Long-Range OASDI Projection 

Methodology 

Intermediate Assumptions of the 2021

Trustees Report 

August 2021

Office of the Chief Actuary

Social Security Administration
A. Flow Charts

2
Overview of Long-Range OASDI Projection Methodology

Process 2:

Economics

Process 1:

Demography

Process 4:

Trust Fund Operations and Actuarial Status

Process 3:

Beneficiaries

Chart 1:

Social Security Administration

Office of the Chief Actuary

August 2021

3
Trustees ultimate assumptions

Fertility

Mortality

LPR Immigration

Other-than-LPR Immigration

1.2 Mortality

Inputs: Historical 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, undercounts, marital status data, other-than-LPR immigrant population 

data, and estimates of population in other components of Social Security area. 

Outputs: Historical Social Security area population (including starting population); Historical other-thanLPR immigrant population

1.6 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

1.7 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 

1.8 Projected Population

Inputs: Historical U.S. family data 

Outputs: Projected data – Social Security area population

Economics, Beneficiaries, and Trust Fund Operation and Actuarial Status 

Note: 1.2, 1.3, 1.4, and 1.5 also provide outputs used by these processes

1.1 Fertility 

Inputs: Historical U.S. births and female 

resident population 

Outputs: Historical and projected 

central birth rates

1.3 LPR Immigration

Inputs: Historical LPR U.S. immigration 

levels 

Outputs: Historical and projected annual

LPR immigration and legal emigration levels 

Chart 2: Demography – Process 1

Social Security Administration

Office of the Chief Actuary

August 2021

1.5 Other-than-LPR Immigration

Inputs: Historical levels of the

foreign-born population

Outputs: Historical and projected annual 

Other-than-LPR immigration and emigration

levels; projected other-than-LPR immigrant

population

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Trustees Ultimate Economic Assumptions

Average real wage

Productivity

Average hours worked

Inflation

Full-employment unemployment rate

Ratio of OASDI taxable payroll to covered earnings

2.2 Class of Worker

Inputs: Historical BLS data, 

population (Demography), & 

economic factors

Outputs: Wage workers & selfemployed by age and sex 

2.3 AWI Series

Inputs: Historical AWI, Wages

Outputs: Historical and Projected AWI 

2.1 Real & Potential GDP, Nominal GDP

Inputs: Historical NIPA (BEA) data

Outputs: Real, potential, and nominal GDP 

2.3 Covered Employment

Inputs: Historical U.S. & covered employment

data, population including other-than-LPR immigrant 

population & DACA/DAPA immigrants (Demography) 

Outputs: Covered worker rates, covered 

worker levels, & total employed (all by age, 

sex, type of worker) 

2.2 U. S. Wages & Income

Inputs: Historical NIPA (BEA) data & employment

(BLS) by sector 

Outputs: Wages & SE income by sector 

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

Inputs: Taxable earnings, covered workers

Outputs: Average taxable earnings 

2.4 Effective taxable payroll

Outputs: Effective taxable payroll

Chart 3: Economics – Process 2

Social Security Administration

Office of the Chief Actuary

August 2021

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 Covered Earnings

Inputs: Historical NIPA & covered earnings

data by sector 

Outputs: Historical & projected covered 

earnings by type of worker 

Beneficiaries, 

Trust Fund Operations and Actuarial Status

2.3 Taxable Maximum

Inputs: Historical taxable maximum,AWI

Outputs: Historical & projected taxable max. 

2.5 Revenues

Outputs: Short-range payroll tax revenue Short-Range Trust Fund Operations

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3.1 Fully-insured (FI) population

Inputs: Covered workers, median earnings,

and AWI (Economics), population including otherthan-LPR immigrant and DACA (Demography), 

net LPR immigration (Demography), other-thanLPR population attaining DACA status

(Demography), earnings distribution, historical 

FI population (historical and short-range 

projections).

Outputs: FI population (historical and projected),

historical and projected fully insured rates

3.1 Disability-insured (DII) population

Inputs: Historical DII population 

Outputs: DII population (historical and projected)

3.2 Disabled-worker beneficiary (DIB) population

Inputs: Historical DII population, 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, employment

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 parent aged 62+ 

(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 beneficiary population

Inputs: Historical widow beneficiary population,

SS area population by marital status (Demography)

and other relationships

Outputs: Insured and uninsured widow beneficiary

population (projected)

Chart 4: Beneficiaries – Process 3

Social Security Administration

Office of the Chief Actuary

August 2021

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 OAB benefits, but not receiving those benefits.

Trustees ultimate assumptions

Disability incidence rates 

Disability recovery rates 

Disability mortality rates

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Chart 5: Trust Fund Operations and Actuarial Status – Process 4

4.3 Payroll taxes

Inputs: Payroll tax rate, effective taxable 

payroll (Economics), incurred-to-cash lag factor,

short-range estimates 

Outputs: Payroll taxes

4.1 Taxation of benefits to benefits ratio

Inputs: Historical and projected percent of benefits

taxable and average marginal tax rate for the 

short-range period and same estimates with $0

threshold amounts from the Office of Tax Analysis

In the Department of the Treasury

Outputs: TOB as a percent of benefits (projected) 

4. 3 Taxation of benefits (TOB)

Outputs: Taxes on benefits

4.3 Administrative expenses

Inputs: Short-range administrative expenses; 

total beneficiary population and AWI, 

assumed increase in productivity (Economics),

Outputs: Administrative expenses

4.3 Benefit payments

Inputs: Starting average benefits, OAB population and DIB population

(Beneficiaries), married and divorced aged population (Demography), 

Cost-of-Living Adjustments and AWI (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 interchange

Inputs: Data from Railroad Retirement Board and 

AWI, covered workers, taxable payroll (Economics), 

short range estimates of railroad interchange 

Outputs: Net payments to RRB 

4. 3 Interest income

Inputs: Short-range estimates

of interest income

Outputs: 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

August 2021

Trustees ultimate assumptions

Real interest rate, CPI

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), Taxable Maximum; 

historical and projected fully insured rates by sex and age, 

historical and projected beneficiaries (Beneficiaries)

Outputs: Projected AIME distributions for new 

entitlements 

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B. 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.

This element introduces key projected variables used in the subprocess. 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 symbol indicates that the

calculation of this variable cannot 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,

this element includes how often additional data are expected to be received.

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

level of disaggregation of the data.

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Process 1:

Demography

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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 (TR). For the 2021 report, the 

projection period covers the years 2021 through 2095. 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 eight subprocesses: FERTILITY, MORTALITY, LPR (Lawful 

Permanent Resident) IMMIGRATION, HISTORICAL POPULATION, OTHER-THAN-LPR

IMMIGRATION, MARRIAGE, DIVORCE, and PROJECTED POPULATION. The following chart displays 

the key outputs of each subprocess: 

Subprocess Key Outputs

FERTILITY • Birth rates, by age of mother

MORTALITY • Probabilities of death, by age and sex

LPR

IMMIGRATION

• LPR immigrants, by age and sex

• Legal emigrants, by age and sex

• Adjustments of status from other-than-LPR status to LPR status, by age

and sex

HISTORICAL 

POPULATION

• Historical estimates of the Social Security area total population, by age,

sex, and marital status

• Historical estimates of the other-than-LPR population, by age and sex

OTHER-THANLPR 

IMMIGRATION

• Other-than-LPR immigrants, by age and sex

• Other-than-LPR emigrants, by age and sex

• Projected other-than-LPR populations, by age, sex, and type (neverauthorizeds, nonimmigrants, visa-overstayers)

• Historical estimates of the other-than-LPR population, by age, sex, and

type

MARRIAGE • Marriage rates, by age-of-husband crossed with age-of-wife

DIVORCE • Divorce rates, by age-of-husband crossed with age-of-wife

PROJECTED 

POPULATION

• Projected total populations, by age, sex, and marital status

1 The Social Security area population is composed of: (1) residents of the 50 States and the District of Columbia (adjusted for net 

census undercount); (2) civilian residents of Puerto Rico, the Virgin Islands, Guam, American Samoa, and the Northern Mariana

Islands; (3) Federal civilian employees and persons in the U.S. Armed Forces abroad and their dependents; (4) non-citizens living 

abroad who are insured for Social Security benefits; and (5) all other U.S. citizens abroad.

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1.1. FERTILITY

1.1.a. Overview

The National Center for Health Statistics (NCHS) collects data on annual numbers of births by single year of 

age of mother and the U.S. Census Bureau produces estimates of the female resident population by single year 

of age. Age-specific birth rates (bbxx

zz) for a given year z are defined as the ratio of (1) births (BBxxzz) during the year 

to mothers at the specified age x to (2) the midyear female population (PPxx

zz) at that age. The total fertility rate

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

equals the sum of the age-specific birth rates for all ages x during the year. One can also interpret the total 

fertility rate as the average number of children that would be born to a woman if she were to survive her 

childbearing years and experience, at each age in her life, the age-specific birth rate of year z. There is also a 

cohort total fertility rate (CC RRtt ). The cohort total fertility rate for a given cohort born in year t equals the sum 

of the age-specific birth rates for all ages x in each cohort’s lifetime.

The FERTILITY subprocess combines the historical values of bbxx

zz and the ultimate CTTTTRRzz to develop 

projections of bbxx

zz. The primary equations of this subprocess are given below: 

bbxx

zz = bbxxzz(∙) (1.1.1) 

(1.1.2) 

(1.1.3) 

1.1.b. Input Data

Trustees Assumptions - 

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

cohort TFR. For the 2021 Trustees Report, the ultimate TFR is 2.00 and it is assumed to be attained

starting with the cohort born in 2007.

Other input data - 

2. From the NCHS, annual numbers of births by age of mother2 (10-14, 15, 16, 17, ..., 48, 49-54) for years

1980-2019. In general, the NCHS provides an annual update including one additional year of final birth

data. Previous historical years are only updated if the NCHS makes a historical revision to their data.

3. From the U.S. Census Bureau, estimates of the July 1st female resident population by single year of age

for ages 14-49 for 1980-2019. In general, each year, Census provides updated data for years after the

most recent decennial census.

4. From the 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.

2 Births at ages less than 14 are treated as having occurred at age 14, and births reported to mothers older than 49 are treated as having 

occurred at age 49.

TTTTRRzz = �bbxx

zz

xx

CC RRtt = �bbxx

tt+xx

xx

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5. From the NCHS, birth rate data for the first, second, and third quarters of 2019 and 2020, by five-year 

age group (2020 data is provisional). In general, the NCHS provides data for a new year through the 

first quarter annually at the time the fertility projections need to be finalized. However, data through the 

third quarter was available for the 2021 TR. 

1.1.c. Development of Output

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 end of the 75-year projection period. For historical years prior to 1980, age-specific birth 

rates come from the NCHS. For years 1980 through the remainder of the historical period, age-specific birth 

rates are calculated as: bbxx

zz = BBxx

zz

PPxx

zz, using birth data from the 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 assumed ultimate cohort total fertility rate. This process consists of the following steps:

1. Calculate the age-specific birth rates, bbxx

zz, for each year during the period 1980-2019. 

2. For 2020, estimate bbxx

2020 values by taking the bbxx2019 values and multiplying them by the weighted 

average (using 2019 final data for the weighting) of the first three quarters of 2020 NCHS five-year agegroup data over the weighted average of the first three quarters of 2019 NCHS five-year age-group data. 

Ages in the exact middle of each age group (for instance, 27 is the exact middle of the 25-29 age group) 

only use that particular age-group ratio but other ages use a weighted average of the ratios for the age 

group they are in and the next closest age group. 

3. Calculate regression slopes and intercepts for each age series of bbxx

zz from 1975-2020. 

4. The starting values of the projection process are the bbxx

zz values from the last provisional historical data 

year (2020). Thus, these are denoted as bbxx

2020. 

5. Calculate the ultimate year for each age. This is equal to 2020 + age – 13. 

6. For the projection years (2021 and later), calculate preliminary bbxx

zz values by:

a. For ages under 20: Keeping the gap from the bbxx

2020 values and the regression lines constant until 

the ultimate year for each age. However, the value for each particular bbxx

zz must be greater than or 

equal to 90% of the prior year’s value (bbxx

zz−1). 

b. For ages 20 – 22: Linearly closing y percent of the gap from the bbxx

2020 values and the regression 

lines by the nth projected year, where y is equal to (x – 19) / (30 – 19) and n is equal to x – 13. 

Then, the value of bbxx

zz stays constant from year n and later. 

c. For ages 23 – 29: Linearly closing y percent of the gap from the bbxx

2020 values and the regression 

lines by the 10th projected year, where y is equal to (x – 19) / (30 – 19). Then, the value of bbxx

zz

stays at a constant value away from the regression line until the ultimate year, at which point bbxx

zz

stays constant for future years.

d. For ages 30 and older: Linearly closing the gap from the bbxx

2020 values to the regression lines in 

the 10th projected year (2030). The values of bbxx

zz then follow the regression line until the ultimate 

year for each age. The values of bbxx

zz stay constant for that year and onwards. 

7. Then, preliminary cohort total fertility rates, CC RRpp

tt , are calculated as the sum of all bbxxzz values for each 

cohort born in year t (� bbxx

tt+xx 49

xx= 14 ).

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8. Next, calculate the weight (w) to use on the ultimate cohort TFR of 2.00. Then, 1 - w will be the weight

to apply to the preliminary cohort total fertility rates, CC RRpp

tt .

w = �

� bbxx

49 tt+xx

xx= aa+1

� bbxx

49 tt+xx

xx= 14 �

max(aa,15)−14

where a is the age of each cohort in 2020.

9. Final cohort total fertility rates, CC RRtt, are calculated as ww ∗ 2.00 + (1 − ww) ∗ CC RRpp

tt .

10. Now, adjust projected rates (2021 and later), bbxx

zz, on a cohort basis so that the values of CC RRtt from Step

9 are hit (multiply each projected bbxx

zz by CC RRtt/ CC RRpptt .)

11. After Step 10 is complete for all years, impacts from the COVID-19 pandemic are factored in. The 2021

rates in Step 10 are multiplied by a factor of 0.92 from ages 14 – 39, and this factor increases to 1 on

linear grade-in basis from ages 40 – 45. For 2022, the rates in Step 10 are multiplied by a factor of 0.96

from ages 14 – 39, and this factor increases to 1.00 on linear grade-in basis from ages 40 – 45. For years

2024-26, the decreases in 2021 and 2022 are made up for on a cohort basis evenly over each year on a

cohort-basis (i.e., add 1/3 of the sum of the decrease in 2021 and 2022 to the step 10 rates for each year

2024-26 for each cohort).

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1.2. MORTALITY

1.2.a. Overview

The National Center for Health Statistics (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 number of deaths occurring during the year to persons between exact ages x and x+y to (2) the 

midyear population between exact ages x and x+y. For historical years prior to 1968, yMx are calculated from 

NCHS and Census data by sex. For historical years beginning in 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 the NCHS, the yMx are distributed by cause of death 

for years 1979 and later.3

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

quantified by calculating the percentage reductions in log linear regressions of central death rates (yAAx). In 

order to project future yMx, the Board of Trustees of the OASDI Trust Funds assumes an ultimate annual 

percentage reduction (yyAAAAxx

uu) that will be realized during the projection period for each sex and cause of death. 

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 (ee̊xx) is defined as the average number of years of life remaining for people who are age x 

and are assumed to experience the probabilities of death for a given year throughout their lifetime. It 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, male and female combined, in the corresponding age groups of the 

standard population, the 2010 U.S. Census resident population (ySPx). Thus, if the age-adjusted death rate for a 

particular year and sex is multiplied by the total 2010 U.S. Census resident population, the result gives the 

number of deaths that would have occurred for that sex in the 2010 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. They 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 2010 U.S. Census resident 

population. 

MORTALITY projects annual yMx, which are then used to calculate additional outputs. The equations for this 

subprocess are given below:

 yMx = yMx (·) (1.2.1) 

 

 yAAx = yAAx (·) (1.2.2) 

3 Data needed to project central death rates by cause of death were obtained from Vital Statistics tabulations for years since 1979. For 

the years 1979-98, adjustments were made to the distribution of the numbers of deaths by cause in order to reflect the revision in the 

cause of death coding that occurred in 1999, making the data for the years 1979-98 more comparable with the coding used for the 

years 1999 and later. The adjustments are comparability ratios created using published data from the National Center for Health 

Statistics and calculated using their methodology. 

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 qx = qx (·) (1.2.3) 

 

 ee̊xx = ee̊xx (·) (1.2.4) 

 (1.2.5) 

 

 (1.2.6) 

 

where yyMMxx,ss

zz 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 -

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

yAAx by sex, age group (less than 15, 15-49, 50-64, 65-84, and 85+), and cause of death (Cardiovascular 

Disease, Cancer, Accidents and Violence, Respiratory Disease, Dementia, and All Other). The annual 

percentage reductions reach their ultimate values 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 -

2. Annual numbers of registered deaths by sex and age group for the period 1900-67. 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.

3. The monthly number of births, by sex, for years 1938-2019. These data are updated annually, when the 

NCHS provides an additional year of data. 

4. The number of infant deaths, by age, sex, and age group (under 1 day, 1-2 days, 3-6 days, 7-27 days, 28 

days-1 month, 2 months, 3 months, ..., 11 months, 1 year, 2 years, 3 years, and 4 years), for years 1939-

2019. These data are updated annually, when the NCHS provides an additional year of data. 

5. The population of states in the Death Registration area by age group (0-4, 5-9, 10-14, ..., 65-69, 70-74, 

and 75+) and sex, for years 1900-39. These data are not updated. 

6. The number of registered deaths, by sex and age group (85-89, 90-94, and 95+), used for the years 1900-

67. These data are not updated. 

7. Starting values for qx for infant and toddler age groups (under 1 day, 1-2 days, 3-6 days, 7-27 days, 28 

AAAA ss

zz =

� yySSPPxx

xx

∙ MMyy xx,ss

zz

�yySSPPxx

xx

AA AA zz =

�� yySSPPxx,ss

xx

∙ MMyy xx,ss

zz

ss

�� yySSPPxx,ss

xxss

15
days-1 month, 2 months, 3 months, ..., 11 months, 1 year, 2 years, 3 years, and 4 years) from 1939-41 

decennial life tables. These data are not updated. 

8. From the NCHS public use records, deaths by sex, single year of age, cause of death, and marital status 

from 1968-2019. Marital status is not available until 1979, and cause of death is only used for 1979 and 

later.

U.S. Census Bureau Data -

9. Estimates of the July 1 resident population by single year of age (0 through 100+) for years 1980-2019. 

Each year, Census provides an additional year of data and updated data for years after the most recent 

decennial census.

10. Standard Population by year, sex, and age: 1980, 1990, 2000, and 2010. Used to standardize death rates

for comparison. Updated every decennial census. 

11. U.S. resident population by sex, age group, and year 1900-39 (0, 1-4, 5-9, ..., 70-74, and 75+. These data 

are not updated. 

12. The resident population at ages 75-79 and 80-84, by sex, for years 1900-40 (at ten-year intervals). 

These data are not updated. 

13. The resident population, by sex and age group (0, 1-4, 5-9, ..., 80-84, and 85+), for 1940-59. These data 

are not updated. 

14. Resident population by single year of age and sex for 1960-79 (ages 0 through 59 for 1960-69 and ages 

0 through 84 for 1970-79). These data are not updated. 

15. The United States and Armed Forces overseas (USAF) population, by sex and single year of age for 

1960-69 (ages 60 through 85+ for 1960-67 and ages 60 through 84 for 1968-69). These data are not 

updated. 

16. Population, by 5-year age group to split 85+ pre-1968. These data are not updated. 

17. Estimates of the population by marital status, sex, and age from the American Community Survey 

(ACS) public use microdata sample (PUMS) files for years 2000-19. In general, an additional year of 

data is available each year.

 

CMS Data - 

18. Annual numbers of deaths of all Medicare enrollees, by sex and single year of age (ages 65 and over), 

1968-87. These data are not updated. 

19. Annual numbers of deaths of all Medicare enrollees, by sex and single year of age (ages 65 and over), 

for the period 1988-2005. These data are not updated. 

20. Annual numbers of deaths of Medicare enrollees who are also Social Security or Railroad Retirement 

Board beneficiaries, by sex and single year of age (ages 65 and over), for the period 1988-2005. These 

data are not updated. 

21. Annual numbers of deaths of all Medicare enrollees who are also Social Security or Railroad Retirement 

Board beneficiaries, by sex and single year of age (ages 65 and over), for the period 2006-19. These data 

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are updated annually, when the CMS provides an additional year or years of preliminary data and 

replaces prior year (or years) preliminary data with final data. 

22. Annual numbers all Medicare enrollees, by sex and single year of age (ages 65 and over), 1968-87. 

These data are not updated. 

23. Annual numbers of all Medicare enrollees, by sex and single year of age (ages 65 and over), for the 

period 1988-2006. These data are not updated. 

24. Annual numbers of Medicare enrollees who are also Social Security or Railroad Retirement Board 

beneficiaries, by sex and single year of age (ages 65 and over), for the period 1988-2006. These data are 

not updated. 

25. Annual numbers of all Medicare enrollees who are also Social Security or Railroad Retirement Board 

beneficiaries, by sex and single year of age (ages 65 and over), for the period 2006-19. These data are 

updated annually, when the CMS provides an additional year (or years) of preliminary data and replaces 

prior year (or years) preliminary data with final data.

26. Factors for ratioing age 65 Medicare deaths between 1988 and 2005. These data are not updated. 

Other Input Data - 

27. Internally developed resident population by single year of age (85 – 100+) and sex, 1968-79. These data 

were developed from USAF population data and are not updated. 

28. List of NCHS 113 cause of death codes found in PUMS data file mapped to the causes used in Trustees 

Report. 

1.2.c. Development of Output

Equation 1.2.2 - Percentage Reductions in Log Linear Regressions of Central Death Rates (yyAAAAxx)

TheyyAAAAxx, by sex and cause, are calculated based on the decline in the yMx for the period 2008 through 2019, 

and distributed by 21 age groups,4 2 sexes, and 6 causes of death.

5

 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 assumed ultimate values for the central death rates (yyAAAAxx

uu), as set by the Board of Trustees of the OASDI 

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

are specified by six causes of death for the following five age groups: under 15, 15-49, 50-64, 65-84, and 85 and 

older. Male and female values are assumed to be equal to each other. 

The starting values of yyAAAAxx, by the 21 age groups, sex, and cause, are assumed to equal the percentage 

reductions in log linear regressions of yMx for the period 2008-19 when that percentage reduction is nonnegative. However, if that percentage reduction is negative, then the starting values are assumed to be 75 

percent of the percentage reduction. The weights are 0.2, 0.4, 0.6, and 0.8 for the earliest four years of the 12 

years and are 1.0 for all other years. Available Medicare preliminary data is used for overall levels with the last 

available NCHS data year cause of death percentages carrying forward. For each year after the last data year, 

4 Age groups are: 0, 1-4, 5-9, 10-14, ..., 90-94, and 95+ 5 The six causes of death are: Cardiovascular Disease, Cancer, Accidents and Violence, Respiratory Disease, Dementia, and All 

Other.

17
the yyAAAAxx are calculated by transitioning from the starting values of yyAAAAxx to the Trustees’ assumed ultimate 

values, yyAAAAxx

uu. This is accomplished by repeating the following steps for each historical year after the last data 

year and for the first 24 years of the projection:

1. The difference between the prior year’s calculated yyAAAAxx and the assumed ultimate yyAAAAxx

uu is

calculated. Note that for the first year of this process, the starting values of yyAAAAxx, as defined above,

are used instead of the prior year’s yyAAAAxx.

2. The current year’s yyAAAAxx is the assumed ultimate yyAAAAxx

uu plus 80 percent of the difference calculated

in step 1.

For the 25th year of the projection, the yyAAAAxxare set equal to their assumed ultimate values, yyAAAAxx

uu. 

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 6 causes 

of death. The starting year for the projections of the yMx is 2019, 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 values 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 

exponential of the value for the most recent year falling on a weighted least square line, where the logarithm of

yMx is regressed on year, over the last 12 years. The weights are 0.2, 0.4, 0.6, and 0.8 for the earliest four years 

of the 12 years and are 1.0 for all other years. 

For years after 2019, yMx are projected, by sex and cause of death, by applying the respective yyAAAAxx to the prior 

year yMx. 

The COVID-19 pandemic impacts death rates. Factors were incorporated to account for these impacts. For ages 

15 and older, death rates were increased for years 2020-23 (by 16.4% in 2020, 15% in 2021, 4% in 2022, and 

1% in 2023). For ages 0 through 14, death rates were decreased in years 2020-22 (by 14% in 2020, 10% in 

2021 in 2% for 2022). 

Equation 1.2.3 – Probabilities of death (qx)

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 94, 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. This study, titled Life Tables for the United States Social 

Security area 1900-2100, can be found at: 

http://www.ssa.gov/OACT/NOTES/s2000s.html. (Choose study number 120.) 

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

becomes progressively lower. This is 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, ..., and 11 months. After the last

18
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. For men, probabilities of death 

at each ages 95 and older are calculated as follows: 

qqxx = qqxx−1 ∙ �

qq94

qq93

∙

99−xx

5

 + 1.05 ∙

xx−94

5 � x = 95, 96, 97, 98, 99 

qqxx = 1.05 ∙ qqxx−1 x = 100, 101, 102, ... 

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 (neonatal) and for qx, where x represents age last birthday for ages 0 through 100 (with 100 representing the 

age group 100 and older). Because life table values of probabilities of death are based on exact ages, values for 

qx representing age last birthday are derived as follows:

1⁄2q0 = 1 – L0 / l0 for neonatal 

qx = 1 – Lx+1 / Lx for ages 0 to 99 

q100 = 1 – T101 / T100 for age group 100 and older 

See Actuarial Study number 120 for the definitions of the life table terms. This study can be found at: 

http://www.ssa.gov/OACT/NOTES/s2000s.html. (Choose study number 120; then section IV.A in the table of 

contents.) 

 

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

differential in mortality by marital status is significant. To reflect this, future relative differences in death rates 

by marital status are projected to be the same as observed during calendar years 2015-19. These rates were 

developed by: 

1. Taking the five-year age-group deaths from the public use NCHS data by marital status and dividing by 

the equivalent population sums from the ACS to get preliminary five-year age-group death rates by 

marital status.

2. Adjusting the older age groups death rates for consistency with prior age groups. 

19
3. Adjusting the older age groups death rates further so that all marital statues gradually reach the same 

value at the 95+ age group. 

4. Converting these five-year age-group death rates to single year of age by using a modified H.S. Beers 

method of interpolation.

5. Converting these death rates to probabilities of death.

Equation 1.2.4 – Life expectancy 

Actuarial Study number 120 presents background information on the calculation of life expectancy, ee̊xx, from the 

probabilities of death (qx,). This study can be found at: http://www.ssa.gov/OACT/NOTES/s2000s.html. 

(Choose study number 120; then IV.A in the table of contents.) 

20
Appendix: 1.2-1 

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

by age group and cause of death. For comparison purposes, rates are also presented for two

historical periods. Note that although the male and female ultimate rates are the same, the 

historical rates differ.

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

Historical Alternative II* Historical Alternative II*

2020 TR 2021 TR 2020 TR 2021 TR 

1979 to

2019

2009 to 

2019

2044 to 

2094

2045 to 

2095

1979 to 

2019

2009 to 

2019

2044 to 

2094

2045 to 

2095

Under Age 15 Male Female

Cardiovascular Disease 1.94 2.24 2.3 1.9 1.68 1.63 2.3 1.9

Cancer 2.35 1.69 1.5 1.5 1.98 1.50 1.5 1.5

Accidents and Violence 2.39 0.26 1.0 1.0 2.07 -0.08 1.0 1.0

Respiratory Disease 2.28 2.07 2.0 2.0 2.46 2.63 2.0 2.0

Dementia 3.07 3.93 N/A 0.1 1.80 -1.78 N/A 0.1

Other** 2.25 1.81 1.7 1.7 2.14 1.70 1.7 1.7

Resulting Total *** 2.28 1.54 1.53 1.51 2.12 1.44 1.56 1.54

Ages 15 - 49 Male Female

Cardiovascular Disease 1.78 0.75 1.5 1.3 1.19 0.42 1.5 1.3

Cancer 1.88 2.25 1.5 1.5 1.58 1.77 1.5 1.5

Accidents and Violence 0.28 -2.44 0.7 0.7 -0.21 -2.35 0.7 0.7

Respiratory Disease 0.44 1.91 0.5 0.5 -0.47 2.08 0.5 0.5

Dementia 1.06 0.50 N/A 0.1 0.96 1.84 N/A 0.1

Other** 0.14 0.31 0.8 0.8 -0.09 -0.06 0.8 0.8

Resulting Total *** 0.72 -0.75 0.85 0.82 0.49 -0.21 0.92 0.89

Ages 50 - 64 Male Female

Cardiovascular Disease 2.36 0.19 2.2 1.5 1.96 0.07 2.2 1.5

Cancer 1.55 2.05 1.5 1.5 1.22 1.39 1.5 1.5

Accidents and Violence -0.39 -3.34 0.5 0.5 -0.68 -2.73 0.5 0.5

Respiratory Disease 0.45 -0.33 0.7 0.7 -1.17 -0.75 0.7 0.7

Dementia -2.51 -2.79 N/A 0.1 -3.23 -3.52 N/A 0.1

Other** -0.34 -0.65 0.6 0.6 -0.31 -0.83 0.6 0.6

Resulting Total *** 1.23 0.03 1.05 0.95 0.82 0.03 1.05 0.98

Ages 65 - 84 Male Female

Cardiovascular Disease 2.73 1.32 2.2 1.9 2.61 1.70 2.2 1.9

Cancer 1.07 2.19 0.9 0.9 0.35 1.85 0.9 0.9

Accidents and Violence 0.25 -1.78 0.5 0.5 -0.13 -1.57 0.5 0.5

Respiratory Disease 0.49 1.51 0.3 0.3 -1.82 1.07 0.3 0.3

Dementia -6.65 -1.89 N/A 0.1 -7.73 -2.38 N/A 0.1

Other** -0.29 -0.63 0.3 0.3 -0.44 0.16 0.3 0.3

Resulting Total *** 1.37 0.93 0.79 0.74 0.81 0.93 0.73 0.68

Ages 85 and older Male Female

Cardiovascular Disease 1.67 1.02 1.2 1.5 1.87 1.25 1.2 1.5

Cancer 0.01 0.84 0.5 0.5 -0.29 0.14 0.5 0.5

Accidents and Violence -0.82 -1.79 0.3 0.3 -1.18 -2.15 0.3 0.3

Respiratory Disease -0.45 1.59 0.2 0.2 -1.57 0.52 0.2 0.2

Dementia -9.48 -2.14 N/A 0.1 -10.32 -2.35 N/A 0.1

Other** -0.83 0.07 0.2 0.3 -0.78 0.75 0.2 0.3

Resulting Total *** 0.35 0.39 0.53 0.58 0.23 0.17 0.50 0.54

Total Male Female

Cardiovascular Disease 2.27 1.00 2.18 1.27

Cancer 1.04 1.88 0.62 1.45

Accidents and Violence 0.12 -2.40 -0.27 -2.16

Respiratory Disease 0.20 1.34 -1.54 0.70

Dementia -7.71 -2.06 -8.77 -2.37

Other** -0.20 -0.25 -0.25 0.20

Resulting Total *** 1.02 0.45 0.75 0.74 0.62 0.45 0.71 0.69

* Alternative 1 is 1/3 times Alternative 2; Alternative 3 is 2.0 times Alternative 2.

21
** Other includes dementia in the 2020 TR but not in the 2021 TR.

***Resulting total represents average annual percent reduction in age-adjusted death rates for the last 50 years of the 75-year projection period.

22
1.3. LPR IMMIGRATION

1.3.a. Overview

LPR immigration is defined as those persons who have been admitted into the United States and been granted 

lawful permanent resident status. Legal emigration consists of LPR immigrants and U.S. citizens who depart 

the Social Security area population to reside elsewhere. 

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

immigration (Lz) and legal emigration (Ez), by age and sex, based on assumptions set by the Trustees for each 

category. In addition, the LPR 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-thanLPR population to LPR status (AOSz

). 

Each fiscal year,

6

 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 censuses. 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 LPR immigration and annual legal 

emigration estimates by age and sex. 

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

projection period are summarized below:

NNNNWWxx,ss

zz = NNNNWWxx,sszz (∙) (1.3.1) 

AAAASSxx,ss

zz = AAAASSxx,sszz (∙) (1.3.2) 

LLxx,ss zz = NNNNWWxx,ss

zz + AAAASSxx,sszz (1.3.3) 

xx,ss

zz = xx,sszz (∙) (1.3.4) 

NN xx,ss zz = LLxx,ss zz − xx,ss

zz (1.3.5) 

where NNLLxx,ss zz are the number of net LPR immigrants by age (x) and sex (s) for year z.

 

1.3.b. Input Data

Trustees Assumptions - 

1. Each year the Board of Trustees of the OASDI Trust Funds specifies the total annual assumed values for 

LPR immigration and legal emigration. For the 2021 Trustees Report, the ultimate values for LPR

immigration and legal emigration are 1,050,000 and 262,500, respectively (both reached in 2026). 

Department of Homeland Security – 

2. Historical LPR immigration by fiscal year (1941-73), 5-year age group (0-4, 5-9, ..., and 80-84), and 

sex. These data will not be updated.

3. Legalizations due to Immigration Reform and Control Act of 1986 (IRCA) by type (pre-1982s and 

SAWs), single year of age (0-99 and unknown age), sex (including unknown) and month for the years 

1989-2011. These data will not be updated.

6 The federal fiscal year begins on October 1 of the previous calendar year and ends on September 30 of the specified calendar year.

23
4. Historical LPR immigration by fiscal year (1973-2019), single year of age (0 through 99, and unknown 

age), sex (including unknown), and class of admission (New Arrival, Adjustment of Status, Refugee, 

and Asylee). These data are updated annually, with the DHS providing an additional year of data each 

year.

5. Total adjustments of status for the years 1966 to 1972 (OCACT further estimates total adjustments of 

status for 1963-65). These data will not be updated.

U.S. Census Bureau – 

6. Unpublished estimates of annual legal emigration by five-year age groups (0-4, 5-9, ..., and 80-84) and 

sex for 1990 based on the change between the 1980 and 1990 censuses. These data are updated 

occasionally (based on having new data from an outside source and on OCACT resource time 

constraints).

Other input data - 

7. Legal emigration conversion factors. These estimates were developed internally by five-year age groups 

(0-4, 5-9, ..., and 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).

1.3.c. Development of Output

Equations 1.3.1 and 1.3.2 – LPR Immigration

The Trustees specify the aggregate number of LPR immigrants 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. 

 

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

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

The DHS provides data on LPR 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. Refugee and Asylee LPR admissions are subtracted from the DHS adjustment of status data and added 

into the new arrival category.

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

3. For each class of admission (new arrivals and adjustments of status), the historical data for the last 10 

years (from 2010-19) are combined to create an average age-sex distribution.

NNNNWWxx,ss

zz , the expected number of new arrival LPR immigrants by age (x) and sex (s) for each year (z), is

calculated by applying the age-sex distribution for new arrivals to the Trustees’ assumed level of new arrivals. 

24
The Trustees’ assumed number of adjustments of status is multiplied by the age-sex distribution of adjustments 

of status to calculate AAAA xx,ss

zz . 

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 assuming a ratio of legal emigration to LPR immigration. For the 2021 Trustees Report, the ratio is 

assumed to be 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 censuses. 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. 

For each sex (s), the Beers formula is used to interpolate and distribute each five-year age group into a single 

year of age (x) 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: 

xx,ss

zz = .25 ∗ �� �LLxx,ss zz

100

xx=0

ff

ss=mm

� ∙ EE xx,ss

25
1.4. HISTORICAL POPULATION

1.4.a. Overview

The HISTORICAL subprocess provides estimates of the Social Security area population for each year in the 

period December 31, 1940, through December 31, 2018. 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 by age, sex, and marital status (and by other characteristics) 

every ten years for the decennial census. Generally, each subsequent year, the Census Bureau publishes a 

“post-censal” population estimate. This subprocess combines these census and post-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 historical estimates of the total Social Security area 

population (PPxx,ss

zz ) and other-than-LPR population ( xx,sszz ). Combining the total populations by single year of age 

and sex with an estimated marital status matrix provides the total Social Security area historical population by 

single year of age, sex, and marital status (PPxx,ss,mm zz ). These estimates are then used as the basis for the 

PROJECTED POPULATION subprocess described in section 1.8. The primary equations for this subprocess 

are given below: 

PPxx,ss

zz = PPxx,sszz (·) (1.4.1) 

PPxx,ss,mm zz = PPxx,ss,mm zz (·) (1.4.2) 

xx,ss

zz = xx,sszz (·) (1.4.3) 

26
1.4.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

1. Probabilities of death from the MORTALITY subprocess, by age last birthday and sex, for years 1941-

2019. These data are updated every year.

2. The number of new arrival LPR immigrants plus adjustments of status LPR immigrants by age and sex

for years 1941-2018. These data are from the LPR IMMIGRATION subprocess and are updated each

year.

3. The number of legal emigrants by age and sex for years 1941-2018. These data are from the LPR

IMMIGRATION subprocess and are updated each year.

4. The number of adjustments of status by age and sex for years 1941-2018. These data are from the LPR

IMMIGRATION subprocess and are updated each year.

5. The number of other-than-LPR immigrants legalized under the Immigration Reform and Control Act of

1986 (IRCA) from the LPR IMMIGRATION subprocess. These data are reproduced each year and

updated if new data is available.

6. Birth rates by single year of age of mother (14-49) for the years 1941-2019 from the FERTILITY

subprocess. These data are updated each year.

U.S. Census Bureau Data - 

7. Estimates of U.S resident population and Armed Forces overseas population as of each July 1 (1940-79)

by sex and single-year of age through 84, and for the group aged 85 and older. These data are generally

not updated.

8. Estimates of the U.S. resident population for each decennial census (April 1) 1970-2010 by sex and

single year of age 0 through 85+. New decennial census estimates come out about every ten years.

9. Estimates of total U.S. resident population and total U.S. resident population plus Armed Forces

overseas population for each January of each decennial census year from 1990 and 2010. New

decennial census estimates come out about every ten years.

10. Estimates of U.S resident population, and U.S. resident plus Armed Forces overseas population as of

each July 1 (1980-2019) by sex and single year of age 0 through 99, and ages 100 and older. Generally,

the U.S. Census Bureau restates the data back to the most recent decennial census and includes one

additional year of data.

11. Estimates of U.S resident population, and U.S. resident population plus Armed Forces overseas

population as of each January 1 (1981-2019) by sex and single-year of age 0 through 99, and ages 100

and older. Generally, the U.S. Census Bureau restates the data back to the most recent decennial census

(April) and includes one additional year of data.

12. Estimates of the population by marital status, sex, and age from the American Community Survey

(ACS) public use microdata sample (PUMS) files for years 2000-19. In general, an additional year of

data is available each year.

27
13. Undercount factors by single year of age (0-85+) and sex, estimated using post-censal survey or 

demographic analysis data. These data are updated after each decennial census.

14. The total annual population estimates for Puerto Rico, Virgin Islands, Guam, Northern Mariana Islands, 

and American Samoa for years 1951-2019. For each Trustees Report, an additional data year is 

downloaded from the U.S. Census Bureau’s international database. Historical data back to 1951 is also 

obtained if any changes have occurred. 

15. Decennial census population estimates, by varying degree of age detail and sex, for decennial censuses 

from 1950-2000 for territories and components outside the 50 states, D.C., and armed forces overseas. 

Most data are aggregated into 18 age groups for each sex, though single year of age data is available for 

young ages in the territories for 1960 and 1970 and for all ages starting in 1980. New estimates are 

added as they become available.

16. July populations of the territories by single year of age and sex from 2000-19. An additional year of 

data is available each year.

17. From the ACS PUMS, number of existing marriages from 2000-19 by age of husband crossed with age 

of wife. In addition, starting with the 2012 ACS, number of existing marriages by age of each spouse is 

available for same-sex couples. Final grids for same-sex couples are adjusted based on reported samesex marriages from the states through 2014. Generally, an additional year of data is available each year.

18. From ACS PUMS, flows of foreign-born ins and Cuban ins by single year of age, sex, and year of entry 

used to produce total other-than-LPR estimates for January 1, 2013-19. 

19. From decennial census PUMS (via the University of Minnesota’s IPUMS website), number of existing 

marriages for decennial census years 1940-2000 by age group of husband crossed with age group of 

wife. New estimates are added as they become available.

20. From decennial census PUMS (via the University of Minnesota’s IPUMS website), estimates of the 

population by marital status, age, and sex for decennial census years 1940-2000. New estimates are 

added as they become available.

21. Estimates of net immigration by age and sex of the U.S. resident population plus armed forces overseas 

(USAF) population from April 1, 2000, through July 1, 2019. An additional year of data is available 

each year.

22. Total Americans overseas estimate based on international data sources and estimates of federal 

employees and military in Iraq and Afghanistan. The data from the various international sources are 

derived from different years but center around the year 2003. Additional data will be updated as they 

become available. 

23. Total Civilian population in Alaska and Hawaii for years 1940-49. These data are not updated. 

Other input data - 

24. From the Department of State, old historical total estimates of outside area populations (federal 

employees overseas, overseas dependents of federal employees and military, and other Americans 

overseas) for various years between 1951 and 1990. 

25. The SSA Annual Statistical Supplement provides estimates of the total number of OASDI beneficiaries 

28
living abroad as of December 31, for most years 1957-2019. Age group data is also available for 0 – 17, 

18 – 54, and 55 – 61 starting in 1997. For each Trustees Report, an additional year of data is available. 

Age group data is updated for each decennial census year.

26. From the National Center for Health Statistics (NCHS), births by month and sex of child, for years

1931-2019. Each year, NCHS provides another year of data.

27. From the NCHS, National Survey of Family Growth (NSFG) public-use data that help split up the

population eligible for same-sex marriage into marital statuses starting in 2013. These survey data are

from 2011-15. This data is updated as they become available.

28. From the NCHS, National Survey of Family Growth (NSFG) public-use data that split up the total

population, by sex, into the population eligible for same-sex marriage and the population eligible for

opposite-sex marriage. These survey data are from 2011-15 and 2015-17. This data is updated as they

become available.

29. From the Department of Homeland Security (DHS), the number of unauthorized immigrants and

nonimmigrants from January 1, 2005-12. In addition, other estimates from the Unauthorized Immigrant

Population Reports and emails from DHS are used to estimate January 1, 2012, through January 1, 2019,

unauthorized immigrants and nonimmigrants including an adjustment for shift in reference date,

undercount of nonimmigrants, legally resident immigrants, foreign-born flows from 1980 and later of

LPR immigrants, mortality, and emigration.

