort consists of women age 14 in 1961 and

age 49 in 1996. (Provisional data for 1997 were available and used by SSA in their 1999

projections. These data are ignored for this discussion.) The first cohort consists of women

age 14 in 1931 and age 49 in 1966. See Figure 1. Specifically, define .

The fertility distribution, , is used as a weighting mechanism to project the completed

cohorts in Step 3. 

Figure 1. Completed Cohorts

(The diagonal lines along “y-14=z-1931” follow a cohort. To illustrate, the most recently 

available completed cohort consists of women age 14 in 1961 and age 49 in 1996.)

3. Project the fertility distribution.

We project by,z by grading historical values of by,z into by,ultimate, separately for each cohort of

women, so that the ultimate total fertility rate is achieved in the 24th projection year.

Specifically, in Figure 1 we project rates by completing cohorts. The most recent completed

cohort is identified in Figure 1. For the next cohort, consisting of women age 14 in 1962 and

age 49 in 1997, only the information for fertility at age 49 in 1997 is not available. For the

following cohort, consisting of women age 14 in 1963 and age 49 in 1998, only information

for fertility at ages 48 and 49 are not available.

by z,

number of births to a female age y

( ) midyear number of females age y =------------------------------------------------------------------------------------

by t, { }y=14

49

by

1995 ∑

z=1965

by z, –(49–y) = ( ) ⁄31

{ } by

Age(y)

4 9

1 4

Period(z)

1931 1961 1966 1988 1996 2023
15

Thus, we recursively forecast, for z = 1962, ...,

 for y = 14, ..., 49.

Here, the lagged (by period) cohort fertility rates, , are either actual fertility rates or

computed from the prior recursion. To determine the period specific Factor(z): 

a. We examine the sum of the actual cohort fertility rates and the lagged cohort fertility rates

within the cohort identified by the period z for y = 14.

b. We take a weighted average of this sum and the assumed ultimate total fertility rate. Here

the weights use the fertility distribution, { }, computed in Step 2. These give greater

weight to the ultimate total fertility rate when less actual data are used in Step 3(a) and

vice versa.

c. This weighted average minus the sum of actual fertility rates is then rescaled to yield

Factor(z). This rescaling is done to ensure that the projected total fertility rate grades into

the ultimate.

4. Calculate the projected number of new-borns.

P(0, male, 1, z) = by,z ( P(y, female, ms, z)) × (1.05/2.05).

P(0, female, 1, z) = by,z ( P(y, female, ms, z)) × (1.00/2.05).

For the intermediate assumption of the 1999 Trustees Report, the 1999 fertility rate is 2.03 and

reaches its ultimate value of 1.90 in 2023. The ultimate low-cost assumption is 2.20 and the highcost assumption is 1.60. The ultimate values are based on the opinions of the Trustees.

3.3.4 Marriage—number of new marriages by (xy).

Data are from the “Marriage Registration Area” (MRA), obtained from the National Center for

Health Statistics (NCHS), 1957-1988. In 1988, the MRA consisted of 42 states and DC; it

accounted for 80% of all marriages in the US (yet excludes Nevada). These data allow us to

compute marriage rates:

Central marriage rate for (xy) for year z

= .

Here, the number of unmarried males and females are enumerated at mid-year.

To summarize this, use the “age-adjusted central marriage rate,” which we interpret to be

.

b

ˆ

yz y , + –14 b

ˆ = yz y , + –15×Factor z( )

b

ˆ

yz y , + –15

by

49 ∑y=14

4

∑ms=1

49 ∑y=14

4

∑ms=1

mrxy z,

number of marriages for ( ) xy

number of unmarried males aged x number of unmarried females aged y =----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

number of marriages for ( ) xy ∑x y,

number of unmarried males aged x ∑x number of unmarried females aged y ∑y

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
16

Specifically, using the definition of the central marriage rate, we define the year z age-adjusted

central marriage rate to be 

MRz = .

Here, “SP” refers to the standard population, that is, the Marriage Registration Area population

taken at mid-year, 1982.

1. Calculate mrxy,z for each year z = 1957-1988.

2. Calculate the marriage bivariate distribution.

Use 1978, 1979 and 1981-1988 (1980 was not available) historical rates of mrxy,z to calculate

an age-specific marriage distribution. Average and graduate these rates to get a single

bivariate distribution, called amrxy.

3. Calculate the age-specific central marriage rates for provisional years 1989-1995.

For each provisional year, rescale the distribution in Step 2 (amrxy) so that the total number of

marriages obtained by applying the rescaled values of amrxy to estimates of unmarried

population in the SS Area yields the estimate of the total number of new marriages in the SS

Area.

Thus, determine the year z Factor through the expression:

Factor(z) × (2 × Number of Marriages in year z) = 

.

This yields:

mrxy,z = amrxy / Factor(z).

4. Calculate age-adjusted central marriage rates.

For each year 1957-1997, calculate the age-adjusted central marriage rates. The ultimate ageadjusted central marriage rate for 2023 and beyond is defined to be 95% of the average for

1989-1997. Determine the age-adjusted rates for 1998-2022 by blending the values between

1997 and 2023.

5. Project the marriage distribution.

For every year after 1995, calculate mrxy,z by rescaling amrx,y so that the age-adjusted central

marriage rate determined in Step 4 is achieved.

These projections assume that the marriage possibilities are the same for single, widowed and

divorced. Future relative differences in marriage rates by previous marital status were

assumed to be the same as the average of those experienced during 1979 and 1981-1988. This

yields mrxy,z(ms) for ms = 1, 3, 4.

∑ m

x y, r

xy z, SP( ) unmarried males aged x SP( ) unmarried females aged y

∑x

SP( ) unmarried males aged x ∑ySP( ) unmarried females aged y

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

∑ a

x y, mr

xy ∑ ( ) midyear ms=1,3,4 P( ) x male ms z , , , ∑ ( ) midyear ms=1,3,4 P( ) y female ms z , , ,
17

6. Calculate the projected number of marriages.

C(x, male, ms, z)=

, ms = 1, 3, 4.

C(y, female, ms, z) = 

, ms = 1, 3, 4.

CJL(x, y, z+1) = mrxy,z × (mid-year PJL(x, y, z)).

Here, these calculations are done iteratively because the population, P, is at the beginning of

the year. 

3.3.5 Divorces—Number of divorces by (xy).

Data are from the “Divorce Registration Area” (DRA), obtained from the National Center for

Health Statistics (NCHS), 1979-1988. In 1988, the DRA consisted of 31 states and accounted for

about 48% of all divorces. These data allow us to compute divorce rates, defined as

central divorce rate for (xy) for year z = .

To summarize this, use the “age-adjusted central divorce rate,” defined as

DRz =.

Here, “SP” refers to the standard population, that is, the Divorce Registration Area population

taken at mid-year, 1982. Note that for the denominator, we have: 

Σx,y number of married couples (xy)=Σx,y P(x, y)=Σx P(x, males, ms=2)=Σy P(y, females, ms=2).

1. Calculate drxy,z for each year z = 1978-1988.

Determine the year z Factor through the expression:

Factor(z) = (Number of Divorces in SSA population in year z) / 

(Number of Divorces in DRA population in year z).

This yields:

.

For these rates, calculate an age-adjusted central divorce rate.

2. Calculate the divorce bivariate distribution.

Use 1978-1988 historical rates of drxy,z to calculate an age-specific divorce distribution.

Average and graduate these rates to get a single bivariate distribution, called adrxy.

∑ m

y

rxy z, ( ) ms ( ) midyear P( ) x male ms z , , , ( ) midyear P( ) y female ms z , , ,

∑ mx rxy z, ( ) ms ( ) midyear P( ) x male ms z , , , ( ) midyear P( ) y female ms z , , ,

drxy z,

number of divorces for ( ) xy

( ) mid-year number of married couples ( ) xy =---------------------------------------------------------------------------------------------------------

∑ d

x y, rxy z, SP(married couples age ( ) xy )

∑x y, SP(married couples age ( ) xy )

---------------------------------------------------------------------------------------------------

drxy z,

number of divorces for ( ) xy in DRA Factor z × ( )

( ) mid-year number of married couples ( ) xy in SSA =---------------------------------------------------------------------------------------------------------------------------
18

3. Calculate the age-specific central divorce rates for provisional years 1989-1997.

Use the most recent year from NCHS’s estimates of total number of divorces to get the initial

age-adjusted central divorce rate. Rescale the distribution in Step 2 to get age-specific divorce

rates. Call the rescaled rates drxy,z. Because recent rates have been stable, use this as the

projection of future divorce rates.

4. Calculate the projected number of divorces.

.

.

SJL(x, y, z+1) = drxy,z × (mid-year PJL(x, y, z)).

Here, these calculations are done iteratively because the population, PJL, is at the beginning of

the year. 

3.3.6 Immigrants

In the 1999 Trustees Report, the estimate of net immigration is 900,000 per year for each of the

next 75 years (central assumption). 

Specifically, they assume 800,000 legal immigrants, 200,000 emigrants and 300,000 other-thanlegal immigrants each year. The age-sex distribution of the legal immigrants was based on data

supplied by the INS on immigration during 1978 through 1999. The age-sex distribution of the

emigrants was based on an article by Warren and Peck (Demography, 1980). The age-sex

distribution of other-than-legal immigrants was based on unpublished Census Bureau estimates of

the undocumented population counted in the 1980 census.

These three pieces yield the age-sex distribution of net immigrants. The marital status was

distribution as existed in the population at the beginning of the year.

S( ) x male z , , ∑ d

y

rxy z, ( ) midyear PJL = ( ) xyz , ,

S( ) y female z , , ∑ d

x rxy z, ( ) midyear PJL = ( ) xyz , ,
19

4. Short-Range Employment and Earnings Projections

This section describes employment and earnings projections as they pertain to the OASDI

covered economy. For both employment and earnings, we begin by developing projections as they

pertain to the US economy, then convert them to the OASDI covered economy. We begin with

two economic assumptions that underlie the projections: inflation (CPI-W) and Gross Domestic

Product (GDP). This discussion includes consideration of the GDP price deflator. Models of

employment use these assumptions, as well as labor force participation rates, unemployment rates

and disability prevalence rates. 

4.1 Inflation Rate and GDP

Relatively little attention is given to forecasts of inflation. Forecasts of GDP are more complex.

4.1.1 Inflation Rate

The Bureau of Labor Statistics began publishing the CPI monthly in 1913 and the CPI-W in 1978.

