Long-Range OASDI Projection 

Methodology 

Intermediate Assumptions of the 2008 Trustees 

Report 

 June 2008 

 Office of the Chief Actuary 

 Social Security Administration 
I. Flow Charts 
Overview of Long-Range OASDI Projection Met

Process 

Econo

Process 1:

Demography

Process 4:

Trust Fund Operations and Actuarial S

Process 3:

Beneficiaries

Chart 1:
Trustees ultimate assumptions

Fertility

Mortality

Immigration

1.2 Mortality rates

Inputs: Historical number of U.S. deaths by cause and 

U.S. resident population; medicare deaths and enrollments

Outputs: Historical and projected death probabilities 

1.4 Historical Population

Inputs: Historical U.S. population, undercoun

status data and immigration prevalence estima

estimates of population in other components o

Security area. 

Outputs: Historical Social Security area popul

gender, and marital status (including starting 

Historical other than legal population by age, s

marital status 

1.5 Marriage

Inputs: Historical number of 

marriages, remarriage data, and 

consistent population (detailed data for 

a subset of the U.S. population) 

Outputs: Historical and projected 

central marriage rates

1.6 Divorce

Inputs: Historical number of divorces 

and consistent population (detailed 

data for a subset of the U.S. 

population) 

Outputs: Historical and projected 

central divorce rates 

1.7 Projected Population

Inputs: Historical U.S. family data 

Outputs: Projected data – Social Security are

by age, sex, and marital status, other than lega

by age, sex and marital status, children by age 

and average family size 

Economics, Beneficiaries, and T

Operation and Actuarial St

1.1 Fertility 

Inputs: Historical U.S. births and female 

resident population 

Outputs: Historical and projected central birth rates

1

Inputs: His

Outputs: Hi

annual imm

Demography – Process 1

Social Security Administration

Office of the Chief Actuary

June 2008

Chart 2:
Trustees Ultimate Economic Assumptions

Average real wageProductivityAverage hours workedInflationFull-employment unemployment rate

2.2 Class of Worker

Inputs: Historical BLS data, population (Demography), & economic factorsOutputs: Wage workers & selfemployed by age and sex 

2.3 AWI Series

Inputs: Historical AWI 

2.1 Real & Potential GDP, NInputs: Historical NIPA (BEAOutputs: Real, potential, and n

2.3 Covered Employment

Inputs: Historical U.S. & covered employmentdata, population including illegal immigrants (Demography) Outputs: Covered worker rates, covered worker levels, & total employed (all by age, sex, type of worker) 

2.2 U. S. Wag

Inputs: Historical NIPA (

(BLS) by sector 

Outputs: Wages & SE inc

2.3 Average Covered Earnings

Outputs: Projected average covered

earnings by type of worker

2.4 Taxable Earnings

Inputs: Historical distribution of earnings 

Outputs: Taxable wages, taxable SE income 

multi-employer refunds 

2.4 Average Taxable Earnings

Outputs: Average taxable earnings 

2.4 Effective taxable payroll

Outputs: Effective taxable payroll

Chart 3: Economics – Process 2

S

2.1 U. S. Employment

Inputs: Historical BLS data, population (Demography), disability prevalence 

rates (from prior TR), life expectancies (from Demography), & economic factors 

Outputs: Historical & projected labor force participation & unemployment rates by age and sex

2.3 Cov

Inputs: Historical 

data by sector 

Outputs: Historica

earnings by type of 

Beneficiaries, 

Trust Fund Operations and Actuarial Status

2.3 Taxable Maximum

Inputs: Historical taxable maximum 
3.1 Fully-insured (FI) population

Inputs: Covered workers, median earnings,and AWI (Economics); SS area population (Demography); earnings distribution, historical FI population (historical and short-rangeprojections).Outputs: FI population (historical and projected)

3.1 Disability-insured (DII) population

Inputs: Historical DII population 

Outputs: DII population (historical and projected)

3.2 Disabled-worker beneficiary (DIB) populationInputs: Base period incidence, recovery, and mortality rates. Projected Data -- Assumed ultimate changes in incidence rates, recovery rates, and mortality rates (Demography) from base period Outputs: DIB population and conversions to OAB (projected)

3.3 Old-Age beneficiary (OAB) population

Inputs: Historical OAB population, labor force 

participation rates (Economics), and scheduled 

reductions for early retirement and increases for

delayed retirement 

Outputs: OAB population (projected) 

3.3 Auxiliary Beneficiaries of Retired and Deceased Workers

Inputs: Historical auxiliary beneficiaries of retired and deceased

workers, SS area population by marital status (Demography), 

number of children with at least one retired parent (Demography),

number of children with at least one deceased parent 

(Demography), average number of children per family 

(Demography) and other relationships 

Outputs: Auxiliary beneficiaries of retired and deceased workers 

by type of benefit (projected) 

Trust Fund Operations and Actuarial Status

3.3 Widow benef

Inputs: Historical widow SS area population by marand other relationshipsOutputs: Insured and uninpopulation (projected)

Chart 4: Beneficiaries – Process 3

Soci

Of

3.2 DIB Auxiliary Beneficiaries

Inputs: Historical beneficiaries by type of benefit, Population (Demography), other relationships Outputs: Auxiliary beneficiaries of disabled workers by type of benefit (projected) 

Note: Insured widow refers to widow beneficiaries who are insured for OAIB benefits, but not receiving those benefits

Trustees ultimate assumptions

Disability incidence rates 

Disability recovery rates 

Disability mortality rates
Chart 5: Trust Fund Operations and Actuarial Status – 

4.3 Payroll 

Inputs: Payroll tax ratepayroll (Economics), incshort-range estimates Outputs: Payroll taxes

4.1 Fraction benefits taxable

Inputs: Historical and projected short-range data on 

income taxation of benefits from Office of Tax Analysis

in the Department of the Treasury and data from 

current population survey 

Outputs: TOB as of a percent of benefits (projected) 

4. 3 Taxation of benefits (TOB)

Outputs: Taxes on benefits

4.3 Administr

Inputs: Short-range adtotal beneficiary populaassumed increase in prOutputs: Administrativ

4.3 Benefit payments

Inputs: Starting average benefits, OAB population, DIB population,

married and divorced aged population (Demography), Cost-of-Living Adjustments (Economics), post-entitlement factors, assumed benefit relationships between workers and auxiliaries, shortrange estimates of benefit payments 

Outputs: Scheduled benefit payments during year, average scheduled

benefits 

4. 3 Railroad inte

Inputs: Data from Railroad AWI, covered workers, taxashort range estimates of raiOutputs: Net payments to R

4. 3 Interest income

Inputs: Short-range estimatesof interest incomeOutputs: Interest income, annual yield rate on the OASI, DI, and combined funds

Trust Fund Operations and Actuarial Status

Output: Summarized income and cost rates and actuarial balances; 

open Group unfunded obligations; annual income rate, cost rate and 

Social Security Administration Balance: Dollar trust fund operations and trust fund ratios

Office of the Chief Actuary

June 2008

Trustees ultimate aReal interest rate, C

4.2 AIME Levels for newly-entitled OABs and DIBs

Inputs: Sample of newly-entitled OABs and DIBs; sample

of earnings from CWHS; SS area population (Demography);

covered workers, average taxable earnings (Economics); 

and National Average Wage Index (AWI), Tax Maximum 

Outputs: Projected AIME distributions for new 

entitlements 
1

II. Process Descriptions 

The long-range programs used to make projections for the annual Trustees Report are grouped 

into four major processes. These include Demography, Economics, Beneficiaries, and Trust 

Fund Operations and Actuarial Status. Each major process consists of a number of subprocesses. 

Each subprocess is described in terms of three elements: 

• This overview attempts to provide a general description of the purpose of each 

subprocess. Key projected variables used in the subprocess are introduced. Some 

variables are represented as being dependent in an equation, where the dependent 

variable is defined in terms of one or more independent variables. Independent variables 

may include previously calculated dependent variables or data provided from outside the 

subprocess. Other key variables are referenced by “(·)” following the variable name. This 

indicates that the calculation of this variable can not easily be communicated by an 

equation and, thus, requires a more complex discussion. 

• Input Data – Data used in the subprocess are described. These data include those from 

other subprocesses, ultimate long-range assumptions provided by the Board of Trustees 

of the OASDI Trust Funds, data from other offices of the Social Security Administration, 

and data from outside the Social Security Administration (e.g., estimates of the U.S. 

population). Data description includes data source and data detail (e.g., define age detail 

of data). In addition, an indication of how often additional data are expected to be 

received is included. 

• Development of Output – The key variables are described in greater detail, including the 

level of disaggregation of the data. 
2

Process 1: 

Demography 
3

1. Demography 

The primary purpose of the Demography Process is to provide estimates of the projected Social 

Security area population1 for each year of the 75-year projection period in the Trustees Report. 

For the 2008 report, the projection period covers the years 2008 through 2082. The Demography 

Process receives input data mainly from other government agencies and provides output data to 

the Economics, Beneficiaries, and Trust Fund Operations and Actuarial Status processes. 

The Demography Process is composed of seven subprocesses: FERTILITY, IMMIGRATION, 

MORTALITY, HISTORICAL POPULATION, MARRIAGE, DIVORCE, and PROJECTED 

POPULATION. As a rough overview, FERTILITY projects birth rates by age of mother, 

IMMIGRATION projects numbers of immigrants by age and sex, and MORTALITY projects 

probabilities of death by age and sex. HISTORICAL POPULATION combines population 

estimates from different sources to obtain historical estimates of the Social Security Area 

population by single year of age, sex and marital status. MARRIAGE projects marriage rates by 

age-of-wife crossed with age-of-husband and DIVORCE projects divorce rates by age-ofhusband crossed with age-of-wife. PROJECTED POPULATION starts with the latest estimates 

of the Social Security Area population from HISTORICAL POPULATION and projects the 

population by age, sex, and marital status using projected values from FERTILITY, 

IMMIGRATION, MORTALIY, MARRIAGE, and DIVORCE. 

1.1. FERTILITY 

1.1.a. Overview 

The National Center for Heath Statistics (NCHS) collects data on annual numbers of births and 

the U.S. Census Bureau produces estimates of the resident population. Birth rates for historical 

years are calculated from these data by single year of age of mother. Age-specific birth rates 

( z bx ) for a given year z are defined as the ratio of (1) births ( z Bx ) during the year to mothers at the 

specified age x to (2) the midyear female population ( z Px ) at that age. The total fertility rate 

z TFR summarizes the age-specific fertility rates for a given year. The total fertility rate for a 

given year z is defined as the sum of the age-specific birth rates for all ages x during the year z. 

It can be interpreted as the number of children born to a woman if she were to survive her 

 

1

 The Social Security area population consists of all persons who are potentially eligible to either receive benefits 

under the Social Security program or who have the potential to work in covered employment. This population 

consists of residents of the U.S. and its territories, citizens living abroad, and beneficiaries living abroad. 
4

childbearing years and experience the age-specific fertility rates of year z throughout her 

childbearing years. 

The FERTILITY subprocess combines the historical values of z bx and z TFR with an ultimate 

assumed future value of the TFR to develop projections of z bx . The primary equations of this 

subprocess are given below: 

z bx = z bx (

.

) (1.1.1) 

= ∑x

z

x

z TFR b (1.1.2) 

1.1.b. Input Data

Trustees Assumptions - 

Each year the Board of Trustees of the OASDI Trust Funds sets the ultimate assumed values 

for the TFR. The TFR reaches its ultimate value in the 25th year of the projection period. 

Under the intermediate assumptions underlying the 2008 Trustees Report, the ultimate TFR

is 2.0 and it is assumed to be reached in 2032. 

Other input data - 

• From NCHS, annual numbers of births by age of mother2 (10-14, 15, 16, 17, ..., 48, 

49-54) for years 1980-2004. In general, NCHS provides an annual update including 

one additional year of birth data. The previous historical years are only updated if 

NCHS makes a historical revision to their data. 

• From the U.S. Census Bureau, estimates of the July 1st female resident population by 

single year of age for ages 14-49 for 1980-2004. Each year, Census provides updated 

data for years after the most recent decennial census 

• NCHS historical birth rates, by single year of age of mother (14-49) for the period 

1917-79. No updates of these data are needed. 

1.1.c. Development of Output 

 

2

 The ages provided include 10-14, 15, 16, 17, ..., 48, 49-54. Births at ages less than 14 are treated as having 

occurred at age 14 and ages reported to mothers older than 49 are treated as having occurred at age 49. 
5

Equation 1.1.1 - Age-specific birth rates 

The FERTILITY subprocess produces the age-specific birth rates, by childbearing ages 14 

through 49, for years 1941 through the 75-year projection period. For historical years prior to 

1980, age-specific birth rates were obtained from NCHS. For years 1980 through the remaining 

historical period, age-specific birth rates are calculated as: z

x

z

z x

x P

B b = , using birth data from NCHS 

and estimates of the July 1st female resident population from the U.S. Census Bureau. 

The age-specific birth rates are projected using a process that is consistent with both the 

observed trends in recent data and the ultimate assumed total fertility rate. This process consists 

of the following steps: 

1. Averaged birth rates by age group3, designated as z

5 bx , are calculated from the agespecific birth rates z bx for each year during the period 1979-2004. 

2. To calculate the starting values of the projection process, the z

5 bx from the last five years 

of historical data are averaged using weights of 5, 4, 3, 2 and 1 for years 2004, 2003, 

2002, 2001, and 2000 respectively. 

3. For each z

5 bx , the slope of the least squares line is calculated based on a regression over 

the period 1979-2004. 

4. For 2005, each of the seven starting values of z

5 bx (from Step 2) is projected forward by 

adding 100 percent of their respective slope (from Step3). Then, the total fertility rate, 

TFR z, is calculated such that it is equal to 5 times the sum of each z

5 bx . For the age 

group 14-49, 6 times the sum is included since this age group contains one additional age. 

5. For the next year, 2006, the same calculation is done except each z

5 bx for 2005 is 

projected forward by adding 96 percent of the respective slope (from Step3). For 

subsequent projection years (2007-2032), an arithmetically decreasing portion4

 is added 

to the previous year’s value of z

5 bx . 

6. A preliminary total fertility rate, z TFRp , is calculated from the estimated values of z

5 bx

(from Step 5) and is calculated in the same manner as Step 4. 

 

3

 The average is calculated by giving each age in the group equal weight without regard to population. The age 

groups calculated are 14-19, 20-24, 25-29, 30-34, 35-39, 40-44, and 45-49. 

4

 Each year of the projection the slope is reduced by four percentage points. 
6

7. For years 2007 and later, an adjustment is made so that the annual TFR z is consistent 

with the Trustees’ assumed ultimate level5

. For 2007, the TFR z is assumed to equal the 

level estimated for 2006 and then decrease linearly until reaching the ultimate value in 

2032. 

8. To ensure the assumed total fertility rate is achieved, each value of z

5 bx (step 5) is 

multiplied by the ratio of the assumed z TFR (step 7) and the respective value of TFRp 

(Step 6).

9. The final step of the projection method disaggregates the adjusted z

5 bx into single age 

birth rates by multiplying the z

5 bx (Step 8) by the ratio of the single year z bx to the z5 bx

for each of the respective ages and age groups as calculated in the last year of complete 

historical data (Step 1). 

1.2 MORTALITY 

1.2.a. Overview 

The NCHS collects data on annual numbers of deaths and the U.S. Census Bureau produces 

estimates of the U.S. resident population. Central death rates (yMx) are defined as the ratio of (1) 

the annual number of deaths occurring during the year to persons between exact ages x and x+y

to (2) the mid-year population between exact ages x and x+y. For historical years prior to 1968, 

yMx, are calculated from the NCHS and Census data by sex. For historical years after 1968, the 

same data are used in the calculations for ages under 65 but data from the Centers for Medicare 

and Medicaid Services (CMS) are used for ages 65 and over. Based on death by cause data from 

NCHS, the yMx, are distributed by cause of death for years 1979 and later6. 

Over the last century, death rates have decreased substantially. The historical improvement in 

mortality is quantified by calculating the average annual percentage reduction (yAAx) in the 

central death rate. In order to project future yMx, the Board of Trustees of the OASDI Trust 

 

5

 For 2005 and 2006, z TFR is assumed to equal z TFRp . 

6

 Data needed in order to project central death rates by cause of death were obtained from Vital Statistics 

tabulations for years since 1979. For the years 1979-1998, adjustments were made to the distribution of the numbers 

of deaths by cause. The adjustments were needed in order to reflect the revision in the cause of death coding that 

occurred in 1999, making the data for the years 1979-1998 more comparable with the coding used for the years 1999 

and later. The adjustments were based on comparability ratios published by the National Center for Health 

Statistics. 
7

Funds determines the ultimate average annual percentage reduction that will be realized during 

the projection period ( u

y AAx ). 

The basic mortality outputs of the MORTALITY subprocess that are used in projecting the 

population are probabilities of death by age and sex (qx). The probability that a person age x will 

die within one year (qx) is calculated from the central death rates (the series of yMx). 

Period life expectancy ( ) is defined as the average number of years of life remaining for people 

who are age x and are assumed to experience the assumed probabilities of death throughout their 

lifetime. It is generated from the probabilities of death for a given year and is a summary statistic 

of overall mortality for that year. 

Age-adjusted death rates (ADR) are also used to summarize the mortality experience of a single 

year, making different years comparable to each other. Age-adjusted death rates are a weighted 

average of the yMx, where the weights used are the numbers of people in the corresponding age 

groups of the standard population, the 2000 U.S. Census resident population ( y x SP ). Thus, if 

the age-adjusted death rate for a particular year and sex is multiplied by the total 2000 U.S. 

Census resident population, the result gives the number of deaths that would have occurred in the 

2000 U.S. Census resident population if the yMx for that particular year and sex had been 

experienced. Age-sex-adjusted death rates (ASDR) are calculated to summarize death rates for 

both sexes combined and are calculated as a weighted average of the yMx, where each weight is 

the number of people in the corresponding age and sex group of the 2000 U.S. Census resident 

population. 

MORTALITY projects annual yMx which are then used to calculate the program’s additional 

outputs. The equations for this subprocess, 1.2.1 through 1.2.6, are given below: 

 yMx = yMx (·) (1.2.1) 

 

 yAAx = yAAx (·) (1.2.2) 

 qx = qx (·) (1.2.3) 

 
8

 = (·) (1.2.4) 

∑

∑ ⋅

=

x

y x

z

y x s

x

y x

z

s SP

SP M

ADR

,

 (1.2.5) 

∑∑

∑∑ ⋅

=

s x

y x s

s

z

y x s

x

y x s

z

SP

SP M

ASDR

,

, ,

 (1.2.6) 

where z

y M x,s refers to the central death rate between exact age x and x+y by sex in year z; 

ySPx denotes the number of people in the standard population (male and female combined) who 

are between exact age x and x+y; and ySPx,s denotes the number of people by sex in the standard 

population who are between exact age x and x+y. 

1.2.b. Input Data

Trustees Assumptions -

Each year the Board of Trustees of the OASDI Trust Funds sets the ultimate assumed 

values for the yAAx by sex, age group7 and cause of death8. The average annual percentage 

reductions reach their ultimate value in the 25th year of the 75-year projection period. The 

ultimate rates of reduction by sex, age group, and cause of death can be found in Appendix 

1.2-1. 

NCHS Data -

• Annual numbers of registered deaths by sex and age group for the period 1900-1978. 

These data are not updated. Registered deaths refer to deaths in the Death Registration 

area. Since 1933, the Death Registration area has included all of the U.S. 

• Annual numbers of deaths by sex, age group, and cause for the period 1979-2004. 

Each year, a new year of data is generally received. In addition, revised data are often 

available for years beginning with 1999 (1999 was the starting year of the latest 

international classification of diseases – ICD10). 

 

7

 Age groups are: less than 15, 15-49, 50-64, 65-84, 85+ 

8

 The seven causes of death are: Heart Disease, Cancer , Vascular Disease, Violence, Respiratory Disease, Diabetes 

Mellitus, and Other 
9

• The monthly number of births by sex for years 1938-2004. These data are updated 

annually, when NCHS provides an additional year of data. 

• The number of infant deaths by age sex and age group9 for years 1938-2004. These 

data are updated annually, when NCHS provides an additional year of data. 

• Deaths for 1995 and 1996 by sex, 4 marital statuses, and 21 age groups. The age 

groups are generally 5-year age groups and are as follows: 0, 1-4, 5-9, 10-14, ...., 

95+). These data are updated as resources are available. 

• The population of states in the Death Registration area by age group10 and sex for 

years 1900-1939. These data are not updated. 

• The number of registered deaths by sex and age groups (85-89, 90-94, and 95+) for the 

years 1900- 1967. These data are not updated. 

U.S. Census Bureau Data -

• Estimates of the July 1 resident population by single year of age (0 through 100+) for 

years 1980-2004. Each year, Census provides an additional year of data and updated 

data for years after the most recent decennial census. 

• From the Current Population Survey (CPS), the population by sex, marital status, and 

age group11 for the years 1995 and 1996. These data are updated as resources are 

available. 

• The resident population by sex, martial status, and age group12 as of as of July 1, 1995 

and 1996. These data are updated when new NCHS death data by marital status are 

incorporated. 

• The resident population by sex and age group13 for years 1900-1939. These data are 

not updated. 

• The resident population at ages 75-79 and 80-84, by sex, for years 1900-1940 (at ten 

 

9

 Age groups are: under 23 hours, 1-2 days, 3-6 days, 7 -27 days, 28 days-1 month, 2 months, 3 months,..., 11 

months 

10 Age groups are: 0, 1-4, 5-14, 15-24, ..., 75-84, 85+ 

11 Age groups are: 15-17, 18-19, 20-24, 25-29,..., 40-44, 45-54, ..., 65-74, and 85+ 12 Age groups are: 15-19, 20-24, 25-29, ..., 95+ 

13 Age groups are: 0, 1-4, 5-14, 15-24, ..., 75-84, 85+ 
10

year intervals). These data are not updated. 

• The resident population by sex and age groups14 for 1940-2000. These data are not 

updated. 

 

Centers for Medicare and Medicaid Services Data - 

• Annual numbers of deaths by sex and single year of age (ages 65 and over) for the 

period 1968-2004. These data are updated annually, when CMS provides an 

additional year of data. 

• Annual numbers of Medicare enrollments (who are insured for Social Security 

benefits) by sex and single year of age (ages 65 and over) for the period 1968-2004. 

These data are updated annually, when CMS provides an additional year of data. 

Other input data - 

• From the previous year’s Trustees Report the July 1, 1995 and 1996 Social Security 

area population by sex, martial status, and single year of age (5 through 100+). These 

data are updated when new NCHS death data by marital status are incorporated. 

1.2.c. Development of Output

Equation 1.2.2 - Average Annual Percentage Reduction ( y AAx )

The y AAx by sex and cause are calculated based on the decline in the yMx for the period 1984 

through 2004 and distributed by 21 age groups15, 2 sexes, and 7 causes of death16. The values 

are calculated as the complement of the exponential of the slope of the least-squares line through 

the logarithms of the yMx. 

The ultimate assumed values for the ( u

y AAx ), as set by the Board of Trustees of the OASI and DI 

Trust Funds, are assumed to be reached in the 25th year of the 75-year projection period. The 

assumed ultimate values are specified by sex, seven causes of death, and for the following five 

age groups: under age 15, 15-49, 50-64, and 65-84, and 85 and older. 

 

14 Age groups for years prior to 1980 are: 0, 1-4, 5-9, ..., 85+. For years 1980-1982, the age groups are: 0, 1-4, 5-9, 

..., 95+. For years 1983 and later, the age groups are 0, 1-4, 5-9, ..., 85+. 15 Age groups are: 0, 1-4, 5-9, 10-14, ......, 90-95, and 95+ 

16 The seven causes of death are: Heart Disease, Vascular Disease, Violence, Cancer, Respiratory Disease, Diabetes 

Mellitus, and Other. 
11

The values of y AAx by the 21 age groups, sex, and cause for 2005 through 2007 are assumed to 

equal the average y AAx based on the decline in the yMx for the period 1984-2004. If, however, 

the average y AAx for a particular group during the period is negative, then 75 percent of the 

average rate is used. For years after 2007, a method of graduation is used that causes the 

absolute difference between the current y AAx and the ultimate u

y AAx to decrease rapidly until it 

reaches the Trustees’ ultimate assumed value, u

y AAx . This is accomplished by repeating the 

following steps for each year of the projection: 

1. The absolute value of the distance between the prior year’s calculated y AAx and the 

ultimate assumed u

y AAx is calculated. 

2. If the ultimate assumed u

y AAx is greater than the prior year’s y AAx , 80 percent of the 

difference is subtracted from the ultimate assumed u

y AAx . If the ultimate assumed 

u

y AAx is less than the prior year’s y AAx , then 80 percent of the difference is added to 

the ultimate assumed u

y AAx . 

3. These steps are repeated until the 25th year at which time the y AAx are set equal to 

their ultimate assumed values. 

Equation 1.2.1 – Central Death Rates (yMx) 

Values of yMx are determined for each historical and projected year by the 21 age groups, 2 

sexes, and 7 causes of death. The starting year for the projections of the yMx is 2004, and is the 

most recent data year in the historical period. However, instead of using the historical data for 

yMx in this year as the starting point for mortality projections, starting yMx are calculated to be 

consistent with the trend inherent in the last 12 years of available data. Each starting value for 

the yMx, by sex and cause of death, is computed as the value for the most recent year falling on a 

weighted least square line, where yMx is regressed on year, over the last 12 years. The weights 

are 0.2, 0.4, 0.6, and 0.8 for the earlier four years of the 12 years and are 1.0 for all other years. 

For years after 2004, yMx are projected by sex and cause of death by applying the respective 

y AAx to the prior year yMx. 

Equations 1.2.3 – Probabilities of death (qx)
12

In order to project population by age and sex, probabilities of death are applied to determine the 

projected number of deaths that will occur in the population. These probabilities, denoted as qx,

reflect the probability a person age x will die within one year, where x refers to age last birthday 

as of the beginning of each year. For each year in the historical and projection period, separate 

qx, series are estimated by sex. 

Different methods of projecting qx are used for age 0, for ages 1 through 4, for ages 5 through 95 

and for ages 95 and above. The following descriptions provide a brief discussion of these 

different methods. Additional detail is provided in Actuarial Study number 120 located at the 

following internet site: 

http://www.socialsecurity.gov/OACT/NOTES/as120/LifeTables_Foreword.html. 

• Values for qx at Age 0: During the first year of life, mortality starts at an extremely high 

level, which becomes progressively lower, unlike mortality at other ages which does not 

change very much within a single year of age. Thus, it is particularly important at age 0 to 

estimate accurately the pattern of mortality throughout the year of age, as described above, 

for the calculation of q0. For the period 1940 through the last historical year, q0 is 

calculated directly from tabulations of births by month and from tabulations of deaths at 

ages 0, 1-2, 3-6, 7-28 days, 1 month, 2 months, ..., 11 months. After the last historical year, 

q0 is calculated from 1M0, assuming that the ratio of q0 to 1M0 measured for the last 

historical year would remain constant thereafter. 

• Values for qx at Ages 1 – 4: For the period 1940 through the last year of historical data, 

probabilities of death at each age 1 through 4 (qx, x = 1, 2, 3, 4) are calculated from 

tabulations of births by year and from tabulations of deaths at ages 1, 2, 3, and 4 years. 

After the last historical year, each qx (where x = 1, 2, 3, 4) is calculated from 4M1 assuming 

that the ratio of qx to 4M1 measured for the last historical year would remain constant 

thereafter. 

• Values for qx at Ages 5 – 94: Probabilities of death for these ages are calculated from the 

projected central death rates, 5Mx. As mentioned above, the calculations are discussed in 

detail in Actuarial Study number 120. 

• Values for qx at Ages 95+: It has been observed that the mortality rates of women, though 

lower than those of men, tend to increase faster with advancing age than those of men. An 

analysis of Social Security charter Old-Age Insurance beneficiaries has shown that at the 

very old ages mortality increases about five percent per year of age for men and about six 

percent per year for women. Probabilities of death at each age 95 and older are calculated 

as follows for men: 
13

For women, the same formulas are used, except that 1.06 is substituted for 1.05. The 

larger rate of growth in female mortality would eventually, at a very high age, cause 

female mortality to be higher than male mortality. At the point where this crossover 

would occur, female mortality is set equal to male mortality. 

The values of qx used in projecting the population are based on age last birthday and are 

calculated by sex for 1/2q0 and for qx where x represents age last birthday and equals 0, 1, 2, ....., 

99. Because life table values of probabilities of death are based on exact ages, values for qx

representing age last birthday for ages 0 through 99 are derived by averaging the life table values 

of probabilities of death at ages x and x+1. Deaths occurring during the first six months of life 

are calculated directly from the life tables’ values and are applied to births during the year. 

Deaths occurring in the population at ages 100 and older are projected as a group. 

In addition, probabilities of death are broken down further into marital status. Historical data 

indicate differential in mortality by marital status is significant. To reflect this, projected relative 

differences in death rates by marital status are projected to be the same as observed during 

calendar years 1995 and 1996. 

Equation 1.2.4 –Life expectancy 

Actuarial Study number 120 presents background information on the calculation of life 

expectancy, from the probabilities of death (qx,). This study, titled Life Tables for the United 

States Social Security Area 1900-2100, can be accessed at the following internet site: 

http://www.socialsecurity.gov/OACT/NOTES/as120/LifeTables_Foreword.html. 

1.3. IMMIGRATION 

1.3.a. Overview 

Immigration consists of legal immigration, legal emigration, other immigration and other 

emigration. Legal immigration is defined as those persons who have been admitted into the 

United States and been granted legal permanent resident (LPR) status. Legal emigration consists 

of legal permanent residents and U.S. Citizens who depart the Social Security area population to 

reside elsewhere. Other immigrants include persons, other than LPRs, who enter the U.S. and 
14

reside for 6 months or longer such as undocumented immigrants, temporary workers, and foreign 

students. Other emigration includes other immigrants who depart the Social Security area for 

another country in addition to those who adjust status to become an LPR. 

For each year z of the projection period, the IMMIGRATION subprocess produces estimates of 

legal immigration (Lz), legal emigration (Ez), and other immigration (Oz), by age and sex, based 

on assumptions set by the Trustees for each category. Estimates of other emigration are not 

developed in this subprocess, but rather are developed in the projected population subprocess 

documented in section 1.7. In addition, the IMMIGRATION subprocess disaggregates the 

estimates of Lz into those who have been admitted into the United States during the year (NEWz) 

and those who adjusted from the other-immigrant population to LPR status (AOSz) 

Each fiscal year17, the Department of Homeland Security (DHS) collects data on the number of 

persons granted LPR status by age, sex, and class of admission. The U.S Census Bureau 

provided OCACT with an unpublished estimate of the annual number of legal emigrants, by sex 

and age, based on the change between the 1980 and 1990 census. The Census Bureau also 

estimated the aggregate number of net other immigrants who entered the country during 1975-

1980, by age and sex. These historical data are used as a basis for developing age-sex 

distributions that are applied to the Trustees’ aggregate immigration assumptions to produce 

annual immigration and emigration estimates by age and sex. 

The primary equations of IMMIGRATION, by age (x) and sex(s), for each year (z) of the 75-

year projection period are summarized below: 

( ) , , = ⋅ z

x s

z NEWx s NEW (1.3.1) 

( ) , , = ⋅ z

x s

z AOSx s AOS (1.3.2) 

z

x s

z

x s

z Lx s NEW AOS , = , + , (1.3.3) 

( ) , , = ⋅ z

x s

z Ex s E (1.3.4) 

z

x s

z

x s

z NLx,s = L , − E , (1.3.5) 

( ) , , = ⋅ z

x s

z Ox s O (1.3.6) 

 

1.3.b. Input Data

Trustees Assumptions - 

 Each year the Board of Trustees of the OASDI Trust Funds specifies the total annual assumed 

values for legal immigration, legal emigration, and other immigration. For the 2008 Trustees 

 

17 The federal fiscal year begins on October 1 and ends on September 30 of the next calendar year. 
15

Report, the ultimate values for legal immigration and emigration are 1,000,000 and 250,000 

respectively (both reached in 2010). For other immigration, the Trustees set the annual level at 

1,500,000 persons per year for each year of the projection period. 

Other input data - 

• Historical legal immigration from DHS by fiscal year (1996-2006), single year of age (0 

through 84), sex, and class of admission (New Arrival, Adjustment of Status, Refugee, 

and Asylee). This data is updated annually, with DHS providing an additional year of 

data each year. 

• Unpublished estimates of annual legal emigration from The U.S Census Bureau by fiveyear age groups (0-4, 5-9,..., 80-84) and sex based on the change between the 1980 and 

1990 census. These data are updated occasionally (based on having new data from an 

outside source and on OCACT resource time constraints). 

• Legal emigration conversion factors. These estimates were developed internally by fiveyear age groups (0-4, 5-9,..., 80-84) and sex to reflect the fact that the estimated number 

of people leaving the United States is not equivalent to the number of people leaving the 

Social Security Area. These data are updated when annual legal emigration estimates are 

updated (see above). 

• Unpublished tabulations from the U.S Census Bureau of the cumulative number net other 

immigrants entering the country during 1975-1980 by five-year age groups (0-4, 5-9,..., 

80-84) and sex. These data are updated occasionally (based on having new data from an 

outside source and on OCACT resource time constraints). 

 

1.3.c. Development of Output

Equations 1.3.1 and 1.3.2 – Legal Immigration 

The Trustees specify the aggregate amount of legal immigration for each year of the 75-year 

projection period. In order to incorporate the numbers of new immigrants into the Social 

Security area population projections, the total level of new immigrants is disaggregated by age 

and sex. 

There are two ways for an immigrant to be admitted into the U.S. for lawful permanent 

residence: 

(1) New arrivals such as persons living abroad who are granted an LPR visa and then enter 

the U.S. through a port of entry. Refugees and asylees that are granted LPR status are 

also treated as new arrivals in the OCACT model. 
16

 

(2) Adjustments of status, who are people already residing in the U.S. as other immigrants 

and have an application for adjustment to LPR status approved by DHS. 

The DHS provides data on legal immigrants by sex, single year of age, classification of 

admission, and fiscal year of entry. The 10 most recent years of data are used to calculate 

separate age-sex distributions for both new arrivals and adjustments of status by taking the 

following steps: 

1. The data for the last ten years of single-year of age data are combined into five-year age 

groups. 

2. Refugee and Asylee LPR admissions are subtracted from the adjustment of status data 

and added into the new arrival category. 

3. The data are converted from fiscal year data to calendar year data. 

4. For each class of admission, new arrival and adjustment of status, the historical data for 

the last 10 years (from 1997-2006) are combined into an average age-sex distribution. 

5. The distributions by five year age group are disaggregated into a single year of age-sex 

distribution using the H.S. Beers method of interpolation. 

Based on trends in the historical data, it is assumed that fifty percent of all new LPR admissions 

will be new arrivals and the other fifty percent will consist of adjustments of status. Thus, z NEWx,s , the expected number of new arrival legal immigrants by age (x) and sex (s), is 

calculated by applying the age-sex distribution for new arrivals to one half of the Trustees 

assumed level of legal immigration. The remaining half of the Trustees’ assumed number of 

legal immigrants is multiplied by the age-sex distribution of adjustments of status to 

calculate z AOSx,s . 

Equation 1.3.4 – Legal Emigration 

The Trustees specify the aggregate amount of legal emigration for each year of the projection 

period. This is done by setting the ratio of emigration to legal immigration. For the 2008 

Trustees Report, the ratio is set at 25 percent. 

In order to produce the number of emigrants from the Social Security area population, the total 

level of emigrants is disaggregated by age and sex. The disaggregation is based on a distribution 

of emigrants, by sex and five-year age groups, provided to OCACT in unpublished estimates by 

Census that are based on changes between the 1980 and 1990 census. Since the emigration 

numbers estimated by Census are for all people leaving the United States, they are adjusted 

downward by a series of conversion factors so the data correspond to the number of people 

leaving the Social Security area population. 
17

For each sex, the Beers formula is used to interpolate and distribute each five-year age group into 

a single year of age-sex distribution, EDISTx,s. For each projection year, this distribution is used 

to distribute the assumed level of total legal emigrants by age and sex using the following 

equation: 

∑∑= =

=

f

s x m

x s x s

z Ex s L EDIST

84

0

, , , .25( )*

Equation 1.3.6 – Other Immigration 

The term “other immigration” refers to persons entering the U.S. in a manner other than being 

lawfully admitted for permanent residence. This includes temporary immigrants (persons legally 

admitted for a limited period of time) in addition to undocumented immigrants living in the U.S. 

The Trustees specify the aggregate amount of other immigrants for each year of the projection 

period. For each projection year, an age-sex distribution is used to distribute this assumption by 

age and sex. This age-sex distributions is denoted as ODISTx,s and is developed from a weighted 

average of the distribution of adjustments of status from Equation 1.3.2 and an age-sex 

distribution of non-adjusting other immigrants. 

The age distribution of the adjustments of status is modified to incorporate a five year set back 

based on the assumption that adjustments of status enter the U.S. five years earlier on average. 

This age-sex distribution is denoted as ODIST1x,s. The age distribution of non-adjusting other 

immigrants, ODIST2x,s is derived from an unpublished census estimate of net other immigration 

during the period 1975-80 using assumed levels of persistence. The two age distributions are 

then combined using the following formula: 

ODISTx,s w ODIST x,s w ODIST2x,s = ( 1 ) + (1− )

Where w is a weighting factor equal to the Trustees ultimate assumed level of adjustments of 

status increased by a factor18 of 1.25 divided by the Trustees ultimate assumed level of other 

immigration. For the 2008 Trustees Report, this w equals 0.625. Thus, for each year (z) other 

immigration is defined by the following equation: 

x s

z Ox,s ODIST , = 1,500,000 ∗ 

1.4. HISTORICAL POPULATION 

 

18 This factor is meant to take into account that a large number of people who have the potential to adjust to LPR 

status may die or return to their native country prior to doing so. 
18

1.4.a Overview 

For each historical year, the HISTORICAL subprocess provides estimates of the Social Security 

area population by for the period 1941 through 2006. The Social Security area population 

consists of: 

• U.S. resident population and armed forces overseas plus 

• Net census undercount plus 

• Civilian residents of Puerto Rico, the Virgin Islands, Guam, the Northern Mariana 

Islands, and American Samoa plus 

• Federal civilian employees overseas plus 

• Dependents of armed forces and federal civilian employees overseas plus 

• Residual beneficiaries living abroad plus 

• Other citizens overseas 

The U.S. Census Bureau collects population data and tabulates it by age, sex, and marital status 

every ten years for the decennial census. The decennial census includes data from the 50 states, 

the District of Columbia, U.S. territories and citizens living abroad. Each subsequent year, the 

Census Bureau publishes an estimate of the post-censal population. This subprocess combines 

these censal estimates, along with the estimates of the other components of the Social Security 

area population listed above and components of change described in sections 1.1 to 1.3 to 

develop smoothed estimates of the Social Security area population by single year of age and sex 

( z Px,s ). Combining this population with an estimated marital status matrix provides the Social 

Security area population by single year of age, sex, and marital status ( z Px,s,m ). These estimates 

are then used as the basis for the POPULATION PROJECTION process described in section 1.7. 

The primary equations for this subprocess, 1.4.1 and 1.4.2 are given below: 

z Px,s = z Px,s (·) (1.4.1) 

z Px,s,m = z Px,s,m (·) (1.4.2) 

1.4.b. Input Data 

Long-Range OASDI Projection Data - 

Demography 

• Probabilities of death from MORTALITY, by age last birthday and sex, for years 

1941-2005. These data are updated every year. 
19

• The number of new legal immigrants by age and sex for years 1941-2005. These 

data are from the IMMIGRATION subprocess and are updated each year. 

U.S. Census Bureau Data - 

• Decennial census total population estimates. A new estimate is available every ten 

years. 

• Estimates of U.S resident population and Armed Forces population overseas as of 

each July 1 (1980-2006) by sex and single-year of age 0 through 99, and ages 100 

and older. Each year, the U.S. Census Bureau restates the data back to the most 

recent decennial census and includes one additional year of data. 

• Estimates of the 1940, 1950, and 1960 counts of the U.S. population and armed 

forces overseas by sex and single year of age (0-84) and the age group 85+. These 

data are not updated. 

• Estimates of the population by age group19, sex, and marital status for years 1940-

2006. An additional year of data is added for each Trustees Report. 

• Estimates of the population by marital status, which have more age groups than the 

CPS, and sex for years 1982-1989 and 1992-2000. These data are not updated. 

• Undercount factors by single year of age (0-85+) and sex, estimated using postcensal survey data. These data are updated after each decennial census. 

• The total annual civilian population estimates for Puerto Rico, Virgin Islands, 

Guam, Northern Marianas, and American Samoa for years 1940-2006. For each 

Trustees Report, an additional data year is downloaded from the U.S. Census 

Bureau’s international database. 

• Estimates of U.S resident population and Armed Forces population overseas as of 

each July 1 (1940-1979) by sex and single-year of age through 84, and for the group 

aged 85 and older. These data are not updated. 

• From the U.S. Census Bureau 1980 Census of Population, Subject Report on 

Marital Status No. PC80-2-4C, number of existing marriages in 1980 by age group 

of husband crossed with age group of wife. These data are not updated. 

 

19 Age groups are: 15-17, 18-19, 20-24, 25-29, ..., 55-64, 65-74, 75-84, 85+ 
20

Other input data - 

• From the Centers for Medicare and Medicaid (CMS), the population insured for 

Social Security benefits by single year of age (85-100+) and sex for years 1968-

2006. The last year of data is provisional. Each year, CMS provides a final year of 

data to replace the prior year’s provisional data and a new provisional year of data. 

• The SSA Annual Statistical Supplement provides estimates of the total number of 

OASDI Beneficiaries living abroad for years 1987-2006. For each Trustees Report, 

an additional year of data is available. 

• Output from the Urban Institute’s microsimulation model, POLISIM, regarding 

marriage prevalence for the period 1980-2006 by age of husband and age of wife. 

For each Trustees Report, the data may be revised and an additional year of data 

may be added. 

1.4.c. Development of Output

Equation 1.4.1 – Historical Population by age and sex ( z Px,s )

The Census Bureau's estimate of the residents of the 50 States, D.C., and U.S. Armed Forces 

overseas is used as a basis for calculating z Px,s . The base estimate is adjusted for net census 

undercount and increased for other U.S. citizens living abroad (including residents of US 

territories) and for non-citizens living abroad who are insured for Social Security benefits. 

The estimates of the number of residents of the fifty States and D.C. and Armed Forces overseas, 

as of July 1 of each year, by sex for single years of age through 84, and for the group aged 85 or 

older, are obtained from the Census Bureau. Adjustments for net census undercount are 

estimated using post-censal survey data from the Bureau of the Census. The numbers of persons 

in the other components of the Social Security Area as of July 1 are estimated by sex for single 

years of age through 84, and for the group aged 85 or older, from data of varying detail. 

Numbers of civilian residents of Puerto Rico, the Virgin Islands, Guam, American Samoa, and 

the Northern Mariana Islands are estimated from data obtained from the Bureau of the Census. 

Numbers of Federal civilian employees overseas, dependents of these Federal civilian 

employees, dependents of Armed Forces overseas, and other citizens overseas covered by Social 

Security are also based on estimates used by the Bureau of Census. The overlap among the 

components, believed to be small, is ignored. 
21

The first step of the process is to estimate z Px,s as of January 1st for each decennial census year 

and the last year of historical data (2006 for the 2008 Trustees Report). For ages 0-84, z Px,s is set 

equal to the estimate from the decennial Census plus the undercount adjustment and other 

component populations. The decennial census estimates are as of April 1 but are converted to a 

January 1st population based on the surrounding applicable intercensal July20 population 

estimates. The population for final historical year is estimated based on the surrounding postcensal July populations. For ages 85 and over, data from the Center for Medicare and Medicaid 

Statistics (CMS) are used to distribute the population into single-year of age. 

For years between the decennial census years and years between the 2000 census and the last 

historical data year, populations are estimated taking into account the components of changes 

due to births, deaths, and legal immigration during that time period. These intercensal estimates 

are then multiplied by the appropriate age-sex-specific ratios so that the error of closure at the 

decennial census years is eliminated. 

Equation 1.4.2 – Historical Population by age, sex, and marital status ( z Px,s,m )

Since eligibility for auxiliary benefits is dependent on marital status, the Social Security area 

population is disaggregated by marital status. The four marital states are defined as single 

(having never been married), married, widowed, and divorced. 

The distribution of the number of existing marriages is based on the 1980 Census Marital Status 

Report, which contains the number married couples in 1980 by age group of husband crossed 

with age group of wife. Additional tabulations from the POLISM model for 1980 through 2006 

are incorporated to adjust these marital prevalence grids for changes since 1980. Multiplying the 

previous year values by the ratio the current year POLISM value to the previous year POLISM 

value ensures that the 1980 and later grids are consistent with the pre-1980 grids. The grids are 

transformed from age grouped numbers to single year of age figures from ages 14 to 100+ for 

husband and wife using the two dimensional H.S. Beers method of interpolation. 

Percentages of single, married, widowed, and divorced persons are calculated by taking the 

estimate for each marital status category and dividing them by the total number of people for 

each age group and sex from either the CPS or the more detailed Census numbers if available. 

Then, for each sex, if one age group has a higher or lower percentage than the surrounding age 

groups, an average of the surrounding groups replaces the original value. These percentages are 

multiplied by the total populations calculated in Equation 1.4.1 for each age, sex, and year to get 

a preliminary population for each age, sex, and marital status. 

 

20 For years prior to decennial years 1960 and earlier the April 1 population estimates are used. 
22

To keep the marriage prevalence grids and the marital status percentages smooth, several 

smoothing algorithms are used. First, the married population is adjusted so that the number of 

married males equals the number of married females. Next, the marital prevalence grids are 

smoothed so that each age of husband crossed with age of wife cell is an average of values in its 

diagonal in the grid. Finally, the number of married persons for each age and sex is set equal to 

the marginal total of the associated year’s marital prevalence grid. 

1.5. MARRIAGE

1.5.a Overview

The National Center for Heath Statistics (NCHS) collected detailed data on the annual number of 

new marriages in the Marriage Registration area (MRA), by age of husband crossed with age of 

wife, for the period 1978 through 1988 (excluding 1980). In 1988, the MRA consisted of 42 

States and D.C. and accounted for 80 percent of all marriages in the U.S. Estimates of the 

unmarried population in the MRA were obtained from NCHS by age and sex. Marriage rates for 

this period are calculated from these data. 

NCHS stopped collecting data on the annual number of new marriages in the MRA in 1989. 

Less detailed data on new marriages from a subset of the MRA were obtained for the years 1989-

1995. These data are used to determine marriage rates by adjusting the more detailed age-ofhusband crossed with age-of-wife data from the earlier years to match the aggregated levels for 

these years. 

Age-specific marriage rates ( z mx, y ˆ ) for a given year z are defined as the ratio of (1) number of 

marriages for given age-of-husband (x) crossed with age-of-wife (y) to (2) a theoretical midyear 

unmarried population at that age ( z Px, y ). The theoretical midyear population is defined as the 

geometric mean21 of the midyear unmarried males and unmarried females. 

 

21 The square root of the product of the midyear unmarried male and unmarried female populations. 
23

An age-adjusted central marriage rate ( z AMˆR ) summarizes the z mx, y ˆ for a given year. The 

standard population chosen for age adjusting is the unmarried males and unmarried females in 

the marriage registration area (MRA) as of July 1, 1982. The first step in calculating the total 

age-adjusted central marriage rate for a particular year is to determine an expected number of 

marriages by applying the age-of-husband age-of-wife specific central marriage rates for that 

year to the square root of the product of the corresponding age groups in the standard population. 

The z AMˆR is then obtained by dividing: 

• The expected number of marriages by 

• The square root of the product of (a) the number of unmarried males, ages 15 and older, 

and (b) the unmarried females, ages 15 and older in the standard population. 

The MARRIAGE subprocess projects annual z mx, y ˆ by age-of-husband crossed with age-of-wife. 

The equations for this subprocess, 1.5.1 and 1.5.2, are given below: 

z

x y

z mx, y m , ˆ = ˆ (·) (1.5.1) 

∑

∑ ⋅

=

x y

S

x y

z

x y

x y

S

x y

z

P

P m

AMR

,

,

,

,

, ˆ

ˆ (1.5.2) 

where S Px, y is the theoretical unmarried population in the MRA as of July 1, 1982 (the square root 

of the product of the corresponding age groups in the standard population) and x and y refer to 

the age of males and females, respectively.

1.5.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

• Estimates of the Social Security area population as of January 1, by age, sex, and marital 

status for years 1978-1988, excluding 1980. These data are updated each year based on 

output of the HISTORICAL POPULATION subprocess. 

• Estimates of the Social Security area population as of January 1, by age, sex, and marital 

status for years 1989-2006. These data are updated each year based on output of the 

HISTORICAL POPULATION subprocess. 
24

 Assumptions - 

For each Trustees Report ultimate values for the z AMˆR are assumed. The z AMˆR reaches its 

ultimate value in the 25th year of the 75-year projection period. For 2008, the intermediate 

ultimate z AMˆR assumption is 4,000 per 100,000 unmarried couples. 

NCHS Data - 

• Number of new marriages in the MRA, by age-of-husband crossed with age-of-wife, for 

calendar years 1978 through 1988, excluding 1980. These data are no longer available 

for years after 1988. The data vary in detail by year. They are broken out by single year 

age-of-husband crossed with single year age-of-wife for many ages (particularly younger 

ages). 

 

• Number of unmarried males and females in the MRA for calendar years 1978 through 

1988, excluding 1980. These data are no longer available for years after 1988. The data 

are generally broken out by single year age for ages under 40 and by age groups 40-44, 

45-49, 50-54, 55-59, 60-64, 65-74, and 75+. 

• Number of new marriages, in a subset of the MRA, by age-group-of-husband crossed 

with age-group-of-wife (age groups include 15-19, 20-24, 25-29, 30-34, 35-44, 45-54, 

55-64, and 65+), for calendar years 1989-1995. These data are updated as data becomes 

available and internal resources are sufficient to examine and interpret such new data. 

• The total number of marriages in the United States for the period 1978-2006. Each year, 

NCHS publishes the total number of marriages for a more recent year. 

• Number of marriages in the MRA for years 1979 and 1981-1988 by age group (age 

groups include 14-19, 20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 65+), sex, and prior 

marital status (single, widowed, and divorced). These data are no longer available for 

years after 1988. 

• Number of unmarried people in the MRA for years 1979 and 1981-1988 by age group 

(age groups include 14-19, 20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 65+), sex, and 

prior marital status (single, widowed, and divorced). These data are no longer available 

for years after 1988. 

1.5.c. Development of Output 

Equation 1.5.1 - 
25

Age-specific marriage rates are determined for a given age-of-husband crossed with age-of-wife, 

where ages range from 14 through 100+. The historical period includes years of complete NCHS 

data on the number of marriages and the unmarried population in the Marriage Registration Area 

(MRA) for the period 1978 through 1988, excluding 1980. Provisional data are used for the 

period 1989 through 1995 and total number of marriages is used for the period 1996 through 

2006. The projection period of the MARRIAGE subprocess begins one year after the last 

historical data year. 

The historical age-specific marriage rates are calculated for each year in the historical period 

based on NCHS data of the number of new marriages by age-of-husband crossed with age-ofwife and the number of unmarried persons by age and sex. The formula use in the calculations is 

given below: 

z

x y

z

z x y

x y P

M

m

,

,

,

ˆ

ˆ = , where 

• z M x, y ˆ is the number of marriages in year z; 

• ( z Px, y ) is the geometric mean22 of the midyear unmarried males and unmarried females 

in year z; and 

• x refers to age of males and y refers to the age of females. 

The rates for the period 1978 through 198823 are then averaged, graduated, and loaded into an 87 

by 87 matrix (age-of-husband crossed with age-of-wife for ages 14 through 100+), denoted as 

MarGrid. This matrix is used in the calculation of the age-specific marriage rates for all later 

provisional years and the years in the projection period. 

For the first part of the provisional period, 1989-1995, NCHS provided data on the number of 

marriages in a subset of the MRA by age-group-of-husband crossed with age-group-of-wife (age 

groups include 15-19, 20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 65+). These data are used 

to change the distribution of MarGrid by these age groups. For each age-group-of-husband 

crossed with age-group-of-wife, the more detailed marriage rates in MarGrid that are contained 

within this group are adjusted so that the number of marriages obtained by using the rates in 

MarGrid match the number implied by the MRA subset. 

For each year of the provisional period, an expected total number of marriages is calculated by 

multiplying the rates in the MarGrid (or the adjusted MarGrid for years 1989-1995) by the 

corresponding geometric mean of the unmarried males and unmarried females in the Social 

Security area population. All rates in MarGrid (or the adjusted MarGrid for years 1989-1995) 

 

22 The square root of the product of the midyear unmarried male and unmarried female populations. 23 Data for 1980 is not available and excluded from the calculations. 
26

are then proportionally adjusted to correspond to the total number of marriages estimated in the 

year for the Social Security area population. This estimate is obtained by increasing the number 

of marriages reported in the U.S. to reflect the difference between the Social Security area 

population and the U.S. population. 

The provisional age-specific rates are then graduated using the Whittaker-Henderson method and 

are used to calculate the age-adjusted rates for each year. The age-adjusted marriage rates are 

expected to reach their ultimate value in the 25th year of the 75-year projection period. Rather 

than use the last year of provisional data to calculate the starting rate, the rates for the past five 

years are averaged to derive the starting value. The annual rate of change in the age-adjusted 

marriage rate is calculated by taking the 26th root of the ratio of the ultimate value and the 

starting value. Thus, to calculate the rate for a projected year, the rate of change is applied to the 

prior year’s rate (or the starting value for the first year of the projection period). 

To obtain the age-of-husband-age-of-wife-specific rates for a particular year from the ageadjusted rate projected for that year, the age-of-husband-age-of-wife-specific rates in MarGrid 

are proportionally scaled so as to produce the age-adjusted rate for the particular year. 

A complete projection of age-of-husband-age-of-wife-specific marriage rates was not done 

separately for each previous marital status. However, experience data indicate that the 

differential in marriage rates by prior marital status is significant. Thus, future relative 

differences in marriage rates by prior marital status are assumed to be the same as the average of 

those experienced during 1979 and 1981-1988. 

1.6. DIVORCE

1.6.a. Overview 

For the period 1979 through 1988, the National Center for Heath Statistics (NCHS) collected 

data on the annual number of divorces in the Divorce Registration area (DRA), by age-group-ofhusband crossed with age-group-of-wife. In 1988, the DRA consisted of 31 States and 

accounted for about 48 percent of all divorces in the U.S. These data are then inflated to 

represent an estimate of the total number of divorces in the Social Security area. This estimate 

for the Social Security Area is based on the total number of divorces during the corresponding 

calendar year in the 50 States, the District of Columbia, Puerto Rico, and the Virgin Islands. 

Divorce rates for this period are calculated using this adjusted data on number of divorces and 

estimates of the married population by age and sex in the Social Security Area. 

An age-of-husband crossed with age-of-wife specific divorce rate ( z dx, y ˆ ) for a given year z is 

defined as the ratio of (1) the number of divorces in the Social Security area for the given age of 
27

husband and wife ( z Dx, y ˆ ) to (2) the corresponding number of married couples in the Social 

Security area ( z Px, y ) with the given age of husband (x) and wife (y). An age-adjusted central 

divorce rate ( z ADRx, y ˆ ) summarizes the z dx, y ˆ for a given year. 

The z ADˆR is calculated by determining the expected number of divorces by applying: 

• The age-of-husband crossed with age-of-wife specific divorce rates to 

• The July 1, 1982 population of married couples in the Social Security area by 

corresponding age-of-husband and age-of-wife. 

The expected number of divorces is then divided by the total number of married couples in that 

year. 

The DIVORCE subprocess projects annual z dx, y ˆ by age-of-husband crossed with age-of-wife. 

The primary equations, 1.6.1 and 1.6.2, are given below: 

z

x y

z dx, y d , ˆ ˆ = (·) (1.6.1) 

∑

∑ ⋅

=

x y

S

x y

z

x y

x y

S

x y

z

P

P d

ADR

,

,

,

,

, ˆ

ˆ (1.6.2) 

where S Px, y is the number of married couples in the Social Security area population as of July 1, 

1982 and x and y refer to the age of husband and age of wife, respectively. 

1.6.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

• Social Security area population of married couples by age-of-husband crossed with ageof-wife as of January 1 for years 1979-2006. These data are updated each year from the 

HISTORICAL POPULATION subprocess. 

• Social Security area population of married couples by age-of-husband crossed with ageof-wife for some projected years. These data are updated each year from PROJECTED 
28

POPULATION subprocess of the prior year’s Trustees Report. 

• The total population in the Social Security area for years 1979-2006. An additional year 

of data is added each Trustees Report. 

Assumptions - 

Each year the ultimate assumed value for the age-adjusted divorce rate is established. The 

rate reaches its ultimate value in the 25th year of the 75-year projection period. For 2008, the 

ultimate assumed z ADˆR is 2,000 per 100,000 married couples. 

NCHS Data - 

• The number of divorces in the divorce registration area (DRA), by age-of-husband 

crossed with age-of-wife, for calendar years 1979 through 1988. These data are no 

longer available for years after 1988. The data are broken out by single year age-ofhusband crossed with single year age-of-wife for many ages (particularly younger ages). 

 

• The total number of divorces in the United States for years 1979-1988. No new data are 

available. 

• The total number of divorces in the United States for the period for 1989-2006. 

Additional years of data are incorporated as they become available, which is generally 

every year. If no new data is available, data for the most recent year is used as a proxy. 

• The total number of divorces in Puerto Rico and the Virgin Islands for years 1989-2006. 

The most recent year of data was obtained in 2000; the 2000 figures are used as a proxy 

for 2001-200624. New data are incorporated as they become available and resources are 

sufficient to validate their use. 

Other Input Data- 

• From the U.S. Census Bureau, the total population in the U.S for years 1979-1988. No 

new data are needed. 

• From the U.S. Census Bureau, the total population in the U.S., in Puerto Rico, and the 

Virgin Islands for years 1989-2006. The most recent year of data was obtained in 2000; 

 

24 Data for 1988 was used to estimate the number of Puerto Rico and Virgin Island divorces for 1989-1997. 
29

the 2000 figures are used as a proxy for 2001-200625. New data are incorporated as they 

become available and resources are sufficient to validate their use. 

1.6.c. Development of Output

Equation 1.6.1 - 

Age-specific divorce rates are defined for ages 14 through 100+. Detailed NCHS data on the 

number of divorces by age-group-of-husband crossed with age-group-of-wife are available for 

the period 1979 through 1988. Provisional data on the total number of divorces in the United 

States are used for the period 1989 through 2006. 

 

First, the detailed NCHS data on divorces by age group is disaggregated into single year of age x

and y (ages 14-100+) using the H.S. Beers method of interpolation. Then, the age-specific 

divorce rates ( z dx, y ˆ ) are calculated for the period 1979-1988 by taking the number of divorces 

(inflated to represent the Social Security Area, z Dx, y ) and dividing by the married population in 

the Social Security Area at that age-of-husband and age-of-wife ( z Px, y ). The formula for this 

calculation is given below: 

 z

x y

z

z x y

x y P

D

d

,

,

,

ˆ ˆ = (A.6.3) 

These rates are then averaged, graduated26, and loaded into an 87 by 87 matrix (age-of-husband 

crossed with age-of-wife for ages 14 through 100+), denoted as DivGrid. DivGrid will be used 

in the calculation of the age-specific divorce rates for all later years including the projection 

period. 

For each year in the provisional period (1989-2006), an expected number of total divorces in the 

Social Security area is obtained by applying the age-of-husband crossed with age-of-wife rates in 

DivGrid to the corresponding married population in the Social Security Area. The rates in 

DivGrid are then proportionally adjusted so that they would yield an estimate of the total number 

of divorces in the Social Security area. The estimate of total divorces is obtained by adjusting 

the reported number of divorces in the U.S. for (1) the differences between the total divorces in 

the U.S. and in the combined U.S., Puerto Rico, and Virgin Islands area and (2) the difference 

between the population in the combined U.S., Puerto Rico, and Virgin Islands area and in the 

Social Security area. 

The values over the period 1994-2006 are averaged and used as the starting value for 2006 and 

the age-adjusted divorce rate is calculated. The rate is expected to reach its ultimate value in the 

 

25 Data for 1988 was used to estimate the number of Puerto Rico and Virgin Island divorces for 1989-1997. 

26 Using the Whittaker-Henderson method of graduation. 
30

25th year of the 75-year projection period. The annual rate of change in the age-adjusted 

marriage rate is calculated by taking the 26th root of the ratio of the ultimate value and the 

starting value. Thus, to calculate the age-adjusted rate for a projected year, the rate of change is 

applied to the prior year’s rate (or to the starting value for the first year of the projection period). 

To obtain age-specific rates for use in the projections, the age-of-husband-age-of-wife-specific 

rates in DivGrid are adjusted proportionally so as to produce the age-adjusted rate assumed for 

that particular year. 

1.7. POPULATION PROJECTION

1.7.a. Overview 

For the 2008 Trustees Report, the starting population for the population projections is the 

January 1, 2006 Social Security area population, by age, sex, and marital status, produced by the 

HISTORICAL subprocess. The Social Security area population is then projected using the 

component method. The components of change include births, deaths, net legal immigration, 

and net other immigration. The components of change are applied to the starting population by 

age and sex to prepare an estimated population as of January 1st 2007 and to project the 

population through the 75-year projection period (years 2008-82). There is a separate equation 

for each of the components of change as follows: 

= (⋅) z

s

z Bs B (1.7.1) 

Where z Bs is the number of births of each sex (s) born in year z. 

( ) , , = ⋅ z

x s

z Dx s D (1.7.2) 

Where z Dx,s is the number of deaths at age (x), and sex (s) that are expected to occur in year z. 

 z

x s

z

x s

z NLx,s = L , −E , (1.7.3) 

Where z NLx,s is equal to net legal immigration, by age (x) and sex (s), that is assumed to occur in 

year z. z Lx,s and z Ex,s are the respective number of legal immigrants27 and emigrants that are 

expected to occur in year z, by age (x) and sex (s). In addition, z Lx,s is the sum of the number of 

 

27 Legal immigrants are defined as persons being granted legal permanent resident status. 
31

new arrival legal immigrants ( z NEWx,s ) and the number of legal immigrants adjusting status 

( z AOSx,s ) that are expected to occur in year z, by age (x) and sex (s). All of these values are 

calculated in and provided by the IMMIGRATION subprocess (1.3). 

 ( ) , , = ⋅ z

x s

z NOx s NO (1.7.4) 

Where z NOx,s is the number of net other immigrants28, by age (x) and sex (s), for year z. 

Once the components of change are calculated, the following equation is used to calculate the 

Social Security area population by age and sex: 

1

1,

1 −

−

− − z

x s

z Bs D for ages = 0 

z Px,s = (1.7.5) 

1

1,

1

1,

1

1,

1

1,

−

−

−

−

−

−

−

− − + + z

x s

z

x s

z

x s

z Px s D NI NO for ages >0 

Where z Px,s is the population, by age (x) and sex (s), as of January 1st of year z. Note that for age 

equal to zero, 1

1,

−

−

z D g represents perinatal deaths. 

The population is further disaggregated into the following four marital statuses: single (never 

married), married, widowed, divorced. The following equation shows the population by age (x), 

sex (s), and marital status (m) for each year z: 

 ( ) , , , , = ⋅ z

x g m

z Px g m P (1.7.6) 

In addition to projecting the total Social Security area population, this subprocess also projects 

the other immigrant population by age (x) and sex (s) using the following equation: 

 

 1

1,

1

1,

1

, 1,

−

−

−

−

− = − + − z

x s

z

x s

z

x s

z OPx s OP NO D (1.7.8) 

Where, z OPx,s is equal to the other immigrant population, by age(x) and sex (s) as of January 1st

of year z. z Dx,s are the number of deaths in the other immigrant population by age (x) and sex (s) 

(see equation 1.7.2). 

 

28 Other immigrants include all immigrants, other than legal permanent residents, who stay for 6 months or more. 

They include unauthorized immigrants, temporary workers, and students. 
32

1.7.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

 IMMIGRATION 

• Projected numbers of legal immigrants, who are new arrivals, by single year of 

age (0-84) and sex for years beginning with the starting year and ending with 

2101. Each year, these data are updated. 

• Projected numbers of legal immigrants, who are adjustments of status, by single 

year of age (0-84) and sex for years beginning with the starting year and ending 

with 2101. Each year, these data are updated. 

• Projected numbers of legal emigrants by single year of age (0-84) and sex for 

years beginning with the starting year and ending with 2101. Each year, these 

data are updated. 

• Projected numbers of other immigrants by age (0-84) and sex for years beginning 

with the starting year and ending with 2101. Each year, these data are updated. 

 FERTILITY 

• Historical birth rates by single year of age of mother (14-49) for the years 

beginning with 1941 and ending with the year prior to the starting year. Each 

year, these data are updated. 

• Projected birth rates by single year of age of mother (14-49) for the years 

beginning with the starting year and ending with 2101. Each year, these data are 

updated. 

 MORTALITY 

• Historical probabilities of death by age last birthday (including perinatal mortality 

factor, single year of age for ages 0-99, and age group 100+) and sex for years 

beginning with 1941 and ending with the year prior to the starting year. Each 

year, these data are updated. 

• Projected probabilities of death by age last birthday (including perinatal mortality 

factor, single year of age for ages 0-99, and age group 100+) and sex for the years 

beginning with the starting year and ending with 2101. Each year, these data are 

updated. 

• Marital factors to distribute probabilities of death by marital status. Factors are 

dimensioned by sex, single year of age (ages 14-100+) and marital status. Each 

year, these data are updated. 
33

HISTORICAL POPULATION 

• Social Security area population by single year of age (0-99 and 100+), sex, and 

marital status as of the starting date and one year prior to the starting date. These 

data are updated each year. 

• Married couples by single year of age of husband crossed with single year of age 

of wife as of the starting date and one year prior to the starting date. These data 

are updated each year. 

• Women of childbearing years (14-49) by single year of age as of January 1 

beginning with 1941 and ending with the starting year. Each year, these data are 

updated. 

• Children 18 and under by single year of age as of January 1 beginning with 1941 

and ending with the starting year. Each year, these data are updated. 

• Married couples with children by single year of age of husband (ages 14-83) 

crossed with single year of age of wife (ages 14-49) as of January 1 beginning 

with 1941 and ending with the starting year. Each year, these data are updated. 

• Married men by age group (1-15, 2-25, 25-29, ..., 60-64) as of January 1 

beginning with 1960 and ending with the starting year. Each year, these data are 

updated. 

MARRIAGE

• Projected central marriage rates by single year of age of husband (ages 14-100+) 

crossed with single year of age of wife (ages 14-100+) for each year of the projection 

period. These data are updated annually.

• Averaged and graduated marriage rates for the period 1979 and 1981-1988 by age 

(ages 14-100+), sex, and prior marital status (single, divorced, and widowed). These 

data are updated annually.

 DIVORCE

• Projected central divorce rates by single year of age of husband (14-100+) crossed 

with single year of age of wife (14-100+) for each year of the projection period. 

These data are updated annually.

U.S. Census Bureau Data - 

• CPS data on the average number of children per married couple with children by age 

group of householder (age groups 20-24, 25-29, 30-34,..., 55-64) for 1960-2006. 

Each year, an additional year of data is added. 
34

• Estimate29 of the residual immigrant population, by age group (0-17, 18-29, 30-49, 

50-64 and 65+) and sex, as of January 1, 2000. These data are not updated. 

• From the Census Bureau Current Population Survey, March 2000, estimates of the 

Foreign Born Non-citizen Population by 5-year age group (0-4, 5-9, ..., 75-79, 80-84, 

85+) and sex. These data will not be updated. 

Department of Homeland Security Data – 

• An estimate of the age distribution of non-immigrants by age (0-84) and sex. These 

data are updated annually. 

• An estimate30 of the size of the other immigrant population as of January 1, 2006. 

These data are updated annually. 

1.7.c. Details of Output

Equation 1.7.1 - Births 

The number of births for the Social Security area, z Bx , is computed for each year z of the 

projection period by applying the age-specific birth rate to the mid year female population aged 

14 to 49. 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ + =

+

2

1

,

z

x

z

z x

x

z

x

FP FP

B b 

where, 

 z bx = birth rate of mothers age x in year z;

 

29 See “Evaluating Components of International Migration: The Residual Foreign Born” by Joseph Costanzo, 

Cynthia J. Davis, Caribert Irazi, Daniel M. Goodkind, and Roberto R. Ramirez. Issued January 2002. 

30 See “Estimates of the Unauthorized Immigrant Population Residing in the United States: January 2006” by 

Michael Hoefer, Nany Rytina, and Christopher Campbell. 
35

 z Bx = number of births to mothers age x in year z; and 

 z FPx = female population age x at the beginning of year z.

The number of births in a given year is disaggregated by sex by assuming a gender ratio of 105 

male births for every 100 female births. 

Equation 1.7.2 – Deaths 

The number of deaths for the Social Security area by age (x) and sex (s), z Dx,s , is computed for 

each projection year by applying the death probabilities for each age (x) and sex (s), z

x s q , , to the 

exposed population at the beginning of the year. 

z

x s

z

x s

z Dx,s = q , P , 

Deaths for the other immigrant population are calculated in the same manner, replacing z Px,s

with z OPx,s . 

Equation 1.7.4 – Net Other Immigration 

Net other immigration by age (x) and sex (s) for year z, z NOx,s , consists of other immigration less 

other emigration. Thus we have the following equation: 

z

x s

z

x s

z NOx,s = O , − OE , 

Other immigration by age (x) and sex (s), z Ox,s is calculated in the IMMIGRATION subprocess 

(1.3) for each year z of the long-range projection period. Other emigration by age (x) and sex 

(s), z OEx,s , consists of departures from the Social Security area population and those who adjust 

status to legal permanent residents. Therefore, other emigration can be expressed via the 

following equation: 

z

x s

z

x s

z OEx,s = AOS , + OD , 

Where z AOSx,g is the annual number of people who adjust status to legal permanent resident 

status. Adjustments of status are assumed to equal one half of all legal immigrants and are 

calculated in the IMMIGRATION subprocess. 
36

z ODx,s is equal to the annual number of other immigrants who depart the Social Security area by 

age (x) and sex (s). Ideally, other departures would be modeled utilizing rates of emigration by 

age, sex, and year of entry. However due to the scarcity of available data on other immigrants, 

calculating rates of emigration by this level of detail is not feasible at this time. As an 

alternative, the total level of departures was modeled based on changes in the estimated size of 

the other immigration population during the time period 2000-05. The total number of other 

departures during that time was split into two pieces (1) a fixed component that is expressed as a 

percentage of recent arrivals and (2) a rate based component that varies by age and sex. Thus, z ODx,s is defined by the following equation: 

z

x s

z

x s

z ODx,s = FD , + RD , 

Modeling the z ODx,s in this manner recognizes two key points of other emigration: (1) as the size 

of the exposed population increases the overall number of departures is likely to increase and (2) 

as the average duration of stay increases the overall gross departure rate is likely to decrease. 

The fixed component, FDx,s , is calculated directly from the age distribution of other immigrants 

by assuming that the number of fixed exits will come from relatively recent arrivals that do not 

adjust status. The following equation shows the calculation: 

FDx,s Ox 2,s Nadj x 2,s 0.10( ) * = − − 

Where Ox,s is the assumed level of other immigration for a given year z and Nadj x,s is equal to the 

percentage of new other immigrants that are not expected to have the potential to adjust status. 

SinceOx,s , is constant for each year of the long-range projection period, the values of FDx,s

remain fixed for each year z. 

The remaining numbers of departures, z RDx,s , are assumed to be directly influenced by the size of 

the exposed other immigrant population. Thus, rates of emigration by age (x) and sex (s), x s r , , 

were calculated and averaged over the period 2000-05 and then applied to the exposed 

population for each year of the projection period. The exposed population is calculated by 

subtracting deaths, fixed departures, and adjustments of status from the beginning of year other 

immigrant population. 

* ( *(1 ) ) , , , , , ,

z

x s x s

z

x s

z

x s x s

z RDx s = r OP − q − FD − AOS 
37

Equation 1.7.6 – Disaggregating the population by marital status 

Once the population is projected by single year of age and sex, it is then disaggregated into the 

following four marital states; single, married, widowed, and divorced. Estimates of the Social 

Security area population by single year of age (0-99 and 100+), sex, and marital status as of the 

starting date of the population projection are obtained from the HISTORICAL POPULATION 

subprocess. In addition, the HISTORICAL POPULATION subprocess provides the number of 

married couples by single year of age of husband crossed with single year of age of wife as of 

the starting date. 

All births are assigned to the single category. For a given age and sex, deaths are assigned by 

marital status according to the relative differences in death rates by marital status observed for 

that age and sex during the calendar years 1995 and 1996, as determined in the MORTALIY 

subprocess. For a given age and sex, immigrants are assigned by marital status according to the 

beginning of year marital distribution of the Social Security area population for that age and sex. 

Once the number of marriages, divorces, and widowing during a year are determined, the 

population by sex, age, and marital status is updated to represent end of year. The unmarried 

population at the end of the year is estimated from the population at the beginning of the year by 

subtracting deaths and marriages and adding new immigrants, widows (or widowers), and 

divorces during the year. The married population at the end of the year is estimated from the 

population at the beginning of the year by reducing the population for divorces, widows (or 

widowers), dissolutions of marriages when both husband and wife dies, and by increasing the 

population for new immigrants and marriages during the year. 

Numbers of new marriages are determined for each projection year. The annual number of 

marriages occurring at each age of husband crossed with each age of wife is obtained by 

multiplying the age-of-husband and-age-of-wife-specific marriage rates with the geometric mean 

of the midyear unmarried male population and the midyear female unmarried population. 

The midyear unmarried male and female populations31 are estimated from the beginning of the 

year unmarried populations. The age-specific midyear male unmarried population is calculated 

by adjusting the number of unmarried males at the beginning of the year to represent midyear 

using the relationship between the two points in time in the prior year. The midyear female 

unmarried population is approximated similarly. 

 

31 The midyear populations exposed to marriage are the unmarried populations (sum of those single, widowed, and 

divorced). 
38

The numbers of marriages are then distributed by previous marital status in the same proportions 

as would have been produced by applying the previous marital-status-specific marriage rates 

from the MARRIAGE subprocess to the population by marital status at the beginning of the year. 

Numbers of new divorces are determined for each projection year. The number of divorces 

during a year, occurring at each age of husband crossed with each age of wife, is obtained by 

multiplying the age-of-husband by age-of-wife divorce rates for that year with the midyear 

number of married couples in that age crossing. 

The midyear married couples are estimated from the beginning of the year married couples. The 

number of age-of-husband by age-of-wife midyear married couples is calculated by adjusting the 

number of married couples at the beginning of the year to represent midyear using the 

relationship between the two points in time in the prior year. 

Widowings are computed by applying general population probabilities of death to the marriage 

prevalence at the beginning of the year. Widowings and deaths by marital status are then 

reconciled for internal consistency. 
39

Appendix: 1.2-1 

The Board of Trustees of the OASDI Trust Funds sets the ultimate rates of mortality reduction 

by sex, age group, and cause of death. These ultimate rates are listed in the tables below for the 

current and prior trustees reports. For comparison purposes, rates are also presented for an 

historical period. 