30. From the Office of Personnel Management (OPM), total estimates of the number of federal employees

overseas from July 1, 1998-2013. These estimates are updated as they become available on the OPM

website.

31. From the OPM, the number of federal employees overseas by single year of age and sex from a subset of

the OPM data source above. Years 1980-2019 are available. These estimates are updated as they

become available.

32. From the Department of Defense, total numbers of armed forces in Puerto Rico, the Virgin Islands,

Guam, and American Samoa each decennial census year starting in 1990. These data are updated as

they become available.

33. Using 2015 TR death rates and historical populations, an assumed December 31, 1940, 85+ distribution.

These data are not updated.

34. Assumed January total populations added to the Social Security for years 1951, 1957, and 1961 when

new territories were added to the Social Security area. These data are not updated.

35. Armed forces counts, by age group and sex, from 1940-57. These data are not updated.

1.4.c. Development of Output

Equation 1.4.1 – Historical Population by age and sex (PPxx,ss

zz )

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 PPxx,ss

zz . 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. 

29
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. January 1 and April 1 estimates by sex for single years of age through 84, and for the group 

aged 85 or older for selected years starting in 1990 and 1970, respectively, are also obtained for from the 

Census Bureau. Adjustments for net census undercount are estimated using post-censal survey data from the 

Census Bureau. Population counts over age 65 after the last Census year are modified to be consistent with 

OCACT mortality and Census USAF net immigration data. 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 people residing in Puerto Rico, the Virgin Islands, 

Guam, American Samoa, and the Northern Mariana Islands are estimated from data obtained from the Census 

Bureau. Numbers of Federal civilian employees overseas are based on estimates from the Office of Personnel 

Management (OPM). Dependents of Federal civilian employees and Armed Forces overseas are based on the 

stock of Federal civilian employees from OPM and the stock of armed forces overseas from the Census Bureau. 

Other citizens overseas covered by Social Security are also based on estimates compiled by the Census Bureau. 

The overlap among the components, believed to be small, is ignored. 

The first step of the process is to estimate PPxx,ss

zz as of December 31st for certain “tab years” (1940, 1950, 1956, 

1960, each December prior to a decennial Census year after [1969 through 2009], and the last year of historical 

data [2018 for the 2021 Trustees Report]). For ages 0-84, PPxx,ss

zz for each tab year, is set equal to an undercount 

adjustment plus other component populations plus: 

• The averaged surrounding July 1 U.S. population and armed forces overseas counts from the

Census Bureau prior to 1970

• Modified April 1 U.S. populations from the Census Bureau for decennial census years from 1970

through 2000.

• The January 1 U.S. population and armed forces overseas counts from the Census Bureau modified

by OCACT mortality rates and Census USAF net immigration for ages over 65 for 2010 and 2019.

For ages 85 and over, PPxx,ss

zz for each tab year is set equal to [Built Up Pops Age x, Sex s] * [Total 85+ for Sex 

s]/[Total Built Up 85+ for Sex s], where the built up estimates are created by taking into account deaths and 

immigration data from the previous tab year and [Total 85+ for Sex s] is the sum of the calculated U.S. 

population and armed forces overseas calculated using the same method listed above for each year for ages 0-

84. 

For years between the tab years, populations are estimated taking into account the components of changes due 

to births, deaths, legal emigration, adjustments of status, and net LPR immigration (or total net immigration, if 

known) during that time period. These estimates are then multiplied by the appropriate age-sex-specific ratios 

so that the error of closure at the tab years is eliminated. 

Equation 1.4.2 – Historical Population by age, sex, and marital status (PPxx,ss,mm zz )

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 are available for decennial census years 1940-2000 from 

Census public use microdata sample (PUMS) files. These data are aggregated by age group of husband crossed 

with age group of wife. Additional tabulations from the American Community Survey from 2000-19 are 

incorporated to adjust these marital prevalence grids for changes since 2000. 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. 

30
Percentages of single, married, widowed, and divorced persons are calculated by using the H.S. Beers method 

of interpolation on compiled data by age group and sex based on Census and/or ACS PUMS. Data is converted 

to a December basis for each year by taking a weighted average of surrounding Census and/or ACS data. Note 

that the ACS is not used until 2006, the first year grouped quarters were included. 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. 

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

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

number of married women (though, this is not forced to be ultimately true once same-sex marriages were 

federally recognized as described in the next paragraph). Then, 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. Finally, the other marital 

statuses population totals are adjusted to keep the total number of people in all marital statuses the same as 

calculated before splitting into marital statuses.

The population is modeled to include the following population statuses for December 31, 2013, and later: 

heterosexual, gay, and lesbian. Gay and lesbian populations are broken out assuming 2.5% of the male 

population is gay and 4.5% of the female population is lesbian. (Note that this means we assume 2.5% of the 

male population and 4.5% of the female population are in an existing same-sex marriage, or would same-sex 

marry, versus opposite-sex marry.) Marriage grids of age of older spouse crossed with age of younger spouse 

for same-sex couples are needed starting December 31, 2013. The grids and populations were produced using 

data from the American Community Survey, National Survey of Family Growth, and state-level same-sex 

marriage data. 

Equation 1.4.3 – Historical Other-Than-LPR Population by age and sex ( xx,ss

zz )

This subprocess also estimates historical levels of other-than-LPR in the population, by age and sex. For each 

year, an initial net residual estimate by single year of age and sex is backed out from estimates of beginning and 

end of year populations, births, deaths, LPR immigrants, adjustments of status, and legal emigrants. This net 

residual equals the implied initial other in minus other out. These residuals are then modified to ensure 

reasonableness. Next, using these modified net residuals, along with adjustments of status and other-than-LPR 

deaths (using the same death rates as for the total population), an initial other-than-LPR stock is built. These 

stocks are then modified to ensure reasonableness. After 2000, one further adjustment is done to the stocks. 

From January 2001 through January 2004, the total other-than-LPR populations are set equal to the values that 

linearly grade from the final OCACT January 2000 total other-than-LPR population to a DHS-based January 

2005 total other-than-LPR population. From January 2005 through January 2012, the total other-than-LPR 

population is forced to match DHS-based total other-than-LPR population estimates. For January 2013 through 

January 2019, the total other-than-LPR populations are estimated based on the DHS method and emailed data 

from DHS. 

31
1.5. OTHER-THAN-LPR IMMIGRATION

1.5.a. Overview

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

lawfully admitted for permanent residence, and who reside in the U.S. for at least 6 months. This includes 

temporary immigrants (persons lawfully admitted for a limited period of time, such as temporary workers and 

foreign students), also called nonimmigrants, in addition to undocumented immigrants living in the U.S. These

undocumented immigrants can be split into those that were never authorized to enter the U.S. and those that 

were nonimmigrants but overstayed their visas (visa-overstayers). The term “other-than-LPR emigration” 

refers to those in the other-than-LPR immigrant population who leave the Social Security area.

For each year z of the projection period, the OTHER-THAN-LPR IMMIGRATION subprocess produces 

estimates of other-than-LPR immigration ( xx,ss,tt zz ), by age (x), sex, and type (t) based on assumptions set by the 

Trustees. Estimates of projected other-than-LPR emigration ( xx,ss,tt zz ), by age, sex, and type are also developed 

in this subprocess. 

The Department of Homeland Security (DHS) estimated the stock of nonimmigrants by age group and sex for 

April 2008, December 2010, and April 2016. The HISTORICAL POPULATION subprocess already produces 

historical estimates of other-than-LPR immigrants. These historical data are used to develop recent estimates of 

the other-than-LPR stock by age, sex, and type, where type is never-authorizeds, nonimmigrants, and visaoverstayers.

The primary equations of OTHER-THAN-LPR IMMIGRATION, by age (x), sex (s), and type (t) for each year 

(z) of the 75-year projection period are summarized below:

xx,ss,tt zz = xx,ss,tt zz (∙) (1.5.1) 

xx,ss,tt zz = xx,ss,tt zz (∙) (1.5.2) 

NN xx,ss,tt zz = xx,ss,tt zz − xx,ss,tt zz − AAAA xx,ss,tt zz (1.5.3) 

where NN xx,ss,tt

ZZ are the number of net other-than-LPR immigrants, by age (x), sex (s), and type (t) for year z, and 

AAAA xx,ss,tt

ZZ are the number of adjustments to LPR status from the LPR IMMIGRATION subprocess, by age (x), 

sex (s), and type (t) for year z;

xx,ss,tt zz = xx−1,ss,tt

zz−1 + xx,ss,tt zz − xx,ss,tt zz − AAAA xx,ss,tt zz − xx,ss,tt zz (1.5.4) 

where, xx,ss,tt zz is equal to the other-than-LPR immigrant population, by age (x), sex (s), and type (t) as of 

December 31st of each year (z), xx,ss,tt zz are the number of deaths in the other-than-LPR immigrant population by 

age (x), sex (s), and type (t) for each year (z), and AAAA xx,ss,tt zz are the number of adjustments to LPR status by age 

(x), sex (s), and type (t) for each year (z). 

32
1.5.b. Input Data

Trustees Assumptions - 

1. Each year the Board of Trustees of the OASDI Trust Funds specifies the assumed total annual values for 

other-than-LPR immigration. The ultimate annual level was set at 1,350,000 persons per year for each 

year beginning in 2026. The level of other-than-LPR immigration was estimated at 1,100,000 for 2019. 

Due to COVID effects, the level was then estimated to drop to 420,000 and 880,000, for years 2020 and 

2021, respectively. Finally, the level was estimated to increase to 1,350,000 for year 2022, and increase 

again to 1,750,000 for years 2023-25. 

Long-Range OASDI Projection Data - 

Demography 

2. Historical and projected probabilities of death by age last birthday (including a neonatal mortality factor, 

single year of age for ages 0-99, and age group 100+) and sex, for years 1941-2100. These data are 

updated each year from the MORTALITY program.

3. Historical net other-than-LPR immigration by single year of age (-1-99+)7

 and sex for years 1961-2018. 

These data are updated each year from the HISTORICAL program.

4. Historical December 31 other-than-LPR immigrants by single year of age (0-100+) and sex for years 

1963-2018. These data are updated each year from the HISTORICAL program. 

5. Historical July 1 other-than-LPR immigrants by single year of age (0-100+) and sex for years 1964-

2018. These data are updated each year from the HISTORICAL program.

6. Final historical year (on a December 31 basis). This datum is updated each year from the HISTORICAL 

program.

7. Historical new arrivals by single year of age (-1-100+) and sex for years 1941-2018. These data are 

updated each year from the LPR IMMIGRATION program. 

8. Historical and projected adjustments of status by single year of age (-1-100+) and sex for years 1941-

2100. These data are updated each year from the LPR IMMIGRATION program.

Department of Homeland Security – 

9. Components of the unauthorized immigrant population by year for 2005-12, from the Unauthorized 

Immigrant Population Reports. These data are updated as new data become available. 

10. Components of the LPR population by year for 2005-11, from the Unauthorized Immigrant Population 

Reports. Components of the LPR population by year for 2012-19, from unpublished DHS estimates. 

These data are updated as new data become available.

11. Nonimmigrant stock in April 2008, December 2010, and April 2016 by age-group and sex. These data 

are updated as new data become available and internal resources are sufficient to examine and interpret 

such new data. 

7 Age -1 represents births that occur during the year.

33
12. Nonimmigrant admissions by class of admission for various fiscal years 1981-2016. These data are 

updated as new data become available and internal resources are sufficient to examine and interpret such 

new data. 

13. Total nonimmigrants as of January 1, 2005-11, from the Unauthorized Immigrant Population Reports. 

Total nonimmigrants as of January 1, 2012-19, from unpublished DHS estimates. These data are 

updated as new data become available.

14. Total annual approvals for initial grants under the 2012 Deferred Action for Childhood Arrivals

(DACA) initiative, for fiscal years 2013-18. These data are updated as new data become available. 

15. End-of-year population of people with DACA status, by sex (including unknown) and single year of age 

(0-50, including unknown), for years 2013-19. These data are updated as new data become available.

U.S. Census Bureau – 

16. From the American Community Survey (ACS), foreign-born new persons by ACS year (2000-19), entry 

year (1900-2019), age (0-100) and sex. These data are updated as new data become available.

17. From the ACS, total foreign-born population and total population for 2000-19, and total population in 

Puerto Rico for 2005-19, used to calculate undercount factors (Note that the population referred to in 

each case is the beginning-of-year population). These data are updated as new data become available.

18. From the 2012 ACS, persons, by entry year (1900-2012), age (0-100) and sex, that are: 

• Foreign-born citizens

• Foreign-born non-citizens that are in school or are high-school graduates 

• Non-citizen parents of citizen children

• Non-citizen parents of citizen children that are in school or are high school graduates 

These data are not updated. 

19. From the 2012 ACS, persons, by entry year (1900-2012), age (0-100) and sex, that are eligible for

temporary protected status (TPS) based on originating from various countries by certain dates and are: 

• Foreign-born citizens

• Foreign-born non-citizens that are in school or are high-school graduates 

• Non-citizen parents of citizen children

• Non-citizen parents of citizen children that are in school or are high school graduates 

These data are not updated. 

Other input data - 

20. The number of those potentially eligible under the 2012 DACA initiative by age group and an overall 

split by sex, from the Migration Policy Institute. These data are updated as new data become available 

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

21. Internally developed numbers of those that were potentially eligible under the 2014 DACA initiative that 

were not eligible under the 2012 DACA initiative by age and sex. These data will not be updated. 

22. Internally developed numbers of those that were potentially eligible under the Deferred Action for 

Parents of Americans and LPRs (DAPA) initiative, by age and sex. These data will not be updated. 

23. Internally developed factors of potential DACA stock attaining DACA status by sex and ages 5-100 for 

34
the first, second, and ultimate DACA years. These data are updated as new data become available and 

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

24. Internally developed factors to apply to other-than-LPR immigrants that enter as nonimmigrants. These 

data will not be updated. 

25. Internally developed factors used to create the nonimmigrant other in distribution by age and sex for 

each year. These factors ensure that there will be enough nonimmigrant stock to transfer to LPR status. 

These data will not be updated. 

26. Internally developed overstay percentages by age. These data are based off a RAND Corporation

document using data from the 1980s, and are adjusted based on insights from the DHS. These data are 

updated as new data become available and internal resources are sufficient to examine and interpret such 

new data. 

27. Internally developed rates of departure for the non-DACA/DAPA potential/actual never-authorizeds for 

non-recent arrivals. These data are updated as new data become available and internal resources are 

sufficient to examine and interpret such new data. 

28. Internally developed rates of departure for the non-DACA/DAPA potential/actual non-immigrants. 

These data are set to initial rates in 2015 (when the Executive Actions went into effect including 

decreased deportation of non-felons) and then gradually increase to the ultimate rates in 2025. These 

data are updated as new data become available and internal resources are sufficient to examine and 

interpret such new data.

29. Internally developed rates of departure for the non-DACA/DAPA potential/actual visa overstayers. 

These data are updated as new data become available and internal resources are sufficient to examine 

and interpret such new data. 

30. Internally developed rates of departure for non-DACA potential/actual never authorizeds for non-recent 

arrivals to use prior to 2015 (when the Executive Actions went into effect including decreased 

deportation of non-felons). These data are updated as new data become available and internal resources 

are sufficient to examine and interpret such new data. 

31. Internally developed rates of departure for the non-DACA potential/actual visa overstayers to use prior 

to 2015 (when the Executive Actions went into effect including decreased deportation of non-felons). 

These data are updated as new data become available and internal resources are sufficient to examine 

and interpret such new data. 

32. Internally developed number of other-than-LPR immigrants, by age and sex, for years 1999-2010. 

These data will not be updated. 

1.5.c. Development of Output

The ACS provides data to help derive the number of foreign-born new arrivals, which is then used to separate 

the historical net other-than-LPR immigration into those entering and those leaving. There are several other key 

inputs that go into this calculation, including an estimated undercount factor. This factor accounts for (1) 

differences between the foreign-born data from the ACS and the component pieces obtained from DHS, (2) 

differences between the ACS (Public Use Microdata Sample) and Census’ total population, and (3) the foreignborn residing in Puerto Rico. The estimated other-than-LPR immigration is calculated by taking the foreign 

born from the ACS (after smoothing and applying the undercount factors) and subtracting the LPR new arrivals. 

The estimated historical other-than-LPR emigration is then calculated as the difference between the net other35
than-LPR immigration (calculated in the HISTORICAL subprocess) and the estimated historical other-thanLPR immigration. A series of steps are then taken to smooth the two categories. Based on various 

assumptions, the historical other-than-LPR immigrants are split into those who arrive or depart the Social 

Security area as a never-authorized immigrant, nonimmigrant, and visa-overstayer immigrant.

Equation 1.5.1 – Other-Than-LPR Immigration

For each projection year, an age-sex-type distribution is used to distribute the aggregate number of other-thanLPR immigrants by age, sex, and type. This age-sex-type distribution is denoted as ODISTx,s,t and is developed 

by using average historical estimates of other-than-LPR immigrants entering the country from 2000 through 

2007. 

The assumed total level of other-than-LPR immigration is denoted by TT zz. Thus, for each year (z) other-thanLPR immigration is defined by the following equation:

xx,ss,tt zz = TT zz ∙ TTxx,ss,tt

Equation 1.5.2 – Other-Than-LPR Emigration

xx,ss,tt zz denotes the annual number of other-than-LPR immigrants who depart the Social Security area by age 

(x), sex (s), and type (t). These estimates are based on 2014 TR build-up of stocks from 2008 through 2010 

including other-than-LPR immigration discussed above, deaths, adjustments of status (from the LPR 

IMMIGRATION subprocess), and assumptions about the number of departures from each type. Deaths for the 

other-than-LPR immigrant population use the same death probabilities as the total population:

 xx,ss,tt zz = qqxx,ss

zz ∙ PPxx,ss,tt zz

Then, for this 2008-10 period, rates are calculated by dividing xx,ss,tt zz by xx,ss,tt zz for each age, sex, and type. 

After smoothing and adjusting for the effects of the recent recession, these rates are used to calculate xx,ss,tt zz in 

projected years by being applied to the other-than-LPR stock populations xx,ss,tt

zz−1 for the overstayer and 

nonimmigrant stocks. For the never authorized stock, these rates are further adjusted and split into two 

categories so that recent arrivals are exposed to twice the rates as the residual never authorized stock. For the 

potential DACA population, and for those that are already in the DACA population, the exit rates are lower than 

for those not eligible for DACA.

This subprocess also splits historical other-than-LPR immigrants into the various categories. It is assumed that 

all other-than-LPR immigrants were nonimmigrants as of December 31, 1963. Between December 31, 1963, 

and December 31, 2010, the percentage of total other-than-LPR immigrants by age and sex in each type is 

linearly interpolated from the percentages at those two points in time. Between December 31, 2010, and 

December 31, 2015, a similar interpolation is done from the percentages at those two points in time. A final 

adjustment ensures the total nonimmigrants are appropriate, based on DHS nonimmigrant admissions or, if 

available, stock estimates. 

Finally, this subprocess also projects the DACA population, a subset of the other-than-LPR immigrant 

population, by age (x) and sex (s). The DACA population consists of other-than-LPR immigrants who meet 

specific criteria and are granted authorization to work. The eligible DACA population is estimated separately 

by those that meet the age, residency, and educational requirements. Rates are applied to the eligible population 

to estimate the net number of individuals who actually apply and obtain DACA status. A final adjustment 

insures that the DACA population by age and sex is appropriate, based on DHS stock estimates. 

Note that the DAPA and the 2014 DACA are no longer being applied to this subprocess. Furthermore, it is 

assumed that there will be no new 2012 DACA’s for years 2019-20. These assumptions may change according 

to future laws, executive actions, and/or court rulings that may affect the DACA program.

36
37
1.6. MARRIAGE

1.6.a Overview

The National Center for Health 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, by single year of age 

(or age group if single year of age was not available) and sex, were obtained from the NCHS. Marriage rates 

for this period are calculated from these data. The age-of-husband crossed with age-of-wife marriage grid rates 

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. 

Beginning in 1989, the NCHS no longer collected data on the annual number of new marriages in the MRA. 

However, for years 1989-95, they supplied less detailed data on new marriages from a subset of the MRA. 

Beginning in 2008, the American Community Survey (ACS) started asking if a person was married in the last 

12 months. Using this question, along with ages of spouses, grids of new marriages by age-group-of-husband 

crossed with age-group-of-wife were developed for years 2007 and later. For the years between 1995 and 2007, 

the marriage grids were linearly interpolated. 

Age-specific marriage rates (mm�xx,yy

zz ) for a given year (z) are defined as the ratio of (1) the number of marriages 

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

those ages (PPxx,yy

zz ). The theoretical midyear population is defined as the geometric mean8 of the midyear 

unmarried male population and unmarried female population. 

An age-adjusted central marriage rate (AA

�zz) summarizes the mm�xx,yy

zz for a given year. The standard population 

chosen for age adjusting is the unmarried male population and unmarried female population in the Social 

Security area population as of July 1, 2010. 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-ageof-wife specific central marriage rates for that year to the geometric mean of the corresponding age groups in 

the standard population. 

The AA

�zz is then obtained by dividing: 

• The expected number of marriages by

• The geometric mean of (1) the number of unmarried men, ages 15 and older, and (2) the unmarried

women, ages 15 and older, in the standard population.

The MARRIAGE subprocess projects annual mm�xx,yy

zz by age-of-husband crossed with age-of-wife. The equations 

for this subprocess are given below:

mm�xx,yy

zz = mm�xx,yyzz (·) (1.6.1) 

 (1.6.2) 

8 The geometric mean, as used in this document, is the square root of the product of two numbers.

AA

�zz =

�PPxx,yy

SS

xx,yy

∙ mm�xx,yy

zz

�PPxx,yy

SS

xx,yy

38
where and x and y refer to the age of men and women, respectively, and PPxx,yy

SS is the theoretical unmarried 

population in the Social Security area population as of July 1, 2010 (the geometric mean of the corresponding 

age groups in the standard population). 

1.6.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

1. Estimates of the Social Security area population as of December 31, by age, sex, and marital status for

years 1977-2018. These data are updated each year based on output of the HISTORICAL

POPULATION subprocess.

2. Final historical year (on a December 31 basis). This datum is updated each year from the HISTORICAL

POPULATION subprocess.

 Assumptions - 

3. For each Trustees Report, ultimate values for the AA

�zz are assumed. The AA�zz reaches its ultimate 

value in the 25th year of the 75-year projection period. For the 2020 report, the ultimate 

AA

�zz assumption is 4,000 per 100,000 unmarried couples. 

NCHS Data - 

4. 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 not 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).

5. Number of unmarried men and women in the MRA for calendar years 1978 through 1988, excluding

1980. These data are not 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+.

6. Number of new marriages, in a subset of the MRA, by age-group-of-husband crossed with age-group-ofwife (age groups include 15-19, 20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 65+), for calendar years

1989-95. These data are updated as new data become available and internal resources are sufficient to

examine and interpret such new data.

7. The total number of new marriages in the MRA less marriages in those states not included in the MRA

unmarried population for the period 1957-88. These data are not updated.

8. The total number of new marriages in the United States for the period 1989-2019. Normally, each year,

the NCHS publishes the total number of marriages for one more year.

9. Number of new marriages in the MRA for years 1979 and 1981-88 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 not available for years after 1988.

10. Number of unmarried people in the MRA (in thousands) for years 1982 - 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,

39
widowed, and divorced). These data are not available for years after 1988. 

11. Total Marriages and Remarriages for years 1979 and 1981-88. 

U.S. Census Bureau Data - 

12. Estimates of new marriages by age-group-of-husband crossed with age-group-of-wife from the 

American Community Survey (ACS) public use microdata sample (PUMS) files occurring, on average, 

at the end of years 2007-18. An additional year of data is available each year. 

13. Data for the 2010 Standard Population. The marriage program uses the unmarried population (single + 

widow + divorce). 

Other Input Data - 

14. From the vital statistics offices in various states, number of same-sex marriages from 2004-12. These 

data are updated as they become available.

1.6.c. Development of Output

Equation 1.6.1 – Age-Specific Marriage Rates 

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 MRA for the period 1978 through 1988, excluding 1980. Data 

for a subset of the MRA, available by age group only, are used for the period 1989 through 1995, and ACS 

new-married grids by age group are used for the period 2008 through 2016. The marriage grids by age group 

for the years 1996 through 2007 are linearly interpolated. The total number of marriages from NCHS are also 

used in the age-specific marriage rate calculations for the period 1989-2018. The projection period of the 

MARRIAGE subprocess begins in 2019. 

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-of-wife and the number of unmarried 

persons by age and sex. The formula used in the calculations is given below:

mm�xx,yy

zz = 

MM�xx,yyzz

PPxx,yy

zz , where 

• x refers to the age of men and y refers to the age of women; 

• MM�xx,yy

zz is the number of marriages in year z; and 

• PPxx,yy

zz is the geometric mean of the midyear unmarried men and unmarried women in year z. 

The rates for the period 1978 through 19889 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 historical years and the years in the projection 

period. 

For the period 1989-2018, the NCHS and ACS provided data on the number of marriages by age-group-ofhusband 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-groupof-husband crossed with age-group-of-wife, the more detailed marriage rates in MarGrid that are contained 

9 Data for 1980 is not available and is excluded from the calculations.

40
within this group are adjusted so that the number of marriages obtained by using the rates in MarGrid match the 

number implied in the subset. 

For each year of the entire 1989-2018 period, an expected total number of marriages is calculated by 

multiplying the rates in the MarGrid (or the adjusted MarGrid) by the corresponding geometric mean of the 

unmarried men and unmarried women in the Social Security area population. All rates in MarGrid (or the 

adjusted MarGrid) 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. In addition, we also subtract out same-sex marriages from the NCHS data, as we handle those in a 

later step. The 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 data to calculate the starting rate, we calculate the weighted 

average of the rates for the past five historical data years to derive the starting value. The annual rate of change 

decreases in absolute value as the ultimate year approaches.

To obtain the age-of-husband-age-of-wife-specific rates for a particular year from the age-adjusted 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. The MarGrid rates are then adjusted to produce two sets 

of marriage rates: opposite-sex marriage rates and same-sex marriage rates. 

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

previous marital status. However, 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 1981-88. 

41
1.7. DIVORCE

1.7.a. Overview

For the period 1979 through 1988, the National Center for Health Statistics (NCHS) collected data on the 

annual number of divorces in the Divorce Registration Area (DRA), by age-group-of-husband crossed with agegroup-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 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 (x) crossed with age-of-wife (y) specific divorce rate (dd̂

xx,yy

zz ) 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 husband and wife (�xx,yy

zz ) 

to (2) the corresponding number of married couples in the Social Security area (PPxx,yy

zz ) with the given age of 

husband and wife. An age-adjusted central divorce rate (AAAA�zz) summarizes the dd̂

xx,yy

zz for a given year. 

The AAAA�zz 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, 2010, population of married couples in the Social Security area by corresponding age-ofhusband and age-of-wife.

The DIVORCE subprocess projects annual dd̂

xx,yy

zz by age-of-husband crossed with age-of-wife. The primary 

equations are given below:

dd̂

xx,yy

zz = dd̂

xx,yy

zz (·) (1.7.1) 

 (1.7.2) 

where x and y refer to the age of husband and age of wife, respectively, and PPxx,yy

SS is the number of married 

couples in the Social Security area population as of July 1, 2010. 

AAAA�zz =

�PPxx,yy

SS

xx,yy

∙ dd̂

xx,yy

zz

�PPxx,yy

SS

xx,yy

42
1.7.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

1. Social Security area population of married couples by age-of-husband crossed with age-of-wife as of 

December 31 for years 1978-2018. These data are updated each year from the HISTORICAL 

POPULATION subprocess. In addition, the standard population is based on the averaged 2009 and 

2010 December 31 marriage grids from the 2015 TR. 

2. The total July 1 population in the Social Security area for years 1979-2018. However, only years 1979-

88, 1998-2000, and 2008-18 data are used. An additional year of data is added for each additional year 

of divorce data from the NCHS with a maximum of the final historical year. 

3. The total July 1 population in the U.S. resident population plus armed forces overseas for years 1979-

2018. However, only years 1979-88, 1998-2000, and 2008-18 data are used. An additional year of data 

is added for each additional year of divorce data from the American Community Survey (ACS). 

4. The total July 1 population in Puerto Rico and the Virgin Islands for years 1979-2018. However, only 

years 1988, 1998-2000, and 2008-18 are used. An additional year of data is added for each additional 

year of divorce data from the ACS. 

5. Final historical year (on a December 31 basis). This datum is updated each year from the HISTORICAL 

POPULATION subprocess. 

Assumptions - 

6. Each year, the assumed ultimate 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 the 2021 report, the assumed 

ultimate AAAA�zz is 1,700 per 100,000 married couples. 

NCHS Data - 

7. The number of divorces in the DRA, by age-of-husband crossed with age-of-wife, for calendar years 

1979 through 1988. These data are not available for years after 1988. The data are broken out by single 

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

 

8. The total number of divorces in the United States for the period for 1979-2019. For years 1992+, the 

number of divorces are derived by multiplying the rate times the population. Data is updated when it 

becomes available. 

9. The total number of divorces in Puerto Rico and the Virgin Islands for years 1988, 1998, 1999, and 

2000. New data are incorporated as they become available and resources are sufficient to validate their 

use. 

State Divorce Data - 

10. Since NCHS stopped collecting state-specific divorce data by age of husband crossed with age of wife, 

we directly contacted various state health departments for their most recent data. We were able to get 

this data from 18 states. The years and age groups available vary by state. In general, the years were 

from 2009-12. These 18 states that had these data available online, or that sent us the data via email, are 

43
Alabama, Alaska, Idaho, Kansas, Kentucky, Michigan, Missouri, Montana, Nebraska, New Hampshire, 

Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, and Wyoming. 

Census Bureau Data – 

11. The number of divorces for years 2008-18 in Puerto Rico, estimated using the 2008-19 American 

Community Survey (ACS) public use microdata sample (PUMS) files. A new year of data is generally 

available each year.

1.7.c. Development of Output

Equation 1.7.1 - 

Age-specific divorce rates are calculated 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. Data on the total number of divorces in the United States are used for the period 1989 through 2018. 

With the data from the various states, we developed an age-group-of-husband crossed with age-group-of-wife 

grid for 2011. 

 

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

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

divorce rates (dd̂

xx,yy

zz ), for each year (z) are calculated for the period 1979-88 by taking the number of divorces 

(inflated to represent the Social Security area, �xx,yy

zz ) and dividing by the married population in the Social 

Security area at that age-of-husband and age-of-wife (PPxx,yy

zz ). The formula for this calculation is given below: 

 dd̂

xx,yy

zz = 

DD�xx,yyzz

PPxx,yy

zz (1.7.3) 

These rates are then averaged, graduated,

10 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 is then adjusted using the state data grid 

developed for 2011. DivGrid for years after 1988 is a weighted average of the 1988 DivGrid and the 2011 state 

data single year grid. This state data single year of age grid is derived by ratioing the 1988 DivGrid cells using 

the original state age-group data. DivGrid is used in the calculation of the age-specific divorce rates for all later 

years including the projection period. 

For each year in the 1989-2019 period, 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 starting age-adjusted divorce rate is set to a weighted average of the past five years of data. This ageadjusted rate is assumed to reach its ultimate value in the 25th year of the 75-year projection period. The annual 

rate of change decreases in absolute value as the ultimate year approaches.

10 Using a two-dimensional Whittaker-Henderson method of graduation from http://www.howardfamily.ca/graduation/index.html. 

This graduation is also used by the Society of Actuaries in their mortality improvement scales.

44
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. 

45
1.8. PROJECTED POPULATION

1.8.a. Overview

For the 2021 Trustees Report, the starting population for the population projections is the December 31, 2018, 

Social Security area population, by age, sex, and marital status, produced by the HISTORICAL POPULATION 

subprocess. (For this section, section 1.8, the term “starting year” refers to the year 2018.) The Social Security 

area population is then projected using a component method. The components of change include births, deaths, 

net LPR immigration, and net other-than-LPR immigration. The components of change are applied to the 

starting population by age and sex to prepare estimated populations as of December 31, 2019 and 2020, and to 

project the population through the 75-year projection period (years 2021-95). 

Beginning with December 31, 2013, the historical and projected populations are modeled using the following 

population statuses: heterosexual, gay, and lesbian. The gay and lesbian populations in the HISTORICAL 

POPULATION program are broken out assuming 2.5% of the male population and 4.5% of the female 

population is gay or lesbian, and the same is true for cohorts born in the PROJECTED POPULATION program. 

There is a separate equation for each of the components of change as follows: 

BBss,pp

zz = BBss,ppzz (∙) (1.8.1) 

where BBss,pp

zz is the number of births of each sex (s) by population status (p) born in year z; 

xx,ss,pp zz = xx,ss,pp zz (∙) (1.8.2) 

where xx.ss,pp zz is the number of deaths by age (x), sex (s), and population status (p) that occurs in year z; and 

 NN xx,ss

zz = NNLLxx,ss zz + NN xx,sszz (1.8.3) 

where NN xx,ss

zz is the total net immigration (both LPR and other-than-LPR) by age (x), sex (s), and population 

status (p), NN xx,ss zz is the net LPR immigration (produced by the LPR IMMIGRATION subprocess), and NN xx,ss

zz is 

the net other-than-LPR immigration (produced by the OTHER-THAN-LPR IMMIGRATION subprocess). The 

population program further disaggregates the new immigration, NN xx,ss

zz , by population status into NN xx,ss,pp zz . 

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

area population by age, sex, and population status: 

 

PP0,ss,pp = BBss,pp

zz − 0,ss,pp zz + NN 0,ss,pp zz for age = 0

 (1.8.4) 

PPxx,ss,pp zz = PPxx−1,ss,pp

zz−1 − xx,ss,pp zz + NN xx,ss,pp zz for ages > 0 

where PPxx,ss,pp zz is the population, by age (x), sex (s), and population status (p), as of December 31st of each year (z). 

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

widowed, and divorced. The following equation shows the population by age (x), sex (s), population status (p), 

and marital status (m) for each year (z): 

 PPxx,ss,pp,mm zz = PPxx,ss,pp,mm zz (∙) (1.8.5) 

The children (ages 0-18) population is further disaggregated into the following four parent statuses (i.e., fates): 

both parents are alive, only father is alive, only mother is alive, and both parents deceased. The following 

46
equation shows the children population by age of child (x), sex of parent (s), age group of parent (g), and fate of 

parent (f) for each year (z): 

 CCxx,ss,gg,ff zz = CCxx,ss,gg,ff zz (∙) (1.8.6) 

1.8.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

FERTILITY

1. Historical birth rates by single year of age of mother (14-49) for the years beginning with 1941 and 

ending with the starting year. These data are updated each year. 

2. Projected birth rates by single year of age of mother (14-49) for the years beginning with the year after 

the starting year and ending with 2100. These data are updated each year.

MORTALITY

3. Historical probabilities of death by age last birthday (including neonatal 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 

starting year. These data are updated each year.

4. Projected probabilities of death by age last birthday (including neonatal mortality factor, single year of 

age for ages 0-99, and age group 100+) and sex for the years beginning with the year after the starting 

year and ending with 2100. These data are updated each year. 

5. Factors to distribute probabilities of death by marital status. They are dimensioned by sex, single year 

of age (ages 14-100+), and marital status. These data are updated each year. 

LPR IMMIGRATION

6. Projected numbers of LPR immigrants who are new arrivals, by single year of age (-1-100) and sex for 

years beginning with the year after the starting year and ending with 2100. These data are updated each 

year. Note that age -1 represents births that occur during the year. 

7. Projected numbers of legal emigrants by single year of age (-1-100) and sex for years beginning with the 

year after the starting year and ending with 2100. These data are updated each year. Note that age -1 

represents births that occur during the year. 

8. Projected numbers of LPR immigrants who are adjustments of status, by single year of age (-1-100) and 

sex for years beginning with the year after the starting year and ending with 2100. These data are 

updated each year. Note that age -1 represents births that occur during the year. 

HISTORICAL POPULATION

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

population status (eligible for or in an opposite-sex, same-sex male, or same-sex female marriage) for 

the years beginning with 1940 and ending with the starting year. These data are updated each year. 

10. Married couples by single year of age of spouse 1 (ages 14-100+) crossed with single year of age of 

spouse 2 (ages 14-100+) for the years beginning with 1940 and ending with the starting year by 

marriage type (opposite-sex, same-sex male, and same-sex female). These data are updated each year. 

47
11. Other-than-LPR population by age and sex for the years beginning with 1963 and ending with the

starting year. These data are updated each year.

12. Final historical year (on a December 31 basis). This datum is updated each year from the HISTORICAL

POPULATION subprocess.

OTHER-THAN-LPR IMMIGRATION

13. Projected numbers of other-than-LPR immigrants entering the country by age (-1-100) and sex for years

beginning with the year after the starting year and ending with 2100. These data are updated each year.

14. Projected numbers of other-than-LPR immigrants leaving the country by age (-1-100) and sex for years

beginning with the year after the starting year and ending with 2100. These data are updated each year.

15. Other-than-LPR population by age and sex for the years beginning with the year after the starting year

and ending with 2100. These data are updated each year.

MARRIAGE

16. 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 each

year.

17. Projected central same-sex marriage rates by single year of age of spouse 1 (ages 14-100+) crossed with

single year of age of spouse 2 (ages 14-100+) for each year of the projection period. These data are

updated each year.

18. Averaged and graduated marriage rates for the period 1979 and 1981-88 by single year of age (ages 14-

100+), sex, and prior marital status (single, divorced, and widowed). These data are updated each year.

19. Total number of marriages for the years beginning with 1989 and ending with 2019. These data are

updated each year.

DIVORCE

20. 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 each year.

U.S. Census Bureau Data - 

21. 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, 35-39, 40-44, 45-49, 50-54, and 55-64) for 1960-2020.

(Note that the program splits the last age group, which is a 10-year age group, into two 5-year age

groups.) An additional year of data is added each year.

1.8.c. Development of Output

Equation 1.8.1 - Births

The number of births in 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 midyear female population aged 14 to 49 as follows:

BBxx

zz = bbxxzz �

FFPPxx

zz+FFPPxxzz+1

2 �

where, 

48
 BBxx

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

 bbxx

zz = birth rate of mothers age x in year z; and

 xx

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

The total number of births in a given year is the sum of the number of births to mothers at each age. This total 

number of births is disaggregated by sex by assuming a sex ratio of 1048 male births for every 1000 female 

births. The total number of births is also disaggregated by population status by assuming 2.5% of boys that are 

born are gay and 4.5% of girls that are born are lesbian. (Note: These percentages include assuming that onehalf of those born bisexual will want to enter into a same-sex marriage.)

Equation 1.8.2 – Deaths

The number of deaths for the Social Security area by age (x), sex (s), and population status (p), xx,ss,pp zz , is 

computed for each projection year (z) by applying the death probabilities for each age and sex, qqxx,ss

zz , to the 

exposed population at the beginning of the year. 

xx,ss,pp zz = qqxx,ss

zz PPxx,ss,pp zz

Equation 1.8.5 – Disaggregating the population by marital status 

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

population status 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, marital status, and population 

status as of the starting year 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 and number of married male/male and 

female/female marriages, single year of age of spouse 1 crossed with single year of age of spouse 2, as of the 

starting year. 

All births are assigned to the single marital status. For a given age, sex, and population status, 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 MORTALITY subprocess. For a 

given age, sex, and population status, 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 widowings during a year are determined, the population by age, 

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

end of the year is estimated from the unmarried population at the beginning of the year by factoring in deaths, 

marriages, new unmarried immigrants, widowings, and divorces during the year. The married population at the 

end of the year is estimated from the married population at the beginning of the year by factoring in divorces, 

widowings, dissolutions of marriages when both husband and wife dies, new married immigrants, and 

marriages during the year. 

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

marriages occurring at each age of husband crossed with each age of wife is obtained by multiplying the age-ofhusband-specific and age-of-wife-specific marriage rates with the geometric mean of the midyear unmarried 

male population and the midyear unmarried female population. 

49
The age-specific midyear unmarried male population11 is estimated from the beginning of the year unmarried 

population. It is calculated by adjusting the number of unmarried men at the beginning of the year to represent 

midyear using the relationship between the prior beginning of year and the current beginning of year unmarried 

male populations. The midyear female unmarried population is approximated similarly.

The numbers of marriages are then distributed by previous marital status (single, widowed, divorced) 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 

crossed with age-of-wife divorce rates for that year with the midyear number of married couples in that age 

crossing. 

The number of age-of-husband crossed with age-of-wife midyear married couples is estimated from the 

beginning of the year married couples. It is calculated by adjusting the number of married couples at the 

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

beginning of the prior year and the beginning of the current year. 

Marriages and divorces for same-sex couples are calculated similarly.

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. 

Equation 1.8.6 – Disaggregating the children by parent survival status 

Once the population is projected by single year of age, sex, population status, and marital status, the number of 

children are then categorized by age of father, age of mother, and orphan status. The HISTORICAL 

POPULATION subprocess provides the historical number of children (ages 0-18), number of women (ages 14-

49), and the number of married couples by single year of age of husband crossed with single year of age of 

wife. The projected number of children (ages 0-18), number of women (ages 14-49), and marriage grid age of 

husband crossed with age of wife is calculated in the projected population. 

For women aged 14-49, births are calculated by multiplying the age-specific birth rate, from the FERTILITY 

subprocess, with the number of women at the corresponding age. The births are then distributed to the age of 

husband in the same proportions as the age of husband crossed with age of wife married couples grid. 

Each year the number of children is then rolled forward a year to the next age of husband, age of wife, and child 

age. Parent survival is calculated based on the deaths rates from the MORTALITY subprocess. The number of 

orphans consists of children with at least one parent deceased. The calculated number of children by age of 

father and age of mother must match the number of children in the historical or projected population. To 

accomplish this, the calculated number of children is multiplied by the ratio of the number of children in the 

historical or projected population to the number of children by age of father and age of mother that was 

calculated using the fertility rates. For any remaining difference, an adjustment of one is made for each age of 

husband crossed with age of wife until the total number of children match.

Once the population is projected by single year of age, sex, population status, marital status, and children, the 

mean number of children per married couple with children is determined by year and age of householder. The 

historical mean number of children by year and age of householder in the population program is calculated from 

the number of children categorized by age of father, age of mother, and the number of married men by age 

11 The midyear population exposed to marriage is the unmarried population (sum of those single, widowed, and divorced).

50
group from the HISTORICAL POPULATION subprocess. Linear regression is used to model the relationship 

between the mean number of children in the population program to the mean number of children from the U.S. 

Census Bureau. The regression model is then used to project the mean number of children by age of 

householder in the population program. 