Social Security benefits are indexed using the CPI-W. Here, SSA OCACT grades current

quarterly growth rates into the ultimate assumptions over a 5 to 10-year period.

For the intermediate assumption of the 1999 Trustees Report, the 1999 CPI-W is 1.9% and

reaches its ultimate value of 3.3% in 2008. The ultimate low-cost assumption is 2.3% and the

high-cost assumption is 4.3%. The ultimate values are based on the opinions of the Trustees. 

4.1.2 GDP

The projection of GDP is more complex. These projections are used to project labor force

participation in Section 4.2 and earnings in Section 4.3.

Underlying the projections of GDP is the concept of “potential GDP,” denoted as KGDP, an

estimate of what the economy could produce at high rates of resource utilization. If the potential is

less than the actual GDP, then this signals an expansionary period. Here, constraints on capacity

begin to bind and inflationary pressures build. Conversely, if the potential exceeds actual GDP,

then this signals a recession. Thus, the ratio, real to potential,

RTP = (real GDP)/(KGDP)

is a measure of the business cycle.

The Congressional Budget Office (CBO) produces historical values of potential GDP. These are

calculated by fitting neoclassical growth models to five sectors of the US economy. To illustrate,

for the non-farm business sector (which comprised 77% of the US economy in 1994), the model

was

log(GDP) = constant + 0.7 × log(Hours Worked) + 0.3 × log(capital) + residual.

Here, the residual is generally ascribed to technological factors of production.
20

The primary advantage of using a growth model to calculate potential output is that it explicitly

includes capital as a factor of production. A detailed discussion of the method of calculating

potential GDP can be found in “CBO’s method for estimating potential output,” CBO

Memorandum, October, 1995. 

Potential GDP increases according to increases in hours worked (and thus size of the labor force),

capital and technology factors of production. It grows smoothly over time, unlike actual GDP. For

the short-run, KGDP growth is the sum of growth in each of full-employment labor force, the

average number of hours worked per year and labor productivity (defined as output per hour

worked). The labor productivity parameter includes both capital and technology factors of

production.

For the SSA short-range assumptions, projections of KGDP were determined using an

econometric model that initially assumed RTP = 1. Output from this model yields projections of

full-employment employment. Projections of full-employment annual growth in hours worked

and labor productivity are from the ultimate assumptions of the most recent Trustees intermediate

assumptions; in 1998 these were -0.1% and 1.26%, respectively.

Short-range projections of GDP are computed using projections of KGDP, defined above, and

projections of RTP. Projections of RTP are calculated using projections of the civilian

unemployment rate. This is done through a regression equation, using current and lagged values

of RTP as explanatory variables (“Okun’s Law”). The SSA OCACT uses the relationship:

URt

 = β0 + β1 RTPt + β2 RTPt-1 + β3 RTPt-2 + β4 RTPt-3 + εt,

where is the first difference operator. Using this relationship, forecast values of UR can be used

to recursively forecast RTP. The SSA OCACT also uses forecast values of RTP to forecast UR, to

make sure that these forecasts are in agreement (see Section 4.2.2).

The GDP price deflator index reflects domestic production only whereas the CPI reflects price

changes in all components of consumption. The ultimate rates of the GDP price deflator are

assumed to be smaller than the ultimate rates of CPI-W. The wedge, which is the difference in the

growth of the price deflator and the growth of the CPI, is set by grading current values into the

long-range value of –0.1%. (Alternative terminology: the “price adjustment” is the ratio of the

GDP price deflator to the CPI.)

4.2 Employment

In this section, we discuss SSA models of labor force participation rates and unemployment rates.

These are roughly defined as:

LFPR = labor force participation rate =

and

UR = unemployment rate = 1 – .

Monthly data are available from the Bureau of Labor Statistics (BLS). The goal is to produce

quarterly projections of LFPR and UR, by cohort, using these variables as well as productivity

(GDP) measures and disability prevalence rates as inputs. In this section, “cohort” refers to

∆ ∆∆ ∆ ∆

∆

number of people working or seeking work

non institutionalized – population ---------------------------------------------------------------------------------------------------------

number of people working

number of people working or seeking work ---------------------------------------------------------------------------------------------------------
21

grouping by age, sex, marital status and presence of own child or children less than age 6; there

were 103 groups in 1998. Another possibility is to decompose employment by industry (as is done

for earnings, see Section 4.3). Although the changing demographic makeup of future populations

will change the employment picture, the same argument could be made for the changing industrial

composition. Certainly, historical changes in industrial composition have precipitated large

changes in aggregate employment. Nonetheless, this approach is not adopted, in part due to data

limitations and in part due to the difficulty in predicting future changes in industrial composition.

To reiterate, this section begins with projections of US economy (BLS) concepts of labor and

unemployment; Section 4.2.4 considers related concepts for the Social Security Area population.

The models of this section, and Section 4.3, are also used by other governmental agencies

including OMB and CBO.

4.2.1 Labor Force Participation Rates

As described above, cohorts are defined through age, sex, marital status and presence of children

less than age 6. For 1998, the age groups included 16 to 17, 18 to 19, five-year age groups from 20

to 84, and 85 and older. Further, the 60 to 64 age group was disaggregated to 60 to 61 and 62 to

64. Marital status types include married with a spouse present, married with an absent spouse and

never married.

Most of the LFPRs were calculated from the March Current Population Survey (CPS), using the

ratio of the civilian labor force to the civilian noninstitutional population. Some male LFPRs are

defined as the ratio of the civilian labor force to the sum of the civilian noninstitutional population

and the military; this allows us to assess the impact of the military size on the labor force. SSA

OCACT has a detailed historical description of the size of the military.

The model of LFPR is a cohort-specific, time series regression model. Specifically, for each

cohort, the response is the LFPR, observed over a period of time. In 1998, for many cohorts the

observation period was 1962-1997, for 36 observations. There are several exogenous variables;

many of these are common to all cohorts and some specific to individual cohorts. Some of the

common exogenous variables are:

1. Business cycle—RTP—the ratio of real to potential GDP, described in Section 4.1.2.

2. Disability prevalence ratio. This is the ratio of the number of disabled-worker beneficiaries in

current-pay status to the Social Security Area population. If one is unable to work through

disability, then one would not participate in the labor force.

3. Time trends are used to quantify trends in LFPRs. To illustrate, time trends account for the

increasing participation by women in the labor force.

Many variables were specific to individual cohorts.

Males

1. Military rate. This is the ratio of those in the military to the sum of the civilian noninstitutional

population and the military. These rates are for males, age groups containing ages 20-54, only.

If one is in the military, then one would not participate in the civilian labor force. This variable

allows us to separate the effect of the military. 

2. Spouse labor force participation rate. Used for males age 25-44.
22

Older Workers

1. The adjusted replacement rate is the ratio of OASDI benefits to a person’s earnings in the last

year of work. It is used for males and females age 62-70. As the adjusted replacement rate

increases, LFPRs should decrease.

2. The retirement earnings test is a variable representing the maximum amount of income a

retired person can earn without having his or her benefit reduced. In the future, this is the ratio

of the current year’s maximum allowable earnings to the previous year’s average wage index.

It is used for males and females age 62-71.

Teen Workers

1. The school rate is defined as the ratio of those in school to the civilian noninstitutional

population.

2. The Federal minimum wage.

Further, SSA OCACT is contemplating adding the following variables to the teen model:

1. A variable for teen motherhood.

2. The dropout rate is defined as the ratio of high school dropouts to the population of high

school students.

One must project each of these exogenous variables to obtain projections for the LFPRs.

In 1999, the labor force increased by 1.2%. Projections show that this increase grades down,

reaching 0.1% in 2050.

4.2.2 Unemployment Rates

Let UR(age, sex, year) be the age/sex unemployment rate by quarter. Estimate the equation:

UR(age, sex, t) = β0(age, sex) + β1(age, sex) RTPt

 + β2(age, sex) RTPt-1

+ β3(age, sex) RTPt-2 + β4(age, sex) RTPt-3 + ε(age, sex, t) for historical t.

This estimation yields bj(age, sex), for j = 0, 1, 2, 3, 4. For future quarters z, project

UR(age, sex, z) = b0(age, sex) + b1(age, sex) RTPz + b2(age, sex) RTPz-1

+ b3(age, sex) RTPz-2 + b4(age, sex) RTPz-3 .

After 10 years, we assume no changes in the unemployment rate. That is, for future years z

UR(age, sex, 10+z) = UR(age, sex, 10) for z = 1, 2, ..., 65.

For the intermediate assumption of the 1999 Trustees Report, the unemployment rate is 4.6% in

1999. It reaches its ultimate value of 5.5% in 2005. The ultimate low-cost assumption is 4.5% and

the high-cost assumption is 6.5%. The ultimate values are based on the opinions of the Trustees. 

∆ ∆∆

∆ ∆

∆ ∆∆

∆ ∆
23

4.2.3 Employment by Sector

Using projections of the population, labor force participation rates and unemployment rates, we

may summarize the age/sex household employment as

number of workers(age, sex, z) = LFPR(age, sex, z) × (1 – UR(age, sex, z)) × P(age, sex, z).

This yields total (BLS) household employment

Employment(z) = Σage,sex {number of workers(age, sex, z)}.

Because earnings are projected by sector of economy, it is of interest to decompose this forecast

into economy specific pieces. The most important split is to decompose employment into

agricultural and nonagricultural pieces. Another split is by the class of worker because we are

interested in differences among wage workers, self-employed workers and unpaid family

workers. Thus, there are six categories: agricultural (1) wage workers, (2) self-employed workers

and (3) unpaid family workers, as well as nonagricultural (4) wage workers, (5) self-employed

workers and (6) unpaid family workers.

4.2.4 Covered Employment

US economy (BLS) employment described in Section 4.2.3 differs from OASDI covered

employment in some important aspects. First, BLS employment includes some non OASDI

employment such as qualified government employees, student workers, election workers and

other small categories. Qualified government employees include Federal employees hired prior to

1984 and certain state and local government employees. Second, BLS employment covers

employment for ages 16 and over whereas OASDI employment pertains to all age groups. Third,

a worker need only work part of the year in order to be covered under the OASDI program.

However, LFPRs are determined by examining averages of weekly numbers of people in the labor

force. Thus, the two concepts measure different aspects of participation in the labor force.