Annual Rates of Reduction in Central Death Rates by Age Group, Sex and Cause 

 Historical 

Ultimate Intermediate 

Assumption Historical 

Ultimate Intermediate 

Assumption 

 2007TR 2008TR 2007TR 2008TR 

1979 to 

2004 

2031-

2081 

2032-

2082 

1979 to 

2004 

2031-

2081 

2032-

2082 

Under Age 15 Male Female 

Heart Disease 2.97 1.0 1.0 2.70 1.0 1.0 

Cancer 2.72 2.0 2.0 2.27 2.0 2.0 

Vascular Disease 1.34 0.6 0.6 1.24 0.6 0.6 

Violence 2.97 0.9 0.9 2.38 0.9 0.9 

Respiratory Disease 3.22 2.5 2.5 3.23 2.5 2.5 

Diabetes Mellitus 1.13 1.8 1.8 3.17 1.8 1.8 

Other 2.74 1.8 1.8 2.63 1.8 1.8 

Total 2.79 1.6 1.6 2.59 1.6 1.6 

Ages 15 - 49 Male Female 

Heart Disease 2.41 2.3 2.3 1.13 2.2 2.2 

Cancer 1.69 0.5 1.0 1.57 0.5 1.0 

Vascular Disease 1.64 1.8 1.8 1.88 1.8 1.8 

Violence 1.17 0.8 0.8 0.52 0.8 0.8 

Respiratory Disease 0.89 0.5 0.5 -0.19 0.5 0.5 

Diabetes Mellitus -1.55 0.3 0.3 -0.94 0.3 0.3 

Other -1.03 0.8 0.8 -0.85 0.6 0.8 

Total 1.00 0.9 0.9 0.61 0.7 0.9 

Ages 50 - 64 Male Female 

Heart Disease 3.36 2.0 2.2 2.60 2.2 2.2 

Cancer 1.41 0.4 1.0 1.05 0.4 1.0 

Vascular Disease 2.36 1.5 1.5 2.08 1.6 1.6 

Violence 1.23 0.8 0.8 0.74 0.8 0.8 

Respiratory Disease 1.25 0.6 0.7 -1.02 0.7 0.7 

Diabetes Mellitus -2.72 0.3 0.3 -1.49 0.3 0.3 

Other 0.17 0.9 0.9 -0.09 0.8 0.9 

Total 1.83 0.8 1.1 1.07 0.7 1.0 

Ages 65 - 84 Male Female 

Heart Disease 2.85 1.7 1.8 2.58 1.8 1.8 
40 

Cancer 0.35 0.5 0.5 -0.58 0.5 0.5 

Vascular Disease 2.71 2.5 2.5 2.08 2.6 2.6 

Violence 0.87 1.2 1.2 0.23 1.2 1.2 

Respiratory Disease 0.06 0.2 0.2 -3.18 0.2 0.2 

Diabetes Mellitus -2.57 0.6 0.6 -1.52 0.6 0.6 

Other -0.52 0.3 0.3 -1.68 0.3 0.3 

Total 1.31 0.7 0.7 0.47 0.7 0.7 

Ages 85 and older Male Female 

Heart Disease 1.01 1.2 1.2 1.18 1.2 1.2 

Cancer -0.93 0.4 0.4 -0.87 0.3 0.3 

Vascular Disease 1.70 1.9 1.9 1.75 1.8 1.8 

Violence -0.75 0.9 0.9 -0.75 0.9 0.9 

Respiratory Disease -1.84 0.2 0.2 -3.06 0.2 0.2 

Diabetes Mellitus -3.21 0.6 0.6 -1.95 0.5 0.5 

Other -2.34 0.2 0.2 -3.51 0.2 0.2 

Total -0.11 0.6 0.6 -0.15 0.6 0.6 
41 

Process 2: 

Economics 
42 

2. Economics 

The Office of the Chief Actuary uses the Economic process to project OASDI employment and 

earnings-related variables, such as the average wage for indexing and the effective taxable 

payroll. The Economic process receives input data from the Demography process and provides 

output data to the Beneficiaries and the Trust Fund Operations & Actuarial Status processes. 

The Economic Process is composed of four subprocesses, U.S. EMPLOYMENT, U.S. 

EARNINGS, COVERED EMPLOYMENT AND EARNINGS, and TAXABLE PAYROLL. As 

a rough overview, U.S. EMPLOYMENT and U.S. EARNINGS project U.S. employment and 

earnings data, respectively, while COVERED EMPLOYMENT AND EARNINGS converts 

these employment and earnings variables to OASDI covered concepts. TAXABLE PAYROLL, 

in turn, converts OASDI covered earnings to taxable concepts, which are eventually used to 

estimate future payroll tax income and future benefit payments. 

U.S. EMPLOYMENT and U.S. EARNINGS produce quarterly output, while the output from 

COVERED EMPLOYMENT AND EARNINGS is annual. TAXABLE PAYROLL produces 

both. 

Two appendices are at the end of this documentation. The first appendix, 2-1, provides details of 

the equations mentioned below. The second appendix, 2-2, provides a listing with explanations 

of acronyms used in this documentation. 

2.1. U.S. EMPLOYMENT (USEMP)

2.1.a. Overview

The Bureau of Labor Statistics (BLS) publishes historical monthly estimates for civilian U.S. 

employment-related concepts from the Current Population Survey (CPS). The principal measures 

include the civilian labor force (LC) and its two components – employment (E) and 

unemployment (U), along with the civilian noninstitutional population (N). Historical estimates 

for N by age, sex, and marital status are tabulated within the Economic Process from the CPS. 

For each disaggregated age/sex/marital status group, N is also projected, using the military 

population (M) and the growth rate projected for the Social Security area population (P) (see 

Demography Process input). The BLS also publishes values for the civilian labor force 

participation rate (LFPR) and the civilian unemployment rate (RU). The LFPR is defined as the 

ratio of LC to N, while the RU is the ratio of U to LC, expressed to a base of 100. 

For each age/sex group, USEMP projects quarterly and annual values for these principal 

measures of U.S. employment. Equations 2.1.1 through 2.1.5 outline the subprocess’ overall 

structure and solution sequence for the total economy. 
43 

 N year = [(Nyear-1 + M year-1)*(Pyear/ Pyear-1)] – Myear (2.1.1) 

LFPR = LFPR(·) (2.1.2) 

LC = LFPR * N (2.1.3) 

RU = RU(·) (2.1.4) 

E = LC * (1 -RU / 100) (2.1.5) 

 where the subscript year in equation (2.1.1) represents the projection year. 

The Demography Process estimates historical values for the total SSA area population (P) and 

the other immigrant population (OP). USEMP projects annual values for total employed OP 

(EO) and various sub-components, including the portion of EO whose earnings are reported and 

posted to the Master Earnings File (EO_MEF), those EO whose earnings are reported posted to 

the Earnings Suspense File (EO_ESF), those EO in the underground economy (EO_UND), and 

EO_MEF who are OASDI covered (EO_MEFC). Equations 2.1.6 through 2.1.10 outline the 

overall structure of the subprocess used to estimate EO and its sub-components. 

EO = E * OP / P (2.1.6) 

EO_MEF = EO_MEF(·) (2.1.7) 

EO_MEFC = EO_MEFC(·) (2.1.8) 

EO_ESF = EO_ESF(·) (2.1.9) 

EO_UND = EO_UND(·) (2.1.10) 

Finally, for each age/sex group, USEMP projects “at-any-time” employed other immigrant 

population (TEO). EO represents the average annual number of individuals in the other 

immigrant population who were employed each month during a calendar year. TEO represents 

the total number of individuals in the other immigrant population who had any employment 

during the calendar year. (EO can be roughly viewed as the average number of jobs worked by 

OP during a calendar year, while TEO represents the total number of individuals who worked 

those jobs.) Effectively, Equations 2.1.11 through 2.1.15 convert every EO age-sex 

sub-component to an at-any-time TEO age-sex sub-component counterpart. 

TEO = TEO(·) (2.1.11) 

TEO_MEF = TEO_MEF(·) (2.1.12) 
44 

TEO_MEFC = TEO_MEFC(·) (2.1.13) 

TEO_ESF = TEO_ESF(·) (2.1.14) 

TEO_UND = TEO_UND(·) (2.1.15) 

2.1.b. Input Data

Long-Range OASDI Projection Data 

These data are updated each year. 

Demography 

• Social Security area population as of year end (1940 – 2085) by age, marital status 

(single, married, widowed, divorced) and sex (M, F). 

• “Other immigrant” population as of year end (2006 – 2085) by age, marital status 

(single, married, widowed, divorced) and sex (M, F). 

• Number of children by age of child and age of mother. 

• Life expectancy by age and sex. 

Trust Fund Operations and Actuarial Status – The Trust Fund Operations and Actuarial 

Status Process provides no input to the Economic Process sections. However, the LFPRs use 

input from the Outgo Process from the prior year’s Trustees Report. That is, the projected 

LFPRs for the 2008 Trustees Report use input from the 2007 Trustees Report that includes 

projections for the disability prevalence rates by age and sex, and the primary insurance 

amount (PIA) replacement rates by age and sex. The disability prevalence rate is defined as 

the ratio of the number of disabled worker beneficiaries to the Social Security area 

population. The PIA replacement rate is defined as the ratio of a hypothetical medium scaled 

worker’s PIA to his/her career-average indexed earnings level. 

Trustees Assumptions 

Each year the Board of Trustees of the OASDI Trust Funds sets the ultimate assumed values 

for key economic variables: 

• Real wage differential 

• Annual percentage change in total economy productivity 

• Annual percentage change in average hours worked 

• Ratio of wages to compensation (RWSD) 

• Ratio of compensation to GDP (RWSSY) 
45 

• Annual percentage change in the price differential 

• Annual percentage change in CPI 

• Annual trust fund real interest rate 

• Unemployment rate 

These ultimate values are generally implemented during the last half of the short-range (first 

10 years) of the projection horizon. Earlier projected values are set to provide a smooth 

transition from the latest actual historical values to the assumed long-range ultimate ones. As 

a by-product of this process, values for the GDP deflator (PGDP), real GDP, and potential 

GDP are set. The ratio (RTP) of real to potential GDP is an important summary measure of 

the business cycle. 

It is important to note that the Trustees also agree on the assumed short-range values for the 

above variables. 

Addfactors 

Addfactors are adjustments that move an estimate closer to an expected value. Addfactors 

may be used for a variety of reasons associated with data availability, structural changes in 

the data and/or model, and perceived temporary aberrations in recent historical data. 

Addfactors were included directly in equation 21.2 for male and female LFPRs ages 16 to 19, 

and on the aggregate LC and RU. Addfactors were also included on all male and female 

LFPRs age about 40 and over to reflect changes in life expectancy. 

The need for addfactors is reviewed each year and addfactors are implemented if necessary. 

Other input data 

• U.S. armed forces (EDMIL) by age and sex, estimated by the Department of Defense and 

published by the Census Bureau on a monthly basis (1948-2000) by single year of age (17 

to 64) and sex. These data are no longer produced by Census. 

• EDMIL by age and sex, estimated by the Economic Process as the difference in monthly 

resident plus Armed Forces overseas population and the monthly civilian population. These 

two populations are available from the Census Bureau on a monthly basis (April 2000 to 

July 2006) by single year of age (16 to 69) and sex. These data are updated several times a 

year. 

• Data from the March Supplement of the CPS by year (1968-2004), for the civilian 

noninstitutional population, labor force, military, and unemployment. These data are 

available from the BLS by single year of age (16 to 85+), sex, marital status (never married, 

married with a spouse present, and married with no spouse present), and presence of 

children. These data are updated by the BLS annually. This subprocess updates the data 
46 

every other year (or more often, based on its time constraints). 

2.1.c. Development of Output

Equation 2.1.1 - Labor Force Participation Rate (LFPR) 

The LFPR is disaggregated by age and sex. Age groups include 16 to 17 (i.e., 16-17), 18-19, 

20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55, 56, ... , 74, 75-79, 80-84, and 85 and 

over. For age groups between 20 and 54, male and female LFPRs are further disaggregated 

by marital status, categories of which include never married, ever married with spouse 

present, and ever married with spouse absent (includes separated, widowed, and divorced). 

Female LFPRs disaggregated by age (between 20 and 44) and by marital status are further 

disaggregated by presence of own child. The groups for presence of own child include 

females with at least one own child under the age of six and females with no own child(ren) 

under the age of six. Thus, USEMP contains 107 LFPR equations, 46 for males and 61 for 

females. 

Given the level of demographic disaggregation, the aggregate LFPR is dependent on the 

projected distribution of the population by age, sex, marital status, and presence of own child. 

Each disaggregated LFPR, however, is dependent on the input variables that are most 

relevant to the demographic group. For example, only the LFPRs for younger males are 

dependent on the military, while only the LFPRs for relevant older workers are dependent on 

changes to the normal retirement age (NRA). Specific examples of the impact of input data 

on the disaggregated LFPRs are presented below. 

• Military Ratio (RM) is defined as the ratio of U.S. Armed Forces to the total 

noninstitutional population. An increase in RM lowers the LFPR. The RM affects the 

LFPRs for younger aged males. 

• Disability prevalence ratio (RD) is defined as the ratio of disabled worker beneficiaries to 

the Social Security area population. An increase in RD lowers the LFPR. The RD affects 

the LFPRs for males and females below the NRA. 

• Ratio of real to potential GDP (RTP) is a measure of the business cycle. An increase in 

RTP leads to an increase in the LFPR. The RTP affects most LFPRs. 

• The PIA replacement rate (PIARR) is defined as the average ratio of a hypothetical 

worker’s PIA to career-average wage level. This value is projected for hypothetical 

workers with medium-scaled earnings patterns32 who retire at ages 62 through NRA. The 

PIARR is adjusted to include the reduction for early retirement and the delayed retirement 

credit, two adjustments that are affected by the NRA. An increase in the adjusted PIARR 

leads to a decrease in the LFPR. The adjusted PIARR affects the LFPRs for those between 

the ages of 62 and 70. This variable needs to be considered due to the increase in NRA 

 

32 More details on the hypothetical scaled workers are provided in Actuarial Note #2005.3, located at the following 

internet address: www.socialsecurity.gov/OACT/NOTES/ran3/index.html. 
47 

and other changes that are scheduled in present law. 

• The Earnings Test Ratio (RET) is defined as the ratio of the maximum amount of earnings 

before an OASDI benefit is reduced to the average wage index. An increase in the RET 

leads to an increase in the LFPR. The RET is used in LFPRs for those between the NRA 

and age 69. This variable needs to be considered due to the increase in this maximum 

amount that is scheduled in present law. 

• The Family Size Ratio (RFS) is defined as the ratio of the number of children under 6 to 

mothers of a certain age. An increase in the RFS lowers the LFPR. The RFS affects the 

LFPRs for females aged 20 to 44 with at least one own child. 

• An LFPR increases with its lagged cohort. For example, the change in the LFPR for 

females aged 25-29 between 2005 and 2010 is dependent on the change in the LFPR for 

females aged 20-24 between 2000 and 2005. Lagged cohort variables affect female LFPRs 

age 20 and over, and male LFPRs age 55 and over. 

• The LFPR for males ever married spouse present falls with increases in their spouse’s 

LFPR. 

• An increase in life expectancy leads to an increase in LFPRs. The LFPRs for those 

approximately aged 40 and over are affected. 

Equation 2.1.3 - Unemployment Rate (RU) 

The RU is disaggregated by age and sex. The age groups include 16-17, 18-19, 20-24, 25-29, 

30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, and 75 and over. Thus, 

USEMP contains 28 RU equations, 14 for males and 14 for females. 

The aggregate RU is dependent on the projected distribution of the labor force by age and 

sex. Each disaggregated RU is specified using a first-difference model and is only dependent 

on one input, the distributed lag in the change in the RTP. Coefficients are estimated by 

regression and constrained to an expected aggregate behavior whereby a 2.0 percentage point 

change in the RTP elicits a 1.0 percentage point change in the RU. Furthermore, projections 

are constrained to the ultimate age-sex-adjusted RU set by the Trustees. 

Equation 2.1.6 to 2.1.14 – Employed Other Immigrant Population (EO) and At-Any-Time 

Employed other Immigrant Population (TEO) 

EO is estimated by sex and single-year of age from 16 to 100. Thus, USEMP contains 170 

equations, 85 for males and 85 for females. Based on various assumptions, we separate each 

age-sex EO into visa-status components including those authorized to work, those not 

authorized to work but previously authorized, and those never authorized to work. We 

separate EO never authorized to work into those who worked in 2001 and earlier and those 

who began working in 2002 and later, since we believe that those who worked in 2001 and 

earlier are more likely to have OASDI covered wages. Each disaggregated employment 

group is then further separated into EO_MEF, EO_MEFC, EO_ESF, and EO_UND. 
48 

Every age-sex EO sub-component is converted to its age-sex TEO sub-component 

counterpart using an age-sex “conversion weight.” For example, if the sub-component of EO 

is for males age 20 to 24, the conversion weight is defined as the ratio of total economy-wide 

at-any-time employed males age 20 to 24 (TEM2024) to the sum of CPS and military male 

employment age 20 to 24. However, TEM2024 is by definition the sum of at-any-time 

employment posted and not posted to the MEF, of which, the latter group includes the 

portion of TEO who are male age 20 to 24 in the underground economy. Thus, we must use 

proxies for the conversion weights. For males age 20 to 24, our proxy conversion rate is 

defined as the ratio of the sum of OASDI covered employment posted to the MEF, EO_ESF, 

and EO_UND to the sum of CPS and military employment. Effectively, this method assumes 

that the conversion weight for each age-sex sub-component of EO is approximately equal to 

the conversion rate for each age-sex sub-component of E. 

The estimation methodology for the other immigrant employment and earnings will be 

described in detail in appendix 2.3. (forthcoming) 

2.2. U.S. EARNINGS (USEAR) 

2.2.a. Overview 

In the CPS data, E is separated by class of worker. The broad categories include wage and salary 

workers (EW), the self-employed (ES), and unpaid family workers (EU). For the nonagricultural 

sector, a self-employed participation rate (SEPR) is defined as the ratio of ES to E, the 

proportion of employed persons who are self-employed. For the agricultural sector, the SEPR is 

defined as the ratio of ES to the civilian noninstitutional population. 

USEAR projects quarterly values for these principle classes of employment. Equations 2.2.1 

through 2.2.4 outline the subprocess’ overall structure and solution sequence. 

SEPR = SEPR(·) (2.2.1) 

ES = SEPR * E (2.2.2) 

EU = EU(·) (2.2.3) 

EW = E - ES - EU (2.2.4) 

In the National Income and Product Accounts (NIPA), the Bureau of Economic Analysis (BEA) 

publishes historical quarterly estimates for gross domestic product (GDP), real GDP, and the 

GDP price deflator (PGDP). PGDP is equal to the ratio of nominal to real GDP. Potential (or 
49 

full-employment) GDP is a related concept defined as the level of real GDP that is consistent 

with a full-employment aggregate RU. 

USEAR projects quarterly values for these output measures. Potential GDP is based on the 

change in (1) full-employment values for E (including U.S. armed forces), (2) average hours 

worked per week, and (3) productivity. Full-employment values for E are derived by solving 

USEMP under full-employment conditions, while the full-employment values for the other 

variables (average hours worked and productivity) are set by assumption. Projected real GDP is 

set equal to the product of potential GDP and RTP. RTP reaches 1.0 in the short-range period 

and remains at 1.0 thereafter. Nominal GDP is the product of real GDP and PGDP. The growth 

rate in PGDP is set by assumptions. 

The BEA also publishes quarterly values for the principal components of U.S. earnings, 

including total wage worker compensation (WSS), total wage and salary disbursements (WSD), 

and total proprietor income (Y). These concepts can be aggregated and rearranged. Total 

compensation (WSSY) is defined as the sum of WSS and Y. The total compensation ratio 

(RWSSY) is defined as the ratio of WSSY to the GDP. The income ratio (RY) is defined as the 

ratio of Y to WSSY. The earnings ratio (RWSD) is defined as the ratio of WSD to WSS. 

USEAR projects quarterly values for these principle components of U.S. earnings using 

Equations 2.2.5 through 2.2.11. 

RWSSY = RWSSY(·) (2.2.5) 

WSSY = RWSSY * GDP (2.2.6) 

RY = RY(·) (2.2.7) 

Y = RY * WSSY (2.2.8) 

WSS = WSSY - Y (2.2.9) 

RWSD = RWSD(·) (2.2.10) 

WSD = RWSD * WSS (2.2.11) 

2.2.b. Input Data

Long-Range OASDI Projection Data 

Demography- (See Section 2.1.b.) 
50 

Economics - Data from Section 2.1 include the total employed (E), E by age and sex, LFPRs 

by age and sex, the aggregate unemployment rate (RU), and the full-employment concepts 

for LC, RU, and E. 

Trustees Assumptions - (See Section 2.1.b.) 

Addfactors 

Addfactors were included on some employment and output variables to smooth the transition 

between the latest historical data and the projected values. The need for addfactors is 

reviewed each year and addfactors are implemented if necessary. 

Other input data 

• Ratio of OASDI covered to NIPA wages, and ratio of OASDI taxable to covered wages. 

NIPA wages by sector are available quarterly and annually from 1947 to 2005. They are 

published by the BEA and updated several times during the year. OASDI covered and 

taxable wages (1971 to 2004) are updated annually by the Economic process. Covered and 

taxable data for more recent historical years are estimated from preliminary tabulations of 

Form 941 and W-2 data. Projected values for covered ratios are set to the latest historical 

year. 

• OASDI employee, employer, and self-employed tax rates from 1937 to 2080. These 

contribution rates are set according to the Social Security Act of 1935 as amended through 

2005. The rates are updated when legislation mandates a change. 

• The October ratio of the number of teenagers enrolled in school to the civilian 

noninstitutional population by sex and age group (16-17 and 18-19) for the period 1947 to 

2004. An additional new year of data from the Census Bureau is usually available for 

including in preparation of the next annual Trustees Report. Projected values are set to 

levels from the latest historical year. 

• The historical CPI for medical services is published monthly by the BLS. Quarterly values 

are projected based on the projected growth in the aggregate CPI and an additional 

amount defined as the growth rate differential in the two price measures that was assumed 

in the latest President’s Fiscal Year Budget. The series is updated annually. 

• U.S. armed forces (EDMIL) by age and sex were estimated by the Department of Defense 

and published by the Census Bureau on a monthly basis (1948-2000) by single year of age 

(17 to 64) and sex. These data are no longer produced by Census. 
51 

• EDMIL by age and sex are estimated by the Economic process as the difference in the 

monthly resident plus Armed Forces overseas population and the monthly civilian 

population. These two populations are available from the Census Bureau on a monthly 

basis (April 2000 to July 2006) by single year of age (16 to 69) and sex. These data are 

updated several times a year. 

• Wages for railroad workers are wages covered by the Railroad Retirement Act. The 

annual data are for the period 1971 to 2004. An additional year of data from the Railroad 

Retirement Board is usually available for including in preparation of the next annual 

Trustees Report. 

• The Federal minimum hourly wage is based on the Fair Labor Standards Act from the 

Department of Labor for 1938 to 2006. The wage is updated when there is legislation 

mandating a change. 

• Time trends (set by Economic process) are used in the agriculture sector for employment, 

real output, and compensation in the short-range period. These short-range trends are 

extended for each year’s Trustees Report, reflecting a new short-range period. 

2.2.c. Development of Output

Equation 2.2.1 - Self-Employed Participation Rate (SEPR) 

The SEPR is disaggregated by age, sex, and industry. The age groups include 16-17, 18-19, 

20-24, 25-34, 35-44, 45-54, 55-64, and 65 and over. The industry groups include agriculture 

and non-agriculture. 

For the non-agriculture sector, the SEPRs by age and sex are defined as the ratio of the nonagriculture self-employment to total employment. Thus, the aggregate non-agriculture SEPR 

is dependent on the projected distribution of employment by age and sex. All non-agriculture 

SEPRs by age and sex are dependent on the RTP. Increases in the RTP lead to decreases in 

the SEPRs. For female age groups between 20 and 64, the non-agriculture SEPRs are also 

dependent on the groups LFPRs. Increases in the LFPRs lead to increases in the SEPRs. 

For the agriculture sector, the male SEPRs by age are defined as the ratio of agriculture selfemployment to the civilian noninstitutional population. Thus, the aggregate agriculture SEPR 

for males is dependent on the projected distribution of the population by age. The agriculture 

SEPRs for males by age are dependent on the ratio of total agriculture employment (EA) to 

the total civilian population aged 16 and over. (EA is projected in a farm sub-program. Real 

farm output is projected to increase with the population, while farm productivity, defined as 

output per worker, is projected to continue to follow its historical trend. EA is projected as 
52 

the ratio of farm output to farm productivity.) An increase in the ratio of EA to the total 

civilian population aged 16 and over leads to an increase in the agriculture SEPRs for males. 

The female SEPRs by age for the agriculture sector are defined as the ratio of the female to 

male agriculture self-employment. Thus, the aggregate agriculture SEPR for females is 

dependent on the projected distribution of male agriculture employment by age. For female 

age groups between 18 and 64, the SEPRs are dependent on the RTP and the corresponding 

ratio of total female to male employment . Generally, an increase in the RTP leads to 

increases in the SEPRs. An increase in the total employment ratio also leads to an increase in 

the SEPR. 

Equation 2.2.3 - Unpaid Family Workers (EU) 

EU is disaggregated by age, sex, and industry. The age groups include 16-17, 18-19, 20-24, 

25-34, 35-44, 45-54, 55-64, and 65 and over. The industry groups include agriculture and 

non-agriculture. 

From 1970 to 2005, the level of EU fell from about 0.5 to 0.03 million in the agriculture 

sector and from about 0.5 to 0.09 million in the nonagriculture sector. For projections, the 

levels of EU by age and sex in the agriculture sector are assumed to be constant and about 

five thousand or less. The EUs by age and sex in the nonagriculture sector are projected as a 

constant ratio to ES. 

Equation 2.2.5 - Total Compensation Ratio (RWSSY) 

The Trustees set the ultimate annual growth rate for RWSSY. For the short-range period, 

total WSS, WSD, and Y are aggregated from sector components. Total GDP, WSS, and 

WSD are divided into the farm and nonfarm sectors. The nonfarm sector is further separated 

into the government and government enterprises, households, non-profit institutions, and 

residual (private nonfarm business excluding government enterprises (PBNFXGE)) sectors. 

Total Y is divided into the farm and residual (i.e., PBNFXGE) sectors. 

The methodology used to estimate GDP, WSS, WSD, and Y differs by sector. 

Farm - Nominal GDP is the product of real GDP and the farm price deflator. Real farm GDP 

is projected from estimates of real farm per capita output. EA is projected from estimates of 

farm productivity. EAW is projected to continue its historical increase relative to EA. Farm 

compensation (WSSPF) is the product of estimates for average farm compensation 

(AWSSPF) and EAW, while farm proprietor income (YF) is the product of estimates of 

average farm proprietor income (AYF) and EAS. AYF is projected based, in part, on the 

growth in average compensation in the private sector. 
53 

Government and Government Enterprises - This sector is further disaggregated to Federal 

Civilian, Federal Military, and State and Local. In each sector, WSD is the product of 

estimates for average wages and employment. WSS is the sum of WSD and estimates for 

non-wage components of compensation. GDP is the sum of WSS and estimates of 

consumption of fixed capital. 

Household - WSS is the product of estimates for average compensation and employment. 

WSD is WSS less employer contributions for the OASDHI tax. GDP is the sum of WSS and 

the gross value added of owner-occupied housing. 

Nonprofit Institutions - The Nonprofit Institutions sector is further disaggregated to Health, 

Education, and Social Services sectors. In each sector, WSS is the product of estimates for 

average compensation and employment. WSD is WSS less the estimates for non-wage 

components of compensation. GDP is WSS plus a residual component of output. 

Private Nonfarm Business Excluding Government Enterprises (PBNFXGE) - GDP in the 

PBNFXGE sector is total economy-wide GDP less the sum of the other sector GDPs. WSS is 

projected as a ratio to GDP less Y. The ratio is projected to be mostly stable, varying only 

temporarily with changes in RTP. Y is projected as a ratio to GDP. 

Thus, total labor compensation (WSSY) is summed from sector components, while the total 

compensation ratio (RWSSY) is the ratio of total WSSY to total GDP. It is important to note 

that the pure program-generated estimate for the total RWSSY is adjusted to ensure a smooth 

transition between the latest historical data and the Trustees’ ultimate assumptions. 

Equation 2.2.7 - Income Ratio (RY) 

Y is disaggregated to the farm and PBNFXGE sectors. In the PBNFXGE sector, the Y is 

projected as a ratio to GDP in the sector. In the farm sector, Y is projected based, in part, on 

the growth in average compensation in the private sector. 

Equation 2.2.10 - Earnings Ratio (RWSD) 

In the NIPA, the difference between the WSS and WSD is defined as employer contributions 

for employee pension and insurance funds (OLI) and employer contributions for government 

social insurance (SOC). OLI is mostly health and life insurance, and pension and profit 

sharing. SOC is composed of employer contributions to Federal and State & Local 

government social insurance funds. Federal government funds include OASDI, HI, UI, and 

other small groups. State and Local government funds mostly include workers’ 

compensation. 

RWSD is defined as the ratio of WSD to WSS and is projected for the federal military, 

federal civilian government, state and local government, and private sectors of the economy. 
54 

Over the long-range period, the projected values for RWSD in each sector are set to the 

trustees’ assumed ultimate annual growth rate. Over the short-range period, each projected 

value for RWSD for each sector is the sum of the model’s “raw” estimate and an adjustment. 

The adjustment guarantees that the projected value for RWSD matches the BEA’s latest 

published historical quarterly value for the variable. For subsequent quarters, this adjustment 

or “difference” may be increased, decreased, or held constant, depending on the assumed 

nature of the difference. For example, the projected value for the RWSD for the federal 

military sector has the largest adjustment, averaging about -0.01 for CY 2007. We believe 

this difference is associated with a temporary federal government contribution to the 

military’s thrift savings plan to meet manpower requirements for the wars in Iraq and 

Afghanistan. Consequently, this adjustment to RWSD for the federal military sector is 

eliminated in 2008 and later. The adjustments for RWSD in state and local government and 

private sectors were about -0.01 and 0.01, respectively, and are held constant in subsequent 

quarters of the short-range projection horizon. 

2.3. OASDI COVERED EMPLOYMENT AND EARNINGS (COV) 

2.3.a. Overview 

Total at-any-time employment (TE) is defined as the sum of total OASDI covered employment 

(TCE) and total noncovered employment (NCE). TCE can be decomposed to workers who only 

report OASDI covered self-employed earnings (SEO) and to wage and salary workers who 

report some OASDI covered wages (WSW). Combination workers (CMB_TOT) are those who 

have both OASDI covered wages and self-employed income. Workers with some selfemployment income (CSW) are the sum of SEO and CMB_TOT. 

Some of these concepts can be rearranged. The total employed ratio (RTE) is defined as the ratio 

of TE to the sum of EW, ES, and EDMIL, while the combination employment ratio (RCMB) is 

defined as the ratio of CMB_TOT to WSW. 

COV projects annual values for TE and the principle measures of OASDI covered employment. 

Equations 2.3.1 through 2.3.9 outline the overall structure and solution sequence used to project 

these concepts. 

RTE = RTE(·) (2.3.1) 

TE = RTE * (EW + ES + EDMIL) (2.3.2) 

NCE = NCE(·) (2.3.3) 

TCE = TE - NCE (2.3.4) 
55 

SEO = SEO(·) (2.3.5) 

WSW = TCE - SEO (2.3.6) 

RCMB = RCMB(·) (2.3.7) 

CMB_TOT = RCMB * WSW (2.3.8) 

CSW = SEO + CMB_TOT (2.3.9) 

Total OASDI covered earnings is defined as the sum of OASDI covered wages (WSC) and total 

covered self-employed income (CSE_TOT). Both components can be expressed as ratios to their 

U.S. earnings counterparts. The covered wage ratio (RWSC) is defined as the ratio of WSC to 

WSD, while the covered self-employed ratio (RCSE) is the ratio of CSE_TOT to Y. 

COV projects annual values for the principal measures of OASDI covered earnings using 

Equations 2.3.10 through 2.3.13. 

RWSC = RWSC(·) (2.3.10) 

WSC = RWSC * WSD (2.3.11) 

RCSE = RCSE(·) (2.3.12) 

CSE_TOT = RCSE * Y (2.3.13) 

COV can now project various annual measures of average OASDI covered earnings, including 

the average covered wage (ACW), average covered self-employed income (ACSE), and average 

covered earnings (ACE). 

ACW = WSC / WSW (2.3.14) 

ACSE = CSE_TOT / CSW (2.3.15) 

ACE = (WSC + CSE_TOT) / TCE (2.3.16) 

The average wage index (AWI) is based on the average wage of all workers with wages from 

Forms W-2 posted to the Master Earnings File (MEF). By law, it is used to set the OASDI 

contribution and benefit base (TAXMAX). 
56 

COV projects annual values for the AWI and TAXMAX. 

AWI = AWI(·) (2.3.17) 

TAXMAX = TAXMAX(·) (2.3.18) 

2.3.b. Input Data

Long-Range OASDI Projection Data 

Demography - (See Section 2.1.b.) 

Economics- Employment and earnings-related data from Sections 1.1 and 1.2. 

Trustees Assumptions - (See Section 2.1.b.) 

Addfactors 

Addfactors were included on some employment variables to smooth the transition from the 

latest historical data to program estimates. The need for addfactors is reviewed each year and 

addfactors are implemented if necessary. 

Other input data 

• The ratio of maximum quarterly population within a year to the annual value for that 

year is calculated from 1959 through the year of latest available data by 5-year age 

group and sex. The population, defined as the sum of the civilian noninstitutional 

population and the military is updated quarterly from CPS and military data. 

• Ratios of OASDI covered to NIPA wages by sector. NIPA wages by sector are 

available quarterly and annually from 1947 to 2005. They are published by the BEA 

and updated several times during the year. OASDI covered wages (1971 to 2004) are 

updated annually by the Economic process. Covered data for the latest historical year 

are estimated from tabulations of Form 941 and W-2 data. 

• The ratio of other immigration to employment by age and sex is calculated within 

COV using employment (by age and sex) generated in USEMP and the number of 

other immigrants (by age and sex) from demography. The series is calculated over the 

period 1997 to 2099. It is updated annually with other immigration data (from the 
57 

Demography process) and employment generated from USEMP. 

• The change in noncovered workers due to change in the ratio of other immigration to 

employment. This "loss" to OASDI covered employment due to the change in the 

relative number of other immigrants is calculated within COV from 1997 to the end 

of the projection period. The data for this series is based on the ratio of other 

immigration to employment described above. The series is updated annually with 

other immigration data (from the Demography process) and employment generated 

from USEMP. 

• Ratio of disabled worker beneficiaries to the Social Security area population is 

produced by 5-year age group and sex for the years 1970 to 2099. The Social Security 

area population is produced by the Demography process and updated annually for the 

Trustees Report. The number of disabled worker beneficiaries are annual data from 

the prior year’s Trustees Report (Disability subprocess), and are updated annually. 

• U.S. armed forces (EDMIL) by age and sex were estimated by the Department of 

Defense and published by the Census Bureau on a monthly basis (1948-2000) by 

single year of age (17 to 64) and sex. These data are no longer produced by Census. 

• EDMIL by age and sex are estimated by the Economic process as the difference in 

the monthly resident plus Armed Forces overseas population and the monthly civilian 

population. These two populations are available from the Census Bureau on a 

monthly basis (April 2000 to July 2006) by single year of age (16 to 69) and sex. 

These data are updated several times a year. 

• Railroad employment is covered by the Railroad Retirement Act. The annual 

historical data are for the period 1971 to 2004. An additional new year of historical 

data from the Railroad Retirement Board is usually available for inclusion in 

preparation of the next annual Trustees Report. 

• Data obtained from Office of Research, Evaluation, and Statistics (ORES) are 

tabulations of quarterly Form 941 data. Data currently used are the OASDI, HI, and 

income taxable wages by sector for the most recent five years. The data represent 

changes in reported wages since the prior quarterly report. The most recent data are 

appended to previously reported data. Annual totals are computed and used to derive 

estimates of OASDI covered wages by sector for the latest historical years. 

• Data obtained from the most recently available 1.0% CWHS active file, maintained 

on Social Security’s mainframe and made available by ORES. The years of data are 

1951 to the third year prior to the current Trustees Report year. The data are used for 

comparison of OASDI covered earnings from other sources. 
58 

• Data obtained from extracting information from the 1.0% Employee-Employer Files, 

maintained on Social Security’s mainframe and made available by ORES. Each year 

two files are created: a Version 1 file for the third year prior to the current Trustees 

Report and a Version 3 file for the fifth year prior to the current Trustees Report. Data 

currently being used are government and farm sector OASDI, HI, and total wages and 

employment. Data from the latest files are used to estimate OASDI covered wages for 

the years available on each file. 

• Data obtained from quarterly IRS Form 941 file, provided by Office of Systems (OS). 

Data currently used are the OASDI and HI taxable wages for 1978 to the most recent 

year available. The data represent changes in reported wages since the prior quarterly 

report. The most recent data are appended to previously reported data. Annual totals 

are computed and used to derive estimates of HI taxable wages, which are then used 

to develop OASDI covered wages for the most recent historical years. 

• Data for the most recent ten years from the Quarterly EPOXY Report, received in 

hard-copy and, more recently, electronic formats obtained from OS. The data 

currently used are the total number of workers with OASDI taxable earnings, total 

number of workers with OASDI self-employed taxable earnings, distribution of 

number of HI workers by wage intervals, distribution of number of OASDI workers 

by wage intervals, number of persons with OASDI taxable wages, number of persons 

with HI taxable wages, number of persons with OASDI taxable self-employment, and 

number of persons with HI taxable self-employment. 

• Data obtained from the Quarterly Trust Fund Letter, received from Office of 

Financial Policy and Operations (OFPO). Data currently used are OASDI and HI 

taxable wages accumulated from all Forms 941 and W-2 to date, and changes in selfemployment earnings and self-reported tips since the prior Letter. These data are for 

years 1978 to the most recent year available. 

• Data obtained from OS on amounts of OASDI taxable wages on the Earnings 

Suspense File for 1937 through the second year prior to the current Trustees Report 

year. The data are used in estimating total OASDI covered employment. 

2.3.c. Development of Output

Equation 2.3.1 - Ratio of Total Employment (RTE) 

Since CPS data is only available for those aged 16 and over, RTEs could not be constructed 

or projected. For those aged 9 and under, we used covered population ratios (CPR), defined 

as the ratio of OASDI covered employment to the Social Security area population. CPRs for 

those 9 and younger are disaggregated by single-year of age and sex. Projected values for 
59 

CPRs by age and sex age are set to their latest historical levels. Thus, the aggregate CPR for 

those aged 9 and under is dependent on the projected age-sex distribution of the population. 

For those aged 10-15, we used total population ratios (TPR), defined as the ratio of TE to the 

Social Security area population. The TPRs are disaggregated by sex and age, including those 

aged 10-13 and 14-15. The TPR for males aged 10-13 is projected to remain constant at its 

latest historical level. The TPR for females aged 10-13, and the TPRs for males and females 

aged 14-15, are dependent on the RTP. An increase in the RTP leads to an increase in the 

TPRs. 

The RTE for those aged 16 and over is defined as the ratio of TE to the sum of EW and ES 

(or alternatively, E less EU) and EDMIL. The RTE is disaggregated by sex and age, 

including those aged 16-17, 18-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 

60-64, 65-69, and 70 and over. Thus, COV contains 26 RTE equations, 13 for males, and 13 

for females. 

The aggregate RTE for those aged 16 and over is dependent on the projected age-sex 

distribution of employment. Each disaggregated RTE is dependent on its corresponding 

age-sex employment ratio. The employment ratio is roughly defined as the ratio of E to N. 

Increases in the employment ratio lead to decreases in the RTEs. 

Equation 2.3.3 - Non-Covered Employment (NCE) 

NCE is disaggregated by age and sex. Age groups include 14-15, 16-17, 18-19, 20-24, 25-29, 

30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, and 70 and over. Employment may 

not be OASDI covered for a variety of reasons mostly related to the type of work. 

Consequently, NCE is further disaggregated to the type-of-work components listed below. 

Federal Civilian Government - All Federal civilian employees are HI (i.e., Medicare) 

covered. All Federal Civilian employees hired in January 1984 and later are covered under 

the Federal Employees Retirement System (FERS) and are OASDI covered. Employees hired 

before January 1984 are covered under the Civil Service Retirement System (CSRS) and are 

not OASDI covered. This “closed group” of relatively older CSRS employees is projected to 

fall to near zero by 2030. 

State and Local Government - In 1983, about 70 percent of State and Local Government 

(S&L) employment and wages were covered under OASDI and HI. Beginning April 1986, 

all newly hired S&L employees were covered under HI. Beginning January 1990, all S&L 

employees not under an S&L retirement system were covered under OASDHI. 

By 2002, about 30 and 10 percent of S&L employment (and also wages) are still not covered 

under OASDI, and HI respectively. The closed group of relatively older S&L employees not 

covered under HI is projected to fall to near zero by 2020. S&L employment not covered 

under OASDI is projected to grow at about the same rate as the labor force. 
60 

Students at Public Schools - Prior to 2000, students working at S&L public schools were 

covered under OASDI and HI if the other school employees were covered. In 2000, 

legislation offered an “open season” allowing schools to remove their students from 

coverage. Virtually all major schools opted for removal. Hence, almost no students working 

at their public schools are covered under OASDI or HI. Students at public schools are 

projected to grow at about the same rate as the population aged 18 to 24. 

Election Workers - Most S&L election workers are subject to an earnings test and are not 

covered under OASDHI. The earnings test was raised from $100 to $1,000 beginning 

January 1995 and indexed beginning in 2000. Election workers are projected to grow at 

about the same rate as LC. 

Private Household - The threshold for coverage of domestic employees’ earnings was raised 

from $50 per calendar quarter to $1,000 per calendar year (CY) per employee. Domestic 

workers are no longer covered if under age 18. Private household employment is projected to 

grow at about the same rate as E and vary with RTP. 

Students at Private Schools - All students working in private schools are not covered under 

OASDHI. Students at private schools are projected to grow at about the same rate as the 

population aged 18 to 24. 

Railroad - Employers do not submit payments for payroll taxes to the IRS for railroad 

employees. Railroad employees are projected by the Railroad Retirement Board. 

Other Noncovered Workers - Set at a constant amount of 0.4 million to reflect relatively 

small and shrinking groups such as paperboys. 

Underground Economy Workers - Set to the at-any-time employed in the other immigrant 

population who have no reported earnings and therefore are part of the underground 

economy (i.e., TEO_UND). 

Equation 2.3.5 - Self-Employed Only (SEO) 

SEO is projected to grow at the same rate as ES. 

Equation 2.3.7 - Ratio of Combination Workers (RCMB) 

Total CMB_TOT can be separated into two groups depending on whether they have OASDI 

covered wages under or over the TAXMAX. CMB_TOT with covered wages under the 

TAXMAX have taxable wages and self-employed income. CMB_TOT with covered wages 

over the TAXMAX have taxable wages only. CMB_TOT with covered wages over the 
61 

TAXMAX would have paid taxes on their self-employed income if the TAXMAX had been 

eliminated. 

Total CMB_TOT is projected as a ratio to WSW. This ratio is dependent on the RTP. If RTP 

rises, then the CMB_TOT falls. 

Equation 2.3.10 - Ratio of Covered Wages (RWSC) 

RWSC is disaggregated by the following sectors: Federal Civilian government, Federal 

Military, S&L government, and Private. 

Federal Civilian government - Total Federal civilian employment and wages are split by 

retirement system. Those under FERS are OASDI covered, while those under CSRS are not. 

Employment and wages are projected for workers under each retirement system. 

Employment under CSRS is a closed group that is expected to fall to zero by about 2030. 

Employment under FERS is defined as total Federal employment less employment under 

CSRS. Total Federal civilian employment is projected to grow at an average annual rate of 

about 0.2 percent from 2004 to the end of the short-range period, and about equal to the 

growth in the LC thereafter. The growth rates in the average wage for those under CSRS and 

FERS are projected based on, for the first five years, pay raises assumed under the most 

recent OMB FY Budget and on the growth rate in the CPI. Hence, the RWSC for the Federal 

civilian employment is defined as the ratio of wages for employment under FERS to total 

Federal civilian wages. 

Federal Military - The RWSC for the Federal military sector is projected to remain constant 

at its latest actual historical level. 

S&L government - The RWSC for the S&L government sector is projected to remain 

constant at its latest actual historical level. 

Private - The private sector is separated into sub-sectors including private households, farm, 

railroad, tips, and a residual private “base”. The RWSCs for the private household and farm 

sub-sectors are projected to remain constant at their latest actual historical levels. By 

definition, the RWSCs for the railroad and tips sub-sectors are projected to remain constant 

at 0.0 and 1.0, respectively. The projected RWSC for the private base sub-sector is dependent 

on the ratio of EO wage workers in the private base sub-sector who are covered under the 

OASDI program to all EO wage workers in the private base sub-sector. We assume that all of 

EO will be wage workers employed in the private residual base sub-sector of the economy 

and that the proportion of EO that is covered under the OASDI program will decrease. 

Therefore, we assume that the RWSC for the private residual base sector will also decrease. 

The estimation methodology for the other immigrant employment and earnings will be 

described in detail in Appendix 2.3. (forthcoming) 
62 

Equation 2.3.12 - Ratio of Covered Self-Employed Earnings (RCSE) 

The RCSE is projected to remain constant at its latest actual historical level. 

Equation 2.3.17 - Average Wage Index (AWI) 

The growth in the AWI is projected to be equal to the growth in an economy-wide average 

wage (ACWC) defined as the ratio of WSD to total wage workers (covered and noncovered). Total wage workers are projected as the sum of WSW and the various groups of 

non-covered wage workers discussed above. 

Equation 2.3.18 - OASDI Taxable Maximum (TAXMAX) 

By law, the growth in the AWI is used to increase the TAXMAX. 

2.4. Effective TAXABLE PAYROLL (TAXPAY) 

2.4.a. Overview 

TAXPAY estimates historical annual taxable earnings data including total employee OASDI 

taxable wages (WTEE), total employer taxable wages (WTER), and total self-employed taxable 

income (SET). By law, each employee is required to pay the OASDI tax on wages from all 

covered jobs up to the TAXMAX, while each employer is required to pay the OASDI tax on the 

wages of each worker up to the TAXMAX. If an employee works more than one covered wage 

job and the sum of all covered wages exceeds the TAXMAX, the employee but not the employer 

is due a refund. Hence, WTER is greater than WTEE. The difference (i.e., WTER less WTEE) is 

defined as multi-employer refund wages (MER). 

TAXPAY also estimates the historical annual effective OASDI taxable payroll (ETP). ETP is the 

amount of earnings in a year which, when multiplied by the combined employee-employer tax 

rate, yields the total amount of taxes due from wages and self-employed income in the year. ETP 

is used in estimating OASDI income and in determining income and cost rates and the actuarial 

balance. ETP is defined as WTER plus SET less one-half of MER. 

TAXPAY projects annual values for ETP after first estimating its components. The components 

in turn are estimated by a collection of ratios. The employee taxable ratio (RWTEE) is defined as 

the ratio of WTEE to WSC. The multi-employer refund wage ratio (RMER) is defined as the 
63 

ratio of MER to WSC. The self-employed net income taxable ratio (RSET) is defined as the ratio 

of SET to CSE_TOT. Equations 2.4.1 through 2.4.8 outline the projection methodology. 

RWTEE = RWTEE(·) (2.4.1) 

WTEE = RWTEE * WSC (2.4.2) 

RMER = RMER(·) (2.4.3) 

MER = RMER * WSC (2.4.4) 

WTER = WTEE + MER (2.4.5) 

RSET = RSET(·) (2.4.6) 

SET = RSET * CSE_TOT (2.4.7) 

ETP = WTER + SET - 0.5 * MER (2.4.8) 

Over the short-range projection horizon (i.e., first 10 years), TAXPAY also projects annual 

OASDI wage tax liabilities (WTL) and self-employment tax liabilities (SEL). In Equation 2.4.9, 

WTL is the product of the effective taxable wages, defined as WTER less one-half of MER, and 

the combined OASDI employee-employer tax rate (TRW). In Equation 2.4.10, SEL is the 

product of SET and the OASDI self-employed tax rate (TRSE). 

WTL = WTER * TRW (2.4.9) 

SEL = SET * TRSE (2.4.10) 

Also over the short-range horizon, TAXPAY decomposes WTL into quarterly wage tax 

liabilities (WTLQ) then to quarterly wage tax collections (WTLQC). TAXPAY also decomposes 

SEL into quarterly self-employed net income tax collections (SELQC). 

WTLQ = WTLQ(·) (2.4.11) 

WTLQC = WTLQC(·) (2.4.12) 

SELQC = SELQC(·) (2.4.13) 
64 

Finally, over the first two projected quarters, TAXPAY estimates of WTLQC and SELQC are 

replaced with ones from the most recent OMB FY Budget. And, over the first four projected 

quarters, TAXPAY includes estimates for appropriation adjustments (AA). 

AA = AA(·) (2.4.14) 

2.4.b. Input Data

Long-Range OASDI Projection Data 

Economics - Data from Sections 2.1, 2.2, and 2.3 

Trustees Assumptions - (See Section 2.1.b.) 

Addfactors 

Addfactors were included for RWTEE and RSET. The need for addfactors is reviewed each 

year and addfactors are implemented if necessary. 

Other input data 

• OASDI employee, employer, and self-employed tax rates from 1937 to the end of the 

long-range period. These contribution rates are set according to the Social Security 

Act of 1935 and amendments to the Act through 2004. The rates are updated when 

legislation mandates a change. 

• Proportions of OASDI tax liabilities for self-employment earnings for the current and 

prior calendar year estimated to be collected in each quarter through the end of the 

short-range period. (In any particular quarter, some self-employed individuals are 

paying taxes on earnings from the prior year and some are paying from the current 

year’s earnings.) Values are derived from historical data from the Office of Tax 

Analysis (OTA) in the Department of the Treasury for the amount of selfemployment taxes transferred to the OASDI Trust Funds in each month split by the 

calendar year (either the current or the prior) in which the self-employment income 

was earned. The data are updated every year after historical information for a 

complete new year is received (usually in March). 

• Payday adjustments are established by analysis of the calendar to determine the 

number of likely paydays (particularly Fridays) in a quarter. Data for payday 

adjustments are available for calendar years covering the short-range period. Since 

the number of Fridays in future calendars are fixed, the payday adjustments do not 

require updating between trustee reports. 
65 

• FICA appropriation adjustments – Estimated amounts of OASI and DI appropriation 

adjustments to include newly reported tax liability amounts including correction of 

past transfers of estimated amounts to the trust funds. Values are derived from 

historical data from the OTA for the amount of OASI and DI tax liability by quarter, 

SSA’s OS tabulations of taxable wages from IRS Forms 941, quarterly certification 

letter data from SSA’s OFPO, and our revenue model estimates of tax liabilities. 

Values are estimated for the four quarters of the trustees report year and for the 

following two quarters. 

• Time trend adjustments to RWTEE for each calendar year of the short-range period. 

Historical analysis suggests a “trend” rate of decline in RWTEE of about 0.0016 per 

year through 2001. This trend reflects a movement toward greater amounts of wages 

being paid to workers earning above the taxable maximum. We expect this trend to 

continue to the end of the short-range projection horizon, but at a slower rate. 

Consequently, we assume an adjustment factor of 0.4 such that the trend annual rate 

of decline from 2002 to the end of the short-range projection horizon is about 0.0006 

per year (i.e., 0.0016 * 0.4). The time trend has not been updated since first decided 

upon. It will be changed if and when it is deemed appropriate. 

• Data obtained from ORES by email for the amounts of single and multi-employer 

refunds for the latest 5 years. Each year, data are updated. 

• Data obtained from ORES are tabulations of quarterly Form 941 data. Data currently 

used are the OASDI, HI, and income taxable wages by sector for the most recent five 

years. The data represent changes in reported wages since the prior quarterly report. 

The most recent data are appended to previously reported data. Annual totals are 

computed and used to derive estimates of OASDI taxable wages by sector for the 

latest historical years. 

• Data obtained from the most recently available 1.0% CWHS active file, maintained 

on Social Security’s mainframe and made available by ORES. The years of data are 

1951 to the third year prior to the current Trustees Report year. The data are used for 

comparison of OASDI taxable earnings from other sources. 

• Data obtained from quarterly IRS Form 941 file, provided by OS. Data currently used 

are the OASDI and HI taxable wages for 1978 to the most recent year available. The 

data represent changes in reported wages since the prior quarterly report. The most 

recent data are appended to previously reported data. Annual totals are computed and 

used to derive estimates of OASDI taxable wages for the most recent historical years. 

• Data for the most recent ten years from the Quarterly EPOXY Report, received in 

hard-copy and, more recently, electronic formats obtained from OS. The data 
66 

currently used are the total number of workers with OASDI taxable earnings, total 

number of workers with OASDI self-employed taxable earnings, distribution of 

number of HI workers by wage intervals, distribution of number of OASDI workers 

by wage intervals, number of persons with OASDI taxable wages, number of persons 

with HI taxable wages, number of persons with OASDI taxable self-employment, 

number of persons with HI taxable self-employment, number of workers with singleemployer excess wages, and number of workers with multi-employer excess wages. 

• Data obtained from the Quarterly Trust Fund Letter, received from OFPO. Data 

currently used are OASDI and HI taxable wages accumulated from all Forms 941 and 

W-2 to date, and changes in self-employment earnings and self-reported tips since the 

prior Letter. These data are for for years 1978 to the most recent year available. 

2.4.c. Development of Output 

Equation 2.4.1 - Employee Taxable Ratio (RWTEE) 

Over the short-range projection horizon, the projected value for RWTEE is the sum of the 

model’s “raw” estimate and an “addfactor.” The raw estimate for RWTEE is dependent on 

the distribution of workers by wage interval, the RELMAX, RTP, the age-sex distribution of 

wage workers, and a time trend adjustment. The projected distribution of workers by wage 

interval is an average (or amalgam) distribution over the 1993 through 2004 period. Holding 

other factors constant, a distribution with relatively more workers with wages over the 

TAXMAX leads to a lower RWTEE. The RELMAX is defined as the ratio of the TAXMAX 

to the ACW. A higher RELMAX leads to a higher RWTEE. An increase in the RTP also 

leads to a higher RWTEE. The change in the projected RWTEE due to the change in the 

age-sex distribution of wage workers is calculated by allowing employment by age and sex to 

change while holding taxable ratios (and average covered wages) by age and sex constant to 

levels in 1996. The time trend adjustment reduces the level of RWTEE by about 0.6 

percentage point over the short-range projection horizon. 

The addfactor is the product of a “base” adjustment and an assumed weight. The base 

adjustment is defined as the actual value for RWTEE in the latest historical (or base) year 

less the raw estimated value for the same period. The weight has an assumed value of 0.9 for 

the first projected year, then values of 0.8 in the second projected year, 0.7 in the third 

projected year,..., and 0.0 in the tenth projected year (i.e., the end of the short-range 

projection horizon). The addfactor is necessary because we assume that the distribution of 

wage workers by earnings interval in the base year will gradually change to the amalgam 

distribution by the end of the short-range period and remain constant thereafter. 

Over the long-range projection horizon, RWTEE is assumed to remain constant. 
67 

RWTEEs are also projected for various sub-aggregates including Federal Civilian employees 

under FERS and CSRS, Federal Civilian employees under CSRS only, S&L employees 

covered under OASDI, S&L employees covered under HI only, U.S. armed forces, and 

agriculture. The RWTEE for each sub-aggregate is dependent only on its sub-aggregate 

RELMAX, that is, the ratio of the TAXMAX to the sub-aggregate’s average covered wage. 

Equation 2.4.3 - Multi-Employer Refund Wage Ratio (RMER) 

The RMER is functionally related to the RWTEE. As RWTEE approaches one, then RMER 

approaches zero. In between the limit values, RMER is positive. Given the present position 

of RWTEE and RMER on the function, a projected decline in RWTEE leads to an increase in 

RMER. 

The projected RMER is also dependent on RU. An increase in RU leads to a decrease in 

RMER. 

Equation 2.4.6 - Self-Employed Net Income Taxable Ratio (RSET) 

The RSET is disaggregated by type of self-employed worker, SEO and CMB_TOT. 

SEO - The RSET is dependent on the distribution of self-employed workers by income 

interval and a RELMAX. The projected distribution of self-employed workers by income 

interval is set to the 1996 distribution. The RELMAX is defined here as the ratio of the 

TAXMAX to the average income for SEO. A higher RELMAX leads to a higher RSET. 

CMB_TOT - Taxable self-employed net income for CMB_TOT is projected in two steps. 

First, a taxable earnings (wages and self-employed income) ratio for CMB_TOT is projected 

based on the 1996 distribution and a RELMAX defined as the ratio of the TAXMAX to the 

average covered earnings. The projected level of taxable earnings for CMB_TOT is the 

product of the estimated taxable earnings ratio for CMB_TOT and their covered earnings. 

Second, a taxable wage ratio for CMB_TOT is projected based on a RELMAX defined as the 

ratio of the TAXMAX to the average covered wage for CMB_TOT. The projected level of 

taxable wages for CMB_TOT is the product of the estimated taxable wage ratio for 

CMB_TOT and their covered wages. 

Taxable self-employed net income for CMB_TOT is obtained by subtracting taxable wages 

from taxable earnings for CMB_TOT. 

A “combined” RSET is calculated as the ratio of taxable self-employed net income for SEO 

and CMB_TOT to CSE_TOT. As with the RWTEE, the combined RSET is adjusted over the 

short-range period due to other factors (i.e., RTP, the age-sex distribution of workers, and a 
68 

trend). The effect of the other factors are taken from RWTEE and “scaled.” That is, RSET is 

adjusted by a percent effect (as opposed to percentage point) that is equal to the percent 

change in RWTEE due to changes in these other factors. 

It is important to note that while the RWTEE is held constant after the short-range period, the 

RSETs for self-employed workers are not. After the short-range period, the projected RSETs 

for SEO and CMB_TOT continue to be dependent on their respective RELMAXs. Since by 

law the TAXMAX grows at the rate of the AWI and since ACSE is assumed to grow faster 

than the ACW (since only ACW declines with the growth in fringe benefits), the RELMAXs 

for self-employed workers decline over the long-range period while the RELMAX for wage 

workers is approximately constant. Hence, the RSETs for SEO and CMB_TOT are projected 

to decline over the long-range period while the RWTEE is held constant. 

Equation 2.4.11 - Quarterly Wage Tax Liabilities (WTLQ) 

The total WTLQ is summed from sector components that include the Federal Civilian, 

Federal Military, S&L, Private Household, Farm, Self-reported Tips, and residual Private 

Nonfarm. Sector WTLQ is determined by computing ratios of quarterly to annual liabilities 

for each quarter. For the Private Nonfarm, S&L, Federal Civilian and Military sectors, these 

“WTLQ ratios” are calculated for each quarter. Each is dependent on the quarterly 

distribution of WSD and the RWTEE for the relevant sector, and on a payday adjustment that 

takes into account the actual number of paydays that fall into a particular calendar quarter. 

WTLQ ratios are also calculated for each quarter for the other sectors. However, these are 

expected to be constants over the projection horizon. 

Equation 2.4.12 - Quarterly Wage Tax Collections (WTLQC) 

Employers incur tax liabilities when they pay wages to their employees. These liabilities are 

required to be deposited with the U.S. Treasury by employers based on the amount of total 

payroll tax liability (income taxes plus Social Security and Medicare taxes withheld) 

accumulated. Some very large employers must deposit their tax liabilities the next banking 

day after paying their employees. Other levels of accumulated tax liabilities require 

depositing within three days, by the middle of the following month, or by the end of the 

month following the quarter. If employers follow these deposit requirements, the result is that 

all tax liability for a particular quarter is deposited by the last day of the month following the 

end of the quarter. Thus, the WTLQC for any particular quarter are the sum of the tax 

liabilities deposited for wages paid in the same quarter and the liabilities deposited for wages 

paid in the prior quarter. 

WTLQC is summed from sector components that include the Federal Civilian, Federal 

Military, Farm, S&L, and residual Private Nonfarm (including Private Household and Selfreported Tips). For the Federal Civilian and Military sectors, the WTLQC is set equal to its 

respective WTLQ since tax liabilities for the two sectors are collected immediately. The 

WTLQC for Farm is also set equal to its WTLQ, due in part to the fact that farms report tax 
69 

liabilities annually. For the S&L and Private Nonfarm sectors, WTLQC is the product of 

WTLQ and the proportion of WTLQ that should be deposited in the month following the end 

of each quarter. This proportion is based on the deposit requirements and estimates of 

accumulated tax liabilities, which in turn are based on firm size (or total wages paid). 

Equation 2.4.13 - Quarterly Self-Employed Net Income Tax Collections (SELQC) 

For wage workers, annual liabilities (WTL) are distributed to quarterly liabilities (WTLQ), 

which in turn are distributed to quarterly collections (WTLQC). However, for self-employed 

workers, annual liabilities (SEL) are distributed directly to SELQC, since the SSA only 

receives self-employed liability amounts on an annual basis (from tabulations of Form 1040 

Schedule SE provided by IRS). 

SEL for a particular calendar year is distributed as collections to the four quarters of that year 

and to the first three quarters of the next year. This distribution uses quarterly proportions 

that are based on an historical pattern of the amount of SEL collected in each month, as 

estimated by the OTA. The OTA estimates reflect IRS regulations that require self-employed 

workers to deposit estimated tax liabilities four times a year (January, April, June, and 

September). 

Equation 2.4.14 - Appropriation Adjustments (AA) 
70

We estimate WTLQC and SELQC for the next two quarters based on projected levels of 

WSD and Y in the various OMB FY Budgets. The Treasury uses these estimates to make 

initial appropriations to the OASDI Trust Funds over the period. Roughly one year after an 

initial appropriation has been made for a quarter, the initial appropriation is adjusted based 

on certified taxable wages reported on Forms 941 and W-2 and taxable self-employment 

income reported on Forms 1040 Schedule SE. This appropriation adjustment occurs 

quarterly and includes amounts due to newly-reported wages and self-employment income 

for all earlier periods. 

FICA appropriation adjustments for wages are projected for all quarters for which we know 

what the Treasury will transfer. This generally means that we make estimates for adjustments 

to occur through the second quarter of the year following the Trustees Report year. The 

projected adjustment for each quarter is composed of two parts. The first estimates the error 

in the initial appropriation for the fourth earlier quarter. This error is defined as the difference 

between the Treasury’s initial appropriation and that portion of TAXPAY’s latest estimate 

for that quarter which is expected to be certified at the point when the adjustment is made. 

The second part is an estimate of the tax liability from additional certified wages for all 

previous periods and is based on an average of additional amounts over a recent historical 

period. These estimates are currently made in separate Excel files (generally named 

“EstimatedAppAdjAlt2.xls” and placed in a folder unique to the particular Trustees Report, 

e.g., \\wmpiet\usr\wmpiet\Excel\TR06), where they are further documented in a “Notes” 

sheet in the Excel file. 

Appropriation adjustments for self-employment income are projected over the entire 

projection horizon based on the historical pattern of reporting. These estimates are made in 

the TAXPAY. 
71 

Appendix 2-1 

Equations 

2.1 U.S. Employment (USEMP) 

MALE LFPR Equations - Annual 

 

Regressions using March CPS Data 

Aged 20 to 44 

PM2024NM = 0.55951 + 0.00198 - 1.0 * RM2024D - 0.91435 * RMM2024NM - 0.33947 * RNM2024S.1 + 0.16484 * NM2024NM / 

(NM2024NM + NM2024MS + NM2024MA) + 0.21031 

 * RTP4Q.1 + PM2024_A94C + PM2024_A94M 

PM2529NM = 0.71186 - 1.0 * RM2529D - 0.92991 * RMM2529NM + 0.06580 * NM2529NM/ (NM2529NM + NM2529MS + NM2529MA) 

+ 0.15942 * RTPL2T5 + PM2554_A94C 

 + PM2554_A94M 

PM3034NM = 0.83231 - 1.0 * RM3034D - 0.71864 * RMM3034NM + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM3539NM = 0.82140 - 0.02915 - 1.0 * RM3539D - 0.84057 * RMM3539NM + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM4044NM = 0.73248 + 0.02540 - 1.0 * RM4044D - 0.00000 * RMM4044NM + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM2024MS = 1.00368 + 0.01443 - 1.0 * RM2024D - 1.05842 * RMM2024MS - 0.14902 * RNM2024S.1 + PM2024_A94C + PM2024_A94M 

PM2529MS = 0.99457 - 1.0 * RM2529D - 1.22879 * RMM2529MS - 0.01937 * (PF2529MS - PF2554_A94C - PF2554_A94M) + 

PM2554_A94C + PM2554_A94M 

PM3034MS = 0.96492 - 1.0 * RM3034D - 1.26554 * RMM3034MS - 0.03628 * (PF3034MS - PF2554_A94C - PF2554_A94M) + 0.05 * 

RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM3539MS = 0.94746 - 1.0 * RM3539D - 1.02117 * RMM3539MS - 0.01377 * (PF3539MS - PF2554_A94C - PF2554_A94M) + 0.05 * 

RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM4044MS = 0.95152 - 0.00165 - 1.0 * RM4044D - 1.14303 * RMM4044MS - 0.02197 * (PF4044MS - PF2554_A94C - PF2554_A94M) + 

0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM2024MA = 0.55549 + 0.04400 - 1.0 * RM2024D - 0.30242 * RMM2024MA + 0.38966 * RTP4Q.1 - 0.20116 * RNM2024S.1 + 

PM2024_A94C + PM2024_A94M 

PM2529MA = 0.73674 - 1.0 * RM2529D - 0.89617 * RMM2529MA + 0.19750 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM3034MA = 0.87897 - 1.0 * RM3034D - 0.59344 * RMM3034MA + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM3539MA = 0.87523 - 1.0 * RM3539D - 0.20124 * RMM3539MA + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

PM4044MA = 0.87250 - 0.02214 - 1.0 * RM4044D - 1.41032 * RMM4044MA + 0.05 * RTPL2T5 + PM2554_A94C + PM2554_A94M 

Aged 75 and Over 

PM7579 = 0.58899 * PM65O_A94MM * (PM7074.5 / PM65O_A94MM.5) 

PM8084 = 0.52749 * PM65O_A94MM * (PM7579.5 / PM65O_A94MM.5) 

PM85O = 0.48912 * PM65O_A94MM * (PM8084.5 / PM65O_A94MM.5) 

Regressions using Annual CPS Data 

Aged 16 to 19 

PM1617 = 0.35974 * DIFF (RTP) + 0.31790 * DIFF (RTP.1) + 0.46318 * DIFF (DROPOUT1012M) + PM1617.1 

TPM1819 = 0.25962 * DIFF (RTP) + 0.26610 * DIFF (DROPOUT1012M) - 1.44724 * DIFF (NM1819M / (NM1819M + NM1819)) + 

TPM1819.1 

Aged 45 to 54 

PM4549NM = -1.0 * RM4549D + 0.02887 * RTPL1T4 + 0.75041 

PM5054NM = -1.0 * RM5054D + 0.77072 

PM4549MS = -1.0 * RM4549D - 0.01488 * PF4549MS + 0.15238 * RTPL1T4 + 0.83034 

PM5054MS = -1.0 * RM5054D - 0.00463 * PF5054MS + 0.19639 * RTPL1T4 + 0.76277 

PM4549MA = -1.0 * RM4549D + 0.00850 * 84 + 0.18962 

PM5054MA = -1.0 * RM5054D + 0.43104 * RTPL1T4 + 0.42746 

Aged 55 to 74 
72 

PM55 = 0.11202 * RTP.3 - 1.0 * RM55D + 0.01523 - 0.27650 + (0.24398 - 0.11202) -0.01 + (MOVAVG (3, PM5054_FE.2 + 

PM2554_94M_TE.2 + PM2554_90C_TE.2 + RM5054D.2) - 0.05338 

 * RTP.3 - 1)) 

PM56 = 0.10041 * RTP.3 - 1.0 * RM56D - 0.00180 + (PM55.1 + RM55D.1 - 0.11202 * RTP.4) 

PM57 = 0.13081 * RTP.3 - 1.0 * RM57D - 0.04182 + (PM56.1 + RM56D.1 - 0.10041 * RTP.4) 

PM58 = 0.24841 * RTP.3 - 1.0 * RM58D - 0.12905 + (PM57.1 + RM57D.1 - 0.13081 * RTP.4) 

PM59 = 0.25992 * RTP.3 - 1.0 * RM59D - 0.02818 + (PM58.1 + RM58D.1 - 0.24841 * RTP.4) 

PM60 = 0.31289 * RTP.3 - 1.0 * RM60D - 0.08886 + (PM59.1 + RM59D.1 - 0.25992 * RTP.4) 

PM61 = 0.32660 * RTP.3 - 1.0 * RM61D - 0.04412 + (PM60.1 + RM60D.1 - 0.31289 * RTP.4) 

PM62 = (1.0 - 1.0 * DIFF (RRADJ_M62) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (RTP.2)) * (PM62.1 + RM62D.1) - RM62D 

PM63 = (1.0 - 1.0 * DIFF (RRADJ_M63) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (RTP.2)) * (PM63.1 + RM63D.1) - RM63D 

PM64 = (1.0 - 1.0 * DIFF (RRADJ_M64) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (RTP.2)) * (PM64.1 + RM64D.1) - RM64D 

PM65 = (1.0 - 1.0 * DIFF (RRADJ_M65) + 0.100 * DIFF (RETEST65) + 0.15 * DIFF (RTP.2)) * PM65.1 

PM66 = (1.0 - 1.0 * DIFF (RRADJ_M66) + 0.100 * DIFF (RETEST66) + 0.15 * DIFF (RTP.2)) * PM66.1 

PM67 = (1.0 - 1.0 * DIFF (RRADJ_M67) + 0.100 * DIFF (RETEST67) + 0.15 * DIFF (RTP.2)) * PM67.1 

PM68 = (1.0 - 1.0 * DIFF (RRADJ_M68) + 0.100 * DIFF (RETEST68) + 0.15 * DIFF (RTP.2)) * PM68.1 

PM69 = (1.0 - 1.0 * DIFF (RRADJ_M69) + 0.100 * DIFF (RETEST69) + 0.15 * DIFF (RTP.2)) * PM69.1 

PM70 = (1.0 - 1.0 * DIFF (RRADJ_M70) + 0.15 * DIFF (RTP.2)) * PM70.1 

PM71 = (0.04127 + 0.91152) * PM70.1 

PM72 = (0.02632 + 0.90027) * PM71.1 

PM73 = (0.05478 + 0.91456) * PM72.1 

PM74 = (-0.02105 + 0.87355) * PM73.1 

MALE LFPR Equations - Quarterly 

Regressions using March CPS Data 

Aged 20 to 44 

PM2024NM = 0.55951 + 0.00198 - 1.0 * RM2024D - 0.91435 * RMM2024NM - 0.33947 * RNM2024S +0.16484 * NM2024NM / 

(NM2024NM + NM2024MS + NM2024MA) +0.21031 * RTP.1 

 + PM2024_A94C + PM2024_A94M 

PM2529NM = 0.71186 - 1.0 * RM2529D - 0.92991 * RMM2529NM +0.06580 * NM2529NM / (NM2529NM + NM2529MS + NM2529MA) 

+0.15942 * MOVAVG (4, RTP.2) + PM2554_A94C 

 + PM2554_A94M 

PM3034NM = 0.83231 - 1.0 * RM3034D - 0.71864 * RMM3034NM + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + PM2554_A94M 

PM3539NM = 0.82140 - 0.02915 - 1.0 * RM3539D - 0.84057 * RMM3539NM + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + 

PM2554_A94M 

PM4044NM = 0.73248 + 0.02540 - 1.0 * RM4044D - 0.00000 * RMM4044NM + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + 

PM2554_A94M 

PM2024MS = 1.00368 + 0.01443 - 1.0 * RM2024D - 1.05842 * RMM2024MS - 0.14902 * RNM2024S + PM2024_A94C + PM2024_A94M 

PM2529MS = 0.99457 - 1.0 * RM2529D - 1.22879 * RMM2529MS - 0.01937 * MOVAVG (4, (PF2529MS.1 - PF2554_A94C.1 - 

PF2554_A94M.1)) + PM2554_A94C + PM2554_A94M 

PM3034MS = 0.96492 - 1.0 * RM3034D - 1.26554 * RMM3034MS - 0.03628 * MOVAVG (4, (PF3034MS.1 - PF2554_A94C.1 - 

PF2554_A94M.1)) + 0.05 * MOVAVG (4, RTP.2) 

 + PM2554_A94C + PM2554_A94M 

PM3539MS = 0.94746 - 1.0 * RM3539D - 1.02117 * RMM3539MS - 0.01377 * MOVAVG (4, (PF3539MS.1 - PF2554_A94C.1 - 

PF2554_A94M.1)) + 0.05 * MOVAVG (4, RTP.2) 

 + PM2554_A94C + PM2554_A94M 

PM4044MS = 0.95152 - 0.00139 - 1.0 * RM4044D - 1.14303 * RMM4044MS - 0.02197 * MOVAVG (4, (PF4044MS.1 - PF2554_A94C.1 - 

PF2554_A94M.1)) + 0.05 * MOVAVG (4, RTP.2) 

 + PM2554_A94C + PM2554_A94M 

PM2024MA = 0.55549 + 0.04400 - 1.0 * RM2024D - 0.30242 * RMM2024MA +0.38966 * RTP.1 - 0.20116 * RNM2024S + PM2024_A94C 

+ PM2024_A94M 

PM2529MA = 0.73674 - 1.0 * RM2529D - 0.89617 * RMM2529MA +0.19750 * MOVAVG (4, RTP.2) + PM2554_A94C + PM2554_A94M 

PM3034MA = 0.87897 - 1.0 * RM3034D - 0.59344 * RMM3034MA + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + PM2554_A94M 

PM3539MA = 0.87523 - 1.0 * RM3539D - 0.20124 * RMM3539MA + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + PM2554_A94M 

PM4044MA = 0.87250 - 0.02214 - 1.0 * RM4044D - 1.41032 * RMM4044MA + 0.05 * MOVAVG (4, RTP.2) + PM2554_A94C + 

PM2554_A94M 

Aged 75 and Over 

PM7579 = 0.58899 * PM65O_A94MM * MOVAVG (4, PM7074.20) 
73 

PM8084 = 0.52749 * PM65O_A94MM * MOVAVG (4, PM7579.20) 

PM85O = 0.48912 * PM65O_A94MM * MOVAVG (4, PM8084.20) 

Regressions using Annual CPS Data 

Aged 16 to 19 

PM1617 = 0.35974 * DIFF (RTP.1) + 0.31790 * DIFF (RTP.5) + 0.46318 * DIFF (DROPOUT1012M) + PM1617.1 

TPM1819 = 0.25962 * DIFF (RTP.1) + 0.26610 * DIFF (DROPOUT1012M) - 1.44724 * DIFF (RM1819M) + TPM1819.1 

Aged 45 to 54 

PM4549NM = -1.0 * RM4549D + 0.02887 * MOVAVG (4, RTP.1) + 0.75041 

PM5054NM = -1.0 * RM5054D + 0.77072 

PM4549MS = -1.0 * RM4549D - 0.01488 * PF4549MS + 0.15238 * MOVAVG (4, RTP.1) + 0.83034 

PM5054MS = -1.0 * RM5054D - 0.00463 * PF5054MS + 0.19639 * MOVAVG (4, RTP.1) + 0.76277 

PM4549MA = -1.0 * RM4549D + 0.00850 * 84 + 0.18962 

PM5054MA = -1.0 * RM5054D + 0.43104 * MOVAVG (4, RTP.1) + 0.42746 

Aged 55 to 74 

PM55 = 0.11202 * MOVAVG (5, RTP.10) - 1.0 * RM55D + 0.01523 -0.27650 + (0.24398 -0.11202) -0.01 + (PM5054L_FE) 

PM56 = 0.10041 * MOVAVG (5, RTP.10) - 1.0 * RM56D - 0.00180 + (PM55.4 + RM55D.4 - 0.11202 * MOVAVG (5, RTP.14)) 

PM57 = 0.13081 * MOVAVG (5, RTP.10) - 1.0 * RM57D - 0.04182 + (PM56.4 + RM56D.4 - 0.10041 * MOVAVG (5, RTP.14)) 

PM58 = 0.24841 * MOVAVG (5, RTP.10) - 1.0 * RM58D - 0.12905 + (PM57.4 + RM57D.4 - 0.13081 * MOVAVG (5, RTP.14)) 

PM59 = 0.25992 * MOVAVG (5, RTP.10) - 1.0 * RM59D - 0.02818 + (PM58.4 + RM58D.4 - 0.24841 * MOVAVG (5, RTP.14)) 

PM60 = 0.31289 * MOVAVG (5, RTP.10) - 1.0 * RM60D - 0.08886 + (PM59.4 + RM59D.4 - 0.25992 * MOVAVG (5, RTP.14)) 

PM61 = 0.32660 * MOVAVG (5, RTP.10) - 1.0 * RM61D - 0.04412 + (PM60.4 + RM60D.4 - 0.31289 * MOVAVG (5, RTP.14)) 

PM62 = (1.0 - 1.0 * DIFF (RRADJ_M62) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * (PM62.1 + RM62D.1) - 

RM62D 

PM63 = (1.0 - 1.0 * DIFF (RRADJ_M63) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * (PM63.1 + RM63D.1) - 

RM63D 

PM64 = (1.0 - 1.0 * DIFF (RRADJ_M64) + 0.100 * DIFF (RETEST64U) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * (PM64.1 + RM64D.1) - 