51
Process 2: 

Economics

52
2. Economic

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 five subprocesses, U.S. EMPLOYMENT, U.S. 

EARNINGS, COVERED EMPLOYMENT AND EARNINGS, TAXABLE PAYROLL, and 

REVENUES. 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. REVENUES converts taxable 

concepts into projected OASDI wage tax liabilities (WTL) and self-employment tax liabilities 

(SEL) for the short range period. 

U.S. EMPLOYMENT and U.S. EARNINGS produce output by quarter, while the output from 

COVERED EMPLOYMENT AND EARNINGS and TAXABLE PAYROLL are calendar year 

amounts. REVENUES produces amounts of wages paid to employees during a quarter and tax 

liabilities owed on those wages, as well as taxes collected on those amounts by quarter and by 

fiscal and calendar year. 

Two appendices are at the end of this documentation. The first appendix, 2-1, provides details for 

most of the equations given in the following descriptions of the Economic process. The second 

appendix, 2-2, provides a listing with explanations of acronyms used in this documentation. 

53
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). 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 many of these concepts, the BLS publishes historical 

data disaggregated by age, gender, marital status, and presence of children.

For various disaggregated groups1

, USEMP projects quarterly and annual values for these 

principal measures of U.S. employment and population. Equations 2.1.1 through 2.1.6 outline the 

subprocess’ overall structure and solution sequence for the total economy. We project that the 

military population (M) will remain constant over the projection horizon. We also project that 

the sum of N and M will grow at the same annual rate projected for the Social Security area 

population (P) (see Demography Process input).

M t

 = M2020 (2.1.1) 

N t = [(N t-1 + M t-1)*( P t / P t-1)] – M t (2.1.2) 

RU = RU(·) (2.1.3) 

LFPR = LFPR(·) (2.1.4) 

LC = LFPR * N (2.1.5) 

E = LC * (1 -RU / 100) (2.1.6) 

Note: the superscript t represents the projection year.

The Demography Process estimates historical values for the total Social Security area population 

(P) and an important component, the other-than-lawful-permanent-resident, or other-than-LPR,

population (OP). OP is further disaggregated into components by visa status: those temporarily

authorized to reside or work in the US (OP_A), those who have overstayed their authorization

(OP_NA), and those who were never authorized to reside or work in the US (OP_NO). Similarly,

USEMP projects annual values for E and employed OP (EO), including its visa-status

components (EO_A, EO_NA, EO_NO). USEMP also separates EO to those whose earnings are

reported and posted to the Master Earnings File (EO_MEF), those whose earnings are reported

posted to the Earnings Suspense File (EO_ESF), those in the underground economy (EO_UND).

1 Group disaggregation includes age and gender. Some groups are additionally disaggregated by marital status and 

by presence of children.

54
A further subgroup of EO_MEF is also calculated: those who are OASDI covered (EO_MEFC). 

Equations 2.1.7 through 2.1.14 outline the overall structure of the subprocess used to estimate 

EO and its sub-components. 

EO_A = EO_A(·) (2.1.7) 

EO_NA = E * OP_NA / N (2.1.8) 

EO_NO = E * OP_NO / N (2.1.9) 

EO = EO_A + EO_NA + EO_NO (2.1.10) 

EO_MEF = EO_MEF(·) (2.1.11) 

EO_MEFC = EO_MEFC(·) (2.1.12) 

EO_ESF = EO_ESF(·) (2.1.13) 

EO_UND = EO – EO_MEF – EO_ESF (2.1.14) 

Finally, for each age/gender group, USEMP projects total “at-any-time” employed other-thanLPR population (TEO). EO represents the average weekly employment of the other-than-LPR

population during a calendar year. TEO represents the total number of individuals in the otherthan-LPR 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 2.1.15 

through 2.1.19 convert every EO age-gender sub-component to an at-any-time TEO age-gender 

sub-component counterpart. 

TEO_MEF = TEO_MEF(·) (2.1.15) 

TEO_MEFC = TEO_MEFC(·) (2.1.16) 

TEO_ESF = TEO_ESF(·) (2.1.17) 

TEO_UND = TEO_UND(·) (2.1.18) 

TEO = TEO_MEF + TEO_ESF + TEO_UND (2.1.19) 

55
2.1.b. Input Data

Long-Range OASDI Projection Data 

These data are updated each year.

Demography 

1. Social Security area population as of year-end (1941 – 2100) by age, marital status 

(single, married, widowed, divorced) and gender (M, F) 

2. “Other-than-LPR” population as of year-end (1964 – 2100) by age, gender (M, F), 

and visa status (OP_A, OP_NA, and OP_NO) 

3. Number of children by age of child and age of mother (1960-2100) 

4. Life expectancy by age and gender (1950-2100) 

5. Exit rates (probability of leaving the “other-than-LPR” population by other than 

death) by age and gender. 

6. Mortality rates by age and gender (1941-2100) 

Trust Fund Operations and Actuarial Status – The Trust Fund Operations and Actuarial 

Status Process provides no direct input to the Economic Process sections. However, the 

LFPRs generally use input based on the Outgo Process from the prior year’s Trustees Report. 

For example, the projected LFPRs for the 2021 Trustees Report used input from the 2020 

Trustees Report. This is acceptable practice as long as the ultimate disability incidence rate 

assumption in not changed from the prior year. This input includes: 

7. projections for the disability prevalence rates by age and gender (originally from the 

Beneficiaries subprocess) 

8. projections for the disability-insured population (originally from the Beneficiaries 

subprocess) 

9. primary insurance amount (PIA) replacement rates by age and gender. 

The disability prevalence rate is defined as the ratio of the number of disabled worker 

beneficiaries to the disability-insured 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 average annual 

growth rate values for key economic variables:

10. Real wage 

11. Total economy productivity 

12. Average hours worked 

13. Ratio of wages to compensation (RWSD) 

14. Ratio of compensation to GDP (RWSSY) 

15. GDP deflator (PGDP) 

16. Consumer Price Index (CPI) 

56
The Board also sets ultimate values for:

17. Annual trust fund real interest rate 

18. Unemployment rate 

These ultimate values are typically reached 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 real GDP and potential GDP are set. The ratio (RTP) 

of real to potential GDP is an important summary measure of the economic cycle.

The Trustees also agree on the assumed short-range values for the listed variables.

Addfactors 

19. Addfactors are adjustments that move an estimate closer to an expected value. They

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 on male and female LFPRs starting around 

age 40 to reflect the effects of projected changes in life expectancy. Addfactors are 

also used to modify LFPRs of several specific age-sex groups to ensure a reasonable 

shape of the age-LFPR profile. Another addfactor is applied to the labor force in the 

first few projection years to phase out the differences between the model-predicted 

values and recent historical data. 

Other input data 

20. U.S. armed forces (EDMIL) by age and gender, 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 gender. These data are no longer produced by 

Census. 

21. EDMIL by age and gender, 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 December 2019) by single year of age (16 to 69) and 

gender. These data are updated once a year. 

22. Data for the mobilized military reservist population, by branch of service (September 

2001-September 2016) are reported by the US Department of Defense weekly. These 

data are no longer reported by the Department of Defense. 

23. Data from the March Supplement of the Joint BLS/Census Current Population 

Survey (CPS) by year (1968-2019), for levels of the civilian noninstitutional 

population, labor force, military, and unemployment. These data are available from 

the U.S. Census Bureau by single year of age (16 to 85+), gender, marital status 

(never married, married with a spouse present, and married with no spouse present), 

57
and presence of children. These data are updated by the U.S. Census Bureau for the 

BLS annually. This subprocess updates the data every other year (or more often, 

based on time availability). 

24. Data from the March Supplement of the CPS by year (1992-2020), for levels of the 

civilian noninstitutional population. These data are available from the U.S. Census 

Bureau by single year of age (16 to 85+), gender, and educational attainment level. 

These data are updated by the U.S. Census Bureau for the BLS annually. This 

subprocess updates the data every year, if time availability allows. 

25. Data from the CPS (1948-2021) for levels of civilian employment, civilian labor 

force, civilian unemployment, and civilian noninstitutional population. These data are 

available from the BLS by age group and gender. These data are updated by the BLS 

monthly. This subprocess updates the data several times a year. 

26. Data from the CPS by year (1994-2020), for the civilian noninstitutional population. 

These data are available from the BLS by single year of age (16 to 85+), gender, 

marital status, labor force employment status, and (for those not in the labor force) 

reason for not being in the labor force. These data are updated by the BLS monthly. 

Monthly data are used to calculate annual averages. This subprocess updates the data 

every year, if time availability allows. 

27. Data from the Current Employment Statistics survey (CES) (1964 (varies) to

September 2020) for establishment employment, average hourly earnings, average 

weekly earnings, and average weekly hours. These data are available from the BLS 

by sector. These data are updated by the BLS monthly. This subprocess updates the 

data several times a year. 

28. Unpublished data from the CPS (1965 - October 2020) for male and female civilian 

labor force participation rates for older workers. These data are available from the 

BLS by single year of age (ages 55-79) and by group (75 and over, and 80 and over). 

These data are updated by the BLS monthly. This subprocess updates the data several 

times a year. 

2.1.c. Development of Output

Equation 2.1.3 - Unemployment Rate (RU) 

The RU is disaggregated by age and gender. 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 men and 14 for women. Each disaggregated RU is 

specified using a first-difference model that depends on the distributed lag in the change in 

the ratio of real to potential GDP (RTP) and an adjustment to ensure that values converge to 

its estimated trend level. Coefficients are estimated by regression. Furthermore, projections 

are constrained to the ultimate age-gender-adjusted RU set by the Trustees. The aggregate 

age-sex-adjusted RU is dependent on the projected distribution of the labor force by age and 

58
gender. See Appendix 2-1 for details on the equations.

Equation 2.1.4 - Labor Force Participation Rate (LFPR) 

The LFPR is disaggregated by age and gender. 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, ... 99, 100 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 (which 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 

women with at least one child under the age of six and women without a child under the age 

of six. Thus, USEMP contains 153 LFPR equations, 69 for men and 84 for women. See 

Appendix 2-1 for details on the equations. 

Given the level of demographic disaggregation, the aggregate LFPR is dependent on the 

projected distribution of the population by age, gender, 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 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.

• Disability prevalence ratio (RD) is defined as the ratio of disabled worker beneficiaries to 

the disability-insured population. An increase in RD lowers the LFPR because disabled 

worker beneficiaries tend to exit the labor force. To reflect this, projected LFPRs for each 

age-sex group are adjusted for disability by dividing them by (1+RD). This adjustment 

implicitly assumes that disability can strike any person in a given age-sex group with 

equal probability. For ages 62 to NRA, RDs are not “pure” RDs in that they are subject to 

the confounding effect of the availability of retirement benefits. For example, at age 62, a 

marginally disabled individual may opt to begin receiving retirement benefits rather than 

go through an uncertain disability application/appeals process. For ages NRA and above, 

RDs are unavailable because at the NRA all disabled-worker beneficiaries become retiredworker beneficiaries. To avoid these problems, RDs for ages 62-74 are set to their cohort 

RD at age 61. For example, the RD for men age 62 in year (t) is set to the RD for men age 

61 in year (t-1). For those ages 75 and older, the lagged cohort variable provides 

information on the influence of disability prevalence rates on labor force participation. 

• The unemployment rate (RU) is a measure of the economic cycle. An increase in the 

lagged and current unemployment rate leads to a decrease in the LFPR. The RU affects 

LFPRs for ages up to 54. 

• The normal retirement age (NRA) is assumed to affect the LFPRs for those age 62 

through 69 through an earnings test and replacement rate. The replacement rate is defined 

as the ratio of a hypothetical worker’s PIA to career-average wage level. This value is 

projected for hypothetical workers with medium-scaled earnings patterns2 who retire at 

ages 62 through 69. The replacement rate is adjusted to include the reduction for early 

2 More details on the hypothetical scaled workers are provided in Actuarial Note 2020.3, located at: 

www.ssa.gov/OACT/NOTES/ran3/index.html. 

59
retirement and the delayed retirement credit. An increase in the NRA decreases the

adjusted replacement rates, which, in turn, leads to increases in the LFPRs for those 

between the ages of 62 and 69. The potential earnings test tax rate (POT_ET_TXRT) is 

used in LFPRs between 62 and 69. It is defined as a tax rate on monthly retirement 

benefits faced by an individual who opts to collect Social Security benefits before 

reaching NRA while continuing to work and earn income. An increase in the NRA from 

66 to 67 leads to an increase in the potential tax rate for those age 66, which, in turn, leads 

to a decrease in their LFPR.

• The level of education attainment affects LFPRs for ages 55 and older for men and 50 and 

older for women. As the average level of educational attainment in any given age-sex 

group rises, LFPRs generally increase. 

• The composition of population by marital status also affects LFPRs. For ages up to 54, 

LFPRs are disaggregated by marital status. For ages 55 to 74 (both men and women), the 

effect of marital status is captured by the proportion of people in any given age group who 

are married with spouse present. 

• A LFPR increases with its lagged cohort. Lagged cohort variables affect LFPRs for age 75 

and over. 

• For those approximately age 40 and over, an increase in life expectancy leads to an 

increase in LFPRs.

Equation 2.1.7 to 2.1.19 – Employed Other-than-LPR Population (EO) and At-Any-Time 

Employed Other-than-LPR Population (TEO) 

EO is estimated by gender and single-year of age from 16 to 100 based on OP and estimated 

employment-to-population ratios by visa-status component (OP_A, OP_NA, OP_NO). For 

this purpose, OP_A is further disaggregated into subgroups by visa type that differ in 

employment patterns or OASDI coverage status. The other two components are assumed to 

have equal employment-to-population ratio as the LPR population of the same age and 

gender. This portion of USEMP contains 4,250 equations, for 85 ages, 2 genders, and 25 

components and subgroups. We separate EO_NO 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 component is then 

further separated into EO_MEF, EO_MEFC, EO_ESF, and EO_UND. 

Every EO sub-component by age, gender, and visa status is converted to its age-gender TEO 

sub-component counterpart using an age-gender conversion weight. For example, if the 

sub-component of EO is for never authorized men age 20 to 24, the conversion weight is 

defined as the ratio of total economy-wide at-any-time employed men age 20 to 24 

(TEM2024) to the sum of military and CPS civilian male employment age 20 to 24. For 

authorized workers and students on temporary visas, conversion weights take into account 

their partial presence in the year of arrival and the year of departure. 

60
2.2. U.S. EARNINGS (MODSOL2) 

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, the 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. 

MODSOL2 projects quarterly values for these principal 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). Real GDP is equal to the ratio of nominal GDP to PGDP. Potential 

(or full-employment) GDP is a related concept defined as the level of real GDP that is consistent 

with a full-employment aggregate RU. 

MODSOL2 projects quarterly values for these output measures. Potential GDP is based on the 

change in full-employment values for: (1) 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. RTP is the ratio of real 

GDP to potential GDP and is set by assumption. RTP reaches 1.0 in the short-range period and 

remains at 1.0 thereafter. Projected real GDP is set equal to the product of potential GDP and 

RTP. 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. 

61
MODSOL2 projects quarterly values for these principal 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 

1. Demography- (See Section 2.1.b.) 

2. Economics - Data from Section 2.1 include the total employed (E), E by age 

and gender, LFPRs by age and gender, the aggregate unemployment rate 

(RU), and the full-employment concepts for LC, RU, and E. 

3. Trustees Assumptions - (See Section 2.1.b.) 

Addfactors 

4. 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 they are 

implemented if necessary. 

Other input data 

5. Data from the NIPA (1929 (varies) to 2020) for GDP, income, wages, 

compensation, personal consumption expenditures, investment, employer 

contributions for employee pension and insurance funds, and employer 

contributions for government social insurance. They are published by the 

BEA quarterly and/or annually. This subprocess updates the data several times 

a year. 

6. OASDI employee, employer, and self-employed tax rates from 1937 to 2100. 

62
These contribution rates are set according to the Social Security Act of 1935 

as amended through 2015. The rates are updated when legislation mandates a 

change. 

7. The historical Consumer Price Index (CPI) is published monthly by the BLS. 

This subprocess updates the data several times a year. 

8. 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. 

9. U.S. armed forces (EDMIL) by age and gender 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 gender. These data are 

no longer produced by Census. 

10. EDMIL by age and gender 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 December 2019) by single 

year of age (16 to 69) and gender. These data are updated once a year. 

11. Wages for railroad workers are wages covered by the Railroad Retirement 

Act. The annual data are for the period 1971 to 2017. An additional year of 

data from the Railroad Retirement Board is usually available for including in 

preparation of the next annual Trustees Report. 

12. Unpublished data from the CPS (1988-2019) on employment by class of 

worker (i.e., agricultural, nonagricultural, unpaid family, private industry, 

government, wage and salary, self-employed). These data are available from 

the BLS by age group and gender. These data are updated by the BLS 

annually. This subprocess updates the data annually. 

13. Data from the NIPA (1947-2020) for wages and compensation of households 

and institutions are published by the BEA quarterly. This subprocess updates 

the data several times a year. 

14. Other program-related parameters, including the average indexing wage, the 

benefit increase, the taxable maximum, and the annual retirement earnings test 

exempt amounts, are obtained annually from the Short-Range section of 

OCACT. This subprocess updates the data annually. 

15. Unpublished data from the CES & CPS for total hours worked in the 

economy. These data are available from the BLS. These data are updated by 

the BLS quarterly (1948-2020) and annually (1948-2019). This subprocess 

63
updates the data several times a year. 

16. The Federal minimum hourly wage is based on the Fair Labor Standards Act 

from the Department of Labor for 1938 to 2020. The wage is updated when 

there is legislation mandating a change. 

17. 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, gender, 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 nonagriculture.

For the nonagriculture sector, the SEPRs by age and gender are defined as the ratio of the

nonagriculture self-employment to total employment. Thus, the aggregate nonagriculture 

SEPR is dependent on the projected distribution of employment by age and gender. All 

nonagriculture SEPRs by age and gender are dependent on the RTP. Increases in the RTP 

lead to decreases in the SEPRs. 

For the agriculture sector, the male SEPRs by age (as well as the female SEPR for ages 16-

17) are defined as the ratio of agriculture self-employment to the civilian noninstitutional 

population. Thus, the aggregate agriculture SEPR for men is dependent on the projected 

distribution of the population by age. The agriculture SEPRs for men 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 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 men. 

The female SEPRs by age (for ages 18 and higher) for the agriculture sector are defined as 

the ratio of the female to male agriculture self-employment. Thus, the aggregate agriculture 

SEPR for women is dependent on the projected distribution of male agriculture employment 

by age. For female age groups age 18 and over, 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. 

64
Equation 2.2.2 – Self-Employed Workers (ES) 

ES is disaggregated by age, gender, 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 

nonagriculture. For the nonagricultural sector, ES is derived from SEPR by scaling it to the 

total nonagricultural self-employed workers (ENAS), which is projected as a constant share 

of nonagricultural employment over the long range. For the agricultural sector, it is similarly 

scaled to the total agricultural self-employed workers (EAS), which is projected as the 

residual after subtracting projected wage workers and unpaid family workers from total 

agricultural employment.

Equation 2.2.3 - Unpaid Family Workers (EU)

EU is disaggregated by age, gender, 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 

nonagriculture.

From 1970 to 2014, the level of EU fell from about 0.5 to 0.02 million in the agriculture 

sector and from about 0.5 to 0.06 million in the nonagricultural sector. For projections, the 

levels of EU by age and gender in the agriculture sector are assumed constant at about five 

thousand or less. The EUs by age and gender in the nonagricultural sector are projected as a 

constant ratio to ES. 

Equation 2.2.4 - Wage Workers (EW)

For the nonagricultural sector, the number of wage workers is the residual after subtracting 

self-employed workers and unpaid family workers from total workers. For the agricultural 

sector, we first project wage workers, and the number of self-employed workers is the 

residual after subtracting wage workers and unpaid family workers from total agricultural 

workers. Agricultural wage workers in each age/gender group are projected as a function of 

the business cycle and the age-gender-group’s share of total US workers. The age groups 

include 16-17, 18-19, 20-24, 25-34, 35-44, 45-54, 55-64, and 65 and over. The 

nonagriculture sector is further disaggregated: private household workers are projected by 

age and sex, while Federal Government (Civilian and Military, separately) and State & Local 

Government workers are projected in total.

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, nonprofit 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. 

65
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 AWSSPF. 

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 to grow with GDP and the ratio of EAS to 

total employment in the sector. 

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. (see description for Equation 2.2.5) 

Equation 2.2.10 - Earnings Ratio (RWSD) 

In the NIPA, the difference between 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 

66
other small groups. State and Local government funds mostly include workers’ 

compensation.

RWSD is defined as the ratio of WSD to WSS. RWSD is projected to mostly decline on a 

year-by-year basis over the entire 75-year projection horizon due to projected increases in 

employer contributions to employee group health insurance premiums (ECEGHIP) and 

pensions. ECEGHIP is projected by the Center for Medicare and Medicaid Services (CMS). 

Employer contributions to employee pension funds are assumed to increase as life 

expectancy increases. 

67
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. 

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. The combination employment ratio (RCMB) is defined as the ratio of 

CMB_TOT to WSW.

(Equation 2.3.1 not used in this version.) (2.3.1) 

TE = TE(·) (2.3.2) 

NCE = NCE(·) (2.3.3) 

TCE = TE - NCE (2.3.4) 

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) 

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RCSE = RCSE(·) (2.3.12) 

CSE_TOT = RCSE * Y (2.3.13) 

COV projects 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 reported 

on Forms W-2 and posted to the Master Earnings File (MEF). By law, it is used to set the 

OASDI contribution and benefit base (TAXMAX).

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 

1. Demography - (See Section 2.1.b.) 

2. Economics- Employment and earnings-related data from Sections 2.1 and 2.2. 

3. Trustees Assumptions - (See Section 2.1.b.) 

Addfactors 

4. 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 they are implemented if necessary. 

Other input data 

5. Ratios of OASDI covered to NIPA wages by sector. NIPA wages by sector 

are available quarterly and annually from 1947 to 2020. They are published by 

the BEA and updated several times during the year. OASDI covered wages 

(1971 to 2018) are updated annually by the Economic process. Covered data 

69
for the latest historical year are estimated from tabulations of Form 941 and 

W-2 data. 

6. U.S. armed forces (EDMIL) by age and gender 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 gender. These data are 

no longer produced by Census. 

7. EDMIL by age and gender 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 December 2019) by single 

year of age (16 to 69) and gender. These data are updated once a year. 

8. Railroad employment is covered by the Railroad Retirement Act. The annual 

historical data are for the period 1971 to 2018. 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. 

9. 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. 

10. 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. 

11. Data obtained from extracting information from the 1.0% EmployeeEmployer 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. 

12. Data obtained from quarterly IRS Form 941 files, 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 

70
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.

13. Data from the Quarterly EPOXY Report, received in hard copy and, more 

recently, electronic formats obtained from OS. The data currently used are the 

number of workers with OASDI taxable earnings, number of workers with HI 

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 earnings, 

and number of persons with HI taxable self-employment earnings. Data are 

also available on an age-sex specific basis for number of persons with OASDI 

taxable wages, number of persons with HI taxable wages, number of persons 

with OASDI taxable self-employment earnings, and number of persons with 

HI taxable self-employment earnings.

14. 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 self-employment earnings and self-reported tips since the prior 

Letter. These data are for years 1978 to the most recent year available. 

15. 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. 

 

16. Ratio of OASDI covered to NIPA wages, and ratio of OASDI taxable to 

covered wages. NIPA wages by sector are available quarterly from 1947 to 

2020 and annually from 1947 to 2020. They are published by the BEA and 

updated several times during the year. OASDI covered and taxable wages 

(1971 to 2018) 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 for the military, state and local, farm, and 

private household sectors. The projected value for the federal civilian sector 

covered ratio is projected to grow to 1.0 by 2030. The projected values for the 

private nonfarm business and the private sector vary with the relative size of 

the other-than-LPR population. 

2.3.c. Development of Output

Equation 2.3.2 - Total Employment (TE)

Based on the CPS, BLS estimates the total number of persons with any work experience 

71
(WE) during a calendar year. Average weeks worked (AWW) during a calendar year is 

defined as AWW = E * 52 / WE. Based on a 100 percent count of earnings reports (i.e., Form 

W-2 and Schedule SE) tabulated by SSA, OCACT estimates the total number of persons 

employed at any time during a calendar year (TE). Compared to WE, TE is a broader 

measure of employment. WE is an estimate of the number of workers in the civilian 

noninstitutional US population age 16 and over. TE is an estimate of employment in the 

broader Social Security area population, which includes U.S. territories, the military, and 

institutions. TE also includes employment of workers who age 15 and younger.

AWW is disaggregated by gender and age and is projected as a function of a time trend and 

unemployment rate. WE is projected as (E * 52) / AWW. TE is projected as the product of 

its lagged value and the growth rate for WE. TE is adjusted by two multiplicative factors due 

to differences between E and TE over the recent historical period. The first factor accounts 

for the difference in growth between N and P between the last historical value for TE and the 

last historical value for E. The second factor adjusts the model estimate to the value of our 

most recent historical year, and our latest estimate based on partial quarterly data for that 

year. 

Equation 2.3.3 - Noncovered Employment (NCE) 

NCE is disaggregated by age and gender. 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 2013, about 28 and 4 percent of S&L employment (and 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 2030. S&L employment not covered 

under OASDI is projected to grow at about the same rate as the labor force.

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 

72
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.

Underground Economy Workers - Set to the at-any-time employed in the other-than-LPR

population who have no reported earnings and therefore are part of the underground 

economy (i.e., TEO_UND). 

Foreign Students and Exchange Visitors 

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 

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 increases.

Equation 2.3.10 - Ratio of Covered Wages (RWSC) 

RWSC is disaggregated by the following sectors: Federal Civilian government, Federal 

73
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. 

Hence, the RWSC for the Federal civilian employment is defined as the ratio of wages for 

employment under FERS to total Federal civilian wages. 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 be constant over 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. 

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.

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 the average wage for 

employees with any wages (covered and noncovered) posted to the MEF (AWS_MEF). Total 

wages posted to the MEF (WS_MEF) is equal to WSC less wages posted to the ESF plus any 

non-OASDI covered wages posted to the MEF. Similarly, the total number of employees 

with any wages posted to the MEF (WSW_MEF) is equal to WSW less employees posted 

only to the ESF plus any employees with no OASDI covered wages posted to the MEF. 

Equation 2.3.18 - OASDI Taxable Maximum (TAXMAX) 

By law, the growth in the AWI is used to increase the TAXMAX.

74
2.4. Effective TAXABLE PAYROLL (TAXPAY) 

2.4.a. Overview

TAXPAY estimates annual OASDI taxable earnings values including total employee taxable 

wages (WTEE), total employer taxable wages (WTER), and taxable self-employment income 

(SET). By law, each individual is required to pay the employee share of OASDI tax on wages 

from all covered jobs and the self-employment tax from self-employment income up to the 

TAXMAX. Each employer is required to withhold the employee share of the OASDI tax on the 

wages of each worker up to the TAXMAX, as well as paying the identical employer share. If an 

employee works more than one covered wage job and the sum of all covered wages exceeds the 

TAXMAX, the employee is due a refund. The employers involved are not due the refund. Hence, 

WTER is greater than WTEE. The difference (i.e., WTER less WTEE) is defined as multiemployer refund wages (MER). Individuals with covered wage employment who are also selfemployed only owe taxes on their self-employment income to the extent that it does not exceed 

the TAXMAX after being added to the individual’s covered wages. 

TAXPAY estimates the annual OASDI effective taxable payroll (ETP) using the components 

discussed above. 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 selfemployment 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.

The components of ETP 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 ratio of MER to WSC. The self-employment 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) 

75
In order to conform to the Trustees’ assumption that the ratio of ETP to the sum of WSC and 

CSE_TOT is 0.825 in the final short range year (see below), TAXPAY solves equations 2.4.1 

through 2.4.8 iteratively, altering the trend adjustment on RWTEE until the assumed ratio is 

reached.

2.4.b. Input Data

1. Trustees Assumptions 

The Board of Trustees of the OASDI Trust Funds assumes that the ratio of effective OASDI 

taxable payroll to covered earnings for the final calendar year of the short-range period (2030) is 

0.825. 

Data used to obtain values input directly to model 

2. 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. 

3. 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 in estimating OASDI taxable wages for 1951 through 1977. 

4. Data for taxable wages and self-employment income for 1978 on and total 

OASDI taxable earnings for 1951 on from the quarterly EPOXY Report, provided 

by OS. The data currently used in subprocess 2.4 are the amounts of OASDI 

taxable earnings, wages, and self-employment income and amounts of multiemployer excess wages. 

5. Data obtained from the Quarterly Trust Fund Letter (QTFL), 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 income and selfreported tips since the prior QTFL. The wage data are for years 1978 to the most 

recent year available and the self-employment income data for years 1951 to the 

most recent year available. 

Long-Range OASDI Projection Data 

Historical and projected data from Section 2.3 are used as inputs. 

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 consisting of four components. The raw estimate 

for RWTEE is dependent on the distribution of workers by wage interval, the RELMAX, 

76
RTP, the age-gender distribution of wage workers, a time trend adjustment, and a base-year 

error adjustment. The projected distribution of workers by wage interval is an average (or 

amalgam) distribution over the 2000 through 2018 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 leads to a lower RWTEE. The change in the projected RWTEE due 

to the change in the age-gender distribution of wage workers is calculated by allowing 

employment by age and gender to change while holding taxable ratios (and average covered 

wages) by age and gender 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 

base-year error adjustment starts with the value obtained by subtracting the estimated value 

of RWTEE for the latest historical (or base) year from the actual value and phases this 

amount out linearly over the ten years of the short-range projection period.

Equation 2.4.2 - Employee Taxable Wages (WTEE) 

WTEE is computed by multiplying the ratio of taxable employee wages to covered wages by 

the level of covered wages. 

Equation 2.4.3 - Multi-Employer Refund Wage Ratio (RMER) 

The RMER is functionally related to the RWTEE. As RWTEE approaches one, 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.

RMER is assumed to remain constant in years after the short-range projection period. 

Equation 2.4.4 - Multi-Employer Refund Wages (MER) 

MER is computed by multiplying the ratio of multi-employer refund wages to covered wages 

by the level of covered wages. 

Equation 2.4.5 - Employer Taxable Wages (WTER) 

WTER is computed by adding employer taxable wages to multi-employer refund wages. 

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. 

77
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 2015 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-employment income) ratio for CMB_TOT is 

projected based on the 2015distribution 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 the sum of taxable self-employment 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-gender distribution of 

workers, and a 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 2.4.7 - Taxable Self-Employment Income (SET)

SET is computed by multiplying the self-employment income taxable ratio by the level of 

covered self-employment income.

Equation 2.4.8 – Effective Taxable Payroll (ETP)

ETP is computed by adding employer taxable wages and taxable self-employment income 

and subtracting from that total one-half of multi-employer refund wages. (Only employees 

can obtain refunds of excess taxes withheld in multi-employer refund wage cases.) 

As noted above, in order to meet the Trustees’ assumption that the ratio of ETP to total 

78
covered earnings is 0.825 in the last year of the short-range period, equations 2.4.1 through 

2.4.8 are solved repeatedly with changes to the time-trend adjustment in equation 2.4.1 until 

the ratio is obtained.

79
2.5. REVENUES 

2.5.a. Overview

Over the short-range projection horizon (i.e., first 10 years), REVENUES computes tax liabilities 

from wages and self-employment income, as well as the amount of taxes to be transferred from 

the trust funds to the general fund of the Treasury due to multi-employer refund wages. In 

Equation 2.5.1, WTL is the product of taxable wages and the combined OASDI employeeemployer tax rate (TRW). In Equation 2.5.2, SEL is the product of SET and the OASDI selfemployed tax rate (TRSE). In Equation 2.5.3, MERL is the product of MER and the OASDI 

employee tax rate (TRWEE).

WTL = WTER * TRW (2.5.1) 

SEL = SET * TRSE (2.5.2) 

MERL = MER * TRWEE (2.5.3) 

Also over the short-range horizon, REVENUES decomposes WTL into quarterly wage tax 

liabilities (WTLQ), then to quarterly wage tax collections (WTLQC). REVENUES also 

decomposes SEL into quarterly self-employment income tax collections (SELQC).

WTLQ = WTLQ(·) (2.5.4) 

WTLQC = WTLQC(·) (2.5.5) 

SELQC = SELQC(·) (2.5.6) 

When determining the amount of payroll tax collections for the year, REVENUES subtracts the 

amount MERL from the sum of the WTLQC amounts. 

 

Finally, over the first two projected quarters, REVENUES estimates of WTLQC and SELQC are 

replaced with ones from the most recent OMB FY Budget.

2.5.b. Input Data

Data used to obtain values input directly to model

1. Data obtained from ORES as tabulations of quarterly Form 941 data. Data currently used 

are the OASDI, HI, and income taxable wages by sector (Federal Civilian, military, farm, 

and State and Local) 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. 

2. Data obtained from quarterly IRS Form 941 files, provided by OS. Data currently used 

are the OASDI and HI taxable wages for 1978 to the most recent year available. The 

80
OASDI data include separate amounts for tips and for agricultural wages. 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 total and farm taxable wages for the most recent historical years. 

3. Data from the DB2 database named MCWHS, maintained by Office of Systems. This 

database contains a table with MEF detail records for SSNs in the 1% CWHS sample. 

OCACT uses the table, in conjunction with sector information from the employeeemployer and IRS Form 941 files described in items 11 and 12 of section 2.3.b, to 

produce estimates of OASDI and HI taxable wages for the Federal Civilian, military, and 

State and Local government sectors. 

Values input directly to model

Historical and projected data from Sections 2.1, 2.2, and 2.3 are used as input. Data for the 

following variables have final year of 2100. Each variable is shown with the starting year of 

the data. 

4. ADDSETREEOD Total add factor to OASDI taxable to covered

 self-employment income ratio, 2015 

5. ADDWSTREEOD Total add factor to OASDI taxable to covered 

 wage ratio, 2015 

6. ADDWSTREEODTREND Component of total add factor to OASDI taxable 

 to covered wage ratio due to trend in ratio, 2015 

7. AIW Average wage for indexing ($), 1971 

8. AWSCFM Average covered wage for farm workers ($), 1971 

9. AWSCML Average covered wage for military ($), 1971 

10. DMWCHI Deemed military wage credits for HI ($ millions),

1983 

11. DMWCOD Deemed military wage credits for OASDI ($

millions), 1983 

12. ECFCHO Number of HI-only covered Federal Civilian 

 workers (millions), 1983 

13. ECFCOD Number of OASDI covered Federal Civilian 

 workers (millions), 1983 

14. ECHITOT Number of HI covered workers (millions), 1987 

15. ECSEHI Number of HI covered self-employed workers 

 (millions), 1988 

16. ECSENOMAX Number of covered self-employed workers if no 

 taxable maximum (millions), 1988

17. ECSEO Number of OASDI covered self-employed only

 workers (millions), 1981 

18. ECSEOD Number of OASDI covered self-employed 

 workers (millions), 1981 

19. ECSLNOIS Number of non-OASDI covered State and Local 

81
 workers including students (millions), 1983 

20. ECSLP91 Number of State and Local workers covered 

 under OASDI under pre-1991 law (millions), 1983 

21. ECSLNRP Number of OASDI covered State and Local 

 workers with no retirement plan (millions), 1983

22. ECSLOD Number of OASDI covered State and Local 

workers (millions), 1983 

23. ECWSHI Number of HI covered wage workers (millions),

 1981 

24. ECWSOD Number of OASDI covered wage workers 

(millions), 1981 

25. ECWSOD_MEF Number of OASDI covered wage workers on the 

 Master Earnings File (MEF) in millions, 1981 

26. ECWSOD(sex, age)_MEF Number of OASDI covered wage workers on the 

 Master Earnings File (MEF) in millions by sex

 (M/F) and age group (Under 16, 16-19, 20-24, 

25-29, ..., 60-64, 65-69, 70 and over (millions), 

1981 

27. ESLCG Number of State and Local workers not covered

under HI (millions), 1983

28. ESLSTUD Number of noncovered students at public schools 

employed by their school (millions), 1983 

29. GAPLAG Ratio of real to potential GDP (units), 1971

30. RTP Ratio of real to potential GDP (units), 1971

31. RU Civilian unemployment rate (percent), 1971 

32. SEECCMB Self-employed earnings of all SE workers who

 also earned wages in same year ($ millions), 1991 

33. SEECHI HI covered self-employed earnings ($ millions), 

 1991 

34. SEECNOMAX Covered self-employed earnings if no taxable 

maximum ($ millions), 1991

35. SEECOD OASDI covered self-employed earnings 

($ millions), 1991 

36. SEECOD_OLD OASDI covered self-employed earnings 

excluding self-employed earnings of workers with 

covered wages greater than or equal to the 

OASDI taxable maximum ($ millions), 1971

37. SEETODCMB OASDI taxable self-employment earnings of 

 combination workers ($ billions), 1995 

38. SEETODEXOG Total OASDI taxable self-employment earnings 

 ($ millions), 1995 

39. SEETODSEO OASDI taxable self-employment earnings of self- 

 employed only workers ($ billions), 1995 

40. TAXMAXHI HI taxable maximum ($) – 0 indicates no

maximum, 1971 

41. TAXMAXOD OASDI taxable maximum ($), 1971 

82
42. TCFCD Proportion of annual Federal Civilian wages 

earned in each quarter (units), 1971 

43. TCMD Proportion of annual military wages earned in 

 each quarter (units), 1971 

44. TCPD Proportion of annual private sector wages earned 

in each quarter (units), 1971 

45. TCSLD Proportion of annual State and Local wages 

earned in each quarter (units), 1971 

46. TETODCMB Total OASDI taxable earnings of combination

workers ($ millions), 1995 

47. WSCCMB Wages earned in same year by all SE workers

 with both types of earnings ($ millions), 1991 

48. WSCFCHO HI Covered wages of Federal Civilian HI-only

workers ($ millions), 1983 

49. WSCFCOD OASDI Covered wages of Federal Civilian

workers ($ millions), 1971 

50. WSCFM Covered wages of farm workers ($ millions), 1971 

51. WSCHI HI covered wages ($ millions), 1971 

52. WSCML Covered wages of members of the Armed Forces 

 ($ millions), 1971 

53. WSCOD OASDI covered wages ($ millions), 1971 

54. WSCOD_SF OASDI covered wages on the Suspense File 

 ($ millions), 1971 

55. WSCPHH Covered wages of private household workers 

 ($ millions), 1971 

56. WSCPNF Covered wages of private nonfarm workers 

 ($ millions), 1971 

57. WSCSLHI HI covered State and Local wages ($ millions), 

 1971 

58. WSCSLNRP Covered wages of State and Local workers with

 no retirement plan ($ millions), 1991 

59. WSCSLOD OASDI covered State and Local wages 

($ millions), 1971 

60. WSCSLP91 Wages of State and Local workers covered under 

 OASDI under pre-1991 law ($ millions), 1971 

61. WSD Total NIPA wages ($ millions), 1971 

62. WSP Total NIPA private sector wages ($ millions),

 1971 

63. WSS Total NIPA compensation ($ millions), 1971 

64. WSSLCG Wages of State and Local workers not covered 

under HI ($ millions), 1983 

65. WSSLNOIS Wages of non-OASDI covered State and Local

workers including students ($ millions), 1983 

66. WSSLSTUD Wages of noncovered students at public schools 

 employed by their school ($ millions), 1983 

67. WSMEREFODEXOG OASDI multi-employer refund wages 

83
 ($ millions), 2014 

68. WSTEEODEXOG Total OASDI taxable wages ($ millions), 2015 

69. WSTRRTPHI Wages of railroad workers taxable under HI 

 ($ millions), 1971 

70. WSTTIPSSR Taxable tips reported by tip earner instead of 

employer ($ millions), 1978 

71. WTWPO Proportion of annual Postal Service wages earned

in each quarter (units), 1971 

Other direct input data 

72. FICA, SECA, and Federal Employer tax transfers by month from the Department of the 

Treasury for years 1984 to 2020. 

73. FICA, SECA, and Federal Employer tax transfers by month from the Department of the 

Treasury for January 2021 through May 2021. 

74. FICA and SECA tax transfers by month split by liability period from the Department of 

the Treasury for January 1984 to June 2021. 

75. Historical annual HI taxable self-employment earnings for 1983 to 1993. (Values from 

1994 on are equal to HI covered earnings and are obtained from subprocess COV.) Does 

not affect SOSI

76. Historical annual OASDI taxable self-employment earnings for 1971 to 2019. 

77. Historical annual HI multi-employer refund wages for 1983 to 1993 (Values for 1994 on 

are zero because of the elimination of the HI taxable maximum.) Does not affect SOSI

78. Historical annual OASDI multi-employer refund wages for 1971 to 2019. 

79. Historical annual HI single-employer refund wages for 1991 to 1993 (No values prior to 

1991 because HI taxable maximum equals OASDI taxable maximum for those years. 

Values for 1994 on are zero because of the elimination of the HI taxable maximum.) 

Does not affect SOSI

80. Historical annual OASDI single-employer refund wages for 1971 to 2019. 

81. Historical annual HI taxable wages for 1983 to 1993. (Values from 1994 on are equal to 

HI covered wages and are obtained from subprocess COV.) Does not affect SOSI

82. Historical annual OASDI taxable wages for 1971 to 2019. 

83. Historical annual HI-only taxable Federal Civilian wages for 1983 to 1993. (Values 

from 1994 on are equal to HI-only covered wages and are obtained from subprocess 

COV.) Does not affect SOSI 

84
84. Historical annual OASDI taxable Federal Civilian wages for 1983 to 2019. 

85. Historical annual HI taxable Federal Civilian wages for 1983 to 1993. (Values from 

1994 on are equal to HI covered wages and are obtained from subprocess COV.) Does 

not affect SOSI

86. Historical annual OASDI taxable farm sector wages for 1971 to 2019. 

87. Historical annual HI taxable farm sector wages for 1991 to 1993. (Values from 1994 on 

are equal to HI covered wages and are obtained from subprocess COV.) Does not affect 

SOSI

88. Historical annual OASDI taxable military sector wages for 1971 to 2019. 

89. Historical annual HI taxable military sector wages for 1991 to 1993. (Values from 1994 

on are equal to HI covered wages and are obtained from subprocess COV.) Does not 

affect SOSI

90. Historical annual OASDI taxable State and Local government sector wages for 1971 to 

2019. 

91. Historical annual HI taxable State and Local government sector wages for 1983 to 1993. 

(Values from 1994 on are equal to HI covered wages and are obtained from subprocess 

COV.) Does not affect SOSI

92. Historical annual OASDI taxable tips for employees as reported by employers for 1971 

to 2019. 

93. Historical and projected annual OASDI taxable tips for employers as reported by 

employers for 1980 to 1987. (No tips were taxable for employers prior to 1980. 