Use the following steps to forecast covered employment:

1. Use SSA administrative records to estimate the number of persons in covered employment for

ages 16 and over as well as under age 16. Denote these series as CE16O(t) and CEU16(t),

respectively.

2. For under age 16, disaggregate these by age and sex and write each cohort as a proportion of

the population, CEU16(age, sex, t)/P(age, sex, t). Use a time series of each ratio to determine

a projected constant (that varies by age and sex). Use this constant with the projected

population to project the under age 16 number of covered workers, CEU16(age, sex, z).

3. Forecast non OASDI covered employment for ages 16 and over, NCE16O(z), by separately

considering each type of employment. These include medically qualified government

employees, student workers, election workers and other small categories. This yields

NCE16O(age, sex, z).
24

4. For each age and sex group ages 16 and over, forecast the total employed, denoted as

TE16O(age, sex, z). To do this:

4.a First create historical values of 

ratio(age, sex, t) = TE16O(age, sex, t)/(Adjusted Employment + Military)(age, sex, t).

Here, TE16O(age, sex, t) = CE16O(age, sex, t)+ NCE16O(age, sex, t). The Adjusted

Employment is BLS employment, taken as the maximum over 4 quarters, adjusted for

unpaid family workers. 

4.b Fit a regression equation of the form ratio(age, sex, t) = function(x1, RTP),

where x1 = (Adjusted Employment + Military)(age, sex, t)/P(age, sex, t).

4.c Use this fitted regression equation with projected values of x1 and RTP to get projected

values of ratio(age, sex, z).

4.d Use projected values of (Adjusted Employment + Military)(age, sex, z) and

NCE16O(age, sex, z) to get projected values of CE16O(age, sex, z).

4.e Define projections of covered employment as:

CE(age, sex, z)= CE16O(age, sex, z)+ CEU16(age, sex, z).

5. For the self-employed, return to BLS household data. Denote EAS(age, sex, z) to be the

agricultural, self-employed employment and EANS(age, sex, z) to be the nonagricultural, selfemployed employment. Then, for covered employment, define self-employed forecast

recursively as

with an adjustment for qualified government employees.

6. Forecasts of wage-and-salary workers are derived as:

WSW(age, sex, z) = CE(age, sex, z) – SEO(age, sex, z).

7. Finally some adjustments are needed for combination workers, those with OASDI and selfemployed net earnings and workers with some self-employed net earnings.

4.3 Earnings

SSA OCACT calls forecasting earnings by itself the “direct analysis.” The direct analysis covers

real earnings in all covered OASDI employment (Yang and Goss, 1992). This direct analysis has

been examined on a demographic cohort basis (age and sex). Although employment is projected

on a demographic cohort basis, projections of earnings are done by examining different segments

of the economy.

The approach is to first forecast US economy earnings. These are done using BEA National

Income and Production Accounts (NIPA). Then, these earnings are converted to OASDI covered

earnings. Section 5.1 describes the conversion of OASDI covered earnings to taxable earnings.

SEO( ) age sex z , , SEO( ) age sex z , , –1 EAS( ) age sex z , , +EANS( ) age sex z , ,

EAS( ) age sex z , , –1 +EANS( ) age sex z , , –1 = ×-------------------------------------------------------------------------------------------------
25

4.3.1 US Economy Earnings

US economy earnings are forecast by sector of the economy, not demographic cohorts. These

sectors are:

• Sectors whose total nominal output is primarily defined as wage compensation. These are: 

Government and government enterprises (federal civilian, federal military, state and local), 

private households and nonprofit institutions; and

• Private business excluding government enterprises. These are: agricultural and private 

nonagricultural business.

1. Forecast wages in government enterprises, private households and nonprofit institutions

according to the following steps. These comprise sectors whose total nominal output is

primarily defined as wage compensation.

1.a Determine the average wage. Forecast this wage as function of historical trends. For

government sectors, we also use knowledge of relevant pay raises plus grade creeps,

knowledge of private sector average wage growth rates, and so on, for the forecasts.

1.b Determine forecasts of total wages as forecasts of average wage from step (1) times

population forecasts. Call these forecasts WS.

1.c Determine forecasts of other labor income (OLI). OLI includes payments for fringe

benefits such as life and health insurance.

1.d Determine forecasts of employer contributions to social insurance (SOC). SOC includes

OASDI contributions.

1.e Determine forecasts of total earnings (which equals GDP for these sectors) as 

WSS = WS + OLI + SOC.

2. For the agricultural sector, forecast GDP using a crude supply/demand model. Call these

projected values GDPPF.

3. For the private nonagricultural business, excluding government enterprises, determine

projected values of GDP. Recall that forecasts of GDP were described in Section 4.1.2. This is

computed as a residual. That is, define

GDPPNA = GDP – GDPPF – (sum of government GDP = WSS).

4. Relate labor returns to GDP for the agricultural and private nonagricultural business sectors.

4.a Fit a model of GDP for the agricultural and private nonagricultural business sectors,

GDPPNA and GDPPF, respectively. For each sector GDP, define the response as the

return to labor, (WSS + Y)/GDP. Here, Y is the proprietor’s income, from the NIPA

accounts. With this response, fit a regression model using RTP as an explanatory variable.

4.b Using forecasts of RTP, forecast the response for each sector. Use forecasts of GDP to

determine forecasts of WSS+Y. Split WSS and Y into separate components based on

projected relative employment growth of wage and self-employed workers assuming

constant relative earnings. This yields forecasts of WSS.

4.c For each sector, forecast OLI and SOC.

4.d For each sector, determine forecasts of wage and salaries as WSS = WS + OLI + SOC.
26

4.3.2 OASDI Economy Earnings

Using SSA administrative records, we may determine covered wages by sector. The sectors are:

(1) Federal Civilian, (2) Federal Military, (3) State and Local, (4) Private Household, (5) Private

Railroad, (6) Private Farm and (7) Private “Residual.” We then use the relative sizes of these

sectors with the projections of the relative sizes of the US economy earnings to determine

projections of the OASDI economy earnings, by sector.

For self-employment earnings, consider both OASDI covered and non-covered earnings. For

covered OASDI earnings, relate the growth rate to the growth in proprietor income from both the

farm and non-farm sectors. This is then split into factors for self-employed only and combination

workers, based on relative employment growths of the two types of workers (assuming constant

relative earnings). 
27

5. Short-Range Revenue Projections

This section begins with the Social Security covered population employment and earnings

projections, developed in Sections 4.2 and 4.3. Following this, projections of taxable earnings are

developed. These are used in the revenue projections described in Section 2.2.1.

5.1 Calendar Year Taxable Wages, by Sector

Section 4.3 developed OASDI covered earnings, by sector. Because earnings are only covered up

to a maximum, we now bridge from covered earnings to taxable earnings. We first estimate

taxable wages for each of the following sectors:

Taxable wages for the private non-farm sector is computed as the difference between (1) and the

sum of (2)-(5).

For the all wage “sector,” the SSA OCACT examines an historical distribution of wages. To

illustrate, the 1999 Trustees Report uses 1997 SSA administrative data. This distribution is

rescaled by dividing by the average covered wage. Then, for each projection year, we examine 

.

We examine this ratio in the context of our distribution. This allows us to calculate the appropriate

OASDI annual taxable ratio, that is, the ratio of taxable to covered wages, as

,

where f is the density of wages. These taxable ratios are adjusted to take into account the secular

decrease in the ratio over time. These taxable ratios are applied to projections of covered wages to

get projections of taxable wages.

For sectors (2)-(5), we use similar procedures. The wage distribution may come from other

sources (not necessarily SSA administrative records) and often is not as recent as the all wage

sector.

1. All wage workers 4. State and Local

2. Federal Civilian 5. Farm

3. Military

ratio1z

maximum taxable wagez

average covered wagez

=-----------------------------------------------------------

ratio2z

∫ w

ratio

f w( )dw

∫wf w( )dw

=------------------------------
28

5.2 Multi-Employer Refund Wages

Employees having total wages exceeding the taxable maximum that worked for more than one

employer during the year are eligible for a refund of social security taxes if their total contribution

exceeds the maximum tax. The SSA OCACT estimates the amount of wages on which refunds are

owed by computing the ratio of refund wages to total covered wages as a function of (1) the ratio

of taxable wages excluding refunds to total covered wages and (2) the unemployment rate.

5.3 Taxable Self-Employment Earnings

For self-employed only workers, the SSA OCACT uses historical sample data or earnings

distributions to estimate taxable ratios.

Also consider combination workers, those wage workers who also have earnings from selfemployment. The SSA OCACT uses historical data on the total earnings distribution of

combination workers and data on the wage distribution. With these data, estimates of wages

below the taxable maximum are made. This then yields the taxable self-employment earnings of

combination workers. 

5.4 OASDI Tax Collections

The amount of tax collections for the Federal government sector follows equation (2.5). That is, 

Contributions(z) = Employee Taxable Wages(z) × Employee Payroll Tax Rate(z)

+ Employer Taxable Wages(z) × Employer Payroll Tax Rate(z)

+ Self-Employment Taxable Earnings(z) × Self-Employed Tax Rate(z). (2.5)

However, for other sectors, the payment of taxes on these liabilities occurs with a lag.

To compute collections, estimates of quarterly taxable wages are needed. Adjustments are also

done for the proportion of tax liabilities to that collected. Special adjustments are required for the

self-employed who often pay much of their tax liability in the following year.
29

6. Short-Range Benefit Projections

We begin with some terminology. A worker obtains fully insured status when his or her quarters

of coverage reaches 40 (this can vary in some minor ways by age and year). Permanently insured

status is achieved when the worker is fully insured at his or her age and has a sufficient number of

quarters to be fully insured at normal retirement age. Currently insured status is a weaker form. It

requires only six quarters of coverage within the 13-quarter period ending with the quarter of

death or entitlement to old-age benefits. Disability insured status requires fully insured status plus

a recent connection to the labor force. 

Future benefit payments are estimated by projecting the number of beneficiaries and the average

benefit, by type of beneficiary. However, the short-range projections differ substantially from the

long-range projections. In general, the short-range projections are (1) more frequent (done on a

quarterly basis) and (2) handle finer gradations of beneficiary classes. This section considers

short-range projections.

To project benefits, we first project the number of beneficiaries and then the average benefit

amount. Specifically, Section 6.1 describes the projection of the fully insured and disability

insured population. Section 6.2 describes the projection of the disability beneficiaries, including

disabled workers and their auxiliaries. Section 6.3 provides analogous description for the old-age

and survivor beneficiaries. Section 6.4 projects benefit amounts, both for new awards and

amounts to beneficiaries that are in current-payment status.