RM64D 

PM65 = (1.0 - 1.0 * DIFF (RRADJ_M65) + 0.100 * DIFF (RETEST65) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM65.1 

PM66 = (1.0 - 1.0 * DIFF (RRADJ_M66) + 0.100 * DIFF (RETEST66) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM66.1 

PM67 = (1.0 - 1.0 * DIFF (RRADJ_M67) + 0.100 * DIFF (RETEST67) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM67.1 

PM68 = (1.0 - 1.0 * DIFF (RRADJ_M68) + 0.100 * DIFF (RETEST68) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM68.1 

PM69 = (1.0 - 1.0 * DIFF (RRADJ_M69) + 0.100 * DIFF (RETEST69) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM69.1 

PM70 = (1.0 - 1.0 * DIFF (RRADJ_M70) + 0.15 * DIFF (MOVAVG (5, RTP.6))) * PM70.1 

PM71 = (0.04127 + 0.91152) * PM70.4 

PM72 = (0.02632 + 0.90027) * PM71.4 

PM73 = (0.05478 + 0.91456) * PM72.4 

PM74 = (-0.02105 + 0.87355) * PM73.4 

Aggregation of Equations from Regressions using March CPS Data 

Using Quarterly Seasonal Adjustment Weights 

Aged 20 to 44 

TPM2024 = ((PM2024NM * RM2024NM + PM2024MS * RM2024MS + PM2024MA * RM2024MA) + 0.006) * 1.021 

TPM2529 = ((PM2529NM * RM2529NM + PM2529MS * RM2529MS + PM2529MA * RM2529MA) + 0.005) * 0.997 

TPM3034 = ((PM3034NM * RM3034NM + PM3034MS * RM3034MS + PM3034MA * RM3034MA) + 0.005) * 0.997 

TPM3539 = ((PM3539NM * RM3539NM + PM3539MS * RM3539MS + PM3539MA * RM3539MA) + 0.010) * 0.999 

TPM4044 = ((PM4044NM * RM4044NM + PM4044MS * RM4044MS + PM4044MA * RM4044MA) + 0.010) * 0.999 

PM4549 = ((PM4549NM * RM4549NM + PM4549MS * RM4549MS + PM4549MA * RM4549MA) + 0.003) * 0.999 

PM5054 = ((PM5054NM * RM5054NM + PM5054MS * RM5054MS + PM5054MA * RM5054MA) + 0.003) * 0.999 

Aged 75 and Over 

PM75O = ((PM7579 * NM7579/NM75O+ PM8084 * NM8084/NM75O+ PM85O* NM85O/NM75O) + 0.000) * 1.000 

Aggregation of Equations from Regressions using Annual CPS Data 

Aged 55 to 74 
74 

PM5559 = (PM55 * NM55 + PM56 * NM56 + PM57 * NM57 + PM58 * NM58 + PM59 * NM59) / (NM55 + NM56 + NM57 + NM58 + 

NM59) 

PM6064 = (PM60 * NM60 + PM61 * NM61 + PM62 * NM62 + PM63 * NM63 + PM64 * NM64)/ (NM60 + NM61 + NM62 + NM63 + 

NM64) 

PM6569 = (PM65 * NM65 + PM66 * NM66 + PM67 * NM67 + PM68 * NM68 + PM69 * NM69)/ (NM65 + NM66 + NM67 + NM68 + 

NM69) 

PM7074 = (PM70 * NM70 + PM71 * NM71 + PM72 * NM72 + PM73 * NM73 + PM74 * NM74)/ (NM70 + NM71 + NM72 + NM73 + 

NM74) 

Male LFPRs - full employment 

PM1617_FE = PM1617 + 0.35974 * (1 -RTP.1) + 0.31790 * (1 -RTP.5) 

TPM1819_FE = TPM1819 + 0.25962 * (1 -RTP.1) 

TPM2024_FE = TPM2024 + (0.21031 * (NM2024NM + NM2024M - MM2024MS - MM2024MA) + 0.00000 * (NM2024MS + 

MM2024MS) + 0.38966 * (NM2024MA 

 + MM2024MA)) / ((NM2024NM + NM2024MS + NM2024MS) + NM2024M) * (1 -RTP.1) 

TPM2529_FE = TPM2529 + (0.15942 * (NM2529NM + NM2529M - MM2529MS - MM2529MA) + 0.00000 * (NM2529MS + 

MM2529MS) + 0.19750 * (NM2529MA 

 + MM2529MA)) / ((NM2529NM + NM2529MS + NM2024MA) + NM2529M) * (1 -MOVAVG (4, RTP.2)) 

TPM3034_FE = TPM3034 + (0.05000 * (NM3034NM + NM3034M - MM3034MS - MM3034MA) + 0.05000 * (NM3034MS + 

MM3034MS) + 0.05000 * (NM3034MA 

 + MM3034MA)) / ((NM3034NM + NM3034MS + NM3034MA) + NM3034M) * (1 -MOVAVG (4, RTP.2)) 

TPM3539_FE = TPM3539 + (0.05000 * (NM3539NM + NM3539M - MM3539MS - MM3539MA) + 0.05000 * (NM3539MS + 

MM3539MS) +0.05000 * (NM3539MA 

 + MM3539MA)) / ((NM3539NM + NM3539MS + NM3539MA) + NM3539M) * (1 -MOVAVG (4, RTP.2)) 

TPM4044_FE = TPM4044 + (0.05000 * (NM4044NM + NM4044M - MM4044MS - MM4044MA) + 0.05000 * (NM4044MS + 

MM4044MS) + 0.05000 * (NM4044MA 

 + MM4044MA)) / ((NM4044NM + NM4044MS + NM4044MA) + NM4044M) * (1 -MOVAVG (4, RTP.2)) 

PM4549_FE = PM4549 + (0.02887 * NM4549NM + 0.15238 * NM4549MS + 0.00000 * NM4549MA) / (NM4549NM + NM4549MS + 

NM4549MA) * (1 -MOVAVG (4, RTP.1)) 

PM5054_FE = PM5054 + (0.00000 * NM5054NM + 0.19639 * NM5054MS + 0.43104 * NM5054MA) / (NM5054NM + NM5054MS + 

NM5054MA) * (1 -MOVAVG (4, RTP.1)) 

PM5559_FE = PM5559 + (0.11202 * NM55 + 0.10041 * NM56 + 0.13081 * NM57 + 0.24841 * NM58 + 0.25992 * NM59) / (NM55 + 

NM56 + NM57 + NM58 + NM59) 

 * (1 -MOVAVG (5, RTP.10)) 

PM6064_FE = PM6064 + (0.31289 * NM60 + 0.32660 * NM61 + 0.15 * 0.55 * NM62 + 0.15 * 0.48 * NM63 + 0.15 * 0.44 * NM64) / 

(NM60 + NM61 + NM62 + NM63 + NM64) 

 * (1 -MOVAVG (5, RTP.10)) 

PM6569_FE = PM6569 + (0.15 * 0.38 * NM65 + 0.15 * 0.34 * NM66 + 0.15 * 0.33 * NM67 + 0.15 * 0.30 * NM68 + 0.15 * 0.24 * 

NM69) / (NM65 + NM66 + NM67 + NM68 + NM69) 

 * (1 -MOVAVG (5, RTP.10)) 

PM7074_FE = PM7074 + (0.15 * 0.18 * NM70 + 0.00000 * NM71 + 0.00000 * NM72 + 0.00000 * NM73 + 0.00000 * NM74) / (NM70 

+ NM71 + NM72 + NM73 + NM74) 

 * (1 -MOVAVG (5, RTP.10)) 

PM5054L_FE = MOVAVG (8, PM5054_FE.8 + PM2554_A90C.8 + PM2554_A94M.8 + RM5054D.8) 

PM7074L = MOVAVG (8, PM7074.16 / PM65O_A94MM.16) 

PM7579L = MOVAVG (8, PM7579.16 / PM65O_A94MM.16) 

PM8084L = MOVAVG (8, PM8084.16 / PM65O_A94MM.16) 

FEMALE LFPR Equations - Annual 

Regressions using March CPS Data 

Aged 20 to 44 

PF2024NMC6U = -1.00 * RF2024D + 0.96222 * RTPL1T4 - 1.0801 * PFW2024NM - 0.1 * IF2024NMC6U +0.11117 - 0.25881 + 0.005 

PF2529NMC6U = -1.00 * RF2529D + 0.91191 * RTPL1T4 - 0.06000 * IF2529NMC6U - 0.61008 * PFW2529NM + 0.13672 - 0.21084 

PF3034NMC6U = -1.00 * RF3034D - 0.06000 * IF3034NMC6U - 0.46290 * PFW3034NM + 1.30921 * MOVAVG (3, PF2529NM_FE.4 + 

PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF2529D.4) 

 + 0.14328 - 0.37975 

PF3539NMC6U = -1.00 * RF3539D - 0.65032 * PFW3539NM + 0.75635 

PF4044NMC6U = -1.00 * RF4044D - 0.06000 * IF4044NMC6U + 2.80447 * MOVAVG (3, PF3539NM_FE.4 + PF2554_94M_TE.4 + 

PF2554_94C_TE.4 + RF2529D.4) + 0.21194 * RTPL1T4 

 - 1.92826 
75 

PF2024NMNC6 = -1.00 * RF2024D + 0.13031 * RTPL1T4 + 0.55986 * MOVAVG (2, PF1819_FE.3 + PF1619_94M_TE.3 + 

PF1619_90C_TE.3) + 0.28086 + 0.005 

PF2529NMNC6 = -1.00 * RF2529D + 0.87626 

PF3034NMNC6 = -1.00 * RF3034D + 1.75050 * MOVAVG (3, PF2529NM_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + 

RF2529D.4) + 0.19793 * RTPL1T4 - 0.81095 

PF3539NMNC6 = -1.00 * RF3539D + 0.65953 * MOVAVG (3, PF3034NM_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + 

RF3034D.4) + 0.32043 * RTPL1T4 - 0.02382 

PF4044NMNC6 = -1.00 * RF4044D + 0.57971 * MOVAVG (3, PF3539NM_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + 

RF3539D.4) + 0.34356 

PF2024MSC6U = -1.00 * RF2024D - 0.1 * IF2024MSC6U + 0.01086 * 87 + 0.04411 * RTPL1T4 + 0.03335 - 0.32002 + 0.005 

PF2529MSC6U = -1.00 * RF2529D + 1.0 * MOVAVG (3, PF2024_FE.4 + PF2024_94M_TE.4 + PF2024_94C_TE.4 + RF2024D.4) -0.1 * 

IF2529MSC6U + 0.11923 * RTPL1T4 + 0.00572 * 88 

 + 0.05218 - 0.59301 

PF3034MSC6U = -1.00 * RF3034D + 1.03276 * MOVAVG (3, PF2529_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF2529D.4) - 

0.06606 * IF3034MSC6U + 0.06988 * RTPL1T4 

 - 0.10472 

PF3539MSC6U = -1.00 * RF3539D - 0.1 * IF3539MSC6U + 1.05734 * MOVAVG (3, PF3034_FE.4 + PF2554_94M_TE.4 + 

PF2554_94C_TE.4 + RF3034D.4) + 0.15040 * RTPL1T4 - 0.15161 

PF4044MSC6U = -1.00 * RF4044D + 0.93189 * MOVAVG (3, PF3539_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3539D.4) + 

0.05375 - 0.09385 

PF2024MSNC6 = -1.00 * RF2024D + 0.66513 * MOVAVG (2, PF1819_FE.3 + PF1619_94M_TE.3 + PF1619_90C_TE.3) - 0.02309 + 

0.40392 + 0.005 

PF2529MSNC6 = -1.00 * RF2529D + 0.75346 * MOVAVG (3, PF2024_FE.4 + PF2024_94M_TE.4 + RF2024D.4) + 0.15260 * RTPL1T4 + 

0.15786 

PF3034MSNC6 = -1.00 * RF3034D + 0.72921 * MOVAVG (3, PF2529_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF2529D.4) + 

0.27929 

PF3539MSNC6 = -1.00 * RF3539D + 0.70122 * MOVAVG (3, PF3034_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3034D.4) + 

0.33338 * RTPL1T4 - 0.01765 - 0.03387 

PF4044MSNC6 = -1.00 * RF4044D + 0.83686 * MOVAVG (3, PF3539_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3539D.4) + 

0.16837 

PF2024MAC6U = -1.00 * RF2024D + 0.41498 * RTPL1T4 - 0.31052 * IF2024MAC6U - 0.08075 * PFW2024MA + 0.68113 * MOVAVG 

(2, PF1819_FE.3 + PF1619_94M_TE.3 

 + PF1619_90C_TE.3) + 0.09208 + 0.11197 +0.263 + 0.005 

PF2529MAC6U = -1.00 * RF2529D + 0.32708 * RTPL1T4 + 0.39869 * MOVAVG (3, PF2024_FE.4 + PF2024_94M_TE.4 + 

PF2024_94C_TE.4 + RF2024D.4) - 0.19425 * IF2529MAC6U 

 - 0.27997 * PFW2529MA + 0.39831 

PF3034MAC6U = -1.00 * RF3034D + 0.15332 * MOVAVG (3, PF2529_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF2529D.4) - 

0.21611 * IF3034MAC6U - 0.48469 * PFW3034MA 

 + 0.09521 + 0.90844 

PF3539MAC6U = -1.00 * RF3539D + 0.45383 * MOVAVG (3, PF3034_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3034D.4) + 

0.10467 + 0.30563 

PF4044MAC6U = -1.00 * RF4044D + 0.83908 * MOVAVG (3, PF3539_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3539D.4) + 

0.20826 * RTPL1T4 - 0.18854 

PF2024MANC6 = -1.00 * RF2024D + 0.87285 * MOVAVG (2, PF1819_FE.3 + PF1619_94M_TE.3 + PF1619_90C_TE.3) - 0.07951 + 

0.2418 + 0.005 

PF2529MANC6 = -1.00 * RF2529D + 0.82169 

PF3034MANC6 = -1.00 * RF3034D + 0.05157 * MOVAVG (3, PF2529_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF2529D.4) + 

0.80559 

PF3539MANC6 = -1.00 * RF3539D + 0.20191 * MOVAVG (3, PF3034_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3034D.4) + 

0.70206 

PF4044MANC6 = -1.00 * RF4044D + 0.41386 * MOVAVG (3, PF3539_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF3539D.4) + 

0.07702 * RTPL1T4 - 0.030022 + 0.48116 

Aged 45 to 54 

PF4549NM = -1.00 * RF4549D + 0.26468 * MOVAVG (3, PF4044NM_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4044D.4) + 

0.57522 

PF5054NM = -1.00 * RF5054D + 0.37747 * MOVAVG (3, PF4549NM_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4549D.4) + 

0.68899 * RTPL1T4 - 0.22031 
76 

PF4549MS = -1.00 * RF4549D + 0.92026 * MOVAVG (3, PF4044_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4044D.4) + 

0.16000 * RTPL1T4 - 0.09969 

PF5054MS = -1.00 * RF5054D + 0.97734 * MOVAVG (3, PF4549_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4549D.4) - 

0.01843 

PF4549MA = -1.00 * RF4549D + 0.39804 * MOVAVG (3, PF4044_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4044D.4) + 

0.22670 * RTPL1T4 + 0.30580 

PF5054MA = -1.00 * RF5054D + 0.46765 * MOVAVG (3, PF4549_FE.4 + PF2554_94M_TE.4 + PF2554_94C_TE.4 + RF4549D.4) + 

0.24122 * RTPL1T4 + 0.20279 

Aged 75 and Over 

PF7579 = 0.51019 * PF7074.5 

PF8084 = 0.50704 * PF7579.5 

 PF85O = 0.55432 * PF8084.5 

Regressions using Annual CPS Data 

Aged 16 to 19 

PF1617 = 0.12385 * DIFF (RTP) + 0.17046 * DIFF (RTP.1) + 0.56079 * DIFF (DIFFDONM1617) + PF1617.1 

PF1819 = 0.22735 * DIFF (RTP) + 0.14711 * DIFF (RTP.1) + 0.15129 * DIFF (RAM1819) - 0.14961 * DIFF (RNF1819S) + PF1819.1 

Aged 55 to 74 

PF55 = 0.80973 * MOVAVG (3, PF5054.2 + PF2554_90C_TE.2 + PF2554_94M_TE.2 + RF5054D.2) - 1.0 * RF55D + 0.16573 * RTP.1 - 

0.05150 

PF56 = 0.94452 * (PF55.1 + RF55D.1 + 0.16573 * (1 - RTP.2)) - 1.0 * RF56D + 0.09741 * RTP.2 - 0.07766 

PF57 = 1.01984 * (PF56.1 + RF56D.1 + 0.09741 * (1 - RTP.3)) - 1.0 * RF57D + 0.14837 * RTP.2 - 0.17199 

PF58 = 0.83467 * (PF57.1 + RF57D.1 + 0.14837 * (1 - RTP.3)) - 1.0 * RF58D + 0.09913 * RTP.2 - 0.01364 

PF59 = 0.82721 * (PF58.1 + RF58D.1 + 0.09913 * (1 - RTP.3)) - 1.0 * RF59D + 0.14296 * RTP.2 - 0.06068 

PF60 = 0.74197 * (PF59.1 + RF59D.1 + 0.14296 * (1 - RTP.3)) - 1.0 * RF60D + 0.12539 * RTP.2 - 0.01822 

PF61 = 1.03326 * (PF60.1 + RF60D.1 + 0.12539 * (1 - RTP.3)) - 1.0 * RF61D + 0.25650 * RTP.2 - 0.29862 

PF62 = ((PF61 + RF61D + 0.25650 * (1 - RTP.2)) / (PM61 + RM61D + 0.32660 * (1 - RTP.3))) * (PM62 + RM62D + 0.15 * (1 - RTP.2)) - 

RF62D 

PF63 = ((PF62.1 + RF62D.1) / (PF62.2 + RF62D.2) - 1.0 * DIFF (RRADJ_F63 -RRADJ_F62.1) + 0.15 * DIFF (RTP.2 -RTP.3) +0.1 * DIFF

(RETEST64U-RETEST64U.1)) 

 * (PF63.1 + RF63D.1) - RF63D 

PF64 = ((PF63.1 + RF63D.1) / (PF63.2 + RF63D.2) - 1.0 * DIFF (RRADJ_F64 -RRADJ_F63.1) + 0.15 * DIFF (RTP.2 -RTP.3) +0.1 * DIFF

(RETEST64U-RETEST64U.1)) 

 * (PF64.1 + RF64D.1) - RF64D 

PF65 = (0.75538 * (PF64.1 + RF64D.1) / (PM64.1 + RM64D.1) + 0.15565) * PM65 

PF66 = (PF65.1/PF65.2 - 1.0 * DIFF (RRADJ_F66 - RRADJ_F65.1) + 0.15 * DIFF (RTP.2 - RTP.3) + 0.1 * DIFF (RETEST66 - 

RETEST65.1)) * PF66.1 

PF67 = (PF66.1/PF66.2 - 1.0 * DIFF (RRADJ_F67 - RRADJ_F66.1) + 0.15 * DIFF (RTP.2 - RTP.3) + 0.1 * DIFF (RETEST67 - 

RETEST66.1)) * PF67.1 

PF68 = (PF67.1/PF67.2 - 1.0 * DIFF (RRADJ_F68 - RRADJ_F67.1) + 0.15 * DIFF (RTP.2 - RTP.3) + 0.1 * DIFF (RETEST68 - 

RETEST67.1)) * PF68.1 

PF69 = (PF68.1/PF68.2 - 1.0 * DIFF (RRADJ_F69 - RRADJ_F68.1) + 0.15 * DIFF (RTP.2 - RTP.3) + 0.1 * DIFF (RETEST69 - 

RETEST68.1)) * PF69.1 

PF70 = (PF69.1/PF69.2 - 1.0 * DIFF (RRADJ_F70 - RRADJ_F69.1) + 0.15 * DIFF (RTP.2 - RTP.3)) * PF70.1 

PF71 = 0.89763 * PF70.1 

PF72 = 0.91226 * PF71.1 

PF73 = 0.86723 * PF72.1 

PF74 = 0.88162 * PF73.1 

FEMALE LFPR Equations - Quarterly 

Regressions using March CPS Data 

Aged 20 to 44 

PF2024NMC6U = -1.00 * RF2024D + 0.96222 * MOVAVG (4, RTP.1) - 1.0801 * PFW2024NM - 0.1 * IF2024NMC6U + 0.11117 - 0.25881 

+ 0.005 

PF2529NMC6U = -1.00 * RF2529D + 0.91191 * MOVAVG (4, RTP.1) - 0.06000 * IF2529NMC6U - 0.61008 * PFW2529NM + 0.13672 - 

0.21084 
77 

PF3034NMC6U = -1.00 * RF3034D - 0.06000 * IF3034NMC6U - 0.46290 * PFW3034NM + 1.30921 * PF2529NML_FE + 0.14328 - 

0.37975 

PF3539NMC6U = -1.00 * RF3539D - 0.65032 * PFW3539NM + 0.75635 

PF4044NMC6U = -1.00 * RF4044D - 0.06000 * IF4044NMC6U + 2.80447 * PF3539NML_FE + 0.21194 * MOVAVG (4, RTP.1) - 1.92826 

PF2024NMNC6 = -1.00 * RF2024D + 0.13031 * MOVAVG (4, RTP.1) + 0.55986 * PF1819L_FE + 0.28086 + 0.005 

PF2529NMNC6 = -1.00 * RF2529D + 0.87626 

PF3034NMNC6 = -1.00 * RF3034D + 1.75050 * PF2529NML_FE + 0.19793 * MOVAVG (4, RTP.1) - 0.81095 

PF3539NMNC6 = -1.00 * RF3539D + 0.65953 * PF3034NML_FE + 0.32043 * MOVAVG (4, RTP.1) - 0.02382 

PF4044NMNC6 = -1.00 * RF4044D + 0.57971 * PF3539NML_FE + 0.34356 

PF2024MSC6U = -1.00 * RF2024D - 0.1 *IF2024MSC6U + 0.01086 * 87 + 0.04411 * MOVAVG (4, RTP.1) + 0.03335 - 0.32002 + 0.005 

PF2529MSC6U = -1.00 * RF2529D + 1.0 * PF2024L_FE - 0.1 * IF2529MSC6U + 0.11923 * MOVAVG (4, RTP.1) + 0.00572 * 88 + 

0.05218 - 0.59301 

PF3034MSC6U = -1.00 * RF3034D + 1.03276 * PF2529L_FE - 0.06606 * IF3034MSC6U + 0.06988 * MOVAVG (4, RTP.1) - 0.10472 

PF3539MSC6U = -1.00 * RF3539D - 0.1 * IF3539MSC6U + 1.05734 * PF3034L_FE + 0.15040 * MOVAVG (4, RTP.1) - 0.15161 

PF4044MSC6U = -1.00 * RF4044D + 0.93189 * PF3539L_FE + 0.05375 - 0.09385 

PF2024MSNC6 = -1.00 * RF2024D + 0.66513 * PF1819L_FE - 0.02309 + 0.40392 + 0.005 

PF2529MSNC6 = -1.00 * RF2529D + 0.75346 * PF2024L_FE + 0.15260 * MOVAVG (4, RTP.1) + 0.15786 

PF3034MSNC6 = -1.00 * RF3034D + 0.72921 * PF2529L_FE + 0.27929 

PF3539MSNC6 = -1.00 * RF3539D + 0.70122 * PF3034L_FE + 0.33338 * MOVAVG (4, RTP.1) - 0.01765 - 0.03387 

PF4044MSNC6 = -1.00 * RF4044D + 0.83686 * PF3539L_FE + 0.16837 

PF2024MAC6U = -1.00 * RF2024D + 0.41498 * MOVAVG (4, RTP.1) - 0.31052 * IF2024MAC6U - 0.08075 * PFW2024MA + 0.68113 * 

PF1819L_FE +0.09208 + 0.11197 + 0.263 + 0.005 

PF2529MAC6U = -1.00 * RF2529D + 0.32708 * MOVAVG (4, RTP.1) + 0.39869 * PF2024L_FE - 0.19425 * IF2529MAC6U - 0.27997 * 

PFW2529MA + 0.39831 

PF3034MAC6U = -1.00 * RF3034D + 0.15332 * PF2529L_FE - 0.21611 * IF3034MAC6U - 0.48469 * PFW3034MA + 0.09521 + 0.90844 

PF3539MAC6U = -1.00 * RF3539D + 0.45383 * PF3034L_FE + 0.10467 + 0.30563 

PF4044MAC6U = -1.00 * RF4044D + 0.83908 * PF3539L_FE + 0.20826 * MOVAVG (4, RTP.1) - 0.18854 

PF2024MANC6 = -1.00 * RF2024D + 0.87285 * PF1819L_FE - 0.07951 + 0.2418 + 0.005 

PF2529MANC6 = -1.00 * RF2529D + 0.82169 

PF3034MANC6 = -1.00 * RF3034D + 0.05157 * PF2529L_FE + 0.80559 

PF3539MANC6 = -1.00 * RF3539D + 0.20191 * PF3034L_FE + 0.70206 

PF4044MANC6 = -1.00 * RF4044D + 0.41386 * PF3539L_FE + 0.07702 * MOVAVG (4, RTP.1) - 0.03002 + 0.48116 

Aged 45 to 54 

PF4549NM = -1.00 * RF4549D + 0.26468 * PF4044NML_FE + 0.57522 

PF5054NM = -1.00 * RF5054D + 0.37747 * PF4549NML_FE + 0.68899 * MOVAVG (4, RTP.1) - 0.22031 

PF4549MS = -1.00 * RF4549D + 0.92026 * PF4044L_FE + 0.16000 * MOVAVG (4, RTP.1) - 0.09969 

PF5054MS = -1.00 * RF5054D + 0.97734 * PF4549L_FE - 0.01843 

PF4549MA = -1.00 * RF4549D + 0.39804 * PF4044L_FE + 0.22670 * MOVAVG (4, RTP.1) + 0.30580 

PF5054MA = -1.00 * RF5054D + 0.46765 * PF4549L_FE + 0.24122 * MOVAVG (4, RTP.1) + 0.20279 

Aged 75 and Over 

PF7579 = 0.51019 * MOVAVG (4, PF7074.20) 

PF8084 = 0.50704 * MOVAVG (4, PF7579.20) 

PF85O = 0.55432 * MOVAVG (4, PF8084.20) 

Regressions using Annual CPS Data 

Aged 16 to 19 

PF1617 = 0.12385 * DIFF (RTP.1) + 0.17046 * DIFF (RTP.5) + 0.56079 * DIFF (DIFFDONM1617) + PF1617.1 

PF1819 = 0.22735 * DIFF (RTP.1) + 0.14711 * DIFF (RTP.5) + 0.15129 * DIFF (RAM1819) - 0.14961 * DIFF (RNF1819S) + PF1819.1 

Aged 55 to 74 

PF55 = 0.80973 * PF5054L_FE - 1.0 * RF55D + 0.16573 * MOVAVG (5, RTP.2) - 0.05150 

PF56 = 0.94452 * (PF55.4 + RF55D.4 + 0.16573 * (1 -MOVAVG (5, RTP.6))) - 1.0 * RF56D + 0.09741 * MOVAVG (5, RTP.6) - 0.07766 
78 

PF57 = 1.01984 * (PF56.4 + RF56D.4 + 0.09741 * (1 -MOVAVG (5, RTP.10))) - 1.0 * RF57D + 0.14837 * MOVAVG (5, RTP.6) - 0.17199 

PF58 = 0.83467 * (PF57.4 + RF57D.4 + 0.14837 * (1 -MOVAVG (5, RTP.10))) - 1.0 * RF58D + 0.09913 * MOVAVG (5, RTP.6) - 0.01364 

PF59 = 0.82721 * (PF58.4 + RF58D.4 + 0.09913 * (1 -MOVAVG (5, RTP.10))) - 1.0 * RF59D + 0.14296 * MOVAVG (5, RTP.6) - 0.06068 

PF60 = 0.74197 * (PF59.4 + RF59D.4 + 0.14296 * (1 -MOVAVG (5, RTP.10))) - 1.0 * RF60D + 0.12539 * MOVAVG (5, RTP.6) - 0.01822 

PF61 = 1.03326 * (PF60.4 + RF60D.4 + 0.12539 * (1 -MOVAVG (5, RTP.10))) - 1.0 * RF61D + 0.25650 * MOVAVG (5, RTP.6) - 0.29862 

PF62 = ((PF61 + RF61D + 0.25650 * (1 -MOVAVG (5, RTP.10))) / (PM61 + RM61D + 0.32660 * (1 -MOVAVG (9, RTP.10)))) * (PM62 + 

RM62D + 0.15 * (1 -MOVAVG (5, RTP.10))) -RF62D 

PF63 = ((PF62.4 + RF62D.4) / (PF62.5 + RF62D.5) - 1.0 * DIFF (RRADJ_F63 - RRADJ_F62.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - 

MOVAVG (5, RTP.10)) +0.1 * DIFF (RETEST64U 

 - RETEST64U.4)) * (PF63.1 + RF63D.1) - RF63D 

PF64 = ((PF63.4 + RF63D.4) / (PF63.5 + RF63D.5) - 1.0 * DIFF (RRADJ_F64 - RRADJ_F63.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - 

MOVAVG (5, RTP.10)) +0.1 * DIFF (RETEST64U 

 - RETEST64U.4)) * (PF64.1 + RF64D.1) - RF64D 

PF65 = (0.75538 * (PF64.4 + RF64D.4) / (PM64.4 + RM64D.4) + 0.15565) * PM65 

PF66 = (PF65.4/PF65.5 - 1.0 * DIFF (RRADJ_F66 - RRADJ_F65.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - MOVAVG (5, RTP.10)) +0.1 * 

DIFF (RETEST66 - RETEST65.4)) * PF66.1 

PF67 = (PF66.4/PF66.5 - 1.0 * DIFF (RRADJ_F67 - RRADJ_F66.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - MOVAVG (5, RTP.10)) + 0.1 * 

DIFF (RETEST67 - RETEST66.4)) * PF67.1 

PF68 = (PF67.4/PF67.5 - 1.0 * DIFF (RRADJ_F68 - RRADJ_F67.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - MOVAVG (5, RTP.10)) +0.1 * 

DIFF (RETEST68 - RETEST67.4)) * PF68.1 

PF69 = (PF68.4/PF68.5 - 1.0 * DIFF (RRADJ_F69 - RRADJ_F68.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - MOVAVG (5, RTP.10)) +0.1 

* DIFF (RETEST69 - RETEST68.4)) * PF69.1 

PF70 = (PF69.4/PF69.5 - 1.0 * DIFF (RRADJ_F70 - RRADJ_F69.4) + 0.15 * DIFF (MOVAVG (5, RTP.6) - MOVAVG (5, RTP.10))) * 

PF70.1 

PF71 = 0.89763 * PF70.4 

PF72 = 0.91226 * PF71.4 

PF73 = 0.86723 * PF72.4 

PF74 = 0.88162 * PF73.4 

Maximums for Female LFPRs 

PF2024NMC6U_M = MIN (PF2024NMC6U, 0.75) 

PF2529NMC6U_M = MIN (PF2529NMC6U, 0.75) 

PF3034NMC6U_M = MIN (PF3034NMC6U, 0.75) 

PF3539NMC6U_M = MIN (PF3539NMC6U, 0.75) 

PF4044NMC6U_M = MIN (PF4044NMC6U, 0.75) 

PF2024NMNC6_M = MIN (PF2024NMNC6, 0.80) 

PF2529NMNC6_M = MIN (PF2529NMNC6, 0.89) 

PF3034NMNC6_M = MIN (PF3034NMNC6, 0.89) 

PF3539NMNC6_M = MIN (PF3539NMNC6, 0.85) 

PF4044NMNC6_M = MIN (PF4044NMNC6, 0.85) 

PF4549NM_M = MIN (PF4549NM, 0.85) 

PF5054NM_M = MIN (PF5054NM, 0.85) 

PF2024MSC6U_M = MIN (PF2024MSC6U, 0.65) 

PF2529MSC6U_M = MIN (PF2529MSC6U, 0.70) 

PF3034MSC6U_M = MIN (PF3034MSC6U, 0.70) 

PF3539MSC6U_M = MIN (PF3539MSC6U, 0.70) 

PF4044MSC6U_M = MIN (PF4044MSC6U, 0.70) 

PF2024MSNC6_M = MIN (PF2024MSNC6, 0.85) 

PF2529MSNC6_M = MIN (PF2529MSNC6, 0.85) 

PF3034MSNC6_M = MIN (PF3034MSNC6, 0.85) 

PF3539MSNC6_M = MIN (PF3539MSNC6, 0.85) 

PF4044MSNC6_M = MIN (PF4044MSNC6, 0.85) 

PF4549MS_M = MIN (PF4549MS, 0.85) 

PF5054MS_M = MIN (PF5054MS, 0.85) 

PF2024MAC6U_M = MIN (PF2024MAC6U, 0.85) 

PF2529MAC6U_M = MIN (PF2529MAC6U, 0.75) 

PF3034MAC6U_M = MIN (PF3034MAC6U, 0.75) 

PF3539MAC6U_M = MIN (PF3539MAC6U, 0.75) 

PF4044MAC6U_M = MIN (PF4044MAC6U, 0.75) 

PF2024MANC6_M = MIN (PF2024MANC6, 0.87) 

PF2529MANC6_M = MIN (PF2529MANC6, 0.88) 

PF3034MANC6_M = MIN (PF3034MANC6, 0.88) 
79 

PF3539MANC6_M = MIN (PF3539MANC6, 0.88) 

PF4044MANC6_M = MIN (PF4044MANC6, 0.88) 

PF4549MA_M = MIN (PF4549MA, 0.88) 

PF5054MA_M = MIN (PF5054MA, 0.85) 

Quarterly Weighted Equations from Regressions using March CPS Data 

Aged 20 to 44 by Marital Status 

PF2024NM = (PF2024NMC6U_M * RF2024NMC6U + (1 - RF2024NMC6U) * PF2024NMNC6_M) 

PF2024MS = (PF2024MSC6U_M * RF2024MSC6U + (1 - RF2024MSC6U) * PF2024MSNC6_M) 

PF2024MA = (PF2024MAC6U_M * RF2024MAC6U + (1 - RF2024MAC6U) * PF2024MANC6_M) 

PF2529NM = (PF2529NMC6U_M * RF2529NMC6U + (1 - RF2529NMC6U) * PF2529NMNC6_M) 

PF2529MS = (PF2529MSC6U_M * RF2529MSC6U + (1 - RF2529MSC6U) * PF2529MSNC6_M) 

PF2529MA = (PF2529MAC6U_M * RF2529MAC6U + (1 - RF2529MAC6U) * PF2529MANC6_M) 

PF3034NM = (PF3034NMC6U_M * RF3034NMC6U + (1 - RF3034NMC6U) * PF3034NMNC6_M) 

PF3034MS = (PF3034MSC6U_M * RF3034MSC6U + (1 - RF3034MSC6U) * PF3034MSNC6_M) 

PF3034MA = (PF3034MAC6U_M * RF3034MAC6U + (1 - RF3034MAC6U) * PF3034MANC6_M) 

PF3539NM = (PF3539NMC6U_M * RF3539NMC6U + (1 - RF3539NMC6U) * PF3539NMNC6_M) 

PF3539MS = (PF3539MSC6U_M * RF3539MSC6U + (1 - RF3539MSC6U) * PF3539MSNC6_M) 

PF3539MA = (PF3539MAC6U_M * RF3539MAC6U + (1 - RF3539MAC6U) * PF3539MANC6_M) 

PF4044NM = (PF4044NMC6U_M * RF4044NMC6U + (1 - RF4044NMC6U) * PF4044NMNC6_M) 

PF4044MS = (PF4044MSC6U_M * RF4044MSC6U + (1 - RF4044MSC6U) * PF4044MSNC6_M) 

PF4044MA = (PF4044MAC6U_M * RF4044MAC6U + (1 - RF4044MAC6U) * PF4044MANC6_M) 

Aged 20 to 54 

PF2024 = (PF2024NM * RF2024NM + PF2024MS * RF2024MS + PF2024MA * RF2024MA) * 1.015 

PF2529 = (PF2529NM * RF2529NM + PF2529MS * RF2529MS + PF2529MA * RF2529MA) * 0.999 

PF3034 = (PF3034NM * RF3034NM + PF3034MS * RF3034MS + PF3034MA * RF3034MA) * 0.999 

PF3539 = (PF3539NM * RF3539NM + PF3539MS * RF3539MS + PF3539MA * RF3539MA) * 0.996 

PF4044 = (PF4044NM * RF4044NM + PF4044MS * RF4044MS + PF4044MA * RF4044MA) * 0.996 

PF4549 = (PF4549NM_M * RF4549NM + PF4549MS_M * RF4549MS + PF4549MA_M * RF4549MA) * 0.998 

PF5054 = (PF5054NM_M * RF5054NM + PF5054MS_M * RF5054MS + PF5054MA_M * RF5054MA) * 0.998 

Aged 55 to 74 

PF5559 = (PF55 * NF55 + PF56 * NF56 + PF57 * NF57 + PF58 * NF58 + PF59 * NF59)/ (NF55 + NF56 + NF57 + NF58 + NF59) 

PF6064 = (PF60 * NF60 + PF61 * NF61 + PF62 * NF62 + PF63 * NF63 + PF64 * NF64)/ (NF60 + NF61 + NF62 + NF63 + NF64) 

PF6569 = (PF65 * NF65 + PF66 * NF66 + PF67 * NF67 + PF68 * NF68 + PF69 * NF69)/ (NF65 + NF66 + NF67 + NF68 + NF69) 

PF7074 = (PF70 * NF70 + PF71 * NF71 + PF72 * NF72 + PF73 * NF73 + PF74 * NF74)/ (NF70 + NF71 + NF72 + NF73 + NF74) 

Aged 75 and Over 

PF75O = (PF7579 * NF7579/NF75O + PF8084 * NF8084/NF75O + PF85O * NF85O/NF75O) * 1.006 

Female LFPRs - full employment 

PF1617_FE = PF1617 + 0.12385 * (1 -RTP.1) + 0.17046 * (1 -RTP.5) 

PF1819_FE = PF1819 + 0.22735 * (1 -RTP.1) + 0.14711 * (1 -RTP.5) 

PF2024_FE = PF2024 + (0.04411 * NF2024MSC6U + 0.00000 * NF2024MSNC6 + 0.41498 * NF2024MAC6U + 0.00000 * 

NF2024MANC6 + 0.96222 * NF2024NMC6U +0.13031 

 * NF2024NMNC6) / (NF2024NM + NF2024MS + NF2024MA) * (1 -MOVAVG (4, RTP.1)) 

PF2529_FE = PF2529 + (0.11923 * NF2529MSC6U + 0.15260 * NF2529MSNC6 + 0.32708 * NF2529MAC6U + 0.00000 * 

NF2529MANC6 +0.91191 * NF2529NMC6U +0.00000 

 * NF2529NMNC6) / (NF2529NM + NF2529MS + NF2529MA) * (1 -MOVAVG (4, RTP.1)) 

PF3034_FE = PF3034 + (0.06988 * NF3034MSC6U + 0.00000 * NF3034MSNC6 + 0.00000 * NF3034MAC6U + 0.00000 * 

NF3034MANC6 + 0.00000 * NF3034NMC6U +0.19793 

 * NF3034NMNC6) / (NF3034NM + NF3034MS + NF3034MA) * (1 -MOVAVG (4, RTP.1)) 

PF3539_FE = PF3539 + (0.15040 * NF3539MSC6U + 0.33338 * NF3539MSNC6 + 0.00000 * NF3539MAC6U + 0.00000 * 

NF3539MANC6 + 0.00000 * NF3539NMC6U +0.32043 

 * NF3539NMNC6) / (NF3539NM + NF3539MS + NF3539MA) * (1 -MOVAVG (4, RTP.1)) 
80 

PF4044_FE = PF4044 + (0.00000 * NF4044MSC6U + 0.00000 * NF4044MSNC6 + 0.20826 * NF4044MAC6U + 0.07702 * 

NF4044MANC6 +0.21194 * NF4044NMC6U +0.00000 

 * NF4044NMNC6) / (NF4044NM + NF4044MS + NF4044MA) * (1 -MOVAVG (4, RTP.1)) 

PF4549_FE = PF4549 + (0.00000 * NF4549NM + 0.16000 * NF4549MS + 0.22670 * NF4549MA) / (NF4549NM + NF4549MS + 

NF4549MA) * (1 -MOVAVG (4, RTP.1)) 

PF5054_FE = PF5054 + (0.68899 * NF5054NM + 0.00000 * NF5054MS + 0.24122 * NF5054MA) / (NF5054NM + NF5054MS + 

NF5054MA) * (1 -MOVAVG (4, RTP.1)) 

PF5559_FE = PF5559 + (0.16573 * NF55 + 0.09741 * NF56 + 0.14837 * NF57 + 0.09913 * NF58 + 0.14296 * NF59) / (NF55 + 

NF56 + NF57 + NF58 + NF59) 

 * (1 -MOVAVG (5, RTP.4)) 

PF6064_FE = PF6064 + (0.12539 * NF60 + 0.25650 * NF61 + 0.15 * 0.41 * NF62 + 0.15 * 0.36 * NF63 + 0.15 * 0.35 * NF64) / 

(NF60 + NF61 + NF62 + NF63 + NF64) 

 * (1 -MOVAVG (5, RTP.4)) 

PF6569_FE = PF6569 + (0.15 * 0.26 * NF65 + 0.15 * 0.23 * NF66 + 0.15 * 0.21 * NF67 + 0.15 * 0.18 * NF68 + 0.15 * 0.15 * 

NF69) / (NF65 + NF66 + NF67 + NF68 + NF69) 

 * (1 -MOVAVG (5, RTP.4)) 

PF7074_FE = PF7074 + (0.15 * 0.13 * NF70 + 0.00000 * NF71 + 0.00000 * NF72 + 0.00000 * NF73 + 0.00000 * NF74) / (NF70 + 

NF71 + NF72 + NF73 + NF74) 

 * (1 -MOVAVG (5, RTP.4)) 

PF1819L_FE = MOVAVG (8, PF1819_FE.10 + PF1619_94M_TE.10 + PF1619_90C_TE.10) 

PF2024L_FE = MOVAVG (13, PF2024_FE.14 + PF2024_90C_TE.14 + PF2024_94M_TE.14 + RF2024D.14 - PF2024_ADJWF.14) 

PF2024NMC6UL_FE = MOVAVG (13, PF2024NMC6U.14 + PF2024_94C_TE.14 + PF2024C_94M_TE.14 + RF2024D.14 

 - PF2024_ADJWF.14 + (0.96222 * NF2024NMC6U.14)/ NF2024NMC6U.14 * (1 -MOVAVG (4, RTP.1))) 

PF2529L_FE = MOVAVG (13, PF2529_FE.14 + PF2554_90C_TE.14 + PF2554_94M_TE.14 + RF2529D.14 - PF2529_ADJWF.14) 

PF2529NML_FE = MOVAVG (13, PF2529NM.14 + PF2554_94C_TE.14 + PF2554_94M_TE.14 + RF2529D.14 - PF2529_ADJWF.14 

 + (0.91191 * NF2529NMC6U.14 + 0.00000 * NF2529NMNC6.14)/ NF2529NM.14 * (1 -MOVAVG (4, RTP.1))) 

PF3034L_FE = MOVAVG (13, PF3034_FE.14 + PF2554_90C_TE.14 + PF2554_94M_TE.14 + RF3034D.14 - PF3034_ADJWF.14) 

PF3034NML_FE = MOVAVG (13, PF3034NM.14 + PF2554_94C_TE.14 + PF2554_94M_TE.14 - PF3034_ADJWF.14 + RF3034D.14 

 + (0.00000 * NF3034NMC6U.14 + 0.19793 * NF3034NMNC6.14)/NF3034NM.14 * (1 -MOVAVG (4, RTP.1))) 

PF3539L_FE = MOVAVG (13, PF3539_FE.14 + PF2554_90C_TE.14 + PF2554_94M_TE.14 + RF3539D.14 - PF3539_ADJWF.14) 

PF3539NML_FE = MOVAVG (13, PF3539NM.14 + PF2554_94C_TE.14 + PF2554_94M_TE.14 + RF3539D.14 - PF3539_ADJWF.14 

 + (0.00000 * NF3539NMC6U.14 + 0.32043 * NF3539NMNC6.14)/ NF3539NM.14 * (1 -MOVAVG (4, RTP.1))) 

PF4044L_FE = MOVAVG (13, PF4044_FE.14 + PF2554_90C_TE.14 + PF2554_94M_TE.14 + RF4044D.14) 

PF4044NML_FE = MOVAVG (13, PF4044NM.14 + PF2554_94C_TE.14 + PF2554_94M_TE.14 + RF4044D.14 + (0.21194 

 * NF4044NMC6U.14 + 0.00000 * NF4044NMNC6.14)/ NF4044NM.14 * (1 -MOVAVG (4, RTP.1))) 

PF4549L_FE = MOVAVG (13, PF4549_FE.14 + PF2554_90C_TE.14 + PF2554_94M_TE.14 + RF4549D.14) 

PF4549NML_FE = MOVAVG (13, PF4549NM.14 + PF2554_94C_TE.14 + PF2554_94M_TE.14 + RF4549D.14 + (0.00000 * 

NF4549NM.14)/ NF4549NM.14 * (1 -MOVAVG (4, RTP.1))) 

PF5054L_FE = MOVAVG (8, PF5054_FE.8 + PF2554_90C_TE.8 + PF2554_94M_TE.8 + RF5054D.8) 

Civilian Labor Force 

LM1617 = PM1617 * NM1617 

LM1819 = TPM1819 * (NM1819 + NM1819M) 

LM2024 = TPM2024 * (NM2024 + NM2024M) 

LM2529 = TPM2529 * (NM2529 + NM2529M) 

LM3034 = TPM3034 * (NM3034 + NM3034M) 

LM3539 = TPM3539 * (NM3539 + NM3539M) 

LM4044 = TPM4044 * (NM4044 + NM4044M) 

LM4549 = PM4549 * NM4549 

LM5054 = PM5054 * NM5054 

LM5559 = PM5559 * NM5559 

LM6064 = PM6064 * NM6064 

LM6569 = PM6569 * NM6569 

LM7074 = PM7074 * NM7074 

LM75O = PM75O* NM75O 

LM7579 = PM7579 * NM7579 

LM8084 = PM8084 * NM8084 

LM85O = PM85O* NM85O 

LCM = LM1617 + LM1819 + LM2024 + LM2529 + LM3034 + LM3539 + LM4044 + LM4549 + LM5054 + LM5559 + LM6064 + 

LM6569 + LM7074 + LM75O 

LM2534 = LM2529 + LM3034 

LM3544 = LM3539 + LM4044 
81 

LM4554 = LM4549 + LM5054 

LM5564 = LM5559 + LM6064 

LM65O = LM6569 + LM7074 + LM75O 

Females 

LF1617 = PF1617 * NF1617 

LF1819 = PF1819 * NF1819 

LF2024 = PF2024 * NF2024 

LF2529 = PF2529 * NF2529 

LF3034 = PF3034 * NF3034 

LF3539 = PF3539 * NF3539 

LF4044 = PF4044 * NF4044 

LF4549 = PF4549 * NF4549 

LF5054 = PF5054 * NF5054 

LF5559 = PF5559 * NF5559 

LF6064 = PF6064 * NF6064 

LF6569 = PF6569 * NF6569 

LF7074 = PF7074 * NF7074 

LF75O = PF75O* NF75O 

LF7579 = PF7579 * NF7579 

LF8084 = PF8084 * NF8084 

LF85O = PF85O* NF85O 

LCF = LF1617 + LF1819 + LF2024 + LF2529 + LF3034 + LF3539 + LF4044 + LF4549 + LF5054 + LF5559 + LF6064 + LF6569 + 

LF7074 + LF75O 

LF2534 = LF2529 + LF3034 

LF3544 = LF3539 + LF4044 

LF4554 = LF4549 + LF5054 

LF5564 = LF5559 + LF6064 

LF65O = LF6569 + LF7074 + LF75O 

LC = LCM + LCF 

DLF1617_FE = (PF1617_FE - PF1617) * NF1617 

DLF1819_FE = (PF1819_FE - PF1819) * NF1819 

DLF2024_FE = (PF2024_FE - PF2024) * NF2024 

DLF2529_FE = (PF2529_FE - PF2529) * NF2529 

DLF3034_FE = (PF3034_FE - PF3034) * NF3034 

DLF3539_FE = (PF3539_FE - PF3539) * NF3539 

DLF4044_FE = (PF4044_FE - PF4044) * NF4044 

DLF4549_FE = (PF4549_FE - PF4549) * NF4549 

DLF5054_FE = (PF5054_FE - PF5054) * NF5054 

DLF5559_FE = (PF5559_FE - PF5559) * NF5559 

DLF6064_FE = (PF6064_FE - PF6064) * NF6064 

DLF6569_FE = (PF6569_FE - PF6569) * NF6569 

DLF7074_FE = (PF7074_FE - PF7074) * NF7074 

DLCF_FE = DLF1617_FE + DLF1819_FE + DLF2024_FE + DLF2529_FE + DLF3034_FE + DLF3539_FE + DLF4044_FE + 

DLF4549_FE + DLF5054_FE + DLF5559_FE + DLF6064_FE 

 + DLF6569_FE + DLF7074_FE 

DLM1617_FE = (PM1617_FE - PM1617) * NM1617 

DLM1819_FE = (TPM1819_FE - TPM1819) * (NM1819 + NM1819M) 

DLM2024_FE = (TPM2024_FE - TPM2024) * (NM2024 + NM2024M) 

DLM2529_FE = (TPM2529_FE - TPM2529) * (NM2529 + NM2529M) 

DLM3034_FE = (TPM3034_FE - TPM3034) * (NM3034 + NM3034M) 

DLM3539_FE = (TPM3539_FE - TPM3539) * (NM3539 + NM3539M) 

DLM4044_FE = (TPM4044_FE - TPM4044) * (NM4044 + NM4044M) 

DLM4549_FE = (PM4549_FE - PM4549) * NM4549 

DLM5054_FE = (PM5054_FE - PM5054) * NM5054 

DLM5559_FE = (PM5559_FE - PM5559) * NM5559 

DLM6064_FE = (PM6064_FE - PM6064) * NM6064 

DLM6569_FE = (PM6569_FE - PM6569) * NM6569 

DLM7074_FE = (PM7074_FE - PM7074) * NM7074 

DLCM_FE = DLM1617_FE + DLM1819_FE + DLM2024_FE + DLM2529_FE + DLM3034_FE + DLM3539_FE + DLM4044_FE + DLM4549_FE + DL
82 

 + DLM6064_FE + DLM6569_FE + DLM7074_FE 

Unemployment Rates 

Totals 

MALES 

RM1617 = RM1617.1 + (-44.4261 * DIFF (RTP) - 2.1644 * DIFF (RTP.1) - 15.0910 * DIFF (RTP.2) - 27.8537 * DIFF (RTP.3)) * 

50.00/44.05 

RM1819 = RM1819.1 + (-47.9124 * DIFF (RTP) - 31.9746 * DIFF (RTP.1) - 11.6764 * DIFF (RTP.2) + 2.8763 * DIFF (RTP.3)) * 

50.00/44.05 

RM2024 = RM2024.1 + (-58.0805 * DIFF (RTP) - 14.6504 * DIFF (RTP.1) - 17.3907 * DIFF (RTP.2) - 8.3721 * DIFF (RTP.3)) * 

50.00/44.05 

RM2529 = RM2529.1 + (-42.4466 * DIFF (RTP) - 16.4626 * DIFF (RTP.1) - 12.0763 * DIFF (RTP.2) - 2.6912 * DIFF (RTP.3)) * 

50.00/44.05 

RM3034 = RM3034.1 + (-21.9947 * DIFF (RTP) - 14.3423 * DIFF (RTP.1) - 7.7729 * DIFF (RTP.2) - 4.5343 * DIFF (RTP.3)) * 

50.00/44.05 

RM3539 = RM3539.1 + (-25.1969 * DIFF (RTP) - 4.8918 * DIFF (RTP.1) - 11.6627 * DIFF (RTP.2) - 9.4142 * DIFF (RTP.3)) * 

50.00/44.05 

RM4044 = RM4044.1 + (-14.7303 * DIFF (RTP) - 12.8348 * DIFF (RTP.1) - 7.4111 * DIFF (RTP.2) - 6.4487 * DIFF (RTP.3)) * 

50.00/44.05 

RM4549 = RM4549.1 + (-18.1162 * DIFF (RTP) - 11.8573 * DIFF (RTP.1) - 7.3805 * DIFF (RTP.2) + 0.9708 * DIFF (RTP.3)) * 

50.00/44.05 

RM5054 = RM5054.1 + (-18.8477 * DIFF (RTP) - 11.0262 * DIFF (RTP.1) - 6.6450 * DIFF (RTP.2) - 4.7406 * DIFF (RTP.3)) * 

50.00/44.05 

RM5559 = RM5559.1 + (-22.8478 * DIFF (RTP) - 11.8787 * DIFF (RTP.1) + 0.6517 * DIFF (RTP.2) - 3.0202 * DIFF (RTP.3)) * 

50.00/44.05 

RM6064 = RM6064.1 + (1.4997 * DIFF (RTP) - 9.8165 * DIFF (RTP.1) + 0.4070 * DIFF (RTP.2) - 15.0849 * DIFF (RTP.3)) * 

50.00/44.05 

RM6569 = RM6569.1 + (-9.7596 * DIFF (RTP) + 11.8572 * DIFF (RTP.1) - 18.3547 * DIFF (RTP.2) + 6.1962 * DIFF (RTP.3)) * 

50.00/44.05 

RM7074 = RM7074.1 + (19.6295 * DIFF (RTP) - 12.5956 * DIFF (RTP.1) - 27.9350 * DIFF (RTP.2) + 6.5664 * DIFF (RTP.3)) * 

50.00/44.05 

RM75O = RM75O.1 + (- 5.5101 * DIFF (RTP) - 18.5248 * DIFF (RTP.1) - 17.9157 * DIFF (RTP.2) + 23.5855 * DIFF (RTP.3)) * 

50.00/44.05 

FEMALES 

RF1617 = RF1617.1 + (-20.9377 * DIFF (RTP) - 3.4543 * DIFF (RTP.1) - 32.5068 * DIFF (RTP.2) - 8.8148 * DIFF (RTP.3)) * 

50.00/44.05 

RF1819 = RF1819.1 + (-39.2646 * DIFF (RTP) - 5.1023 * DIFF (RTP.1) + 3.6786 * DIFF (RTP.2) - 27.3641 * DIFF (RTP.3)) * 

50.00/44.05 

RF2024 = RF2024.1 + (-26.8299 * DIFF (RTP) - 11.1330 * DIFF (RTP.1) - 11.4402 * DIFF (RTP.2) - 4.0048 * DIFF (RTP.3)) * 

50.00/44.05 

RF2529 = RF2529.1 + (-14.8770 * DIFF (RTP) - 8.8852 * DIFF (RTP.1) - 12.9537 * DIFF (RTP.2) - 0.6317 * DIFF (RTP.3)) * 

50.00/44.05 

RF3034 = RF3034.1 + (-10.3084 * DIFF (RTP) - 0.6837 * DIFF (RTP.1) - 18.4113 * DIFF (RTP.2) - 2.0406 * DIFF (RTP.3)) * 

50.00/44.05 

RF3539 = RF3539.1 + (-17.8370 * DIFF (RTP) - 2.3913 * DIFF (RTP.1) - 6.8006 * DIFF (RTP.2) - 5.0086 * DIFF (RTP.3)) * 50.00/44.05 

RF4044 = RF4044.1 + (-6.9101 * DIFF (RTP) - 9.4509 * DIFF (RTP.1) - 3.6043 * DIFF (RTP.2) - 1.8449 * DIFF (RTP.3)) * 50.00/44.05 

RF4549 = RF4549.1 + (-1.6363 * DIFF (RTP) - 19.4549 * DIFF (RTP.1) + 10.7519 * DIFF (RTP.2) - 8.6682 * DIFF (RTP.3)) * 

50.00/44.05 

RF5054 = RF5054.1 + (-12.0818 * DIFF (RTP) + 0.3229 * DIFF (RTP.1) - 15.0622 * DIFF (RTP.2) - 3.0337 * DIFF (RTP.3)) * 

50.00/44.05 

RF5559 = RF5559.1 + (2.7183 * DIFF (RTP) - 9.8009 * DIFF (RTP.1) - 6.1773 * DIFF (RTP.2) - 6.3238 * DIFF (RTP.3)) * 50.00/44.05 

RF6064 = RF6064.1 + (-11.7151 * DIFF (RTP) - 1.9990 * DIFF (RTP.1) - 3.1837 * DIFF (RTP.2) - 10.6383 * DIFF (RTP.3)) * 

50.00/44.05 

RF6569 = RF6569.1 + (-8.7042 * DIFF (RTP.2) - 4.6979 * DIFF (RTP.3)) * 50.00/44.05 

RF7074 = RF7074.1 + (0.2827 * DIFF (RTP.2) - 14.1285 * DIFF (RTP.3)) * 50.00/44.05 

 RF75O = RF75O.1 + (-11.6993 * DIFF (RTP) + 13.5790 * DIFF (RTP.1) + 8.9530 * DIFF (RTP.2) - 22.2054 * DIFF (RTP.3)) * 

50.00/44.05 

EQ RUM = (RM1617 * LM1617 + RM1819 * LM1819 + RM2024 * LM2024 + RM2529 * LM2529 + RM3034 * LM3034 + RM3539 * 

LM3539 + RM4044 * LM4044 + RM4549 * LM4549 
83 

 + RM5054 * LM5054 + RM5559 * LM5559 + RM6064 * LM6064 + RM6569 * LM6569 + RM7074 * LM7074 + RM75O * 

LM75O)/ LCM 

EQ RUF = (RF1617 * LF1617 + RF1819 * LF1819 + RF2024 * LF2024 + RF2529 * LF2529 + RF3034 * LF3034 + RF3539 * LF3539 + 

RF4044 * LF4044 + RF4549 * LF4549 + RF5054 

 * LF5054 + RF5559 * LF5559 + RF6064 * LF6064 + RF6569 * LF6569 + RF7074 * LF7074 + RF75O * LF75O)/ LCF 

EQ RU = (RUM * LCM + RUF * LCF) / LC 
84 

2.2 U.S. Earnings (USEAR) 

Annual Employment Equations 

Class of Worker 

Nonagricultural 

Wage Workers 

Private Household Workers 

EF1617NAWPH = MAX (0.001, -0.20802 * RTP - 0.40988 * RTP.1 + 0.01015 + 61.2465 * 1/YEAR - 0.00965 * MINW/CPIW_U + 0.01561 

* NU10/NF1617 - 0.13398) * EF1617 

EF1819NAWPH = MAX (0.001, -0.03363 * RTP - 0.12989 * RTP.1 - 0.00661 + 8.44701 * 1/YEAR - 0.00539 * MINW/CPIW_U + 0.00345 

* NU10/NF1819 + 0.07597) * EF1819 

EF2024NAWPH = MAX (0.001, -0.18707 * MOVAVG (5, RTP) - 0.00223 + 2.12060 * 1/YEAR + 0.00820 * NU10/NF2024 + 0.14537) * 

EF2024 

EF2534NAWPH = MAX (0.001, 0.01874 * RTP - 0.04167 * MOVAVG (5, RTP.1) - 0.00090 + 1.55167 * 1/YEAR + 0.01021 * 

NU10/NF2534 - 0.00170) * EF2534 

EF3544NAWPH = (0.00622 * RTP - 0.06062 * MOVAVG (5, RTP.1) + 0.00008 + 0.29372 * MOVAVG (3, EF2534NAWPH.9/EF2534.9) + 

0.06187) * EF3544 

EF4554NAWPH = (0.02788 * RTP - 0.10996 * MOVAVG (5, RTP.1) - 0.00349 + 0.53068 * MOVAVG (3, EF3544NAWPH.9/EF3544.9) + 

0.08883) * EF4554 

EF5564NAWPH = (0.05939 * RTP - 0.10618 * MOVAVG (2, RTP.1) - 0.00579 + 0.66195 * MOVAVG (3, EF4554NAWPH.9/EF4554.9) + 

0.05966) * EF5564 

EF65ONAWPH = (0.22642 * RTP - 0.02069 + 0.33505 * MOVAVG (3, EF5564NAWPH.9) - 0.19707) 

EM1617NAWPH = MAX (0.001, -0.05284 * RTP - 0.17833 * RTP.1 - 0.00768 + 9.19738 * 1/YEAR - 0.00588 * MINW/CPIW_U + 0.16862) 

* EM1617 

EM1819NAWPH = MAX (0.001, -0.07122 * RTP - 0.03737 * RTP.1 - 0.00282 + 3.76796 * 1/YEAR - 0.00499 * MINW/CPIW_U + 0.08727) 

* EM1819 

EM2024NAWPH = MAX (0.001, -0.00450 * RTP - 0.02345 * RTP.1 - 0.00113 - 0.00057 * MINW/CPIW_U + 0.03265) * EM2024 

EM2534NAWPH = MAX (0.001, -0.00490 * RTP.1 - 0.00054 - 0.00051 * MINW/CPIW_U + 0.00789) * EM2534 

EM3544NAWPH = (-0.00446 * RTP.1 - 0.00041 - 0.00053 * MINW/CPIW_U + 0.00726) * EM3544 

EM4554NAWPH = (-0.00039 + 0.00129) * EM4554 

EM5564NAWPH = (-0.00015 + 0.00200) * EM5564 

EM65ONAWPH = (-0.00679 + 0.64405 * MOVAVG (3, EM5564NAWPH.9) + 0.00231) 

Government 

Other 

Self-employed 

EF1617NAS = (0.12015 * RTP.1 - 0.10551) * EF1617 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef1617nas/ef1617 = 0.12015 * rtp.1 - 0.10551 

 (1.96868) (1.73441) 

 Sum Sq 0.0000 

 Std Error 0.0030 

 LHS Mean 0.0142 

 R-Squared 0.5637 

 R Bar Squared 0.4182 

 F-stat 1, 3 3.8757 

 D.W. (1) 1.5620 

 D.W. (2) 2.3626 

EF1819NAS = (0.11184 * RTP.1 - 0.10241) * EF1819 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 
85 

 Date: 9 NOV 2005 

 ef1819nas/ef1819 = 0.11184 * rtp.1 - 0.10241 

 (2.99537) (2.75170) 

 Sum Sq 0.0000 

 Std Error 0.0018 

 LHS Mean 0.0090 

 R-Squared 0.7494 

 R Bar Squared 0.6659 

 F-STAT 1, 3 8.9722 

 D.W. (1) 3.2586 

 D.W. (2) 0.9766 

EF2024NAS = (0.08908 * RTP.1 - 0.07176) * EF2024 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef2024nas/ef2024 = 0.08908 * rtp.1 - 0.07176 

 (2.54605) (2.05763) 

 Sum Sq 0.0000 

 Std Error 0.0017 

 LHS Mean 0.0170 

 R-Squared 0.6836 

 R Bar Squared 0.5782 

 F-STAT 1, 3 6.4824 

 D.W. (1) 2.6600 

 D.W. (2) 1.5247 

EF2534NAS = (0.00906 * RTP.1 + 0.03539) * EF2534 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef2534nas/ef2534 = 0.00906 * rtp.1 + 0.03539 

 (0.34277) (1.34366) 

 Sum Sq 0.0000 

 Std Error 0.0013 

 LHS Mean 0.0444 

 R-Squared 0.0377 

 R Bar Squared 0.2831 

 F-STAT 1, 3 0.1175 

 D.W. (1) 3.0818 

 D.W. (2) 1.1094 

EF3544NAS = (-0.01869 * RTP.1 + 0.08087) * EF3544 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef3544nas/ef3544 = -0.01869 * rtp.1 + 0.08087 

 (0.70565) (3.06320) 

 Sum Sq 0.0000 

 Std Error 0.0013 

 LHS Mean 0.0622 

 R-Squared 0.1424 

 R Bar Squared 0.1435 

 F-STAT 1, 3 0.4979 

 D.W. (1) 2.2440 

 D.W. (2) 2.1852 

EF4554NAS = (0.07232 * RTP.1 - 0.00701) * EF4554 
86 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef4554nas/ef4554 = 0.07232 * rtp.1 - 0.00701 

 (2.86756) (0.27876) 

 Sum Sq 0.0000 

 Std Error 0.0012 

 LHS Mean 0.0651 

 R-Squared 0.7327 

 R Bar Squared 0.6436 

 F-STAT 1, 3 8.2229 

 D.W. (1) 1.7821 

 D.W. (2) 2.7029 

EF5564NAS = (0.07872 * RTP.1 + 0.00466) * EF5564 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef5564nas/ef5564 = 0.07872 * rtp.1 + 0.00466 

 (1.38159) (0.08196) 

 Sum Sq 0.0000 

 Std Error 0.0028 

 LHS Mean 0.0831 

 R-Squared 0.3889 

 R Bar Squared 0.1851 

 F-STAT 1, 3 1.9088 

 D.W. (1) 2.6092 

 D.W. (2) 2.2686 

EF65ONAS = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef6569nas/ef6569 = 0.10940 

 (37.7493) 

 Sum Sq 0.0002 

 Std Error 0.0065 

 LHS Mean 0.1094 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 3.0431 

 D.W. (2) 1.2204 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef7074nas/ef7074 = 0.12265 

 (16.4939) 

 Sum Sq 0.0011 

 Std Error 0.0166 

 LHS Mean 0.1226 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 1.0289 

 D.W. (2) 1.7188 
87 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef75onas/ef75o = 0.14137 

 (17.7500) 

 Sum Sq 0.0013 

 Std Error 0.0178 

 LHS Mean 0.1414 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 1.6889 

 D.W. (2) 1.2345 

EM1617NAS = (-0.23035 * RTP.1 + 0.24985) * EM1617 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em1617nas/em1617 = -0.23035 * rtp.1 + 0.24985 

 (5.08538) (5.53372) 

 Sum Sq 0.0000 

 Std Error 0.0022 

 LHS Mean 0.0203 

 R-Squared 0.8961 

 R Bar Squared 0.8614 

 F-STAT 1, 3 25.8611 

 D.W. (1) 2.4658 

 D.W. (2) 1.6839 

EM1819NAS = (-0.05782 * RTP.1 + 0.07265) * EM1819 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em1819nas/em1819 = -0.05782 * rtp.1 + 0.07265 

 (3.43044) (4.32458) 

 Sum Sq 0.0000 

 Std Error 0.0008 

 LHS Mean 0.0150 

 R-Squared 0.7969 

 R Bar Squared 0.7291 

 F-STAT 1, 3 11.7679 

 D.W. (1) 3.3262 

 D.W. (2) 1.0399 

EM2024NAS = (-0.09206 * RTP.1 + 0.11567) * EM2024 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em2024nas/em2024 = -0.09206 * rtp.1 + 0.11567 

 (2.44839) (3.08618) 

 Sum Sq 0.0000 

 Std Error 0.0018 

 LHS Mean 0.0239 

 R-Squared 0.6665 

 R Bar Squared 0.5553 

 F-STAT 1, 3 5.9946 
88 

 D.W. (1) 2.1493 

 D.W. (2) 1.7046 

EM2534NAS = (-0.09661 * RTP.1 + 0.14843) * EM2534 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em2534nas/em2534 = -0.09661 * rtp.1 + 0.14843 

 (2.81478) (4.33847) 

 Sum Sq 0.0000 

 Std Error 0.0017 

 LHS Mean 0.0522 

 R-Squared 0.7254 

 R Bar Squared 0.6338 

 F-STAT 1, 3 7.9230 

 D.W. (1) 1.8300 

 D.W. (2) 2.9632 

EM3544NAS = (0.02739 * RTP.1 + 0.05236) * EM3544 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em3544nas/em3544 = 0.02739 * rtp.1 + 0.05236 

 (0.61129) (1.17241) 

 Sum Sq 0.0000 

 Std Error 0.0022 

 LHS Mean 0.0797 

 R-Squared 0.1108 

 R Bar Squared 0.1857 

 F-STAT 1, 3 0.3737 

 D.W. (1) 2.5508 

 D.W. (2) 2.2676 

EM4554NAS = (0.06217 * RTP.1 + 0.03411) * EM4554 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em4554nas/em4554 = 0.06217 * rtp.1 + 0.03411 

 (1.91738) (1.05544) 

 Sum Sq 0.0000 

 Std Error 0.0016 

 LHS Mean 0.0961 

 R-Squared 0.5507 

 R Bar Squared 0.4009 

 F-STAT 1, 3 3.6764 

 D.W. (1) 2.5497 

D.W. (2) 1.5554 

EM5564NAS = (-0.04776 * RTP.1 + 0.16626) * EM5564 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em5564nas/em5564 = -0.04776 * rtp.1 + 0.16626 

 (0.60480) (2.11226) 

 Sum Sq 0.0000 

 Std Error 0.0039 

 LHS Mean 0.1187 
89 

 R-Squared 0.1087 

 R Bar Squared 0.1884 

 F-STAT 1, 3 0.3658 

 D.W. (1) 2.9234 

 D.W. (2) 1.9432 

EM65ONAS = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O) 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em6569nas/em6569 = 0.16527 

 (53.9126) 

 Sum Sq 0.0002 

 Std Error 0.0069 

 LHS Mean 0.1653 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 1.7716 

 D.W. (2) 2.9645 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em7074nas/em7074 = 0.17798 

 (22.9265) 

 Sum Sq 0.0012 

 Std Error 0.0174 

 LHS Mean 0.1780 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 1.7116 

 D.W. (2) 2.1991 

 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em75onas/em75o = 0.19058 

 (20.1892) 

 Sum Sq 0.0018 

 Std Error 0.0211 

 LHS Mean 0.1906 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 2.7330 

 D.W. (2) 0.9992 

Unpaid Family Workers 

EF1617NAU = 0.00012 * ENAS 

EF1819NAU = 0.00025 * ENAS 

EF2024NAU = 0.00024 * ENAS 

EF2534NAU = 0.00117 * ENAS 

EF3544NAU = 0.00218 * ENAS 

EF4554NAU = 0.00226 * ENAS 

EF5564NAU = 0.00083 * ENAS 

EF65ONAU = (0.00027 + 0.00021 + 0.00008) * ENAS 
90 

EM1617NAU = 0.00028 * ENAS 

EM1819NAU = 0.00033 * ENAS 

EM2024NAU = 0.00050 * ENAS 

EM2534NAU = 0.00044 * ENAS 

EM3544NAU = 0.00043 * ENAS 

EM4554NAU = 0.00052 * ENAS 

EM5564NAU = 0.00037 * ENAS 

EM65ONAU = (0.00023 + 0.00010 + 0.00011) * ENAS 

Agricultural 

Wage Workers 

EM1617AW = EAW * (-0.00594 - 0.09353 * RTP + 5.28754 * EM1617/E + 0.08116) 

EM1819AW = EAW * (-0.00131 - 0.18120 * RTP + 3.87151 * EM1819/E + 0.16636) 

EM2024AW = EAW * (-0.00664 + 0.10493 * RTP + 2.00153 * EM2024/E - 0.08191) 

EM2534AW = EAW * (-0.02065 + 0.38358 * RTP - 0.98380 * EM2534/E + 0.00751) 

EM3544AW = EAW * (0.00402 - 0.15663 * RTP + 1.72119 * EM3544/E + 0.05679) 

EM4554AW = EAW * (0.00834 + 0.03746 * RTP + 0.46522 * EM4554/E + 0.00144) 

EM5564AW = EAW * (-0.00655 + 0.03521 * RTP + 0.46852 * EM5564/E - 0.00037) 

EM65OAW = EAW * (-0.00114 + 0.07640 * RTP + 3.25911 * EM65O/E - 0.10058) 

EF1617AW = EAW * (-0.00055 - 0.05470 * RTP + 1.41760 * EF1617/E + 0.04979) 

EF1819AW = EAW * (0.00102 - 0.07375 * RTP + 0.78394 * EF1819/E + 0.07226) 

EF2024AW = EAW * (0.00112 - 0.05971 * RTP + 0.57256 * EF2024/E + 0.05907) 

EF2534AW = EAW * (0.00623 + 0.08868 * RTP + 1.00897 * EF2534/E - 0.15142) 

EF3544AW = EAW * (0.00687 - 0.00259 * RTP + 0.51319 * EF3544/E - 0.00937) 

EF4554AW = EAW * (0.00185 + 0.08747 * RTP + 0.28022 * EF4554/E - 0.08053) 

EF5564AW = EAW * (-0.00140 - 0.03001 * RTP - 0.59383 * EF5564/E + 0.07088) 

EF65OAW = EAW * (0.00096 + 0.06768 * RTP + 1.04213 * EF65O/E - 0.07359) 

Self-employed 

EM1617AS = NM1617 * (0.00528 + 0.00404) 

EM1819AS = NM1819 * (0.00309 + 0.28448 * EA / (NM16O+ NF16O) - 0.00165) 

EM2024AS = NM2024 * (-0.00181 + 0.97958 * EA / (NM16O+ NF16O) - 0.01093) 

EM2534AS = NM2534 * (-0.00263 + 1.23186 * EA / (NM16O+ NF16O) - 0.01021) 

EM3544AS = NM3544 * (-0.00151 + 1.66765 * EA / (NM16O+ NF16O) - 0.01450) 

EM4554AS = NM4554 * (-0.00381 + 2.86654 * EA / (NM16O+ NF16O) - 0.03175) 

EM5564AS = NM5564 * (-0.00460 + 2.78817 * EA / (NM16O+ NF16O) - 0.02398) 

EM65OAS = NM65O * (0.00079 + 1.76904 * EA / (NM16O+ NF16O) - 0.01437) 

EF1617AS = NF1617 * (0.00181 + 0.00030) 

EF1819AS = EM1819AS * (-0.02393 + 0.63672 * RTP + 0.98791 * EF1819/EM1819 - 1.43926) 

EF2024AS = EM2024AS * (0.07353 - 0.40207 * RTP + 0.57572 * EF2024/EM2024 - 0.01117) 

EF2534AS = EM2534AS * (0.16575 + 0.16967 * RTP + 0.55503 * EF2534/EM2534 - 0.43412) 

EF3544AS = EM3544AS * (0.15848 + 0.37839 * RTP + 0.37764 * EF3544/EM3544 - 0.45362) 

EF4554AS = EM4554AS * (0.21947 + 0.29497 * RTP + 0.58974 * EF4554/EM4554 - 0.51966) 

EF5564AS = EM5564AS * (0.20892 + 0.36294 * RTP + 0.65320 * EF5564/EM5564 - 0.66626) 

EF65OAS = EM65OAS * (0.16242 + 0.54916 * RTP + 0.06199 * EF65O/EM65O - 0.47556) 