Employer taxable tips equal employee in 1988 and after.) 

94. Quarterly OASDI and HI taxable wages for calendar year 2020. (These values do not 

add up to the annual values as described above. These quarterly distributions are used to 

split the annual 2020 values.) HI values do not affect SOSI

95. Historical FICA and SECA appropriation adjustments for OASI, DI, and HI by month 

for 1968 to 2020. HI values do not affect SOSI

96. Actual FICA and SECA appropriation adjustments for OASI, DI, and HI for March 

2021 and preliminary values for June 2021. HI values do not affect SOSI

97. Historical FICA revenues for OASI, DI, and HI by quarter for 1984 to 2020. HI values 

do not affect SOSI

85
98. Historical SECA revenues for OASI, DI, and HI by quarter for 1984 to 2020. HI values 

do not affect SOSI

99. Historical Federal Employer revenues for OASI, DI, and HI by quarter for 1984 to 2020. 

HI values do not affect SOSI

100. Historical Deposits by States for OASI, DI, and HI by quarter for 1984 to 2020. (This 

is an obsolete type of revenue which has had no valid non-zero amount since 2002.) 

HI values do not affect SOSI

101. Historical single-employer refunds of excess taxes for OASI, DI, and HI by quarter for 

1984 to 2020. HI values do not affect SOSI

102. Historical FICA credits for OASI and DI by quarter for 1984 to 2020. 

103. Historical SECA credits for OASI, DI, and HI by quarter for 1984 to 2020. HI values 

do not affect SOSI

104. Historical multi-employer refunds of excess taxes for OASI, DI, and HI by month for 

1968 to 2020. HI values do not affect SOSI

Miscellaneous historical covered employment and earnings data: 

105. HI Covered self-employed workers for 1986 to 1987 – variable ECSEHI. Does not 

affect SOSI

106. Number of OASDI covered wage workers for 1971 to 1980 – variable ECWSOD. 

107. HI covered self-employment earnings for 1971 to 1990 – variable SEECHI. Does not 

affect SOSI

108. Covered self-employment earnings if there were no taxable maximum for 1971 to 

1990 – variable SEECNOMAX. 

109. OASDI covered self-employment earnings for 1971 to 1990 – variable SEECOD. 

Miscellaneous historical and fixed projected data: 

110. Quarterly distribution of annual OASDI taxable farm wages for 1971 to 2100 – 

variable TTFMD. 

111. Quarterly OASDI covered private nonfarm sector wages for 1971 to 1975 – variable 

QWSCPNF. 

112. Quarterly OASDI covered State and Local government sector wages for 1971 to 1977 

– variable QWSCSLOD. 

86
113. Quarterly OASDI covered military sector wages for 1971 to 1977 – variable 

QWSCML. 

114. Quarterly OASDI covered Federal Civilian sector wages for 1971 to 1977 – variable 

QWSCFCOD. 

115. Quarterly OASDI taxable private nonfarm sector wages for 1971 to 1977 – variable 

QWSTPNFEEOD. 

116. Quarterly OASDI taxable State and Local government sector wages for 1971 to 

1980Q1 – variable QWSTSLEEOD. 

117. Quarterly OASDI taxable military sector wages for 1971 to 1977 – variable 

QWSTMLEEOD. 

118. Quarterly OASDI taxable Federal Civilian sector wages for 1971 to 1977 – variable 

QWSTFCEEOD. 

119. Quarterly OASDI taxable farm sector wages for 1971 to 1980Q2 – variable 

QWSTFMEEOD. 

120. OASDI employee, employer, and self-employment tax rates from 1971 to 2100. These 

contribution rates are set according to the Social Security Act of 1935 and subsequent 

changes to the Act and to the Internal Revenue Code. The rates are updated when 

legislation mandates a change. The rates were unchanged from 2000 to 2015. The 

Bipartisan Budget Act of 2015 reallocated the OASI and DI employee-employer and 

self-employment tax rates for years 2016 through 2018. The OASDI rates remain the 

same and the rates revert to the ones in effect for 2000 to 2015 in 2019 and thereafter – 

variables RATEEO, RATEED, RATEEH, RATERO, RATERD, RATERH, RATSEO, 

RATSED, RATSEH. 

121. Annual OASDI employee credit tax rate for 1984 – variable CRATEEOD. 

122. Annual OASDI self-employment credit tax rates for 1984 to 1989 – variable 

CRATSEODH. 

123. Annual reductions in OASDI employee and self-employment tax rates due to the 

payroll tax holiday for 2011 and 2012. 

124. Annual trend variable for taxable to covered wage ratio calculation for 1971 to 2100 – 

variable TREND. (No longer used) 

125. Annual trend variable for taxable to covered self-employment earnings ratio 

calculation for 1971 to 2100 – variable SETRND. (No longer used) 

126. Average OASDI covered wages by age groups and gender for 1996. 

87
127. Ratio of OASDI taxable to covered wages by age groups and gender for 1996. 

128. Corrections to prior FICA appropriation adjustments made in March 2000. 

129. Projected single-employer refund wages by calendar year for 2020 through 2031. 

130. Projected ratio of OASDI taxable tips for the current year to the prior year for 2020 

through 2031. 

131. FICA and SECA appropriation adjustments for OASI and DI related to HIRE Act of 

2010. 

132. Estimated quarterly transfers provided to OTA for calendar years 2000 through 2021, 

2nd quarter. 

133. Data needed to compute estimates of the ACA’s additional HI tax effective starting 

2013. Does not affect SOSI

134. Estimated tax transfers by liability period for the ACA’s additional HI tax for 2013Q1 

through 2021Q2 used in computing adjustments. Does not affect SOSI

135. Estimated tax transfers for the ACA’s additional HI tax for 2013Q1 through 2021Q2 

used in computing adjustments. Does not affect SOSI

136. Estimated SECA appropriation adjustments for OASI, DI, and HI in December 2022. 

HI values do not affect SOSI

137. Estimated FICA and SECA appropriation adjustments for OASI, DI, and HI for 

differences between actual liabilities for 2021 transferred in January through June 

2021 and estimated liabilities in Trustees Report. HI values do not affect SOSI

2.5.c. Development of Output 

Equation 2.5.1 – Annual Covered Wage Tax Liabilities (WTL) 

WTL is computed by multiplying the combined OASDI employee-employer tax rate by the 

OASDI taxable wages input from the PAYROLL subprocess. REVENUES estimates annual 

taxable wages for the Federal Civilian, Federal Military, S&L, Private Household, Farm, 

Self-reported Tips, and residual Private Nonfarm sectors. Liabilities by sector are computed 

by multiplying the combined OASDI employee-employer tax rate by OASDI taxable wages 

for each sector.

Equation 2.5.2 – Annual Self-Employed Income Tax Collections (SEL) 

SEL is computed by multiplying the OASDI self-employment tax rate by the OASDI self88
employment taxable income input from the PAYROLL subprocess. 

Equation 2.5.3 – Annual Multi-Employer Refund Wage Liabilities (MERL) 

MERL is computed by multiplying the OASDI employee tax rate by the OASDI multiemployer refund wages input from the PAYROLL subprocess. 

Equation 2.5.4 – Quarterly Covered Wage Tax Liabilities (WTLQ) 

Total WTLQ is summed from sector components that include Federal Civilian, Federal 

Military, S&L, Private Household, Farm, Self-reported Tips, and residual Private Nonfarm. 

Sector WTLQs are determined by computing ratios of quarterly to annual liabilities for each 

quarter. These are calculated for the Private Nonfarm, S&L, Federal Civilian and Military 

sectors. 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 for the other sectors are 

assumed to be constants over the projection horizon. 

Equation 2.5.5 - Quarterly Wage Tax Collections (WTLQC) 

Employers incur tax liabilities when they pay wages to their employees. These liabilities are 

required to be deposited in the general fund of 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 and by the middle of the following month. 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 are 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 are set equal to 

their respective WTLQ since tax liabilities for the two sectors are considered collected 

immediately. The WTLQC for Farm is also set equal to its WTLQ, due in part to the fact that 

farms report tax liabilities annually. For the S&L and Private Nonfarm sectors, the WTLQC 

amount is computed by adding the product of WTLQ and the proportion of WTLQ that 

should be deposited in the same quarter in which the wages were paid to the WTLQ from the 

previous quarter which was not deposited in that quarter. Each quarter’s 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). Separate proportions are estimated for the S&L and 

the Private Nonfarm sector because of the large difference in wage distributions between 

them.

Equation 2.5.6 - Quarterly Self-Employed Income Tax Collections (SELQC) 

89
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 self-employment 

income is only reported on an annual basis (on IRS Form 1040 Schedule SE). 

SEL for a particular calendar year are 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 selfemployed workers to deposit estimated tax liabilities four times a year (January, April, June, 

and September) and to make up any shortfall when filing Federal income tax returns in the 

following year. The program computes the collection distribution ratios based on the OTA 

estimates, which are input to the program. The ratios for projected years are determined by 

averaging the ratios for all years 1997 through the most recent year for which the OTA 

estimates are complete.

90
Appendix 2-1 

Equations

2.1 U.S. Employment (USEMP) 

UNEMPLOYMENT RATES, PRELIMINARY

[Full estimation details for these equations are available upon request.]

MALE

RM1617_P = RM1617_P(-1) + [ -31.52172*D(RTP) - 24.81520*D(RTP(-1)) - 14.72058*D(RTP(-2)) 

 - 31.33966*D(RTP(-3)) ]

RM1819_P = RM1819_P(-1) + [ -56.74492*D(RTP) - 24.87344*D(RTP(-1)) - 35.84160*D(RTP(-2)) 

 - 0.70217*D(RTP(-3)) ]

RM2024_P = RM2024_P(-1) + [ -52.29093*D(RTP) - 19.73984*D(RTP(-1)) - 15.03600*D(RTP(-2)) 

 - 13.47522*D(RTP(-3)) ]

RM2529_P = RM2529_P(-1) + [ -39.13841*D(RTP) - 24.46060*D(RTP(-1)) - 17.51574*D(RTP(-2)) 

 - 0.81036*D(RTP(-3)) ]

RM3034_P = RM3034_P(-1) + [ -23.76350*D(RTP) - 22.76416*D(RTP(-1)) - 8.88851*D(RTP(-2)) 

 - 11.24022*D(RTP(-3)) ]

RM3539_P = RM3539_P(-1) + [ -28.26931*D(RTP) - 9.02630*D(RTP(-1)) - 14.93420*D(RTP(-2)) 

 - 9.03795*D(RTP(-3)) ]

RM4044_P = RM4044_P(-1) + [ -18.16004*D(RTP) - 23.06573*D(RTP(-1)) - 9.94244*D(RTP(-2)) 

 - 4.34840*D(RTP(-3)) ]

RM4549_P = RM4549_P(-1) + [ -22.41979*D(RTP) - 16.69081*D(RTP(-1)) - 11.82097*D(RTP(-2)) 

 - 1.04890*D(RTP(-3)) ]

RM5054_P = RM5054_P(-1) + [ -23.03219*D(RTP) - 11.75062*D(RTP(-1)) - 8.80293*D(RTP(-2)) 

 - 10.36992*D(RTP(-3)) ]

RM5559_P = RM5559_P(-1) + [ -25.47548*D(RTP) - 14.31543*D(RTP(-1)) - 6.15894*D(RTP(-2)) 

 - 1.00513*D(RTP(-3)) ]

RM6064_P = RM6064_P(-1) + [ -2.10594*D(RTP) - 17.27891*D(RTP(-1)) - 4.87379*D(RTP(-2)) 

 - 15.36088*D(RTP(-3)) ]

RM6569_P = RM6569_P(-1) + [ -13.51567*D(RTP) - 2.41017*D(RTP(-1)) - 17.92290*D(RTP(-2)) 

 + 1.48482*D(RTP(-3)) ] 

RM7074_P = RM7074_P(-1) + [ -9.76394*D(RTP) - 7.44785*D(RTP(-1)) - 15.23719*D(RTP(-2)) 

 + 7.17596*D(RTP(-3)) ]

RM75O_P = RM75O_P(-1) + [ 2.47935*D(RTP) - 27.63188*D(RTP(-1)) + 8.35078*D(RTP(-2)) 

 - 3.11058*D(RTP(-3)) ]

FEMALE

RF1617_P = RF1617_P(-1) + [ -13.33857*D(RTP) - 1.17140*D(RTP(-1)) - 69.40326*D(RTP(-2)) 

 + 9.53209*D(RTP(-3)) ]

RF1819_P = RF1819_P(-1) + [ -42.47852*D(RTP) - 11.03359*D(RTP(-1)) - 0.89011*D(RTP(-2)) 

 - 33.04213*D(RTP(-3)) ]

RF2024_P = RF2024_P(-1) + [ -23.03635*D(RTP) - 17.33653*D(RTP(-1)) - 10.59182*D(RTP(-2)) 

 - 7.73281*D(RTP(-3)) ]

RF2529_P = RF2529_P(-1) + [ -15.61692*D(RTP) - 12.87215*D(RTP(-1)) - 15.16923*D(RTP(-2)) 

 - 3.55380*D(RTP(-3)) ]

RF3034_P = RF3034_P(-1) + [ -14.71130*D(RTP) - 6.25917*D(RTP(-1)) - 18.72755*D(RTP(-2)) 

 - 2.42329*D(RTP(-3)) ]

RF3539_P = RF3539_P(-1) + [ -19.78502*D(RTP) - 7.31538*D(RTP(-1)) - 8.69549*D(RTP(-2)) 

 - 5.45418*D(RTP(-3)) ]

91
RF4044_P = RF4044_P(-1) + [ -8.62310*D(RTP) - 10.87758*D(RTP(-1)) - 6.86064*D(RTP(-2)) 

 - 4.08914*D(RTP(-3)) ]

RF4549_P = RF4549_P(-1) + [ -9.41764*D(RTP) - 14.45854*D(RTP(-1)) - 0.04687*D(RTP(-2)) 

 - 4.15977*D(RTP(-3)) ]

RF5054_P = RF5054_P(-1) + [ -11.37880*D(RTP) - 4.16526*D(RTP(-1)) - 12.32611*D(RTP(-2)) 

 - 5.79074*D(RTP(-3)) ]

RF5559_P = RF5559_P(-1) + [ -9.11833*D(RTP) - 2.89447*D(RTP(-1)) - 17.40333*D(RTP(-2)) 

 + 0.37368*D(RTP(-3)) ]

RF6064_P = RF6064_P(-1) + [ -21.93195*D(RTP) + 2.80763*D(RTP(-1)) - 11.61244*D(RTP(-2)) 

 - 1.60187*D(RTP(-3)) ]

RF6569_P = RF6569_P(-1) + [ 6.59281*D(RTP) + 5.16431*D(RTP(-1)) - 35.27026*D(RTP(-2)) 

 + 8.58449*D(RTP(-3)) ]

RF7074_P = RF7074_P(-1) + [ -4.25967*D(RTP) + 10.26851*D(RTP(-1)) - 19.18862*D(RTP(-2)) 

 + 6.93390*D(RTP(-3)) ]

RF75O_P = RF75O_P(-1) + [ -40.60841*D(RTP) + 42.55417*D(RTP(-1)) - 29.60376*D(RTP(-2)) 

 - 14.09088*D(RTP(-3)) ]

UNEMPLOYMENT RATES, AGE-GENDER ADJUSTED, PRELIMINARY

RUM_ASA_P = (RM1617_P * LM1617_BY + RM1819_P * LM1819_BY + RM2024_P * LM2024_BY 

+ RM2529_P * LM2529_BY + RM3034_P * LM3034_BY + RM3539_P * LM3539_BY 

+ RM4044_P * LM4044_BY + RM4549_P * LM4549_BY + RM5054_P * LM5054_BY 

+ RM5559_P * LM5559_BY + RM6064_P * LM6064_BY + RM6569_P * LM6569_BY 

+ RM7074_P * LM7074_BY + RM75O_P * LM75O_BY)/ LCM_BY

RUF_ASA_P = (RF1617_P * LF1617_BY + RF1819_P * LF1819_BY + RF2024_P * LF2024_BY 

+ RF2529_P * LF2529_BY + RF3034_P * LF3034_BY + RF3539_P * LF3539_BY 

+ RF4044_P * LF4044_BY + RF4549_P * LF4549_BY + RF5054_P * LF5054_BY 

+ RF5559_P * LF5559_BY + RF6064_P * LF6064_BY + RF6569_P * LF6569_BY 

+ RF7074_P * LF7074_BY + RF75O_P * LF75O_BY)/ LCF_BY

RU_ASA_P = (RUM_ASA_P * LCM_BY + RUF_ASA_P * LCF_BY) / LC_BY

UNEMPLOYMENT RATES

MALE

RM1617= RM1617_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM1819= RM1819_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM2024= RM2024_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM2529= RM2529_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM3034= RM3034_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM3539= RM3539_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM4044= RM4044_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM4549= RM4549_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM5054= RM5054_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM5559= RM5559_P * (1 + RU_ASA_ADJ / RU_ASA_P) 

RM6064= RM6064_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM6569= RM6569_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM7074= RM7074_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RM75O = RM75O_P * (1 + RU_ASA_ADJ / RU_ASA_P)

FEMALE

RF1617= RF1617_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF1819= RF1819_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF2024= RF2024_P * (1 + RU_ASA_ADJ / RU_ASA_P)

92
RF2529= RF2529_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF3034= RF3034_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF3539= RF3539_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF4044= RF4044_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF4549= RF4549_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF5054= RF5054_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF5559= RF5559_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF6064= RF6064_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF6569= RF6569_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF7074= RF7074_P * (1 + RU_ASA_ADJ / RU_ASA_P)

RF75O = RF75O_P * (1 + RU_ASA_ADJ / RU_ASA_P)

UNEMPLOYMENT RATES, AGE-GENDER ADJUSTED

RUM_ASA = (RM1617 * LM1617_BY+ RM1819 * LM1819_BY + RM2024 * LM2024_BY + RM2529 * LM2529_BY 

 + RM3034 * LM3034_BY + RM3539 * LM3539_BY + RM4044 * LM4044_BY + RM4549 * LM4549_BY 

 + RM5054 * LM5054_BY + RM5559 * LM5559_BY + RM6064 * LM6064_BY + RM6569 * LM6569_BY 

 + RM7074 * LM7074_BY + RM75O * LM75O_BY)/ LCM_BY

RUF_ASA = (RF1617 * LF1617_BY + RF1819 * LF1819_BY + RF2024 * LF2024_BY + RF2529 * LF2529_BY 

 + RF3034 * LF3034_BY + RF3539 * LF3539_BY + RF4044 * LF4044_BY + RF4549 * LF4549_BY 

 + RF5054 * LF5054_BY + RF5559 * LF5559_BY + RF6064 * LF6064_BY + RF6569 * LF6569_BY 

 + RF7074 * LF7074_BY + RF75O * LF75O_BY)/ LCF_BY

RU_ASA = (RUM_ASA * LCM_BY + RUF_ASA * LCF_BY) / LC_BY

UNEMPLOYMENT RATES, FULL EMPLOYMENT DIFFERENTIALS

MALE

DRM1617_FE = -31.52172*(1 - RTP) - 24.81520*(1 - RTP(-1)) - 14.72058*(1 - RTP(-2)) - 31.33966*(1 - RTP(-3)) 

DRM1819_FE = -56.74492*(1 - RTP) - 24.87344*(1 - RTP(-1)) - 35.84160*(1 - RTP(-2)) - 0.70217*(1 - RTP(-3)) 

DRM2024_FE = -52.29093*(1 - RTP) - 19.73984*(1 - RTP(-1)) - 15.03600*(1 - RTP(-2)) - 13.47522*(1 - RTP(-3)) 

DRM2529_FE = -39.13841*(1 - RTP) - 24.46060*(1 - RTP(-1)) - 17.51574*(1 - RTP(-2)) - 0.81036*(1 - RTP(-3)) 

DRM3034_FE = -23.76350*(1 - RTP) - 22.76416*(1 - RTP(-1)) - 8.88851*(1 - RTP(-2)) - 11.24022*(1 - RTP(-3)) 

DRM3539_FE = -28.26931*(1 - RTP) - 9.02630*(1 - RTP(-1)) - 14.93420*(1 - RTP(-2)) - 9.03795*(1 - RTP(-3)) 

DRM4044_FE = -18.16004*(1 - RTP) - 23.06573*(1 - RTP(-1)) - 9.94244*(1 - RTP(-2)) - 4.34840*(1 - RTP(-3)) 

DRM4549_FE = -22.41979*(1 - RTP) - 16.69081*(1 - RTP(-1)) - 11.82097*(1 - RTP(-2)) - 1.04890*(1 - RTP(-3)) 

DRM5054_FE = -23.03219*(1 - RTP) - 11.75062*(1 - RTP(-1)) - 8.80293*(1 - RTP(-2)) - 10.36992*(1 - RTP(-3)) 

DRM5559_FE = -25.47548*(1 - RTP) - 14.31543*(1 - RTP(-1)) - 6.15894*(1 - RTP(-2)) - 1.00513*(1 - RTP(-3)) 

DRM6064_FE = -2.10594*(1 - RTP) - 17.27891*(1 - RTP(-1)) - 4.87379*(1 - RTP(-2)) - 15.36088*(1 - RTP(-3)) 

DRM6569_FE = -13.51567*(1 - RTP) - 2.41017*(1 - RTP(-1)) - 17.92290*(1 - RTP(-2)) + 1.48482*(1 - RTP(-3)) 

DRM7074_FE = -9.76394*(1 - RTP) - 7.44785*(1 - RTP(-1)) - 15.23719*(1 - RTP(-2)) + 7.17596*(1 - RTP(-3)) 

DRM75O_FE = 2.47935*(1 - RTP) - 27.63188*(1 - RTP(-1)) + 8.35078*(1 - RTP(-2)) - 3.11058*(1 - RTP(-3)) 

FEMALE

DRF1617_FE = -13.33857*(1 - RTP) - 1.17140*(1 - RTP(-1)) - 69.40326*(1 - RTP(-2)) + 9.53209*(1 - RTP(-3)) 

DRF1819_FE = - 42.47852*(1 - RTP) - 11.03359*(1 - RTP(-1)) - 0.89011*(1 - RTP(-2)) - 33.04213*(1 - RTP(-3)) 

DRF2024_FE = -23.03635*(1 - RTP) - 17.33653*(1 - RTP(-1)) - 10.59182*(1 - RTP(-2)) - 7.73281*(1 - RTP(-3)) 

DRF2529_FE = -15.61692*(1 - RTP) - 12.87215*(1 - RTP(-1)) - 15.16923*(1 - RTP(-2)) - 3.55380*(1 - RTP(-3)) 

DRF3034_FE = -14.71130*(1 - RTP) - 6.25917*(1 - RTP(-1)) - 18.72755*(1 - RTP(-2)) - 2.42329*(1 - RTP(-3))

DRF3539_FE = -19.78502*(1 - RTP) - 7.31538*(1 - RTP(-1)) - 8.69549*(1 - RTP(-2)) - 5.45418*(1 - RTP(-3))

DRF4044_FE = -8.62310*(1 - RTP) - 10.87758*(1 - RTP(-1)) - 6.86064*(1 - RTP(-2)) - 4.08914*(1 - RTP(-3))

DRF4549_FE = -9.41764*(1 - RTP) - 14.45854*(1 - RTP(-1)) - 0.04687*(1 - RTP(-2)) - 4.15977*(1 - RTP(-3))

DRF5054_FE = -11.37880*(1 - RTP) - 4.16526*(1 - RTP(-1)) - 12.32611*(1 - RTP(-2)) - 5.79074*(1 - RTP(-3))

DRF5559_FE = -9.11833*(1 - RTP) - 2.89447*(1 - RTP(-1)) - 17.40333*(1 - RTP(-2)) + 0.37368*(1 - RTP(-3)) 

DRF6064_FE = -21.93195*(1 - RTP) + 2.80763*(1 - RTP(-1)) - 11.61244*(1 - RTP(-2)) - 1.60187*(1 - RTP(-3)) 

93
DRF6569_FE = 6.59281*(1 - RTP) + 5.16431*(1 - RTP(-1)) - 35.27026*(1 - RTP(-2)) + 8.58449*(1 - RTP(-3)) 

DRF7074_FE = - 4.25967*(1 - RTP) + 10.26851*(1 - RTP(-1)) - 19.18862*(1 - RTP(-2)) + 6.93390*(1 - RTP(-3)) 

DRF75O_FE = - 40.60841*(1 - RTP) + 42.55417*(1 - RTP(-1)) - 29.60376*(1 - RTP(-2)) - 14.09088*(1 - RTP(-3)) 

UNEMPLOYMENT RATES, FULL EMPLOYMENT DIFFERENTIALS

TOTALS

MALE

RM1617_FE = RM1617 + DRM1617_FE

RM1819_FE = RM1819 + DRM1819_FE

RM2024_FE = RM2024 + DRM2024_FE

RM2529_FE = RM2529 + DRM2529_FE

RM3034_FE = RM3034 + DRM3034_FE

RM3539_FE = RM3539 + DRM3539_FE

RM4044_FE = RM4044 + DRM4044_FE

RM4549_FE = RM4549 + DRM4549_FE

RM5054_FE = RM5054 + DRM5054_FE

RM5559_FE = RM5559 + DRM5559_FE

RM6064_FE = RM6064 + DRM6064_FE

RM6569_FE = RM6569 + DRM6569_FE

RM7074_FE = RM7074 + DRM7074_FE

RM75O_FE = RM75O + DRM75O_FE

FEMALE

RF1617_FE = RF1617 + DRF1617_FE

RF1819_FE = RF1819 + DRF1819_FE

RF2024_FE = RF2024 + DRF2024_FE

RF2529_FE = RF2529 + DRF2529_FE

RF3034_FE = RF3034 + DRF3034_FE

RF3539_FE = RF3539 + DRF3539_FE

RF4044_FE = RF4044 + DRF4044_FE

RF4549_FE = RF4549 + DRF4549_FE

RF5054_FE = RF5054 + DRF5054_FE

RF5559_FE = RF5559 + DRF5559_FE

RF6064_FE = RF6064 + DRF6064_FE

RF6569_FE = RF6569 + DRF6569_FE

RF7074_FE = RF7074 + DRF7074_FE

RF75O_FE = RF75O + DRF75O_FE

LABOR FORCE PARTICIPATION RATES (LFPR) 

[Full estimation details for these equations are available upon request.]

MALE LFPR EQUATIONS

MALE 1617 AND 1819

PM1617_P = [ (- 0.00134*RM1617 - 0.00167*RM1617(-1) - 0.00132*RM1617(-2) - 0.00065*RM1617(-3) 

+ 0.00003*RM1617(-4) + 0.00035*RM1617(-5)) 

 - 0.01009 * TR_M1617 + 0.49638 

+ 0.98199 ] / (1 + RM1617DI)

PM1819_P = [ (- 0.00068*RM1819 - 0.00092*RM1819(-1) - 0.00083*RM1819(-2) - 0.00056*RM1819(-3) 

- 0.00025*RM1819(-4) – 0.00002*RM1819(-5)) 

- 0.00780 * TR_M1819 + 0.47128

+ 0.97741 ] / (1 + RM1819DI)

PM1617 = PM1617_P

94
PM1819 = PM1819_P

MALE 20 TO 54, NEVER MARRIED 

PM2024NM_P = [ (- 0.00053*RM2024 - 0.00074*RM2024(-1) - 0.00071*RM2024(-2) - 0.00054*RM2024(-3) 

- 0.00030*RM2024(-4) – 0.00010*RM2024(-5)) 

- 0.00310 * TR_M2024 

+ 1.12658 ] / (1 + RM2024DI)

PM2529NM_P = [ (- 0.00031*RM2529 - 0.00053*RM2529(-1) - 0.00066*RM2529(-2) - 0.00068*RM2529(-3) 

- 0.00058*RM2529(-4) - 0.00036*RM2529(-5)) 

- 0.00091 * TR_M2529 

+ 0.99893 ] / (1 + RM2529DI)

PM3034NM_P = [ (- 0.00001*RM3034 - 0.00018*RM3034(-1) - 0.00040*RM3034(-2) - 0.00058*RM3034(-3) 

- 0.00064*RM3034(-4) - 0.00047*RM3034(-5)) 

+ 0.89877 ] / (1 + RM3034DI)

PM3539NM_P = [ (0.00048*RM3539 + 0.00037*RM3539(-1) – 0.00007*RM3539(-2) - 0.00058*RM3539(-3) 

- 0.00091*RM3539(-4) - 0.00080*RM3539(-5)) 

+ 0.87015 ] / (1 + RM3539DI)

PM4044NM_P = [ (- 0.00018*RM4044 - 0.00026*RM4044(-1) - 0.00027*RM4044(-2) - 0.00022*RM4044(-3) 

- 0.00014*RM4044(-4) – 0.00006*RM4044(-5)) 

+ 0.83848 ] / (1 + RM4044DI)

PM4549NM_P = [ (0.00004*RM4549 - 0.00011*RM4549(-1) - 0.00036*RM4549(-2) - 0.00059*RM4549(-3) 

- 0.00068*RM4549(-4) - 0.00052*RM4549(-5)) 

+ 0.80657 ] / (1 + RM4549DI)

PM5054NM_P = [ (0.00115*RM5054 + 0.00089*RM5054(-1) - 0.00017*RM5054(-2) - 0.00141*RM5054(-3) 

- 0.00220*RM5054(-4) - 0.00194*RM5054(-5)) 

+ 0.77113 ] / (1 + RM5054DI)

MALE 20 TO 54, MARRIED, SPOUSE PRESENT

PM2024MS_P = [ (- 0.00053*RM2024 - 0.00074*RM2024(-1) - 0.00071*RM2024(-2) - 0.00054*RM2024(-3) 

- 0.00030*RM2024(-4) – 0.00010*RM2024(-5)) - 0.00141 * TR_M2024 

+ 1.10245 ] / (1 + RM2024DI)

PM2529MS_P = [ (- 0.00031*RM2529 - 0.00053*RM2529(-1) - 0.00066*RM2529(-2) - 0.00068*RM2529(-3) 

- 0.00058*RM2529(-4) - 0.00036*RM2529(-5)) 

- 0.00048 * TR_M2529 

+ 1.02497 ] / (1 + RM2529DI)

PM3034MS_P = [ (- 0.00001*RM3034 - 0.00018*RM3034(-1) - 0.00040*RM3034(-2) - 0.00058*RM3034(-3) 

- 0.00064*RM3034(-4) - 0.00047*RM3034(-5)) 

+ 0.97980 ] / (1 + RM3034DI)

PM3539MS_P = [ (0.00048*RM3539 + 0.00037*RM3539(-1) – 0.00007*RM3539(-2) - 0.00058*RM3539(-3) 

- 0.00091*RM3539(-4) - 0.00080*RM3539(-5)) 

+ 0.98104 ] / (1 + RM3539DI)

PM4044MS_P = [ (- 0.00018*RM4044 - 0.00026*RM4044(-1) - 0.00027*RM4044(-2) - 0.00022*RM4044(-3) 

- 0.00014*RM4044(-4) – 0.00006*RM4044(-5)) 

+ 0.98178 ] / (1 + RM4044DI)

PM4549MS_P = [ (0.00004*RM4549 - 0.00011*RM4549(-1) - 0.00036*RM4549(-2) - 0.00059*RM4549(-3) 

- 0.00068*RM4549(-4) - 0.00052*RM4549(-5)) 

+ 0.98395 ] / (1 + RM4549DI)

PM5054MS_P = [ (0.00115*RM5054 + 0.00089*RM5054(-1) - 0.00017*RM5054(-2) - 0.00141*RM5054(-3) 

95
- 0.00220*RM5054(-4) - 0.00194*RM5054(-5)) 

+ 0.97763 ] / (1 + RM5054DI)

MALE 20 TO 54, MARRIED, SPOUSE ABSENT

PM2024MA_P = [ (- 0.00053*RM2024 - 0.00074*RM2024(-1) - 0.00071*RM2024(-2) - 0.00054*RM2024(-3) 

- 0.00030*RM2024(-4) – 0.00010*RM2024(-5)) - 0.00441 * TR_M2024 

+ 1.33014 ] / (1 + RM2024DI)

PM2529MA_P = [ (- 0.00031*RM2529 - 0.00053*RM2529(-1) - 0.00066*RM2529(-2) - 0.00068*RM2529(-3) 

- 0.00058*RM2529(-4) - 0.00036*RM2529(-5)) 

- 0.00061 * TR_M2529 

+ 0.98620 ] / (1 + RM2529DI)

PM3034MA_P = [ (- 0.00001*RM3034 - 0.00018*RM3034(-1) - 0.00040*RM3034(-2) - 0.00058*RM3034(-3) 

- 0.00064*RM3034(-4) - 0.00047*RM3034(-5)) 

+ 0.93031 ] / (1 + RM3034DI)

PM3539MA_P = [ (0.00048*RM3539 + 0.00037*RM3539(-1) – 0.00007*RM3539(-2) - 0.00058*RM3539(-3) 

- 0.00091*RM3539(-4) - 0.00080*RM3539(-5)) 

+ 0.92144 ] / (1 + RM3539DI)

PM4044MA_P = [ (- 0.00018*RM4044 - 0.00026*RM4044(-1) - 0.00027*RM4044(-2) - 0.00022*RM4044(-3) 

- 0.00014*RM4044(-4) – 0.00006*RM4044(-5)) 

+ 0.90958 ] / (1 + RM4044DI)

PM4549MA_P = [ (0.00004*RM4549 - 0.00011*RM4549(-1) - 0.00036*RM4549(-2) - 0.00059*RM4549(-3) 

- 0.00068*RM4549(-4) - 0.00052*RM4549(-5)) 

+ 0.88963 ] / (1 + RM4549DI)

PM5054MA_P = [ (0.00115*RM5054 + 0.00089*RM5054(-1) - 0.00017*RM5054(-2) - 0.00141*RM5054(-3) 

- 0.00220*RM5054(-4) - 0.00194*RM5054(-5)) 

+ 0.85714 ] / (1 + RM5054DI)

MALE AGE 20 TO 54

PM2024_P = (PM2024NM_P * NM2024NM + PM2024MS_P * NM2024MS + PM2024MA_P * NM2024MA) / NM2024

PM2529_P = (PM2529NM_P * NM2529NM + PM2529MS_P * NM2529MS + PM2529MA_P * NM2529MA) / NM2529

PM3034_P = (PM3034NM_P * NM3034NM + PM3034MS_P * NM3034MS + PM3034MA_P * NM3034MA) / NM3034

PM3539_P = (PM3539NM_P * NM3539NM + PM3539MS_P * NM3539MS + PM3539MA_P * NM3539MA) / NM3539

PM4044_P = (PM4044NM_P * NM4044NM + PM4044MS_P * NM4044MS + PM4044MA_P * NM4044MA) / NM4044

PM4549_P = (PM4549NM_P * NM4549NM + PM4549MS_P * NM4549MS + PM4549MA_P * NM4549MA) / NM4549

PM5054_P = (PM5054NM_P * NM5054NM + PM5054MS_P * NM5054MS + PM5054MA_P * NM5054MA) / NM5054

PM2024 = PM2024_P 

PM2529 = PM2529_P

PM3034 = PM3034_P

PM3539 = PM3539_P

PM4044 = PM4044_P

PM4549 = PM4549_P

PM5054 = PM5054_P

PM2024NM = PM2024NM_P * PM2024 / PM2024_P

PM2529NM = PM2529NM_P * PM2529 / PM2529_P

PM3034NM = PM3034NM_P * PM3034 / PM3034_P

PM3539NM = PM3539NM_P * PM3539 / PM3539_P

PM4044NM = PM4044NM_P * PM4044 / PM4044_P

PM4549NM = PM4549NM_P * PM4549 / PM4549_P

PM5054NM = PM5054NM_P * PM5054 / PM5054_P

PM2024MS = PM2024MS_P * PM2024 / PM2024_P

PM2529MS = PM2529MS_P * PM2529 / PM2529_P

96
PM3034MS = PM3034MS_P * PM3034 / PM3034_P

PM3539MS = PM3539MS_P * PM3539 / PM3539_P

PM4044MS = PM4044MS_P * PM4044 / PM4044_P

PM4549MS = PM4549MS_P * PM4549 / PM4549_P

PM5054MS = PM5054MS_P * PM5054 / PM5054_P

PM2024MA = PM2024MA_P * PM2024 / PM2024_P

PM2529MA = PM2529MA_P * PM2529 / PM2529_P

PM3034MA = PM3034MA_P * PM3034 / PM3034_P

PM3539MA = PM3539MA_P * PM3539 / PM3539_P

PM4044MA = PM4044MA_P * PM4044 / PM4044_P

PM4549MA = PM4549MA_P * PM4549 / PM4549_P

PM5054MA = PM5054MA_P * PM5054 / PM5054_P

MALE AGE 55 TO 74

PM55_P = [ 0.00197*EDSCOREM55 - 0.09058*MSSHARE_M55 + 0.95174 ] / (1 + RM55DI)

PM56_P = [ -0.01821*EDSCOREM56 - 0.10617*MSSHARE_M56 + 0.98672 ] / (1 + RM56DI)

PM57_P = [ -0.01861*EDSCOREM57 - 0.21015*MSSHARE_M57 + 1.05211 ] / (1 + RM57DI)

PM58_P = [ 0.01509*EDSCOREM58 - 0.22982*MSSHARE_M58 + 0.99265 ] / (1 + RM58DI)

PM59_P = [ 0.00952*EDSCOREM59 - 0.30748*MSSHARE_M59 + 1.04218 ] / (1 + RM59DI)

PM60_P = [ 0.03704*EDSCOREM60 - 0.32468*MSSHARE_M60 + 0.96171 ] / (1 + RM60DI)

PM61_P = [ 0.00718*EDSCOREM61 - 0.44317*MSSHARE_M61 + 1.07617 ] / (1 + RM61DI)

PM62_P = [ - 0.60*RRADJ_M62 – 0.02*POT_ET_TXRT_62 

 + 0.10092*EDSCOREM62 - 0.55927*MSSHARE_M62 + 1.09868 ] / (1 + RM62DI)

PM63_P = [ - 0.55*RRADJ_M63 – 0.02*POT_ET_TXRT_63 

 + 0.06427*EDSCOREM63 - 0.95029*MSSHARE_M63 + 1.39001 ] / (1 + RM63DI)

PM64_P = [ - 0.50*RRADJ_M64 – 0.02*POT_ET_TXRT_64 

 + 0.05462*EDSCOREM64 - 1.01565*MSSHARE_M64 + 1.40427 ] / (1 + RM64DI)

PM65_P = [ - 0.45*RRADJ_M65 – 0.02*POT_ET_TXRT_65 

 + 0.14092*EDSCOREM65 - 0.56959*MSSHARE_M65 + 0.83637 ] / (1 + RM65DI)

PM66_P = [ - 0.40*RRADJ_M66 – 0.02*POT_ET_TXRT_66 

 + 0.08401*EDSCOREM66 - 0.71602*MSSHARE_M66 + 0.99009 ] / (1 + RM66DI)

PM67_P = [ - 0.35*RRADJ_M67 – 0.02*POT_ET_TXRT_67 

 + 0.09458*EDSCOREM67 - 0.80679*MSSHARE_M67 + 0.98465 ] / (1 + RM67DI)

PM68_P = [ - 0.30*RRADJ_M68 – 0.02*POT_ET_TXRT_68 

 + 0.11230*EDSCOREM68 - 0.91881*MSSHARE_M68 + 0.99375 ] / (1 + RM68DI)

PM69_P = [ - 0.30*RRADJ_M69 – 0.02*POT_ET_TXRT_69 

 + 0.09610*EDSCOREM69 - 0.83697*MSSHARE_M69 + 0.93415 ] / (1 + RM69DI)

PM70_P = [ 0.09997*EDSCOREM70 - 0.22828*MSSHARE_M70 + 0.28131 ] / (1 + RM70DI)

PM71_P = [ 0.12351*EDSCOREM71 + 0.13152*MSSHARE_M71 - 0.04761 ] / (1 + RM71DI)

PM72_P = [ 0.13620*EDSCOREM72 - 0.19020*MSSHARE_M72 + 0.15703 ] / (1 + RM72DI)

PM73_P = [ 0.13710*EDSCOREM73 + 0.26157*MSSHARE_M73 - 0.20437 ] / (1 + RM73DI)

PM74_P = [ 0.13464*EDSCOREM74 + 0.42963*MSSHARE_M74 - 0.34404 ] / (1 + RM74DI)

97
MALE AGE 75 TO 79

PM75_P = PM74(-4) * 0.92 

PM76_P = PM75(-4) * 0.92 

PM77_P = PM76(-4) * 0.92 

PM78_P = PM77(-4) * 0.92 

PM79_P = PM78(-4) * 0.92 

MALE AGE 55 TO 79

PM55 = PM55_P 

PM56 = PM56_P

PM57 = PM57_P

PM58 = PM58_P

PM59 = PM59_P

PM60 = PM60_P

PM61 = PM61_P

PM62 = PM62_P

PM63 = PM63_P

PM64 = PM64_P

PM65 = PM65_P

PM66 = PM66_P

PM67 = PM67_P

PM68 = PM68_P

PM69 = PM69_P

PM70 = PM70_P

PM71 = PM71_P

PM72 = PM72_P

PM73 = PM73_P

PM74 = PM74_P

PM75 = PM75_P

PM76 = PM76_P

PM77 = PM77_P

PM78 = PM78_P

PM79 = PM79_P

MALE AGE 80 AND OVER

PM80_P = PM79(-4) * 0.965 ^ 1 

PM81_P = PM79(-8) * 0.965 ^ 2 

PM82_P = PM79(-12) * 0.965 ^ 3 

PM83_P = PM79(-16) * 0.965 ^ 4 

PM84_P = PM79(-20) * 0.965 ^ 5 

98
PM85_P = MOVAVG(8,PM79(-24)) * 0.965 ^ 6 

PM86_P = MOVAVG(8,PM79(-28)) * 0.965 ^ 7 

PM87_P = MOVAVG(8,PM79(-32)) * 0.965 ^ 8 

PM88_P = MOVAVG(8,PM79(-36)) * 0.965 ^ 9 

PM89_P = MOVAVG(8,PM79(-40)) * 0.965 ^ 10 

PM90_P = MOVAVG(8,PM79(-44)) * 0.965 ^ 11 

PM91_P = MOVAVG(8,PM79(-48)) * 0.965 ^ 12 

PM92_P = MOVAVG(8,PM79(-52)) * 0.965 ^ 13 

PM93_P = MOVAVG(8,PM79(-56)) * 0.965 ^ 14 

PM94_P = MOVAVG(8,PM79(-60)) * 0.965 ^ 15 

PM95_P = PM94_P * 0.965 

PM96_P = PM95_P * 0.965 

PM97_P = PM96_P * 0.965 

PM98_P = PM97_P * 0.965 

PM99_P = PM98_P * 0.965 

PM100_P = PM99_P * 0.965 

PM80O_P = (PM80_P*NM80 + PM81_P*NM81 + PM82_P*NM82 + PM83_P*NM83 + PM84_P*NM84 

 + PM85_P*NM85 + PM86_P*NM86 + PM87_P*NM87 + PM88_P*NM88 + PM89_P*NM89 

 + PM90_P*NM90 + PM91_P*NM91 + PM92_P*NM92 + PM93_P*NM93 + PM94_P*NM94 

 + PM95_P*NM95 + PM96_P*NM96 + PM97_P*NM97 + PM98_P*NM98 + PM99_P*NM99 

 + PM100_P*NM100 ) / NM80O

PM80O = PM80O_P

PM80 = PM80_P * PM80O / PM80O_P

PM81 = PM81_P * PM80O / PM80O_P

PM82 = PM82_P * PM80O / PM80O_P

PM83 = PM83_P * PM80O / PM80O_P

PM84 = PM84_P * PM80O / PM80O_P

PM85 = PM85_P * PM80O / PM80O_P

PM86 = PM86_P * PM80O / PM80O_P

PM87 = PM87_P * PM80O / PM80O_P

PM88 = PM88_P * PM80O / PM80O_P

PM89 = PM89_P * PM80O / PM80O_P

PM90 = PM90_P * PM80O / PM80O_P

PM91 = PM91_P * PM80O / PM80O_P

PM92 = PM92_P * PM80O / PM80O_P

PM93 = PM93_P * PM80O / PM80O_P

PM94 = PM94_P * PM80O / PM80O_P

PM95 = PM95_P * PM80O / PM80O_P

PM96 = PM96_P * PM80O / PM80O_P

PM97 = PM97_P * PM80O / PM80O_P

99
PM98 = PM98_P * PM80O / PM80O_P

PM99 = PM99_P * PM80O / PM80O_P

PM100 = PM100_P * PM80O / PM80O_P

FEMALE LFPR EQUATIONS 

FEMALE 1617 AND 1819

PF1617_P = [ - 0.00214*RF1617 - 0.00256*RF1617(-1) - 0.00184*RF1617(-2) - 0.00062*RF1617(-3) 