6.1 Insured Population

6.1.1 Projection of Fully Insured Population

The projection of the number of workers who are fully or permanently insured is based on data

from the Continuous Work History Sample (CWHS). This is a 1-percent sample of the Master

Earnings File combined with data on the same sample from the Master Beneficiary Record. The

CWHS contains reliable information on workers but has incomplete reporting on deaths. Thus,

the raw count of fully insured workers is overstated. Techniques are used to impute missing

deaths and improve the estimates of fully insured workers.

These projections are also used for Medicare and DI benefits.

6.1.2 Projection of Disability Insured Population

For disability insured status, we first compute the historical ratios

.

We then estimate the equation

Ratio(age, sex, z) = β0(age, sex) + β1(age, sex) LFPR(age, sex, z) + β2(age, sex) z + ε(age, sex, z) 

for historical z. Here, the errors are assumed to follow an AR(1) distribution.

Ratio( ) age sex t , , number in disability insured status age sex t ( ) , ,

number in fully insured status age sex t ( ) , , =---------------------------------------------------------------------------------------------------------------
30

We then project the ratios using projected values of the labor force participation rates (LFPR) as:

Ratio(age, sex, z) = b0(age, sex) + b1(age, sex) LFPR(age, sex, z) + b2(age, sex) z for future z.

The projected ratios are combined with projected numbers in fully insured status to get projected

numbers in disability insured status. That is, 

number in disability insured status(age, sex, z)=

Ratio(age, sex, z) × number in fully insured status(age, sex, z) for future z.

6.2 Disability Beneficiaries

6.2.1 Disabled-Worker Beneficiaries

The numbers of disabled-worker beneficiaries are projected by use of incidence, termination and

withheld rates. Under this method, incidence rates are applied to the disability insured population

who are not already disabled to determine the number of newly-entitled beneficiaries each year.

Termination rates are applied to the beneficiary population to determine the number of

beneficiaries whose benefits terminate each year. Further, benefits may be withheld for various

reasons. This method is suitable because the number of disabled beneficiaries is a relatively small

percentage of the potential and may not remain stable in the future.

Specifically, the disability incidence rate is 

.

The denominator excludes those entitled to benefits. Projections of the incidence rate are

developed based on the judgment of the OCACT staff reflecting recent trends and long-term

averages.

Termination can occur as a result of (a) death, (b) recovery, (c) conversion at retirement or (d) for

other reasons. Termination rates are developed by age/sex/reason. For short-range projections,

there is little anticipated change due to mortality. The pattern of projected recovery rates is based

in part on workload estimates of scheduled disability reviews.

Disability benefits may be withheld due to (a) refusal to accept rehabilitation services, (b) a

pending determination of continuing disability, (c) worker’s compensation benefit or (d) the

worker having substantial earnings during an extended period of eligibility. Withheld percentages

are calculated by age/sex.

The number of beneficiaries in force minus the number withheld equals the number of

beneficiaries in current-payment status.

6.2.2 Auxiliaries of Disabled-Worker Beneficiaries

The following are categories of auxiliary beneficiaries: (a) young wives, (b) young husbands, (c)

aged wives, (d) aged husbands, (e) minor children, (f) disabled children and (g) student children.

For all but young wives and husbands, we project based on historical trends in

.

number of new entitlements to disability benefits

average number of disability insured workers -----------------------------------------------------------------------------------------------------------------------( ) age, sex

number of auxiliary awards

number of disabled worker awards -------------------------------------------------------------------------------------
31

For young wives and husbands, we use because of the

requirement of the presence of a minor child under age 16.

6.3 Old-Age and Survivor Beneficiaries 

6.3.1 Retired-Worker and Insured-Widow(er) Beneficiaries

As with disability beneficiaries, we update retired-worker beneficiaries as:

number of retired-worker beneficiaries(age, sex, z) = 

number of retired-worker beneficiaries(age –1, sex, z –1) 

+ number of retirees(age, sex, z) 

– number of terminations(age, sex, z) 

+ number of conversions(age, sex, z).

The termination rates are defined as the number terminated divided by the number of

beneficiaries. These are projected based on historical trends and on the projected mortality rates. 

The rates of retirement are based on the number of benefit awards to retired workers and insured

widow(er)s divided by the fully insured population minus the number of workers entitled to

insured benefits. Here, insured benefit is either a retired-worker benefit, a disabled-worker

benefit, or an insured widow(er) benefit. The rates of retirement are developed by an analysis of

historical trends, including the effects of changes in the retirement test exempt amounts. 

A portion of the number of retired-worker beneficiaries come from conversion of disabled-worker

beneficiaries at normal retirement age.

6.3.2 Young Auxiliary of Retired or Deceased Worker Beneficiary

The numbers of minor children of retired and deceased workers are related to the non-orphan and

orphan populations, respectively.

6.3.2.a Child Beneficiaries of Retired Workers

These are projected by single year of age by adding the number of new awards to awards in force

and subtracting the number of terminated awards. The projected number of new awards is based

on the number of non-orphan children. To go from in force to in current-payment status, the

withheld rates are projected to be at a constant level.

6.3.2.b Child Beneficiaries of Deceased Workers

These are projected similarly to the Section 6.3.2.a. The projected number of new awards is based

on the number of orphan children.

6.3.2.c Disabled-Child Beneficiaries of Retired and Deceased Workers

These are projected by single year of age by adding the number of new awards to beneficiaries in

force and subtracting the number of terminations.

6.3.2.d Student-Child Beneficiaries of Retired and Deceased Workers

These are projected by single year of age by adding the number of new awards to beneficiaries in

force and subtracting the number of terminations. The number of student children awarded each

year is greater than the number in force, indicating that virtually the entire student child

population is replaced each year.

number of auxiliary awards

number of minor children awards ----------------------------------------------------------------------------------
32

6.3.2.e Young-Spouse Beneficiaries of Retired Workers

Either a young wife or a young husband may be entitled because they are the parents of an eligible

child of a retired worker. These are projected by applying a percentage to the projected number of

eligible child beneficiaries in force.

6.3.2.f Mother/Father Beneficiaries of Deceased Workers

These beneficiaries are entitled because they are the parents of an eligible child of a deceased

worker. These are projected by applying a percentage to the projected number of eligible child

beneficiaries of deceased workers in force.

6.3.3 Aged Auxiliary of Retired or Deceased Worker Beneficiary

6.3.3.a Disabled-Spouse Beneficiaries of Deceased Workers

These beneficiaries are entitled because they are the surviving spouse of an insured worker, and

they are disabled. They are projected in two age groups—ages 50-59 and 60-64—by applying a

percentage to the projected uninsured female/male population in the applicable age group. The

applicable percentages are projected by time series regression.

6.3.3.b Aged-Spouse and Uninsured-Widow(er) Beneficiaries of Retired or Deceased

Workers

These beneficiaries include divorced wives and husbands, as well as surviving uninsured divorced

wives and husbands.

6.3.3.c Parent Beneficiaries of Deceased Workers

These beneficiaries are entitled because they are the parents of a deceased insured worker, and

they are not insured on their own earnings record. They are projected by applying a factor to the

number of parent beneficiaries receiving benefits 6 months prior.

6.4 Benefit Projections

We split types of beneficiaries first by the Old-Age and Survivors Insurance (OASI) and

Disability Insurance (DI) benefits, then by whether the benefit is current (in current-payment) or a

new award. We also subdivide as to whether the award is paid to a primary beneficiary, that is, an

individual who merits the benefit based on his or her own history, or an auxiliary beneficiary, an

individual who merits benefits based on someone else’s history.

This subsection describes projection of benefit amounts and how to combine projections of

benefit amounts and number of beneficiaries to get projected benefit payments.

Projections of the average benefit at award are based on the Continuous Work History Sample

(CWHS); this is a 1% sample of all people with covered earnings. Various modifications to the

CWHS are made because, although it is a sample of the population, it may not appropriately

represent the experience of future populations. To illustrate, it is expected that the percentage of

females eligible for retirement benefits will increase in the future.
33

6.4.1 Average Benefit for Newly-Entitled Beneficiary

Begin with a 10% sample of the CWHS; this results in a 0.1% sample of the SSA population. To

illustrate, there were 2,229 new awards in 1988. Type of beneficiary includes male/female old-age

beneficiary, male/female disabled worker and young/aged/disabled survivor. We do not consider

dependents of workers; only retired and disabled workers, and survivor beneficiaries. (Benefits

for dependents are assumed to be proportional to the primary beneficiary.) Thus, the number

sampled is generally less than 1/1000 of the number of actual awards.

This sample is modified to make it more representative of the population (see Barrick and Zayatz,

1996, pages 114-116). Specifically, 80 males and 220 females were added who have some

earnings but not enough to be insured for old-age benefits. Further, 100 females were added who

are 62 but have no earnings. The idea is to make this sample representative of future (full)

population. The records were created to make the sample comparable to population survey

information. Thus, the total sample was 2,229 + 300 + 100 = 2,629.

The sample gives earnings history of workers by age and sex. To account for future patterns of

employment and earnings levels, the earnings of each worker in the sample are updated to

represent those workers to whom benefits would be awarded in each (future) year of the (10-year)

projection period. Then, at each year, we can compute the old-age benefit using actual and

imputed wage histories, by age and sex. [The details are in Barrick and Zayatz, 1996, pages 114-

116. In some instances, only earnings up to the SS wage base were available; an excess wage

distribution was required. SSA also adjusted earnings for male/female labor force participation

rates and male/female earnings differentials. Earnings before 1951 were not available;

adjustments were necessary.] Section 8.4.4 provides details for the long-range projections.

We then project the sample forward by type of beneficiary and sex to calculate the average benefit

for a new award. The projections began in 1988 but information up to 1995 was known. Thus, the

distribution was rescaled to give the 1995 actual amounts.

This gives us projections for old-age and disabled-worker benefits, by age and sex. Constant

proportions, developed using the 1995 distributions, are used to get projected new awards for

dependent and auxiliary benefits.