Unpaid Family Workers 

EF1617AU = 0.002 

EF1819AU = 0.001 

EF2024AU = 0.001 

EF2534AU = 0.003 

EF3544AU = 0.004 

EF4554AU = 0.005 

EF5564AU = 0.003 

EF65OAU = 0.001 

EM1617AU = 0.006 

EM1819AU = 0.005 
91 

EM2024AU = 0.005 

EM2534AU = 0.002 

EM3544AU = 0.002 

EM4554AU = 0.001 

EM5564AU = 0.001 

EM65OAU = 0.002 

Quarterly Employment Equations 

Class of Worker 

Nonagricultural 

ENA = E - EA 

Wage Workers 

Private Household Workers 

EF1617NAWPH_R = MAX (0.001, -0.20802 * MOVAVG (4, RTP.1) - 0.40988 * MOVAVG (4, RTP.5) + 0.01015 + 61.2465 * 

1/YEAR - 0.00965 * MINW/CPIW_U + 0.01561 * NU10/NF1617 

 - 0.13398) * EF1617 + EF1617NAWPH.ADJ 

EF1819NAWPH_R = MAX (0.001, -0.03363 * MOVAVG (4, RTP.1) - 0.12989 * MOVAVG (4, RTP.5) - 0.00661 + 8.44701 * 

1/YEAR - 0.00539 * MINW/CPIW_U + 0.00345 * NU10/NF1819 

 + 0.07597) * EF1819 + EF1819NAWPH.ADJ 

EF2024NAWPH_R = MAX (0.001, -0.18707 * MOVAVG (20, RTP.1) - 0.00223 + 2.12060 * 1/YEAR + 0.00820 * NU10/NF2024 + 

0.14537) * EF2024 + EF2024NAWPH.ADJ 

EF2534NAWPH_R = MAX (0.001, 0.01874 * MOVAVG (4, RTP.1) - 0.04167 * MOVAVG (20, RTP.5) - 0.00090 + 1.55167 * 

1/YEAR + 0.01021 * NU10/NF2534 - 0.00170) * EF2534 

 + EF2534NAWPH.ADJ 

EF3544NAWPH_R = (0.00622 * MOVAVG (4, RTP.1) - 0.06062 * MOVAVG (20, RTP.5) + 0.00008 + 0.29372 * MOVAVG (12, 

EF2534NAWPH.36/EF2534.36) + 0.06187) * EF3544 

 + EF3544NAWPH.ADJ 

EF4554NAWPH_R = (0.02788 * MOVAVG (4, RTP.1) - 0.10996 * MOVAVG (20, RTP.5) - 0.00349 + 0.53068 * MOVAVG (12, 

EF3544NAWPH.36/EF3544.36) + 0.08883) * EF4554 

 + EF4554NAWPH.ADJ 

EF5564NAWPH_R = (0.05939 * MOVAVG (4, RTP.1) - 0.10618 * MOVAVG (8, RTP.5) - 0.00579 + 0.66195 * MOVAVG (12, 

EF4554NAWPH.36/EF4554.36) + 0.05966) * EF5564 

 + EF5564NAWPH.ADJ 

EF65ONAWPH_R = (0.22642 * MOVAVG (4, RTP.1) - 0.02069 + 0.33505 * MOVAVG (12, EF5564NAWPH.36) - 0.19707) + 

EF65ONAWPH.ADJ 

EM1617NAWPH_R = MAX (0.001, -0.05284 * MOVAVG (4, RTP.1) - 0.17833 * MOVAVG (4, RTP.5) - 0.00768 + 9.19738 * 1/YEAR - 

0.00588 * MINW/CPIW_U + 0.16862) * EM1617 

 + EM1617NAWPH.ADJ 

EM1819NAWPH_R = MAX (0.001, -0.07122 * MOVAVG (4, RTP.1) - 0.03737 * MOVAVG (4, RTP.5) - 0.00282 + 3.76796 * 1/YEAR - 

0.00499 * MINW/CPIW_U + 0.08727) * EM1819 

 + EM1819NAWPH.ADJ 

EM2024NAWPH_R = MAX (0.001, -0.00450 * MOVAVG (4, RTP.1) - 0.02345 * MOVAVG (4, RTP.5) - 0.00113 - 0.00057 * 

MINW/CPIW_U + 0.03265) * EM2024 + EM2024NAWPH.ADJ 

EM2534NAWPH_R = MAX (0.001, - 0.00490 * MOVAVG (4, RTP.5) - 0.00054 - 0.00051 * MINW/CPIW_U + 0.00789) * EM2534 + 

EM2534NAWPH.ADJ 

EM3544NAWPH_R = (-0.00446 * MOVAVG (4, RTP.5) - 0.00041 - 0.00053 * MINW/CPIW_U + 0.00726) * EM3544 + 

EM3544NAWPH.ADJ 

EM4554NAWPH_R = (-0.00039 + 0.00129) * EM4554 + EM4554NAWPH.ADJ 

EM5564NAWPH_R = (-0.00015 + 0.00200) * EM5564 + EM5564NAWPH.ADJ 

EM65ONAWPH_R = (-0.00679 + 0.64405 * MOVAVG (12, EM5564NAWPH.36) + 0.00231) + EM65ONAWPH.ADJ 

ENAWPH_R = EF1617NAWPH_R + EF1819NAWPH_R + EF2024NAWPH_R + EF2534NAWPH_R + EF3544NAWPH_R + 

EF4554NAWPH_R + EF5564NAWPH_R 

 + EF65ONAWPH_R + EM1617NAWPH_R + EM1819NAWPH_R + EM2024NAWPH_R + EM2534NAWPH_R + 

EM3544NAWPH_R + EM4554NAWPH_R 

 + EM5564NAWPH_R + EM65ONAWPH_R 

ENAWPH = IF LONGRANGE = 0 

 THEN ENAWPH_R 

 ELSE ENAWPH.1 * (E_FE/E_FE.1) 

EM1617NAWPH = EM1617NAWPH_R * (ENAWPH/ENAWPH_R) 
92 

EM1819NAWPH = EM1819NAWPH_R * (ENAWPH/ENAWPH_R) 

EM2024NAWPH = EM2024NAWPH_R * (ENAWPH/ENAWPH_R) 

EM2534NAWPH = EM2534NAWPH_R * (ENAWPH/ENAWPH_R) 

EM3544NAWPH = EM3544NAWPH_R * (ENAWPH/ENAWPH_R) 

EM4554NAWPH = EM4554NAWPH_R * (ENAWPH/ENAWPH_R) 

EM5564NAWPH = EM5564NAWPH_R * (ENAWPH/ENAWPH_R) 

EM65ONAWPH = EM65ONAWPH_R * (ENAWPH/ENAWPH_R) 

EF1617NAWPH = EF1617NAWPH_R * (ENAWPH/ENAWPH_R) 

EF1819NAWPH = EF1819NAWPH_R * (ENAWPH/ENAWPH_R) 

EF2024NAWPH = EF2024NAWPH_R * (ENAWPH/ENAWPH_R) 

EF2534NAWPH = EF2534NAWPH_R * (ENAWPH/ENAWPH_R) 

EF3544NAWPH = EF3544NAWPH_R * (ENAWPH/ENAWPH_R) 

EF4554NAWPH = EF4554NAWPH_R * (ENAWPH/ENAWPH_R) 

EF5564NAWPH = EF5564NAWPH_R * (ENAWPH/ENAWPH_R) 

EF65ONAWPH = EF65ONAWPH_R * (ENAWPH/ENAWPH_R) 

EFNAWPH = EF1617NAWPH + EF1819NAWPH + EF2024NAWPH + EF2534NAWPH + EF3544NAWPH + EF4554NAWPH + 

EF5564NAWPH + EF65ONAWPH 

EMNAWPH = EM1617NAWPH + EM1819NAWPH + EM2024NAWPH + EM2534NAWPH + EM3544NAWPH + EM4554NAWPH + 

EM5564NAWPH + EM65ONAWPH 

Government 

Other 

Self-employed 

EF1617NAS_R = (0.12015 * RTP.1 - 0.10551) * EF1617 + EF1617NAS.ADJ 

EF1819NAS_R = (0.11184 * RTP.1 - 0.10241) * EF1819 + EF1819NAS.ADJ 

EF2024NAS_R = (0.08908 * RTP.1 - 0.07176) * EF2024 + EF2024NAS.ADJ 

EF2534NAS_R = (0.00906 * RTP.1 + 0.03539) * EF2534 + EF2534NAS.ADJ 

EF3544NAS_R = (-0.01869 * RTP.1 + 0.08087) * EF3544 + EF3544NAS.ADJ 

EF4554NAS_R = (0.07232 * RTP.1 - 0.00701) * EF4554 + EF4554NAS.ADJ 

EF5564NAS_R = (0.07872 * RTP.1 + 0.00466) * EF5564 + EF5564NAS.ADJ 

EF65ONAS_R = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) + EF65ONAS.ADJ 

EM1617NAS_R = (-0.23035 * RTP.1 + 0.24985) * EM1617 + EM1617NAS.ADJ 

EM1819NAS_R = (-0.05782 * RTP.1 + 0.07265) * EM1819 + EM1819NAS.ADJ 

EM2024NAS_R = (-0.09206 * RTP.1 + 0.11567) * EM2024 + EM2024NAS.ADJ 

EM2534NAS_R = (-0.09661 * RTP.1 + 0.14843) * EM2534 + EM2534NAS.ADJ 

EM3544NAS_R = (0.02739 * RTP.1 + 0.05236) * EM3544 + EM3544NAS.ADJ 

EM4554NAS_R = (0.06217 * RTP.1 + 0.03411) * EM4554 + EM4554NAS.ADJ 

EM5564NAS_R = (-0.04776 * RTP.1 + 0.16626) * EM5564 + EM5564NAS.ADJ 

EM65ONAS_R = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O) + EM65ONAS.ADJ 

ENAS_R = EF1617NAS_R + EF1819NAS_R + EF2024NAS_R + EF2534NAS_R + EF3544NAS_R + EF4554NAS_R + EF5564NAS_R + 

EF65ONAS_R + EM1617NAS_R + EM1819NAS_R 

 + EM2024NAS_R + EM2534NAS_R + EM3544NAS_R + EM4554NAS_R + EM5564NAS_R + EM65ONAS_R 

ENAS = IF LONGRANGE = 0 

 THEN ENAS_R 

 ELSE ENA * (ENAS.1/ENA.1) 

EM1617NAS = EM1617NAS_R * (ENAS/ENAS_R) 

EM1819NAS = EM1819NAS_R * (ENAS/ENAS_R) 

EM2024NAS = EM2024NAS_R * (ENAS/ENAS_R) 

EM2534NAS = EM2534NAS_R * (ENAS/ENAS_R) 

EM3544NAS = EM3544NAS_R * (ENAS/ENAS_R) 

EM4554NAS = EM4554NAS_R * (ENAS/ENAS_R) 

EM5564NAS = EM5564NAS_R * (ENAS/ENAS_R) 

EM65ONAS = EM65ONAS_R * (ENAS/ENAS_R) 

EF1617NAS = EF1617NAS_R * (ENAS/ENAS_R) 
93 

EF1819NAS = EF1819NAS_R * (ENAS/ENAS_R) 

EF2024NAS = EF2024NAS_R * (ENAS/ENAS_R) 

EF2534NAS = EF2534NAS_R * (ENAS/ENAS_R) 

EF3544NAS = EF3544NAS_R * (ENAS/ENAS_R) 

EF4554NAS = EF4554NAS_R * (ENAS/ENAS_R) 

EF5564NAS = EF5564NAS_R * (ENAS/ENAS_R) 

EF65ONAS = EF65ONAS_R * (ENAS/ENAS_R) 

EFNAS = EF1617NAS + EF1819NAS + EF2024NAS + EF2534NAS + EF3544NAS + EF4554NAS + EF5564NAS + EF65ONAS 

EMNAS = EM1617NAS + EM1819NAS + EM2024NAS + EM2534NAS + EM3544NAS + EM4554NAS + EM5564NAS + 

EM65ONAS 

Unpaid Family Workers 

EF1617NAU_R = 0.00012 * ENAS + EF1617NAU.ADJ 

EF1819NAU_R = 0.00025 * ENAS + EF1819NAU.ADJ 

EF2024NAU_R = 0.00024 * ENAS + EF2024NAU.ADJ 

EF2534NAU_R = 0.00117 * ENAS + EF2534NAU.ADJ 

EF3544NAU_R = 0.00218 * ENAS + EF3544NAU.ADJ 

EF4554NAU_R = 0.00226 * ENAS + EF4554NAU.ADJ 

EF5564NAU_R = 0.00083 * ENAS + EF5564NAU.ADJ 

EF65ONAU_R = (0.00027 + 0.00021 + 0.00008) * ENAS + EF65ONAU.ADJ 

EM1617NAU_R = 0.00028 * ENAS + EM1617NAU.ADJ 

EM1819NAU_R = 0.00033 * ENAS + EM1819NAU.ADJ 

EM2024NAU_R = 0.00050 * ENAS + EM2024NAU.ADJ 

EM2534NAU_R = 0.00044 * ENAS + EM2534NAU.ADJ 

EM3544NAU_R = 0.00043 * ENAS + EM3544NAU.ADJ 

EM4554NAU_R = 0.00052 * ENAS + EM4554NAU.ADJ 

EM5564NAU_R = 0.00037 * ENAS + EM5564NAU.ADJ 

EM65ONAU_R = (0.00023 + 0.00010 + 0.00011) * ENAS + EM65ONAU.ADJ 

ENAU_R = EF1617NAU_R + EF1819NAU_R + EF2024NAU_R + EF2534NAU_R + EF3544NAU_R + EF4554NAU_R + 

EF5564NAU_R + EF65ONAU_R + EM1617NAU_R 

 + EM1819NAU_R + EM2024NAU_R + EM2534NAU_R + EM3544NAU_R + EM4554NAU_R + EM5564NAU_R + 

EM65ONAU_R 

ENAU = ENAU_R 

EM1617NAU = EM1617NAU_R * (ENAU/ENAU_R) 

EM1819NAU = EM1819NAU_R * (ENAU/ENAU_R) 

EM2024NAU = EM2024NAU_R * (ENAU/ENAU_R) 

EM2534NAU = EM2534NAU_R * (ENAU/ENAU_R) 

EM3544NAU = EM3544NAU_R * (ENAU/ENAU_R) 

EM4554NAU = EM4554NAU_R * (ENAU/ENAU_R) 

EM5564NAU = EM5564NAU_R * (ENAU/ENAU_R) 

EM65ONAU = EM65ONAU_R * (ENAU/ENAU_R) 

EF1617NAU = EF1617NAU_R * (ENAU/ENAU_R) 

EF1819NAU = EF1819NAU_R * (ENAU/ENAU_R) 

EF2024NAU = EF2024NAU_R * (ENAU/ENAU_R) 

EF2534NAU = EF2534NAU_R * (ENAU/ENAU_R) 

EF3544NAU = EF3544NAU_R * (ENAU/ENAU_R) 

EF4554NAU = EF4554NAU_R * (ENAU/ENAU_R) 

EF5564NAU = EF5564NAU_R * (ENAU/ENAU_R) 

EF65ONAU = EF65ONAU_R * (ENAU/ENAU_R) 

EFNAU = EF1617NAU + EF1819NAU + EF2024NAU + EF2534NAU + EF3544NAU + EF4554NAU + EF5564NAU + EF65ONAU 

EMNAU = EM1617NAU + EM1819NAU + EM2024NAU + EM2534NAU + EM3544NAU + EM4554NAU + EM5564NAU + 

EM65ONAU 

Agricultural 

EA = IF LONGRANGE = 0 
94 

 THEN GDPPF00 / (EXP (-0.20541 + 0.03254 * YEAR - 0.07829 + 0.37854)) 

 ELSE E * EA.1/E.1 

Wage Workers 

EAW = IF LONGRANGE = 0 

 THEN EA * (0.00893 * YEAR + 0.33159 * RTP - 0.67943) 

 ELSE EA * (EAW.1/EA.1) 

EM1617AW_R = MAX (0, EAW * (-0.00594 - 0.09353 * MOVAVG (2, RTP.1) + 5.28754 * EM1617/E + 0.08116) + EM1617AW.ADJ) 

EM1819AW_R = MAX (0, EAW * (-0.00131 - 0.18120 * MOVAVG (2, RTP.1) + 3.87151 * EM1819/E + 0.16636) + EM1819AW.ADJ) 

EM2024AW_R = MAX (0, EAW * (-0.00664 + 0.10493 * MOVAVG (2, RTP.1) + 2.00153 * EM2024/E - 0.08191) + EM2024AW.ADJ) 

EM2534AW_R = MAX (0, EAW * (-0.02065 + 0.38358 * MOVAVG (2, RTP.1) - 0.98380 * EM2534/E + 0.00751) + EM2534AW.ADJ) 

EM3544AW_R = MAX (0, EAW * (0.00402 - 0.15663 * MOVAVG (2, RTP.1) + 1.72119 * EM3544/E + 0.05679) + EM3544AW.ADJ) 

EM4554AW_R = MAX (0, EAW * (0.00834 + 0.03746 * MOVAVG (2, RTP.1) + 0.46522 * EM4554/E + 0.00144) + EM4554AW.ADJ) 

EM5564AW_R = MAX (0, EAW * (-0.00655 + 0.03521 * MOVAVG (2, RTP.1) + 0.46852 * EM5564/E - 0.00037) + EM5564AW.ADJ) 

EM65OAW_R = MAX (0, EAW * (-0.00114 + 0.07640 * MOVAVG (2, RTP.1) + 3.25911 * EM65O/E - 0.10058) + EM65OAW.ADJ) 

EF1617AW_R = MAX (0, EAW * (-0.00055 - 0.05470 * MOVAVG (2, RTP.1) + 1.41760 * EF1617/E + 0.04979) + EF1617AW.ADJ) 

EF1819AW_R = MAX (0, EAW * (0.00102 - 0.07375 * MOVAVG (2, RTP.1) + 0.78394 * EF1819/E + 0.07226) + EF1819AW.ADJ) 

EF2024AW_R = MAX (0, EAW * (0.00112 - 0.05971 * MOVAVG (2, RTP.1) + 0.57256 * EF2024/E + 0.05907) + EF2024AW.ADJ) 

EF2534AW_R = MAX (0, EAW * (0.00623 + 0.08868 * MOVAVG (2, RTP.1) + 1.00897 * EF2534/E - 0.15142) + EF2534AW.ADJ) 

EF3544AW_R = MAX (0, EAW * (0.00687 - 0.00259 * MOVAVG (2, RTP.1) + 0.51319 * EF3544/E - 0.00937) + EF3544AW.ADJ) 

EF4554AW_R = MAX (0, EAW * (0.00185 + 0.08747 * MOVAVG (2, RTP.1) + 0.28022 * EF4554/E - 0.08053) + EF4554AW.ADJ) 

EF5564AW_R = MAX (0, EAW * (-0.00140 - 0.03001 * MOVAVG (2, RTP.1) - 0.59383 * EF5564/E + 0.07088) + EF5564AW.ADJ) 

EF65OAW_R = MAX (0, EAW * (0.00096 + 0.06768 * MOVAVG (2, RTP.1) + 1.04213 * EF65O/E - 0.07359) + EF65OAW.ADJ) 

EAW_R = EF1617AW_R + EF1819AW_R + EF2024AW_R + EF2534AW_R + EF3544AW_R + EF4554AW_R + 

EF5564AW_R + EF65OAW_R + EM1617AW_R + EM1819AW_R 

 + EM2024AW_R + EM2534AW_R + EM3544AW_R + EM4554AW_R + EM5564AW_R + EM65OAW_R 

EM1617AW = EM1617AW_R * (EAW/EAW_R) 

EM1819AW = EM1819AW_R * (EAW/EAW_R) 

EM2024AW = EM2024AW_R * (EAW/EAW_R) 

EM2534AW = EM2534AW_R * (EAW/EAW_R) 

EM3544AW = EM3544AW_R * (EAW/EAW_R) 

EM4554AW = EM4554AW_R * (EAW/EAW_R) 

EM5564AW = EM5564AW_R * (EAW/EAW_R) 

EM65OAW = EM65OAW_R * (EAW/EAW_R) 

EF1617AW = EF1617AW_R * (EAW/EAW_R) 

EF1819AW = EF1819AW_R * (EAW/EAW_R) 

EF2024AW = EF2024AW_R * (EAW/EAW_R) 

EF2534AW = EF2534AW_R * (EAW/EAW_R) 

EF3544AW = EF3544AW_R * (EAW/EAW_R) 

EF4554AW = EF4554AW_R * (EAW/EAW_R) 

EF5564AW = EF5564AW_R * (EAW/EAW_R) 

EF65OAW = EF65OAW_R * (EAW/EAW_R) 

EFAW = EF1617AW+ EF1819AW+ EF2024AW+ EF2534AW+ EF3544AW+ EF4554AW+ EF5564AW+ EF65OAW 

EMAW = EM1617AW+ EM1819AW+ EM2024AW+ EM2534AW+ EM3544AW+ EM4554AW+ EM5564AW+ EM65OAW 

Self-employed 

EAS = EA - EAU - EAW 

EM1617AS_R = MAX (0, NM1617 * (0.00528 + 0.00404) + EM1617AS.ADJ) 

EM1819AS_R = MAX (0, NM1819 * (0.00309 + 0.28448 * EA / (NM16O+ NF16O) - 0.00165) + EM1819AS.ADJ) 

EM2024AS_R = MAX (0, NM2024 * (-0.00181 + 0.97958 * EA / (NM16O+ NF16O) - 0.01093) + EM2024AS.ADJ) 

EM2534AS_R = MAX (0, NM2534 * (-0.00263 + 1.23186 * EA / (NM16O+ NF16O) - 0.01021) + EM2534AS.ADJ) 

EM3544AS_R = MAX (0, NM3544 * (-0.00151 + 1.66765 * EA / (NM16O+ NF16O) - 0.01450) + EM3544AS.ADJ) 

EM4554AS_R = MAX (0, NM4554 * (-0.00381 + 2.86654 * EA / (NM16O+ NF16O) - 0.03175) + EM4554AS.ADJ) 

EM5564AS_R = MAX (0, NM5564 * (-0.00460 + 2.78817 * EA / (NM16O+ NF16O) - 0.02398) + EM5564AS.ADJ) 

EM65OAS_R = MAX (0, NM65O * (0.00079 + 1.76904 * EA / (NM16O+ NF16O) - 0.01437) + EM65OAS.ADJ) 

EF1617AS_R = MAX (0, NF1617 * (0.00181 + 0.00030) + EF1617AS.ADJ) 
95 

EF1819AS_R = MAX (0, EM1819AS.1 * (-0.02393 + 0.63672 * MOVAVG (2, RTP.1) + 0.98791 * EF1819/EM1819 - 4.43926) + 

EF1819AS.ADJ) 

EF2024AS_R = MAX (0, EM2024AS.1 * (0.07353 - 0.40207 * MOVAVG (2, RTP.1) + 0.57572 * EF2024/EM2024 - 0.01117) + 

EF2024AS.ADJ) 

EF2534AS_R = MAX (0, EM2534AS.1 * (0.16575 + 0.16967 * MOVAVG (2, RTP.1) + 0.55503 * EF2534/EM2534 - 0.43412) + 

EF2534AS.ADJ) 

EF3544AS_R = MAX (0, EM3544AS.1 * (0.15848 + 0.37839 * MOVAVG (2, RTP.1) + 0.37764 * EF3544/EM3544 - 0.45362) + 

EF3544AS.ADJ) 

EF4554AS_R = MAX (0, EM4554AS.1 * (0.21947 + 0.29497 * MOVAVG (2, RTP.1) + 0.58974 * EF4554/EM4554 - 0.51966) + 

EF4554AS.ADJ) 

EF5564AS_R = MAX (0, EM5564AS.1 * (0.20892 + 0.36294 * MOVAVG (2, RTP.1) + 0.65320 * EF5564/EM5564 - 0.66626) + 

EF5564AS.ADJ) 

EF65OAS_R = MAX (0, EM65OAS.1 * (0.16242 + 0.54916 * MOVAVG (2, RTP.1) + 0.06199 * EF65O/EM65O- 0.47556) + 

EF65OAS.ADJ) 

EAS_R = EF1617AS_R + EF1819AS_R + EF2024AS_R + EF2534AS_R + EF3544AS_R + EF4554AS_R + EF5564AS_R + 

EF65OAS_R + EM1617AS_R + EM1819AS_R 

 + EM2024AS_R + EM2534AS_R + EM3544AS_R + EM4554AS_R + EM5564AS_R + EM65OAS_R 

EM1617AS = EM1617AS_R * (EAS/EAS_R) 

EM1819AS = EM1819AS_R * (EAS/EAS_R) 

EM2024AS = EM2024AS_R * (EAS/EAS_R) 

EM2534AS = EM2534AS_R * (EAS/EAS_R) 

EM3544AS = EM3544AS_R * (EAS/EAS_R) 

EM4554AS = EM4554AS_R * (EAS/EAS_R) 

EM5564AS = EM5564AS_R * (EAS/EAS_R) 

EM65OAS = EM65OAS_R * (EAS/EAS_R) 

EF1617AS = EF1617AS_R * (EAS/EAS_R) 

EF1819AS = EF1819AS_R * (EAS/EAS_R) 

EF2024AS = EF2024AS_R * (EAS/EAS_R) 

EF2534AS = EF2534AS_R * (EAS/EAS_R) 

EF3544AS = EF3544AS_R * (EAS/EAS_R) 

EF4554AS = EF4554AS_R * (EAS/EAS_R) 

EF5564AS = EF5564AS_R * (EAS/EAS_R) 

EF65OAS = EF65OAS_R * (EAS/EAS_R) 

EFAS = EF1617AS + EF1819AS + EF2024AS + EF2534AS + EF3544AS + EF4554AS + EF5564AS + EF65OAS 

EMAS = EM1617AS + EM1819AS + EM2024AS + EM2534AS + EM3544AS + EM4554AS + EM5564AS + EM65OAS 

Unpaid Family Workers 

EM1617AU_R = MAX (0, 0.002 + EM1617AU.ADJ) 

EM1819AU_R = MAX (0, 0.001 + EM1819AU.ADJ) 

EM2024AU_R = MAX (0, 0.001 + EM2024AU.ADJ) 

EM2534AU_R = MAX (0, 0.003 + EM2534AU.ADJ) 

EM3544AU_R = MAX (0, 0.004 + EM3544AU.ADJ) 

EM4554AU_R = MAX (0, 0.005 + EM4554AU.ADJ) 

EM5564AU_R = MAX (0, 0.003 + EM5564AU.ADJ) 

 EM65OAU_R = MAX (0, 0.001 + EM65OAU.ADJ) 

EF1617AU_R = MAX (0, 0.006 + EM1617AU.ADJ) 

EF1819AU_R = MAX (0, 0.005 + EF1819AU.ADJ) 

EF2024AU_R = MAX (0, 0.005 + EF2024AU.ADJ) 

EF2534AU_R = MAX (0, 0.002 + EF2534AU.ADJ) 

EF3544AU_R = MAX (0, 0.002 + EF3544AU.ADJ) 

EF4554AU_R = MAX (0, 0.001 + EF4554AU.ADJ) 

EF5564AU_R = MAX (0, 0.001 + EF5564AU.ADJ) 

 EF65OAU_R = MAX (0, 0.002 + EF65OAU.ADJ) 

EAU_R = EF1617AU_R + EF1819AU_R + EF2024AU_R + EF2534AU_R + EF3544AU_R + EF4554AU_R + EF5564AU_R + 

EF65OAU_R + EM1617AU_R + EM1819AU_R 

 + EM2024AU_R + EM2534AU_R + EM3544AU_R + EM4554AU_R + EM5564AU_R + EM65OAU_R 
96 

EAU = IF LONGRANGE = 0 

 THEN EAU_R 

 ELSE EAU.1/EA.1 * EA 

EM1617AU = EM1617AU_R * (EAU/EAU_R) 

EM1819AU = EM1819AU_R * (EAU/EAU_R) 

EM2024AU = EM2024AU_R * (EAU/EAU_R) 

EM2534AU = EM2534AU_R * (EAU/EAU_R) 

EM3544AU = EM3544AU_R * (EAU/EAU_R) 

EM4554AU = EM4554AU_R * (EAU/EAU_R) 

EM5564AU = EM5564AU_R * (EAU/EAU_R) 

 EM65OAU = EM65OAU_R * (EAU/EAU_R) 

EF1617AU = EF1617AU_R * (EAU/EAU_R) 

EF1819AU = EF1819AU_R * (EAU/EAU_R) 

EF2024AU = EF2024AU_R * (EAU/EAU_R) 

EF2534AU = EF2534AU_R * (EAU/EAU_R) 

EF3544AU = EF3544AU_R * (EAU/EAU_R) 

EF4554AU = EF4554AU_R * (EAU/EAU_R) 

EF5564AU = EF5564AU_R * (EAU/EAU_R) 

 EF65OAU = EF65OAU_R * (EAU/EAU_R) 

EFAU = EF1617AU + EF1819AU + EF2024AU + EF2534AU + EF3544AU + EF4554AU + EF5564AU + EF65OAU 

EMAU = EM1617AU + EM1819AU + EM2024AU + EM2534AU + EM3544AU + EM4554AU + EM5564AU + EM65OAU 

ANNUAL "AVERAGE HOURS WORKED" EQUATIONS 

Total 

Nonagricultural sector 

Wage Workers 

Males 

AHWM1617NAW = 34.4953 * RTP + 1.03247 * MINW/CPIW_U - 31.4229 * RNM1617S- 0.12369 * 1 + 12.1981 

AHWM1819NAW = 32.4361 * RTP + 12.8742 * RTP.1 + 1.28624 * MINW/CPIW_U- 16.0989 * RNM1819S - 0.27834 * 1 - 8.58664 

AHWM2024NAW = 20.1161 * RTP - 10.2292 * RNM2024S - 2.28628 * (PM2024NM * NM2024NM / (PM2024NM * NM2024NM + 

PM2024MS * NM2024MS + PM2024MA 

 * NM2024MA)) + 23.2252 

AHWM2534NAW = 17.0559 * RTP - 0.29076 * 1 + 0.04542 *YEAR + 22.5121 

AHWM3544NAW = 18.3314 * RTP - 0.30475 * 1 + 0.04409 *YEAR + 22.3275 

AHWM4554NAW = 16.0678 * RTP - 0.12289 * 1 + 0.07446 *YEAR + 21.4366 

AHWM5564NAW = 10.8277 * RTP + 0.23715 * 1 + 30.8975 

AHWM65ONAW = -0.28038 * 1 + 5.40682 * RTP + 25.4797 

Females 

AHWF1617NAW = 17.2598 * RTP + 7.31262 * RTP.1 - 24.9241 * RNF1617S + 16.9218 

AHWF1819NAW = 18.7922 * RTP + 13.1066 * RTP.1 - 18.9417 * RNF1819S- 16.2182 * PF1819 + 0.81920 * 1 + 16.7826 

AHWF2024NAW = -219.154 * PF2024 + 12.4226 * RTP - 0.98470 * 1 + 158.354 * (PF2024)2

 + 98.6034 

AHWF2534NAW = -39.2904 * PF2534 + 39.6515 * (PF2534)2

 + 9.10839 * RTP- 0.33503 * 1 + 35.8525 

AHWF3544NAW = -39.2904 * PF3544 + 39.6515 * (PF3544)2

 + 7.40115 * RTP- 0.38214 * 1 + 36.9133 

AHWF4554NAW = 8.64511 * RTP - 63.8042 * PF4554 + 59.9107 * (PF4554)2

 - 0.58355 * 1 + 44.0723 

AHWF5564NAW = 6.61506 * RTP - 0.28969 * 1 + 8.36882 * PF5564 + 24.8288 

AHWF65ONAW = -0.43916 * 1 + 26.5228 + (8.36882/2) * (PF65O- 0.086) 

Self-employed 

AHWNAS = 24.9592 * RTP - 17.2194 * EFNAS/ENAS + 22.0120 

Unpaid Family Workers 

AHWNAU = 25.5124 * (EF2534NAU + EF3544NAU + EF4554NAU)/ENAU + 19.2730 

Agricultural sector 

Wage Workers 

AHWAW = 6.58073 * RTP + 14.9130 * RTP.1 + 19.7800 
97 

Self-employed 

AHWAS = 2.45830 * PGDPAF/PGDP - 3.61107 * 1 + 44.5318 

Unpaid Family Workers 

AHWAU = 39.3563 

QUARTERLY "AVERAGE HOURS WORKED" EQUATIONS 

Total 

AHW = (AHWNA * ENA + AHWA * EA) / E 

Nonagricultural sector 

AHWNA = (AHWNAW * (E-ENAS-ENAU-EA) + AHWNAS * ENAS + AHWNAU * ENAU) / ENA 

Wage Workers 

AHWNAW = (AHWMNAW * (EM – EMNAS - EMNAU – EMAW - EMAS - EMAU) + AHWFNAW * (EF - EFNAS - EFNAU – EFAW - 

EFAS – EFAU))/ (E – ENAS – ENAU – EA) 

Males 

AHWMNAW1 = AHWM1617NAW * (EM1617 - EM1617NAS - EM1617NAU - EM1617AW - EM1617AS - EM1617AU) 

AHWMNAW2 = AHWM1819NAW * (EM1819 - EM1819NAS - EM1819NAU - EM1819AW - EM1819AS - EM1819AU) 

AHWMNAW3 = AHWM2024NAW * (EM2024 - EM2024NAS - EM2024NAU - EM2024AW - EM2024AS - EM2024AU) 

AHWMNAW4 = AHWM2534NAW * (EM2534 - EM2534NAS - EM2534NAU - EM2534AW - EM2534AS - EM2534AU) 

AHWMNAW5 = AHWM3544NAW * (EM3544 - EM3544NAS - EM3544NAU - EM3544AW - EM3544AS - EM3544AU) 

AHWMNAW6 = AHWM4554NAW * (EM4554 - EM4554NAS - EM4554NAU - EM4554AW - EM4554AS - EM4554AU) 

AHWMNAW7 = AHWM5564NAW * (EM5564 - EM5564NAS - EM5564NAU - EM5564AW - EM5564AS - EM5564AU) 

AHWMNAW8 = AHWM65ONAW * (EM65O - EM65ONAS - EM65ONAU - EM65OAW - EM65OAS - EM65OAU) 

AHWMNAW = (AHWMNAW1 + AHWMNAW2 + AHWMNAW3 + AHWMNAW4 + AHWMNAW5 + AHWMNAW6 + 

AHWMNAW7 + AHWMNAW8) / (EM - EMNAS - EMNAU 

 - EMAW - EMAS - EMAU) 

AHWM1617NAW = 34.4953 * MOVAVG (2, RTP.1) + 1.03247 * MINW/CPIW_U - 31.4229 * RNM1617S - 0.12369 * 1 + 12.1981 + 

AHWM1617NAW.ADJ 

AHWM1819NAW = 32.4361 * MOVAVG (2, RTP.1) + 12.8742 * MOVAVG (2, RTP.5) + 1.28624 * MINW/CPIW_U - 16.0989 * 

RNM1819S - 0.27834 * 1 - 8.58664 + AHWM1819NAW.ADJ 

AHWM2024NAW = 20.1161 * MOVAVG (2, RTP.1) - 10.2292 * RNM2024S - 2.28628 * (PM2024NM * NM2024NM/ (PM2024NM * 

NM2024NM + PM2024MS * NM2024MS + PM2024MA 

 * NM2024MA)) + 23.2252 + AHWM2024NAW.ADJ 

AHWM2534NAW = MIN (45, 17.0559 * MOVAVG (2, RTP.1) - 0.29076 * 1 + 0.04542 *YEAR + 22.5121) + AHWM2534NAW.ADJ 

AHWM3544NAW = MIN (45, 18.3314 * MOVAVG (2, RTP.1) - 0.30475 * 1 + 0.04409 *YEAR + 22.3275) + AHWM3544NAW.ADJ 

AHWM4554NAW = MIN (45, 16.0678 * MOVAVG (2, RTP.1) - 0.12289 * 1 + 0.07446 *YEAR + 21.4366) + AHWM4554NAW.ADJ 

AHWM5564NAW = 10.8277 * MOVAVG (2, RTP.1) + 0.23715 * 1 + 30.8975 + AHWM5564NAW.ADJ 

AHWM65ONAW = -0.28038 * 1 + 5.40682 * MOVAVG (2, RTP.1) + 25.4797 + AHWM65ONAW.ADJ 

Females 

AHWFNAW1 = AHWF1617NAW* (EF1617 -EF1617NAS-EF1617NAU-EF1617AW-EF1617AS-EF1617AU) 

AHWFNAW2 = AHWF1819NAW* (EF1819 -EF1819NAS-EF1819NAU-EF1819AW-EF1819AS-EF1819AU) 

AHWFNAW3 = AHWF2024NAW* (EF2024 -EF2024NAS-EF2024NAU-EF2024AW-EF2024AS-EF2024AU) 

AHWFNAW4 = AHWF2534NAW* (EF2534 -EF2534NAS-EF2534NAU-EF2534AW-EF2534AS-EF2534AU) 

AHWFNAW5 = AHWF3544NAW* (EF3544 -EF3544NAS-EF3544NAU-EF3544AW-EF3544AS-EF3544AU) 

AHWFNAW6 = AHWF4554NAW* (EF4554 -EF4554NAS-EF4554NAU-EF4554AW-EF4554AS-EF4554AU) 

AHWFNAW7 = AHWF5564NAW* (EF5564 -EF5564NAS-EF5564NAU-EF5564AW-EF5564AS-EF5564AU) 

AHWFNAW8 = AHWF65ONAW * (EF65O -EF65ONAS-EF65ONAU-EF65OAW-EF65OAS-EF65OAU) 

AHWFNAW = (AHWFNAW1 + AHWFNAW2 + AHWFNAW3 + AHWFNAW4 + AHWFNAW5 + AHWFNAW6 + AHWFNAW7 + AHWFNAW8) / (EF

 – EFAS – EFAU) 

AHWF1617NAW = 17.2598 * MOVAVG (2, RTP.1) + 7.31262 * MOVAVG (2, RTP.5) - 24.9241 * RNF1617S + 16.9218 + 

AHWF1617NAW.ADJ 
98 

AHWF1819NAW = 18.7922 * MOVAVG (2, RTP.1) + 13.1066 * MOVAVG (2, RTP.5) - 18.9417 * RNF1819S - 16.2182 * PF1819 + 

0.81920 * 1 + 16.7826 + AHWF1819NAW.ADJ 

AHWF2024NAW = -219.154 * PF2024 + 12.4226 * MOVAVG (2, RTP.1) - 0.98470 * 1 + 158.354 * (PF2024)2

 + 98.6034 + 

AHWF2024NAW.ADJ 

AHWF2534NAW = -39.2904 * PF2534 + 39.6515 * (PF2534)2

 + 9.10839 * MOVAVG (2, RTP.1) - 0.33503 * 1 + 35.8525 + 

AHWF2534NAW.ADJ 

AHWF3544NAW = -39.2904 * PF3544 + 39.6515 * (PF3544)2

 + 7.40115 * MOVAVG (2, RTP.1) - 0.38214 * 1 + 36.9133 + 

AHWF3544NAW.ADJ 

AHWF4554NAW = 8.64511 * MOVAVG (2, RTP.1) - 63.8042 * PF4554 + 59.9107 * (PF4554)2

 - 0.58355 * 1 + 44.0723 + 

AHWF4554NAW.ADJ 

AHWF5564NAW = 6.61506 * MOVAVG (2, RTP.1) - 0.28969 * 1 + 8.36882 * PF5564 + 24.8288 + AHWF5564NAW.ADJ 

AHWF65ONAW = -0.43916 * 1 + 26.5228 + (8.36882/2) * (PF65O- 0.086) + AHWF65ONAW.ADJ 

Self-employed 

AHWNAS = 24.9592 * MOVAVG (2, RTP.1) - 17.2194 * EFNAS/ENAS + 22.0120 + AHWNAS.ADJ 

Unpaid Family Workers 

AHWNAU = 25.5124 * (EF2534NAU + EF3544NAU + EF4554NAU)/ ENAU + 19.2730 + AHWNAU.ADJ 

Agricultural sector 

AHWA = (AHWAW * EAW + AHWAS * EAS + AHWAU * EAU) / EA 

Wage Workers 

AHWAW = 6.58073 * MOVAVG (2, RTP.1) + 14.9130 * MOVAVG (2, RTP.5) + 19.7800 + AHWAW.ADJ 

Self-employed 

AHWAS = 2.45830 * PGDPAF/PGDP - 3.61107 * 1 + 44.5318 + AHWAS.ADJ 

Unpaid Family Workers 

AHWAU = 39.3563 + AHWAU.ADJ 

OTHER EMPLOYMENT MEASURES 

Federal Civilian Government and Government Enterprises 

EGFC = IF LONGRANGE = 0 

 THEN (EGFC.1 * 1.00940.25) 

 ELSE (EGFC.1 * (E_FE/E_FE.1)) 

EGEFCPS = IF LONGRANGE = 0 

 THEN (EGEFCPS.1 * 1.00750.25) 

 ELSE (EGEFCPS.1 * (E_FE/E_FE.1)) 

EGGEFC = EGFC + EGEFCPS 

State and Local Government and Government Enterprises 

EGGESL = IF LONGRANGE = 0 

 THEN EGGESL.1 * (LC_FE/LC_FE.4)0.25 

 ELSE EGGESL.1 * (E_FE/E_FE.1) 

Other Employment Measures 

DNEDMIL = IF (EDMIL-EDMIL.4) < 0 

 THEN (EDMIL-EDMIL.4) 

 ELSE 0 

EP = E-EGGESL - EGGEFC – EAS - ENAS 

Compensation and Output Sectors 

Price Deflator for Medical Services 

CPIWMS = CPIWMS.1 * (1 + ((CPIW_U/CPIW_U.4)0.25 - 1) * CPIWMSWT) 

UI and WC Effective Tax Rates 

TMAXUI_SL = TMAXUI_SL.1 *AWSUI.1/AWSUI.2 
99 

RELMAX_UI = TMAXUI_SL/AWSUI.1/1000 

CR_UI = 0.775 

TRATIO_UI = 0.96996 * RELMAX_UI-0.13744 * MOVAVG (4, RTP.1) + 0.10368 * MOVAVG (4, RTP.5) + 0.04887 

TRATE_UI = 0.00143 * MOVAVG (4, RU.5) + 0.00128 * MOVAVG (4, RU.9) + 0.00057 * MOVAVG (4, RU.13) + 0.00356 

RUIWS1 = CR_UI * TRATIO_UI * TRATE_UI 

RUIWS2 = 0.32476 * MOVAVG (4, RUIWS1.8 * (WSP.8 -WSPRRB.8 +WSGGESL.8)) / (WSP.1 -WSPRR2.1 +WSGGESL.1) 

Workers' Compensation 

RWCWS = RWCWS.1 - (RWCWS.1 - 0.0144)/12 

State and Local Government and Government Enterprises 

TAXMAX = IF QTR = 1 

 THEN 300.* ROUND (MOVAVG (4, AWSE.5)/MOVAVG (4, AWSE.9) * 1000.* TAXMAX.1/300 +0.5)/1000 

 ELSE TAXMAX.1 

Wages 

AWSPL = MOVAVG (8, AWSP.1) 

AWSSPL = MOVAVG (8, AWSSP.1) 

AWSGGESL = IF LONGRANGE = 0 

 THEN AWSGGESL.1 * AWSPL/AWSPL.1 

 ELSE AWSGGESL.1 * AVG_GDP/AVG_GDP.1 * (1 + WS_TO_WSS_D/100)0.25

WSGGESL = AWSGGESL * EGGESL 

Employer Contribution for Government Social Insurance 

OASDISL_L = (EMPTROASI + EMPTRDI) * 0.978 * CSLA * WSGGESL 

HISL_L = EMPTRHI * 1.0 * CSLHI * WSGGESL 

SOC_UISL = (-0.02821 * MOVAVG (4, RTP.2) + 0.03145) * WSGGESL 

RSOCSL_WC = RSOCSL_WC.1 - (RSOCSL_WC.1 - 0.176)/12 

SOC_WCSL = RSOCSL_WC * RWCWS * WSGGESL 

SOC_SL = (OASDISL_L + HISL_L + SOC_UISL + SOC_WCSL) 

Employer Contributions for Employee Pension and Insurance funds 

Workers' Compensation - employees and annuitants 

OLI_WCSL = (1 - RSOCSL_WC) * RWCWS * WSGGESL 

Pensions 

OLI_RETSL = WSGGESL * (OLI_RETSL.1/WSGGESL.1) 

Life Insurance - employees and annuitants 

OLI_GLI_SL = 2.0 * EGGESL * ((WSGGESL/EGGESL) +2.0) * 0.075 * 26/1000 

 Health Insurance - employees and annuitants 

OLI_GHI_SL = (OLI_GHI_SL.1 / EGGESL.1) * CPIWMS/CPIWMS.1 * EGGESL * RGR_GHI 

Total 

OLI_SL = (OLI_GLI_SL + OLI_GHI_SL + OLI_WCSL + OLI_RETSL) 

RCWSSL = (1 + (SOC_SL + OLI_SL)/WSGGESL) 

WSSGGESL = IF LONGRANGE = 0 

 THEN RCWSSL*WSGGESL 

 ELSE (WSSGGESL.1/EGGESL.1) * AVG_GDP/AVG_GDP.1 * EGGESL 

WSSGSL = WSSGGESL * WSSGSL.1/WSSGGESL.1 

WSSGESL = WSSGGESL - WSSGSL 

CFCGSL = IF LONGRANGE = 0 

 THEN WSSGSL * RCFCGSL 

 ELSE CFCGSL.1 * WSSGGESL/WSSGGESL.1 

GDPGSL = WSSGSL + CFCGSL 

CFCGESL = IF LONGRANGE = 0 

 THEN WSSGESL * RCFCGESL 

 ELSE CFCGESL.1 * WSSGGESL/WSSGGESL.1 
100 

GDPGESL = WSSGESL + CFCGESL 

GDPGGESL = GDPGSL + GDPGESL 

Federal Civilian General Government and Government Enterprises 

Wages 

General Government and Government Enterprises 

CRAZ1 = IF LONGRANGE = 0 

 THEN ((IF QTR = 1 THEN (0.82429 * (AWSP.6/AWSP.10 - 1) -0.005) ELSE 0)) 

 ELSE (IF QTR = 1 THEN (AWSP.6/AWSP.10 - 1) ELSE 0) 

 MRAZ = IF LONGRANGE = 0 

 THEN ((IF QTR = 1 THEN (0.82429 * (AWSP.6/AWSP.10 - 1) -0.005) ELSE 0)) 

 ELSE (IF QTR = 1 THEN (AWSP.6/AWSP.10 - 1) ELSE 0) 

AWSGGEFC = IF LONGRANGE = 0 

 THEN (AWSGGEFC.1 * (1 +1.0 *CRAZ1 +0.0015)) 

 ELSE AWSGGEFC.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100)0.25

WSGGEFC = AWSGGEFC * EGGEFC 

CSRS workers 

AWEFC_N = IF LONGRANGE = 0 

 THEN (AWEFC_N.1 * (1 +1.0 *CRAZ1 +0.00082)) 

 ELSE AWEFC_N.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100)0.25

WEFC_N = AWEFC_N * TEFC_N 

Government Enterprises (Mostly U.S. Postal Service) 

AWSGEFC = IF LONGRANGE = 0 

 THEN (AWSGEFC.1 * (1 +1.0 *CRAZ1 +0.0015)) 

 ELSE AWSGEFC.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100) 0.25

WSGEFC = AWSGEFC * EGEFCPS 

General Government 

WSGFC = WSGGEFC -WSGEFC 

AWSGFC = WSGFC/EGFC 

Employer Contribution for Government Social Insurance 

General Government and Government Enterprises 

OASDIFC_L = (EMPTROASI + EMPTRDI) * 1.04 * (WSGGEFC - WEFC_N) * ADJ_FSA_FC 

HIFC_L = EMPTRHI* 1.055 * WSGGEFC * ADJ_FSA_FC 

SOCF_UIFC = (-0.05934 * RTP + 0.06165) * WSGGEFC 

SOCF_WC = 0.0159 * WSGGEFC 

SOC_FC = (SOCF_UIFC + SOCF_WC + OASDIFC_L + HIFC_L) 

Employer Contributions for Employee Pension and Insurance funds 

General Government and Government Enterprises 

 Pensions 

OLI_CSRS1 = ((0.174 * WSGEFC + 0.07 * WSGFC) / WSGGEFC) * WEFC_N 

OLI_FERS1 = 0.107 * (WSGGEFC * 0.9 -WEFC_N) 

OLI_FERSFC = 0.048 * (WSGGEFC * 0.9 -WEFC_N) 

OLI_RETFC = OLI_CSRS1 + OLI_FERS1 + OLI_FERSFC + OLIF_RETFCO 

 Life Insurance - employees and annuitants 

OLI_GLI_FC = 2.0 * EGGEFC * ((WSGGEFC/EGGEFC) + 2.0) * 0.075 * 26/1000 
101 

 Health Insurance - employees and annuitants 

OLI_GHI_FC = (OLI_GHI_FC.1 / EGGEFC.1) * CPIWMS/CPIWMS.1 * EGGEFC * RGR_GHI 

OLI_FC = (OLI_GHI_FC + OLI_GLI_FC + OLI_RETFC) 

Compensation 

General Government and Government Enterprises 

RCWSF = (1 + (SOC_FC + OLI_FC)/WSGGEFC) 

WSSGGEFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGGEFC 

 ELSE (WSSGGEFC.1/EGGEFC.1) * AVG_GDP/AVG_GDP.1 * EGGEFC 

WSSGFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGFC 

 ELSE (WSSGFC.1 / (EGGEFC.1 - EGEFCPS.1)) * AVG_GDP/AVG_GDP.1 * (EGGEFC - EGEFCPS) 

WSSGEFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGEFC 

 ELSE (WSSGEFC.1/EGEFCPS.1) * AVG_GDP/AVG_GDP.1 * EGEFCPS 

Consumption of Fixed Capital 

General Government and Government Enterprises 

CFCGFC = IF LONGRANGE = 0 

 THEN WSSGFC * RCFCGFC 

 ELSE CFCGFC.1 * WSSGGEFC / WSSGGEFC.1 

CFCGEFC = IF LONGRANGE = 0 

 THEN WSSGEFC * RCFCGEFC 

 ELSE CFCGEFC.1 * WSSGGEFC / WSSGGEFC.1 

Gross Domestic Product 

General Government and Government Enterprises 

GDPGFC = WSSGFC + CFCGFC 

GDPGEFC = WSSGEFC + CFCGEFC 

GDPGGEFC = GDPGFC + GDPGEFC 

Federal Government Military 

Wages 

AWSGFM = IF LONGRANGE = 0 

 THEN (AWSGFM.1 * (1.0027 +1.0 * MRAZ)) 

 ELSE AWSGFM.1 * AVG_GDP/AVG_GDP.1 * (1 + WS_TO_WSS_D/100) 0.25

WSGFM = AWSGFM * (EDMIL+ EDMIL_R) 

Employer Contribution for Government Social Insurance 

OASDIFM_L = (EMPTROASI + EMPTRDI) * 0.9975 * CML * WSGFM 

HIFM_L = EMPTRHI* 1.0 *CML * WSGFM 

SOCF_UIFM = MAX (0.001, (-0.05263 * DIFF (EDMIL + EDMIL_R) - 0.03079 * RTP + 0.03310)) * WSGFM 

SOCF_MIFM = 0.30 * CPIWMS * (EDMIL + EDMIL_R) 

SOC_FM = (SOCF_UIFM + SOCF_MIFM + OASDIFM_L + HIFM_L) 

Employer Contributions for Employee Pension and Insurance funds 

OLI_RETFM = (OLI_RETFM.1/WSGFM.1 - (OLI_RETFM.1/WSGFM.1 - 0.472)/12) * WSGFM 

Compensation 

RCWSM = (1 + (OLI_RETFM + SOC_FM)/WSGFM) 

WSSGFM = IF LONGRANGE = 0 

 THEN RCWSM * WSGFM 

 ELSE (WSSGFM.1/EDMIL.1) * AVG_GDP/AVG_GDP.1 * EDMIL 
102 

Consumption of Fixed Capital 

CFCGFM = IF LONGRANGE = 0 

 THEN WSSGFM * RCFCGFM 

 ELSE CFCGFM.1 * WSSGFM/WSSGFM.1 

Gross Domestic Product 

GDPGFM = WSSGFM + CFCGFM 

GDPGF = GDPGFC + GDPGFM 

GDPGGE = GDPGGEFC + GDPGGESL + GDPGFM 

Total (Civilian and Military) Federal General Government and Government Enterprises 

WSSGF = WSSGFC + WSSGFM 

WSSGE = WSSGEFC + WSSGESL 

WSSG = WSSGF + WSSGSL 

GDPGE = GDPGEFC + GDPGESL 

GDPG = GDPGF + GDPGSL 

NIPA Farm Output and Earnings 

GDPPF00 = IF LONGRANGE = 0 

 THEN EXP (- 3.52340 + 0.02055 * YEAR) * N_SSA 

 ELSE GDPPF00.1 * GDP00/GDP00.1 

PGDPAF = IF LONGRANGE = 0 

 THEN PGDPAF.1 * ((PGDP/PGDP.1)4

 - 0.01) 0.25 

 ELSE PGDPAF.1 * ((PGDP/PGDP.1)4

)

 0.25

GDPPF = GDPPF00 * PGDPAF 

AYF_K = ((YF.1 /EAS.1) / (WSSPF.1/EAW.1) - 1.594) * 0.8 + 1.594 

WSSPF = IF LONGRANGE = 0 

 THEN EAW * MOVAVG (4, WSSP.2/EP.2) * (3.15749 / (YEAR- 65) - 0.43419 * RTP + 0.68725) 

 ELSE (WSSPF.1/EAW.1) * AVG_GDP/AVG_GDP.1 * EAW 

WSPF = IF LONGRANGE = 0 

 THEN WSSPF * (MOVAVG (12, (WSP.1/WSSP.1)) + 0.015) 

 ELSE (WSPF.1 /WSSPF.1) * (WSP.1/WSSP.1) / (WSP.2/WSSP.2) * WSSPF 

AWSPF = WSPF/EAW 

YF = AYF_K * (WSSPF/EAW) * EAS 

GDP, WSS and WS, Private Households & Nonprofit Institutions 

Private Households 

Compensation & Wages 

WSSPH = IF LONGRANGE = 0 

 THEN (((WSSPH.1/ENAWPH.1)/MOVAVG (4, WSSP.3/EP.3) - 0.41) * 0.875 + 0.41) * MOVAVG (4, WSSP.2/EP.2) * 

ENAWPH 

 ELSE (AVG_GDP/AVG_GDP.1) * ENAWPH * (WSSPH.1/ENAWPH.1) 

WSPH = IF LONGRANGE = 0 

 THEN WSSPH / (1 +CPH* 1 * (EMPTROASI + EMPTRDI + EMPTRHI)) 

 ELSE (AWSPH.1 * ENAWPH.1/WSSPH.1) * (1 + WS_TO_WSS_D/100) 0.25 * WSSPH 

AWSPH = WSPH / ENAWPH 

Owner Occupied Housing 

OOH = OOH.1 * (KGDP00 * PGDP) / (KGDP00.1 * PGDP.1) 

Gross Value Added 

GDPPH = IF LONGRANGE = 0 

 THEN WSSPH + OOH 

 ELSE (AVG_GDP/AVG_GDP.1) * ENAWPH * (GDPPH.1/ENAWPH.1) 
103 

Nonprofit Institutions 

Health Services 

EPHS_EST = IF LONGRANGE = 0 

 THEN EPHS_EST.1 + 0.275/4 

 ELSE EPHS_EST.1 * (E_FE/E_FE.1) 

AWSSPHS = IF LONGRANGE = 0 

 THEN AWSSPHS.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPHS.1 * AVG_GDP/AVG_GDP.1 

WSSPHS = AWSSPHS* EPHS_EST 

Educational Services 

EPES_EST = IF LONGRANGE = 0 

 THEN EPES_EST.1 + 0.075/4 

 ELSE EPES_EST.1 * (E_FE/E_FE.1) 

AWSSPES = IF LONGRANGE = 0 

 THEN AWSSPES.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPES.1 * AVG_GDP/AVG_GDP.1 

WSSPES = AWSSPES* EPES_EST 

Social Services 

EPSS_EST = IF LONGRANGE = 0 

 THEN EPSS_EST.1 + 0.075/4 

 ELSE EPSS_EST.1 * (E_FE/E_FE.1) 

AWSSPSS = IF LONGRANGE = 0 

 THEN AWSSPSS.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPSS.1 * AVG_GDP/AVG_GDP.1 

WSSPSS = AWSSPSS* EPSS_EST 

Gross Value Added 

WSSPNI = WSSPNI.1 * (WSSPHS + WSSPES + WSSPSS) / (WSSPHS.1 + WSSPES.1 + WSSPSS.1) 

WSPNI = IF LONGRANGE = 0 

 THEN WSSPNI * (WSPNI.1/WSSPNI.1) * ((WSP.1/WSSP.1) / (WSP.9/WSSP.9)) (1/8) 

 ELSE WSSPNI * (WSPNI.1/WSSPNI.1) * (1 +WS_TO_WSS_D/100) 0.25

GDPPNI = IF LONGRANGE = 0 

 THEN WSSPNI / ((WSSPNI.1/GDPPNI.1 - 0.866) * 0.8 + 0.866) 

 ELSE WSSPNI /0.866 

Private Output and Compensation 

SOC 

ROASDIP_L = (EMPTROASI + EMPTRDI) * TXRP * CP 

RHIP_L = EMPTRHI * 1.0 * CP 

RSOC_UIP = 0.00109 * MOVAVG (4, RU.2) + 0.00045 * MOVAVG (4, RU.10) + 0.00048 * MOVAVG (4, RU.18) - 0.00331 

RSOC_WCP = RWCWS * RSOCSL_WC 

RSOCF_PBG = 0.00022 

OLI 

ROLI_WCP = RWCWS * (1 - RSOCSL_WC) 

ROLI_SU = 0.0005 

OLI_GLI_P = 0.0025 * EP * AWSP.1 

OLI_GHI_P = (OLI_GHI_P.1 / EP.1) * CPIWMS/CPIWMS.1 * EP * RGR_GHI 

ROLI_PPPS = MAX (ROLI_PPPS.1, 0.00031 * YEAR + 0.00866) 

WSS and YNF 

WSSGGE = (WSSGGESL + WSSGGEFC + WSSGFM) 

GDPPBNFXGE = (GDP – GDPGGE – GDPPF – GDPPH – GDPPNI) 

RWSSPBNFXGE = (-0.35334 * DRTPP - 0.16925 * DRTPP.1 + 0.20074 * DRTPN.1 + 0.16114 * DRTPN.2 + 0.59442) 

ENAW = ENA-ENAS-ENAU 
104 

ENAWPBXGE = ENAW - (ENAWPH + EGGEFC + EGGESL + WSSPNI / (WSSPHS + WSSPES + WSSPSS) * (EPHS_EST + 

EPES_EST + EPSS_EST)) 

ENAWSPBXGE = ENAWPBXGE + ENAS 

AYNF_K = ((YNF.1/ENAS.1 / (WSSPBNFXGE.1/ENAWPBXGE.1)) - 1.65) * 0.9 + 1.65 

AYF = YF/EAS 

AWSSPF = WSSPF/EAW 

AYNF = YNF/ENAS 

AWSSPBNFXGE = WSSPBNFXGE/ENAWPBXGE 

YNF = YNF.1 * (GDPPBNFXGE / GDPPBNFXGE.1) * (ENAS / (ENAS + ENAWPBXGE)) / (ENAS.1 / (ENAS.1 + 

ENAWPBXGE.1)) 

WSSPBNFXGE = (GDPPBNFXGE - YNF) * ((WSSPBNFXGE.1 / (GDPPBNFXGE.1 - YNF.1) - 0.621) * (0.8) + 0.621) 

WSSP = WSSPBNFXGE+WSSPF+WSSPH +WSSPNI 

RCWSP = WSSP / (WSSP - SOCF_RETRR - OLI_GLI_P - OLI_GHI_P) * (1 + ROASDIP_L + RHIP_L + RSOC_UIP + 

RSOC_WCP + RSOCF_PBG + ROLI_WCP + ROLI_SU 

 + ROLI_PPPS) 

WS = IF WS_TO_WSS_DYR = 0 

 THEN (WSGGESL + WSGGEFC + WSGFM + WSSP/RCWSP) 

 ELSE WSS * WS.1/WSS.1 * (1 + WS_TO_WSS_D/100) 0.25

WSP = (WS - WSGGESL - WSGGEFC - WSGFM) 

AWSP = WSP/EP 

AWSSP = WSSP/EP 

Other Variables 

WSD = WS 

WSDP = (WSD –WSGGESL – WSGGEFC – WSGFM) 

AWSE = WS / (E + EDMIL – EAS – ENAS) 

AWSUI = (WS -WSGGEFC -WSGFM) / (E – EGGEFC – EAS – ENAS) 

WSS = (WSSP + WSSGGE) 

OLI = OLI_GGE + OLI_P 

SOC = SOC_GGE + SOC_P 

OLI_GGE = OLI_FC + OLI_SL + OLI_RETFM 

SOC_GGE = SOC_FC + SOC_FM + SOC_SL 

SOC_UIP = RSOC_UIP * WSP 

SOC_WCP = RSOC_WCP * WSP 

OASDIP_L = ROASDIP_L * WSP 

HIP_L = RHIP_L * WSP 

SOCF_PBG = RSOCF_PBG * WSP 

SOCF_RETRR = 0.20 * WSPRRB 

SOC_P = SOC_UIP + SOC_WCP + OASDIP_L + HIP_L + SOCF_PBG + SOCF_RETRR 

OLI_WCP = ROLI_WCP * WSP 

OLI_SU = ROLI_SU * WSP 

OLI_PPPS = ROLI_PPPS * WSP 

OLI_P = OLI_WCP + OLI_SU + OLI_GHI_P + OLI_GLI_P + OLI_PPPS 

OLI_PPS = OLI_PPPS + OLI_RETFC + OLI_RETFM + OLI_RETSL 

OLI_GHI = OLI_GHI_P + OLI_GHI_FC + OLI_GHI_SL 

OLI_GLI = OLI_GLI_P + OLI_GLI_FC + OLI_GLI_SL 

OLI_WC = OLI_WCP + OLI_WCSL 

SOCSL_WC = SOC_WCSL + SOC_WCP 

SOCF_UIFED = SOCF_UIFC + SOCF_UIFM 

SOCF_UIS = (SOC_UIP + SOC_UISL) * RUIWS1 / (RUIWS1 + RUIWS2) 

SOCF_UIF = (SOC_UIP + SOC_UISL) - SOCF_UIS 

SOCF_OASDI = OASDIP_L + OASDISL_L + OASDIFC_L + OASDIFM_L 

SOCF_HI = HIP_L + HISL_L + HIFC_L + HIFM_L 
105 

2.3 OASDI Covered Employment and Earnings (COV) 

Total At-Any-Time Employment 

Males 

Aged 1 through 9 

CEM1 = 0.00026 * NM1 

CEM2 = 0.00031 * NM2 

CEM3 = 0.00025 * NM3 

CEM4 = 0.00019 * NM4 

CEM5 = 0.00036 * NM5 

CEM6 = 0.00042 * NM6 

CEM7 = 0.00165 * NM7 

CEM8 = 0.00239 * NM8 

CEM9 = 0.00279 * NM9 

Aged 10 through 15 

TEM1013 = 0.01969 * (NM10 + NM11 + NM12 + NM13 + NM10[+1] + NM11[+1] + NM12[+1] + NM13[+1])/2 

TEM1415 = (0.42767 * RTP - 1.02624 * NM1415 / (NM1415 + NM1617) + 0.23102) * ((NM14 + NM15 + NM14[+1] + NM15[+1])/2) 

Females 

Aged 1 through 9 

CEF1 = 0.00028 * NF1 

CEF2 = 0.00023 * NF2 

CEF3 = 0.00020 * NF3 

CEF4 = 0.00031 * NF4 

CEF5 = 0.00041 * NF5 

CEF6 = 0.00055 * NF6 

CEF7 = 0.00129 * NF7 

CEF8 = 0.00156 * NF8 

CEF9 = 0.00212 * NF9 

Aged 10 through 15 

TEF1013 = IF YEAR < = 110 

 THEN (0.04615 * RTP - 0.00014 * YEAR - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] + 

NF13[+1])/2 

 ELSE (0.04615 * RTP - 0.00014 * 110 - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] + 

NF13[+1])/2 

TEF1415 = (0.48500 * RTP - 0.79002 * NF1415 / (NF1415 + NF1617) + 0.02205) * ((NF14 + NF15 + NF14[+1] + NF15[+1])/2) 

Total Males, Total Females and Combined Total 

TEM = CEM1 + CEM2 + CEM3 + CEM4 + CEM5 + CEM6 + CEM7 + CEM8 + CEM9 + TEM1013 + TEM1415 + TEM16O 

TEF = CEF1 + CEF2 + CEF3 + CEF4 + CEF5 + CEF6 + CEF7 + CEF8 + CEF9 + TEF1013 + TEF1415 + TEF16O 

TE = TEM + TEF 

Male Disaggregates Aged 16 and Over 

TEM1617 = (-0.0337 - 1.32778 * REM1617_A + 1.11118 + RNM1617MAX-0.5 * 0.0637 - 0.161 * RILEM1519) * (EM1617 

 * REM1617_M * REM2_1617 - EM1617AU - EM1617NAU + NM1617M) 

TEM1819 = (-0.0267 - 0.60094 * REM1819_A + 0.89703 + RNM1819MAX-0.5 * 0.0637 - 0.265 * RILEM1519) * (EM1819 

 * REM1819_M * REM2_1819 - EM1819AU- EM1819NAU + NM1819M) 

TEM2024 = (-0.0196 + 0.02072 + 0.82020 + RNM2024MAX-0.50 * 0.0176 - 0.357 * RILEM2024 -0.80 * (REM2024_A + RM2024D)) 

 * (EM2024 * REM2024_M * REM2_2024 - EM2024AU - EM2024NAU + NM2024M) 

TEM2529 = (-0.0113 + 0.02898 + 0.81312 + RNM2529MAX-0.50 * 0.0214 - 0.416 * RILEM2529 - 0.80 * (REM2529_A + RM2529D)) 

 * (EM2529 * REM2529_M * REM2_2529 - EM2529AU - EM2529NAU + NM2529M) 

TEM3034 = (0.0062 - 0.00445 + 0.55577 + RNM3034MAX-0.50 * 0.0416 - 0.424 * RILEM3034 - 0.50 * (REM3034_A + RM3034D)) 

 * (EM3034 * REM3034_M * REM2_3034 - EM3034AU - EM3034NAU + NM3034M) 

TEM3539 = (-0.0092 + 0.00162 + 0.50480 + RNM3539MAX-0.50 * 0.0279 - 0.423 * RILEM3539 -0.45 * (REM3539_A + RM3539D)) 

 * (EM3539 * REM3539_M * REM2_3539 - EM3539AU - EM3539NAU + NM3539M) 

TEM4044 = (-0.0083 + 0.01717 + 0.41973 + RNM4044MAX-0.50 * 0.0062 - 0.418 * RILEM4044 - 0.40 * (REM4044_A + RM4044D)) 

 * (EM4044 * REM4044_M * REM2_4044 - EM4044AU - EM4044NAU + NM4044M) 
106 

TEM4549 = (-0.0026 - 0.00292 + 0.52707 + RNM4549MAX-0.50 * 0.0010 - 0.410 * RILEM4549 -0.50 * (REM4549_A + RM4549D)) 

 * (EM4549 * REM4549_M * REM2_4549 - EM4549AU-EM4549NAU + NM4549M) 

TEM5054 = (-0.0008 + 0.02301 + 0.53226 + RNM5054MAX - 0.50 * 0.0025 - 0.395 * RILEM5054 -0.50 * (REM5054_A + RM5054D)) 

 * (EM5054 * REM5054_M * REM2_5054 -EM5054AU-EM5054NAU + NM5054M) 

TEM5559 = (-0.0010 - 0.00842 + 0.46888 + RNM5559MAX - 0.50 * 0.0042 - 0.356 * RILEM5559 -0.40 * (REM5559_A + RM5559D)) 

 * (EM5559 * REM5559_M * REM2_5559 -EM5559AU-EM5559NAU + NM5559M) 

TEM6064 = (-0.0030 + 0.04966 + 0.59056 + RNM6064MAX - 0.50 * 0.0051 - 0.248 * RILEM6064 - 0.50 * (REM6064_A + RM6064D)) 

 * (EM6064 * REM6064_M * REM2_6064 -EM6064AU-EM6064NAU) 

TEM6569 = (-0.82949 * REM6569_A + 0.10116 + 1.55172) * (EM6569 * REM6569_M * REM2_6569 - EM6569AU - EM6569NAU) 

TEM70O = (0.01973 * 96 - 0.34903) * (EM70O* REM70O_M * REM2_70O-EM70OAU-EM70ONAU) 

TEM16O = TEM1617 + TEM1819 + TEM2024 + TEM2529 + TEM3034 + TEM3539 + TEM4044 + TEM4549 + TEM5054 + TEM5559 + 

TEM6064 + TEM6569 + TEM70O 

 

Female Disaggregates Aged 16 and Over 

TEF1617 = (0.0106 - 1.52661 * REF1617_A - 0.02280 + 1.17229 + RNF1617MAX + 0.5 * 0.0631 - 0.161 * RILEF1519) * (EF1617 

 * REF1617_M * REF2_1617 - EF1617AU - EF1617NAU + NF1617M) 

TEF1819 = (0.0166 - 0.56521 * REF1819_A + 0.04837 + 0.85527 + RNF1819MAX-0.5 * 0.0631 - 0.252 * RILEF1519) * (EF1819 

 * REF1819_M * REF2_1819 - EF1819AU - EF1819NAU + NF1819M) 

TEF2024 = (0.0202 + 0.02418 + 0.89686 + RNF2024MAX - 0.50 * 0.0349 - 0.318 * RILEF2024 - 0.90 * (REF2024_A + RF2024D)) 

 * (EF2024 * REF2024_M * REF2_2024 - EF2024AU - EF2024NAU + NF2024M) 

TEF2529 = (0.0185 + 0.03554 + 0.68431 + RNF2529MAX - 0.50 * 0.0378 - 0.342 * RILEF2529 - 0.70 * (REF2529_A + RF2529D)) 

 * (EF2529 * REF2529_M * REF2_2529 - EF2529AU - EF2529NAU + NF2529M) 

TEF3034 = (0.0156 + 0.00488 + 0.47083 + RNF3034MAX - 0.50 * 0.0465 - 0.340 * RILEF3034 - 0.45 * (REF3034_A + RF3034D)) 

 * (EF3034 * REF3034_M * REF2_3034 - EF3034AU - EF3034NAU + NF3034M) 

TEF3539 = (0.0156 + 0.000796 + 0.41423 + RNF3539MAX - 0.50 * 0.0318 - 0.343 * RILEF3539 - 0.40 * (REF3539_A + RF3539D)) 

 * (EF3539 * REF3539_M * REF2_3539 - EF3539AU - EF3539NAU + NF3539M) 

TEF4044 = (0.0127 + 0.00312 + 0.35298 + RNF4044MAX - 0.50 * 0.0135 - 0.353 * RILEF4044 - 0.35 * (REF4044_A + RF4044D)) 

 * (EF4044 * REF4044_M * REF2_4044 - EF4044AU - EF4044NAU + NF4044M) 

TEF4549 = (0.0064 + 0.00138 + 0.40080 + RNF4549MAX - 0.50 * 0.0086 - 0.358 * RILEF4549 - 0.40 * (REF4549_A + RF4549D)) 

 * (EF4549 * REF4549_M * REF2_4549 - EF4549AU - EF4549NAU + NF4549M) 

TEF5054 = (0.0037 + 0.01202 + 0.39021 + RNF5054MAX - 0.50 * 0.0089 - 0.336 * RILEF5054 - 0.40 * (REF5054_A + RF5054D)) 

 * (EF5054 * REF5054_M * REF2_5054 - EF5054AU - EF5054NAU + NF5054M) 

TEF5559 = (0.0034 + 0.03036 + 0.32074 + RNF5559MAX - 0.50 * 0.0094 - 0.280 * RILEF5559 - 0.30 * (REF5559_A + RF5559D)) 

 * (EF5559 * REF5559_M * REF2_5559 - EF5559AU - EF5559NAU + NF5559M) 

TEF6064 = (0.0030 + 0.02068 + 0.49318 + RNF6064MAX - 0.50 * 0.0115 - 0.176 * RILEF6064 - 0.45 * (REF6064_A + RF6064D)) 

 * (EF6064 * REF6064_M * REF2_6064 - EF6064AU - EF6064NAU) 

TEF6569 = 1.42 * (EF6569 * REF6569_M * REF2_6569 - EF6569AU - EF6569NAU) 

TEF70O = (0.92002 * TEM70O / (EM70O* REM70O_M * REM2_70O - EM70OAU - EM70ONAU) + 0.12035) * (EF70O * REF70O_M 

* REF2_70O-EF70OAU-EF70ONAU) 

TEF16O = TEF1617 + TEF1819 + TEF2024 + TEF2529 + TEF3034 + TEF3539 + TEF4044 + TEF4549 + TEF5054 + TEF5559 + 

TEF6064 + TEF6569 + TEF70O 

Self-Employed Only 

SEOCMB = 0.039 * (TEFC_N_N + TESL_N_N + EPRRB) 

SEOCMBL1 = 0.039 * (TEFC_N_N.1 + TESL_N_N.1 + EPRRB.1) 

SEO = (SEO.1 * (EAS + ENAS) / (EAS.1 + ENAS.1) + (SEOCMB - SEOCMBL1)) * MULTSEO 

Combination Workers 

CMB_TOT = ((-0.01468 + 0.06227 * RTP.1 -0.0008) * WSWA - SEOCMB) * MULTCMB 

CSW_TOT = SEO + CMB_TOT 

AW_CMBTOT = 1.4953 * ACWA 

W_CMBTOT = AW_CMBTOT * CMB_TOT 

CMB_WRELMAX = TAXMAX/AW_CMBTOT 

CMB Wage Andover Curve 

CMB_WAO1 = IF (CMB_WRELMAX < 0.0543009) 

 THEN 1 - 0.722659 * CMB_WRELMAX0.65 - 0.461913 * CMB_WRELMAX0.8

 ELSE IF (CMB_WRELMAX<0.1086018) 

 THEN -1.02884 * CMB_WRELMAX0.6 + 0.324761 * CMB_WRELMAX1.6 + 1.02015 

 ELSE IF (CMB_WRELMAX < 0.1629027) 

 THEN -0.906607 * CMB_WRELMAX0.7 + 0.947662 

 ELSE IF (CMB_WRELMAX < 0.2172037) 
107 

 THEN -0.813951 * CMB_WRELMAX0.55 + 0.991722 

 ELSE IF (CMB_WRELMAX < 0.3258055) 

 THEN -0.755135 * CMB_WRELMAX0.55 + 0.964593 

 ELSE 0 

 

CMB_WAO2 = IF (CMB_WRELMAX < 0.5430091) 

 THEN -0.649755 * CMB_WRELMAX0.6 + 0.886467 

 ELSE IF (CMB_WRELMAX < 0.7059119) 

 THEN -0.573205 * CMB_WRELMAX0.7 + 0.810122 

 ELSE IF (CMB_WRELMAX < 0.9231155) 

 THEN - 5.22264 * CMB_WRELMAX0.06 + 5.47514 

 ELSE IF (CMB_WRELMAX < 1.0860183) 

 THEN - 2.02619 * CMB_WRELMAX0.15 + 2.27963 

 ELSE IF (CMB_WRELMAX < 1.5204256) 

 THEN 0.605192 * EXP (-0.2 * CMB_WRELMAX) - 0.827158 * EXP (-0.8 * CMB_WRELMAX) 

+ 1.52918 * EXP (- 1.5 * CMB_WRELMAX) - 0.212269 

 ELSE 0 

CMB_WAO3 = IF (CMB_WRELMAX < 1.8462311) 

 THEN 0.19139 * EXP (-0.6 * CMB_WRELMAX) + 0.764408 * EXP (- 1.8 * CMB_WRELMAX) + 0.0194903 

 ELSE IF (CMB_WRELMAX < 2.3077888) 

 THEN 0.12964 * EXP (-0.5 * CMB_WRELMAX) + 0.644861 * EXP (- 1.5 * CMB_WRELMAX) + 0.0183343 

 ELSE IF (CMB_WRELMAX < 2.9865502) 

 THEN 0.361318 * EXP (-0.8 * CMB_WRELMAX) + 0.0219491 

 ELSE IF (CMB_WRELMAX < 4.3440731) 

 THEN 0.193202 * EXP (-0.45 * CMB_WRELMAX) + 0.00425171 

 ELSE IF (CMB_WRELMAX<5.4300913) 

 THEN 0.0560412 * EXP (-0.25 * CMB_WRELMAX) +0.311286 * EXP (-0.8 * 

CMB_WRELMAX) + 0.00297316 

 ELSE 0 

CMB_WAO4 = IF (CMB_WRELMAX < 13.5752283) 

 THEN 0.0995677 * EXP (-0.32 * CMB_WRELMAX) + 0.00355234 

 ELSE IF (CMB_WRELMAX < 21.7203653) 

 THEN 0.041159 * EXP (-0.19 * CMB_WRELMAX) + 0.00156765 

 ELSE IF (CMB_WRELMAX < 678.7614168) 

 THEN 0.265022 * CMB_WRELMAX (-1.555) 

 ELSE 0 

CMB_WAO = IF (CMB_WRELMAX < 0.3258055) 

 THEN CMB_WAO1 

 ELSE IF (CMB_WRELMAX < 1.5204256) 

 THEN CMB_WAO2 

 ELSE IF (CMB_WRELMAX < 5.4300913) 

 THEN CMB_WAO3 

 ELSE CMB_WAO4 

 

CMB = (1 - (CMB_WAO - 0.019)) * CMB_TOT 

CSW = SEO + CMB 

SEOCMB_HI = 0.039 * (TEFC_N_N + TESL_N_N_HI) 

SEO_HI = SEO - SEOCMB_HI 

CMB_HI = CMB_TOT + SEOCMB_HI 

CSW_HI = SEO_HI + CMB_HI 

NIPA Wages 

Private Residual Sector 

WSDPB = WSDP – WSPH – WSPF – WSPRRB – TIPS_SR 

TIPS_SR = (0.000508328 * RTP - 0.000481700) * GDP * 1.26393 
108 

OASDI Wages 

Covered Employment and Wages – Federal Civilian Government 

TEFC = (TEFC.1 / EGGEFC.1) * EGGEFC 

TEFC_N = IF (CSRS.1 > 0) THEN TEFC_N.1/CSRS.1 * CSRS - TEFC_N_SW ELSE 0 

TEFC_N_N = TEFC_N * 0.86 

TEFC_N_O = (TEFC_N - TEFC_N_N) 

TEFC_O = (TEFC - TEFC_N) 

WEFC = (WEFC.1 / WSGGEFC.1) * WSGGEFC 

WEFC_O = (WEFC -WEFC_N) * ADJ_FSA_FC 

Covered Employment and Wages - State and Local Govt. 