+ 0.00050*RF1617(-4) + 0.00091*RF1617(-5) 

 - 0.33769 * RF1617CU6 + 0.01223

 - 0.00981 * TR_F1617 + 0.50143 

+ 0.98698 ] / (1 + RF1617DI)

PF1819_P = [ - 0.00118*RF1819 - 0.00145*RF1819(-1) - 0.00112*RF1819(-2) - 0.00050*RF1819(-3) 

+ 0.00010*RF1819(-4) + 0.00037*RF1819(-5) 

 - 0.42102 * RF1819CU6 - 0.01160

 - 0.00829 * TR_F1819 + 0.55840 

+ 0.98042 ] / (1 + RF1819DI)

PF1617 = PF1617_p

PF1819 = PF1819_p

FEMALE 20 TO 44, NEVER MARRIED WITH AT LEAST ONE CHILD UNDER 6:

PF2024NMC6U_P = [ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5) 

 + 0.69322 ] / (1 + RF2024DI)

PF2529NMC6U_P = [ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5) 

 + 0.72672 ] / (1 + RF2529DI)

PF3034NMC6U_P = [ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5) 

 + 0.72034 ] / (1 + RF3034DI)

PF3539NMC6U_P = [ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.72644 ] / (1 + RF3539DI)

PF4044NMC6U_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.71893 ] / (1 + RF4044DI)

FEMALE 20 TO 44, NEVER MARRIED WITH NO CHILDREN CHILD UNDER 6:

PF2024NMNC6_P = [ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5 

 - 0.00297 * TR_F2024 

 + 1.07188 ] / (1 + RF2024DI)

PF2529NMNC6_P = [ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5) 

 - 0.00077 * TR_F2529 

 + 0.94654 ] / (1 + RF2529DI)

PF3034NMNC6_P = [ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5) 

 + 0.84866 ] / (1 + RF3034DI)

100
PF3539NMNC6_P = [ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.83195 ] / (1 + RF3539DI)

PF4044NMNC6_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.82513 ] / (1 + RF4044DI)

FEMALE 20 TO 44, MARRIED, SPOUSE PRESENT, WITH AT LEAST ONE CHILD UNDER 6:

PF2024MSC6U_P = [ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5) 

 + 0.53561 ] / (1 + RF2024DI)

PF2529MSC6U_P = [ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5) 

 + 0.61916 ] / (1 + RF2529DI)

PF3034MSC6U_P = [ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5 

 + 0.65485 ] / (1 + RF3034DI) 

PF3539MSC6U_P = [ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.66673 ] / (1 + RF3539DI)

PF4044MSC6U_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.67612 ] / (1 + RF4044DI)

FEMALE 20 TO 44, MARRIED, SPOUSE PRESENT WITH NO CHILDREN CHILD UNDER 6:

PF2024MSNC6_P = [ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5) 

 - 0.00175 * TR_F2024 

 + 0.98277 ] / (1 + RF2024DI)

PF2529MSNC6_P =[ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5) 

 - 0.00050 * TR_F2529 

 + 0.88519 ] / (1 + RF2529DI)

PF3034MSNC6_P =[ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5) 

 + 0.80007 ] / (1 + RF3034DI)

PF3539MSNC6_P =[ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.79025 ] / (1 + RF3539DI)

PF4044MSNC6_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.81064 ] / (1 + RF4044DI)

FEMALE 20 TO 44, MARRIED, SPOUSE ABSENT, WITH AT LEAST ONE CHILD UNDER 6:

PF2024MAC6U_P =[ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5) 

101
 + 0.73283 ] / (1 + RF2024DI)

PF2529MAC6U_P = [ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5 

 + 0.76433 ] / (1 + RF2529DI)

PF3034MAC6U_P = [ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5 

 + 0.77183 ] / (1 + RF3034DI)

PF3539MAC6U_P = [ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.77156 ] / (1 + RF3539DI)

PF4044MAC6U_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.76058 ] / (1 + RF4044DI)

FEMALE 20 TO 44, MARRIED, SPOUSE ABSENT WITH NO CHILDREN CHILD UNDER 6:

PF2024MANC6_P = [ - 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5) 

 - 0.00223 * TR_F2024 

 + 0.97444 ] / (1 + RF2024DI)

PF2529MANC6_P = [ 0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5) 

 + 0.00025 * TR_F2529 

 + 0.79370 ] / (1 + RF2529DI)

PF3034MANC6_P = [ 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

 - 0.00090*RF3034(-4) - 0.00087*RF3034(-5) 

 + 0.83788 ] / (1 + RF3034DI)

PF3539MANC6_P = [ 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

 - 0.00074*RF3539(-4) - 0.00066*RF3539(-5) 

 + 0.84820 ] / (1 + RF3539DI)

PF4044MANC6_P = [ 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

 - 0.00176*RF4044(-4) - 0.00160*RF4044(-5) 

 + 0.85568 ] / (1 + RF4044DI)

PF2024NM_P = (PF2024NMC6U_P * NF2024NMC6U + PF2024NMNC6_P * NF2024NMNC6) / NF2024NM

PF2024MS_P = (PF2024MSC6U_P * NF2024MSC6U + PF2024MSNC6_P * NF2024MSNC6) / NF2024MS

PF2024MA_P = (PF2024MAC6U_P * NF2024MAC6U + PF2024MANC6_P * NF2024MANC6) / NF2024MA

PF2529NM_P = (PF2529NMC6U_P * NF2529NMC6U + PF2529NMNC6_P * NF2529NMNC6) / NF2529NM

PF2529MS_P = (PF2529MSC6U_P * NF2529MSC6U + PF2529MSNC6_P * NF2529MSNC6) / NF2529MS

PF2529MA_P = (PF2529MAC6U_P * NF2529MAC6U + PF2529MANC6_P * NF2529MANC6) / NF2529MA

PF3034NM_P = (PF3034NMC6U_P * NF3034NMC6U + PF3034NMNC6_P * NF3034NMNC6) / NF3034NM

PF3034MS_P = (PF3034MSC6U_P * NF3034MSC6U + PF3034MSNC6_P * NF3034MSNC6) / NF3034MS

PF3034MA_P = (PF3034MAC6U_P * NF3034MAC6U + PF3034MANC6_P * NF3034MANC6) / NF3034MA

PF3539NM_P = (PF3539NMC6U_P * NF3539NMC6U + PF3539NMNC6_P * NF3539NMNC6) / NF3539NM

PF3539MS_P = (PF3539MSC6U_P * NF3539MSC6U + PF3539MSNC6_P * NF3539MSNC6) / NF3539MS

102
PF3539MA_P = (PF3539MAC6U_P * NF3539MAC6U + PF3539MANC6_P * NF3539MANC6) / NF3539MA

PF4044NM_P = (PF4044NMC6U_P * NF4044NMC6U + PF4044NMNC6_P * NF4044NMNC6) / NF4044NM

PF4044MS_P = (PF4044MSC6U_P * NF4044MSC6U + PF4044MSNC6_P * NF4044MSNC6) / NF4044MS

PF4044MA_P = (PF4044MAC6U_P * NF4044MAC6U + PF4044MANC6_P * NF4044MANC6) / NF4044MA

FEMALE AGE 45 TO 54

FEMALE 45 TO 54, NEVER MARRIED:

PF4549NM_P = [ 0.00155*RF4549 + 0.00133*RF4549(-1) + 0.00007*RF4549(-2) - 0.00145*RF4549(-3) 

 - 0.00247*RF4549(-4) - 0.00224*RF4549(-5) 

+ 0.80950 ] / (1 + RF4549DI)

PF5054NM_P = [ 0.00093*RF5054 + 0.00074*RF5054(-1) – 0.00008*RF5054(-2) - 0.00104*RF5054(-3) 

 - 0.00168*RF5054(-4) - 0.00149*RF5054(-5) 

+ 0.78085 ] / (1 + RF5054DI)

FEMALE 45 TO 54, MARRIED, SPOUSE PRESENT: 

PF4549MS_P = [ 0.00155*RF4549 + 0.00133*RF4549(-1) + 0.00007*RF4549(-2) - 0.00145*RF4549(-3) 

 - 0.00247*RF4549(-4) - 0.00224*RF4549(-5) 

+ 0.81276 ] / (1 + RF4549DI)

PF5054MS_P = [ 0.00093*RF5054 + 0.00074*RF5054(-1) – 0.00008*RF5054(-2) - 0.00104*RF5054(-3) 

 - 0.00168*RF5054(-4) - 0.00149*RF5054(-5) 

+ 0.48809 

+ 0.16476*EDSCOREF5054 ] / (1 + RF5054DI)

FEMALE 45 TO 54, MARRIED, SPOUSE ABSENT:

PF4549MA_P = [ 0.00155*RF4549 + 0.00133*RF4549(-1) + 0.00007*RF4549(-2) - 0.00145*RF4549(-3) 

 - 0.00247*RF4549(-4) - 0.00224*RF4549(-5) 

+ 0.84789 ] / (1 + RF4549DI)

PF5054MA_P = [ 0.00093*RF5054 + 0.00074*RF5054(-1) – 0.00008*RF5054(-2) - 0.00104*RF5054(-3) 

 - 0.00168*RF5054(-4) - 0.00149*RF5054(-5 

+ 0.81452 ] / (1 + RF5054DI)

FEMALE AGE 20 TO 54

PF2024_P = (PF2024NM_P * NF2024NM + PF2024MS_P * NF2024MS + PF2024MA_P * NF2024MA) / NF2024

PF2529_P = (PF2529NM_P * NF2529NM + PF2529MS_P * NF2529MS + PF2529MA_P * NF2529MA) / NF2529

PF3034_P = (PF3034NM_P * NF3034NM + PF3034MS_P * NF3034MS + PF3034MA_P * NF3034MA) / NF3034

PF3539_P = (PF3539NM_P * NF3539NM + PF3539MS_P * NF3539MS + PF3539MA_P * NF3539MA) / NF3539

PF4044_P = (PF4044NM_P * NF4044NM + PF4044MS_P * NF4044MS + PF4044MA_P * NF4044MA) / NF4044

PF4549_P = (PF4549NM_P * NF4549NM + PF4549MS_P * NF4549MS + PF4549MA_P * NF4549MA) / NF4549

PF5054_P = (PF5054NM_P * NF5054NM + PF5054MS_P * NF5054MS + PF5054MA_P * NF5054MA) / NF5054

PF2024 = PF2024_P 

PF2529 = PF2529_P

PF3034 = PF3034_P

PF3539 = PF3539_P

PF4044 = PF4044_P

PF4549 = PF4549_P

PF5054 = PF5054_P

PF2024NM = PF2024NM_P * PF2024 / PF2024_P

PF2529NM = PF2529NM_P * PF2529 / PF2529_P

PF3034NM = PF3034NM_P * PF3034 / PF3034_P

PF3539NM = PF3539NM_P * PF3539 / PF3539_P

103
PF4044NM = PF4044NM_P * PF4044 / PF4044_P

PF4549NM = PF4549NM_P * PF4549 / PF4549_P

PF5054NM = PF5054NM_P * PF5054 / PF5054_P

PF2024MS = PF2024MS_P * PF2024 / PF2024_P

PF2529MS = PF2529MS_P * PF2529 / PF2529_P

PF3034MS = PF3034MS_P * PF3034 / PF3034_P

PF3539MS = PF3539MS_P * PF3539 / PF3539_P

PF4044MS = PF4044MS_P * PF4044 / PF4044_P

PF4549MS = PF4549MS_P * PF4549 / PF4549_P

PF5054MS = PF5054MS_P * PF5054 / PF5054_P

PF2024MA = PF2024MA_P * PF2024 / PF2024_P

PF2529MA = PF2529MA_P * PF2529 / PF2529_P

PF3034MA = PF3034MA_P * PF3034 / PF3034_P

PF3539MA = PF3539MA_P * PF3539 / PF3539_P

PF4044MA = PF4044MA_P * PF4044 / PF4044_P

PF4549MA = PF4549MA_P * PF4549 / PF4549_P

PF5054MA = PF5054MA_P * PF5054 / PF5054_P

PF2024NMC6U = PF2024NMC6U_P * PF2024 / PF2024_P

PF2529NMC6U = PF2529NMC6U_P * PF2529 / PF2529_P

PF3034NMC6U = PF3034NMC6U_P * PF3034 / PF3034_P

PF3539NMC6U = PF3539NMC6U_P * PF3539 / PF3539_P

PF4044NMC6U = PF4044NMC6U_P * PF4044 / PF4044_P

PF2024NMNC6 = PF2024NMNC6_P * PF2024 / PF2024_P

PF2529NMNC6 = PF2529NMNC6_P * PF2529 / PF2529_P

PF3034NMNC6 = PF3034NMNC6_P * PF3034 / PF3034_P

PF3539NMNC6 = PF3539NMNC6_P * PF3539 / PF3539_P

PF4044NMNC6 = PF4044NMNC6_P * PF4044 / PF4044_P

PF2024MSC6U = PF2024MSC6U_P * PF2024 / PF2024_P

PF2529MSC6U = PF2529MSC6U_P * PF2529 / PF2529_P

PF3034MSC6U = PF3034MSC6U_P * PF3034 / PF3034_P

PF3539MSC6U = PF3539MSC6U_P * PF3539 / PF3539_P

PF4044MSC6U = PF4044MSC6U_P * PF4044 / PF4044_P

PF2024MSNC6 = PF2024MSNC6_P * PF2024 / PF2024_P

PF2529MSNC6 = PF2529MSNC6_P * PF2529 / PF2529_P

PF3034MSNC6 = PF3034MSNC6_P * PF3034 / PF3034_P

PF3539MSNC6 = PF3539MSNC6_P * PF3539 / PF3539_P

PF4044MSNC6 = PF4044MSNC6_P * PF4044 / PF4044_P

PF2024MAC6U = PF2024MAC6U_P * PF2024 / PF2024_P

PF2529MAC6U = PF2529MAC6U_P * PF2529 / PF2529_P

PF3034MAC6U = PF3034MAC6U_P * PF3034 / PF3034_P

PF3539MAC6U = PF3539MAC6U_P * PF3539 / PF3539_P

PF4044MAC6U = PF4044MAC6U_P * PF4044 / PF4044_P

PF2024MANC6 = PF2024MANC6_P * PF2024 / PF2024_P

PF2529MANC6 = PF2529MANC6_P * PF2529 / PF2529_P

PF3034MANC6 = PF3034MANC6_P * PF3034 / PF3034_P

PF3539MANC6 = PF3539MANC6_P * PF3539 / PF3539_P

PF4044MANC6 = PF4044MANC6_P * PF4044 / PF4044_P

FEMALE 55 TO 74

PF55_P = [ 0.18398*EDSCOREF55 + 0.24605*MSSHARE_F55 + 0.26185 ] / (1 + RF55DI)

PF56_P = [ 0.20704*EDSCOREF56 - 0.12398*MSSHARE_F56 + 0.4493 ] / (1 + RF56DI)

PF57_P = [ 0.18422*EDSCOREF57 - 0.08766*MSSHARE_F57 + 0.45094 ] / (1 + RF57DI)

104
PF58_P = [ 0.19406*EDSCOREF58 - 0.06963*MSSHARE_F58 + 0.40382 ] / (1 + RF58DI)

PF59_P = [ 0.21112*EDSCOREF59 + 0.10742*MSSHARE_F59 + 0.24105 ] / (1 + RF59DI)

PF60_P = [ 0.20633*EDSCOREF60 - 0.41539*MSSHARE_F60 + 0.54178 ] / (1 + RF60DI)

PF61_P = [ 0.19349*EDSCOREF61 - 0.66676*MSSHARE_F61 + 0.68556 ] / (1 + RF61DI)

PF62_P = [ - 0.5100*RRADJ_F62 - 0.02*POT_ET_TXRT_62 

 + 0.21249*EDSCOREF62 + 0.01966*MSSHARE_F62 + 0.32876 ] / (1 + RF62DI)

PF63_P = [ - 0.4675*RRADJ_F63 - 0.02*POT_ET_TXRT_63 

 + 0.21116*EDSCOREF63 + 0.02896*MSSHARE_F63 + 0.26792 ] / (1 + RF63DI)

PF64_P = [ - 0.4250*RRADJ_F64 - 0.02*POT_ET_TXRT_64 

 + 0.20467*EDSCOREF64 - 0.32725*MSSHARE_F64 + 0.44786 ] / (1 + RF64DI)

PF65_P = [ - 0.3825*RRADJ_F65 - 0.02*POT_ET_TXRT_65 

 + 0.20002*EDSCOREF65 - 0.05830*MSSHARE_F65 + 0.22187 ] / (1 + RF65DI)

PF66_P = [ - 0.3400*RRADJ_F66 - 0.02*POT_ET_TXRT_66 

 + 0.17479*EDSCOREF66 + 0.22954*MSSHARE_F66 + 0.04361 ] / (1 + RF66DI)

PF67_P = [ - 0.2975*RRADJ_F67 - 0.02*POT_ET_TXRT_67 

 + 0.17673*EDSCOREF67 - 0.43942*MSSHARE_F67 + 0.38490 ] / (1 + RF67DI)

PF68_P = [ - 0.2550*RRADJ_F68 - 0.02*POT_ET_TXRT_68 

 + 0.15513*EDSCOREF68 + 0.35232*MSSHARE_F68 - 0.07497 ] / (1 + RF68DI)

PF69_P = [ - 0.2550*RRADJ_F69 - 0.02*POT_ET_TXRT_69 

 + 0.11603*EDSCOREF69 + 0.87528*MSSHARE_F69 - 0.32696 ] / (1 + RF69DI)

PF70_P = [ 0.09629*EDSCOREF70 + 0.54302*MSSHARE_F70 - 0.25141 ] / (1 + RF70DI)

PF71_P = [ 0.11053*EDSCOREF71 + 0.16137*MSSHARE_F71 - 0.08070 ] / (1 + RF71DI)

PF72_P = [ 0.09151*EDSCOREF72 + 0.25854*MSSHARE_F72 - 0.11711 ] / (1 + RF72DI)

PF73_P = [ 0.08611*EDSCOREF73 + 0.28099*MSSHARE_F73 - 0.12804 ] / (1 + RF73DI)

PF74_P = [ 0.11821*EDSCOREF74 - 0.01277*MSSHARE_F74 - 0.04121 ] / (1 + RF74DI)

FEMALE, AGES 75 TO 79 

PF75_P = PF74(-4) * 0.9 

PF76_P = PF75(-4) * 0.9 

PF77_P = PF76(-4) * 0.9 

PF78_P = PF77(-4) * 0.9 

PF79_P = PF78(-4) * 0.9 

FEMALE AGE 55 TO 79

PF55 = PF55_P

PF56 = PF56_P

PF57 = PF57_P

PF58 = PF58_P

105
PF59 = PF59_P

PF60 = PF60_P

PF61 = PF61_P

PF62 = PF62_P

PF63 = PF63_P

PF64 = PF64_P

PF65 = PF65_P

PF66 = PF66_P

PF67 = PF67_P

PF68 = PF68_P

PF69 = PF69_P

PF70 = PF70_P

PF71 = PF71_P

PF72 = PF72_P

PF73 = PF73_P

PF74 = PF74_P

PF75 = PF75_P

PF76 = PF76_P

PF77 = PF77_P

PF78 = PF78_P

PF79 = PF79_P

FEMALE, AGES 80 AND OVER 

PF80_P = PF79(-4) * 0.965 ^ 1 

PF81_P = PF79(-8) * 0.965 ^ 2 

PF82_P = PF79(-12) * 0.965 ^ 3 

PF83_P = PF79(-16) * 0.965 ^ 4 

PF84_P = PF79(-20) * 0.965 ^ 5 

PF85_P = MOVAVG(8,PF79(-24)) * 0.965 ^ 6 

PF86_P = MOVAVG(8,PF79(-28)) * 0.965 ^ 7

PF87_P = MOVAVG(8,PF79(-32)) * 0.965 ^ 8 

PF88_P = MOVAVG(8,PF79(-36)) * 0.965 ^ 9 

PF89_P = MOVAVG(8,PF79(-40)) * 0.965 ^ 10 

PF90_P = MOVAVG(8,PF79(-44)) * 0.965 ^ 11 

PF91_P = MOVAVG(8,PF79(-48)) * 0.965 ^ 12 

PF92_P = MOVAVG(8,PF79(-52)) * 0.965 ^ 13 

PF93_P = MOVAVG(8,PF79(-56)) * 0.965 ^ 14 

PF94_P = MOVAVG(8,PF79(-60)) * 0.965 ^ 15 

PF95_P = PF94_P * 0.965 

PF96_P = PF95_P * 0.965 

106
PF97_P = PF96_P * 0.965 

PF98_P = PF97_P * 0.965 

PF99_P = PF98_P * 0.965 

PF100_P = PF99_P * 0.965 

PF80O_P = (PF80_P*NF80 + PF81_P*NF81 + PF82_P*NF82 + PF83_P*NF83 + PF84_P*NF84 

 + PF85_P*NF85 + PF86_P*NF86 + PF87_P*NF87 + PF88_P*NF88 + PF89_P*NF89 

 + PF90_P*NF90 + PF91_P*NF91 + PF92_P*NF92 + PF93_P*NF93 + PF94_P*NF94 

 + PF95_P*NF95 + PF96_P*NF96 + PF97_P*NF97 + PF98_P*NF98 + PF99_P*NF99 

 + PF100_P*NF100 ) / NF80O

PF80O = PF80O_P

PF80 = PF80_P * PF80O / PF80O_P

PF81 = PF81_P * PF80O / PF80O_P

PF82 = PF82_P * PF80O / PF80O_P

PF83 = PF83_P * PF80O / PF80O_P

PF84 = PF84_P * PF80O / PF80O_P

PF85 = PF85_P * PF80O / PF80O_P

PF86 = PF86_P * PF80O / PF80O_P

PF87 = PF87_P * PF80O / PF80O_P

PF88 = PF88_P * PF80O / PF80O_P

PF89 = PF89_P * PF80O / PF80O_P

PF90 = PF90_P * PF80O / PF80O_P

PF91 = PF91_P * PF80O / PF80O_P

PF92 = PF92_P * PF80O / PF80O_P

PF93 = PF93_P * PF80O / PF80O_P

PF94 = PF94_P * PF80O / PF80O_P

PF95 = PF95_P * PF80O / PF80O_P

PF96 = PF96_P * PF80O / PF80O_P

PF97 = PF97_P * PF80O / PF80O_P

PF98 = PF98_P * PF80O / PF80O_P

PF99 = PF99_P * PF80O / PF80O_P

PF100 = PF100_P * PF80O / PF80O_P

LFPR EQUATIONS, AGE 16 AND OVER

PM16O_P= (PM1617_P * NM1617 +

PM1819_P * NM1819 +

PM2024_P * NM2024 +

PM2529_P * NM2529 +

PM3034_P * NM3034 +

PM3539_P * NM3539 +

PM4044_P * NM4044 +

PM4549_P * NM4549 +

PM5054_P * NM5054 +

107
PM55_P * NM55 +

PM56_P * NM56 +

PM57_P * NM57 +

PM58_P * NM58 +

PM59_P * NM59 +

PM60_P * NM60 +

PM61_P * NM61 +

PM62_P * NM62 +

PM63_P * NM63 +

PM64_P * NM64 +

PM65_P * NM65 +

PM66_P * NM66 +

PM67_P * NM67 +

PM68_P * NM68 +

PM69_P * NM69 +

PM70_P * NM70 +

PM71_P * NM71 +

PM72_P * NM72 +

PM73_P * NM73 +

PM74_P * NM74 +

PM75_P * NM75 +

PM76_P * NM76 +

PM77_P * NM77 +

PM78_P * NM78 +

PM79_P * NM79 +

PM80O_P * NM80O ) / NM16O

PF16O_P= (PF1617_P * NF1617 +

PF1819_P * NF1819 +

PF2024_P * NF2024 +

PF2529_P * NF2529 +

PF3034_P * NF3034 +

PF3539_P * NF3539 +

PF4044_P * NF4044 +

PF4549_P * NF4549 +

PF5054_P * NF5054 +

PF55_P * NF55 +

PF56_P * NF56 +

PF57_P * NF57 +

PF58_P * NF58 +

PF59_P * NF59 +

PF60_P * NF60 +

PF61_P * NF61 +

PF62_P * NF62 +

PF63_P * NF63 +

PF64_P * NF64 +

PF65_P * NF65 +

PF66_P * NF66 +

PF67_P * NF67 +

PF68_P * NF68 +

PF69_P * NF69 +

PF70_P * NF70 +

PF71_P * NF71 +

PF72_P * NF72 +

PF73_P * NF73 +

PF74_P * NF74 +

PF75_P * NF75 +

PF76_P * NF76 +

PF77_P * NF77 +

PF78_P * NF78 +

PF79_P * NF79 +

PF80O_P * NF80O ) / NF16O

108
P16O_P = (PM16O_P * NM16O + PF16O_P * NF16O) / (NM16O + NF16O)

LABOR FORCE, AGE 16 AND OVER

LCM_P = PM16O_P * NM16O

LCF_P = PF16O_P * NF16O

LC_P = LCM_P + LCF_P

LABOR FORCE PARTICIPATION RATES, FULL EMPLOYMENT 

MALE

DPM1617_FE = (- 0.00134*RM1617_FE - 0.00167*RM1617_FE(-1) - 0.00132*RM1617_FE(-2) 

- 0.00065*RM1617_FE(-3) + 0.00003*RM1617_FE(-4) + 0.00035*RM1617_FE(-5)) – 

(- 0.00134*RM1617 - 0.00167*RM1617(-1) - 0.00132*RM1617(-2) - 0.00065*RM1617(-3) 

+ 0.00003*RM1617(-4) + 0.00035*RM1617(-5))

DPM1819_FE = (- 0.00068*RM1819_FE - 0.00092*RM1819_FE(-1) - 0.00083*RM1819_FE(-2) 

- 0.00056*RM1819_FE(-3) - 0.00025*RM1819_FE(-4) – 0.00002*RM1819_FE(-5)) – 

(- 0.00068*RM1819 - 0.00092*RM1819(-1) - 0.00083*RM1819(-2) - 0.00056*RM1819(-3) 

- 0.00025*RM1819(-4) – 0.00002*RM1819(-5)) 

DPM2024_FE = (- 0.00053*RM2024_FE - 0.00074*RM2024_FE(-1) - 0.00071*RM2024_FE(-2) 

- 0.00054*RM2024_FE(-3) - 0.00030*RM2024_FE(-4) – 0.00010*RM2024_FE(-5)) – 

(- 0.00053*RM2024 - 0.00074*RM2024(-1) - 0.00071*RM2024(-2) - 0.00054*RM2024(-3) 

- 0.00030*RM2024(-4) – 0.00010*RM2024(-5)) 

DPM2529_FE = (- 0.00031*RM2529_FE - 0.00053*RM2529_FE(-1) - 0.00066*RM2529_FE(-2) 

- 0.00068*RM2529_FE(-3) - 0.00058*RM2529_FE(-4) - 0.00036*RM2529_FE(-5)) – 

(- 0.00031*RM2529 - 0.00053*RM2529(-1) - 0.00066*RM2529(-2) - 0.00068*RM2529(-3) 

- 0.00058*RM2529(-4) - 0.00036*RM2529(-5)) 

DPM3034_FE = (- 0.00001*RM3034_FE - 0.00018*RM3034_FE(-1) - 0.00040*RM3034_FE(-2) 

- 0.00058*RM3034_FE(-3) - 0.00064*RM3034_FE(-4) - 0.00047*RM3034_FE(-5)) – 

(- 0.00001*RM3034 - 0.00018*RM3034(-1) - 0.00040*RM3034(-2) - 0.00058*RM3034(-3) 

- 0.00064*RM3034(-4) - 0.00047*RM3034(-5)) 

DPM3539_FE = (0.00048*RM3539_FE + 0.00037*RM3539_FE(-1) – 0.00007*RM3539_FE(-2) 

- 0.00058*RM3539_FE(-3) - 0.00091*RM3539_FE(-4) - 0.00080*RM3539_FE(-5)) – 

 (0.00048*RM3539 + 0.00037*RM3539(-1) – 0.00007*RM3539(-2) - 0.00058*RM3539(-3) 

- 0.00091*RM3539(-4) - 0.00080*RM3539(-5)) 

DPM4044_FE = (- 0.00018*RM4044_FE - 0.00026*RM4044_FE(-1) - 0.00027*RM4044_FE(-2) 

 - 0.00022*RM4044_FE(-3) - 0.00014*RM4044_FE(-4) – 0.00006*RM4044_FE(-5)) – 

(- 0.00018*RM4044 - 0.00026*RM4044(-1) - 0.00027*RM4044(-2) - 0.00022*RM4044(-3) 

 - 0.00014*RM4044(-4) – 0.00006*RM4044(-5)) 

DPM4549_FE = (0.00004*RM4549_FE - 0.00011*RM4549_FE(-1) - 0.00036*RM4549_FE(-2) 

- 0.00059*RM4549_FE(-3) - 0.00068*RM4549_FE(-4) - 0.00052*RM4549_FE(-5)) – 

(0.00004*RM4549 - 0.00011*RM4549(-1) - 0.00036*RM4549(-2) - 0.00059*RM4549(-3) 

- 0.00068*RM4549(-4) - 0.00052*RM4549(-5)) 

DPM5054_FE = (0.00115*RM5054_FE + 0.00089*RM5054_FE(-1) - 0.00017*RM5054_FE(-2) 

- 0.00141*RM5054_FE(-3) - 0.00220*RM5054_FE(-4) - 0.00194*RM5054_FE(-5)) – 

 (0.00115*RM5054 + 0.00089*RM5054(-1) - 0.00017*RM5054(-2) - 0.00141*RM5054(-3) 

- 0.00220*RM5054(-4) - 0.00194*RM5054(-5)) 

FEMALE

DPF1617_FE = (- 0.00214*RF1617_FE - 0.00256*RF1617_FE(-1) - 0.00184*RF1617_FE(-2) 

- 0.00062*RF1617_FE(-3) + 0.00050*RF1617_FE(-4) + 0.00091*RF1617_FE(-5)) – 

109
(- 0.00214*RF1617 - 0.00256*RF1617(-1) - 0.00184*RF1617(-2) - 0.00062*RF1617(-3) 

+ 0.00050*RF1617(-4) + 0.00091*RF1617(-5)) 

DPF1819_FE = (- 0.00118*RF1819_FE - 0.00145*RF1819_FE(-1) - 0.00112*RF1819_FE(-2) 

- 0.00050*RF1819_FE(-3) + 0.00010*RF1819_FE(-4) + 0.00037*RF1819_FE(-5)) – 

(- 0.00118*RF1819 - 0.00145*RF1819(-1) - 0.00112*RF1819(-2) - 0.00050*RF1819(-3) 

+ 0.00010*RF1819(-4) + 0.00037*RF1819(-5)) 

DPF2024_FE = (- 0.00006*RF2024_FE - 0.00026*RF2024_FE(-1) - 0.00050*RF2024_FE(-2) 

- 0.00070*RF2024_FE(-3) - 0.00075*RF2024_FE(-4) - 0.00055*RF2024_FE(-5)) – 

(- 0.00006*RF2024 - 0.00026*RF2024(-1) - 0.00050*RF2024(-2) - 0.00070*RF2024(-3) 

 - 0.00075*RF2024(-4) - 0.00055*RF2024(-5)) 

DPF2529_FE = ( 0.00056*RF2529_FE + 0.00034*RF2529_FE(-1) - 0.00030*RF2529_FE(-2) 

- 0.00101*RF2529_FE(-3) - 0.00143*RF2529_FE(-4) - 0.00121*RF2529_FE(-5)) – 

(0.00056*RF2529 + 0.00034*RF2529(-1) - 0.00030*RF2529(-2) - 0.00101*RF2529(-3) 

 - 0.00143*RF2529(-4) - 0.00121*RF2529(-5)) 

DPF3034_FE = ( 0.00078*RF3034_FE + 0.00075*RF3034_FE(-1) + 0.00024*RF3034_FE(-2) 

- 0.00042*RF3034_FE(-3) - 0.00090*RF3034_FE(-4) - 0.00087*RF3034_FE(-5)) – 

( 0.00078*RF3034 + 0.00075*RF3034(-1) + 0.00024*RF3034(-2) - 0.00042*RF3034(-3) 

- 0.00090*RF3034(-4) - 0.00087*RF3034(-5)) 

DPF3539_FE = ( 0.00040*RF3539_FE + 0.00032*RF3539_FE(-1) – 0.00004*RF3539_FE(-2) 

- 0.00046*RF3539_FE(-3) - 0.00074*RF3539_FE(-4) - 0.00066*RF3539_FE(-5)) – 

( 0.00040*RF3539 + 0.00032*RF3539(-1) – 0.00004*RF3539(-2) - 0.00046*RF3539(-3) 

- 0.00074*RF3539(-4) - 0.00066*RF3539(-5)) 

DPF4044_FE = ( 0.00113*RF4044_FE + 0.00097*RF4044_FE(-1) + 0.00007*RF4044_FE(-2) 

- 0.00102*RF4044_FE(-3) - 0.00176*RF4044_FE(-4) - 0.00160*RF4044_FE(-5)) – 

( 0.00113*RF4044 + 0.00097*RF4044(-1) + 0.00007*RF4044(-2) - 0.00102*RF4044(-3) 

- 0.00176*RF4044(-4) - 0.00160*RF4044(-5)) 

DPF4549_FE = ( 0.00155*RF4549_FE + 0.00133*RF4549_FE(-1) + 0.00007*RF4549_FE(-2) 

- 0.00145*RF4549_FE(-3) - 0.00247*RF4549_FE(-4) - 0.00224*RF4549_FE(-5)) – 

( 0.00155*RF4549 + 0.00133*RF4549(-1) + 0.00007*RF4549(-2) - 0.00145*RF4549(-3) 

- 0.00247*RF4549(-4) - 0.00224*RF4549(-5)) 

DPF5054_FE = ( 0.00093*RF5054_FE + 0.00074*RF5054_FE(-1) – 0.00008*RF5054_FE(-2) 

- 0.00104*RF5054_FE(-3) - 0.00168*RF5054_FE(-4) - 0.00149*RF5054_FE(-5)) – 

( 0.00093*RF5054 + 0.00074*RF5054(-1) – 0.00008*RF5054(-2) - 0.00104*RF5054(-3) 

- 0.00168*RF5054(-4) - 0.00149*RF5054(-5)) 

110
2.2 U.S. Earnings (MODSOL2) 

Equation numbers identify the corresponding equations in the Fortran program EconModSol2EquationsMod.f90.