Number of Newly-Entitled Beneficiaries

Type of Beneficiary

Actual Awards

(in thousands)

Number

from

Sample

Male old-age beneficiary........... 956 919

Female old-age beneficiary ....... 689 628

Young survivor .......................... 385 95

Aged survivor............................ 442 322

Disabled survivor ...................... 15 15

Male disabled worker................ 273 162

Female disabled worker ............ 142 88

Totals ......................................... 2,902 2,229
34

Constant proportions required for:

• Male or female spouses of disabled workers;

• Children (minor, disabled and student) of disabled workers; and

• Survivors of deceased workers. The 11 types of survivors to deceased workers are:

Average new award amounts to dependent beneficiaries of retired workers are projected using a

constant percentage of the average retired-workers’ benefit.

6.4.2 Average Benefit for Beneficiary in Current-Pay Status—Disability

For each type of disability beneficiary, the total amount in force of the disability benefit (DB) is

projected quarterly as:

DB(type, current quarter) = DB(type, prior quarter) 

+ New Amounts(type, current quarter) – Terminated Amounts(type, current quarter).

Here, we have:

New Amounts(type, quarter) = Average New Award(type, quarter) 

× Number of New Awards(type, quarter).

Terminated Amounts (type, quarter)=

Average Amount Terminated (type, quarter) × Number of Terminations(type, quarter).

The new award quantities are described in Sections 6.2 and 6.4.1. The average amount terminated

is estimated as a ratio times the average amount in force at the beginning of the quarter. The

number of disability terminations is described in Section 6.

 The type is comprised of:

• Male and female disabled workers;

• Young wives, young husbands, aged wives and aged husbands of disabled workers; and

• Minor, disabled and student children of disabled workers.

Projections of benefits in force are then split into (1) current-payment status benefits and (2) noncurrent-payment benefits. The largest component of non-current-payment benefits to disabled

workers consists of benefits payable for periods of retroactive entitlement. These retroactive

payments to disabled workers are projected separately.

Aged disabled survivor—

Young survivor— 6. Disabled widow

1. Minor child 7. Disabled widower

2. Disabled child Aged nondisabled survivor—

3. Student child 8. Aged widow

4. Mother (with child in care) 9. Aged widower

5. Father (with child in care) 10. Female parent

11. Male parent
35

The average benefit in current-payment status is derived from the average benefit in force, based

on the historical relationship between the two.

6.4.3 Average Benefit for Beneficiary in Current-Pay Status—Old-Age and Survivors

Insurance

These projections are similar to the disability benefits projections described in Section 6.4.2,

except these are on an annual basis whereas disability projections are performed on a quarterly

basis. Specifically, for each type of old-age and survivors beneficiary, the total amount of benefits

in force (Ben) is projected as:

Ben(type, z) = Ben(type, z–1) + New Amounts(type, z) – Terminated Amounts(type, z).

Here, we have:

New Amounts(type, z) = Average New Award(type, z) × Number of New Awards(type, z)

and

Terminated Amounts(type, z) = 

Average Amount Terminated (type, z) × Number of Terminations(type z).

The average new award quantities are described in Section 6.4.1 and the number of new awards

quantities are described in Section 6.3. The number of terminations is also described in Section 6.3. 

For historical z, the terminated amounts are determined as a residual item, thus reflecting benefit

recomputations and other factors. For future z, we examine the ratio of average amount

terminated to the average award (Ben divided by the number of awards in force). This ratio is

projected based on historical trends. Future average amounts terminated are determined as the

product of this forecast ratio to the benefit in force at the beginning of the year.

The average benefit in current-payment status is then derived from the average benefit in force,

based on the historical relationship between the two.

The average benefit for young and aged wives and for young and aged husbands is based on

projecting the proportion of dependent benefit to primary benefit, using a regression equation

with a time trend.

 The type is comprised of:

• Male and female retired workers;

• Child survivors (minor, disabled and student); and

• Aged widows and widowers, mothers and fathers of child survivors, parents of deceased 

workers and disabled widows and widowers.

The average benefit for minor, disabled and student children of old-age beneficiaries is based on

projecting the proportion of dependent benefit to primary benefit, using a regression equation

with number of beneficiaries as an explanatory variable.

Barrick and Zayatz (1996, Section III.E., page 142) provides additional details.
36

7. Long-Range Revenue Projections

7.1 Employment

The short-range model of employment was described in Section 4.2. In particular, forecasts of the

labor force participation rates were described in Section 4.2.1.

Recall

LFPR = labor force participation rate = and

UR = unemployment rate = 1– .

This section links LFPR and UR, that are US economy concepts, to “covered workers,” an

OASDI concept. Covered workers are those who have paid some Social Security tax during the

year. 

7.1.1 Unemployment Rates

Let UR(age, sex, year) be the age/sex unemployment rate by year. Estimate the equation:

UR(age, sex, t) = β0(age, sex) + β1(age, sex) (1–RTPt) + β2(age, sex) (1–RTPt-1) 

+ ε(age, sex, t) for historical t.

This estimation yields bj(age, sex), for j = 0, 1, 2. For future years z, project

UR(age, sex, z) = b0(age, sex) + b1(age, sex) (1–RTPz) + b2(age, sex) (1–RTPz-1). (7.1)

After 10 years, we assume no changes in the unemployment rate. That is, for future years z

UR(age, sex, 10+z) = UR(age, sex, 10) for z = 1, 2, ..., 65.

7.1.2 Covered Worker Rates

The number of covered workers is available from SSA administrative records. The projected rates

are adjusted to reflect coverage of Federal Civilian employees and illegal immigrants not

participating in OASDI who were not included in historical rates. Define

CWR = covered worker rate = .

The “age-sex total unemployment rate” is

. (7.2)

 Here, is the 1997 labor force.

For each age/sex group, use a regression equation 

CWR (age, sex, t) = 

β0(age, sex) + β1(age, sex) LFPR(age, sex, t) + β2(age, sex) UR(t) + ε(age, sex, t) for historical t.

number of people working or seeking work

non institutionalized – population ---------------------------------------------------------------------------------------------------------

number of people working

number of people working or seeking work ---------------------------------------------------------------------------------------------------------

number of covered workers

SS Area population -------------------------------------------------------------------

UR z( ) ∑ UR

age sex , ( ) age sex z , , ×P age sex ( ) , ,1997 ×LFPR age sex ( ) , ,1997

∑ P

age sex , ( ) age sex , ,1997 ×LFPR age sex ( ) , ,1997

=----------------------------------------------------------------------------------------------------------------------------------------------------------

∑ P

age sex , ( ) age sex , ,1997 ×LFPR age sex ( ) , ,1997
37

This estimation yields b0(age, sex), b1(age, sex) and b2(age, sex). For future years z, project

CWR (age, sex, z) = b0(age, sex) + b1(age, sex) LFPR(age, sex, z) + b2(age, sex) UR(z). (7.3)

Covered worker rates may be either above or below labor force participation rates. A worker need

only work part of the year in order to be covered under the OASDI program. However, LFPRs are

determined by examining averages of weekly numbers of people in the labor force. Thus, the two

concepts measure different aspects of participation in the labor force.

7.1.3 Covered Workers

To estimate the number of covered workers, we use the SSA population, (PO) and the covered

worker rates from equation (7.3). Thus, we have

Number of covered workers(age, sex, z) = PO(age, sex, z) × CWR(age, sex, z).

7.2 Economic Assumptions—GDP

Other economic assumptions, the interest and inflation rates, were described in Sections 2.2.4 and

4.1.1, respectively. This section describes forecasts of GDP using the “potential GDP” concept,

introduced in Section 4.1.2. 

7.2.1 Full-Employment Labor Force Participation Rates

According to Yang and Goss (1992, page 15), future changes in the full-employment labor force

participation rate are estimated “based on historical data.” These historical data were produced by

the Council of Economic Advisors and are now produced by the Congressional Budget Office

(CBO). According to Yang and Goss, 1992, page 41, the relationship between actual and fullemployment LFPRs was analyzed using differences between actual and full-employment

unemployment rates.

For the 1999 Trustees Report, the SSA OCACT used as inputs to this projection “elastic factors”

and RTP (that is, real to potential GDP in 1992 dollars). It turns out that RTP is very close to one,

so this is used for the projections. Thus, full-employment labor force participation rates equal the

actual labor force participation rates. Denote the projected values as LFPRFE(age, sex, z) =

LFPR(age, sex, z).

7.2.2 Full-Employment Unemployment Rates

Full-employment unemployment rates are assumed to be fixed rates for each age-sex group,

representing the lowest sustainable rates of unemployment in a normally operating economy

without rising rates of inflation in prices. The overall full-employment unemployment rate will

change over time due to the changing age/sex composition of the labor force. Denote the

projected values as URFE(z).

For the 1999 Trustees Report, the SSA OCACT used as inputs RTP (that is, real to potential GDP

in 1992 dollars). As with labor force participation rates, it turns out that RTP is very close to one,

so this is used for the projections. Thus, full-employment unemployment rates equal the actual

unemployment rates. Denote the projected values as URFE(age, sex, z) = UR(age, sex, z).
38

7.2.3 Potential GDP

According to Yang and Goss (1992, page 15), future changes in the average number of hours

worked per week and labor productivity (defined as output per hour worked) are estimated “based

on historical data.” Denote these projections as Hours(z) and PH(z). Here, PH is GDP in constant

dollars divided by total number of hours worked (from BLS).

Begin by calculating projections of “full-employment” employment in year z as:

EmploymentFE(z) = LFPRFE(age, sex, z) × (1 – URFE(age, sex, z)) × P(age, sex, z).

Next, calculate potential GDP as

KGDP(z) = EmploymentFE(z) × Hours(z) × 52 × PH(z). (7.4)

Forecasts of hours worked, Hours(z), are based on the ultimate projection of a decline of 0.1% per

year, described in Section 7.3 below. Similarly, forecasts of labor productivity, PH(z), are based

on an assumed ultimate growth rate of 1.26% per year, also described in Section 7.3.

7.2.4 Forecasts of Real to Potential GDP

For the long-range projections, the projected values of RTP(z) do not vary over forecast period, so

RTP(z) = RTP. Specifically, RTP was determined from the ultimate assumed value of the

unemployment rate; this was 5.5% for the 1999 Trustees Report. Thus, using equations (7.1) and

(7.2), we have

0.055 = UR(ultimate) = b0(z) + b1(z) (1 – RTP) + b2(z)(1 – RTP) (7.5)

where we use

, j = 0, 1, 2.

Solution of equation (7.5) yields the long-range projection of RTP.

7.2.5 Forecasts of GDP

We forecast (nominal) GDP using potential GDP (KGDP), real to potential GDP (RTP) and the

GDP price deflator described in Sections 7.2.3, 7.2.4 and 4.1.2, respectively. The projected values

are:

GDP(z) = KGDP(z) × RTP(z) × (GDP price deflator)(z).