TESL = (TESL.1/EGGESLMAX.1) * EGGESLMAX 

TESL_O = (TESL_O.1/TESL.1) * TESL 

TESL_N = (TESL-TESL_O) 

TESL_N_O = (TESL_N_O_HI + TESL_N_O_NHI) 

TESL_N_O_HI = (TESL_N - TESL_N_O_NHI - TESL_N_N_NHI) * CER_MQGE_O 

TESL_N_O_NHI = (TESL_N_O_NHI_S + TESL_N_O_NHI_E + TESL_N_O_NHI_NS) 

TESL_N_S = TESL_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + NM2024.1) 

TESL_N_E = TESL_N_E.1 * (TESL / TESL.1) 

TESL_N_O_NHI_S = TESL_N_S * (TESL_N_O_NHI_S.1/TESL_N_S.1) 

TESL_N_O_NHI_E = TESL_N_E * 0.6 

TESL_N_O_NHI_NS = TESL_N_O_NHI_NS.1 * ESR_NS 

TESL_N_N = (TESL_N - TESL_N_O) 

TESL_N_N_HI = (TESL_N_N - TESL_N_N_NHI) 

TESL_N_N_NHI = (TESL_N_N_NHI_S + TESL_N_N_NHI_E + TESL_N_N_NHI_NS) 

TESL_N_N_NHI_S = (TESL_N_S - TESL_N_O_NHI_S) 

TESL_N_N_NHI_E = (TESL_N_E - TESL_N_O_NHI_E) 

TESL_N_N_NHI_NS = TESL_N_N_NHI_NS.1 * ESR_NS 

WESL = (WESL.1/WSGGESL.1) * WSGGESL 

WESL_O = (WESL_O.1/WSGGESL.1) * WSGGESL 

WESL_N = (WESL - WESL_O) 

WESL_N_HI = (WESL_N - WESL_N_NHI) 

WESL_N_NHI = (WESL_N_NHI_S + WESL_N_NHI_E + WESL_N_NHI_NS) 

WESL_N_NHI_S = WESL_N_NHI_S.1 * (TESL_N_S/TESL_N_S.1) * (AWSGGESL/AWSGGESL.1) 

WESL_N_NHI_E = WESL_N_NHI_E.1 * (TESL_N_E/TESL_N_E.1) * (AWSGGESL/AWSGGESL.1) 

RAWR_NS = IF (AWR_NS = 0) THEN 0 ELSE AWR_NS/AWR_NS.1 

WESL_N_NHI_NS = IF (ESR_NS = 0) THEN 0 ELSE WESL_N_NHI_NS.1 * (TESL_N_O_NHI_NS + TESL_N_N_NHI_NS) / 

 (TESL_N_O_NHI_NS.1 + TESL_N_N_NHI_NS.1) * (AWSGGESL/AWSGGESL.1) * RAWR_NS 

Self-Employed Earnings Sector 

Covered SENE 

CSE_TOT = (YF +YNF) / (YF.1 + YNF.1) * CSE_TOT.1 

CSE_CMB_N = (CSE_TOT / (CMB_TOT + SEO)) / (CSE_TOT.1 / (CMB_TOT.1 + SEO.1)) * (CSE_CMB_N.1 / (CMB_TOT.1 - 

CMB.1)) * (CMB_TOT - CMB) 

CSE = CSE_TOT - CSE_CMB_N 

ACSE_SEO = (CSE_TOT / (SEO + 0.416488 * CMB_TOT)) 

ACSE_CMB_TOT = 0.416488 * ACSE_SEO 

CSE_SEO = ACSE_SEO * SEO 

CSE_CMB_TOT = ACSE_CMB_TOT * CMB_TOT 

CSE_CMB = CSE_CMB_TOT - CSE_CMB_N 

ACSE_CMB = CSE_CMB/CMB 

Present Law OASDI and HI Covered Wages and Earnings 

WSGMLC = CML * WSGFM 

WSGFCA = WEFC_O 

CFCA = WSGFCA/WSGGEFC 

CSLHI = (WESL_O+WESL_N_HI)/WSGGESL 

WSGSLCA = WESL_O 

WSPH_O = CPH * WSPH 

WSPF_O = WSPF_O.1 * WSPF/WSPF.1 
109 

CPF = WSPF_O/WSPF 

WSPRR_O = CPRR * WSPRRB 

CPB_ILL = (CPB) * (WSWA* 0.86 - LOST_MF) / (WSWA * 0.86 + LOST_MF) + (1.5 * 0.5) * (2.0 * LOST_MF) / (WSWA * 0.86 + 

LOST_MF) 

CPB_ADJ = IF REAL_ACW_DYR = 0 

 THEN CPB_ILL 

 ELSE (((REAL_ACW_D + PCH (CPIW_U))/100 *ACWA.1 + ACWA.1) * WSWA - WSPH_O - WSPF_O - WSPRR_O -

TIPS_SR - WSGSLCA – WSGFCA - WSGMLC)/WSDPB 

WSPB_O = CPB_ADJ * WSDPB 

WSPC = WSPH_O + WSPF_O + WSPRR_O + TIPS_SR + WSPB_O 

CP = WSPC/WSDP 

WSCA = (WSPC + WSGSLCA + WSGFCA + WSGMLC) 

COVERNA = (WSCA + CSE) 

ACWA = WSCA/WSWA 

ASE = CSE/CSW 

ASEHI = CSE_TOT/CSW_HI 

ACEA = COVERNA/TCEA 

ACSLW = WESL_O/TESL_O * MULTACSLW 

ACMW = ACMW.1 * AWSGFM/AWSGFM.1 * CML/CML.1 

ACFCW = WEFC_O/TEFC_O 

ACFMW = ACFMW.1 * (AIW.1/AIW.3)0.5

TEPH_N = ENAWPH * (1 -CPH) 

TEP_N_N_S = TEP_N_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + NM2024.1) 

TCEA = (TE - TEPH_N – EPRRB - TEP_N_N_S - TEPO_N - TESL_N_N_NHI_S - TESL_N_N_NHI_E - TESL_N_N_NHI_NS - 

TESL_N_N_HI - TEFC_N_N) 

WSWA = (TCEA-SEO) 

Present Law HI Covered Wages and Earnings 

WSCAHI_ADD = WSCA * WSCAHI_ADD.1/WSCA.1 

TCEAHI = (TCEA + TEFC_N_N + TESL_N_N_HI) 

WSWAHI = TCEAHI - SEO_HI 

WSCAHI = WSCA + WEFC_N + WESL_N_HI + WSCAHI_ADD 

ACWAHI = WSCAHI/WSWAHI 

COVERNHI = WSCAHI + CSE_TOT 

ACEAHI = COVERNHI/TCEAHI 

Complete Coverage concepts 

WSWC = (WSWAHI + TEPH_N + EPRRB + TEP_N_N_S + TEPO_N + TESL_N_N_NHI) + LOST_MF 

ACWC = WSD/WSWC 

AIW = IF AIW_GR_YR = 0 

 THEN AIW.1 *ACWC/ACWC.1 * MULTAIW 

 ELSE AIW.1 * (1 +AIW_GR/100) 

Taxable Maximums 

 RAIW = AIW.2/AIWBASE 

TAXMAXB1 = RAIW * TMAXBASE * 1000/300 

TAXMAXB2 = IF TAXMAXB1 - ROUND (TAXMAXB1) >= 0.5 

 THEN ROUND (TAXMAXB1) +1 

 ELSE ROUND (TAXMAXB1) 

TAXMAXB3 = IF TAXMAXB2 < TAXMAX.1 

 THEN TAXMAX.1 * 1000/300 

 ELSE TAXMAXB2 

TAXMAX = IF BENINC.1 <= 0.001 

 THEN TAXMAX.1 

 ELSE 300 * TAXMAXB3/1000 

Deemed Military Wage Credits 

EDMILAF = EDMIL * 1.1 
110 

EDMILT = (2.00303 - 50.7517/YEAR) * EDMILAF 

EDMILR = EDMILT – EDMILAF 

MWC_ED_O = 1.2 * EDMILAF * 0.997 

MWC_ED_HI = 1.2 * EDMILAF 

AMWC_GO2 = MIN (1.2, AWSGFM * (2/52) * (1/3)) 

MWC_EDR_O = AMWC_GO2 * EDMILR * (1 - 0.017) 

MWC_EDR_HI = MWC_EDR_O + ((1.2 +AMWC_GO2) * 0.5) * EDMILR * 0.017 

MWC_O = MWC_ED_O + MWC_EDR_O 

MWC_HI = MWC_ED_HI+ MWC_EDR_HI 

2-4 Effective Taxable Payroll (TAXPAY)

2-4.1 Ratio of taxable employee to total covered OASDI wages (RWTEE) 

IF(RM.LT.0.439103091)THEN 

 RWTEE=RM-(0.26651/1.5)*RM**1.5-(0.388274/1.9)*RM**1.9 

ELSE IF(RM.LT.1.313896269)THEN 

 RWTEE=(1.17877/1.5)*RM**1.5-(2.9291/0.68)*DEXP(-0.68*RM)-2.31401*RM+4.327630386 

ELSE IF(RM.LT.2.570433485)THEN 

 RWTEE=-(0.0202216/0.25)*DEXP(-0.25*RM)-(1.329/1.4)*DEXP(-1.4*RM)+0.00944271*RM+0.904661863 

ELSE IF(RM.LT.4.418783378)THEN 

 RWTEE=-(0.0654817/0.35)*DEXP(-0.35*RM)-(1.415/1.51)*DEXP(-1.51*RM)+0.000676576*RM+0.954098019 

ELSE IF(RM.LT.14.73231225)THEN 

 RWTEE=-(0.0110626/0.15)*DEXP(-0.15*RM)-(0.0472319/0.45)*DEXP(-0.45*RM)-(0.257195/0.95)*DEXP(- 

0.95*RM)+0.000367645*RM+0.970880621 

ELSE 

 RWTEE=-(0.179935/0.75)*RM**(-0.75)+0.999970738 

END IF 

Where 

 RM = OASDI taxable maximum / average covered OASDI wage 

 RWTEE = Ratio if OASDI taxable employee to covered wages 

2-4.2 Taxable employee OASDI wages (WTEE) 

WTEE = RWTEE * WSC 

Where 

 RWTEE = Ratio of OASDI taxable employee to covered wages 

 WSC = OASDI total covered wages 

 WTEE = OASDI taxable employee wages 

2-4.3 Ratio of multi-employer refund wages to total OASDI covered wages (RMER) 

RMER = ( MER(-1) / WSC(-1) ) - 0.03217 * ( RWTEE – RWTEE(-1) ) - 0.00024*( RU - RU(-1) ) 

Where 

 MER(-1) = Multi-employer refund wages in prior year 

 RMER = Ratio of multi-employer refund wages to total OASDI covered wages 

 RU = Annual average civilian unemployment rate 
111 

 RWTEE = Ratio of OASDI taxable employee to covered wages 

 WSC(-1) = OASDI total covered wages in prior year 

2-4.4 Multi-employer refund wages (MER) 

MER = RMER * WSC 

Where 

 MER = OASDI multi-employer refund wages 

 RMER = Ratio of multi-employer refund wages to total OASDI covered wages 

 WSC = OASDI total covered wages 

2-4.5 Taxable employer OASDI wages (WTER) 

WTER = WTEE + MER 

Where 

 MER = OASDI multi-employer refund wages 

 WTEE = OASDI taxable employee wages 

 WTER = OASDI taxable employer wages 

2-4.6 Ratio of taxable to covered self-employment earnings (RSET) 

Preliminary 

BASECT = 47831.98 

BASECW = 36831.79 

BASEO = 23448.56 

Self-employed only 

SECSEO = CSE - SECCMB 

ASESEO = SECSEO / SEO 

ASEO96 = ASESEO(1996) 

ASESEO = ASESEO * BASEO / ASEO96 

O = TAXMAX / ASESEO 

IF(O.LT.0.021323273)THEN 

 OTR=O-(401.8/3.8)*O**3.8 

ELSE IF(O.LT.0.170586184)THEN 

 OTR=(12.6861/1.1)*O**1.1-(10.7855/1.15)*O**1.15-(.208585/1.9)*O**1.9-1.58102*O-.0000212479 

ELSE IF(O.LT.0.938224014)THEN 

 OTR=-(2.03924/2.5)*DEXP(-2.5*O)+(2.52113/1.6)*O**1.6-(1.11979/2.2)*O**2.2-1.33547*O+.825500132 

ELSE IF(O.LT.1.705861843)THEN 

 OTR=-(.375957/.3)*DEXP(-.3*O)-(.642976/2.3)*DEXP(-2.3*O)-.108863*O+1.555087525 

ELSE IF(O.LT.2.302913488)THEN 

 OTR=-(.248596/.25)*DEXP(-.25*O)-(1.003/2.2)*DEXP(-2.2*O)-.0565126*O+1.368881905 

ELSE IF(O.LT.3.624956417)THEN 

 OTR=-(.207896/.15)*DEXP(-.15*O)-(3.99112/2.5)*DEXP(-2.5*O)-.0699402*O+1.823982598 
112 

ELSE IF(O.LT.5.970516451)THEN 

 OTR=-(.110423/.2)*DEXP(-.2*O)-(.571353/1.25)*DEXP(-1.25*O)-.00842494*O+1.068478626 

ELSE IF(O.LT.12.79396382)THEN 

 OTR=-(.0631844/.2)*DEXP(-.2*O)-(.242063/.65)*DEXP(-.65*O)+.0011163*O+.947373543 

ELSE IF(O.LT.21.32327304)THEN 

 OTR=-(.0218297/.13)*DEXP(-.13*O)-(.0876571/.32)*DEXP(-.32*O)+.000522742*O+.966817185 

ELSE IF(O.LT.213.2327304)THEN 

 OTR=-(2.86725/1.36)*O**(-1.36)+1.00002612 

ELSE 

 OTR=1D0 

END IF 

SETSEO=OTR*SECSEO 

OASDI taxable wages of workers with both wages and self-employment earnings 

AWSCMB=WSCCMB/CMBNT 

AWSCMB96=AWSCMB(1996) 

AWSCMB=AWSCMB*BASECW/AWSCMB96 

CW=TAXMAX/AWSCMB 

IF(CW.LT.0.0543009)THEN 

 CWTR=CW-(.722659/1.65)*CW**1.65-(.461913/1.8)*CW**1.8 

ELSE IF(CW.LT.0.1086018)THEN 

 CWTR=-(1.02884/1.6)*CW**1.6+(.324761/2.6)*CW**2.6+1.02015*CW-.0000130669 

ELSE IF(CW.LT.0.1629027)THEN 

 CWTR=-(.906607/1.7)*CW**1.7+.947662*CW+.002059472 

ELSE IF(CW.LT.0.2172037)THEN 

 CWTR=-(.813951/1.55)*CW**1.55+.991722*CW+.002022215 

ELSE IF(CW.LT.0.3258055)THEN 

 CWTR=-(.755135/1.55)*CW**1.55+.964593*CW+.004355898 

ELSE IF(CW.LT.0.5430091)THEN 

 CWTR=-(.649755/1.6)*CW**1.6+.886467*CW+.011658928 

ELSE IF(CW.LT.0.7059119)THEN 

 CWTR=-(.573205/1.7)*CW**1.7+.810122*CW+.019653316 

ELSE IF(CW.LT.0.9231155)THEN 

 CWTR=-(5.22264/1.06)*CW**1.06+5.47514*CW-.053844798 

ELSE IF(CW.LT.1.0860183)THEN 

 CWTR=-(2.02619/1.15)*CW**1.15+2.27963*CW-.023407805 

ELSE IF(CW.LT.1.5204256)THEN 

 CWTR=-(.605192/.2)*DEXP(-.2*CW)+(.827158/.8)*DEXP(-.8*CW)-(1.52918/1.5)*DEXP(-1.5*CW)-

.212269*CW+2.946985922 

ELSE IF(CW.LT.1.8462311)THEN 

 CWTR=-(.191389/.6)*DEXP(-.6*CW)-(.764408/1.8)*DEXP(-1.8*CW)+.0194903*CW+.719848486 

ELSE IF(CW.LT.2.3077888)THEN 

 CWTR=-(.12964/.5)*DEXP(-.5*CW)-(.644861/1.5)*DEXP(-1.5*CW)+.0183343*CW+.731280763 

ELSE IF(CW.LT.2.9865502)THEN 

 CWTR=-(.361318/.8)*DEXP(-.8*CW)+.0219491*CW+.698954858 

ELSE IF(CW.LT.4.3440731)THEN 

 CWTR=-(.193202/.45)*DEXP(-.45*CW)+.00425171*CW+.82237055 

ELSE IF(CW.LT.5.4300913)THEN 

 CWTR=-(.0560412/.25)*DEXP(-.25*CW)-(.311286/.8)*DEXP(-.8*CW)+.00297316*CW+.854848493 

ELSE IF(CW.LT.13.5752283)THEN 

 CWTR=-(.0995677/.32)*DEXP(-.32*CW)+.00355234*CW+.843717127 
113 

ELSE IF(CW.LT.21.7203653)THEN 

 CWTR=-(.041159/.19)*DEXP(-.19*CW)+.00156765*CW+.883046178 

ELSE IF(CW.LT.678.7614168)THEN 

 CWTR=-(.265022/.555)*CW**(-.555)+1.000103517 

ELSE 

 CWTR=1D0 

END IF 

WSTCMB=CWTR*WSCCMB 

OASDI taxable earnings of workers with both wages and self-employment earnings 

TECCMB=SECCMB+WSCCMB 

ATECMB=TECCMB/CMBNT 

ATECMB96=ATECMB(1996) 

ATECMB=ATECMB*BASECT/ATECMB96 

CT=TAXMAX/ATECMB 

IF(CT.LT.0.0209065)THEN 

 CTTR=CT-(58.6063/3.5)*CT**3.5 

ELSE IF(CT.LT.0.1254391)THEN 

 CTTR=(.320825/1.4)*CT**1.4-(1.90732/2)*CT**2+.967979*CT+.000050526-.00000622 

ELSE IF(CT.LT.0.3345042)THEN 

 CTTR=-(1.77251/1.9)*CT**1.9+(1.18333/2.8)*CT**2.8+1.11299*CT-.003813108-.00000622 

ELSE IF(CT.LT.0.7108215)THEN 

 CTTR=-(.246427/1.35)*CT**1.35-(1.24155/1.8)*CT**1.8+(.55025/2.3)*CT**2.3+1.16953*CT-.001078375-

.00000622 

ELSE IF(CT.LT.0.7944476)THEN 

 CTTR=(3.15997/1.4)*CT**1.4-(4.21829/1D0)*DEXP(-1*CT)-4.46998*CT+4.300993015-.00000622 

ELSE IF(CT.LT.1.0453257)THEN 

 CTTR=(.55343/1.6)*CT**1.6-(1.76791/1.2)*DEXP(-1.2*CT)-.845578*CT+1.479639989-.00000622 

ELSE IF(CT.LT.1.8815863)THEN 

 CTTR=-(.360108/.3)*DEXP(-.3*CT)-(1.24485/2.7)*DEXP(-2.7*CT)-.110244*CT+1.566702582-.00000622 

ELSE IF(CT.LT.3.7631726)THEN 

 CTTR=-(.262138/.6)*DEXP(-.6*CT)+(.208323/1.9)*DEXP(-1.9*CT)-(2.27562/2.7)*DEXP(-

2.7*CT)+.00933849*CT+ 

 .799685739-.00000622 

ELSE IF(CT.LT.4.1813029)THEN 

 CTTR=-(.26942/.6)*DEXP(-.6*CT)+(.266252/1.7)*DEXP(-1.7*CT)+.00905196*CT+.80182568-.00000622 

ELSE IF(CT.LT.10.4532574)THEN 

 CTTR=-(.0592625/.25)*EXP(-.25*CT)-(.541514/1)*DEXP(-1*CT)+.00174723*CT+.88757547-.00000622 

ELSE IF(CT.LT.18.8158632)THEN 

 CTTR=-(.0610012/.25)*DEXP(-.25*CT)+.00174344*CT+.888109189-.00000622 

ELSE IF(CT.LT.522.6628676)THEN 

 CTTR=-(.21993/.5455)*CT**(-.5455)+1.000030393-.00000622 

ELSE 

 CTTR=1D0 

END IF 

TETCMB=CTTR*TECCMB 

SETCMB=TETCMB-WSTCMB 

Ratio OASDI taxable to covered self-employment earnings 

RSET=(SETCMB+SETSEO)/CSE 
114 

Where 

 ASEO96 = Average self-employment earnings of workers with no OASDI taxable 

wages in 1996 

 ATECMB = Average OASDI covered earnings of workers with both OASDI covered 

wages and self-employment earnings 

 ATECMB96 = Average OASDI covered earnings of workers with both OASDI covered 

wages and self-employment earnings in 1996 

 AWSCMB = Average OASDI covered wage of workers with both wages and selfemployment earnings 

 AWSCMB96 = Average OASDI covered wage of workers with both wages and selfemployment earnings in 1996 

 ASESEO = Average self-employment earnings of workers with no OASDI taxable 

wages 

 AWSCMB = Average OASDI covered wage of workers with both wages and selfemployment earnings 

 BASECT = Average total earnings of workers with both self-employment earnings 

and wages in 1% sample data for 1996 used to 

produce equations 

 BASECW = Average OASDI covered wages of workers with both self-employment 

earnings and wages in 1% sample data for 1996 

 used to produce equations 

 BASEO = Average self-employment earnings of workers with no OASDI taxable 

wages in 1% sample data for 1996 used to 

 produce equations 

 CMBNT = Number or workers with both OASDI taxable wages and self-employment 

earnings 

 CSE = OASDI covered self-employment earnings 

 CT = Ratio OASDI taxable maximum to average earnings of workers with both 

self-employment earnings and OASDI 

 taxable wages 

 CW = Ratio OASDI taxable maximum to average self-employment earnings of 

workers with both self-employment earnings 

 and OASDI taxable wages 

 CTTR = Ratio of OASDI taxable to covered earnings for workers with both wages 

and self-employment earnings 

 CWTR = Ratio of OASDI taxable to covered wages for workers with both wages 

and self-employment earnings 

 O = Ratio OASDI taxable maximum to average self-employment earnings of 

workers with no OASDI taxable wages 

 OTR = Ratio of OASDI taxable self-employment to covered earnings for workers 

with no OASDI taxable wages 

 SECCMB = OASDI covered self-employment earnings of workers with both selfemployment earnings and OASDI taxable wages 
115 

 SECSEO = OASDI covered self-employment earnings of workers with no OASDI 

taxable wages 

 SEO = Number or workers with OASDI covered self-employment earnings and 

no OASDI taxable wages 

 SETCMB = OASDI taxable self-employment earnings of workers with both OASDI 

taxable wages and self-employment earnings 

 SETSEO = OASDI taxable self-employment earnings of workers with no OASDI 

taxable wages 

 TAXMAX = OASDI taxable maximum 

 TECCMB = OASDI covered earnings of workers with both wages and self-employed 

earnings 

 TETCMB = OASDI taxable earnings of workers with both wages and self-employed 

earnings 

 WSCCMB = OASDI covered wages of workers with both wages and self-employed 

earnings 

 WSTCMB = OASDI taxable wages of workers with both wages and self-employed 

earnings 

2-4.7 OASDI taxable self-employment earnings (SET) 

SET = SETR * CSE 

Where 

 CSE = OASDI covered self-employment earnings 

 SET = OASDI taxable self-employment earnings 

 SETR = Ratio of OASDI taxable to covered self-employment earnings 

2-4.8 OASDI effective taxable payroll (ETP) 

ETP=WTER+SET-0.5*MER 

Where 

 ETP = OASDI effective taxable payroll 

 MER = OASDI multi-employer refund wages 

 SET = OASDI taxable self-employment earnings 

 WTER = Annual OASDI taxable employer wages 

2-4.9 OASDI taxable wage liability (WTL) 

WTL = WTER * TRW 

Where 

 TRW = OASDI combined employee-employer tax rate 

 WTL = Annual OASDI taxable wage liabilities 
116 

 WTER = Annual OASDI taxable employer wages 

2-4.10 OASDI taxable self-employment liability (SEL) 

SEL = SET * TRSE 

Where 

 SEL = OASDI taxable self-employment earnings liabilities 

 SET = OASDI taxable self-employment earnings 

 TRSE = OASDI self-employment tax rate 

2-4.11 OASDI quarterly taxable wage liability (WTLQ) 

Federal Civilian 

 Annual total wages (OASDI + MQGE) 

BAFCW = 34198.84 

AWCFC = WCFC / ECFC * BAFCW / AWCFCTOT97 

T=MAX/AWCFC 

IF(T.LT.0.014620379)THEN 

 FCTR=T-(1.04262/1.73)*T**1.73 

ELSE IF(T.LT.0.292407578)THEN 

 FCTR=-(1.22471/1.6)*T**1.6+(.826746/1.8)*DEXP(-1.8*T)+1.8535*T-.459368449 

ELSE IF(T.LT.0.760259704)THEN 

 FCTR=-(.635082/2D0)*T**2+(.604884/2.9)*T**2.9-(.403213/4.6)*T**4.6+.910343*T+.002291358 

ELSE IF(T.LT.1.228111829)THEN 

 FCTR=-(.162181/1.7)*T**1.7+(.143632/2.7)*T**2.7-(.312012/3.4)*T**3.4+.841165*T+.011332647 

ELSE IF(T.LT.1.520519407)THEN 

 FCTR=-(1.34084/3.5)*T**3.5+(1.09868/5D0)*T**5-(.404253/5.8)*T**5.8+1.17397*T-.222555715 

ELSE IF(T.LT.2.339260627)THEN 

 FCTR=(.671304/.5)*DEXP(-.5*T)-(3.27076/1.4)*DEXP(-1.4*T)+.126626*T+.353367869 

ELSE IF(T.LT.3.50889094)THEN 

 FCTR=(.0571643/.95)*DEXP(-.95*T)-(3.17633/1.8)*DEXP(-1.8*T)+.000623031*T+.996284293 

ELSE IF(T.LT.4.970928832)THEN 

 FCTR=-(12.3148/2.25)*DEXP(-2.25*T)+.0000698013*T+.999222265 

ELSE 

 FCTR=-(.0285502/2D0)*T**(-2D0)+1.00007094 

END IF 

WTFCTOT=FCTR*WCFC 

Where 

 AWCFC = Average covered Federal Civilian wages (OASDI plus MQGE) 

 AWCFCTOT97 = Average covered Federal Civilian wages (OASDI plus MQGE) for 

1997 
117 

 BAFCW = Average Federal Civilian wages (OASDI plus MQGE) in 1% sample 

data for 1997 used to produce equations 

 ECFC = Covered Federal Civilian employment (OASDI plus MQGE) 

 FCTR = Ratio of taxable to covered Federal Civilian wages (OASDI plus 

MQGE) 

 MAX = OASDI taxable maximum 

 T = Ratio of the OASDI taxable maximum to average covered Federal 

Civilian wages (OASDI plus MQGE) 

 WCFC = Covered Federal Civilian wages (OASDI plus MQGE) 

 WTFCTOT = Taxable Federal Civilian wages (OASDI plus MQGE) 

Annual MQGE wages 

BAFCW = 50147.72 

AWCFC = WCFC / ECFC * BAFCW / AWCFCHO97 

T = MAX / AWCFC 

IF(T.LT.0.019941085)THEN 

 FCTR=T-(0.0450661/1.47)*T**1.47 

ELSE IF(T.LT.0.099705424)THEN 

 FCTR=-(.0518044/1.9)*T**1.9-(.0368056/2.3)*T**2.3+.99479*T+.0000248091 

ELSE IF(T.LT.0.358939528)THEN 

 FCTR=-(.05907/1.25)*T**1.25-(.0746657/2.9)*T**2.9+1.02092*T-.00032173 

ELSE IF(T.LT.0.558350377)THEN 

 FCTR=-(2.4664/1.4)*T**1.4+(4.82919/2.3)*T**2.3-(3.97473/3)*T**3+1.83998*T-.026694932 

LSE IF(T.LT.0.797643395)THEN 

 FCTR=(.609091/2.1)*T**2.1-(1.16086/4)*T**4+.788373*T+.043208139 

ELSE IF(T.LT.1.196465093)THEN 

 FCTR=(2.35647/.4)*DEXP(-.4*T)-(3.87811/1.2)*DEXP(-1.2*T)-(1.1179/2.5)*DEXP(-2.5*T)+.738296*T2.83402534 

ELSE IF(T.LT.1.694992215)THEN 

 FCTR=-(.422884/1.3)*DEXP(-1.3*T)-(6.90241/3D0)*DEXP(-3*T)-.0229917*T+1.068147457 

ELSE IF(T.LT.2.592341034)THEN 

 FCTR=(.557032/1.2)*DEXP(-1.2*T)-(5.40739/2.2)*DEXP(-2.2*T)+.0102014*T+.960037325 

ELSE 

 FCTR=-(32.3187/3.5)*DEXP(-3.5*T)+1.000030482 

END IF 

WTFCHO=FCTR*WCFC 

Where 

 AWCFC = Average covered Federal Civilian MQGE wages 

 AWCFCHO97 = Average covered Federal Civilian MQGE wages for 1997 

 BAFCW = Average Federal Civilian MQGE wages in 1% sample data for 1997 

used to produce equations 

 ECFC = Covered Federal Civilian MQGE employment 

 FCTR = Ratio of taxable to covered Federal Civilian MQGE wages 

 MAX = OASDI taxable maximum 
118 

 T = Ratio of the OASDI taxable maximum to average covered Federal 

Civilian MQGE wages 

 WCFC = Covered Federal Civilian MQGE wages 

 WTFCHO = Taxable Federal Civilian MQGE wages 

Annual OASDI taxable wages 

WTFC = WTFCTOT – WTFCHO 

Where 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTFCHO = Taxable Federal Civilian MQGE wages 

 WTFCTOT = Taxable Federal Civilian wages (OASDI plus MQGE) 

Quarterly OASDI covered wages 

CFCQD(1) = .98357 * TCFCD(I,1) + FCPD(I,1) 

CFCQD(2) = .98909 * TCFCD(I,2) + FCPD(I,2) 

CFCQD(3) = 1.01833 * TCFCD(I,3) + FCPD(I,3) 

CFCQD(4) = 1.00814 * TCFCD(I,4) + FCPD(I,4) 

QWCFCOD(J) = CFCQD(J) * WTFC 

Where 

 CFCQD = Proportion of annual OASDI covered Federal Civilian wages paid in each 

quarter 

 FCPD = Payday variable for Federal Civilian wages based on calendar 

 I = Calendar year 

 J = Quarter 

 TCFCD = Proportion of annual NIPA Federal Civilian wages paid in each quarter 

 QWCFCOD = Quarterly OASDI covered Federal Civilian wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

Quarterly OASDI taxable wages 

IF(FCTR.LE.0.928)FCQD(2)=CFCQD(2)+.27522*(1.-FCTR)-.15127*(1.-FCTR)**2+.35146*(1.-FCTR)**3 

IF(FCTR.LE.0.993)THEN 

 FCQD(3)=CFCQD(3)+.28047*(1.-FCTR)-4.73021*(1.-FCTR)**2+25.3606*(1.-FCTR)**3-58.1741*(1.-FCTR)**4+45.1465*(1.-FCTR)**5 

 FCQD(4)=CFCQD(4)-.75095*(1.-FCTR)+3.65109*(1.-FCTR)**2-16.9355*(1.-FCTR)**3+23.9578*(1.-FCTR)**4 

END IF 

c First quarter is always 100 percent taxable. 

QWTFC(I,1)=QWCFC(I,1) 

IF(FCTR.LE.0.928)THEN 

c Compute taxable for 2nd-4th quarter. 

 FCQ=FCQD(2)+FCQD(3)+FCQD(4) 

 WTFC2=WTFC-QWTFC(I,1) 

 FCQD(2:4)=FCQD(2:4)/FCQ 

 QWTFC(I,2:4)=FCQD(2:4)*WTFC2 

ELSE IF(FCTR.LE.0.993)THEN 

c Second quarter covered is completely taxable. 
119 

 QWTFC(I,2)=QWCFC(I,2) 

 QWTFC(I,3)=FCQD(3)*WTFC 

 QWTFC(I,4)=WTFC-QWTFC(I,1)-QWTFC(I,2)-QWTFC(I,3) 

ELSE 

c Second and third quarter covered is completely taxable. 

 QWTFC(I,2)=QWCFC(I,2) 

 QWTFC(I,3)=QWCFC(I,3) 

 QWTFC(I,4)=WTFC-QWTFC(I,1)-QWTFC(I,2)-QWTFC(I,3) 

END IF 

Where 

 CFCQD = Proportion of annual OASDI covered Federal Civilian wages paid in each 

quarter 

 FCQ = Sum of proportions of annual OASDI covered Federal Civilian wages paid 

in each quarter for quarters two to four 

 FCQD = Proportion of annual OASDI taxable Federal Civilian wages paid in each 

quarter 

 FCTR = Ratio annual OASDI taxable to covered Federal Civilian wages 

 I = Calendar year 

 TCFCD = Proportion of annual NIPA Federal Civilian wages paid in each quarter 

 QWCFC = Quarterly OASDI covered Federal Civilian wages 

 QWTFC = Quarterly OASDI taxable Federal Civilian wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTFC2 = Total OASDI taxable Federal Civilian wages paid in quarters two to four 

 Quarterly OASDI taxable wage liabilities 

WTLQFCEE(I, J) = QWTFC(I, J) * TRWEE(I) 

WTLQFCER(I, J) = QWTFC(I, J) * TRWER(I) 

WTLQFC(I, J) = WTLQFCEE(I, J) + WTLQFCER(I, J) 

Where 

 I = Calendar year 

 J = Quarter 

 TRWEE = OASDI employee tax rate 

 TRWER = OASDI employer tax rate 

 WTLQFC = Quarterly OASDI taxable Federal Civilian combined employee-employer 

wage liabilities 

 WTLQFCEE = Quarterly OASDI taxable Federal Civilian employee wage liabilities 

 WTLQFCER = Quarterly OASDI taxable Federal Civilian employer wage liabilities 

Military wages 

 Annual OASDI taxable wages 

BACMW = 16439.95 

ACMW = AWCML * BACMW / AWCML97 
120 

T = MAX / ACMW 

IF(T.LT.0.060827432)THEN 

 MTR=T-(.712875/2)*T**2 

ELSE IF(T.LT.0.182482295)THEN 

 MTR=(.71197/1.8)*T**1.8-(1.59752/2D0)*T**2+.97587*T+0.000542413 

ELSE IF(T.LT.0.608274315)THEN 

 MTR=-(1.75026/2D0)*T**2+(2.86837/3D0)*T**3-(1.90346/4D0)*T**4+1.10056*T-.006441373 

ELSE IF(T.LT.1.094893767)THEN 

 MTR=-(.700864/1.4)*T**1.4-(.40042/3.3)*T**3.3+(.197091/4.1)*T**4.1+1.33615*T-.056637087 

ELSE IF(T.LT.1.703168082)THEN 

 MTR=(21.3527/.3)*DEXP(-.3*T)-(21.1277/0.5)*DEXP(-.5*T)+(2.73027/1.1)*DEXP(-1.1*T)+4.34833*T31.56802874 

ELSE IF(T.LT.2.311442397)THEN 

 MTR=-(33.3894/1.2)*T**1.2+(14.9436/1.6)*T**1.6-(2.58041/2.1)*T**2.1+21.3365*T-.872981629 

ELSE IF(T.LT.3.163026438)THEN 

 MTR=-(.076094/.3)*DEXP(-.3*T)-(1.59668/1.4)*DEXP(-1.4*T)-.0271355*T+1.182946986 

ELSE IF(T.LT.4.257920205)THEN 

 MTR=(.482918/1.5)*T**1.5-(9.21141/.9)*DEXP(-.9*T)+(25.93/1.5)*DEXP(-1.5*T)-1.14706*T+3.246003821 

ELSE 

 MTR=-(9.00723/1.8)*DEXP(-1.8*T)+1.000285789 

END IF 

WTML=MTR*WCML 

Where 

 ACMW = Average OASDI covered military wages adjusted for level used to 

produce equations 

 AWCML = Average OASDI covered military wages 

 AWCML97 = Average OASDI covered military wages in 1997 

 BACMW = Average OASDI covered military wages in 1% sample data for 1997 used 

to produce equations 

 MAX = OASDI taxable maximum 

 MTR = Ratio of OASDI taxable to covered military wages 

 T = Ratio of the OASDI taxable maximum to average covered military wages 

 WCML = Annual OASDI covered military wages 

 WTML = Annual OASDI taxable military wages 

Quarterly OASDI covered wages 

CMLQD(1)=.97978*TCMLD(I,1)*MLPD(I,1) 

CMLQD(2)=1.002*TCMLD(I,2)*MLPD(I,2) 

CMLQD(3)=1.02145*TCMLD(I,3)*MLPD(I,3) 

CMLQD(4)=.99689*TCMLD(I,4)*MLPD(I,4) 

QWCML=CMLQD(J)*WCML 

Where 

 CMLQD = Proportion of annual OASDI covered military wages paid in each quarter 

 I = Calendar year 
121 

 J = Quarter 

 MLPD = Payday variable for military wages based on calendar 

 QWCML = Quarterly OASDI covered military wages 

 TCMLD = Proportion of annual NIPA military wages paid in each quarter 

 WCML = Annual OASDI covered military wages 

Quarterly OASDI taxable wages 

T=MAX/AWCML 

IF(MLTR.LT.0.776)QML(1)=CMLQD(1)+.393565-.018307*T-3.44641/T+15.6381/T**2-40.0168/T**3+62.0449/T**4-57.525/T**5+30.2498/T**6-

7.8664/T**7+.674629/T**8 

IF(MLTR.LT.0.952)QML(2)=CMLQD(2)+.844748-.0401062*T-7.24247/T+32.4957/T**2-83.3328/T**3+129.374/T**4-122.526/T**5+68.2737/T**6-

20.1479/T**7+2.34289/T**8 

IF(MLTR.LT.0.985)QML(3)=CMLQD(3)-2.62266+.125592*T+22.5832/T-105.727/T**2+300.027/T**3-540.915/T**4+622.304/T**5-

441.658/T**6+175.722/T**7-29.8987/T**8 

IF(MLTR.LT.1.)QML(4)=CMLQD(4)+2.37295-.111565*T-21.1954/T+106.049/T**2-330.637/T**3+658.869/T**4-835.626/T**5+648.641/T**6-

279.392/T**7+50.9246/T**8 

IF(MLTR.LT.0.776)THEN 

 QWTML(I,1:4)=QML(1:4)*WTML 

ELSE IF(MLTR.LT.0.952)THEN 

 QWTML(I,1)=QWCML(I,1) 

 TOTWG1=WTML-QWTML(I,1) 

 Q1=QML(2)+QML(3)+QML(4) 

 QML(2:4)=QML(2:4)/Q1 

 QWTML(I,2:4)=QML(2:4)*TOTWG1 

ELSE IF(MLTR.LT.0.985)THEN 

 QWTML(I,1)=QWCML(I,1) 

 QWTML(I,2)=QWCML(I,2) 

 TOTWG1=WTML-QWTML(I,1)-QWTML(I,2) 

 Q1=QML(3)+QML(4) 

 QML(2:4)=QML(2:4)/Q1 

 QWTML(I,2:4)=QML(2:4)*TOTWG1 

ELSE IF(MLTR.LT.1.)THEN 

 QWTML(I,1)=QWCML(I,1) 

 QWTML(I,2)=QWCML(I,2) 

 QWTML(I,3)=QWCML(I,3) 

 QWTML(I,4)=WTML-QWTML(I,1)-QWTML(I,2)-QWTML(I,3) 

END IF 

Where 

 AWCML = Average OASDI covered military wages 

 CMLQD = Proportion of annual OASDI covered military wages paid in each quarter 

 MLTR = Ratio of OASDI taxable to covered military wages 

 MAX = OASDI taxable maximum 

 I = Calendar year 

 Q1 = Sum of proportions of annual OASDI taxable military wages paid in each 

quarter for last three or two quarters in year 

 QML = Proportion of annual OASDI taxable military wages paid in each quarter 

 QWCML = Quarterly OASDI covered military wages 

 QWTML = Quarterly OASDI taxable military wages 

 T = Ratio of the OASDI taxable maximum to average covered military wages 

 TOTWG1 = Annual OASDI taxable military wages for all quarters except first or first 

and second 

 WTML = Annual OASDI taxable military wages 

 Quarterly OASDI taxable wage liabilities 
122 

WTLQMLEE(I, J) = QWTML(I, J) * TRWEE(I) 

WTLQMLER(I, J) = QWTML(I, J) * TRWER(I) 

WTLQML(I, J) = WTLQMLEE(I, J) + WTLQMLER(I, J) 

Where 

 I = Calendar year 

 J = Quarter 

 TRWEE = OASDI employee tax rate 

 TRWER = OASDI employer tax rate 

 WTLQML = Quarterly OASDI taxable military combined employee-employer wage 

liabilities 

 WTLQMLEE = Quarterly OASDI taxable military employee wage liabilities 

 WTLQMLER = Quarterly OASDI taxable military employer wage liabilities 

Federal 

WCF = WCFC + WCML 

QWCF = QWCFC + QWCML 

WTF = WTFC + WTML 

QWTF = QWTFC + QWTML 

WTLQFEE(I,J) = QWTF(I,J) * TRWEE(I) 

WTLQFER(I,J) = QWTF(I,J) * TRWER(I) 

WTLQF(I,J) = WTLQFEE(I,J) + WTLQFER(I,J) 

Where 

 I = Calendar year 

 J = Quarter 

 QWCF = Quarterly OASDI covered Federal wages 

 QWCF C = Quarterly OASDI covered Federal Civilian wages 

 QWCML = Quarterly OASDI covered military wages 

 QWTF = Quarterly OASDI taxable Federal wages 

 QWTFC = Quarterly OASDI taxable Federal Civilian wages 

 QWTML = Quarterly OASDI taxable military wages 

 WCF = Annual OASDI covered Federal wages 

 WCFC = Annual OASDI covered Federal Civilian wages 

 WCML = Annual OASDI covered military wages 

 WTF = Annual OASDI taxable Federal wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTLQF = Quarterly OASDI taxable Federal combined employee-employer wage 

liabilities 

 WTLQFEE = Quarterly OASDI taxable Federal employee wage liabilities 

 WTLQFER = Quarterly OASDI taxable Federal employer wage liabilities 
123 

 WTML = Annual OASDI taxable military wages 

State and Local wages 

 Annual OASDI taxable wages 

BACW = 21583.61 

AWCSL = WCSL / ESLC * BACW / AWCSLOD97

S = MAX / ASLC 

IF(S.LT.0.02316573)THEN 

 SLTR=S-(1.1803/1.71)*S**1.71 

ELSE IF(S.LT.0.463314609)THEN 

 SLTR=-(1.54738/1.6)*S**1.6-(.421147/2.5)*S**2.5+(3.34881/.5)*DEXP(-.5*S)+4.39012*S-6.697774474 

ELSE IF(S.LT.0.833966296)THEN 

 SLTR=-(.756943/1.8)*S**1.8+(.485982/2.3)*S**2.3-(.175681/3.2)*S**3.2+.88749*S+.004652169 

ELSE IF(S.LT.1.945921357)THEN 

 SLTR=(3.4167/.3)*DEXP(-.3*S)-(7.26467/.9)*DEXP(-.9*S)+(4.57049/1.5)*DEXP(-1.5*S)+1.0378*S6.245057503 

ELSE IF(S.LT.3.243202261)THEN 

 SLTR=-(2.40293/.2)*DEXP(-.2*S)+(6.44952/.4)*DEXP(-.4*S)-(5.64852/.6)*DEXP(-.6*S)-

.278204*S+5.099074279 

ELSE IF(S.LT.5.559775305)THEN 

 SLTR=-(.0434955/.6)*DEXP(-.6*S)-(4.00403/1.7)*DEXP(-1.7*S)+.00006219*S+.997065459 

ELSE IF(S.LT.18.53258435)THEN 

 SLTR=-(.0272758/.5)*DEXP(-.5*S)+.0000671826*S+.997657785 

 ELSE 

 SLTR=-(.00861948/.7)*S**(-.7)+1.000492941 

END IF 

WTSL=SLTR*WCSL 

Where 

 AWCSL = Average OASDI covered State and Local wages adjusted for average 

wage used to produce equations 

 AWCSLOD97 = Average OASDI covered State and Local wages for 1997 

 BACW = Average OASDI covered State and Local wages in 1% sample data for 

1997 used to produce equations 

 ESLC = OASDI covered State and Local employment 

 MAX = OASDI taxable maximum 

 S = Ratio of the OASDI taxable maximum to average covered State and 

Local wages 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WCSL = OASDI covered State and Local wages 

 WTSL = OASDI taxable State and Local wages 

Quarterly OASDI covered wages 

CSLQD(1)=1.0131455*TCSLD(I,1)+SLPD(I,1) 

CSLQD(2)=1.0431906*TCSLD(I,2)+SLPD(I,2) 
124 

CSLQD(3)=.9060524*TCSLD(I,3)+SLPD(I,3) 

CSLQD(4)=1.0365866*TCSLD(I,4)+SLPD(I,4) 

QWCSL=CSLQD(1:4)*WCSL 

Where 

 CSLQD = Proportion of annual OASDI covered State and Local wages paid in each 

quarter 

 I = Calendar year 

 QWCSL = Quarterly OASDI covered State and Local wages 

 SLPD = Payday variable for State and Local wages based on calendar 

 TCSLD = Proportion of annual NIPA State and Local wages paid in each quarter 

 WCSL = Annual OASDI covered State and Local wages 

Quarterly OASDI taxable wages 

QSL(1)=(CSLQD(1)-.24087*(1.-1./SLTR)) 

QSL(2)=(CSLQD(2)-1.0492*(1.-1./SLTR)+.51259*(1.-1./SLTR**2)-.07643*(1.-1./SLTR**3)) 

QSL(3)=(CSLQD(3)-5.99032*(1.-SLTR**2)+13.238*(1.-SLTR**3)-11.3291*(1.-SLTR**4)+3.52237*(1.-

SLTR**5)) 

QSL(4)=(CSLQD(4)+8.99897*(1.-SLTR**.25)-5.48866*(1.-SLTR**.5)) 

TQSL=QSL(2)+QSL(3)+QSL(4) 

QSL(2:4)= QSL(2:4)/TQSL 

QWTSL(I,1)=QSL(1)*WTSL 

QWTSL(I,2:4)=QSL(2:4)*(WTSL- QWTSL(I,1)) 

Where 

CSLQD = Proportion of annual OASDI covered State and Local wages paid in each 

quarter 

 I = Calendar year 

 QSL = Proportion of annual OASDI taxable State and Local wages paid in each 

quarter 

 QWTSL = Quarterly OASDI taxable State and Local wages 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WTSL = OASDI taxable State and Local wages 

Quarterly OASDI taxable wage liabilities 

WTLQSL(I,J) = QWTSL(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 TRW = OASDI combined employee-employer tax rate 

 WTLQSL = Quarterly OASDI taxable State and Local combined employee-employer 

wage liabilities 
125 

Private household quarterly OASDI taxable wages and liabilities 

QWTPHH(I,J) = WCPHH(I) * QDPHH(J) 

WTLQPHH(I,J) = QWTPHH(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QDPHH = Proportion of annual OASDI taxable private household wages paid in each 

quarter 

 QWTPHH = Quarterly OASDI taxable private household wages 

 TRW = OASDI combined employee-employer tax rate 

 WCPHH = Annual OASDI covered private household wages 

 WTLQPHH = Quarterly OASDI taxable private household combined employeeemployer wage liabilities 

Farm taxable wages 

 Annual OASDI 

BAFMW = 7467.91 

AWCFM97 = ACFMW(1997) 

F = MAX / (ACFMW * BAFMW / AWCFM97) 

IF(F.LT.0.066953142)THEN 

 FMTR=F- (1.30211/1.75)*F**1.75 

ELSE IF(F.LT.0.401718855)THEN 

 FMTR=-(1.18244/1.35)*F**1.35+(.25412/1.75)*F**1.75+1.24681*F-.001598087 

ELSE IF(F.LT.0.669531425)THEN 

 FMTR=-(.508764/.6)*DEXP(-.6*F)-(.300083/2.8)*DEXP(-2.8*F)+.0188542*F+.966550312 

ELSE IF(F.LT.1.87468799)THEN 

 FMTR=-(.638146/.6)*DEXP(-.6*F)-(.0322774/1.5)*DEXP(-1.5*F)-.033706*F+1.133974442 

ELSE IF(F.LT.2.41031313)THEN 

 FMTR=-(2.64644/1.1)*DEXP(-1.1*F)+(17.4638/2)*DEXP(-2*F)-(26.4191/2.5)*DEXP(-

2.5*F)+.00686748*F+.909154345 

ELSE IF(F.LT.4.82062626)THEN 

 FMTR=-(1.06567/1.3)*F**1.3+(.073837/2.1)*F**2.1+1.31021*F-.007628879 

ELSE IF(F.LT.6.427501679)THEN 

 FMTR=-(.178355/.5)*DEXP(-.5*F)-(1.70356/1.3)*DEXP(-1.3*F)+.00115171*F+.959096096 

ELSE IF(F.LT.10.7125028)THEN 

 FMTR=-(.0474377/0.35)*DEXP(-.35*F)-(1.32456/1)*DEXP(-1*F)+.0016146*F+.957903052 

ELSE IF(F.LT.11.38203422)THEN 

 FMTR=-(.0581938/.35)*DEXP(-.35*F)+.00130453*F+.961918378 

ELSE IF(F.LT.24.1031313)THEN 

 FMTR=-(.0492564/.3)*DEXP(-.3*F)+.000761577*F+.97040299 

ELSE 

 FMTR=-(.00304904/.06)*DEXP(-.06*F)+1.000606299 

END IF 

TFMW=FMTR*WCFM 
126 

Where 

 ACFMW = Annual average OASDI covered farm wages 

 AWCFM97 = Annual average OASDI covered farm wages for 1997 

 BAFMW = Average farm wage in 1% sample data for 1997 used to produce equations 

F = Ratio of taxable maximum to annual average OASDI covered farm wages 

adjusted for average wage used in equations 

 FMTR = Ratio of OASDI taxable to covered farm wages 

 MAX = OASDI taxable maximum 

 TFMW = Annual OASDI taxable farm wages 

Quarterly OASDI wages and liabilities 

QWTFM(I,J) = TTFMD(I,J) * TFMW 

WTLQFM(I,J) = QWTFM(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QWTFM = Quarterly OASDI taxable farm wages 

TFMW = Annual OASDI taxable farm wages 

 TRW = OASDI com 

 TTFMD = Proportion of annual OASDI taxable farm wages paid in each quarter 

 WTLQFM = Quarterly OASDI taxable farm combined employee-employer wage 

liabilities 

Quarterly OASDI taxable employee tips 

QWTTIPSEE(I,J) = QDTIP(J) * WTTIPSEE(I) 

QWTTIPSEE(I,2) = QWTTIPSEE(I,2) + WTTIPSSR(I) 

WTLQTIPSEE(I,J) = QWTTIPSEE(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QDTIP = Proportion of annual OASDI taxable tips received in each quarter 

 QWTTIPSEE = Quarterly OASDI taxable tips received by employees 

 WTLQTIPSEE = Quarterly OASDI combined employee-employer wage liabilities on 

taxable tips received by employees 

 TRW = OASDI combined employee-employer tax rate 

 WTTIPSEE = Annual OASDI taxable tips received by employees reported by 

employers 

 WTTIPSSR = Annual OASDI taxable tips received by employees self-reported on 

income tax returns 
127 

Private non-farm OASDI taxable wages and liabilities 

 Annual 

WTPNF = WTER – WTFC – WTML – WTSL – TFMW – WTTIPSEE – WTTIPSSR 

Where 

 TFMW = Annual OASDI taxable farm wages 

 WTSL = Annual OASDI taxable State and Local wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTPNF = Annual OASDI taxable private non-farm wages excluding tips 

 WTTIPSEE = Annual OASDI taxable tips received by employees reported by employers 

 WTTIPSSR = Annual OASDI taxable tips received by employees self-reported on 

income tax returns 

 WTER = Annual OASDI taxable employer wages 

Quarterly 

BACW93 = 21912.00 

NACW = BACW93 / ACW93 * AWC 

X = MAX / NACW 

IF(X.LT.0.91274)THEN 

 TWTR=1D0+.990751*DEXP(X)**(-1)/(-1)-.013904602 

ELSE IF(X.LT.2.05367)THEN 

 TWTR=1D0+(-.003129*X+(1.167562*DEXP(X)**(-1.17)/(-1.17)))-.065747345 

ELSE IF(X.LT.4.791895)THEN 

 TWTR=1D0+(.003962*X+(.770093*X**(-1.85053))/(-1.85053))-.06071106 

ELSE 

 TWTR=1D0+(.267708*X**(-.94))/(-.94)+.00066 

END IF 

IF(TWTR.LT.0.70)THEN 

 QP(1)=-(-0.000575+0.18692*DLOG(TWTR)-0.23133*DLOG(TWTR)**2-

0.10453*DLOG(TWTR)**3+0.04306*DLOG(TWTR)**4+0.01906*DLOG(TWTR)**5)-

0.0325201+PD(1)+TCPD(I,1) 

 QP(2)=-(0.00657+1.7015*TWTR-8.60615*TWTR**2+14.444*TWTR**3-

9.97171*TWTR**4+2.42519*TWTR**5)-0.0080956+PD(2)+TCPD(I,2) 

 QP(3)=-(0.12167+1.31142*TWTR**3-6.31672*TWTR**4+8.03785*TWTR**5-

3.15412*TWTR**6)+0.019325+PD(3)+TCPD(I,3) 

 QP(4)=-(0.1548-0.41354*TWTR**5+0.25874*TWTR**7)+0.0197767+PD(4)+TCPD(I,4) 

ELSE IF(TWTR.LT.0.88)THEN 

 QP(1)=0.224763-0.237056*TWTR+PD(1)+TCPD(I,1) 

 QP(2)=0.190385-0.209676*TWTR+0.00176*(TWTR-0.7)/(0.88-0.7)+PD(2)+TCPD(I,2) 

 QP(3)=-0.052523+0.05309*TWTR+PD(3)+TCPD(I,3) 
128 

 QP(4)=-0.354571+0.38249*TWTR+PD(4)+TCPD(I,4) 

ELSE 

 QP(1)=0.968092-1.877574*TWTR+0.904348*TWTR**2+PD(1)+TCPD(I,1) 

 QP(2)=-0.468266+1.148107*TWTR-0.690132*TWTR**2+PD(2)+TCPD(I,2) 

 QP(3)=-0.850885+1.824094*TWTR-0.981557*TWTR**2+PD(3)+TCPD(I,3) 

 QP(4)=0.350767-1.093966*TWTR+0.766972*TWTR**2+PD(4)+TCPD(I,4) 

END IF 

IF(PTR.LT.0.86)THEN 

 QP(J)=QP(J)+ADJTP(J) 

ELSE 

 IF((ADJCP(J)-ADJTP(J)).NE.0D0)QP(J)=QP(J)+ADJTP(J)+((PTR-BPTR)/(1.-

BPTR))**4*(ADJCP(J)-ADJTP(J)) 

END IF 

QWTPNF(I, J) = QP(J) * WTPNF(I) + QWTTIPSEE(I, J) + QWTPHH(I, J) 

QWTPNF(I, 2) = QWTPNF(I, 2) + WTTIPSSR(I) 

Where 

 ACW93 = Annual average OASDI covered wage for 1993 

 AWC = Annual average OASDI covered wage for current year 

 BACW93 = Annual average OASDI covered wage for 1993 from actual data used to 

determine taxable to covered wage equations 

 I = Calendar year 

 J = Quarter 

 MAX = Annual OASDI taxable maximum 

 NACW = Annual average OASDI covered wage for current year adjusted for 

average from actual data used to determine equations 

 PD = Payday variable for private non-farm based on calendar 

 QP = Proportion of annual OASDI taxable private non-farm wages excluding 

taxable tips paid in each quarter 

 QWTPNF = Quarterly OASDI taxable private non-farm wages including tips 

 TCPD = Proportion of annual NIPA private wages paid in each quarter 

 TWTR = Ratio of OASDI taxable to covered wages computed using equations 

based on data for 1993 

 X = Ratio of annual OASDI taxable maximum to adjusted annual average 

OASDI covered wage (NACW) 

Quarterly OASDI wage liabilities 

WTLQPNF(I,J) = (QWTPNF(I,J) – QWTPHH(I,J)) * TRW(I) 

Where 

 QWTPHH = Quarterly OASDI taxable private household wages 
129 

 QWTPNF = Quarterly OASDI taxable private non-farm wages including tips 

 TRW = OASDI combined employee-employer tax rate 

 WTLQPNF = Quarterly OASDI tax liabilities from taxable private non-farm wages 

including tips, excluding private household taxable wages 

Total quarterly OASDI taxable wages and wage liabilities 

QWT(I,J) = QWTPNF(I,J) + QWTF(I,J) + QWTSL(I,J) + QWTFM(I,J) 

WTLQ(I,J) = QWT(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QWT = Quarterly OASDI taxable wages 

 QWTF = Quarterly OASDI taxable Federal wages 

 QWTFM = Quarterly OASDI taxable farm wages 

 QWTPNF = Quarterly OASDI taxable private non-farm wages including tips 

 QWTSL = Quarterly OASDI taxable State and Local wages 

 WTLQ = Quarterly OASDI taxable wage liabilities 

2-4.12 OASDI quarterly taxable wage liability collections (WTLQC) 

 OASDI taxable private non-farm wages by sub-quarterly periods 

PTR=WTP/WCP 

MR=MAR(I)-.04346*(1.-PTR)+.08497*(1.-PTR)**2 

JR=JUN(I)-.02627*(1.-PTR)-.26844*(1.-PTR)**2 

SR=SEP(I)-.12321*(1.-PTR)-.02344*(1.-PTR)**2 

DR=DEC(I)-.12468*(1.-PTR)-.20710*(1.-PTR)**2 

MWTP(1)=QWTP(I,1)*MR 

MWTP(2)=QWTP(I,1)-MWTP(1) 

MWTP(3)=QWTP(I,2)*JR 

MWTP(4)=QWTP(I,2)-MWTP(3) 

MWTP(5)=QWTP(I,3)*SR 

MWTP(6)=QWTP(I,3)-MWTP(5) 

MWTP(7)=QWTP(I,4)*DR 

MWTP(8)=QWTP(I,4)-MWTP(7) 

Where 

 DEC = Proportion of fourth quarter OASDI covered private non-farm wages 

(excluding tips and household) paid in December 

 DR = Proportion of fourth quarter OASDI taxable private non-farm wages 

(excluding tips and household) paid in December 
130 

 I = Calendar year 

 JR = Proportion of second quarter OASDI taxable private non-farm wages 

(excluding tips and household) paid in June 

 JUN = Proportion of second quarter OASDI covered private non-farm wages 

(excluding tips and household) paid in June 

 MAR = Proportion of first quarter OASDI covered private non-farm wages (excluding 

tips and household) paid in March 

 MR = Proportion of first quarter OASDI taxable private non-farm wages (excluding 

tips and household) paid in March 

 MWTP = OASDI taxable private non-farm wages (excluding tips and household) paid 

in last month and in first two months of quarter 

 PTR = Ratio of annual OASDI taxable private non-farm wages (excluding tips and 

household) to covered private non-farm wages 

 QWTP = Quarterly OASDI taxable private non-farm wages (excluding tips and 

household) 

 SEP = Proportion of third quarter OASDI covered private non-farm wages 

(excluding tips and household) paid in September 

 SR = Proportion of third quarter OASDI taxable private non-farm wages (excluding 

tips and household) paid in September 

 WCP = Annual OASDI covered private non-farm wages 

 WTP = Annual OASDI taxable private non-farm wages (excluding tips and 

household) 

 OASDI taxable private non-farm wages collected on in same quarter wages are paid 

TRAT=RATEE(I,5) 

CA=.95 

MWCP(1)=QWSCPNF(I,1)*MAR(I) 

MWCP(2)=QWSCPNF(I,1)-MWCP(1) 

MWCP(3)=QWSCPNF(I,2)*JUN(I) 

MWCP(4)=QWSCPNF(I,2)-MWCP(3) 

MWCP(5)=QWSCPNF(I,3)*SEP(I) 

MWCP(6)=QWSCPNF(I,3)-MWCP(5) 

MWCP(7)=QWSCPNF(I,4)*DEC(I) 

MWCP(8)=QWSCPNF(I,4)-MWCP(7) 

RCSM=.80 

QRMREQ=750. 

QRWREQ=11250. 

RMF=70786.*WSP(I)/1001400. 

CALL ITERNU(QRMREQ,MWTP(2),MWCP(2),TRAT,RMF,PWCS(1)) 

CALL ITERNU(QRWREQ,MWTP(1),MWCP(1),TRAT,RMF,PWCE(1)) 

CALL ITERNU(QRMREQ,MWTP(4),MWCP(4),TRAT,RMF,PWCS(2)) 

CALL ITERNU(QRWREQ,MWTP(3),MWCP(3),TRAT,RMF,PWCE(2)) 

CALL ITERNU(QRMREQ,MWTP(6),MWCP(6),TRAT,RMF,PWCS(3)) 

CALL ITERNU(QRWREQ,MWTP(5),MWCP(5),TRAT,RMF,PWCE(3)) 

CALL ITERNU(QRMREQ,MWTP(8),MWCP(8),TRAT,RMF,PWCS(4)) 

CALL ITERNU(QRWREQ,MWTP(7),MWCP(7),TRAT,RMF,PWCE(4)) 
131 

DO J=1,4 

 QWTPC(I,J)=PWCS(J)+PWCE(J)*RCSM*CA 

 QWTPF(I,J)=QWSTXPHH(I,J)-QWTPC(I,J) 

END DO 

Where 

 AWSCODXSRT = Annual average OASDI covered private non-farm wages (excluding household) 

 CA = Compliance allowance 

 DEC = Proportion of fourth quarter OASDI covered private non-farm wages (excluding tips and 

household) paid in December 

 I = Calendar year 

 J = Quarter 

 JUN = Proportion of second quarter OASDI covered private non-farm wages (excluding tips and 

household) paid in June 

 MAR = Proportion of first quarter OASDI covered private non-farm wages (excluding tips and 

household) paid in March 

 MWCP = OASDI covered private non-farm wages paid in third month and in first two months of 

each quarter 

 MWTP = OASDI taxable private non-farm wages paid in third month and in first two months of 

each quarter 

 PWCE = OASDI taxable private non-farm wages paid in the third month of each quarter 

 PWCS = OASDI taxable private non-farm wages paid in the first two months of each quarter on 

which taxes are collected in that quarter 

 QWSCPNF = Quarterly OASDI covered private non-farm wages 

 QRMREQ = Monthly deposit requirement 

 QRWREQ = Quarterly deposit requirement 

 QWSTXPHH = Quarterly OASDI taxable private non-farm wages (excluding household) 

 QWTPC = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in 

the quarter the wages were paid 

 QWTPF = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in 

the quarter after the wages were paid 

 RATEE(I,5) = OASDHI employee tax rate 

 RCSM = Proportion of OASDI taxable private non-farm wages wages paid in same quarter in 

which taxes are collected 

 RMF = Current year average wage size of firm 

 SEP = Proportion of third quarter OASDI covered private non-farm wages (excluding tips and 

household) paid in September 

 TRAT = OASDHI employee tax rate 

 WSP = Economy-wide (NIPA) private wages 

SUBROUTINE ITERNU(A11,QPAR,QTOT,T,RMF,AMTOUT) 

 R=QPAR/QTOT 

 X=A11/(T*2.+.10) 

 DO 

 IWH=X*(.16011+.01998*LOG(X/RMF)-.01) 

 FWH=T*2.*X*((-1.4402*LOG(1.+X/RMF)+1.)*(1.-R)+R) 

 A1=IWH+FWH 

 D=A11/A1 

 N1=D*1000. 

 IF(N1.EQ.999.OR.N1.EQ.1000)THEN 

 RTAX=R+(1.-R)*(-1.07115*X/RMF+.38633*(X/RMF)**2+1) 
132 

 TOD=177.16+1142.7*DEXP(-(X/RMF))+1181.26*DEXP(-3.*(X/RMF))-907.88*DEXP(-

4.*(X/RMF))+646.49*DEXP(-5.*(X/RMF))- 

 165.09*DEXP(-6.*(X/RMF))-20.92*X/RMF-2906.07/(X/RMF+1.)**2+831.44/(X/RMF+1.)**3 

 AMTOUT=QPAR-RTAX*TOD*QTOT 

 RETURN 

 END IF 

 X=X*D 

 END DO 

END SUBROUTINE ITERNU 

Where 

 A1 = Total (income plus FICA) taxes withheld 

 A11 = Deposit requirement 

 AMTOUT = OASDI taxable private non-farm wages paid in sub-quarterly period and 

collected on in same quarter 

 D = Ratio of deposit requirement to total taxes withheld 

 FWH = FICA taxes withheld 

 IWH = Income taxes withheld 

 N1 = Ratio of deposit requirement to total taxes withheld times 1000 (used to see 

how close we are to target) 

 QPAR = OASDI taxable private non-farm wages paid in sub-quarterly period 

 QTOT = OASDI covered private non-farm wages paid in sub-quarterly period 

 R = Initial ratio of OASDI taxable to covered private non-farm wages paid in subquarterly period 

 RMF = Current year average wage size of firm 

 RTAX = Ratio of OASDI taxable to covered private non-farm wages paid in subquarterly period 

 T = OASDHI employee tax rate 

 TOD = Proportion of liabilities to be deposited in quarter after that in which wages 

paid 

 X = Taxable wage amount needed to meet deposit requirement 

OASDI taxable private wages collected on in same quarter wages paid and in following 

quarter 

QWTPCQ(I,J)=QWTPC(I,J)+QWTPHHCQ(I,J)+QWTFM(I,J) 

QWTPFQ(I,J)=QWTPF(I,J)+QWTPHHFQ(I,J) 

OASDI taxable State and Local wages collected on in same quarter wages paid and in 

following quarter 

SLTR=WTSL/WCSL 

LMPW(1)=MARSL(I)-.00329*(1.-SLTR**2) 

LMPW(2)=JUNSL(I)-.68187*(1.-SLTR**3)+.52206*(1-SLTR**4) 

LMPW(3)=SEPSL(I)-1.33596*(1.-SLTR)+1.51187*(1.-SLTR**2)-.63523*(1.-SLTR**3) 
133 

LMPW(4)=DECSL(I)-2.03892*(1.-SLTR)+1.90430*(1.-SLTR**2)-.6633*(1.-SLTR**3) 

DO J=1,4 

 SLCR(J)=(1.-LMPW(J))+LMPW(J)*LMCRPR(I-16,J) 

 QWTSLC(I,J)=SLCR(J)*QWTSL(I,J) 

 QWTSLF(I,J)=QWTSL(I,J)-QWTSLC(I,J) 

END DO 

Where 

 DECSL = Proportion of OASDI taxable State and Local wages paid in fourth quarter which are paid in 

December 

 I = Calendar year 

 J = Quarter 

 JUNSL = Proportion of OASDI taxable State and Local wages paid in second quarter which are paid in 

June 

 LMCRPR = Proportion of OASDI taxable State and Local wages paid in final month of quarter on which 

employers are to deposit taxes in the same quarter 

 LMPW = Proportion of quarterly OASDI taxable State and Local wages paid in final month of quarter 

 MARSL = Proportion of OASDI taxable State and Local wages paid in first quarter which are paid in 

March 

 QWTSL = Quarterly OASDI taxable State and Local wages paid in quarter 

 QWTSLC = Quarterly OASDI taxable State and Local wages paid in quarter on which taxes are deposited 

by the employer in the same quarter 

 QWTSLF = Quarterly OASDI taxable State and Local wages paid in quarter on which taxes are deposited 

by the employer in the following quarter 

 SEPSL = Proportion of OASDI taxable State and Local wages paid in third quarter which are paid in 

September 

 SLCR = Proportion of OASDI taxable State and Local wages paid in quarter on which taxes are 

deposited by the employer in the same quarter 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WCSL = Annual OASDI covered State and Local wages 

 WTSL = Annual OASDI taxable State and Local wages 

OASDI taxable wages collected on in same quarter wages paid and in following quarter 

WTQCQ(I,J)= QWTPCQ(I,J)+ QWTSLC(I,J)+QWTF(I,J) 

WTQFQ(I,J)= QWTPFQ(I,J)+ QWTSLF(I,J) 

Where 

 I = Calendar year 

 J = Quarter 

 QWTF = Quarterly OASDI taxable Federal wages 

 QWTPCQ = Quarterly OASDI taxable private wages collected on in same quarter 

wages paid 

 QWTPFQ = Quarterly OASDI taxable private wages collected on quarter following 

that in which wages paid 

 QWTSLCQ = Quarterly OASDI taxable State and Local wages collected on in same 

quarter wages paid 
134 

 QWTSLFQ = Quarterly OASDI taxable State and Local wages collected on in quarter 

following that in which wages paid 

 WTQCQ = Quarterly OASDI taxable wages collected on in same quarter wages paid 

 WTQFQ = Quarterly OASDI taxable wages collected on in quarter following that in 

which wages paid 

Quarterly OASDI wage tax collections 

WTLQC(I,1) = TRW(I-1) * WTQFQ(I-1,4) + TRW(I) * WTQCQ(I,J) 

DO J = 2, 4 

 WTLQC(I,J) = TRW(I) * (WTQFQ(I,J-1) + WTQCQ(I,J)) 

END DO 

Where 

 I = Calendar year 

 J = Quarter 

 TRW = OASDI combined employee-employer tax rate 

 WTLQC = Quarterly OASDI wage tax collections 

 WTQCQ = Quarterly OASDI taxable wages collected on in same quarter wages paid 

 WTQFQ = Quarterly OASDI taxable wages collected on in quarter following that in 

which wages paid 

2-4.13 Quarterly Self-Employed Net Income Tax Collections (SELQC) 

DO J = 1, 4 

 SELQC(I,J) = SECRCY(I,J) * SEL(I) + SECRPY(I,J) * SEL(I-1) 

END DO 

Where 

 I = Calendar year 

 J = Quarter 

 SECRCY = Proportion of OASDI taxable self-employment earnings collected on in same 

year earned 

 SECRPY = Proportion of OASDI taxable self-employment earnings collected on in year 

following that in which earned 

 SEL = OASDI taxable self-employment earnings liabilities 

 SELQC = Quarterly OASDI self-employed net income tax collections 

2-4.14 SECA Appropriation Adjustments (MSECAAA) 

MSECAAA = 0 

DO L = I-2, I-9, -1 

 MSECAAA = MSECAAA + SEAACO(I,J) * SELIAC(L) 
135 

END DO 

Where 

 I = Calendar year 

 J = Quarter 

 L = Liability year 

 MSECAAA = OASDI SECA appropriation adjustment for quarter (assigned to last 

month in quarter) 

 SEAACO = Proportion of past year’s OASDI self-employment tax liability which will 

be reported in current quarter 

 SELIAC = Prior years’ OASDI self-employment tax liability 
136 

Appendix 2-2 

Economic Acronyms

AA Appropriation adjustments 

ACE Average OASDI covered earnings 

ACSE Average OASDI covered self-employed income 

ACW Average OASDI covered wage 

ACWC Average economy-wide wage 

AWI Average wage index calculated by SSA; based on the average wage of all 

workers with wages from Forms W-2 

BEA The Bureau of Economic Analysis 

BLS The Bureau of Labor Statistics 

CMB_TOT Workers that have a combination of both OASDI covered wages and selfemployed income. 

COV Economic Sub-Process: Covered Employment and Earnings 

CPI The Consumer Price Index for Urban Wage Earners and Clerical Workers 

(CPI-W) is an official measure of inflation in consumer prices, published by 

the BLS. 

CPS Current Population Survey, conducted monthly by the Bureau of Census for 

the Bureau of Labor Statistics. It is the source of historical monthly 

economic data (such as labor force, civilian noninstitutional population, and 

unemployment) used to project US employment. 

CSE_TOT Total OASDI covered self-employed income 

CSRS Civil Service Retirement System 

CSW Self-employed only workers (SEO) plus combination workers (CMB_TOT) 

E Total employment, CPS concept 

EA Total agricultural employment 

EDMIL Total number serving in the US Armed Forces estimated by the Department 

of Defense and published by the Census Bureau 

EO Total employment in the other immigrant population 

EO_ESF Total employment in the other immigrant population whose reported 

earnings are posted to the Earnings Suspense File 

EO_MEF Total employment in the other immigrant population whose earnings are 

reported and posted to the Master Earnings File 

EO_MEFC Total employment in the other immigrant population whose earnings are 

reported and posted to the Master Earnings File and are OASDI-covered 

EO_UND Total employment in the other immigrant population that is strictly in the 

underground economy (i.e., with no earnings reported) 

ES Self-employed workers 

ETP Effective annual taxable payroll, equal to total employer taxable OASDI 

wages plus total self-employed taxable income minus one half of the multiemployer refund wages 
137 

EU Unpaid family workers 

EW Wage and salaried workers 

FERS Federal Employee Retirement System 

GDP Gross domestic product 

HI Hospital insurance 

LC US labor force, equal to the sum of number of persons employed and 

number of persons seeking employment 

LFPR Labor force participation rate, defined as the ratio of the number of persons 

in the US labor force to the number of persons in the US noninstitutional 

population. 

MER Multi-employer refund wages 

N Civilian noninstitutional population 

NCE Total noncovered employment 

NIPA The National Income and Product Accounts, published by the BEA, 

providing historical estimates of quarterly earnings and output measures 

NRA Normal retirement age 

OASDI Old-Age, Survivors, and Disability Insurance 

OASDHI Old-Age, Survivors, Disability, and Health Insurance 

OLI Employer contributions for employee pension and insurance funds 

PIA Primary insurance amount 

PIARR PIA replacement rate, defined as the ratio of a hypothetical medium scale 

worker’s PIA to his/her career average indexed earnings. 

PGDP GDP price deflator 

PBNFXGE Private nonfarm business excluding government enterprises 

RCMB Proportion of wage workers who are also self-employed 

(CMB_TOT/WSW) 

RCSE Covered self-employed ratio, defined as the ratio of total covered selfemployment income to total proprietor income (CSE_TOT/Y). 

RD Disability prevalence ratio, defined as the ratio of disabled worker 

beneficiaries to the Social Security area population. 

RELMAX Ratio of the TAXMAX to averaged covered earnings 

RET Earnings test ratio, defined the ratio of the maximum amount of earnings 

before an OASDI benefit is reduced to the average wage index. 

RFS Family size ratio, defined as the ratio of the number of children under 6 

to mothers of a certain age. 

RM Military ratio, the ratio of the US armed forces to the noninstitutionalized population. 

RMER Multi-employer refund wage ratio, defined as the ratio of multi-employer 

refund wages to total OASDI wages. 

RSET Self-employed net income taxable ratio, defined as the ratio of total selfemployed taxable income to total OASDI wages. 

RTE Ratio of total employment to the sum of wage & salary, self-employed 

workers, and the military (TE/(EW + ES + military)) 
138 

RTP A summary measure of the business cycle equal to the ratio of real GDP 

to potential GDP. 

RU Civilian unemployment rate defined as the ratio of the unemployed US 

labor force to the total US labor force. 

RWSC Covered wage ratio, defined as the ratio of OASDI covered wages to 

total wage and salary disbursements (WSC/WSD) 

RWSD Earnings ratio, defined as the ratio of total wage and salary disbursements 

to total wage and worker compensation(WSD/WSS) 

RWSSY Total compensation ratio, defined as the ratio of total compensation to 

gross domestic product (WSSY/GDP) 

RWTEE Employee taxable ratio, defined as the ratio total employee OASDI 

taxable wages to total OASDI covered wages. 

RY Income ratio, defined as the percentage of total compensation attributable 

to proprietor income (Y/WSSY). 