Quarterly Employment Equations

Agricultural Workers

EA = IF LONGRANGE = 0 

THEN GDPPF09 / (1.125 * 1.138 * EXP (-0.20541 + 0.03254 * YEAR - 0.07829 + 0.37854)) 

ELSE E * EA.1/E.1 (20)

Nonagricultural workers

ENA = E – EA (21)

Nonagricultural Self-employed workers

EF1617NAS = (0.12015 * RTP.1 - 0.10551) * EF1617 (3) 

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 (4) 

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

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 (5) 

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 (6) 

Ordinary Least Squares

111
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 (7) 

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 (8) 

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 (9) 

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) (10)

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

112
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

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 (2) 

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 (11)

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)

113
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 (12)

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

D.W. (1) 2.1493 

D.W. (2) 1.7046

EM2534NAS = (-0.09661 * RTP.1 + 0.14843) * EM2534 (13)

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 (14)

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 (15)

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 

114
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 (16)

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

 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) (17)

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 

115
D.W. (2) 0.9992

Nonagricultural Self-employed Workers:

“Raw” equations (before scaling the totals):

Female

EF1617NAS_R = (0.12015 * RTP.1 - 0.10551) * EF1617 + 

EF1617NAS.ADJ (3) 

EF1819NAS_R = (0.11184 * RTP.1 - 0.10241) * EF1819 + 

EF1819NAS.ADJ (4) 

EF2024NAS_R = (0.08908 * RTP.1 - 0.07176) * EF2024 + 

EF2024NAS.ADJ (5) 

EF2534NAS_R = (0.00906 * RTP.1 + 0.03539) * EF2534 + 

EF2534NAS.ADJ (6) 

EF3544NAS_R = (-0.01869 * RTP.1 + 0.08087) * EF3544 + 

EF3544NAS.ADJ (7) 

EF4554NAS_R = (0.07232 * RTP.1 - 0.00701) * EF4554 + 

EF4554NAS.ADJ (8) 

EF5564NAS_R = (0.07872 * RTP.1 + 0.00466) * EF5564 + 

EF5564NAS.ADJ (9) 

EF65ONAS_R = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) + 

EF65ONAS.ADJ (10)

Male 

EM1617NAS_R = (-0.23035 * RTP.1 + 0.24985) * EM1617 + 

EM1617NAS.ADJ (2) 

EM1819NAS_R = (-0.05782 * RTP.1 + 0.07265) * EM1819 + 

EM1819NAS.ADJ (11)

EM2024NAS_R = (-0.09206 * RTP.1 + 0.11567) * EM2024 + 

EM2024NAS.ADJ (12)

EM2534NAS_R = (-0.09661 * RTP.1 + 0.14843) * EM2534 + 

EM2534NAS.ADJ (13)

EM3544NAS_R = (0.02739 * RTP.1 + 0.05236) * EM3544 + 

EM3544NAS.ADJ (14)

EM4554NAS_R = (0.06217 * RTP.1 + 0.03411) * EM4554 + 

EM4554NAS.ADJ (15)

EM5564NAS_R = (-0.04776 * RTP.1 + 0.16626) * EM5564 + 

EM5564NAS.ADJ (16)

EM65ONAS_R = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O) + 

EM65ONAS.ADJ (17)

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 (18)

Total nonagricultural SE workers:

ENAS = IF LONGRANGE = 0 

 THEN ENAS_R 

 ELSE ENA * (ENAS.1/ENA.1) (22)

Final (scaled) equations:

Male 

EM1617NAS = EM1617NAS_R * (ENAS/ENAS_R) (23)

EM1819NAS = EM1819NAS_R * (ENAS/ENAS_R) (102)

EM2024NAS = EM2024NAS_R * (ENAS/ENAS_R) (109)

EM2534NAS = EM2534NAS_R * (ENAS/ENAS_R) (116)

EM3544NAS = EM3544NAS_R * (ENAS/ENAS_R) (123)

EM4554NAS = EM4554NAS_R * (ENAS/ENAS_R) (130)

EM5564NAS = EM5564NAS_R * (ENAS/ENAS_R) (137)

EM65ONAS = EM65ONAS_R * (ENAS/ENAS_R) (144)

Female

EF1617NAS = EF1617NAS_R * (ENAS/ENAS_R) (157)

EF1819NAS = EF1819NAS_R * (ENAS/ENAS_R) (164)

EF2024NAS = EF2024NAS_R * (ENAS/ENAS_R) (171)

116
EF2534NAS = EF2534NAS_R * (ENAS/ENAS_R) (178)

EF3544NAS = EF3544NAS_R * (ENAS/ENAS_R) (185)

EF4554NAS = EF4554NAS_R * (ENAS/ENAS_R) (192)

EF5564NAS = EF5564NAS_R * (ENAS/ENAS_R) (199)

EF65ONAS = EF65ONAS_R * (ENAS/ENAS_R) (206)

EFNAS = EF1617NAS + EF1819NAS + EF2024NAS + EF2534NAS + EF3544NAS + EF4554NAS + EF5564NAS + 

EF65ONAS (212)

EMNAS = EM1617NAS + EM1819NAS + EM2024NAS + EM2534NAS + EM3544NAS + EM4554NAS + EM5564NAS + 

EM65ONAS (150)

Nonagricultural Unpaid Family Workers

“Raw” equations (before scaling the totals):

Female (25-32)

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

Male 

EM1617NAU_R = 0.00028 * ENAS + EM1617NAU.ADJ (24)

EM1819NAU_R = 0.00033 * ENAS + EM1819NAU.ADJ (33)

EM2024NAU_R = 0.00050 * ENAS + EM2024NAU.ADJ (34)

EM2534NAU_R = 0.00044 * ENAS + EM2534NAU.ADJ (35)

EM3544NAU_R = 0.00043 * ENAS + EM3544NAU.ADJ (36)

EM4554NAU_R = 0.00052 * ENAS + EM4554NAU.ADJ (37)

EM5564NAU_R = 0.00037 * ENAS + EM5564NAU.ADJ (38)

EM65ONAU_R = (0.00023 + 0.00010 + 0.00011) * ENAS + EM65ONAU.ADJ (39)

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 (40)

Total Nonagricultural Unpaid Family Workers:

ENAU = ENAU_R (41)

Final (scaled) equations:

EM1617NAU = EM1617NAU_R * (ENAU/ENAU_R) (42)

EM1819NAU = EM1819NAU_R * (ENAU/ENAU_R) (103)

EM2024NAU = EM2024NAU_R * (ENAU/ENAU_R) (110)

EM2534NAU = EM2534NAU_R * (ENAU/ENAU_R) (117)

EM3544NAU = EM3544NAU_R * (ENAU/ENAU_R) (124)

EM4554NAU = EM4554NAU_R * (ENAU/ENAU_R) (131)

EM5564NAU = EM5564NAU_R * (ENAU/ENAU_R) (138)

EM65ONAU = EM65ONAU_R * (ENAU/ENAU_R) (145)

EF1617NAU = EF1617NAU_R * (ENAU/ENAU_R) (158)

EF1819NAU = EF1819NAU_R * (ENAU/ENAU_R) (165)

EF2024NAU = EF2024NAU_R * (ENAU/ENAU_R) (172)

EF2534NAU = EF2534NAU_R * (ENAU/ENAU_R) (179)

EF3544NAU = EF3544NAU_R * (ENAU/ENAU_R) (186)

EF4554NAU = EF4554NAU_R * (ENAU/ENAU_R) (193)

EF5564NAU = EF5564NAU_R * (ENAU/ENAU_R) (200)

EF65ONAU = EF65ONAU_R * (ENAU/ENAU_R) (207)

EFNAU = EF1617NAU + EF1819NAU + EF2024NAU + EF2534NAU + EF3544NAU + EF4554NAU + EF5564NAU + 

EF65ONAU (213)

EMNAU = EM1617NAU + EM1819NAU + EM2024NAU + EM2534NAU + EM3544NAU + EM4554NAU + EM5564NAU + 

EM65ONAU (151)

117
Agricultural Wage Workers

Total Agricultural Wage Workers

EAW = IF LONGRANGE = 0 

 THEN EA * (0.00893 * YEAR + 0.33159 * RTP - 0.67943) 

 ELSE EA*(EAW.1/EA.1) (43)

Raw Disaggregation of EAW:

Male 

EM1617AW_R = MAX (0, EAW * (-0.00594 - 0.09353 * MOVAVG (2, RTP.1) + 5.28754 * EM1617/E + 0.08116) + 

EM1617AW.ADJ) (44)

EM1819AW_R = MAX (0, EAW * (-0.00131 - 0.18120 * MOVAVG (2, RTP.1) + 3.87151 * EM1819/E + 0.16636) + EM1819AW.ADJ) 

 (53)

EM2024AW_R = MAX (0, EAW * (-0.00664 + 0.10493 * MOVAVG (2, RTP.1) + 2.00153 * EM2024/E - 0.08191) + EM2024AW.ADJ) 

 (54)

EM2534AW_R = MAX (0, EAW * (-0.02065 + 0.38358 * MOVAVG (2, RTP.1) - 0.98380 * EM2534/E + 0.00751) + EM2534AW.ADJ) 

 (55)

EM3544AW_R = MAX (0, EAW * (0.00402 - 0.15663 * MOVAVG (2, RTP.1) + 1.72119 * EM3544/E + 0.05679) + EM3544AW.ADJ) 

 (56)

EM4554AW_R = MAX (0, EAW * (0.00834 + 0.03746 * MOVAVG (2, RTP.1) + 0.46522 * EM4554/E + 0.00144) + EM4554AW.ADJ) 

 (57)

EM5564AW_R = MAX (0, EAW * (-0.00655 + 0.03521 * MOVAVG (2, RTP.1) + 0.46852 * EM5564/E - 0.00037) + EM5564AW.ADJ) 

 (58)

EM65OAW_R = MAX (0, EAW * (-0.00114 + 0.07640 * MOVAVG (2, RTP.1) + 3.25911 * EM65O/E - 0.10058) + EM65OAW.ADJ) 

 (59)

Female (45-52)

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 (60)

Final (scaled) equations:

EM1617AW = EM1617AW_R * (EAW/EAW_R) (61)

EM1819AW = EM1819AW_R * (EAW/EAW_R) (104)

EM2024AW = EM2024AW_R * (EAW/EAW_R) (111)

EM2534AW = EM2534AW_R * (EAW/EAW_R) (118)

EM3544AW = EM3544AW_R * (EAW/EAW_R) (125)

EM4554AW = EM4554AW_R * (EAW/EAW_R) (132)

EM5564AW = EM5564AW_R * (EAW/EAW_R) (139)

EM65OAW = EM65OAW_R * (EAW/EAW_R) (146)

EF1617AW = EF1617AW_R * (EAW/EAW_R) (159)

EF1819AW = EF1819AW_R * (EAW/EAW_R) (166)

EF2024AW = EF2024AW_R * (EAW/EAW_R) (173)

EF2534AW = EF2534AW_R * (EAW/EAW_R) (180)

EF3544AW = EF3544AW_R * (EAW/EAW_R) (187)

EF4554AW = EF4554AW_R * (EAW/EAW_R) (194)

EF5564AW = EF5564AW_R * (EAW/EAW_R) (201)

EF65OAW = EF65OAW_R * (EAW/EAW_R) (208)

EFAW = EF1617AW+ EF1819AW+ EF2024AW+ EF2534AW+ EF3544AW+ EF4554AW+ EF5564AW+ 

EF65OAW (214)

EMAW = EM1617AW+ EM1819AW+ EM2024AW+ EM2534AW+ EM3544AW+ EM4554AW+ EM5564AW+ 

EM65OAW (152)

Unpaid Agricultural Family Workers

Raw equations:

Male (71-78)

118
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)

Female (63-70)

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 (79)

Total Unpaid Agricultural Family Workers : 

EAU = IF LONGRANGE = 0 

 THEN EAU_R 

 ELSE EAU.1/EA.1 * EA (80)

Final (scaled) equations : 

EM1617AU = EM1617AU_R * (EAU/EAU_R) (99)

EM1819AU = EM1819AU_R * (EAU/EAU_R) (106)

EM2024AU = EM2024AU_R * (EAU/EAU_R) (113)

EM2534AU = EM2534AU_R * (EAU/EAU_R) (120)

EM3544AU = EM3544AU_R * (EAU/EAU_R) (127)

EM4554AU = EM4554AU_R * (EAU/EAU_R) (134)

EM5564AU = EM5564AU_R * (EAU/EAU_R) (141)

EM65OAU = EM65OAU_R * (EAU/EAU_R) (148)

EF1617AU = EF1617AU_R * (EAU/EAU_R) (161)

EF1819AU = EF1819AU_R * (EAU/EAU_R) (168)

EF2024AU = EF2024AU_R * (EAU/EAU_R) (175)

EF2534AU = EF2534AU_R * (EAU/EAU_R) (182)

EF3544AU = EF3544AU_R * (EAU/EAU_R) (189)

EF4554AU = EF4554AU_R * (EAU/EAU_R) (196)

EF5564AU = EF5564AU_R * (EAU/EAU_R) (203)

EF65OAU = EF65OAU_R * (EAU/EAU_R) (210)

EFAU = EF1617AU + EF1819AU + EF2024AU + EF2534AU + EF3544AU + EF4554AU + EF5564AU + EF65OAU (216)

EMAU = EM1617AU + EM1819AU + EM2024AU + EM2534AU + EM3544AU + EM4554AU + EM5564AU + EM65OAU (154)

Self-employed Agricultural Workers

Total

EAS = EA - EAU - EAW (81)

Raw disaggregation:

EM1617AS_R = MAX (0, NM1617 * (0.00528 + 0.00404) + EM1617AS.ADJ) (62)

EM1819AS_R = MAX (0, NM1819 * (0.00309 + 0.28448 * EA / (NM16O+ NF16O) - 0.00165) +

EM1819AS.ADJ) (90)

EM2024AS_R = MAX (0, NM2024 * (-0.00181 + 0.97958 * EA / (NM16O+ NF16O) - 0.01093) + EM2024AS.ADJ) 

 (91)

EM2534AS_R = MAX (0, NM2534 * (-0.00263 + 1.23186 * EA / (NM16O+ NF16O) - 0.01021) + EM2534AS.ADJ) 

 (92)

EM3544AS_R = MAX (0, NM3544 * (-0.00151 + 1.66765 * EA / (NM16O+ NF16O) - 0.01450) + EM3544AS.ADJ) 

 (93)

EM4554AS_R = MAX (0, NM4554 * (-0.00381 + 2.86654 * EA / (NM16O+ NF16O) - 0.03175) + EM4554AS.ADJ) 

 (94)

EM5564AS_R = MAX (0, NM5564 * (-0.00460 + 2.78817 * EA / (NM16O+ NF16O) - 0.02398) + EM5564AS.ADJ) 

 (95)

EM65OAS_R = MAX (0, NM65O * (0.00079 + 1.76904 * EA / (NM16O+ NF16O) - 0.01437) + EM65OAS.ADJ) (96)

119
EF1617AS_R = MAX (0, NF1617 * (0.00181 + 0.00030) + EF1617AS.ADJ) (82)

EF1819AS_R = MAX (0, EM1819AS.1 * (-0.02393 + 0.63672 * MOVAVG (2, RTP.1) + 0.98791 * EF1819/EM1819 - 4.43926) + 

EF1819AS.ADJ) (83)

EF2024AS_R = MAX (0, EM2024AS.1 * (0.07353 - 0.40207 * MOVAVG (2, RTP.1) + 0.57572 * EF2024/EM2024 - 0.01117) + 

EF2024AS.ADJ) (84)

EF2534AS_R = MAX (0, EM2534AS.1 * (0.16575 + 0.16967 * MOVAVG (2, RTP.1) + 0.55503 * EF2534/EM2534 - 0.43412) + 

EF2534AS.ADJ) (85)

EF3544AS_R = MAX (0, EM3544AS.1 * (0.15848 + 0.37839 * MOVAVG (2, RTP.1) + 0.37764 * EF3544/EM3544 - 0.45362) + 

EF3544AS.ADJ) (86)

EF4554AS_R = MAX (0, EM4554AS.1 * (0.21947 + 0.29497 * MOVAVG (2, RTP.1) + 0.58974 * EF4554/EM4554 - 0.51966) + 

EF4554AS.ADJ) (87)

EF5564AS_R = MAX (0, EM5564AS.1 * (0.20892 + 0.36294 * MOVAVG (2, RTP.1) + 0.65320 * EF5564/EM5564 - 0.66626) + 

EF5564AS.ADJ) (88)

EF65OAS_R = MAX (0, EM65OAS.1 * (0.16242 + 0.54916 * MOVAVG (2, RTP.1) + 0.06199 * EF65O/EM65O- 0.47556) + 

EF65OAS.ADJ) (89)

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 (97)

Final (scaled) equations:

EM1617AS = EM1617AS_R * (EAS/EAS_R) (98)

EM1819AS = EM1819AS_R * (EAS/EAS_R) (105)

EM2024AS = EM2024AS_R * (EAS/EAS_R) (112)

EM2534AS = EM2534AS_R * (EAS/EAS_R) (119)

EM3544AS = EM3544AS_R * (EAS/EAS_R) (126)

EM4554AS = EM4554AS_R * (EAS/EAS_R) (133)

EM5564AS = EM5564AS_R * (EAS/EAS_R) (140)

EM65OAS = EM65OAS_R * (EAS/EAS_R) (147)

EF1617AS = EF1617AS_R * (EAS/EAS_R) (160)

EF1819AS = EF1819AS_R * (EAS/EAS_R) (167)

EF2024AS = EF2024AS_R * (EAS/EAS_R) (174)

EF2534AS = EF2534AS_R * (EAS/EAS_R) (181)

EF3544AS = EF3544AS_R * (EAS/EAS_R) (188)

EF4554AS = EF4554AS_R * (EAS/EAS_R) (195)

EF5564AS = EF5564AS_R * (EAS/EAS_R) (202)

EF65OAS = EF65OAS_R * (EAS/EAS_R) (209)

EFAS = EF1617AS + EF1819AS + EF2024AS + EF2534AS + EF3544AS + EF4554AS + EF5564AS + 

EF65OAS (215)

EMAS = EM1617AS + EM1819AS + EM2024AS + EM2534AS + EM3544AS + EM4554AS + EM5564AS + 

EM65OAS (153)

Nonagricultural Private Household Wage Workers: 

“Raw” equations (before scaling the totals): (229-244)

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 - 

120
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 (245)

Total Private Household Wage Workers:

ENAWPH = IF LONGRANGE = 0 

 THEN ENAWPH_R 

 ELSE ENAWPH.1 * (E_FE/E_FE.1) (246)

Final (scaled) equations:

Male (260-267)

EM1617NAWPH = EM1617NAWPH_R * (ENAWPH/ENAWPH_R)

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)

Female (247-254)

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 (255)

EMNAWPH = EM1617NAWPH + EM1819NAWPH + EM2024NAWPH + EM2534NAWPH + EM3544NAWPH + EM4554NAWPH +

EM5564NAWPH + EM65ONAWPH (268)

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)) (257)

EGEFCPS = IF LONGRANGE = 0 

 THEN (EGEFCPS.1 * 1.00750.25) 

 ELSE (EGEFCPS.1 * (E_FE/E_FE.1)) (256)

EGGEFC = EGFC + EGEFCPS (258)

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) (259)

121
Military

Decrease (if any) in EDMIL compared to a year ago

DNEDMIL = IF (EDMIL-EDMIL.4) < 0 

 THEN (EDMIL-EDMIL.4) 

 ELSE 0 (228)

Private employment

EP = E-EGGESL - EGGEFC – EAS – ENAS (269)

Compensation and Output Sectors

Price Deflator for Medical Services

CPIWMS = CPIWMS.1 * (1 + ((CPIW_U/CPIW_U.4)0.25 - 1) * CPIWMSWT) (287)

Unemployment Insurance and Workers Compensation Effective Tax Rates

TMAXUI_SL = TMAXUI_SL.1 *AWSUI.1/AWSUI.2 (404)

RELMAX_UI = TMAXUI_SL/AWSUI.1/1000 (405)

CR_UI = 0.775 (402)

TRATIO_UI = 0.96996 * RELMAX_UI-0.13744 * MOVAVG (4, RTP.1) + 0.10368 * MOVAVG (4, RTP.5) + 

0.04887 (406)

TRATE_UI = 0.00143 * MOVAVG (4, RU.5) + 0.00128 * MOVAVG (4, RU.9) + 0.00057 * MOVAVG (4, RU.13) + 

0.00356 (407)

RUIWS1 = CR_UI * TRATIO_UI * TRATE_UI (408)

RUIWS2 = 0.32476 * MOVAVG (4, RUIWS1.8 * (WSP.8 -WSPRRB.8 +WSGGESL.8)) / (WSP.1 -WSPRR2.1 

+WSGGESL.1) (409)

Workers' Compensation

RWCWS = RWCWS.1 - (RWCWS.1 - 0.0144)/12 (311)

Wages

Average lagged private-sector wage

AWSPL = MOVAVG (8, AWSP.1) (272)

Average lagged private-sector compensation

AWSSPL = MOVAVG (8, AWSSP.1) (343)

Average wage in state & local government (incl. gov’t enterprises)

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 (273)

Total wages in state & local government (incl. gov’t enterprises)

WSGGESL = AWSGGESL * EGGESL (274)

Employer Contribution for Government Social Insurance in State & Local Government Sector

OASDISL_L = (EMPTROASI + EMPTRDI) * 0.978 * CSLA * WSGGESL (307)

HISL_L = EMPTRHI * 1.0 * CSLHI * WSGGESL (308)

SOC_UISL = (-0.02821 * MOVAVG (4, RTP.2) + 0.03145) * WSGGESL (309)

RSOCSL_WC = RSOCSL_WC.1 - (RSOCSL_WC.1 - 0.176)/12 (310)

SOC_WCSL = RSOCSL_WC * RWCWS * WSGGESL (312)

SOC_SL = (OASDISL_L + HISL_L + SOC_UISL + SOC_WCSL) (313)

Employer Contributions for Employee Pension and Insurance funds in State & Local Government Sector

Workers' Compensation - employees and annuitants

OLI_WCSL = (1 - RSOCSL_WC) * RWCWS * WSGGESL (316)

Pensions

OLI_RETSL = WSGGESL * (OLI_RETSL.1/WSGGESL.1) (317)

122
Life Insurance - employees and annuitants

OLI_GLI_SL = 2.0 * EGGESL * ((WSGGESL/EGGESL) +2.0) * 0.075 * 26/1000 (314)

Health Insurance - employees and annuitants

OLI_GHI_SL = (OLI_GHI_SL.1 / EGGESL.1) * CPIWMS/CPIWMS.1 * EGGESL * RGR_GHI (315)

Total

OLI_SL = (OLI_GLI_SL + OLI_GHI_SL + OLI_WCSL + OLI_RETSL) (318)

RCWSSL = (1 + (SOC_SL + OLI_SL)/WSGGESL) (319)

WSSGGESL = IF LONGRANGE = 0 

 THEN RCWSSL*WSGGESL 

 ELSE (WSSGGESL.1/EGGESL.1) * AVG_GDP/AVG_GDP.1 * EGGESL (320)

WSSGSL = WSSGGESL * WSSGSL.1/WSSGGESL.1 (321)

WSSGESL = WSSGGESL – WSSGSL (324)

CFCGSL = IF LONGRANGE = 0 

 THEN WSSGSL * RCFCGSL 

 ELSE CFCGSL.1 * WSSGGESL/WSSGGESL.1 (322)

GDPGSL = WSSGSL + CFCGSL (323)

CFCGESL = IF LONGRANGE = 0 

 THEN WSSGESL * RCFCGESL 

 ELSE CFCGESL.1 * WSSGGESL/WSSGGESL.1 (325)

GDPGESL = WSSGESL + CFCGESL (326)

GDPGGESL = GDPGSL + GDPGESL (327)

Federal Civilian General Government and Government Enterprises

Wages

General Government and Government Enterprises

Civilian pay raise

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) (270)

Military pay raise 

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) (277)

Average wage in Federal Civilian Government

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 (275)

Total wages in FCG

WSGGEFC = AWSGGEFC * EGGEFC (276)

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 (271)

WEFC_N = AWEFC_N * TEFC_N (283)

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 (290)

WSGEFC = AWSGEFC * EGEFCPS (291)

General Government

WSGFC = WSGGEFC -WSGEFC (292)

AWSGFC = WSGFC/EGFC (378)

123
Employer Contribution for Government Social Insurance

General Government and Government Enterprises

OASDIFC_L = (EMPTROASI + EMPTRDI) * 1.04 * (WSGGEFC - WEFC_N) * ADJ_FSA_FC (284)

HIFC_L = EMPTRHI* 1.055 * WSGGEFC * ADJ_FSA_FC (285)

SOCF_UIFC = (-0.05934 * RTP + 0.06165) * WSGGEFC (281)

SOCF_WC = 0.0159 * WSGGEFC (282)

SOC_FC = (SOCF_UIFC + SOCF_WC + OASDIFC_L + HIFC_L) (286)

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 (293)

OLI_FERS1 = 0.107 * (WSGGEFC * 0.9 -WEFC_N) (294)

OLI_FERSFC = 0.048 * (WSGGEFC * 0.9 -WEFC_N) (295)

OLI_RETFC = OLI_CSRS1 + OLI_FERS1 + OLI_FERSFC + OLIF_RETFCO (296)

Life Insurance - employees and annuitants

OLI_GLI_FC = 2.0 * EGGEFC * ((WSGGEFC/EGGEFC) + 2.0) * 0.075 * 26/1000 (289)

Health Insurance - employees and annuitants

OLI_GHI_FC = (OLI_GHI_FC.1 / EGGEFC.1) * CPIWMS/CPIWMS.1 * EGGEFC * RGR_GHI (288)

OLI_FC = (OLI_GHI_FC + OLI_GLI_FC + OLI_RETFC) (297)

Compensation

General Government and Government Enterprises

RCWSF = (1 + (SOC_FC + 

OLI_FC)/WSGGEFC) (298)

WSSGGEFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGGEFC 

 ELSE (WSSGGEFC.1/EGGEFC.1) * AVG_GDP/AVG_GDP.1 * EGGEFC (300)

WSSGFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGFC 

 ELSE (WSSGFC.1 / (EGGEFC.1 - EGEFCPS.1)) * AVG_GDP/AVG_GDP.1 * (EGGEFC - EGEFCPS) (299)

WSSGEFC = IF LONGRANGE = 0 

 THEN RCWSF * WSGEFC 

 ELSE (WSSGEFC.1/EGEFCPS.1) * AVG_GDP/AVG_GDP.1 * EGEFCPS (303)

Consumption of Fixed Capital

General Government and Government Enterprises

CFCGFC = IF LONGRANGE = 0 

 THEN WSSGFC * RCFCGFC 

 ELSE CFCGFC.1 * WSSGGEFC / WSSGGEFC.1 (301)

CFCGEFC = IF LONGRANGE = 0 

 THEN WSSGEFC * RCFCGEFC 

 ELSE CFCGEFC.1 * WSSGGEFC / WSSGGEFC.1 (304)

Gross Domestic Product

General Government and Government Enterprises

GDPGFC = WSSGFC + CFCGFC (302)

GDPGEFC = WSSGEFC + CFCGEFC (305)

GDPGGEFC = GDPGFC + GDPGEFC (306)

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 (278)

124
WSGFM = AWSGFM * (EDMIL+ EDMIL_R) (279)

Employer Contribution for Government Social Insurance

OASDIFM_L = (EMPTROASI + EMPTRDI) * 0.9975 * CML * WSGFM (331)

HIFM_L = EMPTRHI* 1.0 *CML * WSGFM (332)

SOCF_UIFM = MAX (0.001, (-0.05263 * DIFF (EDMIL + EDMIL_R) - 0.03079 * RTP + 0.03310)) * WSGFM (329)

SOCF_MIFM = 0.30 * CPIWMS * (EDMIL + EDMIL_R) (330)

SOC_FM = (SOCF_UIFM + SOCF_MIFM + OASDIFM_L + HIFM_L) (333)

Employer Contributions for Employee Pension and Insurance funds

OLI_RETFM = (OLI_RETFM.1/WSGFM.1 - (OLI_RETFM.1/WSGFM.1 - 0.472)/12) * WSGFM (328)

Compensation

RCWSM = (1 + (OLI_RETFM + SOC_FM)/WSGFM) (334)

WSSGFM = IF LONGRANGE = 0 

 THEN RCWSM * WSGFM 

 ELSE (WSSGFM.1/EDMIL.1) * AVG_GDP/AVG_GDP.1 * EDMIL (335)

Consumption of Fixed Capital

CFCGFM = IF LONGRANGE = 0 

 THEN WSSGFM * RCFCGFM 

 ELSE CFCGFM.1 * WSSGFM/WSSGFM.1 (336)

Gross Domestic Product

GDPGFM = WSSGFM + CFCGFM (337)

GDPGF = GDPGFC + GDPGFM (387)

GDPGGE = GDPGGEFC + GDPGGESL + GDPGFM (338)

Total (Civilian and Military) Federal General Government and Government Enterprises

WSSGF = WSSGFC + WSSGFM (392)

WSSGE = WSSGEFC + WSSGESL (394)

WSSG = WSSGF + WSSGSL (393)

GDPGE = GDPGEFC + GDPGESL (389)

GDPG = GDPGF + GDPGSL (388)

NIPA Farm Output and Earnings

Real farm output

GDPPF09 = IF LONGRANGE = 0 

 THEN EXP (- 3.52340 + 0.02055 * YEAR) * N_SSA * 1.125 * 1.138 

 ELSE GDPPF09.1 * GDP09/GDP09.1 (19)

Farm sector deflator

PGDPAF = IF LONGRANGE = 0 

 THEN PGDPAF.1 * ((PGDP/PGDP.1)4

 - 0.01) 0.25 

 ELSE PGDPAF.1 * ((PGDP/PGDP.1)4

) 0.25 (223)

Nominal farm output

GDPPF = GDPPF09 * PGDPAF (339)

Farm compensation and wages

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 (360)

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 (381)

AWSPF = WSPF/EAW (382)

Farm proprietors’ income

AYF_K = ((YF.1 /EAS.1) / (WSSPF.1/EAW.1) -5.0)*.8 + 5.0 (395)

YF = AYF_K * (WSSPF/EAW) * EAS (396)

125
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) (340)

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 (383)

AWSPH = WSPH / ENAWPH (384)

Owner Occupied Housing

OOH = OOH.1 * (KGDP09 * PGDP) / (KGDP09.1 * PGDP.1) (341)

Gross Value Added

GDPPH = IF LONGRANGE = 0 

 THEN WSSPH + OOH 

 ELSE (AVG_GDP/AVG_GDP.1) * ENAWPH * (GDPPH.1/ENAWPH.1) (342)

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) (345)

AWSSPHS = IF LONGRANGE = 0 

 THEN AWSSPHS.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPHS.1 * AVG_GDP/AVG_GDP.1 (344)

WSSPHS = AWSSPHS* EPHS_EST (346)

Educational Services

EPES_EST = IF LONGRANGE = 0 

 THEN EPES_EST.1 + 0.075/4 

 ELSE EPES_EST.1 * (E_FE/E_FE.1) (348)

AWSSPES = IF LONGRANGE = 0 

 THEN AWSSPES.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPES.1 * AVG_GDP/AVG_GDP.1 (347)

WSSPES = AWSSPES* EPES_EST (349)

Social Services

EPSS_EST = IF LONGRANGE = 0 

 THEN EPSS_EST.1 + 0.075/4 

 ELSE EPSS_EST.1 * (E_FE/E_FE.1) (351)

AWSSPSS = IF LONGRANGE = 0 

 THEN AWSSPSS.1 * AWSSPL/AWSSPL.1 

 ELSE AWSSPSS.1 * AVG_GDP/AVG_GDP.1 (350)

WSSPSS = AWSSPSS* EPSS_EST (352)

Gross Value Added

WSSPNI = WSSPNI.1 * (WSSPHS + WSSPES + WSSPSS) / (WSSPHS.1 + WSSPES.1 + WSSPSS.1) (353)

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 (391)

GDPPNI = IF LONGRANGE = 0 

 THEN WSSPNI / ((WSSPNI.1/GDPPNI.1 - 0.866) * 0.8 + 0.866) 

 ELSE WSSPNI /0.866 (354)

Private Output and Compensation

ROASDIP_L = (EMPTROASI + EMPTRDI) * TXRP * CP (365)

RHIP_L = EMPTRHI * 1.0 * CP (366)

RSOC_UIP = 0.00109 * MOVAVG (4, RU.2) + 0.00045 * MOVAVG (4, RU.10) + 0.00048 * MOVAVG (4, RU.18) - 0.00331 (367)

126
RSOC_WCP = RWCWS * RSOCSL_WC (368)

RSOCF_PBG = 0.00022 (369)

OLI

ROLI_WCP = RWCWS * (1 - RSOCSL_WC) (370)

ROLI_SU = 0.0005 (371)

OLI_GLI_P = 0.0025 * EP * AWSP.1 (363)

OLI_GHI_P = (OLI_GHI_P.1 / EP.1) * CPIWMS/CPIWMS.1 * EP * RGR_GHI (364)

ROLI_PPPS = MAX (ROLI_PPPS.1, 0.00031 * YEAR + 0.00866) (372)

Employee Compensation and Nonfarm Proprietor Income (WSS and YNF) 

WSSGGE = (WSSGGESL + WSSGGEFC + WSSGFM) (374)

GDPPBNFXGE = (GDP – GDPGGE – GDPPF – GDPPH – GDPPNI) (355)

RWSSPBNFXGE = 0.30026 * RTP.1 + 0.31936 + (0.6038 - (0.30026 * 1.0 + 0.31936)) + RWSSPBNFXGE_ADJ (280)

ENAW = ENA-ENAS-ENAU (356)

ENAWPBXGE = ENAW - (ENAWPH + EGGEFC + EGGESL + WSSPNI / (WSSPHS + WSSPES + WSSPSS) * (EPHS_EST + 

EPES_EST + EPSS_EST)) (357)

ENAWSPBXGE = ENAWPBXGE + ENAS (403)

AYNF_K = ((YNF.1/ENAS.1 / (WSSPBNFXGE.1/ENAWPBXGE.1)) - 1.65) * 0.9 + 1.65 (401)

AYF = YF/EAS (399)

AWSSPF = WSSPF/EAW (398)

AYNF = YNF/ENAS (400)

AWSSPBNFXGE = WSSPBNFXGE/ENAWPBXGE (397)

YNF = YNF.1 * (GDPPBNFXGE / GDPPBNFXGE.1) * (ENAS / (ENAS + ENAWPBXGE)) / (ENAS.1 / (ENAS.1 + 

ENAWPBXGE.1)) (358)

WSSPBNFXGE = RWSSPBNFXGE * (GDPPBNFXGE - YNF) (359)

WSSP = WSSPBNFXGE+WSSPF+WSSPH +WSSPNI (361)

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) (373)

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 (376)

WSD = WS (410)

WSP = (WS - WSGGESL - WSGGEFC - WSGFM) (379)

AWSP = WSP/EP (380)

AWSSP = WSSP/EP (385)

Other Variables

WSDP = (WSD –WSGGESL – WSGGEFC – WSGFM) (411)

AWSE = WS / (E + EDMIL – EAS – ENAS) (377)

AWSUI = (WS -WSGGEFC -WSGFM) / (E – EGGEFC – EAS – ENAS) (386)

WSS = (WSSP + WSSGGE) (375)

OLI_GGE = OLI_FC + OLI_SL + OLI_RETFM (412)

OLI_WCP = ROLI_WCP * WSP (413)

OLI_SU = ROLI_SU * WSP (414)

OLI_PPPS = ROLI_PPPS * WSP (415)

OLI_P = OLI_WCP + OLI_SU + OLI_GHI_P + OLI_GLI_P + OLI_PPPS (416)

OLI = OLI_GGE + OLI_P (417)

SOC_GGE = SOC_FC + SOC_FM + SOC_SL (418)

SOC_UIP = RSOC_UIP * WSP (419)

SOC_WCP = RSOC_WCP * WSP (420)

SOCF_PBG = RSOCF_PBG * WSP (423)

SOCF_RETRR = 0.20 * WSPRRB (362)

SOC_P = SOC_UIP + SOC_WCP + OASDIP_L + HIP_L + SOCF_PBG + SOCF_RETRR (424)

SOC = SOC_GGE + SOC_P (425)

OASDIP_L = ROASDIP_L * WSP (421)

HIP_L = RHIP_L * WSP (422)

OLI_PPS = OLI_PPPS + OLI_RETFC + OLI_RETFM + OLI_RETSL (426)

OLI_GHI = OLI_GHI_P + OLI_GHI_FC + OLI_GHI_SL (428)

OLI_GLI = OLI_GLI_P + OLI_GLI_FC + OLI_GLI_SL (429)

OLI_WC = OLI_WCP + OLI_WCSL (427)

SOCSL_WC = SOC_WCSL + SOC_WCP (430)

SOCF_UIFED = SOCF_UIFC + SOCF_UIFM (431)

SOCF_UIS = (SOC_UIP + SOC_UISL) * RUIWS1 / (RUIWS1 + RUIWS2) (432)

SOCF_UIF = (SOC_UIP + SOC_UISL) - SOCF_UIS (433)

SOCF_OASDI = OASDIP_L + OASDISL_L + OASDIFC_L + OASDIFM_L (434)

127
SOCF_HI = HIP_L + HISL_L + HIFC_L + HIFM_L (435)

TAXMAX = IF (first quarter of the year) THEN

 300 *NINT(0.5+MOVAVG(4,AWSE.5)/MOVAVG(4,AWSE.9)*1000*TAXMAX.1/300)/1000

 ELSE TAXMAX.1 (390)

128
2.3 OASDI Covered Employment and Earnings (MODSOLA) 

Total At-Any-Time Employment (Equations 1–52)

Ages 0 through 15, where s=sex;a=age 0,1,2,3,...15; i=calendar year) (1–10, 21, 22, 27–36, 47, 48)

 he_m_sy(s,a,i) = (he_m_sy(s,a,histend) / nsy_a(s,a,histend) &

 + he_m_sy(s,a,histend-1) / nsy_a(s,a,histend-1) &

 + he_m_sy(s,a,histend-2) / nsy_a(s,a,histend-2) ) / 3 &

 * nsy_a(s,a,i)

HI covered workers age groups 10-13 and 14-15, by sex and calendar year (21, 22, 47, 48)

 he_m_1013(s,i) = sum(he_m_sy(s,10:13,i))

 he_m_1415(s,i) = sum(he_m_sy(s,14:15,i)

HI covered workers age group 15u, by sex and calendar year (23, 49)

 he_m_15u(s,i) = sum(he_m_sy(s,0:9,i)) + he_m_1013(s,i) + he_m_1415(s,i)

OASDI covered = HI covered, by sex, single year of age, and calendar year (11–22, 37–48)

 ce_m_sy(s,a,i)=he_m(s,a,i)

OASDI covered workers age groups 10-13 and 14-15, by sex and calendar year (24, 25, 50, 51)

 ce_m_1013(s,i) = sum(ce_m_sy(s,10:13,i))

 ce_m_1415(s,i) = sum(ce_m_sy(s,14:15,i)

OASDI covered workers age group 15u, by sex and calendar year (26, 52)

 ce_m_15u(s,i) = sum(ce_m_sy(s,0:9,i)) +ce_m_1013(s,i) + ce_m_1415(s,i)

Male Disaggregates Aged 16 and Over

Preliminary

Average Weeks Worked

AWWM1617_P = 0.35417 * TREND_TE - 0.17568 * RM1617 + 8.80229; (53)

AWWM1819_P = 0.28021 * TREND_TE - 0.16633 * RM1819 + 15.4522; (58)

AWWM2024_P = 0.17338 * TREND_TE - 0.32843 * RM2024 + 31.4779; (63)

AWWM2529_P = 0.04353 * TREND_TE - 0.32898 * RM2529 + 46.8304; (68)

AWWM3034_P = 0.04353 * TREND_TE - 0.32898 * RM3034 + 46.8304; (73)

AWWM3539_P = 0.03256 * TREND_TE - 0.26573 * RM3539 + 47.9512; (78)

AWWM4044_P = 0.03256 * TREND_TE - 0.26573 * RM4044 + 47.9512; (83)

AWWM4549_P = 0.03923 * TREND_TE - 0.23146 * RM4549 + 46.8025; (88)

AWWM5054_P = 0.03923 * TREND_TE - 0.23146 * RM5054 + 46.8025; (93)

AWWM5559_P = 0.04481 * TREND_TE - 0.28537 * RM5559 + 45.0196; (98)

AWWM6064_P = 0.14488 * TREND_TE + 0.01910 * RM6064 + 29.5797; (103)

AWWM6569_P = 0.21483 * TREND_TE - 0.23366 * RM6569 + 21.1343; (108)

AWWM70O_P = 0.09069 * TREND_TE + 0.43206 * RM70O + 28.6903; (113)

AWWM1617_PL = 0.35417 * TREND_TE.1 - 0.17568 * RM1617.1 + 8.80229; (55)

AWWM1819_PL = 0.28021 * TREND_TE.1 - 0.16633 * RM1819.1 + 15.4522; (60)

AWWM2024_PL = 0.17338 * TREND_TE.1 - 0.32843 * RM2024.1 + 31.4779; (65)

AWWM2529_PL = 0.04353 * TREND_TE.1 - 0.32898 * RM2529.1 + 46.8304; (70)

AWWM3034_PL = 0.04353 * TREND_TE.1 - 0.32898 * RM3034.1 + 46.8304; (75)

AWWM3539_PL = 0.03256 * TREND_TE.1 - 0.26573 * RM3539.1 + 47.9512; (80)

AWWM4044_PL = 0.03256 * TREND_TE.1 - 0.26573 * RM4044.1 + 47.9512; (85)

AWWM4549_PL = 0.03923 * TREND_TE.1 - 0.23146 * RM4549.1 + 46.8025; (90)

AWWM5054_PL = 0.03923 * TREND_TE.1 - 0.23146 * RM5054.1 + 46.8025; (95)

AWWM5559_PL = 0.04481 * TREND_TE.1 - 0.28537 * RM5559.1 + 45.0196; (100)

129
AWWM6064_PL = 0.14488 * TREND_TE.1 + 0.01910 * RM6064.1 + 29.5797; (105)

AWWM6569_PL = 0.21483 * TREND_TE.1 - 0.23366 * RM6569.1 + 21.1343; (110)

AWWM70O_PL = 0.09069 * TREND_TE.1 + 0.43206 * RM70O.1 + 28.6903; (115)

Work Experience

WEM1617_3_P = EM1617 * 52 / AWWM1617_P; (54)

WEM1819_3_P = EM1819 * 52 / AWWM1819_P; (59)

WEM2024_3_P = EM2024 * 52 / AWWM2024_P; (64)

WEM2529_3_P = EM2529 * 52 / AWWM2529_P; (69)

WEM3034_3_P = EM3034 * 52 / AWWM3034_P; (74)

WEM3539_3_P = EM3539 * 52 / AWWM3539_P; (79)

WEM4044_3_P = EM4044 * 52 / AWWM4044_P; (84)

WEM4549_3_P = EM4549 * 52 / AWWM4549_P; (89)

WEM5054_3_P = EM5054 * 52 / AWWM5054_P; (94)

WEM5559_3_P = EM5559 * 52 / AWWM5559_P; (99)

WEM6064_3_P = EM6064 * 52 / AWWM6064_P; (104)

WEM6569_3_P = EM6569 * 52 / AWWM6569_P; (109)

WEM70O_3_P = EM70O * 52 / AWWM70O_P ; (114)

WEM1617_3_PL = EM1617.1 * 52 / AWWM1617_PL; (56)

WEM1819_3_PL = EM1819.1 * 52 / AWWM1819_PL; (61)

WEM2024_3_PL = EM2024.1 * 52 / AWWM2024_PL; (66)

WEM2529_3_PL = EM2529.1 * 52 / AWWM2529_PL; (71)

WEM3034_3_PL = EM3034.1 * 52 / AWWM3034_PL; (76)

WEM3539_3_PL = EM3539.1 * 52 / AWWM3539_PL; (81)

WEM4044_3_PL = EM4044.1 * 52 / AWWM4044_PL; (86)

WEM4549_3_PL = EM4549.1 * 52 / AWWM4549_PL; (91)

WEM5054_3_PL = EM5054.1 * 52 / AWWM5054_PL; (96)

WEM5559_3_PL = EM5559.1 * 52 / AWWM5559_PL; (101)

WEM6064_3_PL = EM6064.1 * 52 / AWWM6064_PL; (106)

WEM6569_3_PL = EM6569.1 * 52 / AWWM6569_PL; (111)

WEM70O_3_PL = EM70O.1 * 52 / AWWM70O_PL ; (116)

Total Employed

TEM1617_P = ((WEM1617_3_P / WEM1617_3_PL) * (TEM1617.1 - NM1617M.1) + NM1617M) * MULT1_TEM1617 *

MULT2_TEM1617; (57)

TEM1819_P = ((WEM1819_3_P / WEM1819_3_PL) * (TEM1819.1 - NM1819M.1) + NM1819M) * MULT1_TEM1819 * 

MULT2_TEM1819; (62)

TEM2024_P = ((WEM2024_3_P / WEM2024_3_PL) * (TEM2024.1 - NM2024M.1) + NM2024M) * MULT1_TEM2024 * 

MULT2_TEM2024; (67)

TEM2529_P = ((WEM2529_3_P / WEM2529_3_PL) * (TEM2529.1 - NM2529M.1) + NM2529M) * MULT1_TEM2529 * 

MULT2_TEM2529; (72)

TEM3034_P = ((WEM3034_3_P / WEM3034_3_PL) * (TEM3034.1 - NM3034M.1) + NM3034M) * MULT1_TEM3034 * 

MULT2_TEM3034; (77)

TEM3539_P = ((WEM3539_3_P / WEM3539_3_PL) * (TEM3539.1 - NM3539M.1) + NM3539M) * MULT1_TEM3539 * 

MULT2_TEM3539; (82)

TEM4044_P = ((WEM4044_3_P / WEM4044_3_PL) * (TEM4044.1 - NM4044M.1) + NM4044M) * MULT1_TEM4044 * 

MULT2_TEM4044; (87)

TEM4549_P = ((WEM4549_3_P / WEM4549_3_PL) * (TEM4549.1 - NM4549M.1) + NM4549M) * MULT1_TEM4549 * 

MULT2_TEM4549; (92)

TEM5054_P = ((WEM5054_3_P / WEM5054_3_PL) * (TEM5054.1 - NM5054M.1) + NM5054M) * MULT1_TEM5054 * 

MULT2_TEM5054; (97)

TEM5559_P = ((WEM5559_3_P / WEM5559_3_PL) * (TEM5559.1 - NM5559M.1) + NM5559M) * MULT1_TEM5559 * 

MULT2_TEM5559; (102) 

TEM6064_P = ((WEM6064_3_P / WEM6064_3_PL) * (TEM6064.1)) * MULT1_TEM6064 * MULT2_TEM6064; (107)

TEM6569_P = ((WEM6569_3_P / WEM6569_3_PL) * (TEM6569.1)) * MULT1_TEM6569 * MULT2_TEM6569; (112)

TEM70O_P = ((WEM70O_3_P / WEM70O_3_PL ) * (TEM70O.1 )) * MULT1_TEM70O * MULT2_TEM70O; (117)

130
WEM16O_3_P = WEM1617_3_P + WEM1819_3_P + WEM2024_3_P + WEM2529_3_P + WEM3034_3_P + WEM3539_3_P + 

WEM4044_3_P + WEM4549_3_P 

 + WEM5054_3_P + WEM5559_3_P + WEM6064_3_P + WEM6569_3_P + WEM70O_3_P; (190)

AWWM16O_P = EM16O * 52 / WEM16O_3_P; (191)

TEM16O_P = TEM1617_P + TEM1819_P + TEM2024_P + TEM2529_P + TEM3034_P + TEM3539_P + TEM4044_P + TEM4549_P + 

TEM5054_P + TEM5559_P + TEM6064_P + TEM6569_P + TEM70O_P; (118)

Final (Pre-TE.ADD) (192–230) 

Average Weeks Worked

AWWM1617 = AWWM1617_P;

AWWM1819 = AWWM1819_P;

AWWM2024 = AWWM2024_P;

AWWM2529 = AWWM2529_P; 

AWWM3034 = AWWM3034_P;

AWWM3539 = AWWM3539_P;

AWWM4044 = AWWM4044_P; 

AWWM4549 = AWWM4549_P; 

AWWM5054 = AWWM5054_P; 

AWWM5559 = AWWM5559_P;

AWWM6064 = AWWM6064_P;

AWWM6569 = AWWM6569_P;

AWWM70O = AWWM70O_P ; 