For the intermediate assumptions of the 1999 Trustees Report, the annual growth in real GDP is

2.6% in 1999, 2.0% in 2000-2007 and trends down to 1.2% in 2075. 

∑age sex ,

bj

∑ bj age sex , ( ) age sex , ×P age sex ( ) , ,1997 ×LFPR age sex ( ) , ,1997

∑ P

age sex , ( ) age sex , ,1997 ×LFPR age sex ( ) , ,1997

=--------------------------------------------------------------------------------------------------------------------------------------------------
39

7.3 Earnings

SSA OCACT calls forecasting earnings by itself the “direct analysis.” The direct analysis covers

real earnings in all covered OASDI employment (Yang and Goss, 1992). This direct analysis has

been examined on a demographic cohort basis (age and sex).

Forecasts of earnings take a different tact. First, economic cohorts, that is, sectors of the economy,

now segregate the models. Further, in lieu of forecasting average earnings by itself, earnings are

related to productivity. This allows one to decompose wages into intuitively meaningful pieces.

The decomposition is:

.

Symbolically, we have A = W × C × PH × H × G × R, where

Symbol Description

A= Average real wage per worker. Aggregate earnings (from BEA) divided by 

average weekly US employment during the year. 

W=

Ratio of wages to compensation. Compensation is measured by BEA and is 

reported in the National Income and Product Accounts as total employee 

compensation, for wage-and-salary workers, and net proprietors income, for the 

self-employed. For the self-employed, earnings = compensation. For wage-andsalary workers, compensation includes fringe benefits.

C= Compensation per unit of production. Production is GDP in nominal dollars. 

PH=

Units of production per hour worked, called “productivity” or “labor 

productivity.” Total value of production (GDP in real dollars) divided by total 

number of hours worked (from BLS). The hours worked come from unpublished 

data from BLS. It is comparable to the productivity from the total US economy. 

Here, we use productivity due to all types of workers, including government 

workers. This is in lieu of the more common measure from BLS that refers to 

productivity from “private non-farm business sector.”

H= Average hours worked per week per worker × 52. Numbers of workers are from 

BLS CPS reflecting numbers of persons employed, not number of jobs.

G= Price adjustment; it is the ratio of the GDP price deflator index to the CPI for 

Urban Wage Earners and Clerical Workers.

R Residual. There may be inconsistencies in reporting.

Earnings

Worker

---------------------- Earnings

Compensation

-----------------------------------

Compensation

Productionn

----------------------------------- Productionr

Hour ------------------------------ HourWorker

-----------------GDP Deflator

CPI-W = ----------------------------------R

Earnings

Worker

----------------------

Earnings

Compensation

-----------------------------------

Compensation

Productionn

-----------------------------------

Productionr

Hour ------------------------------

Hour

Worker

-----------------

GDP Deflator

CPI-W ----------------------------------
40

This analysis is done by (1) wage workers and (2) the self-employed. Yang and Goss (1992,

Section V.D) describes how GDP is split into these two components. 

For the projections, let ∆ denote percentage change. Then, from 

A = W × C × PH × H × G × R, we have

.

This yields ∆Α ≈ ∆W + ∆C + ∆PH + ∆H + ∆G + ∆R. To summarize these relationships, here are the

ultimate values used in the 1999 Trustees Report (page 148) for wage-and-salary workers. Selfemployed workers are similar except that we assume ∆W = 0 for each alternative. The ultimate

values are based on the opinions of the Trustees. 

7.4 Effective Taxable Payroll

As described in Section 2.2.1, Effective Taxable Payroll (ETP) consists of total earnings subject

to OASDI tax, including wages in military service. ETP is composed of covered earnings of

wage-and-salary workers and self-employed workers. Further, earnings of wage-and-salary

workers are decomposed into the employee and employer portion. These are slightly different due

to adjustments for multi-employer “excess wages.”

Thus, there are three types of taxable earnings: employee taxable wages, employer taxable wages

and effective taxable self-employment income (SEI). Thus, we have

ETP = Employee Taxable Wages + Employer Taxable Wages + Effective Taxable SEI.

7.4.1 Wage-and-Salary Workers

For wage-and-salary workers, earnings are equivalent to wages. To project taxable wages, we use:

Employee(er) Taxable Wages = 

.

1999 Trustees Ultimate Assumptions for Wage-and-Salary Workers

Ultimate Assumption

Symbol Description Low-Cost (I) Intermediate (II) High-Cost (III)

∆W Earnings/Compensation -0.1 -0.2 -0.3

∆C Compensation/Productionn 0.0 0.0 0.0

∆PH Productionr /Hour 1.6 1.3 1.0

∆H Hour/Worker 0.0 -0.1 -0.2

∆G GDP Deflator/CPI-W -0.1 -0.1 -0.1

∆R R 0.0 0.0 0.0

∆A Earnings/Worker 1.4 0.9 0.4

1

∆A

100

+ 1 -------- ∆W

100

+--------     1

∆C

100

+--------     1

∆PH

100

+---------     1

∆H

100

+--------     1

∆G

100

+--------     1

∆R

100

+--------     =

1⁄2 1⁄2

( ) Nominal GDP Compensation

Productionn

-----------------------------------( ) WS Earnings

Compensation × ×-----------------------------------( ) WS

×

OASDI Covered Earnings

Earnings ---------------------------------------------------------------( ) WS OASDI Taxable EarningsOASDI Covered Earnings ×---------------------------------------------------------------( ) WS
41

The projection of nominal GDP was described in Section 7.2.5. The projections of earnings per

compensation and compensation per production for wage-and-salary workers (WS) were

described in Section 7.2.

Growth in OASDI covered earnings are anticipated to differ from the real wage assumption

because (a) real wages are averages over the total US economy as compared to the OASDI

economy and (b) measurements methods differ, so discrepancies will arise. Further, OASDI

taxable earnings differ from OASDI covered earnings due to the annual cap on wages.

To get historical values of the ratio of OASDI covered earnings to total earnings, OASDI earnings

are available from SSA administrative records and total earnings are available from BLS NIPA

accounts. Recent historical values of the ratio of OASDI taxable to covered earnings are also

available from SSA administrative records. This is because, beginning in 1994, total earnings are

subject to HI tax. Prior to this, these were imputed.

For the long-range projections of these two ratios, the SSA OCACT uses the final values from the

short-range projections as the ultimate. These were described in Section 4.3.2. Specifically, the

ratio of OASDI covered earnings to earnings is determined by four sectors of the economy:

Private, Federal Civilian, Federal Military and State and Local. Only the Federal Civilian is

projected to increase after the 10-year short-range period. This is due to the bringing of these

employees into the OASDI system.

Generally, both employees and employers pay SS Tax up to an annual cap in equal amounts, with

one exception. When an employee works for more than one employer and combined wages

exceed the cap, the employee can apply for a refund of excess contributions. Except for this

difference, we have 

Employee Taxable Wages = Employer Taxable Wages.

7.4.2 Self-Employed Workers

The method for projecting taxable earnings from self-employed (SE) workers is similar to wageand-salary workers. The ratio of OASDI Covered Earnings to total US earnings is lower for the

self-employed, in part due to the fact that if a worker’s self-employed income is less than $400,

then no tax is due. To project taxable earnings, we use:

Effective Taxable SEI = 

.

( ) Nominal GDP Compensation

Productionn

×-----------------------------------( ) SE

×

OASDI Covered Earnings

Earnings ---------------------------------------------------------------( ) SE OASDI Taxable EarningsOASDI Covered Earnings ×---------------------------------------------------------------( ) SE
42

8. Long-Range Benefit Projections

As with the short-range projections, future benefit payments are estimated by projecting the

number of beneficiaries and the average benefit, by type of beneficiary. Projections are made for

each sex in three categories of beneficiaries. These are (type): (i) disabled-worker beneficiaries

and their auxiliaries, (ii) retired-worker beneficiaries and their auxiliaries and (iii) survivor

beneficiaries.

Annuity Benefits(z) = Σ Number of current beneficiaries(sex, type, z) × Average benefit(sex, type, z)

+ Σ Number of newly-awarded beneficiaries(sex, type, z) × Average benefit(sex, type, z)

+ Σ Number of newly-awarded beneficiaries(sex, type, z) × Retroactive payments(sex, type, z).

Average Benefit = Average primary insurance (PIA) amount × % PIA payable.

Retroactive payments are payments to cover the time from date of filing for benefits to date of

first payments. A provision in the law allows a beneficiary to receive up to 6 months’ of benefits

retroactively (12 for disabled-worker beneficiaries).

Section 8.1 describes the projection of the fully insured and disability insured population. Section

8.2 describes the projection of the disability beneficiaries, (including retired workers who were

disabled-worker beneficiaries when they attained normal retirement age (NRA)) and their

auxiliaries. Section 8.3 provides analogous description for the old-age and survivor beneficiaries.

Section 8.4 projects benefit amounts, both for new and current awards. 

8.1 Insured Population

8.1.1 Projection of Fully-Insured Population

Age/sex projections of fully insured rates are made for each birth cohort. They are based on

theoretical distributions of workers by accumulated quarters of coverage (QC), as constructed

from past and projected coverage rates and amounts of earnings required for crediting with

quarters of coverage. Model feature—persons at the low end of the wage distribution are more

likely to be earning 0 QCs, whereas persons at the high end of the wage distribution are more

likely to be earning 4 QCs. Model parameters reproduce experience since 1970.

Prior to 1979, earnings were reported quarterly. Thus, a different definition of “quarters of

coverage” was in place than is the case presently. The current (1999) definition is: one QC for

each $740 of wages and self-employment income, reported annually, up to a maximum of 4. Here,

the $740 changes with changes in the National Wage Index.

Projection of the fully-insured population is accomplished as follows:

1. Estimate the distribution of 1990 earnings, using the CWHS. Rescale earnings by dividing by

the median.

2. Begin with projections of covered worker rates, described in Section 7.1, to project the

number of workers by single year of age.

3. For historical years, estimate median earnings by sex/single year of age group.
43

4. For each year, define the cutoffs, as a percentage of the median earnings, required for 0, 1, 2,

3, and 4 QCs. (There are four cutoffs.) Calculate the fraction of the distribution calculated in

step 1 falling into each of the five categories. This provides the fraction falling into 0, 1, 2, 3

and 4 QCs. For years prior to 1979, use different definitions of QC. For years 1979 and on, the

cutoffs are of the form 

c × 250 / (median earnings(age, sex, year)), for c=1, 2, 3, 4.