S&L State and Local government 

SEL Self-employment tax liabilities 

SELQC Quarterly self-employed net income tax collections 

SEO Workers that report only OASDI covered self-employed earnings 

SEPR The self employed participation rate is the proportion of employed 

persons that are self employed 

SET Total self-employed taxable income 

SOC Employer contributions for government social insurance 

SSA Social Security Administration 

TAXMAX OASDI contribution and benefit base 

TAXPAY Economic Sub-Process: Taxable Payroll 

TCE Total OASDI covered employment 

TE Total at-any-time employment 

TEO Total “at any time” employment in the other immigrant population 

TEO_ESF Total “at any time” employment in the other immigrant population whose 

reported earnings are posted to the Earnings Suspense File 

TEO_MEF Total “at any time” employment in the other immigrant population whose 

earnings are reported and posted to the Master Earnings File 

TEO_MEF

C 

Total “at any time” employment in the other immigrant population whose 

earnings are reported and posted to the Master Earnings File and are 

OASDI-covered 

TEO_UND Total “at any time” employment in the other immigrant population that is 

strictly in the underground economy (i.e., with no earnings reported) 

TRSE OASDI self-employed tax rate 

TRW Combined OASDI employee-employer tax rate 

U The number of persons in the labor force who are unemployed 

USEAR Economic Sub-Process: U.S. Earnings 

USEMP Economic Sub-Process: U.S. Employment 

WSC Total OASDI covered wages 
139 

WSD Total wage and salary disbursements 

WSS Total wage worker compensation 

WSSY Total compensation for wage and salary workers and proprietors 

WSW Wage and salary workers that report some OASDI covered earnings 

WTEE Total employee OASDI taxable wages 

WTER Total employer OASDI taxable wages 

WTL Annual OASDI wage tax liabilities 

WTLQ Quarterly OASDI wage tax liabilities 

WTLQC Quarterly OASDI wage tax collections 

Y Total proprietor income 
140 
141 

Process 3: 

Beneficiaries 
142 

3. Beneficiaries 

OCACT uses the Beneficiaries Process to project the fully insured and disability insured 

population, the number of disabled worker and their dependent beneficiaries, the number of 

retired worker and their dependent beneficiaries, and the number of dependent beneficiaries of 

deceased workers. The Beneficiaries Process receives input data from the Economics and 

Demography sections along with data received from the Social Security Administration and 

other government agencies. Output data is provided to the Economic Process and the Trust Fund 

Operations and Actuarial Status Process. 

The Beneficiaries Process is composed of three subprocesses: INSURED, DISABILITY, and 

OLD-AGE AND SURVIVORS. As a rough overview, INSURED projects the number of 

people in the Social Security area population that have sufficient work histories for disability and 

retirement benefit eligibility. DISABILITY projects the number of disabled worker and their 

dependent beneficiaries. OLD-AGE AND SURVIVORS projects the number of retired workers, 

their dependent beneficiaries, and the dependent beneficiaries of deceased workers. 

All programs output data on an annual basis. 

3.1. INSURED 

3.1.a. Overview 

Insured status is a critical requirement for a worker, who has participated in the covered 

economy, to receive Social Security benefits upon retirement or disability. The requirement for 

insured status depends on the age of a worker and his (or her) accumulation of quarters of 

coverage (QC). 

INSURED is a simulation model that estimates the percentage of the population that is fully 

insured (FPRO) and disability insured (DPRO) throughout the projection period. These 

estimates are used in conjunction with estimates of the Social Security area population to 

estimate the number of people that are fully insured (FINPOP) and disability insured (DINPOP). 

FINPOP is then used by the OLD-AGE AND SURVIVORS INSURANCE subprocess, and both 

FINPOP and DINPOP are used by the DISABILITY subprocess. FINPOP and DINPOP are 

projected by age, sex, and cohort. 

For each sex and birth cohort, INSURED simulates 30,000 work histories which represent the 

Social Security area population (SSAPOP). These histories are constructed from past and 

projected cover worker rates, median earnings, and amounts required for crediting QC. 

The equations for this subprocess are given below: 
143 

FPRO = FPRO(·) (3.1.1) 

DPRO = DPRO(·) (3.1.2) 

FINPOP = FPRO * SSAPOP (3.1.3) 

DINPOP = DPRO * SSAPOP (3.1.4) 

3.1.b. Input Data

All data are updated annually, except those that are noted. 

Long-Range OCACT Data 

Demography 

• Social Security area population as of year end (1940 – 2085) by age (0 -100, age 100 

including age 100 and older), marital status (single, married, widowed, divorced) and 

sex (M, F). 

• Number of new “net legal immigrants” (legal immigrants – estimated legal 

emigrants) entering the Social Security area each year (1940 – 2085) by age (14 – 69) 

and sex (M, F). 

• “Other immigrant” population as of year end (2006 – 2085) by age (0 -100, age 100 

including age 100 and older), marital status (single, married, widowed, divorced) and 

sex (M, F). 

Economics 

• Historical annual estimates of covered workers by sex (M, F), age (15 – 74), and 

marital status (single, married, widowed, divorced) for years (1937 – 2006). 

• Annual projections (2007 – 2085) of covered workers that are based on the assumption 

that the portion of “other immigrants” in the Social Security Area stays constant at the 

level of the latest historical estimates by cohort and sex. The data format is the same as 

those in historical period. 

• Annual projection (2004 – 2085) of average wage index and median covered earnings. 

• Total “other immigrant” workers by sex (M, F), age (16 – 95), and for years (2006 – 

2085). 

• “Other immigrant” workers with earnings posted to the Master Earnings File (MEF) by 

sex (M, F), age (16 – 95), and for years (2006 – 2085). 

Beneficiaries 
144 

• Disabled-worker beneficiaries at year end (2006 – 2085) by age (19 – 66), sex (M, F) 

and duration (0 – 10, duration 10 including duration 10 and above) from the previous 

year’s Trustee Report. These data are read in from files that are generated annually 

from the DISABILITY subprocess (#3.2). 

Short-Range OCACT data 

• FINPOP by age (14 – 95, age 95 including age 95 and older) and sex (M, F) from the 

end of year1969 to the end of Short-Range projection period (2017). 

• DINPOP by age (15 – 69) and sex (M, F) from the end of year 1969 to the end of 

Short-Range projection period (2017). 

 

Other input data 

• Historical series of annual median earnings of covered workers by age group (<20, 

20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-61, 62-64, 65-69) and sex 

(M, F) for years 1937-2004. Data are updated using the data in the most recent Social 

Security Annual Statistical Supplement Table 4.B6. 

• Number of disabled workers by age (20-65) and sex (M, F) for years 1958 to the most 

recent data year. Data are updated using the data in the most recent Social Security 

Annual Statistical Supplement Table 5.A1.2.

• The amount required for crediting one quarter of coverage for years 1937-2004 from 

SSA publication. 

• Historical series of annual median earnings of all covered workers for years 1937-

2004. Data are updated using the data in the most recent Social Security Annual 

Statistical Supplement Table 4.B6. 

• The number of all covered workers (wage/salary workers, self-employed workers) by 

sex and amount of earnings for 2004 in the most recent Social Security Annual 

Statistical Supplement Table 4.B7 & 4.B9. These are used to produce the input data 

for the distribution of earnings (FRAC). 

• ANNUAL factor (comparability factor between quarterly and annual reporting of 

earnings) by age (13-69) and sex (M, F) for years prior to 1978. These data are not 

updated. 

3.1.c. Development of Output

Equation 3.1.1 & 3.1.2 - 

Determining the QC distribution 
145 

There are three variables playing important roles in the simulation process starting from age 13 

through 69 of a birth cohort by sex. They include historical and projected covered worker rates, 

the amounts required for crediting QC, and a cumulative worker distribution by earnings level. 

Covered worker rates by age and sex are defined as the ratio of covered workers to the Social 

Security area population. Historical and projected numbers of covered workers and the Social 

Security area population, which are provided by the Economics and Demography sections 

respectively, are used to calculate the rates for ages 15 through 69. For ages 13 and 14, 

INSURED estimates covered worker rates based on the covered worker rates at age 15. 

The amount of earnings needed to earn one QC is specified by law for each year of the historical 

period. Its projection assumes the same growth rate as the Social Security average wage index. 

 

The cumulative worker distribution by earnings level is called ‘FRAC’. It is a function of 

covered earnings relative to median earnings. For a given ratio of covered earnings relative to 

median earnings, FRAC returns the percentage of covered workers whose earnings relative to 

median earnings are less than the given ratio. It is constructed based on the latest historical data. 

It is used for each age and sex and is assumed to remain constant throughout the projection 

period. The program uses FRAC to estimate the percentage of covered workers that earn 0, 1, 2, 

3 or 4 QC in a given year. Thus, for a particular age and sex, the percentages of covered workers 

earning at least n QC are defined as: 

 QCDist = 1 – FRAC ⎥

⎦

⎤ ⎢

⎣

⎡

median earning

n *QC amount , for n = 1,2,3,4 

 where median earnings is for that age and sex. 

Simulation process – assigning QC to records

Once the QCDist is known, the simulation process begins with 30,000 records for each sex and 

birth cohort. Starting with the QC distribution at age 13, INSURED randomly assigns a number 

of QC (1, 2, 3 or 4) to these records based on QCDist. 

For ages 14 to 69, INSURED begins the simulation process by randomly selecting records to 

represent new net legal immigrants from the covered worker portion of 30,000 records. For each 

record, a number of QC (1, 2, 3 or 4) is assigned on a uniform basis. Once a record is assigned a 

number of QC, INSURED nullifies the previous earnings of the record. 

After the records for new immigrants are selected, the rest of the records for ages 14 to 69 are 

either non-covered workers or covered workers. The total number of records assigned as noncovered workers is set equal to (1-covered worker rate) * 30,000. These records receive no QC. 

To identify records as non-covered workers, INSURED uses two parameters (SRCH, SLCT), 

which vary by age and sex. 
146 

SRCH sets a limit on the number of consecutive records to be searched for a non-covered 

worker. In general, the younger age groups have lower SRCH values. SLCT is the number of 

consecutive prior years in which no QC were earned that is required in order for a simulated 

record to be assigned as a non-covered worker. Lower SLCT values are set for the very young 

and older age groups. Sensitivity analyses show that insured percentages are negatively 

correlated with these two parameters. When the female covered worker rates approach the male 

rates, the female SRCH and SLCT values are graded toward the male values1

. 

For each sex and birth cohort, the simulation process of assigning records as non-covered 

workers uses the following approach. This approach, which excludes those records already 

assigned as net legal immigrants during the year, is repeated until the targeted number of noncovered workers is achieved. 

1. One of the records is randomly selected as a starting record. 

2. Beginning with the starting record, each record is examined until a record that 

matches the SLCT criterion is found. 

3. However, if the number of records examined equals the value of SRCH and no 

record matches the SLCT criterion, then the record closest to the SLCT criterion is 

assigned no QC as a non-covered worker. 

Initially, values for SRCH and SLCT are the same as those used in the prior Trustees Report. 

Adjustments to these values are only made when the results are not consistent with historical 

data. 

The final step of the simulation process is to use QCDist to randomly assign QC of 0, 1, 2, 3 or 4 

to the remaining covered worker records, which are not new net legal immigrants, for ages 14-

69. 

Determining Insured Status

Once the simulation process is complete, the insured status for each record at any age can be 

determined based on the total QC assigned up to that age. The simulated fully insured 

percentage (FSIM) is calculated as the percentage of the 30,000 simulated records meeting the 

QC requirements for insured status. The same calculation is applied to the disability-insured 

percentage (DSIM). 

For each sex and cohort, FSIM and DSIM are determined at ages 13 to 69. FSIM is assumed to 

remain the same beyond age 69. 

A multiplicative adjustment is applied to both FSIM and DSIM to reflect future changes in the 

proportion of ‘other immigrants’ in the Social Security area population (OIMPOP) and the 

proportion of ‘other immigrants’ who earnings are posted to the MEF (ADJLPR) from that in the 

base year for each cohort. Thus the adjustment factor is 
147 

 1 [ ( ) * (1 ( ))]

1 [ ( ) * (1 ( ))]

OIMPOP base year ADJLPR base year

OIMPOP projection year ADJLPR projection year

− −

− − by cohort and sex. 

 

A second additive adjustment, DINADD, is made to DSIM. It accounts for workers who fail to 

meet the requirement for disability-insured status solely because of having no earnings while 

receiving disability benefits. INSURED assumes that workers who have been on the disability 

roll for more than 3 years would be in this situation33. Thus, DINADD is 

Social Security Area population

# of workers on the disability roll morethan3 years by age, sex, and cohort. 

If the adjusted results for DSIM are not consistent with historical data, an additional age-sexspecific additive adjustment (DIADJ) is used to bring the simulated results in line with the 

historical estimates. 

Finally, incorporation of Short-Range projections produces FPRO and DPRO. For the first 10 

years, FPRO and DPRO are set equal to Short-Range estimates. The difference in terms of the 

percentage between the Long-Range and Short-Range projections at the end of 10th year is 

linearly phased out during the next ten years by cohort and sex. Afterward, the Long-Range 

projections are assumed. 

Number of Fully Insured and Disability Insured Workers

The numbers of people who are fully insured (FINPOP) and who are disability insured 

(DINPOP) are obtained by applying FPRO and DPRO, respectively, to the Social Security area 

population. These calculations are done by single year of age and sex. For a given age and sex, 

the proportion of the Social Security area population that is insured (FPRO) is assumed to be the 

same for each martial status. 

 

33 Those who are on the roll for less than 4 years are assumed to meet the requirement for disability-insured status 

based on their earnings histories. 
148 

3.2. DISABILITY 

3.2.a. Overview

The Social Security Administration pays monthly disability benefits to workers who are insured 

for disability benefits and meet the definition of “disabled”. Provided that they meet certain 

requirements, spouses and children of disabled-worker beneficiaries may also receive monthly 

benefits. 

DISABILITY projects the number of disabled-worker beneficiaries in current-payment status 

(DIB) at the end of each year by age at entitlement, sex, and duration from entitlement. The 

number of DIB at the end of each year is based on the number of disabled-worker beneficiaries 

who are currently entitled to benefits (CE). The number of CE at the end of year is obtained by 

adding the number of newly entitled CE (New Entitlements) during the year and subtracting the 

number of CE who leave the disability rolls (Exits) during the year to the number of CE at the 

end of the prior year. Disabled-worker beneficiaries who leave the disability rolls (Exits) do so 

by recovering from disabilities (Recoveries), by dying (Deaths), or by converting to retired 

worker status (Conversions). A disabled-worker beneficiary converts to retired worker status 

upon reaching Normal Retirement Age (NRA), the age at which a person first becomes entitled 

to unreduced retirement benefit. 

DISABILITY also projects the number of future dependent beneficiaries of DIB by category, 

age, and sex. The six categories are minor child, student child, disabled adult child, young 

spouse, married aged spouse and divorced aged spouse. The numbers of dependent beneficiaries 

of DIB are obtained by multiplying the relevant subset of the SSA area population (Exposures) 

by a series of probabilities that relate to the regulations and requirements for obtaining benefits 

(Linkages). 

 New Entitlements(year) = ExposureBOY* Incidence Rate(year) (3.2.1) 

 where BOY is beginning of year. 

 Exits(year) = Recoveries(year) + Deaths(year) + Conversions(year) (3.2.2) 

 where Recoveries(year) = CEBOY * Recovery Rate(year) 

 where Deaths(year) = CEBOY * Death Rate(year). 

CEEOY = CEEOY-1 + New Entitlements (year) – Exits(year), (3.2.3) 

 where EOY is end of year, EOY-1 is end of prior year. 

Dependent Beneficiaries of DIB EOY = Exposures EOY * Linkages EOY (3.2.4) 

 

3.2.b. Input Data

Trustees Assumptions 
149 

Each year, the Trustees set the assumption for the ultimate age-sex-adjusted incidence rate and 

the ultimate age-sex-adjusted recovery rate. This is achieved by setting the age-adjusted 

incidence rate and the age-adjusted recovery rate for each sex. The ultimate level for the age-sexadjusted incidence rate is set for 2023, while the ultimate level for the age-sex-adjusted recovery 

rate is set for the twentieth year of the projection period. Using a standard population of 

disability insured who are not in current pay as of December 1999, the age-sex-adjusted 

incidence rate for the 2008 Trustees Report was 5.5 per 1,000. Using a standard population of 

DIBs as of December 1999, the age-sex-adjusted recovery rate for the 2008 Trustees Report was 

9.4 per 1,000. 

Long-Range OCACT Data 

All data is updated annually except those noted otherwise. Population data are as of December 

31. Data as of December 31 of year z-1 are assumed equal to data as of January 1 of year z. 

 Demography

• January Social Security area population by age, sex, and marital status34 (dimensioned 

(0:100+,1:2,1:4)) for years 1971-2086. 

• Total children by sex of parent, age of parent and age of child (dimensioned 

(1:2,19:71,0:18)) for years 1971-2086. 

• Total married lives by age of husband crossed with age of wife (dimensioned 

(14:100+,14:100+)) for years 1971-2086. 

• Average number of children under 16 per couple with children by age group (<25, 25-

29,...,60-64) of head of household (dimensioned (1:9)) for years 1971-2086.. 

• Probabilities of death by sex, age and year (1:2,15:148,2008:2085). 

Economics 

• Unemployment rates by age group (16-19, 20-24,...,60-64), sex and year (1990:2019). 

Beneficiaries (from INSURED subprocess #3.1) 

• Disability-insured population by age, sex and year (15:69,1:2,1969:2085). 

• Fully insured population by age, sex and marital status (14:95+,1:2,1:4) for years 1970-

2085. 

Other input data 

• The December 2007 data from the Master Beneficiary Record (MBR) containing the 

number of DIB by duration of entitlement, age of entitlement, sex and time of year (BOY 

or EOY) (0:50,15:66,1:2,1:2). 

• December data from the MBR containing the number of DIB by age, sex and year 

(15:66,1:2,1969:2007). 

 

34 Single, married, widowed, divorced. 
150 

• December data from the MBR containing the number of dependent beneficiaries by age, 

sex of the account holder, and year for the following beneficiary categories. 

1) Minor child (0:17,1:2,1970:2007) 

2) Student child (18:21,1:2,1970:2007) 

3) Disabled adult child (age group1:935,1:2,1970:2007) 

4) Young spouse (19:64,1:2,1970:2007) 

5) Married aged spouse (62:100,1:2,1970:2007) 

6) Divorced aged spouse (62:100,1:2,1970:2007) 

 Totals for each category are also read. 

• December data from the MBR containing the number of DIB awards by age, sex and year 

(15:67,1:2,1970:2007). 

• December data from the MBR containing (1) the number of DIB total terminations 

(recoveries and deaths) and (2) the number of conversions36. These data are by sex and 

year (1:2,1970:2007). 

• December data from the MBR containing the number of DIB deaths by age, sex and year 

(15:67,1:2,1975:2007). 

• December data from the MBR containing the number of estimated DIB recoveries by 

age, sex and year (15:67,1:2,1975:2007). 

• December data from the MBR containing (1) the number of DIB and (2) the number of 

old-age beneficiaries who at some point in time were converted to retired worker status. 

These data are by age, sex and year: (62:66,1:2,1970:2007) and (65:95+,1:2,1970:2007), 

respectively. 

• December data from the MBR containing the number of DIB entitled to the Hospital 

Insurance portion of Medicare by age group (<25,25-29,...,60-64,65+), sex and year 

(2:11,1:2,1973:2007). 

• Average incidence rates by age and sex (15:66,1:2) for the period 1993-2001 based on 

awards data from 1993-2006 (also known as the base incidence rates). These values are 

updated when time and data are available. 

• Incidence rate projection factors (IPROJG) by age group (15-19,20-24,...,60-64,65-66), 

sex and year (1:2,1:11,2008:2085). 

• Probability of death for DIB’s – in a multiple-decrement environment by duration, age 

and sex (0:10,15:64,1:2) for the period 1996-2000 from Actuarial Study No. 118 (also 

known as the base probability of death). These values are updated when time and data are 

available. 

• Probability of recovery for DIB’s – in a multiple-decrement environment by duration, age 

and sex (0:10,15:64,1:2) for the period 1996-2000 from Actuarial Study No. 118 (also 

known as the base probability of recovery). These values are updated when time and data 

are available. 

• Death rate projection factors (DPROJG) by age group (15-19,20-24,...,60-64), sex and 

 

35 Age groups 1 through 9 are 18-19, 20-24, 25-29,..., 55-59. 

36 Conversions are DIB beneficiaries who become eligible for old-age benefits due to reaching the normal retirement 

age. 
151 

year (1:2,1:10,2008:2085). 

• Recovery rate projection factors (RPROJG) by age group (15-19,20-24,...,60-64), sex 

and year (1:2,1:10,2008:2085). 

• Incurred but not reported (IBNR)37 factors by duration, age and sex (0:10, 15: 69, 1:2) 

based on awards data from 1993-2006. Normally, these values are updated when time 

and data are available. 

• For each year 2000-2085, (1) the Normal Retirement Age (NRA), (2) the proportion of 

DIBs who stay on the DI roll for that age, and (3) the proportion of DIBs who convert to 

an old-age benefit during that year for that age. These values are updated only when there 

is a change in the NRA or in the present law. 

• For the year 2008 and the years 2016-2026, weights for ages 61-66 for linear 

interpolating between one set of incidence rates at a particular NRA and another set of 

incidence rates at the next higher NRA. These values are updated only when there is a 

change in the NRA or in the present law. 

• Special disability workload (SDW) of SSI beneficiaries by age, sex and year 

(29:54,1:2,2008:2010). The total values are from Short-Range and broken down by age 

and sex in a spreadsheet. These values will be updated every year until the SDW is done. 

• The following linkages for the calculations of auxiliary beneficiaries; the probability that 

student is in an eligible school, the probability that adult child is disabled, the probability 

that beneficiary is not subject to the earnings test, and the probability that beneficiary was 

married 10 or more years are estimated and are updated when time and data are available. 

• Retroactive factors38 by year (1969:2006). These values are estimated using OCACT 

beneficiary data. 

• APROJ factors by auxiliary beneficiary category (1:7) for years 2008-2027. These seven 

categories are; minor child, student child, disabled adult child, young wife, young 

husband, age wife and aged husband. These values are calculated using Short-Range 

numbers for auxiliary beneficiaries and pure Long- Range numbers for auxiliary 

beneficiaries. 

3.2.c. Development of Output

Equation 3.2.1 – New Entitlements 

New entitlements are calculated by multiplying age-sex-specific incidence rates to the exposed 

population at the beginning of the year. The exposed population is the disability-insured 

population less the currently entitled population. Future age-sex-specific incidence rates are 

calculated by multiplying the base incidence rates by the incidence rate projection factors 

 

37 IBNR factors reflect the proportion of DIBs entitled to benefits who have been awarded since the year of their 

entitlement. 

38 Retroactive factors for each calendar year are the ratio of the total monthly payments to DIBs to the monthly 

DIBs in current payment status times the average DIB monthly benefit. 
152 

(IPROJGs). The projection of IPROJGs is performed by a side model. For the first ten years of 

the projection (short-range period), IPROJGs by 5-year age group and sex are obtained by using 

regression equations and independent variables of unemployment rates and previous years’ 

incidence rates. The regression equations are described in detail in Appendix 3.2-1. Then the 

IPROJGs are run through the main model and the resulting incidence rates by age group and sex 

are analyzed. If necessary, an adjustment for each year is made to the female IPROJG for any 

age group in order to limit the ratio of (1) female incidence rate to (2) male incidence rate to 

1.10. Again, the IPROJGs are run through the main model with the IPROJGs at the end of the 

short-range period (2017) held constant throughout the rest of the long-range period and the 

resulting ultimate age-adjusted incidence rates (years 2027 and later) for men and women are 

analyzed. If the ultimate age-adjusted incidence rates for men (5.61) and women (5.30) are not 

achieved then adjustments are made to the IPROJGs in the twentieth year of the projection 

period (2027). Ultimate age-sex-specific incidence rates are reached in the twentieth year of the 

projection period. For projection periods between the tenth and twentieth years, the IPROJGs are 

linearly interpolated between the ultimate IPROJGs values and the IPROJGs values at the end of 

short-range period. Additional adjustments to the IPROJGs during the short-range period may be 

made for reconciliation between the long-range model and the short-range model on an 

aggregate level by sex. For the 2008 Trustees Report, ultimate male IPROJG factors are 

adjusted so that the 30-34 age group has higher disability incidence rates than the 25-29 age 

group. Also, IPROJG factors were frozen in 2023 (instead of 2027) to produce a better trend 

line. As a result of freezing the IPROJG factors in 2023, the ultimate age-incidence rates 

increased to 5.65 and 5.33 for men and women respectively. 

Equation 3.2.2 – Exits 

The long-range model projects three types of exits from the disability roll; death, recovery and 

conversion to an old-age beneficiary upon reaching normal retirement age (NRA). Deaths and 

recoveries are projected by multiplying the beginning currently entitled population by the 

probabilities of death only and recovery only, ( (d ) qx ) and ( (r) qx ), respectively. Projected ( (d ) qx ) 

and ( (r) qx ) by age, sex, and duration are calculated by multiplying the base probabilities by the 

respective projection factors by age group and sex for that year. 

For the first ten years, the recovery projection factors (RPROJGs) by age group and sex are 

based on linear interpolation between an estimated starting level for the RPROJGs and an 

estimated tenth year projection target level for the RPROJGs. For each age group and sex, the 

starting RPROJGs are calculated the following way: 

 RPROJGTR08(2007) = RPROJGTR07 (2007) * actual recovery rate(2007) / estimated 

 recovery rate TR07(2007) 

Because there is no apparent upward or downward trend, the average recovery rates for the last 

ten historical years are used as the target values for the 10th year (2017). Then, for each age 

group and sex, the tenth year level of the RPROJGs is calculated the following way: 
153 

 RPROJGTR08(2017) = RPROJGTR08 (2007) * target value recovery rate (2017) / 

 actual recovery rate (2007) 

For the second 10 years of the projection period, the RPROJGs are linearly interpolated between 

the ultimate RPROJG value and the RPROJG value at the end of short-range period (2017). 

Ultimate recovery rates by sex are assumed to be reached in the twentieth year of the projection 

period. Ultimate recovery rates by age group and sex are determined by analyzing historical 

recovery rates. Additional adjustments may be made to the RPROJGs to reconcile with the shortrange model. The calculation of RPROJGs is performed by a side model. 

For the first year of the projection period, the death projection factors (DPROJGs) by age group 

and sex are determined so that they achieve a targeted death rate. The targeted death rate is 

determined by fitting an exponential curve to historical death rates for DIBs by age group and 

sex (see Appendix 3.2-1). For the rest of the projection period, the DPROJGs are assumed to 

improve at the same rate as the general population for that age group and sex. The DPROJGs for 

each year by 5-year age group and sex are calculated the following way: 

DPROJG(year) = DPROJG(year-1) * ( ∑

+

=

x 4

age x

year

age

qx * 

1999

age

DIB) / ( ∑

+

=

x 4 −1

age x

year

age

qx * 

1999

age

DIB) 

For the 2008 Trustees Report, additional adjustments were made to reconcile with the shortrange model. The calculation of DPROJGs is performed by a side model. 

Equation 3.2.3 – Disabled-Worker Beneficiary 

The projection begins with the latest data available from the mainframe of disabled-worker 

beneficiaries in current-payment status (DIBs who have been awarded benefits). This data is 

based on a 100 percent sample of the Master Beneficiary Record (MBR) at the end of the year. 

Disabled-worker beneficiaries are disaggregated by age at entitlement, sex and duration of 

entitlement. This population is converted to a currently entitled population by dividing each age, 

sex and duration cell by the appropriate duration-age-sex-specific IBNR factor. An iterative 

process begins with new entitlements added to and exits subtracted from the previous year’s 

currently entitled population to get the following year’s currently entitled population with 

advancement of duration within the age of entitlement. This currently entitled population is then 

reduced by multiplying by the appropriate duration-age-sex-specific IBNR factor. The result is 

the following year’s disabled-worker beneficiaries in current-payment status. The process is 

performed over each sex, age of entitlement and duration of entitlement throughout the 

projection period. 

Equation 3.2.4 – Dependent Beneficiary of Disabled Workers 
154 

There are six dependent-beneficiary categories; minor child, student child, disabled adult child, 

young spouse, married aged spouse and divorced aged spouse. Projections are disaggregated by 

age of the beneficiary and sex of the account holder. Presented below are the linkages and the 

exposure used in each of the projections of dependent beneficiaries. 

Minor Child

Exposure: Single SSA population by single ages 0-17 

Linkages: pMCAGA = Probability that parent is under NRA 

pMCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pMCDPA = Probability that disability insured parent under 

NRA is disabled 

MCRES = Residual Factor 

Student Child 

Exposure: Single SSA population by single ages 18-19 

Linkages: pSCAGA = Probability that parent is under NRA 

pSCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pSCDPA = Probability that disability insured parent under 

NRA is disabled 

pSCDPC = Probability that student is in an eligible school 

SCRES = Residual Factor 

Disabled Adult Child 

Exposure: Single SSA population by age groups 18-19, 20-24, 25-29, 

 30-34, 35-39, 40-44, 45-49, 50-54, 55-59 

Linkages: pDCAGA = Probability that parent is under NRA 

pDCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pDCDPA = Probability that disability insured parent under 

NRA is disabled 

pDCDPC = Probability that adult child is disabled 

DCRES = Residual Factor 

Young Spouse 

Exposure: Married SSA population by sex and by single ages 20-64 

Linkages: pYSAGA = Probability that account holder is under NRA 

pYSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 

pYSDPA = Probability that disability insured account holder 

under NRA is disabled 

pYSETB = Probability that young spouse is not subject to 

 earnings test 

pYSMCB = Probability that young spouse has a minor child 
155 

 beneficiary in his/her care 

pYSDCB = Probability that young spouse has a disabled child 

 beneficiary in his/her care 

YSRES = Residual Factor 

Married Aged Spouse 

Exposure: Married SSA population by sex and by single ages 62-100 

Linkages: pMSAGA = Probability that account holder is under NRA 

pMSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 

pMSDPA = Probability that disability insured account holder 

under NRA is disabled 

pMSFIB = Probability that beneficiary is not insured 

MSRES = Residual Factor 

Divorced Aged Spouse 

Exposure: Divorced SSA population by sex and by single ages 62-100 

Linkages: pDSDEA = Probability that account holder is living 

pDSAGA = Probability that account holder is under NRA 

pDSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 

pDSDPA = Probability that disability insured account holder 

under NRA is disabled 

pDSFIB = Probability that beneficiary is not insured 

pDSDMB = Probability that beneficiary was married 10 or 

 more years 

The residual factors for each of the dependent categories are estimated using a 10-year Least 

Squares regression formula. These residual factor values are then held constant for the duration 

of the long range period. If the 10-year Least Squares method results in a negative residual 

factor, the last historical residual factor is held instead.

Also, APROJ factors may be developed for a dependent beneficiary category to match short 

range results during the first 10 years of the projection period. These factors are phased out 

linearly over the second ten years of the projection period. 
156 

Appendix: 3.2-1 

The following information provides details about the regression equations used in determining 

incidence rates and IPROJG values by age group and sex for the first ten years of the projection 

period. 

Male

 

Independent Variable: 16-19 unemployment rates 

Independent Variable: 15-19 incidence rates 

Dependent Variable: 15-19 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.79220710 

Standard Deviation: 0.27087301 

Coefficient Intercept: 0.89490922 

Coefficient Slope1: -0.04060960 

Coefficient Slope2: 0.94206907 

 

Independent Variable: 20-24 unemployment rates 

Independent Variable: 20-24 incidence rates 

Dependent Variable: 20-24 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.71246099 

Standard Deviation: 0.25579125 

Coefficient Intercept: 0.17891937 

Coefficient Slope1: 0.03199867 

Coefficient Slope2: 0.79826938 

 

Independent Variable: 25-29 unemployment rates 

Independent Variable: 25-29 incidence rates 

Dependent Variable: 25-29 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.90460449 

Standard Deviation: 0.06219117 

Coefficient Intercept: 0.74487677 

Coefficient Slope1: 0.17971592 

Coefficient Slope2: 0.11700596 

 

Independent Variable: 30-34 unemployment rates 

Independent Variable: 30-34 incidence rates 

Dependent Variable: 30-34 incidence rates 

Observation Period: 1994-2004 
157 

Adjusted R square: 0.85869344 

Standard Deviation: 0.09561554 

Coefficient Intercept: 0.39944807 

Coefficient Slope1: 0.11322310 

Coefficient Slope2: 0.61969161 

 

Independent Variable: 35-39 unemployment rates 

Independent Variable: 35-39 incidence rates 

Dependent Variable: 35-39 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.88647966 

Standard Deviation: 0.10149922 

Coefficient Intercept: 0.64066319 

Coefficient Slope1: 0.23607748 

Coefficient Slope2: 0.51174902 

 

Independent Variable: 40-44 unemployment rates 

Independent Variable: 40-44 incidence rates 

Dependent Variable: 40-44 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.83680625 

Standard Deviation: 0.13246275 

Coefficient Intercept: 1.23477573 

Coefficient Slope1: 0.29462829 

Coefficient Slope2: 0.45117101 

 

Independent Variable: 45-49 unemployment rates 

Independent Variable: 45-49 incidence rates 

Dependent Variable: 45-49 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.78555613 

Standard Deviation: 0.16862224 

Coefficient Intercept: 1.89060052 

Coefficient Slope1: 0.33284681 

Coefficient Slope2: 0.45768926 

 

Independent Variable: 50-54 unemployment rates 

Independent Variable: 50-54 incidence rates 

Dependent Variable: 50-54 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.79989738 

Standard Deviation: 0.26552591 

Coefficient Intercept: 1.49704927 
158 

Coefficient Slope1: 0.53085066 

Coefficient Slope2: 0.63526261 

 

Independent Variable: 55-59 unemployment rates 

Independent Variable: 55-59 incidence rates 

Dependent Variable: 55-59 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.88282633 

Standard Deviation: 0.29214117 

Coefficient Intercept: 1.43729675 

Coefficient Slope1: 0.59028867 

Coefficient Slope2: 0.76646082 

 

Independent Variable: 60-64 unemployment rates 

Independent Variable: 60-64 incidence rates 

Dependent Variable: 60-64 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.78872243 

Standard Deviation: 0.32769450 

Coefficient Intercept: 0.66578456 

Coefficient Slope1: 0.50984634 

Coefficient Slope2: 0.84130036 

 

Female 

Independent Variable: 16-19 unemployment rates 

Independent Variable: 15-19 incidence rates 

Dependent Variable: 15-19 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.82310002 

Standard Deviation: 0.17739624 

Coefficient Intercept: 0.98788191 

Coefficient Slope1: -0.05948284 

Coefficient Slope2: 0.94114088 

 

Independent Variable: 20-24 unemployment rates 

Independent Variable: 20-24 incidence rates 

Dependent Variable: 20-24 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.75413884 

Standard Deviation: 0.20229411 

Coefficient Intercept: 0.26015558 

Coefficient Slope1: 0.00281846 

Coefficient Slope2: 0.85318973 
159 

 

Independent Variable: 25-29 unemployment rates 

Independent Variable: 25-29 incidence rates 

Dependent Variable: 25-29 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.68353891 

Standard Deviation: 0.16990225 

Coefficient Intercept: 0.05004722 

Coefficient Slope1: 0.07694539 

Coefficient Slope2: 0.73561227 

 

Independent Variable: 30-34 unemployment rates 

Independent Variable: 30-34 incidence rates 

Dependent Variable: 30-34 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.77941880 

Standard Deviation: 0.12190682 

Coefficient Intercept: -0.02679705 

Coefficient Slope1: 0.18470427 

Coefficient Slope2: 0.65576148 

 

Independent Variable: 35-39 unemployment rates 

Independent Variable: 35-39 incidence rates 

Dependent Variable: 35-39 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.76781103 

Standard Deviation: 0.16836691 

Coefficient Intercept: 0.37840818 

Coefficient Slope1: 0.28699529 

Coefficient Slope2: 0.54748706 

 

Independent Variable: 40-44 unemployment rates 

Independent Variable: 40-44 incidence rates 

Dependent Variable: 40-44 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.75733974 

Standard Deviation: 0.21095751 

Coefficient Intercept: 0.77159180 

Coefficient Slope1: 0.52415194 

Coefficient Slope2: 0.42662512 

 

Independent Variable: 45-49 unemployment rates 

Independent Variable: 45-49 incidence rates 
160 

Dependent Variable: 45-49 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.80180404 

Standard Deviation: 0.18259355 

Coefficient Intercept: 2.61666324 

Coefficient Slope1: 0.55662272 

Coefficient Slope2: 0.28099690 

 

Independent Variable: 50-54 unemployment rates 

Independent Variable: 50-54 incidence rates 

Dependent Variable: 50-54 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.76597515 

Standard Deviation: 0.17810560 

Coefficient Intercept: 3.31718450 

Coefficient Slope1: 0.45561833 

Coefficient Slope2: 0.49696693 

 

Independent Variable: 55-59 unemployment rates 

Independent Variable: 55-59 incidence rates 

Dependent Variable: 55-59 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.61909066 

Standard Deviation: 0.28935635 

Coefficient Intercept: 5.93141485 

Coefficient Slope1: 0.52684406 

Coefficient Slope2: 0.45565653 

 

Independent Variable: 60-64 unemployment rates 

Independent Variable: 60-64 incidence rates 

Dependent Variable: 60-64 incidence rates 

Observation Period: 1994-2004 

Adjusted R square: 0.87061539 

Standard Deviation: 0.20779946 

Coefficient Intercept: 1.50769461 

Coefficient Slope1: 0.41132859 

Coefficient Slope2: 0.78037057 

 

The following information provides details about the exponentially fitted equations used in 

determining death rates by age group and sex for the first year of the projection period. 

Male
161 

 

Independent Variable: Year 

Independent Variable: 15-19 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.19500 

Standard Deviation: 0.25120 

Coefficient Intercept: 101.78613 

Coefficient Slope1: -0.04932 

 

Independent Variable: Year 

Independent Variable: 20-24 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.65446 

Standard Deviation: 0.08977 

Coefficient Intercept: 86.83726 

Coefficient Slope1: -0.04199 

 

Independent Variable: Year 

Independent Variable: 25-29 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.93034 

Standard Deviation: 0.03482 

Coefficient Intercept: 87.15976 

Coefficient Slope1: -0.04220 

 

Independent Variable: Year 

Independent Variable: 30-34 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.93447 

Standard Deviation: 0.03121 

Coefficient Intercept: 81.08000 

Coefficient Slope1: -0.03908 

 

Independent Variable: Year 

Independent Variable: 35-39 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.90535 

Standard Deviation: 0.02495 

Coefficient Intercept: 54.33316 

Coefficient Slope1: -0.02563 

 

Independent Variable: Year 

Independent Variable: 40-44 death rates 
162 

Observation Period: 1998-2007 

Adjusted R square: 0.73605 

Standard Deviation: 0.02576 

Coefficient Intercept: 32.19943 

Coefficient Slope1: -0.01449 

 

Independent Variable: Year 

Independent Variable: 45-49 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.71566 

Standard Deviation: 0.02529 

Coefficient Intercept: 30.51219 

Coefficient Slope1: -0.01354 

 

Independent Variable: Year 

Independent Variable: 50-54 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.33371 

Standard Deviation: 0.02162 

Coefficient Intercept: 14.76689 

Coefficient Slope1: -0.00559 

 

Independent Variable: Year 

Independent Variable: 55-59 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.90577 

Standard Deviation: 0.01888 

Coefficient Intercept: 42.66305 

Coefficient Slope1: -0.01945 

 

Independent Variable: Year 

Independent Variable: 60-64 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.93276 

Standard Deviation: 0.01776 

Coefficient Intercept: 47.78936 

Coefficient Slope1: -0.02193 

 

Female 

Independent Variable: Year 

Independent Variable: 15-19 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.19568 
163 

Standard Deviation: 0.43268 

Coefficient Intercept: 173.23776 

Coefficient Slope1: -0.08508 

 

Independent Variable: Year 

Independent Variable: 20-24 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.83626 

Standard Deviation: 0.07498 

Coefficient Intercept: 115.95251 

Coefficient Slope1: -0.05657 

 

Independent Variable: Year 

Independent Variable: 25-29 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.82467 

Standard Deviation: 0.05510 

Coefficient Intercept: 82.47329 

Coefficient Slope1: -0.03993 

 

Independent Variable: Year 

Independent Variable: 30-34 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.77932 

Standard Deviation: 0.03927 

Coefficient Intercept: 52.17643 

Coefficient Slope1: -0.02475 

 

Independent Variable: Year 

Independent Variable: 35-39 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.86429 

Standard Deviation: 0.02814 

Coefficient Intercept: 50.11319 

Coefficient Slope1: -0.02366 

 

Independent Variable: Year 

Independent Variable: 40-44 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.72257 

Standard Deviation: 0.03335 

Coefficient Intercept: 39.28514 

Coefficient Slope1: -0.01815 
164 

 

Independent Variable: Year 

Independent Variable: 45-49 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.86607 

Standard Deviation: 0.02022 

Coefficient Intercept: 37.42279 

Coefficient Slope1: -0.01713 

 

Independent Variable: Year 

Independent Variable: 50-54 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.93118 

Standard Deviation: 0.01745 

Coefficient Intercept: 45.89877 

Coefficient Slope1: -0.02128 

 

Independent Variable: Year 

Independent Variable: 55-59 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.96747 

Standard Deviation: 0.01233 

Coefficient Intercept: 47.94449 

Coefficient Slope1: -0.02224 

 

Independent Variable: Year 

Independent Variable: 60-64 death rates 

Observation Period: 1998-2007 

Adjusted R square: 0.94734 

Standard Deviation: 0.01633 

Coefficient Intercept: 49.47948 

Coefficient Slope1: -0.02294 
165 

3.3. Old-Age and Survivors Insurance

3.3.a. Overview

Every month, the Social Security program pays benefits to retired workers and their dependents. 

It also provides benefits to eligible dependents of deceased workers. The OLD-AGE AND 

SURVIVORS subprocess projects the number of people expected to receive benefits over the 

next 75 years. The projection method is very similar to the method used for dependent 

beneficiaries of disabled workers in the DISABILITY subprocess. The projection of 

beneficiaries is computed by multiplying a subset of the Social Security area population by a 

series of probabilities of the conditions that a person must meet to receive benefits. The main 

program receives all necessary input data and performs all preliminary calculations. It then calls 

each individual beneficiary type subroutine where all beneficiary calculations are made. 

Retired workers and their dependent beneficiaries are categorized as follows: 

• retired workers (RWN) by age (62-95+), sex, and marital status (single, married, 

widowed, divorced) 

• aged spouses of retired workers (ASRWN), by age (62-95+), sex of the account holder, 

and marital status of the beneficiary (married, divorced) 

• young spouses of retired workers (YSRWN) by age-group (under 25, 25-29,..., 65-69) and 

sex of the account holder 

• minor, student, and disabled adult children of retired workers (MCRWN, SCRWN, and 

DCRWN, respectively) by age of the child (0-17 for minor, 18-19 for student, age groups 

18-19, 20-24, ..., 55-59, 60+ for disabled adult) and sex of the account holder 

Dependent beneficiaries of deceased workers include: 

• aged spouses of deceased workers, ASDWN, by age (60-95+), sex of the account holder, 

marital status (widowed, divorced) and insured status (insured, uninsured) 

• disabled spouses of deceased workers (DSDWN) by age (50-69), sex of the account 

holder and marital status (widowed, divorced) 

• young spouses of deceased workers (YSDWN) by age-group (under 25, 25-29,..., 65-69), 

sex of the account holder and marital status of the beneficiary (widowed, divorced) 

• minor, student, and disabled adult children of deceased workers (MCDWN, SCDWN, and 

DCDWN, respectively) by age of the child (0-17 for minor, 18-19 for student, age groups 

18-19, 20-24,..., 55-59, 60+ for disabled adult) and sex of the account holder 

Lastly, the number of deaths of insured workers (LUMSUM) is estimated by 5-year age group 

(20-24, 25-29,..., 80-84, 85+) and sex. 
166 

Equations 3.3.1-13 indicate the flow of calculations of beneficiaries. 

ASDWN = ASDWN(⋅) (3.3.1) 

RWN = RWN(⋅) (3.3.2) 

ASRWN = ASRWN(⋅) (3.3.3) 

DSDWN = DSDWN(⋅) (3.3.4) 

MCRWN = MCRWN(⋅) (3.3.5) 

MCDWN = MCDWN(⋅) (3.3.6) 

SCRWN = SCRWN(⋅) (3.3.7) 

SCDWN = SCDWN(⋅) (3.3.8) 

DCRWN = DCRWN(⋅) (3.3.9) 

DCDWN = DCDWN(⋅) (3.3.10) 

 ) YSRWN = YSRWN(⋅ (3.3.11) 

 ) YSDWN = YSDWN(⋅ (3.3.12) 

LUMSUM = LUMSUM (⋅) (3.3.13) 

The appendix 3.3-1 at the end of this section provides a listing with explanation of the acronyms 

used in this documentation. 

 

3.3.b. Input Data

All data are updated annually unless otherwise noted. Timing of data received is denoted ‘BOY’ 

(beginning of year) or ‘EOY’ (end of year). 

Long-Range OCACT Data 

Demography

• Social Security area population by year (EOY 1970-2085), single year of age (0-100+), 

sex, and marital status (single, married, widowed, divorced) 

• Deaths by year (during years 2007-2085), age group (20-24,...,80-84, 85+) and sex 

• Average number of children per family by year (EOY 1970-2085), and age group of the 

householder (20-24,...,60-64) 

• Children by year (EOY 1970-2085), single year of age (0-17), sex of primary account 

holder (parent), status of primary (retired or deceased), and age of the other parent (15-

24,25-29,...,65-69) 

• Married couples by year (EOY 1970-2085), age of husband (62-95+) and age of wife 

(62-95+) 
167 

• Persons with an aged spouse by year (EOY 1970-2085), age group (15-24, 25-29,...,65-

69) and sex 

Economics

• Covered wages and employment in the Federal Civilian and State and Local Sectors 

(during years 1998-2085) 

• Labor force participation rates for age 62 by year (during years 1970-2085) and sex 

Beneficiaries

• Fully insured persons by year (EOY 1970-2085), age (14-95+), sex, and marital status 

(single, married, widowed, divorced) 

• Disabled-worker beneficiaries in current pay by year (EOY 1970-2085), age (62-66) and 

sex

• Converted DI to OAI beneficiaries by year (EOY 1970-2085), age(65-95+) and sex

• Disability prevalence rates by year (EOY 1970-2085), age (50-66) and sex

Short-Range OCACT Data 

• Insured aged spouses of deceased workers by year (EOY 1998-2007), age (60-95+) and 

sex 

• The following is received for EOY 2006 and 2007: 

a. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced) 

b. Retired workers by age (62-95+) and sex 

c. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced) 

d. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced) 

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased) 

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased) 

g. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased) 

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex 

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced) 

j. Total parent beneficiaries 

Note: Each year, data for the most recent historical year is appended. 

• The following is received for EOY 2017: 

a. Retired workers by age group (62-64, 65-69) and sex 

b. Insured widows by age group (60-64,...,80-84,85+) 

c. Uninsured widows by age group (60-64, 65+) 

d. Total disabled widows 
168 

e. Female young spouses of deceased workers 

f. Female aged spouses of retired workers by age group (62-64, 65+) 

g. Female young spouses of retired workers 

h. Minor children by status of parent 

i. Student children by status of parent 

j. Disabled adult children by status of parent 

• Total amount of lump-sum death payments during 2006 

Other Input Data 

• For EOY 1970-2004, obtained from the MBR10PER dataset on the mainframe: 

a. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced) 

b. Retired workers by age (62-95+) and sex 

c. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced) 

d. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced) 

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased) 

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased) 

g. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased) 

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex 

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced) 

j. Total parent beneficiaries 

Note: this data will not be updated 

• Number of beneficiaries with benefits withheld due to receipt of a significant government 

pension by sex and marital status (married, widowed) for EOY 2006 from the 2007 

Annual Statistical Supplement 

• Age distribution of beneficiaries with benefits withheld due to receipt of a significant 

government pension by age (60-95+) and sex, computed as an average from the 2001 

through 2005 WEP 100-percent sample (Note: these values are only updated about every 

five years and will be based on averages from five years of data.)

• Proportions of disabled adult children of retired and deceased workers (proportioned by 

age and sex of the child) from the 2003 MBR ten-percent sample. (Note: The RSB 

program calculates disabled adult children by sex of the primary account holder, not by 

sex of the child. The RSB program outputs a file which is used for Annual Update #9, 
169 

which calculates beneficiaries by sex. Therefore the 2003 proportions are applied to 

estimate the breakdown of disabled adult children by sex of the child. This input file will 

not be updated.) 

• Schedule of normal retirement age (NRA), delayed retirement credit, and actuarial 

reduction factors for ages more than 3 years below NRA and less than 3 years below NRA

for years 1970-2085 from the Social Security website (Note: these values are only 

updated when there is a Social Security law change regarding the NRA) 

• Elasticity factors by age (65-69) and sex for the elimination of the earnings test after 

NRA 

• Prevalence rate regression coefficients (slope and y-intercept value by sex) 

• Regressed prevalence rate by sex for the most recent historical year 

• Adjustment factors which account for the difference between estimated and actual 

historical retired worker prevalence rates by year (EOY 1970-2085), age (63-69) and sex 

• Adjustment factors which account for the difference between projected beneficiary values 

for the tenth year of the projection period made by the Long-Range and Short-Range 

offices. Factors are computed for: 

a. Retired workers by age group (62-64, 65-69) and sex 

b. Insured widows by age group (60-64,...,80-84,85+) 

c. Uninsured widows by age group (60-64, 65+) 

d. Total disabled widows 

e. Female young spouses of deceased workers 

f. Female aged spouses of retired workers by age group (62-64, 65+) 

g. Female young spouses of retired workers 

h. Minor children by status of parent 

i. Student children by status of parent 

j. Disabled adult children by status of parent 

3.3.c. Development of Output

Several acronyms are used to describe the equations presented below. Acronyms that are not 

preceded with a subscript generally refer to the number of beneficiaries. For example, RWN 

refers to the number of retired workers. Acronyms that are preceded with a ‘p’ refer to 

probabilities. For example, FIA pRW refers to the probability that a person is fully insured. 

Equation 3.3.1 – Aged Spouses of Deceased Workers (ASDWN) 
170 

The number of aged spouses of deceased workers (widow(er)s), along with all linkage 

factors, are projected by age, sex of the account holder (sa=1 for male, sa=2 for female), 

marital status and insured status. Age ranges from 60 to 95+, marital status includes 

widowed (mb=1) and divorced (mb=2), and insured status includes insured (in=1) and 

uninsured (in=2). Note that for all variables, a subscript of p denotes that the variable is a 

calculated probability. The projected number of aged spouses of deceased workers is 

calculated as follows: 

FIB GPB RES

POP DEA FIA MBB

pASDW pASDW pASDW

ASDWN ASDW pASDW pASDW pASDW

∗ ∗ ∗

= ∗ ∗ ∗ (3.3.1) 

ASDWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOPmb) for each possible marital 

status. 

ASDWPOP = SSAPOPmb

pASDWDEA represents the probability that the primary account holder (PAH) is deceased. 

For the widowed population, this factor is set equal to one. For the divorced population, this 

factor is set equal to the portion of the total widowed (SSAPOPwid) and married (SSAPOPmar) 

population who are widowed. 

 1 , mb=1 (widowed) 

 

mar wid

wid

SSAPOP SSAPOP

SSAPOP

+

 , mb=2 (divorced) 

pASDWFIA represents the probability that the PAH was fully insured at death. For a given 

age of widow, AW, it is assumed that the age of her deceased husband, AH, ranges from AW6 to AW+12 with a lower and upper bound of 60 and 95+. Further, it is assumed that the 

more likely age of the husband is AW+3. For each age, pASDWFIA is calculated as a 

weighted average of the portion of the Social Security area population who are fully insured 

at each possible age of the husband (FINSAH). For example, for a widow age 70, it is 

assumed that the age of her husband is between 64 and 82, therefore the weighted average of 

the portion of the population who are fully insured males is calculated, applying the highest 

weight of 10 to age 73, and a linearly reduced weight to zero for each age above and below 

73. The same concept is used for widow(er)s with the assumption that the age of his 

deceased wife ranges from AH-12 to AH+6, with a greater likelihood of her age being AH-3. 

Let WEIGHT represent the specific weight applied to each potential age of the spouse. 

 

WEIGHTAH =10 − AW + 3 − AH

pASDWDEA = 
171 

WEIGHTAW =10 − AH − 3− AW

 

∑

∑ +

= −

+

= −

∗

12

6

12

6

AW

AH AW

AH

AW

AH AW

AH AH

WEIGHT

WEIGHT FINS

, sa=1 

 pASDWFIA = 

 

∑

∑ +

= −

+

= −

∗

6

12

6

12

AH

AW AH

AW

AH

AW AH

AW AW

WEIGHT

WEIGHT FINS

, sa=2 

pASDWMBB represents the probability that the widow(er) is not receiving a young-spouse 

benefit for the care of a child. A young-spouse benefit can be received up to age 69 if all 

other eligibility requirements are met. Since the minimum age requirement to receive a 

widow(er) benefit is 60, it is necessary to remove those receiving a young-spouse benefit 

( ab YSDWN ), where ab represents the 5-year age bracket39. A uniform breakdown is assumed 

to divide the age groups into single-age estimates. 

 1 , 65≤age<NRA and in=2 

 0 , elsewhere 

 ASDWPOP pASDWDEA pASDWFIA

YSDWN

∗ ∗

∗ −

60−64 0.2

1 

 

∑

∗

∗ ∗ −

−

69

65

65 69

1

age

age

POP DEA FIA FACTOR

FACTOR

ASDW pASDW pASDW

YSDWN 

 1 

pASDWFIB represents the probability that the aged widow(er) is fully insured. For insured 

widow(er)s, pASDWFIB is the portion of the Social Security area population that is fully 

insured (FINS) at each age, sex, and marital status. For uninsured widow(er)s, pASDWFIB is 

simply one minus the probability for insured widow(er)s. 

 

39 There are no young spouses at NRA or above. 

pASDWMBB = , 65≤age<NRA 

 and in=2 

FACTORage =

, age=60-64 

 and in=2 

, age=60-69 

 and in=1 
172 

 SSAPOPmb

FINS

 , in=1 

 pASDWFIB = 

 SSAPOPmb

FINS 1− , in=2 

pASDWGPB represents the probability that the aged-widow(er)'s benefits are not withheld or 

not offset totally because of receipt of a significant government pension based on earnings in 

noncovered employment. According to the 1977 amendment, the Social Security benefits are 

subject to reduction by up to two-thirds of non-covered government pensions. GPWHLD

represents the total number of widow(er) beneficiaries (for all ages) expected to receive a 

significant government pension. rGPOAGE represents the ratio of the total for each given 

age. If a person is insured, this implies that he/she is eligible to receive Social Security 

benefits based on his/her own earnings regardless of a government pension. Therefore no 

factor is applied. 

 1 

 ASDWPOP pASDWDEA pASDWFIA pASDWMBB pASDWFIB

rGPOAGE GPWHLD

∗ ∗ ∗ ∗

∗

1− , in=2 

pASDWRES represents the probability that a widow(er) eligible to receive widow(er)’s 

benefits, would actual receive the benefits. In particular, for in=1, this factor is equivalent to 

the probability that a widow(er) eligible to receive his/her own retired-worker benefits would 

instead apply for and receive widow(er) benefits. For all historical years, year pASDWRES is 

calculated as the ratio of ASDWN, the actual number of widow(er)s, to the number of persons 

meeting all previously mentioned requirements by age, sex, insured status, and marital status. 

POP DEA FIA MBB FIB GPB

year

RES ASDW pASDW pASDW pASDW pASDW pASDW

ASDWN pASDW ∗ ∗ ∗ ∗ ∗ =

where TRYR is the Trustees Report year. 

For each age, sex, insured status, and marital status, a least squares regression is used over 

the last ten years of historical data to determine a starting value in TRYR-1 for 

year pASDWRES from which future values are projected. In addition, for each sex, insured status, 

and marital status, the regressed values of TRYR−1 pASDWRES are graduated over age using a 

weighted minimized third-difference formula to produce ASDW ESTRES . ASDW ESTRES are the 

preliminary estimates of TRYR+9 pASDWRES , the values in the tenth year of the projection period. 

In addition, adjustments by age group (60-64, 65-69, 70-74, 75-79, 80-84, 85+ for insured; 

pASDWGPB = 

, year<TRYR, 

, in=1 OR 

 year≤1978 
173 

60-64, 65+ for uninsured), ASDW SRADJ , are applied to the tenth year of the projection period 

in order to match the projections made by the Short-Range office. The values 

of year pASDWRES for intermediate years are linearly interpolated between TRYR−1 pASDWRES and 

N,TRYR+9 pRWRES (equal to ASDW ASDW ESTRES ∗ SRADJ ). After the 10th year, these adjustment 

factors are linearly graded to one over the 20 years beyond the end of the short-range period, 

thus gradually eliminating the effect of the short-range adjustment factors, so that we 

ultimately return to long-range projections. 

Equation 3.3.2 – Retired Workers (RWN) 

The numbers of retired-worker beneficiaries, along with all linkage factors, are projected by 

age, sex, and marital status. Age ranges from 62 to 95+, and marital status includes single, 

married, widowed, and divorced (ms=1 to 4). The projected number of retired-worker 

beneficiaries is calculated as follows: 

RWN = RWPOP ∗ pRWFIA ∗ pRWDBB ∗ pRWWBB ∗ pRWRES (3.3.2) 

RWPOP represents the subset of the population from which these beneficiaries are drawn and 

is set equal to the Social Security area population (SSAPOPms) for ms=1 to 4. 

RWPOP = SSAPOPms

pRWFIA represents the probability that the primary account holder (PAH) is insured, and is 

set equal to the portion of the Social Security area population that is fully insured (FINS) for 

ms=1 to 4. 

POP

FIA RW

FINS pRW =

pRWDBB represents the probability that the PAH is not receiving a disabled-worker or 

disability-conversion benefit. This factor is set equal to the portion of fully insured workers 

who are neither disabled-worker beneficiaries nor converted from disabled-worker 

beneficiaries (DIBCON). ASDWN represents the number of aged spouses of deceased 

workers. 

 

 RWPOP pRWFIA

DIBCON

∗

1 , − ms=1-2 

 

⎟

⎠

⎞ ⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∗

+ − DIBCON ASDWN

DIBCON

RWPOP pRWFIA

DIBCON ASDWN 1 , ms=3-4 

pRWDBB = 
174 

pRWWBB represents the probability that the PAH is not receiving a widow(er) benefit, and is 

set equal to the portion of fully insured workers that is not aged spouses of deceased workers. 

 1 , ms=1-2 

 

⎟

⎠

⎞ ⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∗

+ − DIBCON ASDWN

ASDWN

RWPOP pRWFIA

DIBCON ASDWN 1 , ms=3-4 

pRWRESN,year represents the retirement prevalence rate, which is the probability that a fully 

insured worker not receiving disability or widow(er)’s benefits would receive retired-worker 

benefits as of the given age, N, for the given year. In order to estimate the future prevalence 

rate, the program first calculates the historical values of N year pRWRES

, . 

For each historical year and sex, N year pRWRES

, is calculated as the ratio of RWN, the actual 

number of retired workers, to the number of persons meeting all previously mentioned 

requirements by age, sex, and marital status. 

POP FIA DBB WBB

N year

RES RW pRW pRW pRW

RWN pRW

∗ ∗ ∗ = , , N=62-95+ and year<TRYR 

Historical prevalence rates at age 62 and labor force participation rates (LFPRyear) at age 62, 

by sex, follow an inverse linear relationship over the historical period. This relationship is 

assumed to hold in the projection period, and therefore used to calculate REGPRyear, the 

regressed prevalence rate based on the projected LFPRyear at age 62 for each year and sex. 

Note that prevalence rates are calculated on a cohort basis40. The regression equation used to 

estimate the prevalence rates is: 

= −0.97734* + 0.91421 year year REGPR LFPR for male with an R2 value of 0.92637, and 

= −0.78782* + 0.76193 year year REGPR LFPR for female with an R2

 value of 0.78454. 

The future prevalence rate at age 62, year pRWRES

62, , is then set equal to the sum of the regressed 

prevalence rate (REGPRyear) and ERROR, the difference between the actual prevalence rate 

and the regressed prevalence rate in the most recent historical year, which is phased out 

linearly. 

 

40 For example, to calculate the projected number of 65 year olds in a given year, the prevalence rate at age 62 is 

needed. This is actually the prevalence rate that occurred three years ago at age 62. 

pRWWBB
175 

⎟

⎠

⎞ ⎜

⎝

⎛ + − = + ∗

10

9 ( ) max 0, 62, TRYR year pRW REGPR ERROR year year

RES

To compute N year pRWRES

, for ages 63 to 69 in the projection period, several preliminary 

variables must be calculated. These include: 

 MBAPIAN, for N=62,70 (same for both sexes), 

 year ESTPRN , for N=63,69 and by sex, 

 DIFFADJN, for N=63,69 and by sex, 

 year ESTPR N 2 for N=63,69 and by sex, and 

 EARNN, for N=65,69 and by sex. 

MBAPIAN is the ratio of the monthly benefit amount (MBA) to the primary insurance amount 

(PIA) at age N and is calculated on a cohort basis for N=62,70. The calculation of MBAPIAN

is based on the normal retirement age (NRA), delayed retirement credits (DRC), and actuarial 

reduction factors; ARFLE3 when the difference between NRA and age at retirement is less 

than 3, and ARFGT3 when the difference is greater than 3 within each cohort. If a person 

retires after NRA, his/her benefits are increased by DRC for each year the age exceeds NRA. 

If a person retires before NRA, his/her benefits are decreased by ARFLE3 for each of the first 

three years that NRA exceeds the age, and further decreased by ARFGT3 for any remaining 

years. 

 1 , N + (N − NRA) ∗ DRC ≥NRA 

 3 1− (NRA − N) ∗ ARFLE , NRA-3≤N<NRA 

 3 1− 3∗ ARFLE3 − (NRA − 3 − N) ∗ ARFGT , N<NRA-3 

year ESTPRN , the estimated prevalence rate at age N, is then calculated as the prevalence rate 

at age 62 ( 62, year−(N−62) pRWRES ) plus an estimate on the expected portion of the remaining 

probability ( 62, ( 62) 1 − − − year N pRWRES ), that a potential retired worker will actually retire by that 

given age. This estimate is based on MBAPIAN, assuming that the retirement decision by a 

worker is totally and completely influenced by the expected change in the portion of PIA that 

is payable at each age relative to the potential change after the initial eligibility. 

70 62

62, ( 62) 62, ( 62) 62 (1 ) MBAPIA MBAPIA

MBAPIA MBAPIA ESTPR pRW pRW year N N

RES

year N

RES

year

N −

− = + − ∗ − − − −

In the first year of the projection period, an adjustment (DIFFADJN) is made which accounts 

for the difference between the actual and estimated prevalence rate at each age in the most 

recent historical years; For ages 63 and 64, the value used beginning in TRYR is the average 

of the last 5 years’ differences between the actual and estimated PR. This value is held 

 MBAPIAN = 

 , N=62 and year≥TRYR-1 

, N=63-69
176 

constant throughout the projection period. For ages 65 to 69 the difference between the 

actual and estimated prevalence rate is computed for1999, the last year prior to the 

elimination of the earnings test at NRA. The ultimate value of DIFFADJN, reached in 2010, 

is calculated as the average difference of the five years; 1995 through 1999. The values for 

DIFFADJN for years 1999 through 2009 are linearly interpolated. 

ESTPR2 N = ESTPRN + DIFFADJ N

Another adjustment (EARNN) is needed for ages 65 to 69 which take into account the 

scheduled increases in NRA and the elimination of the earnings test at NRA. This 

adjustment measures what portion of the remaining workers, who would not have applied for 

benefits if the earnings test legislation in 2000 had not have been enacted, decide to receive 

benefits and continue to work. 

N N N

N year pRWRES = ESTPR2 + (1− ESTPR2 ) ∗ EARN , , N=65-69 and year≥TRYR 

For age 70, it is assumed that the values of the latest actual N year pRWRES

, by sex would change 

linearly to the ultimate level of 0.995 for male and 0.99 for female over the first 20 years of 

the projection period. 

 [ ] ⎟

⎠

⎞ ⎜

⎝

⎛ + − − − ∗ −

20

19 0.995 0.995 max 0, 70, 1 TRYR year pRW TRYR

RES

= year pRWRES

70,

 [ ] ⎟

⎠

⎞ ⎜

⎝

⎛ + − − − ∗ −

20

19 0.99 0.99 max 0, 70, 1 TRYR year pRW TRYR

RES

For ages 71 and older, N year pRWRES

, is assumed to stay constant at the level when the age was 

70 because there is no incentive to delay applying for benefits beyond age 70. 

, 70, −( −70) = year N

RES

N year pRWRES pRW , for N=71-95+ and year≥TRYR 

In addition, adjustments by age group (62-64, 65-69) and sex, RW SRADJ , are applied to the 

tenth year of the projection period in order to match the projections made by the Short-Range 

office. These adjustments are also applied to N year pRWRES

, for all years after TRYR+9. The 

values of N year pRWRES

, for intermediate years are linearly interpolated between N,TRYR−1 pRWRES

and N,TRYR+9 pRWRES . 

, sa=1 and 

 year≥TRYR 

, sa=2 and 

 year≥TRYR 
177 

For each age, retired workers are further broken down by age at entitlement, AE, by 

multiplying the number of retired workers at age N by the ratio of the incidence rate at AE 

(N-AE years prior) to the prevalence rate at age N. 

N year

RES

year N AE

N year N year AE

AE pRW

INCRATE RWN RWN ,

( )

*

− −

= , AE≤N 

where the incidence rate for a given AE=N and year is calculated as the change in the 

prevalence rate at age N to the prevalence rate at age N-1 in the previous year. 

 N year pRWRES

, , for N=AE=62 

= year

AE INCRATE , −1, −1 − N year

RES

N year pRWRES pRW , for 63≤N=AE≤69 

 1, 1 1 − − − N year pRWRES , for N=AE=70 

Equation 3.3.3 – Aged Spouses of Retired Workers (ASRWN) 

The number of aged spouses of retired workers, along with all linkage factors, are projected 

by age, sex of the account holder (sa=1,2), and marital status of the beneficiary. Age ranges 

from 62 to 95+, and marital status includes married (mb=1) and divorced (mb=2). The 

projected number of aged spouses of retired workers is calculated as follows: 

MBB FIB GPB RES

POP DEA AGA FIA CPA

pASRW pASRW pASRW pASRW

ASRWN ASRW pASRW pASRW pASRW pASRW

∗ ∗ ∗

= ∗ ∗ ∗ ∗ ∗

 (3.3.3) 

ASRWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOPmb) for mb=1,2. 

ASRWPOP = SSAPOPmb

pASRWDEA represents the probability that the PAH is not deceased. For the married 

population, no factor is applied. For the divorced population, the factor is set equal to the 

portion of the total married and widowed population who are married. 

 1 , mb=1 (married) 
178 

 

mar wid

mar

SSAPOP SSAPOP

SSAPOP

+

 , mb=2 (divorced) 

pASRWAGA represents the probability that the PAH is of the required age, and is set equal to 

the portion of the married population with a spouse (PAH) at least age 62 (MAR62PLUS). 

pASRWAGA = 

SSAPOPmar

MAR62PLUS

 

pASRWFIA represents the probability that the PAH is fully insured, and is set equal to the 

portion of married couples of the required age where the PAH is fully insured (FI_PAH). 

For example, when the program is estimating the number of female aged spouse of retired 

workers, this factor will find the portion where their spouse, the male PAH, is fully insured. 

[ ]

∑

∑ ∗ = MAR PLUS

MAR PLUS FI PAH

pASRWFIA 62

62 _

pASRWCPA represents the probability that the PAH is receiving benefits. This factor is set 

equal to the portion of eligible married couples where the PAH is receiving benefits 

(RETIRED). If the beneficiary is divorced, no factor is applied, since it is not required for the 

retired worker to be receiving benefits for the divorced aged spouse to receive benefits. 

 

 1 , year ≥1985 and mb=2 

 [ ]

∑[ ]

∑

∗

∗ ∗

MAR PLUS FI PAH

MAR PLUS FI PAH RETIRED

62 _

62 _ , elsewhere 

pASRWMBB represents the probability that the beneficiary is not receiving a young-spouse 

benefit. If the beneficiary is age 70 or older or if the beneficiary is divorced, no factor is 

applied. Otherwise, this factor is set equal to the portion of potentially eligible widow(er)s 

where the spouse of the PAH is not receiving a young-spouse benefit ( ab YSRWN ), where ab 

represents the 5-year age group.41

 1 , 65≤age<NRA 

 0 , elsewhere 

 

41 There are no young spouses at NRA or above. 

pASRWDEA = 

pASRWCPA = 

FACTORage =
179 

 

POP DEA AGA FIA CPA ASRW pASRW pASRW pASRW pASRW

YSRWN

∗ ∗ ∗ ∗

∗ −

60−64 0.2

1 

 

∑

∗

∗ ∗ ∗ ∗ −

−

69

65

65 69

1

ag

ag

POP DEA AGA FIA CPA

FACTOR

FACTOR

ASRW pASRW pASRW pASRW pASRW

YSRWN

 1 , elsewhere 

 

pASRWFIB represents the probability that the aged spouse is not fully insured, and is 

therefore not receiving a retired-worker benefit based on his/her own earnings. This factor is 

set equal to the portion of the married and divorced population that is not fully insured. For 

example, when the program is estimating the number of female aged spouse of retired 

workers, this factor will find the portion of female beneficiaries that is fully insured. 

SSAPOP

FINS pASRWFIB = 1 , mb=1-2 −

pASRWGPB represents the probability that the aged-spouse's benefits are not withheld 

because of receipt of a significant government pension based on earnings in noncovered 

employment. GPWHLD represents the total number of aged spouse of retired-worker 

beneficiaries (for all ages) expected to receive a significant government pension. rGPOAGE

represents the ratio of the total for each given age. 

 1 , year≤1978 

 

POP DEA AGA FIA CPA FIB ASRW pASRW pASRW pASRW pASRW pASRW

rGPOAGE GPWHLD

∗ ∗ ∗ ∗ ∗

∗ 1− , elsewhere 

pASRWMBB = 

, age=62-64 

 and mb=1

 , 65≤age<NRA 

 and mb=1 

pASRWGPB = 
180 

pASRWRES represents the probability that a person who is eligible to receive aged-spouse 

benefits actually receive the benefits. For all historical years, year pASRWRES is calculated as the 

ratio of ASRWN, the actual number of aged spouses receiving benefits, to the number of 

persons meeting all previously mentioned requirements by age, sex, and marital status. 

POP DEA AGA FIA CPA FIB

year

RES ASRW pASRW pASRW pASRW pASRW pASRW

ASRWN pASRW

∗ ∗ ∗ ∗ ∗ =

For each age, sex , and marital status, a least squares regression is used over the last ten 

years of historical data to determine a starting value in TR-1 for year pASRWRES from which 

future values are projected. In addition, for each sex and marital status, the regressed values 

of TRYR−1 pASRWRES are graduated over age using a weighted minimized third-difference 

formula to compute ASRW ESTRES . ASRW ESTRES are the preliminary estimates of 

TRYR+9 pASRWRES , the values in the tenth year of the projection period. For female spouses, 

additional adjustments by age group (62-64, 65+), ASRW SRADJ , are applied to the tenth year 

of the projection period in order to match the projections made by the Short-Range office. 

The values of year pASRWRES for intermediate years are linearly interpolated between 

TRYR−1 pASRWRES and TRYR+9 pASRWRES (equal to ASRW ASRW ESTRES ∗ SRADJ ). After the 10th year of 

the projection period, these adjustment factors are linearly graded to one over the 20 years 

beyond the end of the short-range period, thus gradually eliminating the effect of the shortrange adjustment factors, so that we ultimately return to the long-range projections. 

Equation 3.3.4 – Disabled Spouses of Deceased Workers (DSDWN) 

The number of disabled spouses of deceased workers, along with all linkage factors, are 

projected by age, sex of the account holder (sa=1 for male, sa=2 for female) and marital 

status. Age ranges from 50 to 69, and marital status includes widowed (mb=1) and divorced 

(mb=2). The projected number of disabled spouses of deceased workers is calculated as 

follows: 

 

SSB DEB RES

POP DEA FIA

pDSDW pDSDW pDSDW

DSDWN DSDW pDSDW pDSDW

∗ ∗

= ∗ ∗ ∗

 (3.3.4) 

DSDWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOPmb) for mb=1,2. 

DSDWPOP = SSAPOPmb

, year<TRYR 
181 

pDSDWDEA represents the probability that the primary account holder is deceased. For the 

widowed population, no factor is applied. For the divorced population, this factor is set equal 

to the portion of the total widowed and married population that is widowed. 

 1 , mb=1 (widowed) 

 

wid mar

wid

SSAPOP SSAPOP

SSAPOP

+

 , mb=2 (divorced) 

pDSDWFIA represents the probability that the PAH was fully insured at death. Given the age 

of the widow, AW, it is assumed that the age of her deceased husband, AH, ranges from AW-6

to AW+12 with a lower and upper bound of 50 and 95+. Further, it is assumed that the more 

likely age of the husband is AW+3. For each age, pDSDWFIA is calculated as a weighted 

average of the portion of the Social Security area population that is fully insured (FINS), at 

each possible age of the husband. For example, if the widow is age 65, it is assumed that the 

age of the husband is between 59 and 77, therefore the weighted average of the portion of the 

population who are fully insured males is calculated, applying the highest weight of ten to 

age 68 and a linearly reduced weight to zero for each age above and below 68. The same 

concept is used for widow(er)s with the assumption that the age of his deceased wife ranges 

from AH-12 to AH+6, with a greater likelihood of her age being AH-3. Let WEIGHT

represent the specific weight applied to each age. 

WEIGHTAH =10 − AW + 3 − AH

WEIGHTAW =10 − AH − 3− AW

 

∑

∑ +

= −

+

= −

∗

12

6

12

6

AW

AH AW

AW

AH AW

AH AH

WEIGHT

WEIGHT FINS

, sa=1 

 pDSDWFIA = 

 

∑

∑ +

= −

+

= −

∗

6

12

6

12

AH

AW AH

AH

AW AH

AW AW

WEIGHT

WEIGHT FINS

 , sa=2 

pDSDWSSB represents the probability that the spouse is indeed disabled and is set equal to the 

disability prevalence rates (DISPREV) by age and sex received from the DISABILITY 

subprocess. 

 

pDSDWSSB = DISPREV

pDSDWDEA = 
182 

pDSDWDEB represents the probability that the disabled spouse is not dually eligible for 

another type of benefit. This factor is assumed to remain at a constant level by sex. 

 0.85 , sa=1 

 pDSDWDEB = 

 0.06 , sa=2 

pDSDWRES represents the probability that a person who is eligible to receive disabled-spouse 

benefits actually receive the benefits. For all historical years, year pDSDWRES is calculated as 

the ratio of DSDWN, the actual number of disabled spouses of deceased workers receiving 

benefits, to the number of persons meeting all previously mentioned requirements by age, 

sex, and marital status. 

POP DEA FIA DEB

year

RES DSDW pDSDW pDSDW pDSDW

DSDWN pDSDW

∗ ∗ ∗ = , year<TRYR 

For ages 50 to 64, and each sex, and marital status, a least squares regression is used over the 

last ten years of historical data to determine a starting value in TR-for year pDSDWRES from 

which future values are projected. In addition, for each sex and marital status, the regressed 

values of TRYR−1 pDSDWRES are graduated over age using a weighted minimized third-difference 

formula to compute DSDW ESTRES . DSDW ESTRES are the preliminary estimates of 

TRYR+9 pDSDWRES , the values in the tenth year of the projection period. For female disabled 

spouses, an adjustment, DSDW SRADJ , is applied to the tenth year of the projection period in 

order to match the projections made by the Short-Range office. The values of 

year pDSDWRES for intermediate years are exponentially interpolated between TRYR−1 pDSDWRES and 

TRYR+9 pDSDWRES (equal to DSDW DSDW ESTRES ∗ SRADJ ). After the 10th year of the projection 

period, the adjustment factors are linearly graded to one over the 20 years beyond the end of 

the short-range period, thus gradually eliminating the effect of the short-range adjustment 

factors, so that we ultimately return to the long-range projections. 