Work Experience

WEM1617_3 = WEM1617_3_P;

WEM1819_3 = WEM1819_3_P;

WEM2024_3 = WEM2024_3_P;

WEM2529_3 = WEM2529_3_P;

WEM3034_3 = WEM3034_3_P;

WEM3539_3 = WEM3539_3_P;

WEM4044_3 = WEM4044_3_P;

WEM4549_3 = WEM4549_3_P;

WEM5054_3 = WEM5054_3_P;

WEM5559_3 = WEM5559_3_P;

WEM6064_3 = WEM6064_3_P;

WEM6569_3 = WEM6569_3_P;

WEM70O_3 = WEM70O_3_P ;

Total Employed

TEM1617 = TEM1617_P;

TEM1819 = TEM1819_P;

TEM2024 = TEM2024_P;

TEM2529 = TEM2529_P;

TEM3034 = TEM3034_P;

TEM3539 = TEM3539_P;

TEM4044 = TEM4044_P;

TEM4549 = TEM4549_P;

TEM5054 = TEM5054_P;

TEM5559 = TEM5559_P;

TEM6064 = TEM6064_P;

TEM6569 = TEM6569_P;

TEM70O = TEM70O_P ;

WEM16O_3 = WEM16O_3_P;

131
AWWM16O = AWWM16O_P ; 

TEM16O = TEM16O_P ; (119)

TEM = TEM16O + HE_M_15U(1,YEAR) (120)

Female Disaggregates Aged 16 and Over

Preliminary

Average Weeks Worked

AWWF1617_P = 0.44829 * TREND_TE - 0.06786 * RF1617 + 0.37331; (121)

AWWF1819_P = 0.24262 * TREND_TE - 0.00950 * RF1819 + 17.0791; (126)

AWWF2024_P = 0.18291 * TREND_TE - 0.06453 * RF2024 + 26.6823; (131)

AWWF2529_P = 0.07674 * TREND_TE - 0.10131 * RF2529 + 40.0210; (136)

AWWF3034_P = 0.07674 * TREND_TE - 0.10131 * RF3034 + 40.0210; (141)

AWWF3539_P = 0.05004 * TREND_TE - 0.10322 * RF3539 + 43.9974; (146)

AWWF4044_P = 0.05004 * TREND_TE - 0.10322 * RF4044 + 43.9974; (151)

AWWF4549_P = 0.08209 * TREND_TE - 0.17307 * RF4549 + 41.1649; (156)

AWWF5054_P = 0.08209 * TREND_TE - 0.17307 * RF5054 + 41.1649; (161)

AWWF5559_P = 0.04868 * TREND_TE + 0.17072 * RF5559 + 41.9580; (166)

AWWF6064_P = 0.14339 * TREND_TE + 0.01918 * RF6064 + 29.1567; (171)

AWWF6569_P = 0.01857 * TREND_TE + 0.64199 * RF6569 + 36.1193; (176)

AWWF70O_P = 0.20193 * TREND_TE + 0.92866 * RF70O + 14.2412; (181)

AWWF1617_PL = 0.44829 * TREND_TE.1 - 0.06786 * RF1617.1 + 0.37331; (123)

AWWF1819_PL = 0.24262 * TREND_TE.1 - 0.00950 * RF1819.1 + 17.0791; (128)

AWWF2024_PL = 0.18291 * TREND_TE.1 - 0.06453 * RF2024.1 + 26.6823; (133)

AWWF2529_PL = 0.07674 * TREND_TE.1 - 0.10131 * RF2529.1 + 40.0210; (138)

AWWF3034_PL = 0.07674 * TREND_TE.1 - 0.10131 * RF3034.1 + 40.0210; (143)

AWWF3539_PL = 0.05004 * TREND_TE.1 - 0.10322 * RF3539.1 + 43.9974; (148)

AWWF4044_PL = 0.05004 * TREND_TE.1 - 0.10322 * RF4044.1 + 43.9974; (153)

AWWF4549_PL = 0.08209 * TREND_TE.1 - 0.17307 * RF4549.1 + 41.1649; (158)

AWWF5054_PL = 0.08209 * TREND_TE.1 - 0.17307 * RF5054.1 + 41.1649; (163)

AWWF5559_PL = 0.04868 * TREND_TE.1 + 0.17072 * RF5559.1 + 41.9580; (168)

AWWF6064_PL = 0.14339 * TREND_TE.1 + 0.01918 * RF6064.1 + 29.1567; (173)

AWWF6569_PL = 0.01857 * TREND_TE.1 + 0.64199 * RF6569.1 + 36.1193; (178)

AWWF70O_PL = 0.20193 * TREND_TE.1 + 0.92866 * RF70O.1 + 14.2412; (183)

Work Experience

WEF1617_3_P = EF1617 * 52 / AWWF1617_P; (122)

WEF1819_3_P = EF1819 * 52 / AWWF1819_P; (127)

WEF2024_3_P = EF2024 * 52 / AWWF2024_P; (132)

WEF2529_3_P = EF2529 * 52 / AWWF2529_P; (137)

WEF3034_3_P = EF3034 * 52 / AWWF3034_P; (142)

WEF3539_3_P = EF3539 * 52 / AWWF3539_P; (147)

WEF4044_3_P = EF4044 * 52 / AWWF4044_P; (152)

WEF4549_3_P = EF4549 * 52 / AWWF4549_P; (157)

WEF5054_3_P = EF5054 * 52 / AWWF5054_P; (162)

WEF5559_3_P = EF5559 * 52 / AWWF5559_P; (167)

WEF6064_3_P = EF6064 * 52 / AWWF6064_P; (172)

WEF6569_3_P = EF6569 * 52 / AWWF6569_P; (177)

WEF70O_3_P = EF70O * 52 / AWWF70O_P ; (182)

WEF1617_3_PL = EF1617.1 * 52 / AWWF1617_PL; (124)

WEF1819_3_PL = EF1819.1 * 52 / AWWF1819_PL; (129)

WEF2024_3_PL = EF2024.1 * 52 / AWWF2024_PL; (134)

WEF2529_3_PL = EF2529.1 * 52 / AWWF2529_PL; (139)

WEF3034_3_PL = EF3034.1 * 52 / AWWF3034_PL; (144)

132
WEF3539_3_PL = EF3539.1 * 52 / AWWF3539_PL; (149)

WEF4044_3_PL = EF4044.1 * 52 / AWWF4044_PL; (154)

WEF4549_3_PL = EF4549.1 * 52 / AWWF4549_PL; (159)

WEF5054_3_PL = EF5054.1 * 52 / AWWF5054_PL; (164)

WEF5559_3_PL = EF5559.1 * 52 / AWWF5559_PL; (169)

WEF6064_3_PL = EF6064.1 * 52 / AWWF6064_PL; (174)

WEF6569_3_PL = EF6569.1 * 52 / AWWF6569_PL; (179)

WEF70O_3_PL = EF70O.1 * 52 / AWWF70O_PL ; (184)

Total Employed

TEF1617_P = ((WEF1617_3_P / WEF1617_3_PL) * (TEF1617.1 - NF1617M.1) + NF1617M) * MULT1_TEF1617 * 

MULT2_TEF1617; (125)

TEF1819_P = ((WEF1819_3_P / WEF1819_3_PL) * (TEF1819.1 - NF1819M.1) + NF1819M) * MULT1_TEF1819 * MULT2_TEF1819;

 (130)

TEF2024_P = ((WEF2024_3_P / WEF2024_3_PL) * (TEF2024.1 - NF2024M.1) + NF2024M) * MULT1_TEF2024 * MULT2_TEF2024; 

 (135)

TEF2529_P = ((WEF2529_3_P / WEF2529_3_PL) * (TEF2529.1 - NF2529M.1) + NF2529M) * MULT1_TEF2529 * MULT2_TEF2529;

 (140)

TEF3034_P = ((WEF3034_3_P / WEF3034_3_PL) * (TEF3034.1 - NF3034M.1) + NF3034M) * MULT1_TEF3034 * MULT2_TEF3034;

 (145)

TEF3539_P = ((WEF3539_3_P / WEF3539_3_PL) * (TEF3539.1 - NF3539M.1) + NF3539M) * MULT1_TEF3539 * MULT2_TEF3539;

 (150)

TEF4044_P = ((WEF4044_3_P / WEF4044_3_PL) * (TEF4044.1 - NF4044M.1) + NF4044M) * MULT1_TEF4044 * MULT2_TEF4044;

 (155)

TEF4549_P = ((WEF4549_3_P / WEF4549_3_PL) * (TEF4549.1 - NF4549M.1) + NF4549M) * MULT1_TEF4549 * MULT2_TEF4549;

 (160)

TEF5054_P = ((WEF5054_3_P / WEF5054_3_PL) * (TEF5054.1 - NF5054M.1) + NF5054M) * MULT1_TEF5054 * MULT2_TEF5054;

 (165)

TEF5559_P = ((WEF5559_3_P / WEF5559_3_PL) * (TEF5559.1 - NF5559M.1) + NF5559M) * MULT1_TEF5559 * MULT2_TEF5559;

 (170)

TEF6064_P = ((WEF6064_3_P / WEF6064_3_PL) * (TEF6064.1)) * MULT1_TEF6064 * MULT2_TEF6064; (175)

TEF6569_P = ((WEF6569_3_P / WEF6569_3_PL) * (TEF6569.1)) * MULT1_TEF6569 * MULT2_TEF6569; (180)

TEF70O_P = ((WEF70O_3_P / WEF70O_3_PL ) * (TEF70O.1 )) * MULT1_TEF70O * MULT2_TEF70O; (185)

WEF16O_3_P = WEF1617_3_P + WEF1819_3_P + WEF2024_3_P + WEF2529_3_P + WEF3034_3_P + WEF3539_3_P + WEF4044_3_P + 

WEF4549_3_P 

 + WEF5054_3_P + WEF5559_3_P + WEF6064_3_P + WEF6569_3_P + WEF70O_3_P; (233)

AWWF16O_P = EF16O * 52 / WEF16O_3_P; (234)

TEF16O_P = TEF1617_P + TEF1819_P + TEF2024_P + TEF2529_P + TEF3034_P + TEF3539_P + TEF4044_P + TEF4549_P + TEF5054_P 

+ TEF5559_P + TEF6064_P + TEF6569_P + TEF70O_P; (186)

Final (Pre-TE.ADD) (235–273)

Average Weeks Worked

AWWF1617 = AWWF1617_P;

AWWF1819 = AWWF1819_P;

AWWF2024 = AWWF2024_P;

AWWF2529 = AWWF2529_P; 

AWWF3034 = AWWF3034_P;

AWWF3539 = AWWF3539_P;

AWWF4044 = AWWF4044_P; 

AWWF4549 = AWWF4549_P; 

AWWF5054 = AWWF5054_P; 

AWWF5559 = AWWF5559_P;

AWWF6064 = AWWF6064_P;

AWWF6569 = AWWF6569_P;

AWWF70O = AWWF70O_P ; 

133
Work Experience

WEF1617_3 = WEF1617_3_P;

WEF1819_3 = WEF1819_3_P;

WEF2024_3 = WEF2024_3_P;

WEF2529_3 = WEF2529_3_P;

WEF3034_3 = WEF3034_3_P;

WEF3539_3 = WEF3539_3_P;

WEF4044_3 = WEF4044_3_P;

WEF4549_3 = WEF4549_3_P;

WEF5054_3 = WEF5054_3_P;

WEF5559_3 = WEF5559_3_P;

WEF6064_3 = WEF6064_3_P;

WEF6569_3 = WEF6569_3_P;

WEF70O_3 = WEF70O_3_P ;

Total Employed

TEF1617 = TEF1617_P;

TEF1819 = TEF1819_P;

TEF2024 = TEF2024_P;

TEF2529 = TEF2529_P;

TEF3034 = TEF3034_P;

TEF3539 = TEF3539_P;

TEF4044 = TEF4044_P;

TEF4549 = TEF4549_P;

TEF5054 = TEF5054_P;

TEF5559 = TEF5559_P;

TEF6064 = TEF6064_P;

TEF6569 = TEF6569_P;

TEF70O = TEF70O_P ;

WEF16O_3 = WEF16O_3_P; (274) 

AWWF16O = AWWF16O_P ; (275) 

TEF16O = TEF16O_P ; (187)

TEF = TEF16O + HE_M_15U(2,YEAR) (188)

Combined, Age 16 and Over

WE16O_3_P = WEM16O_3_P + WEF16O_3_P; (276)

AWW16O_P = E16O * 52 / WE16O_3_P; (277)

WE16O_3 = WE16O_3_P ; (278)

AWW16O = AWW16O_P ; (279) 

TE = TEM + TEF (189)

Underground Economy and the Earnings Suspense File

TE_U = TEO_UND (312)

TEL_SO = TEL_SO.1 * (TE – TEO_UND – TEO_ESF) / (TE.1 – TEO_UND.1 – TEO_ESF.1) (313)

TE_S = TEL_SO + TEO_ESF (314)

TE_SFO_LRP = TEL_SO (389)

WE_SFO_LRP = TE_SFO_LRP * ACWA (390)

TE_SFM_LRP = TE_SFO_LRP (391)

WE_SFM_LRP = TE_SFM_LRP * ACWA * 0.5 (392)

WE_SF_LRP = WE_SFO_LRP + WE_SFM_LRP (393)

WE_SF = WS_EO_ESF + WE_SF_LRP (394)

134
MEF 

TE_M = TE – TE_U – TE_S (315)

TE_MN = TE_RRO_M + TE_SLOO_M + TE_SLOS_M + TE_SLOE_M + TE+PS_M + TE_PH_M + TEO_ASF1 + TEO_ASJ1 + 

TEO_AWH (316)

HE_M = TE_M – TE_MN (317)

WS_MEF = WSCAHI - WE_SF + WSPRRB + WESL_N_NHI + 

 (WESL_N_NHI_S /TESL_N_S) * TE_PS_M + 

 (0.5 * 1.8 / 44.32167) * (AIW.1 / 1000 * PROD / PROD.1 * AHRS / AHRS.1 * PGDP / PGDP.1) * TE_PH_M + 

 WS_EO_ASF1 + WS_EO_ASJ1 + WS_EO_AWJ + WS_EO_AWH (395)

Self-Employed Only

SEOCMB = WSW_HIO_OTH_SE + TEFC_N_N_SE + TESL_N_N_HI_SE (308)

SEOCMBL1 = WSW_HIO_OTH_SE + TEFC_N_N_SE + TESL_N_N_HI_SE (309)

SEO = (SEO.1 * (EAS + ENAS) / (EAS.1 + ENAS.1) + (SEOCMB - SEOCMBL1)) * MULTSEO (310)

Combination Workers 

CMB_TOT = ((-0.01468 + 0.06227 * RTP.1 -0.0008) * WSWA - SEOCMB) * MULTCMB (322)

CSW_TOT = SEO + CMB_TOT

AW_CMBTOT = 1.4953 * ACWA (337)

W_CMBTOT = AW_CMBTOT * CMB_TOT (338)

CMB_WRELMAX = TAXMAX/AW_CMBTOT (344)

CMB Wage Andover Curve (345–349)

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) 

 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) 

135
 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 (350)

CSW = SEO + CMB (353)

SEOCMB_HI = 0.039 * (TEFC_N_N + TESL_N_N_HI)

SEO_HI = SEO - SEOCMB_HI (311)

CMB_HI = CMB_TOT + SEOCMB_HI (351)

CSW_TOT = SEO + CMB_TOT (352)

CSW_HI = SEO_HI + CMB_HI (354)

NIPA Wages

Private Residual Sector

WSDPB = WSDP – WSPH – WSPF – WSPRRB – TIPS_SR (327)

TIPS_SR = (0.000508328 * RTP - 0.000481700) * GDP * 1.26393 + TIPS_SR_ADD (326)

OASDI Wages

Covered Employment and Wages – Federal Civilian Government

TEFC = (TEFC.1 / EGGEFC.1) * EGGEFC (362)

TEFC_N = IF (CSRS.1 > 0) THEN TEFC_N.1/CSRS.1 * CSRS - TEFC_N_SW ELSE 0

TEFC_N_N = HE_WOF_M (319)

TEFC_N_N_SE= HE_WOSF_M (302)

TEFC_N_O = (TEFC_N - TEFC_N_N) (365)

TEFC_O = (TEFC - TEFC_N) (364)

WEFC = (WEFC.1 / WSGGEFC.1) * WSGGEFC (331)

WEFC_O = (WEFC -WEFC_N) * ADJ_FSA_FC (332)

Covered Employment and Wages - State and Local Govt. 

TESL = (TESL.1/EGGESLMAX.1) * EGGESLMAX (280)

TESL_O = (TESL_O.1/TESL.1) * TESL (281)

TESL_N = (TESL-TESL_O) (282)

TESL_N_O = (TESL_N_O_HI + TESL_N_O_NHI) (293)

TESL_N_O_HI = (TESL_N - TESL_N_O_NHI - TESL_N_N_NHI) * CER_MQGE_O (292)

TESL_N_O_NHI = (TESL_N_O_NHI_S + TESL_N_O_NHI_E + TESL_N_O_NHI_NS) (288)

TESL_N_S = TESL_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + 

NM2024.1) (355)

TESL_N_E = TESL_N_E.1 * (TESL / TESL.1) (285)

TESL_N_O_NHI_S = TESL_N_S * (TESL_N_O_NHI_S.1/TESL_N_S.1) (284)

TESL_N_O_NHI_E = TESL_N_E * 0.6 (286)

TESL_N_O_NHI_NS = TESL_N_O_NHI_NS.1 * ESR_NS (287)

TESL_N_N = (TESL_N - TESL_N_O) (294)

TESL_N_N_HI = (TESL_N_N - TESL_N_N_NHI) (295)

TESL_N_N_HI_SE = (TESL_N_N_HI_SE.1 / TESL_N_N_HI.1) * TESL_N_N_HI (303)

TESL_N_N_NHI = (TESL_N_N_NHI_S + TESL_N_N_NHI_E + TESL_N_N_NHI_NS) (291)

TESL_N_N_NHI_S = (TESL_N_S - TESL_N_O_NHI_S) (283)

TESL_N_N_NHI_E = (TESL_N_E - TESL_N_O_NHI_E) (289)

TESL_N_N_NHI_NS = TESL_N_N_NHI_NS.1 * ESR_NS (290)

WESL = (WESL.1/WSGGESL.1) * WSGGESL (297)

WESL_O = (WESL_O.1/WSGGESL.1) * WSGGESL (298)

WESL_N = (WESL - WESL_O) (299)

WESL_N_HI = (WESL_N - WESL_N_NHI) (361)

WESL_N_NHI = (WESL_N_NHI_S + WESL_N_NHI_E + WESL_N_NHI_NS) (360)

WESL_N_NHI_S = WESL_N_NHI_S.1 * (TESL_N_S/TESL_N_S.1) * (AWSGGESL/AWSGGESL.1)(356)

WESL_N_NHI_E = WESL_N_NHI_E.1 * (TESL_N_E/TESL_N_E.1) * (AWSGGESL/AWSGGESL.1)(357)

136
RAWR_NS = IF (AWR_NS = 0) THEN 0 ELSE AWR_NS/AWR_NS.1 (358)

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 (359)

WSW_HIO_OTH = 0 (296)

WSCA_HIO_OTH = WSW_HIO_OTH*(WESL_N/TESL_N) (300)

WSW_HIO_OTH_SE = 0 (301)

HE_WOL_M = TESL_N_N_HI (304)

HE_WOR_M = 0 (305)

HE_WOSL_M = (HE_WOSL_M.1 / HE_WOL_M.1) * HE_WOL_M (306)

HE_WOSR_M = 0 (307)

Self-Employed Earnings Sector

Covered SENE (366–374)

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 (334)

WSGFCA = WEFC_O (333)

CFCA = WSGFCA/WSGGEFC (375)

CSLHI = (WESL_O+WESL_N_HI)/WSGGESL (376)

WSGSLCA = WESL_O (330)

WSPH_O = CPH * WSPH (323)

WSPF_O = WSPF_O.1 * WSPF/WSPF.1 (324)

CPF = WSPF_O/WSPF (377)

WSPRR_O = CPRR * WSPRRB (325)

WSPC = WSPH_O + WSPF_O + WSPRR_O + TIPS_SR + WSPB_O (329)

CP = WSPC/WSDP (378)

WSCA = (WSPC + WSGSLCA + WSGFCA + WSGMLC) (335)

COVERNA = (WSCA + CSE) (379)

ACWA = WSCA/WSWA (336)

ASE = CSE/CSW (380)

ASEHI = CSE_TOT/CSW_HI (381)

ACEA = COVERNA/TCEA (382)

ACSLW = WESL_O/TESL_O * MULTACSLW (383)

ACMW = ACMW.1 * AWSGFM/AWSGFM.1 * CML/CML.1 (384)

ACFCW = WEFC_O/TEFC_O (385)

ACFMW = ACFMW.1 * (AIW.1/AIW.3)0.5 (386)

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)

WSWA = (TCEA-SEO) (321)

Present Law HI Covered Wages and Earnings

WSCAHI_ADD = WSCA * WSCAHI_ADD.1/WSCA.1 

TCEAHI = HE_M + TE_S (318) 

TCEA = TCEAHI – ((TESL_N_N_HI + TEFC_N_N + WSW_HIO_OTH) – 

 (TESL_N_N_HI_SE + TEFC_N_N_SE + WSW_HIO_OTH_SE)) (320)

WSWAHI = TCEAHI - SEO_HI

WSCAHI = WSCA + WEFC_N + WESL_N_HI + WSCA_HIO_OTH (388)

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

137
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 (339)

TAXMAXB1 = RAIW * TMAXBASE * 1000/300 (340)

TAXMAXB2 = IF TAXMAXB1 - ROUND (TAXMAXB1) >= 0.5 

 THEN ROUND (TAXMAXB1) +1 

 ELSE ROUND (TAXMAXB1) (341)

TAXMAXB3 = IF TAXMAXB2 < TAXMAX.1 

 THEN TAXMAX.1 * 1000/300 

 ELSE TAXMAXB2 (342)

TAXMAX = IF BENINC.1 <= 0.001 

 THEN TAXMAX.1 

 ELSE 300 * TAXMAXB3/1000 (343)

Deemed Military Wage Credits

EDMILAF = EDMIL * 1.1

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

138
2.4 Effective Taxable Payroll (TAXPAY)

2.4.1 Ratio of taxable employee to total covered OASDI wages (RWTEE)

if (relmax > 15.01754965d0) then

 RWTEE = -(0.200178d0 / 0.74d0) * relmax**(-0.74d0) + &

 1.000209697d0

else if (relmax > 2.79052673d0) then

 RWTEE = -(0.009321d0 / 0.15d0) * exp(-0.15d0 * relmax) - & 

 (0.055530d0 / 0.40d0) * exp(-0.40d0 * relmax) - & 

 (0.809959d0 / 1.25d0) * exp(-1.25d0 * relmax) + &

 0.000581d0 * relmax + 0.961924965d0

else if (relmax > 1.68599158d0) then

 RWTEE = -(0.104668d0 / 0.30d0) * exp(-0.30d0 * relmax) - & 

 (1.276789d0 / 1.55d0) * exp(-1.55d0 * relmax) - & 

 0.0126230d0 * relmax + 1.054563461d0

else if (relmax > 0.89508398d0) then

 RWTEE = (0.046180d0 / 0.25d0) * exp(-0.25d0 * relmax) - & 

 (1.197836d0 / 1.3d0) * exp(-1.3d0 * relmax) + &

 0.040800d0 * relmax + 0.675476436d0

else if (relmax > 0.39794128d0) then

 RWTEE = (0.371366d0 / 1.5d00) * relmax**1.50d0 - & 

 (1.793426d0 / 0.69d0) * exp(-0.69d0 * relmax) - & 

 0.939072d0 * relmax + 2.604319058d0

else

 RWTEE = relmax - & 

 (0.290789d0 / 1.5d0) * relmax**1.5d0 - & 

 (0.398961d0 / 2.00d0) * relmax**2d0

end if

Where

relmax = OASDI taxable maximum / average covered OASDI wage

RWTEE = Ratio of 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

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

139
WTEE = OASDI taxable employee wages

WTER = OASDI taxable employer wages

2.4.6 Ratio of taxable to covered self-employment earnings (RSET)

Preliminary

BASECT = 77074.88 

BASECW = 59157.14 

BASEO = 38188.22 

Self-employed only

SECSEO = CSE - SECCMB 

ASESEO = SECSEO / SEO

ASEO17 = ASESEO(2017) 

ASESEO = ASESEO * BASEO / ASEO17 

O = TAXMAX / ASESEO

if ( o < 0.026186088d0 ) then

 otr = o - (9.574544d0 / 2.5d0) * o**2.5d0

else if ( o < 0.104744354d0 ) then

 otr = -(1.04227d0 / 1.5d0) * o**1.5d0 + (0.67587d0 / 2.15d0) * o**2.15d0 - & 

 (3.471502d0 / 3.3d0) * o**3.3d0 + 1.110432d0 * o - 0.00049085d0

else if ( o < 0.209488707d0 ) then

 otr = (2.185075d0 / 1.3d0) * o**1.3d0 - (4.972755d0 / 1.75d0) * o**1.75d0 + &

 (3.184795d0 / 2.4d0) * o**2.4d0 + 0.475027d0 * o + 0.00377668d0

else if ( o < 0.471349592d0 ) then

 otr = (7.17629d0 /1.25d0) * o**1.25d0 - (0.28816d0 / 1.6d0) * o**1.6d0 - & 

 (4.650629d0 / 2.4d0) * dexp(-2.4d0 * o) - 6.893912d0 * o + 1.987803109d0

else if ( o < 1.021257449d0 ) then

 otr = -(0.52704d0 / 0.85d0) * dexp(-0.85d0 * o) + (0.369144d0 / 1.55d0) * &

 dexp(-1.55d0 * o) - (0.845421d0 / 3.1d0) * dexp(-3.1d0 * o) - & 

 0.001447d0 * o + 0.665888025d0

else if ( o < 1.309304422d0 ) then

 otr = -(0.174971d0 / 0.55d0) * dexp(-0.55 * o) - (0.393885d0 / 1.75d0) * &

 dexp(-1.75d0 * o) - (0.003202d0 / 2.6d0) * dexp(-2.6d0 * o) + &

 0.013703d0 * o + 0.64673395d0

else if ( o < 1.728281837d0 ) then

 otr = (0.338456d0 / 0.3d0) * dexp(-0.3d0 * o) - (0.904979d0 / 1.15d0) * &

 dexp(-1.15d0 * o) + (0.51182d0 / 2.5d0) * dexp(-2.5d0 * o) + &

 0.185928d0 * o - 0.351278731d0

else if ( o < 2.17344534d0 ) then

 otr = (0.358360d0 / 0.55d0) * dexp(-0.55d0 * o) - (5.475731d0 / 1.85d0) * &

 dexp(-1.85d0 * o) + (9.368262d0 / 2.6d0) * dexp(-2.6d0 * o) + &

 0.121142d0 * o + 0.156160373d0

else if ( o < 3.142330612d0 ) then

 otr = -(0.067751d0 / 0.2d0) * dexp(-0.2d0 * o) - (2.812835d0 / 1.9d0) * &

 dexp(-1.9d0 * o) + (8.107091d0 / 2.75d0) * dexp(-2.75d0 * o) + &

 0.00956d0 * o + 0.79107633d0

else if ( o < 52.372176875d0 ) then

 otr = -(0.024629d0 / 0.1d0) * dexp(-0.1d0 * o) - (0.11274d0 / 0.4d0) * &

 dexp(-0.4d0 * o) + 0.001128d0 * o + 0.893694435d0

else if ( o < 1000d0 ) then

 otr = -(1.22364d0 / 0.85d0) * o**(-0.85d0) + 1.001234831d0

else

 otr = 1d0

end if

SETSEO=OTR*SECSEO

OASDI taxable wages of workers with both wages and self-employment earnings

AWSCMB=WSCCMB/CMBNT 

AWSCMB17=AWSCMB(2017) 

AWSCMB=AWSCMB*BASECW/AWSCMB17

CW=TAXMAX/AWSCMB

if ( cw < 0.0190413d0 ) then

 cwtr = cw - (1.269097d0 /1.72d0) * cw**1.72d0

140
else if ( cw < 0.059164455d0 ) then

 cwtr = (0.733496d0 / 1.45d0) * cw**1.45d0 - (1.932995d0 / 1.6d0) * cw**1.6d0 + &

 0.982734d0 * cw + 0.00003324d0

else if ( cw < 0.160589235d0 ) then

 cwtr = -(1.777645d0 / 1.8d0) * cw**1.8d0 + (1.737345d0 / 2.65d0) * cw**2.65d0 + &

 1.002541d0 * cw - 0.00013743d0

else if ( cw < 0.236657820d0 ) then

 cwtr = -(1.264913d0 / 1.3d0) * cw**1.3d0 + (0.225457d0 / 2.2d0) * cw**2.2d0 + &

 1.381608d0 * cw - 0.00414044d0

else if ( cw < 0.388794990d0 ) then

 cwtr = -(1.257299d0 / 1.2d0) * cw**1.2d0 - (0.286311d0 / 6.5d0) * cw**6.5d0 + &

 1.542586d0 * cw - 0.00150659d0

else if ( cw < 0.540932161d0 ) then

 cwtr = -(1.607077d0 / 1.2d0) * cw**1.2d0 - (1.475696d0 / 1.55d0) * &

 dexp(-1.55d0 * cw) - 1.637803d0 * cw + 0.98777752d0

else if ( cw < 0.862110631d0 ) then

 cwtr = -(0.687757d0 / 0.35d0) * dexp(-0.35d0 * cw) - (0.424043d0 / 1.35d0) * &

 dexp(-1.35d0 * cw) - 0.351856d0 * cw + 2.29858919d0

else if ( cw < 1.081864321d0 ) then

 cwtr = -(0.51421d0 / 0.4d0) * dexp(-0.4d0 * cw) - (0.877948d0 / 2.9d0) * &

 dexp(-2.9d0 * cw) - 0.147171d0 * cw + 1.50626904d0

else if ( cw < 1.572084092d0 ) then

 cwtr = -(4.289368d0 / 0.25d0) * dexp(-0.25d0 * cw) + (4.153888d0 / 0.55d0) * &

 dexp(-0.55d0 * cw) - (2.186503d0 / 1.3d0) * dexp(-1.3d0 * cw) - & 

 1.292888d0 * cw + 11.23676668d0

else if ( cw < 3.211784704d0 ) then

 cwtr = -(0.102092d0 / 0.3d0) * dexp(-0.3d0 * cw) - (0.647197d0 / 1.4d0) * &

 dexp(-1.4d0 * cw) + 0.00085d0 * cw + 0.84811899d0

else if ( cw < 16.904130019d0 ) then

 cwtr = -(0.028188d0 / 0.15d0) * dexp(-0.15d0 * cw) - (0.221879d0 / 0.63d0) * &

 dexp(-0.63d0 * cw) + 0.000527d0 * cw + 0.8767982d0

else if ( cw < 1d3) then

 cwtr = -(0.088498d0 / 0.254d0) * cw**(-0.254d0) + 1.0407112d0

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 

ATECMB17=ATECMB(2017) 

ATECMB=ATECMB*BASECT/ATECMB17 

CT=TAXMAX/ATECMB

if ( ct < 0.025948791d0 ) then

 cttr = ct - (40.88231d0 / 3.3d0) * ct**3.3d0

else if ( ct < 0.051897583d0 ) then

 cttr = -(0.015962d0 / 1.4d0) * ct**1.4d0 - (2.849709d0 / 2.5d0) * ct**2.5d0 + &

 1.005757d0 * ct - 0.00002946d0

else if ( ct < 0.097307968d0 ) then

 cttr = -(1.740332d0 / 2.25d0) * ct**2.25d0 - (4.39659d0 / 4.3d0) * ct**4.3d0 + &

 1.010732d0 * ct - 0.00017087d0

else if ( ct < 0.233539123d0 ) then

 cttr = -(3.007061d0 / 2.35d0) * ct**2.35d0 + (29.74953d0 / 5.5d0) * ct**5.5d0 + &

 1.047821d0 * ct - 0.00257006d0

else if ( ct < 0.376257476d0 ) then

 cttr = -(17.9483d0 / 1.85d0) * ct**1.85d0 + (56.48945d0 / 0.34d0) * dexp(-0.34d0 * ct) + &

 58.06407d0 * ct - 166.16320626d0

else if ( ct < 0.518975828d0 ) then

 cttr = (0.35103d0 / 0.65d0) * dexp(-0.65d0 * ct) - (1.220332d0 / 1.25d0) * &

 dexp(-1.25d0 * ct) + 0.050683d0 * ct + 0.455703736d0

else if ( ct < 0.700617368d0 ) then

 cttr = -(0.158062d0 / 0.45d0) * dexp(-0.45d0 * ct) - (0.865629d0 / 1.25d0) * &

 dexp(-1.25d0 * ct) - 0.139568d0 * ct + 1.069620633d0

else if ( ct < 0.869284513d0 ) then

 cttr = -(10.956926d0 / 0.45d0) * dexp(-0.45d0 * ct) + (13.02327d0 / 1.35d0) * &

 dexp(-1.35d0 * ct) - (8.498083d0 / 2.45d0) * dexp(-2.45d0 * ct) - & 

141
 4.127007d0 * ct + 17.95991367d0

else if ( ct < 1.076874844d0 ) then

 cttr = -(2.015557d0 / 0.35d0) * dexp(-0.35d0 * ct) + (3.017185d0 / 1.2d0) * &

 dexp(-1.2d0 * ct) - (3.225627d0 / 2.0d0) * dexp(-2.0d0 * ct) - & 

 0.725524d0 * ct + 4.75386607d0

else if ( ct < 7.784637426d0 ) then

 cttr = -(0.100861d0 / 0.35d0) * dexp(-0.35d0 * ct) - (0.166637d0 / 1d0) * &

 dexp(-1d0 * ct) - (0.732639d0 /2.15d0) * dexp(-2.15d0 * ct) + &

 0.004175d0 * ct + 0.809186759d0

else if ( ct < 25.948791419d0 ) then

 cttr = -(0.036719d0 / 0.18d0) * dexp(-0.18d0 * ct) - (0.780182d0 / 0.9d0) * &

 dexp(-0.9d0 * ct) + 0.001067d0 * ct + 0.865444162d0

else if ( ct < 1d3 ) then

 cttr = -(0.142018d0 / 0.34d0) * ct**(-0.34d0) + 1.029280103d0

else

 cttr = 1d0

end if

TETCMB=CTTR*TECCMB 

SETCMB=TETCMB-WSTCMB

Ratio OASDI taxable to covered self-employment earnings

RSET = (SETCMB+SETSEO)/CSE 

Where

ASEO17 = Average self-employment earnings of workers with no OASDI taxable wages in 2017 

ATECMB = Average OASDI covered earnings of workers with both OASDI covered wages and self-employment earnings

ATECMB17 = Average OASDI covered earnings of workers with both OASDI covered wages and self-employment earnings in 

2015 

AWSCMB = Average OASDI covered wage of workers with both wages and self-employment earnings

 AWSCMB17 = Average OASDI covered wage of workers with both wages and self-employment earnings in 2017 

ASESEO = Average self-employment earnings of workers with no OASDI taxable wages

AWSCMB = Average OASDI covered wage of workers with both wages and self-employment earnings

 BASECT = Average total earnings of workers with both self-employment earnings and wages in 1% sample data for 2017 used to

 produce equations

 BASECW = Average OASDI covered wages of workers with both self-employment earnings and wages in 1% sample data for

 2017 used to produce equations

BASEO = Average self-employment earnings of workers with no OASDI taxable wages in 1% sample data for 2017 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 self-employment earnings and OASDI taxable 

 wages

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 = RSET * CSE

Where

CSE = OASDI covered self-employment earnings

SET = OASDI taxable self-employment earnings

RSET = Ratio of OASDI taxable to covered self-employment earnings

142
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

143
2.5 Revenues (REVENUES)

2.5.1 OASDI taxable wage liability (WTL)

WTL = WTER * TRW

Where

TRW = OASDI combined employee-employer tax rate

WTL = Annual OASDI taxable wage liabilities

WTER = Annual OASDI taxable employer wages

2.5.2 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

2.5.3 OASDI multi-employer refund wage liability (MERL)

MERL = MER * TRWEE

Where

 MERL = OASDI multi-employer refund wage liabilities

 MER = OASDI multi-employer refund wages

TRWEE = OASDI employee tax rate

2.5.4 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

 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)

144
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*T-2.83402534

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

 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

145
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

First quarter is always 100 percent taxable.

QWTFC(I,1)=QWCFC(I,1) 

IF(FCTR.LE.0.928)THEN

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

 Second quarter covered is completely taxable.

 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

 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

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

146
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*T-31.56802874

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

 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)

147
 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

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

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

148
 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*S-6.245057503

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)

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

149
 J = Quarter

TRW = OASDI combined employee-employer tax rate

WTLQSL = Quarterly OASDI taxable State and Local combined employee-employer wage liabilities

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 employee-employer 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

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

150
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

Private nonfarm 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 nonfarm 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)

 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)

151
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 nonfarm based on calendar

QP = Proportion of annual OASDI taxable private nonfarm wages excluding taxable tips paid in each quarter

QWTPNF = Quarterly OASDI taxable private nonfarm 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

QWTPNF = Quarterly OASDI taxable private nonfarm wages including tips

TRW = OASDI combined employee-employer tax rate

WTLQPNF = Quarterly OASDI tax liabilities from taxable private nonfarm 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 nonfarm wages including tips

QWTSL = Quarterly OASDI taxable State and Local wages

WTLQ = Quarterly OASDI taxable wage liabilities

2.5.5 OASDI quarterly taxable wage liability collections (WTLQC)

OASDI taxable private nonfarm 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 nonfarm wages (excluding tips and household) paid in December

DR = Proportion of fourth quarter OASDI taxable private nonfarm wages (excluding tips and household) paid in December

152
 I = Calendar year

JR = Proportion of second quarter OASDI taxable private nonfarm wages (excluding tips and household) paid in June

JUN = Proportion of second quarter OASDI covered private nonfarm wages (excluding tips and household) paid in June

MAR = Proportion of first quarter OASDI covered private nonfarm wages (excluding tips and household) paid in March

 MR = Proportion of first quarter OASDI taxable private nonfarm wages (excluding tips and household) paid in March

MWTP = OASDI taxable private nonfarm wages (excluding tips and household) paid in last month and in first two months of quarter

PTR = Ratio of annual OASDI taxable private nonfarm wages (excluding tips and household) to covered private nonfarm wages

QWTP = Quarterly OASDI taxable private nonfarm wages (excluding tips and household)

SEP = Proportion of third quarter OASDI covered private nonfarm wages (excluding tips and household) paid in September

SR = Proportion of third quarter OASDI taxable private nonfarm wages (excluding tips and household) paid in September

WCP = Annual OASDI covered private nonfarm wages

WTP = Annual OASDI taxable private nonfarm wages (excluding tips and household)

OASDI taxable private nonfarm 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)) 

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 nonfarm wages (excluding household)

 CA = Compliance allowance

DEC = Proportion of fourth quarter OASDI covered private nonfarm wages (excluding tips and household) paid in 

December

 I = Calendar year

 J = Quarter

JUN = Proportion of second quarter OASDI covered private nonfarm wages (excluding tips and household) paid in 

June

MAR = Proportion of first quarter OASDI covered private nonfarm wages (excluding tips and household) paid in March

 MWCP = OASDI covered private nonfarm wages paid in third month and in first two months of each quarter

MWTP = OASDI taxable private nonfarm wages paid in third month and in first two months of each quarter

PWCE = OASDI taxable private nonfarm wages paid in the third month of each quarter

PWCS = OASDI taxable private nonfarm wages paid in the first two months of each quarter on which taxes are collected 

in that quarter

QWSCPNF = Quarterly OASDI covered private nonfarm wages

 QRMREQ = Monthly deposit requirement

QRWREQ = Quarterly deposit requirement

QWSTXPHH = Quarterly OASDI taxable private nonfarm wages (excluding household)

QWTPC = Quarterly OASDI taxable private nonfarm wages on which employers deposit taxes in the quarter the wages 

were paid

QWTPF = Quarterly OASDI taxable private nonfarm 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 nonfarm 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 nonfarm wages (excluding tips and household) paid in 

September

153
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)

 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 nonfarm 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 nonfarm wages paid in sub-quarterly period

QTOT = OASDI covered private nonfarm wages paid in sub-quarterly period

 R = Initial ratio of OASDI taxable to covered private nonfarm wages paid in sub-quarterly period

 RMF = Current year average wage size of firm

RTAX = Ratio of OASDI taxable to covered private nonfarm wages paid in sub-quarterly 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)

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

154
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

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

2.5.6 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

155
Appendix 2-2 

Economic Acronyms

AA Appropriation adjustments 

ACE Average OASDI covered earnings

ACSE Average OASDI covered self-employed income

ACW

ACWC

ADJ_FSA_FC 

AWEFC_N 

AWI 

AWSE

AWSGEFC

AWSGFC

AWSGFM

AWSGGEFC

AWSGGESL

AWSP

AWSPH

AWSPL

AWSSP

Average OASDI covered wage

Average economy-wide wage

Adjustment to lower federal civilian covered wages relative to NIPA 

wages due to a presumed increase in the relative amount placed into an 

FSA 

Average wage for Federal civilian employees not covered under OASDI 

Average wage index calculated by SSA; based on the average wage of all 

workers with wages from Forms W-2 

Economy-wide average wage

Average wage for the Federal government enterprises

Average wage for the Federal civilian government 

Average wage for the military

Average wage for the Federal government & government enterprises

Average wage for State and local government and government enterprises 

Average wages, private sector

Average wage in private household sector 

Average wages, private sector, 2-year moving average 

Average compensation, private sector

AWSSPBNFXGE

AWSSPES

Average compensation, private nonfarm business, excluding government 

enterprises

Average compensation, private sector, educational services

AWSSPF

AWSSPHS

AWSSPL

AWSSPSS

AWSUI

AWS_MEF 

AYF

AYF_K

AYNF

AYNF_K

Average compensation, private farm, wage workers

Average compensation, private sector, health services 

Lagged average compensation for private sector workers

Average compensation, private sector, social services

Average wage of workers under UI 

Average wage for employees with any wages (covered and noncovered) 

posted to the MEF 

Average proprietor income, private farm 

Ratio of average self-employment income to average wage-worker 

compensation for the agriculture sector

Average proprietor income, private nonfarm business 

Ratio of average self-employment income to average wage-worker 

compensation for the nonagriculture sector

BEA The Bureau of Economic Analysis

BLS

CFCGEFC

CFCGESL

CFCGFC

The Bureau of Labor Statistics

Compensation of fixed capital, Federal government enterprises 

Government consumption of fixed capital, Government enterprises, State 

& local 

Compensation of fixed capital, Federal civilian

156
CFCGFM

CFCGSL

Federal Government Consumption Expenditures, Defense Consumption 

Expenditures 

State & Local Government consumption expenditures, Gross output of 

general government, Value added, consumption of general government 

fixed capital

CMB_TOT

CML

Workers that have a combination of both OASDI covered wages and selfemployed income. 