5. Now organize these percentages by sex and birth cohort. When calibrating the model with real

data from CWHS, there is a tendency to “stick” in two categories. Specifically, following a

birth cohort over time, there is a tendency for people with 0 QCs in one year to have 0 QCs in

the following year. Similarly, people with 4 QCs in one year tend to have 4 QCs in the

following year. Thus, the percentages in 0 QCs and 4 QCs are adjusted for this stickiness.

6. The average number of QCs earned by a cohort (followed over time) is estimated by

accumulating each cohort’s covered worker rates up to the current year, after multiplying the

average number of QCs earned by the covered workers in that year. That is, 

average number of QCs(z) = Σt≤ z covered worker rate (age–t, sex, t) × QC(age–t, sex, t).

Here, QC(age, sex, t) is the “expected” number of quarters in year t for the age/sex group.

7. Apply the definition of fully insured status to the average number of QCs in step 6. The

maximum number of QCs required is 40.

8. To subdivide the fully insured rates by marital status, we use labor force participation rates.

Variations in labor force participation rates by marital status were used to estimate variations

in the covered worker rate by marital status. This yields a preliminary estimate of fully insured

status by marital status. Then, for each age, sex, and marital status, an estimate was made of

what proportion of their past working lifetime was spent in each marital status. The final

estimates of fully insured status by marital status are a weighed average of the preliminary

estimates.

8.1.2 Projection of Disability Insured Population

Examine the ratio of disability insured to fully insured, by age/sex group. Project these ratios to

get the projected disability insured population. Use data from the CWHS.

8.2 Disability Beneficiaries

8.2.1 Disabled-Worker Beneficiaries

As with the short-range projections, the numbers of disabled-worker beneficiaries are projected

by use of incidence and termination rates. Further, these projections began with anticipated

duration of entitlement. Incidence and termination rates vary by age and sex.

Projections of the incidence rate, by age and sex, are developed based on the judgment of the

OCACT staff. Ultimate assumptions are available from the Trustees Report. These projections are

based on 1984-1986 experience. They are updated via a projection factor that reaches its ultimate

value in 2013. The projections are done to reflect recent experience as well as scheduled increases

in the normal retirement age. The incidence rates are applied to the disability insured population
44

(minus those already receiving disabled-worker benefits) to get the number of new entitlements

each year.

Termination can occur as a result of (a) death, (b) recovery, (c) conversion at retirement or (d) for

other reasons (which are ignored in the long-range projections). Death-termination and recovery

rates by age, sex and duration of entitlement, based on 1977-1980 experience, are projected

separately. They are updated by cause-specific factors. To illustrate, the ultimate values of the

recovery rates projection factor are attained in 2013; these ultimate values are 50% lower than

experienced in 1977-1980. These are applied to the disabled-worker population to determine the

number of terminations. Disabled-worker beneficiaries projected beyond the normal retirement

age (NRA) are identified for use in the projections of retired-worker beneficiaries.

8.2.2 Auxiliaries of Disabled-Worker Beneficiaries

Auxiliary beneficiaries consist of (a) aged, (b) young-spouse and (c) child beneficiaries.

Spouse beneficiaries were projected by age, sex and year. These projections begin with P(age,

sex, ms=2, z), that is, the married population. Terminology: the “account holder” is the disabled

worker who has sufficient credits of work for Social Security benefits. They examine the

following ratios:

1. The account holder is under the normal retirement age.

2. The account holder is disability insured.

3. The account holder is disabled and receiving a disabled-worker’s benefit.

4. The spouse is not fully insured.

5. Other factors, including the probabilities that the spouse is not earning enough to have his or

her benefits withheld under the retirement earnings test.

These same factors were applied to the divorced population, P(age, sex, ms=4, z), with two

additional factors. These were:

1. The former spouse (account holder) is still alive.

2. The divorced spouse must have been married to the account holder for at least 10 years.

The number of child beneficiaries of disabled workers were projected by age, sex and year. These

projections begin with the child population, taken from P(age, sex, ms=1, z). They examine the

following ratios:

1. The account-holder parent under the normal retirement age.

2. The account-holder parent is disability insured.

3. The account-holder parent is disabled and receiving a disabled-worker’s benefit.

4. For minor children, a residual factor to account for the discrepancy between the past actual

and estimated number of children.

5. For student children, include the probability of being a full-time secondary student.

6. For disabled children, include the probability of being disabled since age 18.
45

8.3 Old-Age and Survivor Beneficiaries 

In contrast to disability, numbers of retired and survivor beneficiaries are projected by use of

prevalence rates. These rates are applied to the SS Area population by age, sex, marital status and

year.

8.3.1 Old-Age Beneficiaries

8.3.1.a Retired-Worker Beneficiaries

A portion of the number of retired-worker beneficiaries come from conversion of disabled-worker

beneficiaries at normal retirement age.

To get the number of non-converted retired-worker beneficiaries, apply SS Area population, by

age and sex, to the following factors:

1. The proportion fully insured.

2. The proportion not disabled.

3. The proportion not an insured widow or widower beneficiary.

4. The retirement prevalence rate.

The proportion fully insured (1) was described in Section 8.1.1. The number not disabled (2) was

described in Section 8.2.1. The proportion not an insured widow or widower beneficiary (3) will

be described in Section 8.3.2. If the worker’s benefit is much lower than the widow(er)’s benefit,

then the worker may not file a claim. The fourth factor represents the probability that the worker

has actually filed a claim for benefits and is not earning an amount sufficient to have benefits

withheld.

The retirement prevalence rates shown (Wilkin, 1988, Table 6) are the number of retired-worker

beneficiaries in current-pay status divided by the “exposed population,” by age and sex cohort.

Here, the exposed population is the number of fully insured workers minus the sum of (i) the

number of DI beneficiaries who are converted to retirement status, (ii) number of widows and (iii)

number of widowers. In general, these prevalence rates are projected to decrease, reflecting the

scheduled increases in the normal retirement age. (Offsetting this trend is the scheduled changes

in delayed retirement credit. This, as well as the scheduled increases in the normal retirement age,

will substantially alter the ratio of the Monthly Benefit Amount to the Primary Insurance

Amount.)

8.3.1.b Aged-Spouse Beneficiaries of Retired Workers

The benefits of aged-spouse beneficiaries are based on the earnings records of their husbands or

wives, who are referred to as the “account holders.” Aged-spouse beneficiaries were projected by

age, sex and year. These projections begin with P(age, sex, ms=2, z), that is, the married

population. To get the number of beneficiaries, apply the population to the following factors:

1. The proportion of account holders age 62 or over.

2. The proportion of account holders fully insured.

3. The proportion of account holders in current-pay status.

4. The proportion of account holders where the spouse is not fully insured.
46

5. The proportion of account holders where the spouse is not earning enough to have his or her

benefits withheld.

6. The proportion of account holders where the spouse’s benefit is not being withheld because of

receipt of a significant government pension based on earnings in non-covered employment.

7. A residual factor. This accounts for past discrepancies between the actual and estimated

number of beneficiaries. To illustrate, data are not available to account for the requirement

that spouses be married for at least 10 years. This is assumed to be part of the residual factor.

These same factors were applied to the divorced population, P(age, sex, ms=4, z), with two

changes. These were:

1. Do not apply the third factor because divorced spouses do not need to wait for the account

holder to receive benefits. 

2. The former spouse (account holder) is still alive.

8.3.1.c Child Beneficiaries of Retired Workers

The number of child beneficiaries of retired workers were projected by age, sex and year. These

projections begin with the child population, taken from P(age, sex, ms=1, z). They examine the

following ratios:

1. The account-holder parent age 62 or over.

2. The account-holder parent is fully insured.

3. The retirement prevalence rate for insured retired workers.

4. For minor children, a residual factor to account for the discrepancy between the past actual

and estimated number of children.

5. For student children, include the probability of being a full-time secondary student.

6. For disabled children, include the probability of being disabled since age 18.

For each year and age of child, the population model projects the number of children by (x, y), the

age of the mother and the age of the father. It also projects children of single parents (never

married and with deceased spouse).

8.3.1.d Young-Spouse Beneficiaries of Retired Workers

Young-spouse beneficiaries were projected by age, sex and year. These projections begin with

Σms=2,3,4 P(age, sex, ms, z); this is the “once-married” population, that is, the married (ms=2),

widowed (ms=3) and divorced (ms=4) population. They examine the following ratios:

1. The proportion of young spouses who have a child who is a child beneficiary of a retired

worker and the child is either under age 16 or disabled.

2. Factor for the average family size of the account holder.

3. A residual factor.
47

8.3.2 Survivor Beneficiaries

8.3.2.a Aged-Spouse Beneficiaries of Deceased Workers

After retired-workers, this is the most prevalent type of benefit paid. It is also the most complex to

project. Aged-spouse beneficiaries were projected by age, sex and year. These projections begin

with Σms=2,3,4 P(age, sex, ms, z) over age 60; this is the “once-married” population, that is, the

married (ms=2), widowed (ms=3) and divorced (ms=4) population, over age 60. 

To get the number of uninsured widow(er) beneficiaries, apply the population to the following

factors:

1. The proportion of deceased account holders fully insured at the time of death.

2. The proportion of widow(er)s not fully insured.

3. The proportion where the widow(er) is not earning enough to have his or her benefits withheld

because of receipt of a significant government pension based on own earnings.

4. The proportion where the widow(er) is not a young-spouse beneficiary.

5. A residual factor.

To get the number of insured widow(er) beneficiaries, repeat the steps above but:

1. In step 2, use the proportion of widow(er)s fully insured.

2. Do not use step 4, thus assuming that all young-spouse beneficiaries were not fully insured.

3. Use different factors for step 5.

These same factors were applied to the divorced population, P(age, sex, ms=4, z), with two

changes. These were:

1. The former spouse (account holder) is deceased.

2. The divorced spouse must have been married to the account holder for at least 10 years.

8.3.2.b Disabled-Spouse Beneficiaries of Deceased Workers

There are relatively small numbers in this category. Disabled-spouse benefits are not available to

disabled spouses of retired or disabled workers.