For the projection period, for ages 65 to 69 where age is less than NRA, year pDSDWRES is equal 

to year pDSDWRES at age 64 times an adjustment which accounts for the additional ages as NRA 

changes. 

 1 , NRA≥age+1 

 NRA-age , age<NRA<age+1 

FACTORage =
183 

 age

age

year

RES

year

year RES

RES

year

RES FACTOR

pDSDW

pDSDW pDSDW pDSDW ∗ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = ∗

( −64)

,63

,64

,64

Equation 3.3.5-6 – Minor Children of Retired and Deceased Workers (MCRWN and MCDWN ) 

The number of minor children of retired workers, MCRWN, is projected by age of the minor 

(am=0 to 17) and sex of the account holder (sa=1 for male, sa=2 for female), and is 

calculated by multiplying the number of minor children in the most recent historical year, 

BASE_MCRWN, by two factors which reflect changes in (1) the number of children in the 

population, and (2) the proportion of retired workers to the population, at ages where a 

worker is most likely to have a minor child. 

year

sa

year

year sa

sa am

TRYR

sa am

year

sa am POP RATIO

RW RATIO

MCRWN BASE MCRWN POPRATIO

, 20 71

, 62 71

,

1

, , _

_ _ * *

−

− − = (3.3.5) 

An adjustment, MCRW SRADJ , is applied to the tenth year of the projection period in order to 

match the projections made by the Short-Range office. These adjustments are also applied to 

year MCRWNsa, am for all years after TRYR+9. The values of year MCRWNsa, am for intermediate years 

are linearly interpolated between 1

,

TRYR− MCRWNsa am and TRYR MCRW

sa am MCRWN * SRADJ 9,

+ . 

The number of minor children of deceased workers, along with all linkage factors, is 

projected by age of the minor (am=0 to 17) and sex of the account holder (sa=1 for male, 

sa=2 for female), and is calculated as follows: 

MCDWN = MCDWPOP ∗ pMCDWDEA ∗ pMCDWFIA ∗ pMCDWRES (3.3.6) 

MCDWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOP). 

MCDWPOP = SSAPOP

pMCDWDEA represents the status of the parent (PAH). This is set equal to the portion of the 

minor population where at least one parent is deceased. CHI_DEA represents the number of 

children having at least one deceased parent. 

POP

DEA MCDW

CHI DEA pMCDW _ =

pMCDWFIA represents the probability that the parent (PAH) is fully insured. This is set 

equal to the portion of the population aged 25+am to 35+am where the PAH is fully insured 

(FI_PAH). 

, age=65-69 and 

 age<NRA 
184 

[ ]

∑

∑ +

+

+

+

∗

= am

am

am

am

FIA

SSAPOP

SSAPOP FI PAH

pMCDW 35

25

35

25

_

pMCDWRES represents the probability that a child who is eligible to receive minor-child 

benefits actually receive the benefits. For all historical years, year pMCDWRES is calculated as 

the ratio of MCDWN, the actual number of minor children of deceased workers receiving 

benefits, to the number of number of persons meeting all previously mentioned requirements 

by age and sex of the parent. 

POP DEA FIA

year

RES MCDW pMCDW pMCDW

MCDWN pMCDW

∗ ∗ = , year<TRYR 

For each age and sex of parent, a least squares regression is used over the last ten years of 

historical data to determine a starting value in TR-1 for year pMCDWRES from which future 

values are projected. An adjustment, MCDW SRADJ , is applied to the tenth year of the 

projection period in order to match the projections made by the Short-Range office. The 

values of year pMCDWRES for intermediate years are linearly interpolated between the regressed 

values for TRYR−1 pMCDWRES and TRYR MCDW pMCDWRES

* SRADJ +9 . After the 10th year of the 

projection period, the adjustment factors are linearly graded to one over the 20 years beyond 

the end of the short-range period, thus gradually eliminating the effect of the short-range 

adjustment factors, so that we ultimately return to the long-range projections. 

Equation 3.3.7-8 – Student Children of Retired and Deceased Workers (SCRWN and SCDWN) 

The number of student children of retired and deceased workers, along with all linkage 

factors, are projected by age of the student (as=18 to 19) and sex of the account holder (sa=1 

for male, sa=2 for female). The projected number of student children of retired and deceased 

workers is calculated as follows: 

CPA SSB RES

POP DEA AGA FIA

pSCRW pSCRW pSCRW

SCRWN SCRW pSCRW pSCRW pSCRW

∗ ∗

= ∗ ∗ ∗ ∗

 (3.3.7) 

CPA SSB RES

POP DEA AGA FIA

pSCDW pSCDW pSCDW

SCDWN SCDW pSCDW pSCDW pSCDW

∗ ∗

= ∗ ∗ ∗ ∗

 (3.3.8) 
185 

SCRWPOP and SCDWPOP represent the subset of the population from which these 

beneficiaries are drawn and are set equal to the Social Security area population (SSAPOP). 

SCRWPOP = SCDWPOP = SSAPOP

pSCRWDEA and pSCDWDEA represent the status of the parent (PAH). For student children of 

retired workers, this is set equal to the proportion of the subset of the population where 

neither parents are deceased. For student children of deceased workers, this is set equal to 

the proportion of the subset of the population where at least one parent is deceased. 

CHI_DEA represents the number of student children having at least one deceased parent. 

POP

DEA SCRW

CHI DEA pSCRW _ = 1−

POP

DEA SCRW

CHI DEA pSCDW _ =

pSCRWAGA and pSCDWAGA represent the probability that the PAH is age 62 or older. For 

student children of retired workers, this is set equal to the proportion of the student 

population that has one parent age 62 or older, CHI_62+. For student children of deceased 

workers, the factor is set equal to one. 

POP

AGA SCRW

CHI pSCRW + = _ 62

 

pSCDWAGA = 1

pSCRWFIA and pSCDWFIA represent the probability that the PAH is fully insured. For 

student children of retired workers, this is set equal to the portion of the population aged 62 

to 64+as where the PAH is fully insured (FI_PAH). For student children of deceased 

workers, the factor is calculated similarly with the population being aged 25+as to 35+as. 

[ ]

∑

∑ +

+

∗

= as

as

FIA

SSAPOP

SSAPOP FI PAH

pSCRW 64

62

64

62

_

[ ]

∑

∑ +

+

+

+

∗

= as

as

as

as

FIA

SSAPOP

SSAPOP FI PAH

pSCDW 35

25

35

25

_
186 

pSCRWCPA and pSCDWCPA represent the probability that the PAH is receiving benefits. For 

student children of retired workers, this factor is set equal to the portion of the population 

aged 62 to 64+as where the PAH is receiving benefits (RETIRED). For student children of 

deceased workers, this factor is set equal to one. 

[ ]

∑[ ]

∑ +

+

∗

∗ ∗

= as

as

CPA

SSAPOP FI PAH

SSAPOP FI PAH RETIRED

pSCRW 64

62

64

62

_

_

pSCDWCPA = 1

pSCRWSSB and pSCDWSSB represent the probability that the child is indeed attending school 

(full-time elementary or secondary school). This factor is dependent upon the age of the 

child, and is calculated as follows. 

 16

1

as − , year≤1981 

 16

0.5

as − , year>1981 

pSCRWRES and pSCDWRES represent the probability that a child who is eligible to receive 

student-child benefits actually receive the benefits. For all historical years, year pSCRWRES and 

year pSCDWRES are calculated as the ratio of SCRWN and SCDWN, the actual number of student 

children receiving benefits, to the number of number of persons meeting all previously 

mentioned requirements by age and sex of the parent. 

POP DEA AGA FIA CPA SSB

year

RES SCRW pSCRW pSCRW pSCRW pSCRW pSCRW

SCRWN pSCRW

∗ ∗ ∗ ∗ ∗ =

POP DEA AGA FIA CPA SSB

year

RES SCDW pSCDW pSCDW pSCDW pSCDW pSCDW

SCDWN pSCDW

∗ ∗ ∗ ∗ ∗ =

For each age and sex of parent, a least squares regression is used over the last ten years of 

historical data to determine a starting value in TR-1 for year pSCRWRES from which future 

values are projected. An adjustment, SCRW SRADJ , is applied to the tenth year of the 

projection period in order to match the projections made by the Short-Range office. The 

values of year pSCRWRES for intermediate years are linearly interpolated between the regressed 

values for TRYR−1 pSCRWRES and TRYR SCRW pSCRWRES

* SRADJ +9 . After the 10th year of the 

projection period, the adjustment factors are linearly graded to one over the 20 years beyond 

pSCRWSSB =pSCDWSSB = 

, year<TRYR 

, year<TRYR 
187 

the end of the short-range period, thus gradually eliminating the effect of the short-range 

adjustment factors, so that we ultimately return to the long-range projections. Values of 

year pSCDWRES are calculated similarly. 

Equation 3.3.9-10 – Disabled Adult Children of Retired and Deceased Workers (DCRWN and 

DCDWN) 

The number of disabled adult children of retired and deceased workers, along with all linkage 

factors, are projected by age-group of the disabled adult child (ad=1-10) and sex of the 

account holder (sa=1 for male, sa=2 for female). The age groups are 18-19, 20-24, ..., 55-

59, 60+. The projected number of disabled adult children of retired and deceased workers is 

calculated as follows: 

 

CPA SSB RES

POP AGA DEA FIA

pDCRW pDCRW pDCRW

DCRWN DCRW pDCRW pDCRW pDCRW

∗ ∗ ∗

= ∗ ∗ ∗ (3.3.9) 

 

CPA SSB RES

POP AGA DEA FIA

pDCDW pDCDW pDCDW

DCDWN DCDW pDCDW pDCDW pDCDW

∗ ∗ ∗

= ∗ ∗ ∗ (3.3.10) 

All factors are calculated similar to those for student children with the exception of the 

following. 

pDCRWDEA is set equal to the proportion of the married and widowed population who are 

married (for ages of the parent that are reasonable based on the given age range of the 

disabled child). pDCDWDEA is calculated similarly for disabled children of deceased 

workers. 

mar wid

mar

SSAPOP SSAPOP

SSAPOP

+

, ad=1-9 

 pDCRWDEA =

mar wid

mar

SSAPOP SSAPOP

SSAPOP

+

0.25*

, ad=10 

 

mar wid

wid

SSAPOP SSAPOP

SSAPOP

+

 , ad=1-9 

 pDCDWDEA =
188 

0.75 0.25*+

mar + wid

wid

SSAPOP SSAPOP

SSAPOP , ad=10 

pDCRWSSB and pDCDWSSB represent the probability that the adult child is indeed disabled. 

DCPREM is the preliminary calculation of this factor and is assumed to remain constant. For 

the projection period, for ad=6-10, pDCRWSSB and pDCDWSSB are set equal to the 

preliminary factor, plus an adjustment which accounts for the year. 

 0.012 , ad=1-2 

 0.009 , ad=3 

 0.007 , ad=4 

 0.006 , ad=5 

 0.005 , ad=6 

 0.004 , ad=7-10 

 min[ ] 0.005, DCPREM + 0.0001∗ (year − TRYR)

 DCPREM , elsewhere 

Equation 3.3.11-12 – Young Spouses of Retired and Deceased Workers (YSRWN and YSDWN) 

The number of young spouses of retired and deceased-workers, along with all linkage 

factors, are projected by age-group (ab=1-10) of the young spouse and sex of the account 

holder (sa=1 for male, sa=2 for female). Young spouses of deceased workers are also 

projected by marital status of the young spouse (mb=1 for widowed and mb=2 for divorced). 

The age groups are under 25, 25-29 ..., 65-69. The projected number of young spouses of 

retired and deceased-workers is calculated as follows: 

YSRWN = YSRWPOP ∗ pYSRWAGA ∗ pYSRWECB ∗ pYSRWFSB ∗ pYSRWRES (3.3.11) 

YSDWN = YSDWPOP ∗ pYSDWDEA ∗ pYSDWECB ∗ pYSDWFSB ∗ pYSDWRMB ∗ pYSDWRES (3.3.12) 

YSRWPOP and YSDWPOP represent the subset of the population from which these 

beneficiaries are drawn. YSRWPOP is set equal to the married Social Security area population 

(SSAPOPmar) and YSDWPOP is set equal to SSAPOPmb for mb=1-2. 

YSRWPOP = SSAPOPmar

YSDWPOP = SSAPOPmb

pYSDWDEA represent the probability that the PAH is deceased. For mb=1, no factor is 

applied. For mb=2, this factor is set equal to the portion of young spouses that is widowed. 

DCPREM = 

pDCRWSSB 

=pDCDWSBB= 

, ad=7-10 and 

 year>TRYR+1 
189 

 1 , mb=1 (widowed) 

 

wid mar

wid

SSAPOP SSAPOP

SSAPOP

+

, mb=2 (divorced) 

pYSRWAGA and represent the probability that the PAH is of the required age. pYSRWAGA is 

set equal to the portion of the married population who has an aged spouse (AGSP). 

POP

AGA YSRW

AGSP pYSRW =

pYSRWECB and pYSDWECB represent the probability that the young spouse has an entitled 

child in their care. pYSRWECB is set equal to the portion of persons meeting the previously 

mentioned requirements who have a minor or disabled adult child in their care. pYSDWECB

,by marital status, is set equal to the portion of persons meeting the previously mentioned 

requirements who have a minor or disabled adult child in their care. ab MCRWN and 

ab DCRWN represent the total number of minor and disabled adult children of retired workers 

where the other parent (young spouse) is in the age bracket ab. 

POT AGA

ab ab

ab

ECB YSRW pYSRW

MCRWN DCRWN

pYSRW

∗

+ =

( )

POP DEA

total

AGA

total

DEA

total

POP

mb

AGA

mb

DEA

mb

ab ab POP

mb

ECB YSDW pYSDW

YSDW pYSDW pYSDW

YSDW pYSDW pYSDW MCDWN DCDWN

pYSDW

∗

⎥

⎦

⎤ ⎢

⎣

⎡

∗ ∗

∗ ∗

+ ∗

=

pYSRWFSB and pYSDWFSB represent the probability that the young spouse is not already 

receiving benefits based on another child in their care. This factor is set equal to one divided 

by the number of children in the average family (ASOFab) for the given age bracket of the 

spouse. For young spouses of retired workers, no factor is applied for sa=2. 

 ASOFab

1 , sa=1 

 1 , sa=2 

ab

FSB ASOF pYSDW 1 =

pYSDWDEA = 

pYSRWFSB =
190 

pYSDWRMB represents the probability that the spouse is not remarried. This factor is 

assumed to remain constant at 0.600. 

= 0.600 RMB pYSDW

pYSRWRES and pYSDWRES represent the probability that a person who is eligible to receive 

young-spouse benefits actually receive the benefits. For all historical years, year pYSRWRES is 

calculated as the ratio of YSRWN, the actual number of young spouses of retired workers 

receiving benefits, to the number of persons meeting all previously mentioned requirements 

by age, sex, and marital status. year pYSDWRES is calculated similarly, using the number of 

young spouses of deceased workers. 

POP AGA ECB FSB

RES YSRW pYSRW pYSRW pYSRW

YSRWN pYSRW

∗ ∗ ∗ = , year<TRYR 

POP DEA ECB FSB RMB

RES YSDW pYSDW pYSDW pYSDW pYSDW

YSDWN pYSDW

∗ ∗ ∗ ∗ = , year<TRYR 

For each age, sex , and marital status, a least squares regression is used over the last ten years 

of historical data to determine a starting value in TR-1 for year pYSRWRES . In addition, for each 

sex and marital status the regressed values of TRYR−1 pYSRWRES are graduated over age using a 

weighted minimized third-difference formula to compute YSRW ESTRES . YSRW ESTRES are 

the preliminary estimates of TRYR+9 pYSRWRES , the values in the tenth year of the projection 

period. For female young spouses, an adjustment, YSRW SRADJ , is applied to the tenth year of 

the projection period in order to match the projections made by the Short-Range office. The 

values of year pYSRWRES for intermediate years are exponentially interpolated between 

TRYR−1 pYSRWRES and TRYR+9 pYSRWRES (equal to YSRW YSRW ESTRES ∗ SRADJ ). After the 10th year 

of the projection period, the adjustment factors are linearly graded to one over the 20 years 

beyond the end of the short-range period, thus gradually eliminating the effect of the shortrange adjustment factors, so that we ultimately return to the long-range projections. Values 

of year pYSDWRES are calculated similarly. 

Equation 3.3.13 – Number of Deaths of Insured Workers (LUMSUMab) 

The number of deaths of insured workers is projected by sex and 5-year age group (ab=1-14). 

Age groups include 20-24, 25-29,...,80-84, 85+. EXPOSUREab, the estimated number of 

lump-sum payments paid during the year for age group ab, is calculated as the number of 
191 

total deaths during the year times the probability that the deceased was fully insured and has 

a surviving spouse or child. BASE is calculated as the ratio of the actual total amount of 

lump-sum death payments paid in TRYR-1 to the estimated total amount of lump-sum 

payments paid in TRYR-1. LUMSUMab is then calculated for each year in the projection 

period. 

LUMSUMab = EXPOSUREab ∗ BASE (3.3.13) 

Appendix 3.3-1: Glossary 

AB: age group of the beneficiary 

AD: age of the disabled child 

AGSP: married population where at least one spouse is age 62 or older 

AM: age of the minor child 

ARFGT3: actuarial reduction factor for ages more than 3 years below normal retirement age 

ARFLE3: actuarial reduction factor for ages less than 3 years below normal retirement age 

AS: age of the student child 

ASDW: aged spouse of deceased worker by linkage factor, age (60-95+), sex of the account 

holder, marital status (widowed, divorced) and insured status (insured, uninsured). Linkage 

factors are: 

ASDWPOP : population of potential aged spouse of retired workers 

DEA pASDW : probability that the primary account holder (PAH) is deceased 

FIA pASDW : probability that the PAH was fully insured at death 

MBB pASDW : probability that the widow(er) is not receiving a young-spouse benefit for 

 the care of a child 

FIB pASDW : probability that the aged widow(er) is fully insured 

pASDWGPB : probability that the aged-widow(er)'s benefits are not withheld or offset 

 totally because of receipt of a significant government pension based on 

 earnings in noncovered employment 

pASDWRES : probability that a widow(er) eligible to receive his/her own retired-worker 

 benefits would instead apply for and receive widow(er) benefits 

ASDWN: final number of aged spouse of deceased workers (product of all linkage factors) 

ASOF: average number of children in a family, by age group (under 25, 25-29 ..., 65-69) 

ASRW: aged spouse of retired worker by linkage factor, age (62-95+), sex of the account 

holder, and marital status of the beneficiary (married, divorced). Linkage factors are: 

ASRW : POP population of potential aged spouse of retired worker beneficiaries 

DEA pASRW : probability that the primary account holder (PAH) is not deceased 

pASRW : AGA probability that the PAH is of the required age 

FIA pASRW : probability that the PAH is fully insured 

pASRW : CPA probability that the PAH is receiving benefits 
192 

MBB pASRW : probability that the beneficiary is not receiving a young-spouse benefit 

FIB pASRW : probability that the aged spouse is not fully insured 

pASRW : GPB probability that the aged-spouse's benefits are not withheld because of 

 receipt of a significant government pension based on earnings in 

noncovered employment 

pASRW : RES probability that a person who is eligible to receive aged-spouse benefits 

 actually receive the benefits 

ASRWN: final number of aged spouse of retired workers (product of all linkage factors) 

AH: age of husband 

AW: age of wife 

BASE: ratio of actual to estimated total amount of lump-sum death payments paid in TRYR-1 

CHI_62+: number of children having at least one parent aged 62 or older 

CHI_DEA: number of children having at least one deceased parent 

CON: number of persons converted from disabled-worker beneficiaries 

DCDW: disabled child of deceased workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as SCDW. 

DCDW : POP population of potential disabled children 

pDCDW : AGA probability that the PAH is age 62 or older 

DEA pDCDW : probability that the parent is either retired or deceased 

FIA pDCDW : probability that the PAH is fully insured 

pDCDW : CPA probability that the PAH is receiving benefits 

pDCDW : SSB probability that the child is indeed disabled 

pDCDW : RES probability that a child who is eligible to receive disabled-child benefits 

 actually receive the benefits 

DCDWN: final number of disabled children of deceased workers (product of all linkage factors)

DCPREM: preliminary calculation of the probability that a child is disabled, by age 

DCRW: disabled child of retired workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as those for DCDW. 

DCRWN: final number of disabled children of retired workers (product of all linkage factors) 

DIB: number of disabled-worker beneficiaries 

DIFFADJ: adjustment which accounts for the difference between the actual and estimated 

prevalence rate at each age in the most recent historical years 

DISPREV: disability prevalence rate by age and sex 

DRC: delayed retirement credit 

DSDW: disabled spouse of deceased worker by linkage factor, age (50-69), sex of the account 

holder, and marital status (widowed, divorced). Linkage factors are: 

DSDW : POP population of potential beneficiaries 

DEA pDSDW : probability that the primary account holder (PAH) is deceased 

FIA pDSDW : probability that the PAH was fully insured at death 
193 

pDSDW : SSB probability that the spouse is indeed disabled 

DEB pDSDW : probability that the disabled spouse is not receiving another type of benefit 

pDSDW : RES probability that a person who is eligible to receive disabled-spouse 

benefits actually receive the benefits 

DSDWN: final number of disabled spouse of deceased workers (product of all linkage factors) 

ERROR: actual prevalence rate minus the regressed prevalence rate in the most recent historical 

year 

ESTPR: preliminary estimate of the prevalence rate for retired workers 

ESTPR2: secondary estimate of the prevalence rate for retired workers 

ESTRES: preliminary estimate of the RES factor for the tenth year of the projection period 

EXPOSURE: estimated number of lump-sum payments by age group (20-24, 25-29,...,80-84, 

85+) 

FACTOR: adjustment for calculation of MBB factor of aged spouse of deceased worker 

FINS: portion of the SSA population that is fully insured 

FI_PAH: portion of married population where one spouse is fully insured 

FP: status of the parent (retired, deceased) 

GPOAGE: portion, by age, of the total beneficiaries expected to receive a significant 

government pension 

GPWHLD: total number of beneficiaries (for all ages) expected to receive a significant 

government pension 

IN: insured status of the beneficiary 

LFPR: labor force participation rates for age 62, by sex 

LUMSUM: number of deaths of insured workers by sex and age group (20-24,...,80-84,85+) 

MAR62PLUS: number of couples where both husband and wife are age 62 and over 

MS: marital status of the primary account holder 

MB: marital status of the beneficiary 

MBAPIA: ratio of the monthly benefit amount (MBA) to the primary insurance amount (PIA) 

by age (62-70) and sex 

MCDW: minor children of deceased workers by linkage factor, age of the child (0-17) and sex 

of the account holder. Linkage factors are: 

MCDW : POP population of potential minor children 

DEA pMCDW : probability that the parent is either retired or deceased 

FIA pMCDW : probability that the PAH is fully insured 

pMCDW : RES probability that a child who is eligible to receive minor-child benefits 

 actually receive the benefits 

MCDWN: final number of minor children of deceased workers (product of all linkage factors) 

MCRW: minor children of retired workers by linkage factor, age of the child (0-17) and sex of 

the account holder. 

MCRWN: final number of minor children of retired workers (product of all linkage factors) 

NRA: normal retirement age 

PAH: primary account holder 

REGPR: regressed prevalence rate for retired workers 
194 

RETIRED: number of retired workers receiving benefits 

RW: retired workers by linkage factor, age (62-95+), sex, and marital status (single, married, 

widowed, divorced). Linkage factors are: 

RW : POP population of potential retired-worker beneficiaries 

FIA pRW : probability that the primary account holder (PAH) is insured 

DBB pRW : probability that the PAH is not receiving a disabled-worker benefit 

pRW : WBB probability that the PAH is not receiving a widow(er) benefit 

pRW : RES retirement prevalence rate; probability that a fully insured worker (not receiving 

 disability or widow(er)’s benefits) would receive a retired-worker benefit 

RWN: final number of retired workers (product of all linkage factors) 

SA: sex of the account holder 

SCDW: student children of deceased workers by linkage factor, age of the student (18-21) and 

sex of the account holder. Linkage factors are: 

SCDW : POP population of potential student children 

DEA pSCDW : probability that the parent is either retired or deceased 

pSCDW : AGA probability that the PAH is age 62 or older 

FIA pSCDW : probability that the PAH is fully insured 

pSCDW : CPA probability that the PAH is receiving benefits 

pSCDW : SSB probability that the child is indeed attending school 

pSCDW : RES probability that a child who is eligible to receive student-child benefits 

 actually receive the benefits 

SCDWN: final number of student children of deceased workers (product of all linkage factors) 

SCRW: student children of retired workers by linkage factor, age of the student (18-21) and sex 

of the account holder. Linkage factors are same as SCDW. 

SCRWN: final number of student children of retired workers (product of all linkage factors) 

SRADJ: adjustment to match short-range projections in 10th year of projection period 

SSAPOP: Social Security area population by age (0:100), sex, and marital status (single, 

married, widowed, divorced) 

SX: sex of the beneficiary 

TRYR: first year of the projection period 

WEIGHT: estimated probability applied to each possible age of the spouse, given the age of the 

primary account holder 

YSDW: young spouse of deceased worker by linkage factor, age group (under 25, 25-29,...,65-

69), sex of the account holder and marital status (widowed, divorced). Linkage factors are: 

YSDW : POP population of potential young spouse of deceased workers 

DEA pYSDW : probability that the primary account holder (PAH) is of the required age 

pYSDW : ECB probability that the young spouse has an entitled child in their care 

pYSDW : FSB probability that the young spouse is not already receiving benefits based 

on another child in their care 
195 

pYSDWRMB : probability that the young spouse is not remarried 

pYSDW : RES probability that a person who is eligible to receive young-spouse benefits 

 actually receive the benefits 

YSDWN: final number of young spouse of deceased workers (product of all linkage factors) 

YSRW: young spouse of retired worker by linkage factor, age group (under 25, 25-29,...,65-69) 

and sex of the account holder. Linkage factors are: 

YSRW : POP population of potential young spouse of retired workers 

pYSRW : AGA probability that the primary account holder (PAH) is of the required age 

pYSRW : ECB probability that the young spouse has an entitled child in their care 

pYSRW : FSB probability that the young spouse is not already receiving benefits based 

on another child in their care 

pYSRW : RES probability that a person who is eligible to receive young-spouse benefits 

actually receive the benefits 

YSRWN: final number of young spouse of retired workers (product of all linkage factors) 
196 

Process 4: 

Trust Fund 

Operations & 

Actuarial Status 
197 

4. Trust Fund Operations and Actuarial Status 

OCACT uses the Trust Fund Operations and Actuarial Status Process to project (1) the annual 

flow of income from payroll taxes, taxation of benefits, and interest on assets in the trust fund 

and (2) the annual flow of cost from benefit payments, administration of the program, and 

railroad interchange. The annual flows are projected for each year of the 75-year projection 

period. In addition, this subprocess produces annual and summarized values to help access the 

financial status of the Social Security program. 

The Trust Fund Operations and Actuarial Status Process is composed of three subprocesses: 

TAXATION OF BENEFITS, AWARDS, and COST. As a rough overview, TAXATION OF 

BENEFITS projects, for each year during the 75-year projection period, the amount of income 

from taxation of benefits as a percent of benefits paid. AWARDS projects information needed to 

determine the benefit levels of newly awarded retired workers and disabled workers by age and 

sex. COST uses information from the AWARDS and TAXATION OF BENEFITS 

subprocesses, as well as information from other processes, to project the annual flow of income 

and cost to the trust funds. In addition, COST produces annual and summarized measures of the 

financial status of the Social Security program. 

4.1. TAXATION OF BENEFITS 

4.1.a. Overview 

The 1983 Social Security Act specifies including up to 50 percent of the Social Security benefits 

to tax return filer’s adjustable gross income for tax liability if tax return filer’s adjusted gross 

income plus half of his (or her) Social Security benefits is above the specified income threshold 

amount of $25,000 as a single filer (or $32,000 as a joint filer). Moreover, the 1993 OBRA 

(Omnibus Budget Reconciliation Act) increased taxable benefits up to 85 percent if tax return 

filer’s adjusted gross income plus half of his (or her) Social Security benefits is above the 

specified income threshold amount of $34,000 as a single filer (or $44,000 as a joint filer). 

The proceeds from taxing up to 50 percent of the OASDI benefits, as a result of the 1983 Act, 

are credited to the OASI and DI Trust Funds, while additional taxes on the OASDI benefits, as a 

result of the 1993 Act, are credited to the HI Trust Fund. 

Income to the trust funds from such taxation is done by estimating ratios of taxes on benefits to 

benefits for the OASI and DI programs separately. These ratios, called “RTBs,” are applied to 

the projected OASI and DI benefit amounts to estimate tax revenues to the OASI, DI, and HI 

Trust Funds. 
198 

For the short range period (first 10 years of the projection), OCACT (Office of the Chief 

Actuary) uses OTA (Office of Tax Analysis)’s projected estimates: (1) percent of benefits 

taxable, and (2) average marginal tax rates applicable to those OASI and DI benefits. The 

multiplication of the (1) and (2) produces the projected RTBs under the 1983 Act and 1993 Act, 

respectively. 

For each year (yr) after the short range period (11th through 75th year of the projection period), 

the RTB ratios for the OASI benefits and for the DI benefits under the 1983 Act and the 

combined 1983 and 1993 Act are computed with the following formula for each projection year. 

RTB(yr) = RTB(tryr+9) * {AWI(tryr+9)/AWI(yr)}^P + 

 RTB(ultimate)*{1- AWI(tryr+9)/AWI(yr)}^P, (4.1.1) 

where 

 tryr = first year of the projection period (year of the Trustees Report) 

 

 RTB(ultimate) = ratio of taxes on benefits to benefits assuming income 

 threshold amounts equal zero. 

 

 AWI = SSA average wage index series 

 P = exponential parameter for a trend curve line. 

Finally, OCACT applies the projected RTB ratios to its own estimates of the projected OASI and 

DI benefit payments to produce taxation of benefit revenues to the OASI, DI, and HI Trust 

Funds, respectively. 

4.1.b. Input Data 

OCACT Data 

Economics

- Projected SSA wage index series by year, updated yearly 

Other input Data 

- OTA’s projected percent of benefits taxable and average marginal tax rates by 

type of benefit (OASI, DI) and by OASDI Trust Fund and HI Trust Fund for the 

short range period. Updated yearly. 

- OTA’s ultimate ratios of taxes on benefits to benefits (i.e., with income 

thresholds, assumed equal to 0). Such ultimate ratios are provided by OASDI 
199 

Trust Fund and HI Trust Fund on a combined OASDI benefit type basis, and are 

expected to be updated periodically based on OTA’s update. 

4.1.c. Development of Output

For the short range period, OCACT uses OTA’s estimates of benefits taxable and average 

marginal tax rate projections for OASI and DI benefits, under the 1983 Act and 1993 Act, 

respectively. OCACT multiplies these two estimated ratios to compute the projected RTB ratios. 

After the short range period, formula 4.1.1 computes projected ratios of taxes on OASI benefits 

to OASI benefits and projected ratios of taxes on DI benefits to DI benefits under the 1983 Act 

(up to 50 percent of benefits taxable) and under the combined 1983 and 1993 Acts (up to 85 

percent of benefits taxable). This formula essentially provides more weight to the ultimate RTB 

ratios as time progresses, using the ratio of AWI (10th year) to AWI (projection year) as the 

“weight.” Additionally, an exponential parameter P value to the AWI “weights” is set 

judgmentally such that the estimate continues the short range trend into the transitional 11th

through 20th projection years before it approaches the ultimate RTB ratio. For the RTB ratios for 

up to 50 percent of benefits taxable, the P values were set at 0.98 and 0.99 to project smooth 

transitional RTB ratios for OASI and DI benefits, respectively.42

The ultimate RTB ratios used in the projection are based on OTA’s ultimate ratios, reduced by 

about 5 percent. The 5 percent reduction reflects estimates of the effect of the higher proportion 

of “old elderly” beneficiaries in the 2085 projected SSA (Social Security Area) population 

relative to the current SSA population distribution, due to improved mortality. 

For the 2008 Trustees Report, the ultimate RTB ratios for up to 50 percent of OASI and DI 

benefits taxable were set at 0.055 and 0.0275, respectively.43 

Lastly, OCACT applies these projected RTB ratios to its own estimates of OASI and DI benefit 

payments to develop estimated taxation of benefit revenues to the OASI, DI, and HI Trust Funds, 

respectively. 

 

42 For RTB ratios for up to 85 percent of benefits taxable, P values were set at .98 and .99 for OASI and DI benefits, 

respectively. 

43 Ultimate ratios for up to 85 percent of OASI and DI benefits taxable, with the higher $34,000/$44,000 threshold 

amounts, were set at 0.092 and 0.046, respectively. 
200 

4.2. AWARDS 

Each year over 2 million workers begin receiving either retired-worker or disabled-worker 

benefits. The monthly benefits for these new awards are based on their primary insurance 

amount or simply PIA. The PIA is computed using the PIA benefit formula as specified in the 

1977 amendments and the average indexed monthly earnings (AIME). The AIME depends on 

the number of computation years, Y, and the amount earned (earnings level) by a worker in each 

year. For retired-worker beneficiaries who have attained or will attain age 62 in 1991 or later, Y

= 35. 

The AWARDS subprocess selects records from a 10% sample of newly entitled worker 

beneficiaries obtained from the Master Beneficiary Record (MBR).44 The selected sample, 

referred to as “sample”, contains 221,239 beneficiary records, and each record, r, includes a 

worker’s history of taxable earnings under the OASDI program as well as additional information 

such as sex, birth date, month of initial entitlement, and type of benefit awarded. To estimate the 

benefit levels of future newly awarded worker beneficiaries, the earnings records in the sample 

are modified to reflect the expected work histories and earnings levels of future beneficiaries 

(equation 4.2.1). After the modifications, an AIME is computed for each record in the future 

sample of beneficiaries (equation 4.2.2). Each AIME value is then subdivided into bend point 

subintervals45 (equation 4.2.3). As input to the Cost subprocess, the AIME values are used to 

calculate aggregate percentages of AIME in each bend point subinterval for each age at 

entitlement, sex and trust fund (equation 4.2.4). Equations 4.2.1 through 4.2.4 outline the overall 

structure and solution sequence. The subscript n refers to the bend point subinterval and r refers 

to the sample record. 

 Projected Earnings = Projected Earnings (·) (4.2.1) 

 AIME(r) = 12

Highest Indexed Earnings( )

∗

∑

Y

Y r

 (4.2.2) 

 ) AIME (r n = AIME n (·) (4.2.3) 

 PAPn = ∑

∑

r

n

r

n r

bp

AIME ( )

 (4.2.4) 

 where bpn is the length of the nth bend point subinterval, 

 

44 A record is selected if the year of initial entitlement equals 2004 and the beneficiary is in current pay status as of 

Dec. 2004, 2005 or 2006. Retired beneficiaries over age 70 and disability beneficiaries under age 20 or over age 64 

were excluded. 

45 The current law PIA formula has two bend points. For the purposes of PAP, the Awards subprocess instead uses 

30 subintervals. 
201 

 Y is the number of computation years, and 

 AIMEn (r) is the AIME amount contained within the nth interval for record r. 

4.2.b. Input Data

Long-Range OCACT Projection Data 

Demography– 

• Social Security area population by sex and age. 

o From 1951 to 2085 

o Updated annually 

Economics – 

• Covered workers by sex and age--all. 

o From 1951 to 2085 

o Updated annually 

• Covered workers by sex and age—with earnings posted to the Master Earnings File 

(MEF) only. - used with CWHS data to project future earnings levels 

o From 1951 to 2085 

o Updated annually 

• Average Wage Index (AWI), projected values. 

o From 2007 to 2085 

o Updated annually 

• Average Taxable Earnings (ATE) —with earnings posted to the Master Earnings File 

(MEF) only. – used with CWHS data to project future earnings levels 

o From 1951 to 2085 

o Updated annually 

• Projected Covered Worker Rate (for validation) 

o From 2007 to 2085 

o Updated annually 

• COLA (Cost Of Living Adjustment) 

o From 2007 to 2085 

o Updated annually 

• CPI (Consumer Price Index) 

o From 2007 to 2085 

o Updated annually 

Other input data 

• 10% Awards Sample from the MBR and Master Earnings File

o Newly awarded OASI / DI beneficiaries, whose initial entitlement year was 

2004, are in current pay status as of Dec. 2004, 2005 or 2006. 

 SSN

 Type of benefit
202 

 Type of claim (retirement or disability)

 Sex 

 Date of birth 

 Date of initial entitlement 

 PIA amount 

 Type of dual entitlement 

 Dual entitlement status code 

 PIFC 

 LAF 

 Trust fund 

 Earnings histories for each worker from 1951 to 2003 

o Generally updated annually, pending validation of the sample

• Total taxable earnings and number of workers with taxable earnings by age, sex, and 

year from the 2005 Continuous Work History Sample (CWHS).

o From 1951 to 2005

o Updated annually

• AWI, Average Wage Index 

o From 1951 to 2006 

o Data obtained from OCACT internet site. 

o Updated annually 

• Wage base 

o From 1951 to 2008 

o Data obtained from OCACT internet site. 

o Updated annually 

• COLA, cost of living adjustment 

o From 1975 to 2007 

o Data obtained from OCACT internet site. 

o Updated annually 

• Amount of earnings needed to earn one quarter of coverage 

o From 1951 to 2008 

o 1978-2008 data obtained from OCACT internet site. 1951-1977 values 

estimated by applying projection methodology backwards from 1978. 

o Updated annually 

4.2.c. Development of Output 

All equations described below are projected separately for the OASI and DI program. 

Equation 4.2.1 – Projected Earnings 

In order to estimate future benefit levels, the work histories and earnings levels in the current 

sample must be modified to represent those for a sample of worker beneficiaries who are newly 
203 

entitled in future years. There are three distinct modifications that must be made to the earnings 

records. For each future year, changes are made to the earnings records in order to reflect: 

• Changes in Wage Bases. 

For some years, the projected wage base (contribution and benefit base), on an AWI 

discounted basis, is higher than the historical wage base. Therefore, the taxable earnings 

of future beneficiaries may need to include covered earnings above the reported historical 

wage base. Thus, for each record with reported taxable earnings at the wage base in a 

given year, AWARDS imputes his/her covered earnings. 

• Changes in Covered Worker Rates. 

Adjustments are made to work histories to be consistent with the projected changes in the 

economy-wide covered worker rates. Economy-wide covered worker rates are defined as 

the ratio of covered workers (from Economics subprocess) to the Social Security area 

population (from Demography subprocess). 

• Earnings Experience in the CWHS46. 

Earning levels are modified to capture the changes to date that are reflected in the 

average taxable earnings reported in the CWHS by age and sex and the changes expected 

in the future. 

Change in Wage Bases

The earnings posted in the sample are limited by the historical wage base (contribution and 

benefit base). Prior to 1975, the maximum annual amount of earnings on which OASDI taxes 

were paid was determined by ad hoc legislation. After 1974, however, the annual maximum 

level was legislated to be determined automatically, based on the increase in the Social Security 

Average Wage Index (AWI). Prior to these automatic wage base increases, a relatively large 

portion of workers earned amounts above the base. Additional legislation raising the annual 

maximum taxable amount occurred in 1979, 1980, and 1981 to improve the financial future of 

the OASDI Trust Funds. In addition, the AWI used in the automatic calculation of the annual 

taxable maximum was modified in the early 1990s to include deferred compensation amounts. 

Therefore, for each record in the sample with earnings at the wage base, the AWARDS process 

imputes covered earnings above the historical wage base in order to reflect higher maximum 

taxable amounts imposed on future newly entitled beneficiaries. Please refer to appendix 4.2-2 

at the end of this subprocess for details of this imputation. 

Change in Covered Worker Rates

 

46 This file is a 1% sample of individuals who had covered earnings at some point in their work histories. 
204 

The sample’s covered worker rate by age group and sex is defined as the ratio of (1) the number 

of those beneficiaries with covered earnings in the sample to (2) the total number of beneficiaries 

in the sample. For both males and females, the work histories are modified to reflect changes in 

the covered worker rates that would apply to a future sample of beneficiaries. These changes in 

the covered worker rates are based on changes in the economy-wide covered worker rates. The 

economy-wide covered worker rate is defined for an age-sex group in a particular period which 

represents a future sample cohort as the ratio of (1) the number of workers in the economy in this 

group that have some earnings in this period, to (2) the total midyear population in this group in 

this period. Economy-wide covered worker rates are calculated separately for each age-sex group 

and each historical and projected calendar year based on input data from the Economics and 

Demography subprocesses. 

In projecting sample covered worker rates, examination is done of the change in economy-wide 

covered worker rates, by age group, between the “base period” (representing individuals retiring 

in the sample year) and the “projection period” (representing individuals retiring in a year later 

than the sample year). Details of how this change is used to estimate the change in a covered 

worker rate for retired workers from a current period in the sample to a future period is given 

below for male and female, respectively. This presentation presumes that economy-wide 

covered rates increase over time, which is very common for females but not always true for 

males, based on 2008TR data. The calculation of the change in covered worker rate changes 

slightly if there is a reduction in relevant economy-wide covered worker rates. Example 1.1 

gives an example of the calculations done for males if economy-wide covered worker rates 

decline. 

 MALE 

• The ratio of (1) the absolute difference in the economy-wide male covered worker 

rate between the two periods to (2) the potential difference in the economy-wide 

male worker rate in the sample year (i.e., 1 – economy-wide covered worker rate), 

multiplied by 

• The corresponding potential difference in the sample’s male covered worker rates 

(i.e. 1 – sample male covered worker rate)). 

FEMALE 

• The ratio of (1) the absolute difference in the economy-wide female covered 

worker rate between the two periods to (2) the difference between the projected 

sample male covered worker rate and the economy-wide female worker rate in the 

sample year, is multiplied by 

• The corresponding difference between the projected sample male covered worker 

rate and the sample female covered worker rate. 
205 

For additional explanation of this calculation, refer to example 1.1 and 1.2 in appendix 4.2-1 of 

this subprocess. 

Once the covered worker rates for the future sample of beneficiaries are determined, 

modifications to work histories of the sample to attain these rates are generally done by 

randomly removing or adding earnings. For males, the procedure is to select records randomly. 

However, for females, an additional selection criterion is included in order to achieve a 

distribution of the number of years of earnings for retired female beneficiaries. Female records 

with 10 or fewer years of earnings are not modified. A distribution limit is set for those female 

workers with 11 to 25 total years of career earnings within the projection year. This 

distributional limit changes each projected year. In the first year, the distribution limit for 

females is equal to the male distribution plus 97% of the difference between the initial male and 

female distributions within the sample. In each subsequent year, the percentage decreases by 

three percent until it reaches 0%. Thus, the females’ years of earnings distribution for those with 

11 to 25 years of earnings is adjusted to approach that of the males. 

If a record is selected for adding earnings in a particular year, the amount of earnings added is 

based on the career earnings pattern of the selected record. When earnings are added to a record, 

AWARDS calculates the ratio of (1) the record’s Average Indexed Earnings, AIE47, to (2) the 

AIE of a hypothetical worker, w, whose year of birth and sex are the same as the record and 

whose annual earnings are set equal to average taxable earnings. For this purpose, average 

taxable earnings are determined by averaging the earnings over all records in the sample with 

the same sex and year of birth. Then, the amount of earnings48 in year t that is added to the 

record is 

 Earnings(r, t) = PreATEf (sex, t) * (AIE (r) / AIE (w)), 

where PreATEf(sex, t) is the average taxable earnings in year t, for those in the sample 

with the same sex as that of the record and calculated using projected earnings adjusted to 

reflect wage base changes for those retiring in year f. 

For additional explanation of this calculation, refer to example 2 in appendix 4.2-1 of this 

subprocess. 

Earnings Experience in the CWHS

 

47 AIE is the average indexed annual earnings, average over the highest Y years of earnings (similar to AIME, but an 

annual amount). 

48 In this subprocess, earnings histories of projected beneficiaries are all reflected as wage-indexed earnings histories 

in the 2004 sample. 
206 

For historical years beginning with 1951, the AWARDS subprocess uses average taxable 

earnings by age and sex (CWHSATEas) and numbers of covered workers by age and sex 

(CWHSCWas) as tabulated from the most recent CWHS file49. The AWARDS subprocess then 

projects these values from the base year (the last historical year in the CWHS file). Projections 

are made for each year after the base year through the end of the 75-year projection period using 

projected economy-wide number of covered workers by age and sex and annual average taxable 

earnings (ATE) from the Economics process50. 

The numbers of covered workers by age and sex (CWHSCWas) are projected by applying the 

annual growth rates by age and sex in the numbers of economy-wide covered workers50

produced by the Economics subprocess. In addition, CWHSATEas are projected. The first step is 

to determine preliminary CWHSATE'as by using the annual growth rate in the total economy-wide 

ATE50. A further multiplicative adjustment is made to each CWHSATE'as such that the resulting 

aggregate average taxable earnings, determined by combining the projected values of CWHSCWas

and CWHSATEas for the year, produces the same growth rate as the growth in total taxable 

earnings from the Economic process. 

For additional explanation of this calculation, refer to example 3 in appendix 4.2-1 of this 

subprocess. 

The CWHSATEas are then used to change the earnings histories of the sample of newly entitled 

beneficiaries so that the earnings represent newly entitled beneficiaries in future years. The 

historical and projected CWHSATEas will be different from the corresponding average taxable 

earnings of a sample of new entitled workers beneficiaries. This is mainly because the CWHS 

contains earnings for workers who never become entitled to benefits. Thus, the CWHSATEas are 

used to distribute average taxable earnings among age-sex groups of future samples of new 

beneficiaries. 

For a given sex and age-group, the expected annual average taxable earnings of a future sample 

is denoted as ATEf'. ATEf' is computed by using the comparable changes51 in the CWHSATEas. In 

addition, the annual average taxable earnings of the sample (after adjustments to the records’ 

earnings levels for changes in wage bases and covered worker rates) are computed by sex and 

age-group and denoted as ATEf. The difference between these values is the amount by which 

the average annual earnings levels are adjusted. Let 

f ATEf δ(t) = ATE ' − , 

 

49 These historical values are tabulated by the Economic subprocess. 50 These values are based on earnings posted to the Master Earnings File (MEF), excluding earnings posted to the 

suspense file. 

51 The comparable changes reflect the wage-indexed changes in the CWHS ATEas between the year of earnings in the 

sample of new beneficiaries and the year of earnings in the projected sample. 
207 

for each year t. Then, (δ(t) * TotalWorkers(t)) is the total amount of earnings which the model 

distributes for a given sex and age-group in a way so that the average taxable earnings after 

distribution is ATEf'. 

For additional explanation of the calculation δ(t), refer to example 4 in the appendix of this 

subprocess. 

When δ(t) is negative, earnings for the year are decreased. To achieve ATEf' for the given sex 

and age-group, AWARDS multiplies CoveredEarnings(r, t) by a ratio, 

α

δ = + +

ATE ( )

( ) ratio( ) 1

f t

t

t . 

The term, α, is an additional adjustment necessary because covered earnings above the wage 

base, have either no effect or only a partial effect on modifying ATEf to ATEf'. In the 2008 

Trustees Report, α was set equal to -0.06 for both sexes and trust funds (OASI and DI). 

When δ(t) is positive, earnings for the year are increased. However, the method of increasing 

earnings differs between disabled beneficiaries (DIBs) and retired worker beneficiaries (OABs). 

For DIBs, this is done similar to the adjustment when δ(t) is negative, where the ratio is 

multiplied by covered earnings to raise each record’s earnings for year t. If the resulting value 

exceeds the future wage base in year t, taxable earnings would equal the wage base. Hence, 

again, a constant α is added to account for the fact that increasing covered earnings which are 

greater or equal to the future wage base has no effect and covered earnings a little below the 

future wage base has only a partial effect on modifying ATEf'' to ATEf . For the 2008 Trustees 

Report, α = 0.02 for females and α = 0.03 for males. 

However, when earnings for the year are increased for OABs, the ratio takes into account that 

among OABs, there are many more workers with earnings near or above the future wage base. 

In order to account for this, AWARDS first computes z, such that 

∑

∑ ∑

=

= = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ∗ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∗

= 20

1

20

n j

20

n 1

NumberWorkers( , )

2

( ) NumberWorkers( , ) * ( )( ) ( ) NumberWorkers( , )

( )

n

n t

t

n t

h t

t

t n t

z t

δ δ δ

, 

where 

 
208 

(1) NumberWorkers(n, t) equals the number of workers whose earnings in year t fall within the 

nth interval, that is the number of workers whose earnings are greater or equal to IntervalLength 

(t)*(n-1) and less than IntervalLength (t)*n. For this calculation, 

20

WageBase(t) IntervalLength(t) = . Also, TotalWorkers(t) = ∑=

20

1

NumberWorkers( , )

n

n t . 

(2) j(t) is the interval, such that ⎥

⎦

⎥ ⎢

⎣

⎢ = − IntervalLength( )

( ) 20

t

t j(t) δ . 

(3) h(t) is the dollar amount from interval j(t) to the wage base, 

h(t) = IntervaLenght(t) ∗ (21- j(t)). 

Now the covered earnings of OAB records are multiplied by the ratio 

= + +α

ATE ( )

z(t) ratio(t) 1

f t , 

where α =0.03 for males and α = 0.02 for females. 

As AWARDS applies ratio(t) to Earnings(r, t) by each record, it makes sure total adjustment in a 

year does not exceed δ(t)*TotalWorkers(t). 

For additional explanation of this calculation, refer to example 5 in appendix 4.2-1 of this 

subprocess. 

Equation 4.2.2 – Average Indexed Monthly Earnings (AIME)

Step 1: Index Earnings 

To compute an individual’s AIME, all taxable earnings after 1950 are considered. First, the 

earnings are indexed up to the index year, i, which is defined as the year of attaining age 60 for 

retired-worker beneficiaries (eligible for benefits at age 62). For disabled-worker beneficiaries, i

generally equals 2 years before the year of disability onset when disability insured. Thus, 

⎪

⎩

⎪

⎨

⎧

≥

∗ < =

i

i

t

i

r t

Earnings(r, t), if t

, if t

AverageWage ( )

AverageWage ( ) Earnings( , ) IndexedEar nings(r,t)

Step 2: Determine Computation Years 
209 

For each record, the number of computation years, Y, is determined. For a retired-worker 

beneficiary in the sample, Y is 35. 

For a disabled-worker beneficiary, Y is calculated as follows: 

•Determine the number of elapsed years, which is equal to the year of disability onset (not 

later than the year the worker turned age 62) minus the greater of either the year the disabled 

worker turned age 22 or 1951. 

Elapsed Years = min{ }{ } Year of disability onset, Year attained age 62 − max 1951,Year attained age 22

•Divide the elapsed years by five and truncate. Subtract this number (cannot exceed five) 

from the number of elapsed years. 

•Y must be at least 2. 

Step 3: Determine AIME 

Finally, an individual’s AIME is computed by summing the highest Y indexed earnings and 

dividing by the number of months in those years. Hence, for each record, 

Y 12

Highest Y Indexed Earnings(r) AIME(r)

∗ = ∑ . 

Equation 4.2.3 – AIMEn(r)

The Possible AIME value is divided into 30 intervals (bend point subintervals). The length of 

each interval in 1979 dollars is given below: 

 $45, if 0 < n ≤ 13 

 bpn = $100, if 14 ≤ n ≤ 18 

 $200, if 19 ≤ n ≤ 28 

 $1000, if 29 ≤ n ≤ 30 

 

Thus, the interval points of AIME division given below in 1979 dollars, yk, are equal to ∑=

k

n

n

1

 bp

and 

⎭

⎬

⎫

⎩

⎨

⎧

⎥

⎦

⎥ ⎢

⎣

⎢ = − ,5

5

ElapsedYears Y Elapsed Y ears min
210 

 $180, if k = 4 

 yk = $1085, if k = 18 

 $5085, if k = 30. 

For each record (r), the values for bpn are indexed from 1977 to his/her indexing year i using the 

Social Security average wage index (AWI). So for n = 1 to 30, 

AWI(1977)

AWI(i) bpn (r ) = bpn ∗

Next the record’s AIME amount, AIME (r), is compared to the indexed intervals. If 

 

∑

−

=

1

1

 bp ( )

k

n

n r < AIME (r) ≤ ∑=

k

n 1

bp (r) n , 

then AIME (r) falls within the kth interval. And for n = 1 to 30, 

 ) bp (r n , if n < k

 AIMEn (r) = AIME (r) - ∑=

k

n

n r

1

bp , if ( ) n = k

 0, if n > k 

Equation 4.2.4 – Potential AIME Percentages (PAPS) 

Finally, for n = 1 to 30, AWARDS sums the values of AIMEn and bpn across all the records by 

sex, age, and trust fund. The ratio of these values gives the average potential AIME percentages 

PAPn = 

bp ( )

AIME ( )

r

n

r

n

r

r

∑

∑ . 
211 

Appendix 4.2-1

This appendix provides examples to help understand the calculations described in the 

model documentation of the AWARDS subprocess. These examples do not reflect 

actual values.

Example 1.1: (OASI-Male)

Task: In projecting the 2004 sample of newly entitled male beneficiaries to represent 

newly entitled male beneficiaries in 2050, an adjustment to the earnings histories for 

those males age 40-44 is needed to reflect lower covered worker rates expected for males 

in this age group. 

This example illustrates the calculation of the projected covered worker rate for males 

who are age 40-44 in the projection period. We will be comparing the group of males age 

40-44 in the base period with its counterpart group of males age 40-44 in the projection 

period. 

Information given: 

• Newly entitled retired male beneficiaries represented in the 2004 sample 

are age 40-44 in the base period, 1974-1986, and the counterpart group of 

males retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

• Based on the 2004 sample, covered worker rates for males age 40-44 in the 

base period = 88.0%. 

• Economy-wide covered worker rate for males age 40-44 = 85.0% in the 

base period. 

• Economy-wide covered worker rate for males age 40-44 = 75.0% in the 

projection period. 

Calculations: 

1. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the projection period is 100.0% - 75.0% or 25.0%. 

2. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the base period is 100.0% - 85.0% or 15.0%. 

3. The ratio from steps 1 and 2 is 25/15 or 166 2/3 %. 

4. The potential difference in the sample’s covered worker rate for the males 

age 40-44 in the base period is 100.0% - 88.0% or 12.0%. 

5. The ratio from step 3 is multiplied by the potential difference in the 

sample’s covered worker rate for males age 40-44 in the base period to 

yield 20.0% (166 2/3 % * 12.0% = 20.0% ). 

6. The amount in step 5 (20.0%) would be subtracted from 100% to yield the 

sample covered worker rate for males who are age 40-44 in the projection 

period (80.0%). 
212 

Example 1.2 : (OASI - Female ) 

Task: In projecting the 2004 sample of newly entitled female beneficiaries to represent 

newly entitled female beneficiaries in 2050, an adjustment to the earnings histories for 

those females age 40-44 is needed to reflect higher covered worker rates expected for 

females in this age group. 

This example illustrates the calculation of the projected covered worker rate for females 

who are age 40-44 in the projection period. We will be comparing the group of females 

age 40-44 in the base period with its counterpart group of females age 40-44 in the 

projection period. 

Information given: 

• Newly entitled retired female beneficiaries represented in the 2004 sample 

are age 40-44 in the base period, 1974-1986, and the counterpart group of 

females retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

• Based on the 2004 sample, covered worker rates for females age 40-44 in 

the base period = 75.0%. 

• Economy-wide covered worker rate for females age 40-44 = 68.0% in the 

base period. 

• Economy-wide covered worker rate for females age 40-44 = 72.0% in the 

projection period. 

• Projected sample covered worker rate for males age 40-44 = 80.0% in the 

projection period. (as shown in example 1.1 above) 

Calculations: 

1. The absolute difference in the economy-wide covered worker rate for 

females age 40-44 from the base period to the projection period is 72.0% - 

68.0% or 4.0%. 

2. The difference between the projected covered worker rate for males age 

40-44 and the economy-wide covered worker rate for females age 40-44 

in the base period is 80.0% - 68.0% or 12.0%. 

3. The ratio from steps 1 and 2 is 4.0/12.0 or 33 1/3 %. 

4. The difference between projected covered worker rate for males age 40-44 

and sample’s covered worker rate for the females age 40-44 in the base 

period is 80.0%-75.0% or 5.0%. 

5. The ratio from step 3 is multiplied by the potential difference in the 

sample’s covered worker rate for females age 40-44 in the base period to 

yield 1.667% (33 1/3 % * 5.0% = 1.667% ). 
213 

6. The amount in step 5 (1.667%) would be added to the sample covered 

worker rate for females age 40-44 in the base period (75.0%) to yield the 

projected covered worker rate for females who are age 40-44 in the 

projection period (76.667%). 

Example 2: 

Task: In projecting the 2004 sample of newly entitled male OASI beneficiaries to 

represent newly entitled male OASI beneficiaries in 2021, an adjustment to the earnings 

histories for those males age 40-44 is needed to reflect higher covered worker rates 

expected for males in this age group. The amount of increase in the covered worker rates 

is computed as described in example 1 and found to be 4 percent. To achieve this target, 

the desired number of records with zero reported earnings in this age group are randomly 

selected and assigned earnings. 

This example illustrates the calculation of earnings to be assigned to a randomly chosen 

newly entitled retired male record with zero taxable earnings in the base year. 

Information given: 

• Newly entitled retired male beneficiaries represented in the 2004 sample 

are age 40-44 in the base period, 1974-1986, and the counterpart group of 

males retiring in 2021 will be age 40-44 in the projection period, 1991-

2003. 

• Based on the 2004 sample, a male record, r = 60,000 has been randomly 

selected to replace his zero taxable earnings reported in the base year 1981 

with an amount based on his career earnings pattern. This record is age 63 

in 2004, and his year of birth is 1941. 

• A beneficiary retiring at age 63 in 2021 will have a year of birth of 1958. 

And the corresponding projection year to the base year of 1981 is the 

projection year 1998. 

• The Average Indexed Earnings for this record, AIE (60,000), is computed 

to be $43,465. Note: This value is calculated by (1) using the record’s 

annual taxable earnings reported each year through 2003, (2) converting 

them to 2003 year dollars, and then (3) summing the highest 35 years of 

earnings and dividing by 35. 

• The Average Indexed Earnings for a hypothetical worker, AIE(w) whose 

year of birth is 1941 is $41,995. This value is calculated as above given 

the hypothetical worker earned the average taxable earnings in each of the 

base years for males retiring at age 63 in the 2004 sample. 
214 

• The projected Average Taxable Earnings52 of males retiring in 2021 for the 

projection year 1998 (converted to 1981 dollars53) is ATE2020(male,1998) 

= $18,718. 

Calculations: 

1. The ratio of the Average Indexed Earnings for record number 60,000, 

AIE(60,000) to the Average Indexed Earnings of a hypothetical male 

worker born in 1941 and retiring at age 63, AIE(w) is $43,465/$41,995 or 

1.035. 

2. The amount in step 1 (1.035) would be multiplied to ATE2021(male,1998) 

given to be $18,718. This yields the amount of earnings assigned to 

record number 60,000 in the projection year 1998 representing a sample 

retiring in 2021, Thus, Earnings(60,000,1998) = 1.035 * $18,718 which 

equals $19,373. 

Example 3: 

Task: The AWARDS subprocess estimates projected values of Average Taxable 

Earnings by age and sex using the values54 in the 2005 CWHS file supplied by the 

Economic subprocess as the base year on which to build our projections. 

This example illustrates the calculation of the projected Average Taxable Earnings of the 

CWHS in 2006 for 42 year old females, CWHSATE42,female(2006). We will be using the 

number of female covered workers age 42 and the total taxable earnings for females age 

42 as given the in 2005 CWHS data. 

 

Information given: 

• The total number of female covered workers age 42 in 2005 reported in the 

CWHS, CWHSCW42,female(2005) is 17,917. . 

• The total taxable earnings for females age 42 in 2005 reported in the 

CWHS is $527,676,622. 

• The economy-wide number of covered workers for females age 42 in 2005 

is 1,782,357. 

 

52 The average taxable earnings have been computed using projected earnings adjusted for changes in the wage base. 

Adjustments to earnings for changes in covered worker rates and the earnings experience in the CWHS have not 

been applied at this stage in the process. 53 All projection year dollars are converted back to ‘sample year’ dollar amounts. 

54 Because not all earnings are posted for the most recent years for a given CWHS file, adjustment factors, based on 

historical trends, are applied by the Economic subprocess to complete these earnings. For the 2005 CWHS, 

adjustment factors were applied to data in years 2002 through 2005. 
215 

• The economy-wide number of covered workers for females age 42 in 2006 

is 1,745,831. 

• The economy-wide Average Taxable Earnings (ATE) in 2005 is $29,776. 

• The economy-wide ATE in 2006 is $31,078. 

Calculations: 

1. The growth in the economy-wide covered workers for females age 42 

from 2005 to 2006 is 1,745,831/1,782,357 or 0.9795. 

2. The growth rate in the economy-wide covered workers for females age 42 

from step 1 is applied to the CWHS female covered workers age 42 in 

2005, CWHSCW42,female(2005) to yield the projected covered workers for 

females who are age 42 in 2006, CWHSCW42,female(2006), 0.9795*17,917 or 

17,550 

3. The CWHS Average Taxable Earnings for females age 42 in 2005, 

CWHSATE42,female(2005) is computed using the given CWHS total taxable 

earnings and total covered workers for females age 42 in 2005 

($524,676,622 / 17,917 = $29,284). 

4. The economy-wide growth rate in the average taxable earnings from 2005 

to 2006 is $31,078 / $29,776 or 1.044 

5. The growth rate in step 4 (1.044) is applied to the amount in step3

($29,284) to estimate the preliminaryCWHS Average Taxable Earnings 

for females age 42 in 2006, CWHSATE’42,female(2006) = $30,573 

(1.044*$29,284) 

6. The value from step 5 ($30,573) is multiplied by the value in step 2 

(17,550) to yield the preliminary CWHS projected total taxable earnings 

for females age 42 in 2006 ($536,556,150). 

7. Note a final multiplicative adjustment is made to CWHSATE’42,female(2006) 

to obtain CWHSATE42,female(2006). This adjustment is made once the 

preliminary taxable earnings have been computed for each age and sex in 

2006 in order to ensure the growth rate in the aggregate average taxable 

earnings between 2005 and 2006 matches the growth rate in the ATE from 

the Economic process. 

Example 4: 

Task: In projecting the 2004 sample of newly entitled female beneficiaries to represent 

newly entitled female beneficiaries in 2050, the projected Average Taxable Earnings of 

females in the sample (ATEf)

55 for year t = 2020 must be adjusted by an amount, δ(2020), 

to meet a targeted Average Taxable Earnings(ATEf'') for 2020. 

 

55 The average taxable earnings have been computed using projected earnings adjusted for changes in the wage base 

and for changes in covered worker rates. 
216 

This example illustrates the calculation of δ(2020) for the female cohort retiring at ages 

62 to 70 in the projection year 2050. The cohort is age 32 to 40 in the projection year 

2020. The value δ(2020) is the dollar amount in which the average annual earnings levels 

are adjusted for females in this age-group in the year 2020 and retiring in 2050. We will 

be comparing this group of females age 32-40 in the projection 2020 year with its 

counterpart group of females age 32-40 in the base year 1974. 

 

Information given: 

• A cohort of newly entitled retired female beneficiaries retiring at ages 62 to 

70 represented in the 2004 sample are ages 32-40 in the base year, 1974, 

and the counterpart group of females retiring in 2050 are ages 32-40 in the 

projection year, 2020. 

• Based on the 2004 sample, the average taxable earnings for females in the 

base year 1974 is $4,536. 

• For a sample projected to be retiring in 2050, the average taxable earnings 

(ATEf) for females in the projection year 2020 is $4,56456. 

• Based on the 2005 CWHS data, the average taxable earnings for females 

ages 32-40 in the base year 1974 is $4,218. 

• The projected average taxable earnings in the CWHS for females ages 32-

40 in the projection year 2020 (in 1974 dollar amounts) is $4,640. 

Calculations: 

1. The increase in the average taxable earnings for females ages 32-40 in the 

CWHS from the base year 1974 ($4,218) to the projection year 2020 

($4,640)12 is 10 percent. 

2. Based on the value from step 1 the expected annual average taxable 

earnings (ATEf'') of females ages 32-40 in 2020 and retiring in 2050 is 

$4,536*1.10 or $4,990 

3. The difference in ATEf'' ($4,990) and ATEf' ($4,564) yields the δ(2020) 

value $426 ($4,990 - $4,564 = $426). 

Example 5: 

Task: In projecting the 2004 sample of newly entitled female beneficiaries to represent 

newly entitled female beneficiaries in 2033, for year t = 2023, δ(2023) is positive 

indicating an adjustment to earnings histories is needed to reflect higher average taxable 

earnings by this cohort for the projection year 2023. 

 

56 Amount is in 1974 dollars, ‘sample year dollars’. 
217 

This example illustrates the calculation of the ratio(2023) in projection year 2023 for the 

female cohort retiring at ages 62 to 70 in the projection year 2033. The value, 

ratio(2023), is the adjustment ratio that will be applied to this cohort projected covered 

earnings in 2023 in order to achieve the targeted Average Taxable Earnings of this cohort 

for 2023. 

Information given: 

• Earnings in the projection year 2023 for a group of newly entitled female 

beneficiaries retiring in 2033 is the counterpart corresponding to earnings 

in the base year 1994 for the group of newly entitled female beneficiaries 

in the 2004 sample. 

• For newly entitled females retiring in 2033, the average taxable earnings 

(ATE2023) for the projection year 2023 is $19,97057. 

• δ(2023) , the difference in the targeted average taxable earnings ATE2023' 

and ATE2023, is given to be $1,590. 

• The wage base for the projection year 2023 (in 1994 dollar amounts) is 

$57,600 

• The number of females in the projected 2033 sample with earnings below 

the wage base in 2023 is 52,800. 

• The dollar amounts below the wage base in 2023 are divided into 20 equal 

intervals, IntervalLength(2023), of $2,880 each. 

• The number of females in the 2033 sample who in 2023 have earnings 

falling in the 20th interval (their earnings are between $54,720 and 

$57,600) is 465 

• For female OABs the constant α when δ(t) is positive is 0.02. 

Calculations: 

• The interval in which $56,010 (the wage base in 2023 minus δ(2023) or 

$57,600-$1,590) falls within is interval j(2023) and is found by rounding 

δ(2023)/ IntervalLength(2023) or ($1590/$2880) to the lowest integer and 

subtracting this value from 20. This yields interval 20. 

• The dollar amount from interval 20 to the wage base is h(2023), and is 

$2,880*(21-20) or $2,880 

• Using the equation given on page 7 yields, 

( ) ( )

52,800

2

$1,590 465 *

$2,880

$1,590 $1,590 52,800

(2023)

∗ + ∗

z = = $1,594 

 

57 Amount is in 1994 dollars, ‘sample year dollars’. 
218 

Note, the value for z(2023) is higher than δ(2023) in order to adjust for 

those records above or close to the wage base. 

• The ratio multiplied to the covered earnings in 2023 for females retiring in 

2033 is 1 + ($1,594/$19,970) + 0.02, or 1.10. 
219 

Appendix 4.2-2

This appendix provides additional details on how the AWARDS process imputes covered 

earnings above the historical wage base. 

 

To do this, AWARDS first computes the cumulative distribution, F, of the workers in the sample 

by their earnings level. Each historical wage base is divided into 20 equal intervals, n, and each 

interval length in year t is 

20

WageBase(t) IntervalLength(t) = . 

The cumulative distribution F(n, t) is the proportion of workers whose earnings are less than 

IntervalLength(t)*n, for n = 1 to 20. Let NumberWorkers(n, t) be the number of workers whose 

earnings in year t fall within the nth interval, that is the earnings are greater or equal to 

IntervalLength (t)*(n-1) and less than IntervalLength (t)*n. Also, let TotalWorkers(t) be the total 

number of workers in the sample with earnings in year t. Then for any n, 1 ≤ n ≤ 20, 

TotalWorkers( )

NumberWorkers( , )

F ( , ) 1

t

m t

n t

n

m

∑= = . 

Once F(n, t) is computed for n = 1 to 20, AWARDS extends the function for those who had 

earnings at the wage base. To extrapolate F past the historical base (define F(n, t) for n > 20), 

AWARDS groups the maximum earners in each year in the sample based on the number of years 

they had earnings at the wage base during the next four years (0, 1, 2, 3, 4). Under the 

assumption of uniform distribution within each group, AWARDS assigns an F(nr, t) value to 

each record with earnings at the tax maximum beginning with the group that has no other 

earnings at the tax maximum during the next four years and ending with the group that has 

maximum earnings in each of the next four years. Note that for these beneficiaries F(nr, t) > 

F(20,t). Once F(nr, t) is computed for these beneficiaries, values for F(n, t), where n>20 are 

estimated. 

To find F(n, t), where n>20, the log odds transformation is utilized. The odds ratio, 

n,t)

n,t n,t 1- F(

F( ) T( ) = , where n < 20 

is the ratio of (1) the proportion of beneficiaries with earnings levels below the nth interval to (2) 

the proportion of beneficiaries with earnings levels above the nth interval. Next, the natural 

logarithm of the odds ratio is computed, giving the log odds transformation, 
220 

[ ] ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = = 1- F( )

F( ) Y( ) ln T( ) ln

n,t

n,t n,t n,t , where n < 20 

Utilizing the most linear portion of the function at the upper values of n, AWARDS regresses Y 

on those values. The regression line of Y has the form 

Y(n,t) * n ˆ = β 0 + β1

Finally, the amount of covered earnings of a record that has earnings at the taxable maximum is 

determined based on the F(nr, t) value assigned to the record. The F(nr, t) value for this record is 

used in the above equations to determine T(nr, t), Y(nr, t), and then nr, the non-integer value for n

in the regression equation of Yˆ above. Thus, if earnings(r, t) = wage base in year t then 

CoveredEarnings(r, t) = ∗IntervalLength(t) r n + error58, 

where nr is the record’s non-integer value for n in the regression equation of Yˆ above. 

If earnings(r, t) < wage base in year t, then CoveredEarnings (r, t) = earnings(r, t) 

At this point, AWARDS defines the expected taxable earnings of a future sample as, 

⎩

⎨

⎧

≥

< = future wage base (t), CoveredEarnings(r,t) future wage base (t)

CoveredEarnings(r,t) , CoveredEarnings(r,t) future wage base (t) Earnings(r,t)

 

58 The difference between Y(20,t) and Y(20 ) ˆ ,t . 
221 

4.3. Cost 

4.3.a. Overview 

The COST subprocess projects the trust fund operations for each year of the long-range 75 year 

period. The COST subprocess projects the income and cost for each trust fund (OASI and DI). 

The two components of non-interest income are tax contributions and taxation of benefits. The 

other component of income is interest earned on the trust fund assets. The three components of 

cost are scheduled benefits, administrative expenses, and the railroad interchange. Each of these 

components is projected for each trust fund (OASI and DI). The end-of-year assets is computed 

by taking the beginning-of-year assets (ASSETS), adding tax contributions (CONTRIB), taxation 

of benefits (TAXBEN), and interest income (INT), and subtracting scheduled benefits (BEN), 

administrative expenses (ADM), and the railroad interchange (RR). 

Equations 4.3.1 through 4.3.6 outline this overall structure and sequence. 

CONTRIB = CONTRIB(·) (4.3.1) 

BEN = BEN(·) (4.3.2)

 TAXBEN = TAXBEN(·) (4.3.3)

ADM = ADM(·) (4.3.4) 

 RR = RR(·) (4.3.5) 

 

INT = INT(·) (4.3.6) 

 ASSETS ASSETS CONTRIB TAXBEN INT BEN ADM RR EOY BOY = + + +−− −

The COST subprocess produces annual values which help assess the financial status of the 

OASI, DI, and combined funds. These include the annual income rate (ANN_INC_RT), annual 

cost rate (ANN_COST_RT), and trust fund ratio (TFR) as outlined below. 

ANN_INC_RT = ANN_INC_RT (·) (4.3.7) 

ANN_COST_RT = ANN_COST_RT (·) (4.3.8) 

TFR = TFR(·) (4.3.9) 

The COST subprocess also produces summarized values. These values are computed for the 

entire 75-year projection periods, as well as 25- and 50-year periods. These include the actuarial 

balance (ACT_BAL), unfunded obligation (UNF_OBL), summarized income rate 

(SUMM_INC_RT), summarized cost rate(SUMM_COST_RT), and closed group unfunded 

obligation (CLOSEDGRP_UNFOBL). 
222 

ACT_BAL = ACT_BAL(·) (4.3.10) 

UNF_OBL = UNF_OBL(·) (4.3.11) 

SUMM_INC_RT = SUMM_INC_RT(·) (4.3.12) 

SUMM_COST_RT = SUMM_COST_RT(·) (4.3.13) 

CLOSEDGRP_UNFOBL = CLOSEDGRP_UNFOBL(·) (4.3.14) 

The following notation is used throughout this documentation: 

• ni represents the first year of the projection period-2008 for the 2008 TR 

• ni+74 represents the final year of the projection period-2082 for the 2008 TR 

• nf represents the last year the cost program will project-2085 for the 2008 TR 

• nim1 is equal to ni-1 

• nim2 is equal to ni-2 

• ns is equal to ni+9

• nbase, the year of the sample, is equal to 2004 

 

4.3.b. Input Data 

Data received as input from the short-range office are presented first. Then data from long range 

and all other sources are identified separately for each equation. 

Short-range OCACT Data 

• Estimates for the first ten years of the projection period for the first six equations 

mentioned above. 

• Assets at the beginning of year ni. 

 All of this information is updated annually. 

Long-range OCACT and other Data

i. Equation 4.3.1 – Tax Contributions (CONTRIB)

Economics-Process 2 

• Projected effective taxable payroll for years nim1 through nf, updated yearly 

Other

• Projected employee/employer payroll tax rate, by trust fund and year, for years 

1981 through nf, updated as needed (e.g., as required due to legislative changes) 

ii. Equation 4.3.2 – Scheduled Benefits (BEN)
223 

Demography-Process 1 

• Projected number of married and divorced people in the Social Security area 

population age 65 and above for beginning of years nim1 through 2101, updated 

yearly 

Economics -Process 2 

• Historical COLA for years 1975 through nim2, updated yearly 

• Historical CPI for years 1990 through nim1, updated yearly 

• Projected cost of living adjustment (COLA) for years nim1 through nf, updated yearly 

• Historical SSA average wage index for year nim2, updated yearly 

• Projected percent increases in the average wage index for years nim1 through nf, 

updated yearly 

• Coefficients for five dual entitlement equations, updated as needed 

Beneficiaries-Process 3 

• Incurred but not reported (IBNR) DI beneficiary distribution by age, duration of 

disability (0 through 9 years and 10+ years) and sex, updated every few years 

(subprocess #3.2). The number of DI beneficiaries in current-payment status is equal 

to the number of currently entitled DI workers times the IBNR factor. 

• Projected number of disabled workers in current-pay status by sex, age in current-pay, 

and duration of disability (0 through 9 and 10+) for years nim1 through nf, updated 

yearly from subprocess 3.2 

• Projected number of retired worker beneficiaries in current-pay status by sex, age in 

current-pay, and age at entitlement for years nim1 through nf, updated yearly from 

subprocess 3.3 

• Projected number of auxiliary beneficiaries (by benefit category) of retired-worker, 

deceased-worker, and disabled-worker beneficiaries for years nim1 through nf, 

updated yearly from subprocess 3.3 

• Projected number of disability insurance beneficiaries who convert to retirement 

insurance status upon the attainment of normal retirement age by age in current pay, 

for years nim1 through nf, updated yearly from subprocess 3.3 

 Other

• Total (aggregate) PIA and MBA, not actuarially reduced, of DI male and female 

workers in current payment status, updated yearly from the 1-A Table Supplement 

• Total (aggregate) PIA and MBA, actuarially reduced, of DI male and female workers 

in current payment status, updated yearly from the 1-A Table Supplement 

• Cumulative distribution of AIME dollars for newly entitled retired-worker 

beneficiaries by age (62 through 70) and sex, for years nim1 through nf, updated 

yearly from subprocess 4.2 

• Cumulative distribution of AIME dollars for newly entitled disabled-worker 

beneficiaries by age (20 through 64) and sex, for years nim1 through nf, updated 
224 

yearly from subprocess 4.2. Ages 15 through 19 are assumed to have the same 

distribution of dollars as does age 20. Ages 65 and 66 are assumed to have the same 

distribution of dollars as does age 64 

• Age distribution of newly entitled retired-worker beneficiaries in the AIME awards 

sample by sex, updated in years that the sample changes, from subprocess 4.2 

• Starting average PIA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly 

• Starting average PIA matrix for disabled-worker benefits, for the year nim1, by age in 

current-pay, duration and sex, updated yearly 

• Starting average PIA matrix for beneficiaries who convert from disabled worker to 

retirement worker status for the year nim1, by age in current-pay and sex, updated 

yearly 

• Starting average MBA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly 

• Benefit relationships between worker and auxiliary benefits (linkages) for the year 

nim1, for all benefit categories and worker account holders of both sexes, updated 

yearly from qlink.xls 

• Retroactive payment loading factors for auxiliary beneficiary categories for all years, 

for all all benefit categories and worker account holders of both sexes, updated as 

needed 

• Post entitlement factors by sex and duration, for years ni through ns, updated yearly 

• Historical AIME deviation, by sex for years 1995 through nim1, updated yearly 

iii. Equation 4.3.3 – Taxation of Benefits

Trust Fund Operations and Actuarial Status

• Taxation of benefits as a percentage of scheduled benefits by trust fund for years 

nim1 through nf, updated yearly from subprocess #4.1 

iv. Equation 4.3.4 – Administrative Expenses

Economics-Process 2 

• Average wage indexes for years ni through nf, updated yearly 

• Ultimate value of productivity factor for the period ni through nf updated yearly 

Beneficiaries-Process 3 

• Total number of beneficiaries in current-pay status by trust fund for years ni through 

nf, updated yearly 

v. Equation 4.3.5 – Railroad Interchange

Economics-Process 2 

• Number of covered workers in five year age groups, for years ni through nf, updated 
225 

yearly 

• Effective taxable payroll for years nim1 through nf, updated yearly 

• Increase in the average wage index for years nim1 through nf, updated yearly 

 

Beneficiaries-Process 3 

• Total number of beneficiaries in current-pay status by trust fund for years nim1

through nf, updated yearly 

Trust Fund Operations and Actuarial Status

• Taxation of benefits as a percent of the amount of benefits scheduled to be paid, by 

trust fund for years nim2 through nf, updated yearly 

Other input data

• Nominal annual yield rate on the combined OASDI trust fund for years ni through nf, 

updated as the ultimate real interest rate and ultimate CPI are changed by the 

Trustees. Ratio of railroad retirement average benefit to OASI average benefit for the 

year nim1, updated yearly 

• Ratio of railroad disability average benefit to DI average benefit for the year nim1, 

updated yearly 

• Number of railroad beneficiaries (retirement and disability) for each of the two years 

nim2 and nim1, updated yearly 

• Average taxable earnings in railroad employment for each of the two years nim2 and 

nim1, updated yearly 

• Railroad taxable payroll for each of the two years nim2 and nim1, updated yearly 

vi. Equation 4.3.6 – Interest Income

Economics-Process 2 

• Annual increase in the CPI for years ni through nf, updated yearly 

 Trustees assumptions

• Ultimate real interest rate, reviewed annually 

vii. Equations 4.3.7 through 4.3.13 – Annual Values and Summarized Values

All inputs for equations 4.3.7 through 4.3.13 are estimated internally in the Cost program. 

viii. Equation 4.3.14 – Closed Group Unfunded Obligation

Demographics-Process 1 

• Single year population and mortality rate data for years 1941 through 2100, updated 

yearly 

• Population projections by single year of age, 75-99, from nim2 to 2100, updated 
226 

yearly 

Economics-Process 2 

• Historical and projected single-year COLA data and average wage indexing series 

(AWI) data for years 1975 through 2085 (for COLA) and 1951 through 2085 (AWI), 

updated yearly 

• Projected number of covered workers by single year of age 15-74 from year ni 

through nf, updated yearly 

• Aggregate number of covered workers aged less than 15, and aged 75 and over, from 

years ni through nf, updated yearly 

Beneficiaries-Process 3 

• Total projected disabled workers by age for years 2007 to 2085, updated yearly 

 Other

• Total count of beneficiaries in 20 of the 28 beneficiary categories (excluding retired 

workers, disabled workers, aged spouses (married, divorced, and dually entitled 

excess), and aged widow(er)s (married, divorced, and dually entitled excess) from the 

December 2007 Master Beneficiary Record (MBR)59—updated yearly 

• Total benefits paid in 20 of the 28 beneficiary categories (excluding retired workers, 

disabled workers, aged spouses (married, divorced, and dually entitled excess), and 

aged widow(er)s (married, divorced, and dually entitled excess) from the December 

2007 MBR—updated yearly 

• Consumer Price Index data from 1951-1974 from Bureau of Labor Statistics 

• Number of covered workers and average taxable earnings by single year of age 1-14 

for years 1991-2004 from 1 percent Continuous Work History Sample (CWHS), 

updated yearly to include year ni-4 

• Number of covered workers and average taxable earnings by single year of age 75-99 

for years 1991-2004 from 1 percent CWHS, updated yearly to include year ni-4 

• Distribution of assumed age differentials of wives compared to age of husbands—

separate distributions used for aged spouse benefits and aged widow(er) benefits, 

respectively 

4.3.c. Development of Output 

i. Equation 4.3.1 – Payroll Tax Contributions (CONTRIB)

 

59 For disabled adult children of deceased workers and lump-sum beneficiaries, data was extracted from a 1- percent 

sample of the December 2007 MBR, mainframe dataset ACT.TAPEL.CAN1207. For the other 18 auxiliary 

beneficiary categories, data was extracted from the 100 percent December 2007 MBR, mainframe dataset 

ACT.TAPEH.MBR100.D0712.CANSORT. 
227 

It would be natural to estimate the payroll tax contributions by trust fund by multiplying the 

applicable employer/employee tax rate by effective taxable payroll. However, tax contributions 

are reported on a cash basis. That is, tax contribution amounts are attributed to the year in which 

they are actually received by the trust funds, while taxable payroll is attributed to the year in 

which earnings are paid. In other words, the lag between the time the tax liability is incurred and 

when the taxes are actually collected must be reflected. If lag represents the proportion of 

incurred payroll taxes estimated to be received by the trust fund (tf) in year yr, then tax 

contributions (CONTRIB) are given by the formula 

(, ) (, ) ( )

(1 ) ( , 1) ( 1)

CONTRIB tf yr lag tax rate tf yr payroll yr

lag tax rate tf yr payroll yr

=× ×

+ − × −× −

for yr ns ≥ .

The value of lag is estimated from the combined OASI and DI tax contributions estimated to be 

collected in the final year of the short-range period, ns, and is given by 

( )

( )

2 2

1 1

2

1

( , ) ( , 1) ( 1)

( , ) ( ) ( , 1) ( 1)

tf tf

tf

CONTRIB tf ns taxrate tf ns payroll ns

lag

taxrate tf ns payroll ns taxrate tf ns payroll ns

= =

=

− −× −

=

× − −× −

∑ ∑

∑

. 

For the first ten years of the long-range period, tax contributions are set equal to those provided 

by the short-range office. The same value of lag is used for all years, and both trust funds, 

thereafter. 

ii. Equation 4.3.2 – Scheduled Benefits (BEN)

(1) Disabled-Worker Benefits 

Disabled Worker Beneficiary Matrix

The number of disabled-worker beneficiaries for a given year and sex are provided from the 

subprocess 3.2. For each projection year, two matrices are provided – one for males and one 

for females. The structure of each matrix is as follows: 

• 11 columns. The columns are indexed by duration of disability (0-9 and 10+). 

• 52 rows. These rows correspond to the age in current pay, ages 15 through 66. 

 

The COST subprocess, however, only uses 10 durations (0-8 and 9+), and 47 ages (ages 20 

through 66). This requires a manipulation of the matrix of DI beneficiaries in current-pay 

status from subprocess 3.2. For ages in current pay greater than or equal to 30, the duration 9 

and 10+ columns of this matrix are added to give the total number of duration 9+ 
228 

beneficiaries. For ages (ag) between 20 and 30 inclusive, the number of beneficiaries in 

current-pay aged ag and duration ag-20 is the value provided by the DISABILITY 

subprocess added to the number of people in current pay aged ag-j and duration ag-20 for 

j=1,..,5. (For example, the number of people aged 20 of duration 0 is combined with the 

number of people aged 15, 16, 17, 18 and 19 of duration 0; the number of people aged 21 of 

duration 1 is combined with the number of beneficiaries in current-payment status aged 16, 

17, 18, 19, and 20 of duration 1, and so on. In other words, the five nonzero diagonal of the 

matrix provided by the DISABILITY subprocess is “combined with” the diagonal directly 

below it.) 

Building the Average Benefit Matrix for Disabled Workers

In each projection year, the COST subprocess produces an average benefit matrix for each 

sex. Each matrix is a 47 by 10 matrix whose entries are the average benefit amounts of 

disabled worker beneficiaries whose age in current pay is indexed by the rows (ages 20 

through 66) and whose duration of disability is indexed by the columns (durations 0 through 

8 and 9+). 

The 1 percent Master Beneficiary Record (1% MBR) extract is processed by a side model. 

The final product of the side model is two matrices of benefits, one for males and one for 

females, for nim1 (2007 for the 2008 TR). 

For a given year of the projection period, a new average benefit matrix is obtained by moving 

the average benefit matrix from the previous year one year forward. The next few 

paragraphs describe this procedure. 

In general, for each age in current-pay, the age and duration are incremented by 1 and the 

previous PIA amount is given a cost of living adjustment. In addition, the beneficiaries are 

given a workers compensation adjustment. For each duration j = 0,1,...,7, and 8+ and sex, 

let the workers compensation offset factor be denotedwkcomp yr sx dur ( , , ). We have, for 

durations 0 through 8, that 

( , , , ) ( 1, , 1, 1) (1 ( ))

(1 ( , , )).

avgmba yr sx ag dur avgmba yr sx ag dur COLA yr

wkcomp yr sx dur

= − − −×+

× +

A more careful explanation of the last factor, ( , , ), wkcomp yr sx dur is given later in this 

document. See the section titled Average PIAs and MBAs for Disabled-Worker 

Beneficiaries, below. To move duration 8 average benefits to duration 9+ average benefits, 

both average benefits are given a cost of living adjustment. The resulting duration 9+ average 

benefit is the weighted average of the adjusted duration 8 and 9+ average benefits, weighted 

by the numbers of beneficiaries in current-pay status for durations 8 and 9+ respectively. 

The only column that is not handled by this procedure is the duration 0 column. This column 

corresponds to newly entitled disabled-worker beneficiaries, and is handled below. 
229 

 

Average Benefits for Newly Entitled Disabled-Worker Beneficiaries 

The potential AIME percentage values for newly entitled disabled-worker benefits (DPAPs) 

are obtained from the AWARDS subprocess. The two bendpoints of the PIA formula, BP1 

and BP2, are indexed by the increase in the average wage index. In 1979 dollars, the values 

of BP1 and BP2 are $180 and $1,085 respectively. The AIME dollars between 0 and BP1 

are divided into four intervals (each of length $45 in 1979 dollars). The AIME dollars 

between BP1 and BP2 are divided into fourteen intervals (nine of length $45 and five of 

length $100, in 1979 dollars). Twelve additional intervals are added beyond BP2 (ten of 

length $200 and two of length $1,000, in 1979 dollars). 

To determine the average PIA for newly entitled beneficiaries, the DPAP values for each of 

the thirty intervals of AIME dollars are multiplied by the dollar amounts attributable to each 

interval (the length of the interval) and by the associated PIA factors. The distribution of 

prior year disability onset and current year disability onset is taken into consideration. It is 

assumed that this distribution is 6 months for prior year disability onset and 6 months for 

current year disability onset. In the formulas below, j = 1 signifies prior year disability onset 

and j = 2 signifies current year disability onset. 

Let: 

• ( max( 60,1 )) _ (, , ) ( 2) j

avgwg yr ag j Wage Idx sx ag yr avgwg nbase− − + = − for j=1,2. 

• 1

61

(1 ( 1)) (1 ( )) 64

_ (,) (1 ( ( 61)) 64 66.

ag

k

COLA yr COLA yr ag

Cum COLA ag yr COLA yr k ag

=

⎧ + − ×+ <

⎪ = ⎨ + −− ≤ ≤ ⎪

⎩ ∏

2

62

1 ( ) 63

_ (,) (1 ( ( 62)) 63 66.

ag

k

COLA yr ag

Cum COLA ag yr COLA yr k ag

=

⎧ + <

⎪ = ⎨ + −− ≤ ≤ ⎪

⎩

∏

• 6 1 , 12 2

wj = = j=1,2. 

• PIA_factori represent the PIA factor for interval i (equal to 0.90 for intervals i=1,4, 

0.32 for intervals i=5,...,18, and 0.15 for intervals i=19,...,30). 

• AIME_dollarsi represent the length of interval i, expressed in 1979 dollars.

• dpapi (yr,sx,ag) represent the DPAP value for newly entitled disabled workers in 

year yr whose sex is sx and age is ag. 

To take into account the workers compensation offset to disability benefits, administrative 

data is reviewed, from which a factor is developed and applied to the average award benefit. 

We now describe how this factor, facm p yr sx 2( , ) is computed. The 1-A table supplement as 

of the end of December, 2007, contains total award PIA and MBA data for disabled workers, 
230 

by sex, for beneficiaries both non-actuarially reduced and actuarially reduced. Let 

totmba DIB nar yr sx _ _ (,) and totpia DIB nar yr sx _ _ (,) be the total MBA and PIA respectively 

for DIBs that are not actuarially reduced as found in the 1-A table. In the historical period 

1988-nim1 we define facm p yr sx 2( , ) to be the ratio of the total MBA to the total PIA for 

those not actuarially reduced. In other words, 

_ _ (,) 2( , ) . _ _ (,)

totmba DIB nar yr sx facm p yr sx totmba DIB nar yr sx =

In the period ni through ns+9, facm p yr sx 2( , ) is defined as follows. Let 

1/10

2 ( 1, ) 2 ( 1, ) . 2 ( 11, )

facm p yr sx x facm p yr sx facm p yr sx

⎛ ⎞ − = −×⎜ ⎟ ⎝ ⎠ −

This value is further adjusted to reflect that one quarter of the offset amounts end within the 

first entitlement year (as suggested by data). As a result, for yr = ni, ... , ns+9, 

2 ( , ) (1 ) 0.25

0.25 0.75 .

facm p yr sx x x

x

= +− ×

=+×

The factor reaches its ultimate value in years ns+10 and later. 

The preliminary average PIA for newly entitled disabled worker beneficiaries may now be 

defined. It is equal to 

30

1

2

1

_ (, , ) _ _ (,, )

_ (, , ) _ ( , )

2 ( , ).

i ii

i

jj j

j

LR awdpia sx ag yr PIA factor AIME dollars dpap yr sx ag

w Wage Idx sx ag yr Cum COLA ag yr

facm p yr sx

=

=

=××

⎛ ⎞

×× × ⎜ ⎟ ⎝ ⎠

×

∑

∑

The preliminary average PIA for newly entitled benefits is further adjusted by a factor, 

adjpia, designed to be the factor that adjusts the long-range projected newly entitled monthly 

benefit amount (MBA) to the value projected by short range in the short-range period. 

Therefore, for years in the short range period (yr = ni, ... , ns), 

awdpia sx ag yr LR awdpia sx ag yr adjpia sx yr ( , , ) _ ( , , ) ( , ). = ×

Once these average PIAs of newly entitled disabled-worker beneficiaries are computed, their 

values are filled into the average PIA matrices for duration 0 for the appropriate entitlement 

age. 

Average PIAs and MBAs for Disabled-Worker Beneficiaries 

An overall average PIA of newly entitled disabled worker beneficiaries for each sex and 

projection year is computed by taking the weighted average of awdpia(sx,ag,yr), the weights 
231 

being the number of disabled workers in current payment status of duration zero. This value 

is denoted awdpia(sx,yr). 

In addition, an overall average PIA and MBA for all disabled worker beneficiaries in currentpayment status is computed by finding the weighted average of the average PIAs for each 

age in current-pay and duration with the number of people in current pay for each of these 

ages and durations. The average PIAs were already reduced by a workers compensation 

offset factor, as briefly described above; a more careful description is given in this section. 

To get the average MBAs, we apply a factor which reflects the differences in average MBAs 

and PIAs for disabled workers, isolating only the trend in cases with an actuarial reduction. 

We also provide a relatively small reduction to reflect offsets starting and stopping in the 

year of DI entitlement that are not captured by the current method. 

Workers Compensation Offset Factors

For each duration 1,...,7, j = and 8+ and sex we define a workers compensation factor. This 

factor is applied to the average worker PIA matrix as mentioned above. It is 

denoted ( , , ). wkcomp yr sx dur Let 2 _ ( ) facm p pct dur be defined as in the following table. 

Duration Cumulative product above set at x% of 

way between original facm2p and 1 

1 0.396162 

2 0.577085 

3 0.671787 

4 0.732777 

5 0.789194 

6 0.819700 

7 0.842675 

8+ 0.866667 

Then wkcomp yr sx dur (,, )is defined so that 

1

2 _ ( ) 2 ( , ) (1 ( , , )).

dur

j

facm p pct dur facm p yr sx wkcomp yr sx j == ×+ ∏

This is an iterative process which first computes wkcomp yr sx ( , ,1) by solving the above 

equation with dur set equal to 1. The remaining factors for higher durations are then 

computed recursively using the above formula. 

Trend in Average MBA to Average PIA 
232 

This trend is captured in a factor denoted Fam p yr sx 2 ( , ). The 1-A table supplement as of the 

end of December, 2007, contains total award PIA and MBA data for disabled workers, by 

sex, for beneficiaries both non-actuarially reduced and actuarially reduced. Let 

totmba nar yr sx _ (,) and totpia nar yr sx _ (,) be the total MBA and PIA respectively for DIBs 

that are not actuarially reduced as found in the 1-A table. Similarly, let totmba ar yr sx _ (,) and 

totpia ar yr sx _ (,) be the total MBA and PIA respectively for cases that are actuarially 

reduced. In the historical period 1988-nim1 we define fam p yr sx 2( , ) to be the ratio of the 

total MBA to the total PIA for those not actuarially reduced. In other words, 

_ (, ) _ (, ) 2( , ) . _ (, ) _ (, )totmba ar yr sex totpia nar yr sex Fam p yr sex totpia ar yr sex totpia nar yr sex+ = +

In the period ni through ns+9, facm p yr sx 2( , ) is defined by 

1/10

2 ( 1, ) 2 ( , ) 2 ( 1, ) . 2 ( 11, )Fam p yr sx Fam p yr sx Fam p yr sx Fam p yr sx

⎛ ⎞ − = −×⎜ ⎟ ⎝ ⎠ −

The factor reaches its ultimate value in years ns+10 and later. 

More Workers Compensation Offsets 

As mentioned above, we also we provide a relatively small reduction to reflect offsets 

starting and stopping in the year of DI entitlement that are not captured by the current 

method. Administrative data suggests that these factors should be 

Duration Percentage Reduction 

0 0.3400% 

1 0.2020% 

2 0.0664% 

3 0.0336% 

4 0.0121% 

and 0 for higher durations. We define wkcomp_red(dur) to be 1 minus these percentage 

reductions. 

Computation of Average MBA for DI Workers 

The disabled worker PIA as presented in the average benefit matrix was already incremented 

by age and duration using a COLA and a workers compensation adjustment. The average 

PIA by year, age and duration, is denoted ( , , , ). avgpia yr ag sx dur The overall average MBA 

by year and sex is the weighted average of 

avgpia yr ag sx dur wkcomp red dur Fam p yr sx dur ( , , , ) _ ( ) 2 ( , , ), × × the weights being the 

number of DI workers in current payment status by age, sex, and duration. 

DI Conversions
233 

Disabled-worker beneficiaries convert to retired-worker beneficiary status (called DI 

conversions) at normal retirement age (NRA). The average DI conversion benefit for a given 

sex and single age 65 through NRA is the weighted average of the average DI conversion 

benefits for that sex and age, weighted by the number of people in current pay in each 

duration. Both the average conversion benefit for each sex and age 65 though NRA and the 

number of people in current pay for these ages are used in the computation of average retired 

worker benefits (see subsection (2) below). 

(2) Retired-Worker Benefits 

Retired-Worker Beneficiary Matrix

The number of retired-worker beneficiaries for a given year and sex are provided from 

subprocess 3.3. Two matrices are provided – one for males and one for females. The 

structure of each matrix is as follows: 

• 10 columns. The first 9 columns are the age at entitlement, ages 62 through 70. 

The last column is the number of disabled workers who are projected to convert to 

retired-worker beneficiary status (DI conversions) at normal retirement age. 

• 34 rows. These rows correspond to the age in current pay, ages 62 through 94 and 

ages 95+. 

Note that the entries on the diagonal (where age in current-pay equals age at entitlement) is 

the number of new entitlements projected for that year. 

Building the Average Benefit Matrices for Retired Workers

In each projection year, the COST subprocess produces four average benefit matrices. For 

each sex there are two matrices, an average monthly benefit amount (MBA) matrix and the 

average primary insurance amount (PIA) matrix. Each matrix has the same structure as the 

beneficiary matrices. In other words, each matrix is a 34 by 10 matrix whose entries are the 

average benefit amounts of retired worker beneficiaries whose age in current pay is indexed 

by the rows and whose original age at entitlement is indexed by the columns. The final 

column simply gives the average benefits for DI conversions at the various ages in current 

pay. 

The 1% MBR extract is processed by a side model. This side model computes a starting 

matrix for year ni-1. This starting matrix contains the four initial benefit matrices, 

constructed using the most recent data. For a given year of the projection period, the average 

benefit matrix is updated from its previous year’s value incrementing each benefit amount 

(PIA or MBA) by one year of age and increasing it by a cost of living adjustment (COLA). 

MBAs are increased by the appropriate post entitlement factor60 for males and females. 

 

60 Post entitlement factors are used to reflect (a) the higher survival rates for those receiving higher benefits and (b) 
234 

Adjusted age 94 benefits and age 95+ benefits are averaged to get the new average benefit for 

age 95+. DI conversion benefits are handled similarly, except the average conversion 

benefit for each age 64 through 66 is combined (as a weighted average) between the DI 

conversion average benefits computed in subprocess 3.2 and the DI conversions of the 

corresponding age already receiving benefits (provided by subprocess 3.3). 

The entries along the diagonal, the average benefits of newly entitled beneficiaries by age, 

must still be computed. The remainder of this section will explain how these average 

benefits are computed. Once these are computed, all entries are computed and the average 

benefit matrix for the year is complete. 

Average Benefits for Newly Entitled Retired Worker Beneficiaries 

The potential AIME percentage (OPAPs) values for newly entitled retired-worker benefits 

are obtained from subprocess 4.2. The OPAPs for the projection of average benefits for 

newly entitled retired-worker beneficiaries are modified by the COST subprocess. The 

reason is that the age distribution of newly awarded retired worker beneficiaries as 

determined in the awards sample is used for each projection year, i.e., the age-sex 

distribution matches that of the sample. These new potential AIME percentages are denoted 

OPAP1. To incorporate the projected change in the age distribution of projected newly 

awarded retired-worker beneficiaries for the purpose of determining their average benefits, 

we use a “shuttling method.” Additional details about the shuttling method are given in 

Appendix 4.3-1. 

Average benefits for newly eligible retired-worker beneficiaries are calculated by sex for 

single year ages 62 through 69, and ages 70+. The two bendpoints of the PIA formula, BP1 

and BP2, are indexed by the increase in the average wage index. In 1979 dollars, the values 

of BP1 and BP2 are $180 and $1,085 respectively. The AIME dollars between 0 and BP1 

are divided into four intervals (each of length $45 in 1979 dollars). The AIME dollars 

between BP1 and BP2 are divided into fourteen intervals (nine of length $45 and five of 

length $100, in 1979 dollars). Twelve additional intervals are added beyond BP2 (ten of 

length $200 and two of length $1,000, in 1979 dollars). 

To determine the average PIA for newly entitled beneficiaries, the OPAP1 values for each 

interval of AIME dollars is multiplied by the dollar amounts attributable to each interval (the 

length of the interval). More precisely, let 

• PIA_factori be the PIA factor for subinterval i (equal to 0.90 for intervals i=1,4, 0.32 

for intervals i=4,...,18, and 0.15 for intervals i=19,...,30), AIME_dollarsi be the 

length of subinterval i, 

• opap1i (yr,sx,ag) be the modified PAP value for retired workers newly entitled in year 

yr whose sex is sx and whose age is ag. 

 earnings after retirement. 
235 

• ( ( 62)) _ (,) ( 2)

avgwg yr ag Wage Idx ag yr avgwg nbase− − = −

Then the average PIA for these newly entitled retired worker beneficiaries is equal to 

 

30

1

_ (, , )

_ _ ( , ) _ 1 ( , , ). i ii

i

LR awdpia sx ag yr

PIA factor Wage Idx ag yr AIME dollars opap yr sx ag

=

=× ×× ∑

This formula incorporates the fact that the PAP values are the estimated cumulative 

distribution of AIME dollars. The average award MBA for a worker beneficiary is then the 

average award PIA multiplied by the appropriate actuarial reduction factors and delayed 

retirement credits, arfdrc(ag,yr). The average MBA for newly entitled benefits is also 

adjusted by a factor, adjpia, designed to be the factor that adjusts the long-range projected 

newly entitled MBA to the short-range projection in the short-range period. Therefore, 

awdmba sx ag yr LR awdpia sx ag yr adjpia sx yr arfdrc ag yr ( , , ) _ ( , , ) ( , ) ( , ). = ××

Once these average benefits of newly entitled retired-worker beneficiaries are computed, 

their values are filled into the appropriate average benefit matrices. 

For summary purposes, the COST subprocess computes an average PIA and MBA for all 

male and female newly entitled retired-worker beneficiaries, as well as for all retired-worker 

beneficiaries in current-payment status. These are just the respective weighted averages of 

the average PIAs and MBAs by age and sex, the weights being the number of newly entitled 

retired-worker beneficiaries. These average PIAs and MBAs are adjusted in such a way so 

that their values, in the short-range period, match the projection provided by the short-range 

office. In a similar way, the COST subprocess computes an average PIA and MBA for male 

and female retired workers in current payment status, also as a weighted average. 

(3) Annualizing Benefits 

Scheduled benefits are calculated by trust fund and projection year. For each year scheduled 

benefits for each trust fund are found by adding up the appropriate benefit categories. This 

section considers all benefit amounts except the “dual entitlement excess amount.” If a retired 

worker beneficiary is also entitled to spouse or widow(er) benefits and the auxiliary benefits are 

greater, than the amount by which the auxiliary benefit exceeds the worker’s MBA is the dual 

entitlement excess amount. The four categories of excess amounts (dually entitled wives, 

widows, husbands, and widowers) are projected separately. More information is found in 

subsection (4). 

The first step is to annualize benefits by category. The average benefit for a specific auxiliary 

beneficiary category (avgben) is found by multiplying the linkage factor (the assumed 
236 

relationship between an auxiliary beneficiary’s benefit and the corresponding worker benefit) by 

the average benefit of the primary account holder (the account on which the auxiliary beneficiary 

is entitled to receive the benefit; discussion of its computation appears in subsection (2) above). 

In order to annualize benefits, two values are used. The beginning-of-year average benefit for a 

specific auxiliary beneficiary category is found by using the average benefit of the worker 

beneficiary for the prior year. The end-of-year benefit for that category is found by using the 

average benefit of the worker beneficiary for the current year and removing the cost of living 

adjustment. The average benefit by category for each month is found by taking a weighted 

average of the benefits at the beginning and end of the year, the weights being the fractions of 

the year the prior and current year’s beneficiaries have been exposed. Since the new COLA takes 

effect in December of the year, the new COLA must be reflected in the December benefits. If 

cp(cat,yr) is the number of beneficiaries in category cat for year yr, and avgben(cat,yr) is the 

average benefit for category cat for year yr, then the amount of aggregate benefits paid in year yr

is given by the formula 

11

i=0

AggBen( , ) 

(12 ) = ( , 1) ( , 1) ( , ) ( , ) _ ( , ) 12 12

yr cat

i i cp cat yr avgben cat yr cp cat yr avgben cat yr COLA Factor i yr ⎡ − ⎤ × −× −+ × × × ⎢ ⎥ ⎣ ⎦ ∑

where 

1.0 0, ,10 _ (, ) 1.0 ( ) 11.

i

COLA Factor i yr COLA yr i

⎧ = = ⎨

⎩ + =

K

For worker beneficiary categories, the amount is also increased by the retroactive payments that 

were projected to be paid during the year. See section (5), below. A description of beneficiary 

categories is as follows. An odd category number refers to the male account holder, while an 

even category number refers to the female account holder. As an example, for category 4, the 

aged married spouse is the aged married husband of the retired female worker. 

Category Beneficiary Type

# (cat)

Old-Age Insurance Beneficiaries

1 & 2 Retired worker (includes DI conversions) 

3 & 4 Aged married spouse 

5 & 6 Aged divorced spouse 

9 & 10 Young spouse with child 

11 & 12 Child < 18 

13 & 14 Student child 

15 & 16 Disabled adult child 

Disability Insurance Beneficiaries

17 & 18 Disabled worker 

19 & 20 Aged married spouse 

21 & 22 Aged divorced spouse 
237 

25 & 26 Young spouse with child 

27 & 28 Young child 

29 & 30 Student child 

31 & 32 Disabled adult child 

Survivors Insurance Beneficiaries

33 & 34 Aged married widow 

35 & 36 Aged divorced widow 

39 & 40 Young married disabled widow 

41 & 42 Young divorced disabled widow 

43 & 44 Aged parent 

45 & 46 Young married widow with child 

47 & 48 Young divorced widow with child 

49 & 50 Young child 

51 & 52 Student child 

53 & 54 Disabled student child 

55 & 56 Lump sum death benefit ($255) 

(4) Dually Entitled Beneficiaries and Benefits 

Number of Dually Entitled Beneficiaries 

There are four categories of dually entitled beneficiaries. They are the dually entitled wives (1), 

widows (2), widowers (3), and husbands (4). The number of dually entitled husbands is very 

small (currently less than 0.05% of all dually entitled beneficiaries and are expected to remain at 

this level in the future). As a result, the number of dually entitled husbands and their benefits are 

not projected. 

The equations used to project the number of dually entitled beneficiaries each have three terms. 

Each equation has three coefficients, ( ), k

j a j =1, 2,3 (corresponding to each of the categories 

above). These coefficients are provided by the Economics process based on historical series of 

the other terms in the equations. These terms contain the basic quantities (a) projected weighted 

average AIME deviations of newly entitled retired worker beneficiaries for each sex 

[AIME_Dev(yr,sx)] and (b) average PIA of newly entitled retired worker beneficiaries by sex, 

wage indexed to the year of the sample [PIA(yr,sx)]. Therefore, the three equations 

() () () ()

1 23

AIME_Dev(yr,M) AIME_Dev(yr,F) PIA(yr,M) PIA(yr,F) PctExp ( ) PIA(yr,M) PIA(yr,F) PIA(yr,M)

kk k k

yr a a a − = ++

( k =1,2,3) project the percentage of the exposed population entitled to wife (1), widow (2), and 

widower (3) benefits. 

The table below shows the regression coefficients used in the 2008 Trustees report. 
238 

k Type ( )

1

k

a ( )

2

k

a ( )

3

k

a 2 R

1 Wife 0.04 0.05 0.55382 0.9223 

2 Widow 0.15 0.16 0.41284 0.4797 

3 Widower 0.03 0.02 -0.06570 0.7535 

In the above equations, the average PIA of newly entitled beneficiaries by sex has already been 

computed (see subsection (2) above). The remaining paragraphs discuss the methodology used 

to compute the AIME deviations that are used in the above equation. This process requires two 

steps: 

• obtain the AIME deviation in each year by sex and 

• obtain a 10 year historical average of these AIME deviations. 

The projection of a deviation of AIME values [std_dev(yr,sx)] is as follows. The projection uses 

the interval of AIME dollars for 1979. The 1979 bend points are $180 and $1,085. The entire 

interval of AIME dollars is divided into 30 smaller intervals [as was done in the projection of 

average benefits of newly entitled beneficiaries; see subsection (2)]. The left endpoints of these 

intervals ($0, 45, 90, 135, 180, 280, 380, etc.) are the 1979 interval point values. These 1979 

interval point values are wage indexed to the award sample year (2004 for the 2008 Trustees 

Report). Each interval point i, in 2004 wage indexed dollars, is 

AverageWageIndex(2002) Interval Point = (1979 Interval Point ) . AverageWageIndex(1977) i i ×

Each interval point is assigned a probability using the OPAP1 values [see subsection (2)]. Each 

interval is assigned probability 

1

1.0 1 ( , , ) 1 (,, ) 1 ( , , ) 1 ( , , ) 2, , 29.

i

i

i i

opap yr ag sx i

p yr sx ag opap yr ag sx opap yr ag sx i +

⎧ − = = ⎨

⎩ − = K

The average AIME of each newly entitled beneficiary aged ag=62,...,70, by sex (sx) and 

projection year (yr) in sample year (2004) dollars is 

10

1

AvgAIME(yr,sx,ag)= ( , , ) Interval Point . i i

i

p yr sx ag =

∑ ×

The variance of AIME for each newly entitled beneficiary aged ag=62,...,70, by sex (sx) and 

projection year (yr) in sample year (2004) dollars is 

[ ]

30

2

1

VarAIME(yr,sx,ag)= ( , , ) Interval Point AvgAIME(yr,sx,ag) . i i

i

p yr sx ag =

∑ × −
239 

The standard deviation by year, sex, and age is 

std dev yr sx ag _ ( , , ) VarAIME(yr,sx,ag). =

For each year and sex, the standard deviation std_dev(yr,sx) is a weighted average of the 

standard deviations by year, sex, and age, the weights being the percentages of newly entitled 

beneficiaries by sex and age. 

Once the standard deviation of AIME [std_dev(yr,sx)] is computed for the given projection year 

and both sexes, a weighted average of the AIME deviations over the last 10 years (including the 

projection year) is computed. This weighted average for the projection year yr is given by 

 

9 9

_ ( , ) ( ,) _ ( , ) ( ,)

yr yr

i yr i yr

AIME Dev yr sx weight yr i std dev yr sx weight yr i =− =−

⎛ ⎞

= × ⎜ ⎟ ⎝ ⎠ ∑ ∑ with 

weight yr i i yr ( , ) 0.55 0.5 (9 ). = + × +− 

Note that the weight in year i yr = equals 1.0, and that the weights decrease linearly to 0.55 over 

the 10 year look-back period. Note also that the sum of the weights (the denominator in the 

AIME_Dev expression), equals 7.75. 

Average Excess Amount for Dually Entitled Beneficiaries 

The projection of the average excess amounts for two categories of dually entitled beneficiaries 

(wives and widows) is similar to that of the number of dually entitled beneficiaries. The 

structure of the equations used to project these amounts is similar to the equations used to project 

the percentage exposures. While the coefficients provided by the Economics process are 

different, the underlying historical variables and their projections remain the same. 

The equations used to project the average excess amount each have three terms. Each equation k 

has three coefficients, ( ), k

j b 1,2,3 j = provided by the Economics process based on historical 

series of the other terms in the equations. The two equations 

() () () ()

1 23

AIME_Dev(yr,M) AIME_Dev(yr,F) PIA(yr,M) PIA(yr,F) AvgExcPct ( ) PIA(yr,M) PIA(yr,F) PIA(yr,M)

kk k k yr b b b − = ++

( 1,2 k = ) project the average excess benefit amounts of wife (1) and widow (2) beneficiaries as 

a percentage of the male retired worker benefit. 

The table below shows the regression coefficients used in the 2008 Trustees Report. 

k Type ( )

1

k b ( )

2

k b ( )

3

k b 2 R

1 Wife 0.2 0.025 0.24289 0.7161 
240 

2 Widow 0.11 0.01 0.30548 0.7045 

The average excess amount of widower beneficiaries is estimated to be a fixed percentage (46%) 

of the average excess amount of widow beneficiaries. That is, 

(3) (2) AvgExcPct ( ) 0.46 AvgExcPct ( ). yr yr = ×

Annualizing Excess Amounts 

The process to annualize excess amounts is very similar to the process for annualizing auxiliary 

benefits. 

For each dual entitlement category, the number of beneficiaries is simply 

() () ( , ) PctExp ( ) ExposedPop ( ). cat cat cp yr cat yr yr = × With this method, however, no linkage 

factor is used. Instead, the projected average excess amount, as explained above, is used. 

Therefore, 

11 () ()

i=0

AggExcess( , ) 

(12 ) = ( , 1) ( 1) ( , ) ( ) _ ( , ) 12 12

cat cat

yr cat

i i cp cat yr AvgExcAmt yr cp cat yr AvgExcAmt yr COLA Factor i yr ⎡ − ⎤ × −× −+ × × × ⎢ ⎥ ⎣ ⎦ ∑

where 

1.0 0, ,10 _ (, ) 1.0 ( ) 11.

i

COLA Factor i yr COLA yr i

⎧ = = ⎨

⎩ + =

K

(5) Retroactive Payments 

Disabled Workers

For each age and sex the DI area (subprocess 3.2) provides the cumulative distribution, by 

duration, of incurred but not reported cases. Denote this by ibnr sex age dur ( , , ). The number of 

disability beneficiaries currently entitled (by age, sex, and duration) is 

dibce sex age dur dibcp sex age dur ibnr sex age dur ( , , ) ( , , ) / ( , , ). = 

 The associated frequency distribution of incurred but not reported cases is 

ibnr freq sex age dur _ ( , , ). In other words, we have _ ( , ,0) ( , ,0) ibnr freq sex age ibnr sex age =

(duration 0) and for higher durations, 1 9 ≤ dur ≤ and 10+, we have 

ibnr freq sex age dur ibnr sex age dur ibnr sex age dur _ ( , , ) ( , , ) ( , , 1). = −− 

Let dur be a duration, 0 through 9 or 10+. Define 

• 0_ ( ) (1 ( )).

dur

j

Cum COLA dur COLA yr j ==+ − ∏
241 

• For i = 0,...,10,

1.4 0

3 0 and 0 

_ () 12 0 and 0

6 0 and 

dur

dur i

Num Months i

dur i dur

dur i dur

⎧ =

⎪

⎪ > = = ⎨ > << ⎪

⎪

⎩ > =

Then the aggregate retroactive payments for disabled workers, in millions, are defined to be 

66 10

6

20 0 0

_ ( ,)

( , ,0) _ ( ) _ ( , , ) (,, ) . 10 _ ( )

dur

age dur i

retro DIB sex yr

dibce sex age Num Months i ibnr freq sex age dur dibpia age sex dur = == Cum COLA dur

×

= ×× ∑ ∑∑

This is simply added to the disabled worker benefit category by year and sex. 

Retired Worker Beneficiaries

Retired Worker beneficiaries who are currently entitled but change to current payment status 

later are assumed to do so on average 1.5 months after they became entitled. Hence 

70

62

(, , , ) 1.5 ( , , , ) 1000 _ ( ,) . 1 () ageoabicp yr sex age age oabmba yr sex age age

retro OAB sex yr = COLA yr

× ×

= + ∑

In the above formula, ( , , , ) oabicp yr sex age age is the number of newly entitled beneficiaries at 

age equal to age (age in current pay equals age at entitlement equals age) and 

oabmba yr sex age age (, , , )is the corresponding average benefit. The aggregate retroactive 

benefits for old-age beneficiaries are simply added to the retired worker benefit category by year 

and sex. 

Auxiliary Beneficiary Categories

Retroactive payments for auxiliary beneficiaries are similarly linked to the primary worker 

beneficiary. The linkages are a loading of the benefits by auxiliary category for each benefit 

category. Each auxiliary benefit category has a loading factor, and the aggregate benefits by 

category are increased by this loading factor. 

(6) Aggregate Scheduled Benefits (BEN) 

Aggregate benefits by trust fund, BEN(tf,yr), are computed as follows. For each year of the 75-

year long-range projection period, the aggregate benefits by category (including retroactive 

payments, as described above) are summed up to give the annual scheduled benefit levels by 

trust fund. In the short-range period, the long-range values are overridden by the values 

estimated by the short-range office. The difference between long-range scheduled benefits and 

short-range benefits in the 10th year of the short-range period is called the scheduled benefits 

adjustment. In the 10 years after the end of the short-range period, the long-range scheduled 

benefits is adjusted by linearly grading the scheduled benefits adjustment to zero over the 10 

year period. From the 20th year forward, the projection is the pure long-range value. 

iii. Equation 4.3.3 – Taxation of Benefits (TAXBEN)
242 

The taxation of benefits levels in the short-range period, by trust fund, are provided by the shortrange office. These implicitly give, for each year, an estimated taxation of benefits factor, by 

trust fund, equal to the estimated taxation of benefits as a percentage of benefits scheduled to be 

paid. The long-range office projects these factors independently for every year of the projection 

period, also by trust fund. (See subprocess 4.1.) The difference in the factors from both offices at 

the end of the short-range period is phased out linearly over the next ten years. The long-range 

projection of taxation of benefits is estimated by multiplying the projected taxation of benefits 

factors by the benefits scheduled to be paid, by trust fund. If taxben_factor(tf,yr) is the 

percentage of scheduled benefits for the year, by trust funds, estimated to be collected as taxation 

on benefits, then 

TAXBEN tf yr taxben factor tf yr BEN tf yr (, ) _ (, ) (, ) = ×

for yr ns ≥ +10.

iv. Equation 4.3.4 – Administrative Expenses (ADM)

Administrative expenses are estimated separately by trust fund. In the short-range period, the 

short-range office provides the estimates of administrative expenses by trust fund. Thereafter, 

administrative expenses are computed by multiplying the previous year’s administrative 

expenses by three factors: annual changes in total beneficiaries, annual changes in AWI, and one 

minus annual productivity growth. As a formula, if ticp(tf,yr) is the total estimated number of 

beneficiaries in current-pay status by trust fund and year, AWI(yr) is the average wage index in 

year yr, and prod is the ultimate assumed annual growth in productivity, then 

( , ) ( , 1) [ ( , ) / ( , 1)] [ ( ) / ( 1)]

(1 )

ADM tf yr ADM tf yr ticp tf yr ticp tf yr AWI yr AWI yr

prod

= −× − × −

× −

for yr ns > .

v. Equation 4.3.5 – Railroad Interchange (RR)

Railroad interchange is disaggregated by trust fund and projection year. The long-range office 

does a projection for each year in the 75-year period. In the short-range period (first 10 years of 

the 75-year projection period), the short-range office provides the estimates of railroad 

interchange by trust fund and the long-range projection is overridden in these years. Over the 

next five years of the projection period, the estimate of the railroad interchange is a linear 

interpolation between the short-range projection at the end of the short-range period and the 

long-range projection five years hence. During the final 60 years of the projection period, the 

projection is as estimated by the long-range office. 
243 

By trust fund, the total cost in calendar year yr, rr_cost(tf,yr) is the sum of railroad benefits and 

railroad administrative expenses, less the sum of railroad contributions and railroad taxation of 

benefits. By trust fund, the railroad interchange component of total cost is then equal to 

RR tf yr rr tf yr rr tf yr yield yr ( , ) [0.25 _ cost( , 2) 0.75 _ cost( , 1)] [1 1.25 ( )]. = × − + × − ×+

Note that the railroad cost is increased by the yield rate on the combined OASDI trust funds for 

year yr. This formula takes into account the fact that that there is a delay from the end of the 

fiscal year to the time of valuation. 

The total cost in year yr is broken down in to four components: railroad benefits in year yr, 

railroad administrative expenses in year yr, railroad contributions in year yr, and railroad 

taxation of benefits in year yr. 

The average railroad retired worker benefit is estimated to equal the average retired worker 

benefit, multiplied by the ratio of the railroad retirement benefit to the OASI retired worker 

benefit. The aggregate retired worker railroad benefits are estimated by multiplying the average 

railroad retired worker benefit by the number or railroad retirement beneficiaries. The number 

of railroad beneficiaries is estimated to be the previous year’s number of beneficiaries, decreased 

for survivorship plus the estimated number of new railroad employees for the year. 

The aggregate disabled worker railroad benefits (and beneficiaries) are estimated in the same 

way. 

It is assumed that the ratio of OASI taxation of benefits to OASI benefits and DI taxation of 

benefits to DI benefits are both the same for railroad taxation of benefits. The railroad taxation 

of benefits is estimated by multiplying the railroad benefits by these ratios. 

Administrative expenses are computed, by trust fund, to be the maximum of (a) and (b) where (a) 

is an estimated average cost per beneficiary times the number of beneficiaries and (b) is an 

estimated percentage of aggregate benefits times the aggregate railroad benefit levels. 

Railroad contributions are estimated, by trust fund, to be total railroad employment, multiplied 

by average railroad earnings, multiplied by the combined OASDI employer/employee tax rate. 

Railroad earnings are assumed to grow with the increase in the average wage index, and railroad 

employment is assumed to decrease over time. 

vi. Equation 4.3.6 – Interest Income (INT)

In the short-range period, the projection of interest income by trust fund is provided by the shortrange office. In each year of the short-range period, the annual yield rate is defined as the ratio 

of interest earned by a fund to the average level of assets held by the fund during the year. 
244 

The ultimate annual yield rate on each trust fund is equal to the nominal yield, which is the real 

interest rate increased for inflation. As a formula, 

ultimate yield rate real interest rate inflation rate =+ ×+ − (1 ) (1 ) 1.

To get the yield rate for each year between the end of the short-range period and 5 years later 

when the ultimate yield rate is assumed to be reached, the program linearly interpolates between 

the values for these two years. 

The projection of interest income in a given year is the yield rate for that year multiplied by the 

average level of assets. As a formula, 

INT tf yr yield tf yr avg assets tf yr ( , ) ( , ) _ ( , ). = ×

The average level of assets in a trust fund, for a given year, is estimated to be the beginning of 

the year assets, increased by the tax contributions and taxation of benefits income (each exposed 

to the point in the year in which they are estimated to be received, on average), and decreased by 

scheduled benefits, railroad interchange, and administrative expenses (each exposed to the point 

in the year in which they are estimated to be disbursed, on average). 

For all years of the projection period, tax contributions are given an exposure of 0.525, taxation 

of benefits are given an exposure of 0.5, railroad interchange is given an exposure of 0.583, and 

administrative expenses are given an exposure of 0.5. For scheduled benefits, an exposure of 0.5 

is ultimately given. The exposure, ben_exp(yr), is larger than 0.5 in the early years of the 

projection period and grades down smoothly to 0.5. The reason is that in the past, benefits were 

always paid at the beginning of each month. Now benefits are paid out throughout the month, 

based on the birth date of the beneficiary. The average assets held by the trust funds for a given 

year is estimated by the formula 

_ ( , ) ( , ) 0.525 ( , )

0.5 ( , ) ( ) ( , )

0.583 ( , ) 0.5 ( , ).

BOY avg assets tf yr ASSETS tf yr CONTRB tf yr

TAXBEN tf yr ben_exp yr BEN tf yr

RR tf yr ADM tf yr

= +×

+× − ×

− × −×

vii. Equations 4.3.7, 4.3.8 and 4.3.9 – Annual Values 

The annual income rate for a trust fund is computed as the employer/employee tax rate for that 

fund, plus taxation of benefits as a percentage of taxable payroll. 

 

(, ) _ _ (, ) (, ) . ( )TAXBEN tf yr ANN INC RT tf yr taxrate tf yr payroll yr

= +
245 

The annual cost rate for a trust fund is computed as the total cost of providing scheduled benefits 

from that fund as a percentage of taxable payroll. If 

COST tf yr BEN tf yr RR tf yr ADM tf yr ( , ) ( , ) ( , ) ( , ), = ++

then 

(, ) _ _ (, ) . ( )COST tf yr ANN COST RT tf yr

payroll yr =

The trust fund ratio measures the amount of beginning of year assets that can be used to pay 

scheduled benefits. It is expressed as a percentage. 

(, ) (, ) . (, )ASSETS tf yr BOY TFR tf yr BEN tf yr =

viii. Equations 4.3.10, 4.3.11, 4.3.12, and 4.3.13 – Summarized Values 

Present values of cash flows during the year are computed using the yield rate on the combined 

OASDI trust fund for that year. Each component of trust fund operations is exposed, with 

interest, to the point in the year in which, on average, it is received or disbursed. These exposure 

levels, ben_exp(yr), are the same as described above. These exposed levels are then discounted 

to January 1 of the year of the Trustees Report, ni. If yield(j) is the annual yield rate on the 

combined OASDI trust funds for year j and v(yr) is the discounting factor for the year, then 

1 () . [1 ( )]

yr

j ni

v yr

yield j =

=∏ +

For a given year, and trust fund, 

_ ( , ) (1 0.525 ( )) ( , ) ( ),

_ ( , ) (1 0.5 ( )) ( , ) ( ),

_ ( , ) (1 _ ( ) ( )) ( , ) ( ),

_ ( , ) (1 0.583 ( )) (

PV TAX tf yr yield yr TAX tf yr v yr

PV TAXBEN tf yr yield yr TAXBEN tf yr v yr

PV BEN tf yr ben exp yr yield yr BEN tf yr v yr

PV RR tf yr yield yr RR t

=+ × × ×

=+ × × ×

=+ × × ×

=+ × × , ) ( ),

and _ ( , ) (1 0.5 ( )) ( , ) ( ).

f yr v yr

PV ADM tf yr yield yr ADM tf yr v yr

×

=+ × × ×

The target fund for a year is next year’s cost. Its present value is computed as 

PV TARG tf yr BEN tf yr RR tf yr ADM tf yr v yr _ ( , ) [ ( , 1) ( , 1) ( , 1)] ( ), = ++ ++ + ×

Taxable payroll is exposed to the middle of the year when computing present values: 

PV PAYROLL yr yield yr payroll yr v yr _ ( ) (1 0.5 ( )) ( ) ( ). = +× × ×
246 

We also define 

PV INC tf yr PV TAX tf yr PV TAXBEN tf yr _ (, ) _ (, ) _ (, ) = +

and 

PV COST tf yr PV BEN tf yr PV RR tf yr PV ADM tf yr _ ( , ) _ ( , ) _ ( , ) _ ( , ). = ++

Summarized rates are calculated using beginning of period assets and a target fund. 

2

1

2

1

1

1 2

( , ) _ ( ,)

_ _ (, , ) .

_ ()

yr

BOY

j yr

yr

j yr

ASSETS tf yr PV INC tf j

SUMM INC RT tf yr yr

PV PAYROLL j

=

=

⎛ ⎞

+ ⎜ ⎟ ⎝ ⎠ =

∑

∑

The summarized cost rate is similarly computed: 

2

1

2

1

2

1 2

_ ( ,) _ ( , )

_ _ (, , ) .

_ ()

yr

j yr

yr

j yr

PV COST tf j PV TARG tf yr

SUMM COST RT tf yr yr

PV PAYROLL j

=

=

⎛ ⎞ ⎜ ⎟ +

⎝ ⎠ =

∑

∑

The 75-year actuarial balance is computed for a period beginning January 1 of the Trustees 

Report year, ni. It includes both beginning of period assets and a target fund. Therefore, 

75 ( ) _ _ ( , , 74) _ _ ( , , 74). ACTBAL tf SUMM INC RT tf ni ni SUMM COST RT tf ni ni yr

= +− +

In general, an actuarial balance may be computed for any given subperiod of the projection 

period. In general, actuarial balances for a subperiod beginning on January 1 of year ni and 

continuing through the end of year yr are computed using 

, ( ) _ _ ( , , ) _ _ ( , , ). ACTBAL tf SUMM INC RT tf ni yr SUMM COST RT tf ni yr ni yr = −

The unfunded obligation of a trust fund for a given period is the excess of the present value of 

the net cash deficits for each year of that period over the trust fund balance at the beginning of 

the period. The unfunded obligation for the period beginning on January 1 of year ni and 

continuing through the end of year yr is computed using 

_ ( , ) [ _ ( , ) _ ( , )] ( , ).

yr

BOY

j ni

UNF OBL tf yr PV COST tf j PV INC tf j ASSETS tf ni == −− ∑

ix. Equation 4.3.14—Closed Group Unfunded Obligation 
247 

The closed group is defined as individuals who attain specified ages in the first year of the 

projection period (ni). The Statement of Social Insurance displays unfunded obligations for 

closed groups (1) attaining 15 or later in 2008, (2) attaining 62 or older in 2008, and (3) attaining 

15 to 61 in 2008. For each year of the projection period, closed group calculations attribute a 

portion of the items in equations 4.3.1 through 4.3.6 to individuals falling in the defined closed 

group. The calculation of the closed-group unfunded obligation, then, uses the equation above 

but only considering the present values of cost and income attributable to the closed group. 

The following information, developed elsewhere in the “Cost” process, is used for developing 

closed group unfunded obligation amounts: 

• Total number of workers and total taxable earnings by single year of age 15-74 and 

sex, years 1951 through nf, updated yearly 

• Taxable payroll, years ni through nf, updated yearly 

• Payroll tax income, years ni through nf, updated yearly 

• Income from taxation of benefits, years ni through nf, updated yearly 

• Scheduled benefits by beneficiary category, years ni through nf, updated yearly 

• Railroad interchange, years ni through nf, updated yearly 

• Administrative expenses, years ni through nf, updated yearly 

• Yield rate on the combined OASDI trust funds, years ni through nf, updated yearly 

It is important to note that, for dependent beneficiaries, the age of the worker, on whose account 

the benefits are based, determines whether that beneficiary would fall in the closed group. For 

instance, if the closed group were defined as individuals attaining age 15 or later in 2008 and in 

2008 a 3-year-old minor child was receiving benefits on the account of a retired worker aged 63, 

the minor child beneficiary would be considered as part of this closed group because the account 

holder was at least age 15 in 2008. The following describes how the various components of 

income and cost are allocated to the defined closed group in question: 

Payroll Tax Contributions 

Closed group taxable payroll is defined as the percentage of OASDI taxable payroll attributable 

to the closed group in question. An input file of closed group payroll factors, containing these 

percentages by year from 2008 through 2107, is used by the cost program to compute payroll tax 

contributions attributable to the closed group. For each year, the closed group payroll factors are 

determined as follows: 

• The number of projected workers by single year of age (ages 1-99) and sex are 

multiplied by the associated average earnings by age/sex. 

• Then, the portion of total taxable earnings attributable to the closed group is 

calculated. 
248 

For each year of the projection period, the number of workers and average taxable earnings by 

single year of age and sex are determined as follows: 

• For ages 15-74, the number of projected workers comes directly from Economics group 

projections, and the average earnings by age and sex comes directly from the AWARDS 

subprocess. 

• For ages 1-14, the number of projected workers is obtained by averaging the percentage 

of workers at each age relative to the total 1-14 age group, using 14 years of earnings data 

(1991-2004) in the averaging calculations. Average taxable earnings for ages 1-14 are 

obtained by analyzing historical 1991-2004 data of the average earnings at each age 

relative to the age 15 average earnings, and judgmentally assigning a ratio (to age 15 

average earnings) for each age. 

• For ages 75-99, the number of projected workers by age and sex is obtained through first 

developing the ratio of workers in 2004 at each age to the projected population in 2004 at 

that age and then applying that ratio to projected population by age in years 2007 and 

later. Then, the resulting estimated workers are adjusted by an equivalent percentage to 

match the total number of projected workers aged 75 and later, as provided by the 

Economics group. This process is done separately by sex. To obtain the average taxable 

earnings for single years of age 75-99, ratios of average earnings by age 75-99 to overall 

average earnings for all ages is computed for each age 75-99, for earnings years 1991 

through 2004. These ratios by age are then averaged for all 14 years, from which 

earnings ratios to overall average earnings are developed judgmentally. This process is 

done separately by sex. 

Benefits 

Methodologies for computing benefits attributable to the closed groups differs among benefit 

categories, as described below: 

Retired Workers 

For each age in current pay, the number of beneficiaries is multiplied by the corresponding 

average benefit amount across all ages of entitlement. The same applies for DI conversion 

cases. Retroactive benefits for the current year, by age, are then calculated. The closed-group 

factors for old-age benefits for each year are found by summing the benefit amounts 

attributable to the specified closed group, as a proportion of total retired worker benefits for 

all ages. This process is done separately by sex. 

Disabled Workers 

For each age from 20 to the year before normal retirement age, the program adds the 

products of the number of beneficiaries for each duration and the PIA for that duration. 

Retroactive benefits for the current year, by age, are then calculated. The closed-group 
249 

factors for disability benefits are found by summing the total benefit amounts attributable to 

the closed group, as a proportion of total disabled worker benefits for all ages. This process 

is done separately by sex. 

Aged Spouses 

The number of aged wife beneficiaries in current pay status (no dual entitlement) is provided 

by single year of age. Then, for each single year of age, the program allocates total numbers 

of husbands by age, from 5 years younger to 12 years older than the aged wife using an 

assumed distribution. Next, for each age of husband in current pay, the number of husbands 

is multiplied by the weighted average retired worker benefit across all ages of entitlement. 

The closed group factors, then, are obtained by determining the proportion of total benefit 

amounts attributable to the given closed group (based on the husband’s age). 

The same closed group factors are applied to the excess benefit amount for aged wives in 

dual entitlement status (i.e. aged wives with a smaller worker benefit). Aged husbands, a 

very small beneficiary group, get the same closed group benefit factors as do the aged wives, 

described above. 

Aged Widows 

The number of aged widow beneficiaries in current pay status (no dual entitlement) is 

provided by age from 60 to 95. For each single year of age, the program allocates total 

number of aged widows by age of the deceased husband (age the husband would have been if 

he had not died), from 10 years younger to 15 years older than the aged widow using an 

assumed distribution. For each age of deceased husband aged 95 or younger, a real wage 

growth factor is applied to reflect ultimate real wage growth taken to the power to the 

number of years younger than age 96. 

(96 ker ) (1.039 /1.028) deceased wor age Benefitadj − =

This exponent is intended to reflect differences in average levels of benefits, with younger 

deceased husbands having higher benefits based on real wage growth. The closed group 

factors, then, are obtained by determining the proportion of total benefit amounts attributable 

to the closed group 

The same closed group factors are applied to excess benefit amounts for aged widows in dual 

entitlement status (i.e. aged widows with a smaller worker benefit). Aged widowers receive 

the same closed group benefit factors as do aged widows (based on the deceased husband’s 

age). 

Other Beneficiary Categories 
250 

For the 20 other dependent beneficiaries of retired workers, disabled workers, and deceased 

workers, an input file of closed group benefit factors is created, which represents the 

proportion of total (open-group) projected benefits in that category attributable to the given 

closed group age and year. This file is used by the cost program to compute amounts from 

each beneficiary category attributable to the closed group. The file, separately created for 

each closed group run, contains closed group benefit factors for ages 0 through 150 for each 

of the 20 beneficiary categories by sex of the account holder (worker). These input files are 

created by examining a recent sample of Master Beneficiary Record (MBR) data1

 for each of 

the beneficiary categories by age of the worker, and projecting future distributions by age of 

the worker based on population and, for survivor benefits, projected deaths by age. Then, 

adjustments are made for real wage growth to reflect different benefit levels by birth cohort. 

Taxation of Benefits 

Since taxation of benefits is related to benefits, the closed-group taxation of benefit amounts are 

computed by multiplying the total (open-group) taxation of benefit amounts by Trust Fund, by 

the corresponding total closed-group benefit factors by Trust Fund. 

Administrative Expenses 

Since administrative expenses are also assumed to be related to benefits, the closed-group 

administrative expense amounts are computed by multiplying the total (open-group) 

administrative expenses by Trust Fund), by the corresponding total closed-group benefit factors 

by Trust Fund. 

Railroad Interchange 

Since the railroad interchange has both a payroll tax and benefit component, each component is 

multiplied by its corresponding closed-group factor. That is, total payroll tax contributions 

arising from railroad interchange are multiplied by the closed group payroll factor discussed 

above in the “Tax on Contributions” section. Total railroad benefits, by Trust Fund, are 

multiplied by the aggregate closed-group benefit factors by Trust Fund. Closed-group railroad 

administrative expenses and closed-group railroad taxation of benefits are also estimated by 

applying aggregate closed group benefit factors by Trust Fund. The final amount is then the 

difference in the components (closed group railroad income less closed group railroad cost). 
251 

Appendix 4.3-1 

Shuttling Method

In this appendix we discuss the “shuttling method”. 

The shuttling method as presented in the COST model attempts to reorganize the PAPs 

obtained from subprocess 4.2, which maintains a static age-sex distribution of newly entitled 

beneficiaries, in such a way that captures the changing age-sex distribution of newly entitled 

beneficiaries provided by subprocess 3.3. The age-sex distribution of the sample (subprocess 

4.2) and those newly entitled from subprocess 3.3 are aligned in the sample year. This 

alignment persists throughout all years in the long-range period. When we refer to the agesex distribution fom subprocess 3.3 in what follows below, we refer to the aligned age-sex 

distribution. 

Let oadsrs be the age/sex distribution of the sample from subprocess 4.2. Let oabicp be the 

number of newly entitled beneficiaries by age and sex from subprocess 3.3. Let total be the 

total number of newly entitled beneficiaries by sex. The ratio 

(, ) , ( )oabicp sex age

total sex

 for age = 62, ... , 70 gives the age-sex distribution from subprocess 3.3. 

The array rsb_oadscp_sampleyr is the age-sex distribution from subprocess 3.3 from the 

sample year (2004 for the 2008 Trustees Report). 

The value of oadscp is defined, by age and sex, to be: 

(, ) ( , ) ( , ) _ _ ( , ). ( )oabicp sex age oadscp sex age oadsrs sex age rsb oadscp sampleyr sex age total sex

= +−

We will call this the aligned age-sex distribution as obtained from subprocess 3.3. 

For each sex, we construct a matrix oads. Construction of this matrix uses two different agesex distributions: the age-sex distribution of the awards sample and the aligned age-sex 

distribution of newly entitled beneficiaries from subprocess 3.3. The matrix oads is a 9 9 ×

matrix whose rows and columns are indexed consecutively by the ages 62,..., 70. We index 

the rows of this matrix by the age of entitlement of a worker in the projection (ageentRSB) 

and the columns of this matrix by the age of entitlement of a worker in the Awards sample 

(ageentAWD). 

More precisely, for a given sex, let oadsrs be the age distribution of the sample; oadscp be 

the aligned age distribution of newly entitleds from subprocess 3.3. Both arrays oadsrs and 

oadscp are indexed by age, ages = 62, ..., 70. For a given sex, the matrix oads is 

constructed with the following properties: 

70

62

() (, )

ageentAWD

oadscp ageentRSB oads ageentRSB ageentAWD == ∑

and 
252 

70

62

( ) ( , ).

ageentRSB

oadsrs ageentAWD oads ageentRSB ageentAWD == ∑

In other words, the matrix oads has the following properties: 

• The sum of the entries in any row of the matrix is the value of the distribution of the 

projection for the age corresponding to the row. 

• The sum of the entries in any column of the matrix is the value of the distribution of 

the Awards sample for the age corresponding to the column. 

Let opap be the original potential AIME percentages (PAPs) passed to subprocess 4.3 from 

subprocess 4.2. This is a 9 10 × matrix whose rows are indexed by ages at entitlement 62, ..., 

70 and whose columns are indexed by benefit interval 1, ..., 10 (represented by the variable i 

in the formulas below). The values of opap are modified and the results are the PAPs used 

by process 4.3, called opap1. As a formula, 

70

62

70

62

1( , )

( ,) ( , )

.

(, )

ageentAWD

ageentAWD

opap ageentRSB i

opap ageentAWD i oads ageentRSB ageentAWD

oads ageentRSB ageentAWD

=

=

×

=

∑

∑

This formula may be rewritten as follows. 

70

70

62

62

1( , )

(, ) ( ,) .

(, ) =

=

= × ∑

∑ ageentAWD

ageentAWD

opap ageentRSB i

oads ageentRSB ageentAWD opap ageentAWD i

oads ageentRSB ageentAWD

It follows that opap1 may be interpreted as a reweighting of opap. We have 

70

,

62

1( , ) ( , ) ageentRSB ageentAWD

ageentAWD

opap ageentRSB i w opap ageentAWD i == × ∑

with weights ,

(, ). ( ) ageentRSB ageentAWDoads ageentRSB ageentAWD w

oadscp ageentRSB = 

As matrices, opap w opap 1= × (and is another 9 10 × matrix). 

Consider the following example. In this example, the projection year is 2040, and the sex is 

males. 

The oadsrs vector (from subprocess 4.2) is as follows. 

62 63 64 65 66 67 68 69 70

Male 0.4615 0.1466 0.0676 0.2533 0.0555 0.0058 0.0036 0.0030 0.0030

The unaligned age-sex distribution (from subprocess 3.3) is as follows. 
253 

62 63 64 65 66 67 68 69 70

Male 0.3501 0.1383 0.0514 0.1303 0.1196 0.2206 0.0096 0.0136 0.0117

The age-sex distribution (from subprocess 3.3) in 2004, the year of the sample is as follows. 

62 63 64 65 66 67 68 69 70

Male 0.4362 0.1521 0.0694 0.2460 0.0800 0.0059 0.0017 0.0024 0.0062

Hence the aligned age-sex distribution (from subprocess 3.3), that is, the oadscp vector, is as 

follows. 

62 63 64 65 66 67 68 69 70

Male 0.3304 0.1328 0.0496 0.1376 0.0951 0.2205 0.0115 0.0142 0.0085

The matrix oads, computed in this subprocess (4.3) is as follows. An explanation of how this 

matrix is generated appears below. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.3304 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3304

63 0.1311 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1328

64 0.0000 0.0496 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0496

65 0.0000 0.0954 0.0422 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1376

66 0.0000 0.0000 0.0254 0.0696 0.0000 0.0000 0.0000 0.0000 0.0000 0.0951

67 0.0000 0.0000 0.0000 0.1837 0.0368 0.0000 0.0000 0.0000 0.0000 0.2205

68 0.0000 0.0000 0.0000 0.0000 0.0115 0.0000 0.0000 0.0000 0.0000 0.0115

69 0.0000 0.0000 0.0000 0.0000 0.0072 0.0058 0.0012 0.0000 0.0000 0.0142

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024 0.0030 0.0030 0.0085

Total 0.4615 0.1466 0.0676 0.2533 0.0555 0.0058 0.0036 0.0030 0.0030 1.0000

Note that the column total is oadsrs and the row total is oadscp. The oads matrix is 

determined using these row and column sum constraints. The nonzero entries of the oads

matrix zig-zag down and to the right. Starting at the upper left hand corner, the lesser of 

oadsrs and oadscp is put there. So oads(62,62) 0.3304. = In this case (as is usually the case) 

oadscp is less. The difference oadsrs oadscp (62) (62) 0.4615 0.3304 0.1311 − =−= is placed one 

lower, in oads(63,62). Since the sum of the first column is oadsrs(62) and the sum of the 

first row is oadscp(62), we move to the next entry on the right. The difference 

oadscp oads (63) (63,62) 0.1328 0.1311 0.0016, − =−= is oads(63,63). Now we have that the row 

sum is oadscp(63). We want the column sum to be oadsrs(63). We move down to 

oads(64,63). Since 

oadsrs oads oadscp (63) (63,63) 0.1466 0.0016 0.1450 0.1328 (63), − =−=>= by the row sum 

constraint we are forced to have oads(64,63) 0.0496. = Now move one lower. Since 

0.1466 0.0496 0.0016 0.0954 (65) 0.1376, −−=< = oadscp the entry oads(65,63) 0.0954. = The 

column sum is now oadsrs(63), and we move one over to the right. We want to fill in this 

entry. We compute oadscp oads (65) (65,62) 0.1376 0.0954 0.0422 0.0676, − =−=< by the 

column sum constraint we have oads(65,64) 0.0422. = The row constraint is now met, and we 
254 

move down to (66,64). oads We look at (66) 0.0951. oadscp = By the column constraint, 

we cannot place this value in (66,64). oads So to meet the column constraint, we set 

oads(66,64) equal to the difference (64) (65,64) 0.0676 0.0422 0.0254. oadsrs oads − =−= 

Now that this column constraint is met, we move one column over to (66,65). oads Note that 

we cannot put (65) 0.2533 oadsrs = there since then the row constraint would be violated. In 

order to meet the row constraint, 

oads oadscp oads (66,65) (66) (66,64) 0.0951 0.0254 0.0696. = − =−= Since the row 

constraint is met, we move one row down to (67,65). oads We cannot put (67) oadscp there 

since then the column constraint would be violated. Hence 

oads oadsrs oads (67,65) (65) (66,65) 0.2533 0.0696 0.1837. = − =−= Now that the column 

constraint is met, we move one column over to (67,66). oads We cannot put 

oadsrs(66) 0.0555 = there or else the row constraint would be violated. So we put 

oads oadscp oads (67,66) (67) (67,65) 0.2205 0.1837 0.0368 = − =−= there. Now the row 

constraint is met and we move one row down to (68,66). oads Since 

oads oadscp oadsrs (67,66) (68) (66), + < we have (68,66) (66) 0.0115. oads oadscp = = Now 

move one row down to (69,66). oads We cannot put (69) 0.0142 oadscp = there or else the 

column constraint would be violated. Hence 

oads oadsrs oads oads (69,66) (66) (67,66) (68,66) 0.0555 0.0368 0.0115 0.0072 = − − =−−= a

nd the column constraint is met. Now move one column over to (69,67). oads We put 

oads oadsrs (69,67) (67) 0.0058 = = there since that meets the column constraint and the row 

constraint remains unsatisfied. So move over to the next column, (69,68). oads We cannot 

put (68) oadsrs there since that would violate the row constraint. It follows that 

oads oadscp oads oads (69,68) (69) (69,66) (69,67) 0.0142 0.0072 0.0058 0.0012. = − − =−−=

Now the row constraint is satisfied and we move down to the last row and oads(70,68). By 

the column constraint, this entry is forced to be 0.0024. Moving to column 69, again, by the 

column constraint, the entry oads(70,69) is forced to be 0.0030. Finally, by the row and 

column constraints, the last entry, oads(70,70), is 0.0030. 

To obtain the w matrix, normalize the rows by dividing by the row sum. 

\ 62 63 64 65 66 67 68 69 70

62 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

63 0.9877 0.0123 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

64 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0

ageentRSB ageentAWD

.0000

65 0.0000 0.6935 0.3065 0.0089 0.0000 0.0000 0.0000 0.0000 0.0000

66 0.0000 0.0000 0.2676 0.7324 0.0000 0.0000 0.0000 0.0000 0.0000

67 0.0000 0.0000 0.0000 0.8331 0.1669 0.0000 0.0000 0.0000 0.0000

68 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000

69 0.0000 0.0000 0.0000 0.0000 0.5094 0.4085 0.0822 0.0000 0.0000

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2852 0.3516 0.3516
255 

Then, as matrices, 1 , opap w opap = × as one may verify. For display purposes the transposes 

of opap and opap1 are shown. 

 

 opap 62 63 64 65 66 67 68 69 70 

1 0.9993 0.9992 0.999 0.9985 0.9985 0.9964 0.9929 0.99 0.9893 

2 0.989 0.9895 0.986 0.9867 0.9828 0.9245 0.9302 0.9004 0.9163 

3 0.9635 0.9676 0.9627 0.9665 0.9551 0.8182 0.7771 0.7245 0.8272 

4 0.9336 0.9431 0.9318 0.9462 0.9318 0.7063 0.6486 0.5597 0.7364 

5 0.9037 0.9163 0.9068 0.9264 0.9131 0.6373 0.563 0.4703 0.6687 

6 0.8768 0.8913 0.8831 0.9073 0.8909 0.5994 0.5017 0.4193 0.6242 

7 0.8499 0.8671 0.8588 0.888 0.8697 0.5663 0.4846 0.3943 0.5957 

8 0.8235 0.843 0.8362 0.869 0.8525 0.5333 0.4495 0.3733 0.5577 

9 0.7953 0.8178 0.8148 0.8501 0.8363 0.5065 0.4162 0.3587 0.5398 

10 0.7692 0.789 0.7913 0.8308 0.8191 0.4839 0.386 0.3395 0.5064 

11 0.7432 0.7613 0.7674 0.8098 0.8009 0.4617 0.3621 0.325 0.4707 

12 0.7157 0.7324 0.7419 0.7884 0.7849 0.4435 0.3485 0.3071 0.4401 

13 0.688 0.7015 0.7139 0.7649 0.762 0.4328 0.3264 0.2848 0.4118 

14 0.6386 0.6465 0.6671 0.7213 0.7238 0.3989 0.297 0.2557 0.3861 

15 0.5689 0.5702 0.5968 0.6564 0.6685 0.3558 0.2653 0.228 0.3386 

16 0.495 0.4916 0.52 0.5887 0.6098 0.3277 0.2338 0.2053 0.302 

17 0.4218 0.4139 0.4441 0.5201 0.5432 0.3014 0.2124 0.1901 0.2823 

18 0.3502 0.3422 0.3773 0.4561 0.4796 0.2719 0.1857 0.182 0.259 

19 0.2534 0.2513 0.2875 0.366 0.3974 0.2413 0.1608 0.1624 0.2315 

20 0.1481 0.1571 0.1882 0.263 0.293 0.1944 0.1349 0.1294 0.1887 

21 0.0731 0.0816 0.1056 0.1676 0.1979 0.1457 0.0998 0.1025 0.1405 

22 0.0232 0.0282 0.0421 0.0709 0.094 0.0841 0.0631 0.0641 0.0824 

23 0.0036 0.0051 0.0102 0.017 0.0231 0.0248 0.0268 0.023 0.0281 

24 0 0 0 0 0.0004 0.0007 0.0024 0.0018 0.0038 

25 0 0 0 0 0 0 0 0 0 

26 0 0 0 0 0 0 0 0 0 

27 0 0 0 0 0 0 0 0 0 

28 0 0 0 0 0 0 0 0 0 

29 0 0 0 0 0 0 0 0 0 

30 0 0 0 0 0 0 0 0 0 
256 

 opap1 62 63 64 65 66 67 68 69 70 

1 0.9993 0.9993 0.9992 0.9991 0.9986 0.9985 0.9985 0.9972 0.979 

2 0.989 0.989 0.9895 0.9884 0.9865 0.986 0.9828 0.9547 0.9039 

3 0.9635 0.9636 0.9676 0.9661 0.9655 0.9646 0.9551 0.8846 0.7671 

4 0.9336 0.9337 0.9431 0.9396 0.9423 0.9438 0.9318 0.8164 0.6406 

5 0.9037 0.9039 0.9163 0.9134 0.9212 0.9242 0.9131 0.7717 0.561 

6 0.8768 0.877 0.8913 0.8888 0.9008 0.9046 0.8909 0.7398 0.5099 

7 0.8499 0.8501 0.8671 0.8646 0.8802 0.8849 0.8697 0.7141 0.4862 

8 0.8235 0.8237 0.843 0.8409 0.8602 0.8662 0.8525 0.689 0.4555 

9 0.7953 0.7956 0.8178 0.8169 0.8407 0.8478 0.8363 0.6671 0.4346 

10 0.7692 0.7694 0.789 0.7897 0.8202 0.8288 0.8191 0.6466 0.4075 

11 0.7432 0.7434 0.7613 0.7632 0.7985 0.8083 0.8009 0.6263 0.383 

12 0.7157 0.7159 0.7324 0.7353 0.776 0.7878 0.7849 0.6096 0.3621 

13 0.688 0.6882 0.7015 0.7053 0.7513 0.7644 0.762 0.5917 0.338 

14 0.6386 0.6387 0.6465 0.6528 0.7068 0.7217 0.7238 0.556 0.3103 

15 0.5689 0.5689 0.5702 0.5784 0.6404 0.6584 0.6685 0.5076 0.2748 

16 0.495 0.495 0.4916 0.5003 0.5703 0.5922 0.6098 0.4637 0.245 

17 0.4218 0.4217 0.4139 0.4232 0.4998 0.524 0.5432 0.4172 0.2266 

18 0.3502 0.3501 0.3422 0.353 0.435 0.46 0.4796 0.3706 0.208 

19 0.2534 0.2534 0.2513 0.2624 0.345 0.3712 0.3974 0.3142 0.1843 

20 0.1481 0.1482 0.1571 0.1666 0.243 0.268 0.293 0.2397 0.1503 

21 0.0731 0.0732 0.0816 0.089 0.151 0.1727 0.1979 0.1685 0.1139 

22 0.0232 0.0233 0.0282 0.0325 0.0632 0.0748 0.094 0.0874 0.0695 

23 0.0036 0.0036 0.0051 0.0067 0.0152 0.018 0.0231 0.0241 0.0256 

24 0 0 0 0 0 0.0001 0.0004 0.0007 0.0027 

25 0 0 0 0 0 0 0 0 0 

26 0 0 0 0 0 0 0 0 0 

27 0 0 0 0 0 0 0 0 0 

28 0 0 0 0 0 0 0 0 0 

29 0 0 0 0 0 0 0 0 0 

30 0 0 0 0 0 0 0 0 0