These projections begin with Σms=2,3,4 P(age, sex, ms, z) ages 50-64; this is the “once-married”

population, that is, the married (ms=2), widowed (ms=3) and divorced (ms=4) population, ages

50-64. They examine the following ratios:

1. The proportion of deceased account holders fully insured at the time of death.

2. The proportion of widow(er)s disabled and not entitled to a higher disabled-worker benefit or

to a young spouse of a deceased worker benefit.

These same factors were applied to the divorced population, P(age, sex, ms=4, z), with one

change. This was, for the second factor, also account for the fact that the marriage must have

lasted at least 10 years.

8.3.2.c Child Beneficiaries of Deceased Workers

These are projected similarly to the number of child beneficiaries of retired workers.
48

8.4 Benefit Projections

8.4.1 Average Benefit for Newly-Awarded Beneficiary

For the 1999 Trustees Report, the average PIA was estimated from a sample of the Master

Beneficiary Records (MBR). This was a stratified sample of 1997 Old-Age, Survivor and

Disability new awards. The Old-Age and Survivor stratification was based on age; a 1% sample

was selected from ages 62-65 and a 5% sample was selected from ages 66-70. There were 13,801

awards in this sample. Also included was a 5% sample of 1997 disability new awards; there were

11,257 beneficiaries in this sample. From the MBR, information about age, sex and year of

entitlement were available. From the Continuous Work History Sample (CWHS), a history of

earnings was available. 

For projecting into the future, one difficulty is that earnings before 1995 were censored at the

taxable maximum. (In 1994, the maximum was removed for HI taxes. Thus, the MBR began to

retain uncensored wage records.) A complex method is used to approximate the distribution of

earnings as if the taxable maximum were not in effect. With this distribution, one can “simulate”

future earnings for each individual. With the complete “simulated” earnings history on these

25,058 (13,801 + 11,257) new awards, they can be projected into the future. Then, for each

projection year, we can compute the benefit using the projected benefit formula. At this stage the

age distribution of future new awards does not yet change.

8.4.1.a Projection of Future Earnings Distributions

An outline of this procedure is described as follows.

1. For the 1997 awards, compute the earnings distribution for each historical year t =1951, ...,

1996. Let Ft

(w) be the proportion with earnings less than w times the taxable maximum in

year t, where the argument w is a selected multiple. We consider discrete steps of 0.05.

2. Define logit(y) = ln . For each t, fit a regression function to the model

logit(Ft(w)) = αt + βt w + ε, for w=0.05, 0.10, 0.15, ..., 0.95, 1.00.

Call these estimated coefficients at and bt. We will use the fitted equation

logit(Ft(w)) = at + bt w

to estimate earnings for those individuals at the taxable maximum.

y

1–y --------    
49

3. For each year t, consider the sample of individuals at the taxable maximum. This proportion is

1 – Ft

(1.00). For this proportion, count those individuals who:

a. Do not earn the taxable maximum in any of the next 4 years. Call this proportion p0(t).

b. Are at the taxable maximum only once in 4 years. Call this proportion p1(t). 

c. Are at the taxable maximum twice in 4 years. Call this proportion p2(t).

d. Are at the taxable maximum thrice in 4 years. Call this proportion p3(t).

e. Are at the taxable maximum for all 4 of 4 years. Call this proportion p4(t).

Thus, we have p0(t)+ p1(t)+ p2(t)+p3(t)+p4(t) = 1 – Ft(1.00).

Estimate the maximum earnings for each group by first solving for w in each of the following

equations:

a. logit(Ft(1.00)+ p0(t)) = at + bt w1,t

b. logit(Ft(1.00)+ p0(t) + p1(t)) = at + bt w2,t

c. logit(Ft(1.00)+ p0(t) + p1(t) + p2(t)) = at + bt w3,t

d. logit(Ft(1.00)+ p0(t) + p1(t) + p2(t) + p3(t)) = at + bt w4,t

The group corresponding to proportion p4(t) has no maximum earnings. The maximum for each

of the other groups is wj,t times the taxable maximum. Three additional adjustments are made to

the earnings history:

1. Because labor force participation rates differ historically from those projected into the future,

the earnings histories are adjusted to reflect future projected behavior. In particular, women

are expected to participate more in the work force in the future.

2. Earnings were adjusted by the ratio of the Average Taxable Earnings to the Average Covered

Earnings. This adjustment is described in Section 7.4.

3. The earnings history goes back to 1951. Thus, for example, for new awards in 1997 who retire

at age 70, no earnings history is available for their working years 16-23. Some small

adjustments were made to impute these missing data.

The resulting distributions for the historical years are used, in conjunction with estimates of the

proportions of workers in the SSA area population at the taxable maximum in the sample year and

later, to estimate the amount of earnings for future retired-worker and disabled-worker awards.

From these earnings, estimates are made of the average indexed monthly earnings (AIME) for

each such award. Based on these estimates of individual AIMEs, estimates are made of age-sexspecific average primary insurance amounts (PIAs) for retired-worker and disabled-worker

awards.

8.4.1.b Percentage of PIA Payable

This is for retired-worker beneficiaries affected by early retirement reduction and/or delayed

retirement credit. The projections reflect the effects of movement toward earlier retirement.
50

Let x be the age at entitlement (in years, expressed to the nearest twelfth of a year) and let NRA(z)

be the normal retirement age in year z. For 62 ≤ x ≤ NRA, we have

% PIA payable(x, z) = 1– Actuarial Reduction Factor = 

For individuals who retire after the normal retirement age, a delayed retirement credit (DRC) is

available. For example, for individuals who attain age 62 in 2005 and beyond, benefits will

increase by 2/3% for each month (or 8% for each year) of delayed retirement beyond the

applicable NRA. Lesser percentages apply for individuals attaining age 62 before 2005. However,

no credit is received for delayed retirement beyond age 70. 

For any individual, applicable monthly factors are summed to form a DRC Factor. Thus, we have

%PIA payable = 1 + (DRC Factor)

where NRA < x < 70. 

8.4.2 Average Benefit for Retired-Worker Beneficiary in Current-Pay Status

The average benefit for retired-worker beneficiaries in current-payment status can be updated

directly based on a cost-of-living adjustment as well as a post-entitlement factor. That is, 

Average Benefit(age, age at entitlement, sex, z)

= Average Benefit(age–1, age at entitlement, sex, z–1) 

× (1 + %cost-of-living) × Post-Entitlement Factor(sex, duration from entitlement, z).

The post-entitlement factor reflects (1) mortality and (2) earnings. The mortality portion is due to

the fact that individuals with higher earnings enjoy lower mortality. The earnings portion is due to

the fact that individuals with sufficiently high post-entitlement earnings have their benefits

increased.

( ) 1 0– 1= x NRA =

1 12 ( ) NRA x– 5

9 – × --% NRA–3≤x NRA <

0.80 12 ( ) NRA–3–x

5

12 – 62 × -----% ≤ ≤x NRA–3


















51

Sources:

Overall:

Actuarial Projections for OASDI, 1987, by George Andrews and John Beekman, AERF.

Board of Trustees, Federal Old-Age and Survivors Insurance and Disability Insurance Trust

Funds (1999), 1999 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors

Insurance and Disability Insurance Trust Funds (House Document 106-48), Washington, D.C.:

Government Printing Office.

Myers, R. J. (1959), “Methodology Involved in Developing Long-Range Cost Estimates for the

Old-Age and Survivors Insurance and Disability Insurance System,” Actuarial Study No. 49,

Social Security Administration, Baltimore, Maryland.

Advisory Council on Social Security (1991), The Social Security Technical Panel Report to the

1991 Advisory Council on Social Security, Washington, D.C.

Additional Sources by Section:

3. Population Projections

Bell, F. C., A. H. Wade and S. C. Goss (1992). “Life Tables for the United States Social Security

Area 1900-2080,” Actuarial Study No. 107, Social Security Administration, Baltimore, Maryland.

Bell, F. C. (1997). “Social Security Area Population Projections, 1997,” Actuarial Study No. 112,

Social Security Administration, Baltimore, Maryland.

Warren, R. and Peck, J., “Foreign-Born Emigration From the United States: 1960 to 1970”

Demography, February, 1980.

4. Short-Range Employment and Earnings Projections 

CBO Memorandum (October, 1995), “CBO’s method for estimating potential output.” 

Available at the Internet site http://www.cbo.gov/reports.html#0 or directly through the File

Transfer Protocol (ftp) site ftp://ftp.cbo.gov/3xx/doc312/potout.pdf.

5. Short-Range Revenue Projections and Section 6. Short-Range Benefit Projections

Barrick, N. J. and T. A. Zayatz (1996). “Short-Range Actuarial Projections of the Old-Age,

Survivors, and Disability Insurance Program, 1996,” Actuarial Study No. 111, Social Security

Administration, Baltimore, Maryland.

7. Long-Range Revenue Projections

Yang, E. and S. C. Goss (1992), “Economic Projections for the OASDHI Cost and Income

Estimates, 1992,” Actuarial Study No. 108, Social Security Administration, Baltimore, Maryland.
52

8. Long-Range Benefit Projections

Goss, S. C. (1984). “Long-Range Estimates of the Financial Status of the Old-Age, Survivors, and

Disability Insurance Program, 1983,” Actuarial Study No. 91, Social Security Administration,

Baltimore, Maryland.

Wilkin, J. C. (1988). “OASDI Long-Range Beneficiary Projection: 1987,” Actuarial Study

No. 100, Social Security Administration, Baltimore, Maryland.
53

Acknowledgements

It is important to reiterate the fact that these notes summarize an outsider’s view of the SSA

OCACT’s projections methodologies. As such, they are undoubtedly full of errors and

misinterpretations. Thus, although many of the OCACT staff listed below were helpful teachers,

any errors that are still in this summary are the fault of the student (that is, the author).

Thanks go to the following staff for the examination of prior drafts and many helpful telephone

conversations, FAXes and e-mails.

Eli Donkar, Bill Ritchie, and Seung An, Section 2 on Trust Fund Projections.

Felicitie Bell and Alice Wade, Section 3 on Population Projections.

Pat Skirvin, Short-Range Employment and Earnings Projections.

Tony Cheng and Bill Piet, Section 5 on Short-Range Revenue Projections.

Eli Donkar and Steve McKay, Section 6 on Short-Range Benefit Projections.

Rob Baldwin, Section 7 on Long-Range Revenue Projections.

Joe Faber, Seung An, Milt Glanz, Eugene Yang and Bill Ritchie, 

Section 8 on Long-Range Benefit Projections.