Ratio of Federal military OASDI covered wages to NIPA wages

COV

CP

Economic Sub-Process: Covered Employment and Earnings

Ratio of Private OASDI Covered to NIPA wages; OASDI private coverage 

ratio

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

CR_UI 

CRAZ1

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. 

Civilian pay raise

CSE_TOT

CSLA

Total OASDI covered self-employed income

Ratio of State and Local OASDI Covered to NIPA wages

CSRS Civil Service Retirement System

CSW

DNEDMIL

DRTP, DRTPP, 

DRTPN, DRTP1Q, 

DNRTP1Q, 

DPRTP1Q

Self-employed only workers (SEO) plus combination workers 

(CMB_TOT)

Decreases in the military population (as shown by the difference over four 

quarters) 

Dummy variables for positive and negative 

economic cycle trends 

E

E_FE

Total employment, CPS concept (i.e., average of monthly estimates of

total wage and salary workers, plus self-employed, plus unpaid family 

workers)

Civilian employment level at full employment (i.e., at potential GDP)

EA

EAS

EAW

Total agricultural employment

Civilian Employment Level, Self-employed workers: agriculture, SA

Employment by class of worker, agricultural wage workers

EDMIL

EGFC

EGEFCPS

EGGEFC

EGGESL

Total number serving in the US Armed Forces estimated by the 

Department of Defense and published by the Census Bureau 

Federal civilian government employment

Employment, Establishment Data, All Employees: Government, Federal 

Government Enterprises, U.S. Postal Service 

Employment, Establishment Data, All Employees: Government, Federal 

Government, SA 

Employment, State & Local government enterprises 

157
EMPTRDI

EMPTRHI

EMPTROASI

ENA

ENAS

ENAU

ENAW

ENAWPBXGE

ENAWPH

ENAWSPBXGE

DI employer tax rate

HI employer tax rate 

OASI employer tax rate

Civilian Employment Level, Nonagricultural industries, 16 years and over, 

SA

Employment by class of worker, nonagricultural self-employed

Employment by class of worker, nonagricultural unpaid family workers 

Employment by class of worker, nonagricultural wage workers 

Employment for private nonfarm business 

Employment by class of worker, nonagricultural wage workers, private 

household workers 

Employment for private nonfarm business and nonagricultural selfemployed

EO Total employment in the other-than-LPR population

EO_A Total employment in the other-than-LPR population who are temporarily 

authorized to reside or work in the US

EO_ESF Total employment in the other-than-LPR population whose reported 

earnings are posted to the Earnings Suspense File

EO_MEF Total employment in the other-than-LPR population whose earnings are 

reported and posted to the Master Earnings File

EO_MEFC Total employment in the other-than-LPR population whose earnings are 

reported and posted to the Master Earnings File and are OASDI-covered

EO_NA Total employment in the other-than-LPR population who have overstayed 

their authorization

EO_NO Total employment in the other-than-LPR population who were never 

authorized to reside or work in the US

EO_UND

EP

EPES_EST

EPHS_EST

EPSS_EST

Total employment in the other-than-LPR population that is strictly in the 

underground economy (i.e., with no earnings reported) 

Employees in Private industries 

Employees by industry, Private industries, Educational services 

Employment for private health services

Employees by industry, Private industries, Social Assistance

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 

multi-employer refund wages 

EU Unpaid family workers

EW Wage and salaried workers

FERS Federal Employee Retirement System

GDP

GDP05

GDPG

GDPGE

GDPGEFC

GDPGESL

GDPGF

Gross domestic product

GDP, 2005$ 

GDP, General Government 

GDP, Federal and State & local government enterprises 

GDP, Federal civilian government enterprises 

GDP, State & local government enterprises 

GDP, General Government, Federal

158
GDPGFC

GDPGFM

GDPGGE

GDPGGEFC

GDPGGESL

GDPGSL

GDPPBNFXGE

GDPPF

GDPPH

GDPPNI

GDP, Federal civilian

GDP, military 

GDP, Federal and State & local government enterprises

GDP, Federal civilian government and government enterprises 

GDP, State & local government and government enterprises 

GDP, General Government, State & Local 

GDP, private nonfarm business, excluding government enterprises 

GDP, private business sector, farm

GDP, Private Households

GDP, Nonprofit institutions serving households

HI

HIFC_L

HIFM_L

HIP_L

HISL_L

KGDP05

Hospital insurance

HI Employer Liability, Federal Civilian 

HI Employer Liability, Federal Military 

HI Employer Liability, Private 

HI Employer Liability, State & Local

Potential real GDP, 2005$

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.

M

MER

MRAZ

Military population 

Multi-employer refund wages 

Military pay raise

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

OASDIFC_L

OASDIFM_L

OASDIP_L

OASDISL_L

Old-Age, Survivors, and Disability Insurance

OASDI Employer Liability, Federal Civilian

OASDI Employer Liability, Federal Military 

OASDI Employer Liability, Private

OASDI Employer Liability, State & Local

OASDHI Old-Age, Survivors, Disability, and Health Insurance

OLI

OLI_CSRS1

OLI_FC

OLI_FERS1

OLI_FERSFC

OLI_GGE

OLI_GHI

OLI_GHI_FC

OLI_GHI_P

Employer contributions for employee pension and insurance funds

Contributions for CSRS employees’ pay 

Other labor income, Federal civilian 

Contributions for FERS employees’ pay

Employer contributions to Thrift Savings Plan for FERS employees

Other labor income, government and government enterprises 

Other labor income by type, Employer contributions to pension and 

welfare funds, private welfare funds, Group health insurance 

Employer contributions for employee pension & insurance funds, group 

health insurance, Federal civilian government sector 

Employer contributions for employee pension & insurance funds, group 

159
OLI_GHI_SL

OLI_GLI

OLI_GLI_FC

OLI_GLI_P

OLI_GLI_SL

OLI_P

OLI_PPPS

OLI_PPS

OLI_RETFC

OLI_RETFM

OLI_RETSL

OLI_SL

OLI_SU

OLI_WC 

OLI_WCP 

OLI_WCSL 

OLIF_RETFCO

OOH

OP

OP_A

OP_NA

OP_NO

PGDP

PGDPAF

health insurance, private sector

Employer contributions for employee pension & insurance funds, group 

health insurance, State & local government sector 

Employer contributions for employee pension and insurance funds, 

Group life insurance 

Employer contributions for employee pension & insurance funds, group 

life insurance, Federal civilian government sector 

Employer contributions for employee pension & insurance funds, group 

life insurance, private sector

Employer contributions for employee pension & insurance funds, group 

life insurance, State & local government sector 

Employer contributions for employee pension and insurance funds, 

private industries 

Other Labor Income, Private Sector Pension and Profit Sharing 

Employer contributions for employee pension and insurance funds, 

Pension & profit-sharing 

Employer contributions for employee pension and insurance funds, 

Publicly administered government employee retirement plans, Federal 

civilian 

Employer contributions for employee pension and insurance funds, 

Publicly administered government employee retirement plans, Federal 

military 

Employer contributions for employee pension and insurance funds, 

Publicly administered government employee retirement plans, State and 

local

Other labor income, State and local 

Employer contributions for employee pension and insurance funds, 

Supplemental unemployment 

Employer contributions for employee pension and insurance funds, 

Workers’ compensation 

Private employer contribution to other labor income, total for workers' 

compensation 

Employer contributions to workers’ compensation, State and local 

Other government contributions to Federal civilian retirement

Owner-occupied housing 

Other-than-LPR population

Other-than-LPR population who are temporarily authorized to reside or 

work in the US

Other-than-LPR population who have overstayed their authorization

Other-than-LPR population who were never authorized to reside or 

work in the US

Gross Domestic Product Price Index, Units: 2005=100 

Deflator for farm output

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.

160
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

RCWSF

RCWSM

RCWSP

RCWSSL

Covered self-employed ratio, defined as the ratio of total covered selfemployment income to total proprietor income (CSE_TOT/Y).

Ratio of compensation to wages in the Federal government

Ratio of compensation to wages in the military 

Ratio of compensation to wages in the private sector

Ratio of compensation to wages in the State and local sector

RD Disability prevalence ratio, defined as the ratio of disabled worker 

beneficiaries to the disability-insured population.

RELMAX

RELMAX_UI

Ratio of the TAXMAX to averaged covered earnings

Ratio of the aggregate weighted average of the UI taxable maximum to 

the average UI wage

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

RGR_GHI

RHIP_L

Family size ratio, defined as the ratio of the number of children under 6 

to mothers of a certain age.

Product of HI tax rate, private coverage ratio, and the taxable ratio

RM Military ratio, the ratio of the US armed forces to the 

noninstitutionalized population.

RMER

ROASDIP_L

ROLI_PPPS

ROLI_SU

ROLI_WCP 

Multi-employer refund wage ratio, defined as the ratio of multiemployer refund wages to total OASDI wages. 

Product of OASDI tax rate, private coverage ratio, and the taxable ratio 

Ratio of employer contributions to private pension and profit-sharing to 

private wages

Ratio of private employer contributions for employee pension and 

insurance funds, Supplemental unemployment to private wages

Ratio of private employer contribution to other labor income, total for 

workers’ compensation to private wages

RSET

RSOC_UIP

RSOC_WCP

RSOCF_PBG

RSOCSL_WC

Self-employed net income taxable ratio, defined as the ratio of total selfemployed taxable income to total OASDI wages.

Ratio of private employer contributions to social insurance, total for 

unemployment insurance, to private wages 

Ratio of private employer contributions to social insurance, total for 

workers' compensation to private wages

Ratio of private employer insurance contribution to the Pension Benefit 

Guaranty Trust Corporation to private wages 

Ratio of combined Private and State & local sector employer 

contributions to social insurance for workers' compensation to the 

combined Private and State and local sector employer contributions to 

workers' compensation

RTE Ratio of total employment to the sum of wage & salary, self-employed 

workers, and the military (TE/(EW + ES + military))

161
RTP A summary measure of the economic cycle equal to the ratio of real 

GDP to potential GDP

RU

RUIWS

RWCWS

Civilian unemployment rate defined as the ratio of the unemployed US 

labor force to the total US labor force

Effective tax rate for employer contributions to unemployment 

insurance 

Effective tax rate for employer contributions to workers’ compensation

RWSC Covered wage ratio, defined as the ratio of OASDI covered wages to 

total wage and salary disbursements (WSC/WSD)

RWSD

RWSSPBNFXGE

Earnings ratio, defined as the ratio of total wage and salary 

disbursements to total wage and worker compensation(WSD/WSS) 

Ratio of compensation to GDP in private business nonfarm excluding 

government enterprises

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 Self-employed participation rate (the proportion of employed persons 

that are self-employed) 

SET Total self-employed taxable income

SOC

SOC_FC

SOC_FM

SOC_GGE

SOC_P

SOC_SL

SOC_UIP

SOC_UISL

SOC_WCP 

SOC_WCSL

SOCF_HI

SOCF_MIFM

Employer contributions for government social insurance

Employer contributions for social insurance, Federal civilian sector 

Employer contributions for government social insurance, Federal 

government, military sector 

Employer contributions for social insurance, government and 

government enterprises 

Employer contributions for social insurance, private industries 

Employer contributions for social insurance, State and local sector

Private employer contributions to social insurance, total for 

unemployment insurance 

State and local government employer contributions to social insurance, 

total for unemployment insurance 

Private employer contributions to social insurance, total for workers' 

compensation 

State and Local government employer contributions to social insurance, 

total for workers' compensation 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Hospital Insurance 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Military Medical 

162
SOCF_OASDI

SOCF_PBG

SOCF_RETRR

SOCF_UIF

SOCF_UIFC

SOCF_UIFED

SOCF_UIFM

SOCF_UIS

SOCF_WC 

SOCSL_WC

Insurance

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Old-age, Survivors, And 

Disability Insurance 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Pension Benefit 

Guaranty

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Railroad Retirement 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Federal Unemployment 

Tax 

Total federal civilian government employer contributions to 

unemployment insurance 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Federal Employees’ 

Unemployment Insurance 

Total federal government employer contributions to unemployment 

insurance, military 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, State Unemployment 

Insurance 

Contributions for Government Social Insurance, Employer 

Contributions, Federal Social Insurance Funds, Worker’s Compensation 

Contributions for Government Social Insurance, Employer 

Contributions, State and Local Social Insurance Funds, Workers’ 

Compensation

SSA Social Security Administration

TAXMAX OASDI contribution and benefit base

TAXPAY Economic Sub-Process: Taxable Payroll

TCE Total OASDI covered employment

TE

TEFC_N

Total “at any time” employment

Total “at any time” employment, Federal civilian, without Federal 

civilian OASDI

TEO Total “at any time” employment in the other-than-LPR population

TEO_ESF Total “at any time” employment in the other-than-LPR population 

whose reported earnings are posted to the Earnings Suspense File

TEO_MEF Total “at any time” employment in the other-than-LPR population 

whose earnings are reported and posted to the Master Earnings File

TEO_MEFC Total “at any time” employment in the other-than-LPR population 

whose earnings are reported and posted to the Master Earnings File and 

are OASDI-covered

TEO_UND

TMAXUI_SL

Total “at any time” employment in the other-than-LPR population that is 

strictly in the underground economy (i.e., with no earnings reported) 

Taxable maximum for State & local unemployment insurance

163
TRSE OASDI self-employed tax rate

TRW

TXRP

Combined OASDI employee-employer tax rate

OASDI private taxable ratio

U The number of persons in the labor force who are unemployed

MODSOL2 Economic Sub-Process: U.S. Earnings 

USEMP

WEFC_N 

WS

Economic Sub-Process: U.S. Employment

Wages for Federal civilian employees not covered under OASDI 

Compensation of Employees, Wage and Salary Accruals 

WSC Total OASDI covered wages

WSD

WSDP

WSGEFC

WSGFC

WSGFM

WSGGEFC

WSGGESL

WSP

WSPF

WSPH

WSPNI

WSPRRB

WS_MEF

Total wage and salary disbursements

Private wage and salary disbursements 

Government Wages and Salaries, Federal civilian, Government 

Enterprises 

Wage and salary accruals by industry, Government, Federal civilian 

Wage and salary accruals by industry, Government, Federal, Military 

Wages for the Federal government & government enterprises 

Wages for State and local government and government enterprises 

Compensation of Employees, Wage and Salary Accruals 

Wage and salary accruals by industry, Private industries, Farms 

Wage and salary accruals by industry, Private industries, Households 

Wage and salary accruals by industry, Private industries, Nonprofit 

institutions serving households

Wages covered by Railroad Retirement Act

Total wages posted to the MEF

WSS

WSSG

WSSGE

WSSGEFC

WSSGESL

WSSGF

WSSGFC

WSSGFM

WSSGGE

WSSGGESL

WSSGSL

WSSP

WSSPBNFXGE

WSSPES

WSSPF

Total wage worker compensation

Compensation for Federal and State & local government 

Compensation for Federal and State & local government enterprises 

Compensation of employees by industry, Government, Federal 

Compensation of employees by industry, Government, State and local 

government enterprises 

Federal Government Consumption Expenditures, Compensation of 

General Government Employees 

Compensation of employees by industry, Government, Federal civilian 

Compensation of employees by industry, Government, Military 

National Income w/o Capital Consumption Adjustment, Government 

Compensation for the State & local government and government 

enterprises

State & Local Government Consumption Expenditures, Compensation 

of General Government Employees 

Compensation of employees by industry, Private industries 

Compensation in private business nonfarm excluding government 

enterprises

Compensation of employees by industry, Private industries, Educational 

services 

Compensation of employees by industry, Private industries, Farms

164
WSSPH

WSSPHS

WSSPNI

WSSPSS

Compensation of employees by industry, Private industries, Households

Compensation of employees by industry, Private industries, Health 

services

Compensation of employees by industry, Private industries, Nonprofit 

institutions serving households 

Compensation of employees by industry, Private industries, Social 

assistance

WSSY Total compensation for wage and salary workers and proprietors

WSW

WSW_MEF

Wage and salary workers that report some OASDI covered earnings

Total number of employees with any wages posted to the MEF

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

YF

YNF

Total proprietor income

National Income, Proprietors’ income with Inventory Valuation (IVA) 

and Capital Consumption Adjustment (CCAdj): farm sector

National Income, Proprietors’ income with IVA and CCAdj: nonfarm

 

165
Process 3:

Beneficiaries

166
3. Beneficiaries

OCACT uses the Beneficiaries process to project the fully insured and disability insured 

population, the number of disabled workers and their dependent beneficiaries, the number of 

retired workers and their dependent beneficiaries, and the number of dependent beneficiaries of 

deceased workers. The Beneficiaries process receives input data from the Demography and 

Economics processes along with data received from the Social Security Administration and other 

government agencies. Output data is provided to the Economics and Trust Fund Operations and 

Actuarial Status processes.

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 workers 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

(SSAPOP) 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 that represent the

population with permanent legal work authorization. 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: 

FPRO = FPRO(·) (3.1.1) 

167
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 

1. Social Security area population as end of year (1940-2100) by age (0-100, age 100 

including age 100 and older), marital status (single, married, widowed, divorced) and 

sex (M, F).

2. Number of new “net lawful permanent resident (LPR) immigrants” (LPR immigrants 

– estimated legal emigrants) entering the Social Security area each year (1940-2100) 

by age (14-100, age 100 including age 100 and older) and sex (M, F). 

3. “Other-than-LPR immigrant” population as end of year (1963-2100) by age (0-100, 

age 100 including age 100 and older) and sex (M, F). 

4. The population granted deferred action for childhood arrivals (DACAs) as end of year 

(2012-2100) by age (0-100, age 100 including age 100 and older) and sex (M, F). 

5. The population granted deferred action for parental arrivals (DAPAs) as end of year 

(2019-2100) by age (0-100, age 100 including age 100 and older) and sex (M, F). 

6. The population that attain deferred action for childhood arrivals status (DACAATT) 

each year (2013-2100) by age (-1-100, age 100 including age 100 and older) and sex 

(M, F).

7. The population that attain deferred action for parental arrivals status (DAPAATT) 

each year (2019-2100) by age (-1-100, age 100 including age 100 and older) and sex 

(M, F).

Economics 

8. Annual estimates of covered workers posted to the Master Earnings File (MEF) by 

sex (M, F) and age (0-100) for years (1937-2100).

9. Annual projection (2017-2100) of average wage index and median covered earnings. 

10. “Other-than-LPR immigrant” workers with earnings posted to the (MEF) by sex (M, F), 

age (16-100), and for years (1964-2100).

Beneficiaries 

11. Disabled-worker beneficiaries at year end (2019-2100) by age (15-66), sex (M, F) and 

duration (0-10, duration 10 including duration 10 and above) from the previous year’s 

Trustees Report. These data are read in from files that are generated annually from 

168
the Beneficiaries/DISABILITY (#3.2) area. 

Short-Range OCACT data 

12. FINPOP by age (14-95, age 95 including age 95 and older) and sex (M, F) from the 

end of year 1969 to the end of Short-Range projection period (2030) (EOY 1969-

2035 is provided). 

13. DINPOP by age (15-66) and sex (M, F) from the end of year 1969 to the end of 

Short-Range projection period (2030) (EOY 1969-2035 is provided).

 

Other input data 

14. 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, 60-64, 65-69, 70-74, 75-79, 

80-84) and sex (M, F) for years 1937-2017. Data are updated using the CWHS file 

from the mainframe.

15. Number of disabled workers by age (20-69) and sex (M, F) for years 1958-2019. 

Ages 66-69 are zeros. Data are updated using the data from the historical disability 

file “wkrben”.

16. The amount required for crediting one quarter of coverage for years 1937-2017 from 

an OCACT web site.

17. Historical series of annual median earnings of all covered workers for years 1937-

2017. Data are updated using the data in the most recent Social Security Annual 

Statistical Supplement Table 4.B6.

18. The number of all covered workers (wage/salary workers, self-employed workers) by 

sex and amount of earnings for 2017 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 (FRACMOD.f90). (No Change for the 2021 TR)

19. ANNUAL factor (comparability factor between quarterly and annual reporting of 

earnings) by age (13-84) and sex (M, F) for years prior to 1978. (No Change for the 

2021 TR)

20. SLCT factor (adjustment factor to bring simulated fully insured rate in line with 

historical fully insured rate) by age (13-84) and sex (M, F). These data were updated 

for the 2021 TR. 

21. SRCH factor (adjustment factor to bring simulated fully insured rate in line with 

historical fully insured rate) by age (13-84) and sex (M, F). These data were updated 

for the 2021 TR.

22. DIADJ factor (adjustment factor to bring simulated disability insured rate in line with 

historical disability insured rate) by age (13-69) and sex (M, F). These data were 

updated for the 2021 TR.

3.1.c. Development of Output

Equation 3.1.1 & 3.1.2 - 

Determining the QC distribution 

169
There are three variables playing important roles in the simulation process starting from age 13 

through 84 of a birth cohort by sex. They include historical and projected covered worker rates 

of the population with permanent legal work authorization (LEGWK) by age and sex, the 

amounts required for crediting QC, and a cumulative worker distribution by earnings level. 

Covered worker rates of the LEGWK population (CPRO) are the ratio of the LEGWK covered 

workers to the LEGWK Social Security area population. A LEGWK population is its total 

population minus its other-than-LPR immigrant population1

. Historical and projected (total and 

other-than-LPR immigrant) 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 13 through 84. 

The law specifies the amount of earnings needed to earn one QC 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 ‘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 percentage of covered workers 

earning at least n QC is defined as: 

QCDist = 1 – FRAC n QC amount *

median earnings

 

   

, 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 84, INSURED begins the simulation process by randomly selecting records to 

represent new net LPR immigrants and the other-than-LPR immigrant population that attain 

DACA status from the covered worker portion of 30,000 records. For each record, a number of 

QC (0, 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. In 2013, the initial year of eligibility for 

DACAs, we assume that 10 percent of DACAs will retain covered earnings made prior to 

attaining LPR status. We apply this same assumption for newly eligible DACAs in 2021-2022 

when the 2012 DACA program is restored. 

1 The insured model treats those given legal work authorization through the 2012 Deferred Action for Childhood 

Arrivals (DACA) program like LPR immigrants. 

170
After the records for new immigrants are selected, the rest of the records for ages 14 to 84 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. 

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 

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 values2

. 

For each sex and birth cohort, the simulation process of assigning records as non-covered 

workers uses the following approach. This approach is repeated until the targeted number of 

non-covered workers is achieved.

1. One of the records, which is designated as one for LPR immigrants, is randomly 

selected as the 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 LPR immigrants, for ages 14-84. 

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 LEGWK fully insured 

percentage (FSIM_LEG) 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_LEG). 

2 This occurs when the female covered worker rate is greater than 90 percent of the male rate. When the female rate 

is equal to or greater than the male rate, the female SLCT and SRCH parameters are set equal to the male 

parameters. The parameters are linearly interpolated when the female covered worker rate is between 90 and 100 

percent of the male rate.

171
For each sex and cohort, FSIM_LEG is determined at ages 13 to 84. DSIM_LEG is determined 

at ages 13 to 69. 

An adjustment, DINADD, is made to DSIM_LEG. This additive adjustment 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 rolls for more than 3 years would be in this situation3

. Thus, DINADD is 

# of workers on the disability rolls morethan3 years

Social Security Area population by age, sex, and cohort. 

A small proportion of the other-than-LPR immigrant population, OTLPOP, is added to calculate 

the simulated fully insured rate of the Social Security Area population, FSIM. We assume that 

other-than-LPR immigrants who have their earnings posted to the MEF (CW_Other) are threefourths as likely to be insured as the LEGWK population. We project FSIM as 

 

FFFFFFFF_LLLLLL ∗ (LLLLLLLLLL + AA AAAAAA ∗ (CC _OOOO OO/CC ))

by age, sex, and cohort, where ALPHA is equal to 0.75. 

Hence, the simulated fully insured rate of the other-than-LPR immigrant population FSIM _OTL 

is

 

FFFFFFFF_LLLLLL ∗ AA AAAAAA ∗ CC _OOOO OO/CC

OOOO OO

by age, sex, and cohort. 

FSIM_LEG is assumed to remain the same beyond age 84. FSIM_OTL is assumed to remain the 

same beyond age 69. For ages 70 and older, FSIM is projected by multiplying the LEGWK and 

other-than-LPR fully insured rates to their respective populations and dividing the sum by the 

Social Security Area population. 

DSIM and DSIM_OTL are projected in a similar manner by using DSIM_LEG. If the simulated

results for DSIM are not consistent with historical data, an additional age-sex-specific 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 calculated by dividing the Short-Range estimates by the Social 

3 Those who are on the rolls for less than 4 years are assumed to meet the requirement for disability-insured status 

based on their earnings histories.

172
Security area population. The difference in terms of the percentage between the Long-Range 

(FSIM and DSIM) and Short-Range projections at the end of 10th year is linearly phased out 

during the next ten years by cohort and sex. The Long-Range projections are assumed thereafter. 

Number of Fully Insured and Disability Insured Workers

The numbers of Fully Insured and Disability Insured workers are obtained by applying FPRO 

and DPRO, respectively, to the Social Security area population. The result is an estimate of the 

number of people that are fully insured (FINPOP) and disability insured (DINPOP) by single 

year of age and sex, respectively. 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 marital status. 

173
3.2. DISABILITY 

3.2.a. Overview

The Social Security Administration pays monthly disability benefits to disability-insured workers 

who meet the Disability Insurance program’s definition of “disability”. If 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. We base 

the number of DIB at the end of each year on the number of disabled-worker beneficiaries who 

are currently entitled to benefits (CE). We calculate the number of CE at the end of year 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 an 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. We generate the numbers of dependent 

beneficiaries of DIB 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 DIBEOY = Exposures EOY × Linkages EOY (3.2.4) 

 

3.2.b. Input Data

Trustees Assumptions 

Each year, the Trustees set the assumption for the ultimate incidence rates and the ultimate 

recovery rates (on an award rate basis) for the twentieth year of the projection period. For the 

174
2021 Trustees Report, the age-sex-adjusted incidence rate (on an award rate basis) is 5.0 per 

1,000 and the age-sex-adjusted recovery rate (on an award rate basis) is 10.4 per thousand. The 

following chart shows our targeted ultimate incidence rates (on an entitlement rate basis) by age 

group and sex. We further adjust the rates below with a 0.25 percent discount to reflect the 

regulation removing the inability to communicate in English as an education category in the 

disability determination process. 

Using a standard population of disability insured who are not in current pay as of December 

1999, the age-sex-adjusted incidence rate (on an entitlement rate basis) for the 2021 Trustees 

Report is 5.2 per 1,000. Using a standard population of DIBs as of December 1999, the age-sexadjusted recovery rate (on an entitlement rate basis) for the 2021 Trustees Report is 9.3 per 

1,000. 

Long-Range OCACT Data

All data is updated annually except those noted otherwise. Population data are as of December 

31. We assume data as of December 31 of year z-1 is equal to data as of January 1 of year z. 

 Demography 

1. Social Security area population by age, sex, and marital status1 (dimensioned 

(0:100,1:2,1:4)) for years 1970-2100. 

2. Probabilities of death by sex, age and year (1:2,-1:148,2019:2100).

3. Total children by sex of parent, age of parent and age of child (dimensioned 

(1:2,19:71,0:18)) for years 1970-2100. 

4. Total married lives by age of husband crossed with age of wife (dimensioned 

(14:100,14:100)) for years 1970-2100. 

5. Average number of children under 18 per couple with children by age group (<25, 25-

29,...,60-64) of head of household (dimensioned (1:9)) for years 1970-2100. 

Economics 

6. Unemployment rates by age group (16-19, 20-24,...,60-64), sex and year (1990:2032).

Beneficiaries

 INSURED subprocess #3.1 

7. Disability-insured population by age, sex and year (15:69,1:2,1969:2100) from the 2021 

Trustees Report.

8. Disability-insured population by age, sex and year (15:69,1:2,1969:2100) from the 2020 

Trustees Report.

9. Fully insured population by age, sex and marital status (14:95,1:2,1:4) for years 1970-

2100 from the 2021 Trustees Report. 

1 Single, married, widowed, divorced.

<20 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 

Men 1.34 2.05 1.53 2.23 2.83 3.96 5.26 9.01 15.29 17.40 9.14 Women 1.04 1.43 1.52 2.29 3.32 4.64 6.09 9.69 14.52 14.27 7.69 

Age Group

175
10. Lawful Permanent Resident (LPR) fully insured percentage by age, sex and year

(14:95,1:2,1969:2100) from the 2021 Trustees Report 

2020 Trustees Report DISABILITY subprocess #3.2 

11. Death rate projection factors from the 2020 Trustees Report by age group (15-19,20-

24,...,60-64), sex and year (1:2,1:10,2020:2100).

12. Recovery rate projection factors and recovery rates in 2021 Trustees Report format after 

method change using data from the 2020 Trustees Report by age group (15-19,20-

24,...,65-69), sex and year (1:2,1:11,2020:2100) and (1:2,1:10,1970:2100), respectively. 

Other input data 

We update only the most recent year data annually for this category except as noted otherwise 

below: 

13. The December 2020 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) (0:55,15:66,1:2,1:2). 

14. December 2020 and December 2019 data from the MBR containing the number of 

disabled workers in current-payment status by age, sex and year (15:66,1:2,1969:2020). 

15. December 2020 data from the MBR containing the number of disabled workers in 

withheld or suspended status by age, sex and year (15:66,1:2,1969:2020). 

16. 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. 

• Minor child (0:17,1:2,1970:2020) 

• Student child (18:21,1:2,1970:2020) 

• Disabled adult child (age group1:92

,1:2,1970:2020) 

• Young spouse (19:64,1:2,1970:2020) 

• Married aged spouse (62:100,1:2,1970:2020) 

• Divorced aged spouse (62:100,1:2,1970:2020) 

 We also read totals for each category.

17. December data from the MBR containing the number of DIB awards by age, sex and year 

(15:67,1:2,1970:2020). 

18. December data from the MBR containing (1) the number of DIB total terminations 

(recoveries and deaths) and (2) the number of conversions3. These data are by sex and 

year (1:2,1970:2020).

19. December data from the MBR containing the number of DIB deaths by age, sex and year 

(15:67,1:2,1975:2020).

20. December data from the MBR containing the number of estimated DIB recoveries by 

age, sex and year (15:67,1:2,1975:2020).

21. December data from the MBR containing the number of old-age beneficiaries who at 

some point in time were converted to retired worker status. This data is by age, sex and 

year: (62:95+,1:2,1970:2020)

2 Age groups 1 through 9 are 18-19, 20-24, 25-29,..., 55-59. 3 Conversions are DIB beneficiaries who become eligible for old-age benefits due to reaching the normal retirement 

age.

176
22. 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 

(2:11,1:2,1973:2020). This file is not used for the SOSI. 

23. December data from the MBR containing the number of DIB awards by duration, age, 

sex and year (0:5,0:65,1:2,1993:2019). 2019 Awards were retrieved for this year’s TR, 

1993-2018 Awards have not been updated. 

24. Retroactive factors4 by year (1969:2019). These values are estimated using OCACT 

beneficiary data. This file is not used for the SOSI. 

All numbers in the following categories are updated annually unless otherwise noted. 

25. Average incidence rates by age and sex (15:65,1:2) for the base period 2005-2014 based 

on awards data from 2005-2019 (also known as the base incidence rates). We update 

these values when time and data are available. Note that rates for ages 60 through NRA 

are from the 2011 TR.

26. Probability of death for DIB’s – in a multiple-decrement environment by duration, age 

and sex (0:10,15:65,1:2) for the base period 2011-2015. These numbers (also known as 

the base probabilities of death) are from Actuarial Study No. 125. We update these 

values when time and data are available.

27. Probability of recovery for DIB’s – in a multiple-decrement environment by duration, age 

and sex (0:10,15:65,1:2) for the base period 2011-2015. These numbers (also known as 

the base probabilities of recovery) are from Actuarial Study No. 125. We update these 

values when time and data are available.

28. IBNR5

 (incurred but not reported) factors by duration, age and sex (0:10, 15:69, 1:2) 

based on 2005-2014 entitlements (awards data from 2005-2019). We update these values 

when time and data are available. 

29. For each year 2000-2110, (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. We update these values only when there 

is a change in the NRA or in the present law.

30. 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.

31. Short-Range/Long-Range adjustment (APROJ) factors by auxiliary beneficiary category 

(1:7) for years 2021-2100. These seven categories are; minor child, student child, 

disabled adult child, young wife, young husband, age wife and aged husband. We 

calculate these values by comparing Short-Range and Long- Range numbers for auxiliary 

beneficiaries.

32. IPROJG, DPROJG and RPROJG adjustment factors used to adjust incidence, death and 

recovery rates to reconcile between the long-range model and the short-range model.

Adjfaciprojg(1:11, 1:2, 2021-2100), Adjfacdprojg( 1:2, 1:10, 2021-2100) and 

4 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. 

5 IBNR factors reflect the proportion of DIBs entitled to benefits who have been awarded since the year of their 

entitlement.

177
SRAdjustment(1:2,1:11, 2021-2030) adjustment factors are by age group, sex and year.

33. Ultimate RPROJG values by sex and age group UltValueRprojg(1:2,1:10) calculated to 

reach a target value. We update these values when the probabilities of recovery for DIB’s

are updated. 

3.2.c. Development of Output

Equation 3.2.1 – New Entitlements

We calculate new entitlements 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. We calculate future age-sex-specific incidence 

rates by multiplying the base incidence rates by the incidence rate projection factors (IPROJGs). 

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 with the change in unemployment in the two prior 

years as the independent variables. Then, we run the IPROJGs through the main model and 

analyze the resulting incidence rates by age group and sex. We adjust the IPROJGs by age and 

sex to reach “target” incidence rates in the twentieth year of the projection period. These 

“target” ultimate incidence rates are calculated by age group and sex using a no-lag 

unemployment rate regression model for the years 1995-2018. For ages 60-64, rates are 

increased from the regression results to reflect the planned increase in the Social Security 

Normal Retirement Age from 66 to 67. We calculated rates for ages 65 and older using a 

weighted average of our base incidence rates and projected exposure. In 2030, at the end of the 

short-range period, age-sex-specific incidence rates approximate the ultimate rates assumed for 

the long-range period. For projection periods between the tenth and twentieth years, we linearly 

interpolate the IPROJGs 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 necessary for reconciliation between the long-range model and the short-range model. 

For the 2021 Trustees Report, we made IPROJG adjustments in the short-range period to reflect 

that disability applications are expected to increase to pre-pandemic levels as the COVID-19 

pandemic recedes, the economy will continue to recover, and there will be a temporary increase 

in applications partially offsetting reduced levels experienced during the pandemic. 

Equation 3.2.2 – Exits

The long-range model projects three types of exits from the disability rolls; 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 )(

x q ) and ( r)(x q ), respectively. Projected ( d )(x q ) 

and ( r)(

x q ) 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, we derive the recovery projection factors (RPROJGs) by age group and 

sex from 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, we 

178
calculate the starting RPROJGs the following way: 

 RPROJGTR21(2020) = RPROJGTR20(2020) × actual recovery rate(2020) / projected 

 recovery rate TR20(2020) 

Because there is no apparent upward or downward trend, we use the average recovery rates for 

the last ten historical years as the target values for the 10th year (2030). Then, for each age group 

and sex, we calculate the tenth year’s RPROJGs as follows: 

 RPROJGTR21(2030) = RPROJGTR21(2020) ×target value recovery rate(2030) / 

 actual recovery rate(2020) 

For the second 10 years of the projection period, we linearly interpolate between the ultimate 

RPROJG value and the RPROJG value at the end of short-range period (2030). Ultimate 

recovery rates by age group and sex are determined by analyzing historical recovery rates. We 

may make additional adjustments to the RPROJGs to reconcile with the short-range 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. For the 2021 Trustees Report, we made DPROJG adjustments in 2021 and 2022 to better

reflect the extra mortality expected from the pandemic. For the rest of the projection period, we 

assume the DPROJGs improve at the same rate as the general population for that age group and 

sex. We calculate the DPROJGs for each year by 5-year age group and sex the following way: 

DPROJG(year) = DPROJG(year-1) x 4 year 1999

age age age x

qx DIB

+

=

 

× ×     ∑ / x 4 year 1 1999

age age age x

qx DIB

+ −

=

    ×

  ∑

Equation 3.2.3 – Disabled-Worker Beneficiaries

The projection begins with the latest data available from the mainframe of disabled-worker 

beneficiaries in current-payment status. This data is from a 100 percent sample of the Master 

Beneficiary Record (MBR) at the end of the year. We split up disabled-worker beneficiaries by 

age at entitlement, sex and duration of entitlement. We convert this population to a currently 

entitled population by dividing each age, sex and duration cell by the appropriate duration-agesex-year-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. We 

reduce this currently entitled population by multiplying by the appropriate duration-age-sexyear-specific IBNR factor. The result is the following year’s disabled-worker beneficiaries in 

current-payment status. The process repeats over each sex, age of entitlement and duration of 

entitlement throughout the projection period. 

Equation 3.2.4 – Dependent Beneficiary of Disabled Workers 

There are six dependent-beneficiary categories; minor child, student child, disabled adult child, 

179
young spouse, married aged spouse and divorced aged spouse. We disaggregate projections by 

age of the beneficiary and sex of the account holder. We detail below the linkages and exposures 

used in each category 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: Total 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+ pYSDCB= Probability that young spouse has a minor child 

 or a disabled child 

 beneficiary in his/her care 

YSRES = Residual Factor

Married Aged Spouse 

180
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

We estimate the residual factors for each of the dependent categories using a 10-year Least 

Squares regression formula. We then hold these residual factor values constant for the duration 

of the long-range period. If the 10-year Least Squares method results in a negative residual 

factor, we hold the last historical residual factor instead. For the 2021 Trustees Report, so that 

the 2020 experience during the pandemic does not skew our regression results, we retain the 

regression period of 2010-2019 from the 2020 Trustees Report.

We develop factors for a dependent beneficiary category to match short-range results during the 

first 10 years of the projection period. We phase these factors out linearly over the second ten 

years of the projection period. 

Details about the regression equations used in determining incidence rates and death rates by age 

group and sex are available upon request.

181
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. We compute the projection of 

beneficiaries 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 it makes all beneficiary calculations.

We categorize retired workers and their dependent beneficiaries 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, 18-21 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, 18-21 for student, age groups 

18-19, 20-24,..., 55-59, 60+ for disabled adult) and sex of the account holder 

Lastly, we estimate the number of deaths of insured workers (LUMSUM) by 5-year age group 

(20-24, 25-29,..., 80-84, 85+) and sex. 

182
Equations 3.3.1-13 indicates 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

We update all data annually unless otherwise noted. Timing of data received is denoted ‘BOY’ 

(beginning of year) or ‘EOY’ (end of year). 

Long-Range OCACT Data 

Demography 

1. Social Security area population by year (EOY 1970-2100), single year of age (0-100+), 

sex, and marital status (single, married, widowed, divorced) 

2. Deaths by year (during years 2020-2100), age group (20-24,...,80-84, 85+) and sex 

3. Average number of children per family by year (EOY 1970-2100), and age group of the 

householder (20-24,...,60-64) 

4. Children by year (EOY 1970-2100), single year of age (0-18), sex of primary account 

holder (parent), status of primary (62+ or deceased), and age of the other parent (15-

19,20-24,...,65-69, 70+, total ages) 

5. Married couples by year (EOY 1970-2100), age of husband (62-95+) and age of wife 

(62-95+) 

6. Persons with an aged spouse by year (EOY 1970-2100), age group (15-24, 25-29,...,65-

69) and sex 

7. Probabilities of death by year (EOY 1941-2100), single year of age (-1,100), and sex 

183
Economics 

8. Covered wages and employment in the Federal Civilian and State and Local Sectors 

(during years 1998-2100) 

9. Employment rates for age 62 by year (during years 1977-2100) and sex 

Beneficiaries

10. Fully insured persons by year (EOY 1969-2100), age (14-95+), sex, and marital status 

(single, married, widowed, divorced) 

11. Lawful permanent resident (LPR) fully insured rate by year (EOY 1969-2100), age (14-

95+), and sex

12. Disabled-worker beneficiaries in current pay by year (EOY 1970-2100), age (62-66) and 

sex

13. Converted DI to OAI beneficiaries by year (EOY 1970-2100), age (62-95+) and sex 

14. Disability prevalence rates by year (EOY 1970-2100), age (50-69) and sex 

Short-Range OCACT Data 

15. For EOY 1975-2005: 

a. Aged spouses of deceased workers by age (60-95+), sex, and insured status 

b. Retired workers by age (62-95+) and sex 

c. Aged spouses of retired workers by age (62-95+) and sex 

d. Disabled widow(er)s by age (50-64) and sex and marital status

e. Minor children by age (0-17) and status of parent (retired, deceased)

f. Student children by age (18-21) and status of parent (retired, deceased) 

g. Disabled adult children by age (20-95+) and status of parent (retired, deceased)

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64,65-65) and 

sex

i. Young spouses of deceased workers by age group (under 25, 25-29,...,60-64,65-65) 

and sex

Note: We will not update this data.

16. Insured aged spouses of deceased workers by year (EOY 1974-2020), age (60-95+) and 

sex 

17. Retired worker beneficiaries in-current-pay status by age (62-70, 70+) and sex for EOY 

2019-2030 

18. We receive the following for EOY 2020: 

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 (50-66), 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 (18-21), sex of parent and status of parent (retired, deceased)

184
g. Disabled adult children by age group (18-19, 20-24,...,55-59, 60+), sex of parent and 

status of parent (retired, deceased)

h. Young spouses of retired workers by age group (under 25, 25-29,...,65-66) and sex

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-66), sex and 

marital status (widowed, divorced) 

j. Total parent beneficiaries

19. We receive the following for EOY 2030: 

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, 65-67, 68-70, 71+) 

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 

20. Total amount of lump-sum death payments during 2019 

21. Insured aged spouses in current pay by single year of age as of the end of the year for 

years 1974-2020. 

Other Input Data 

22. For EOY 1970-1974, obtained from the MBR10PER dataset on the mainframe: 

j. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced) 

k. Retired workers by age (62-95+) and sex 

l. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced) 

m. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced) 

n. Minor children by age (0-17), sex of parent and status of parent (retired, deceased) 

o. Student children by age (18-21), sex of parent and status of parent (retired, deceased)

p. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased)

q. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex 

r. Young spouses of deceased workers by age group (under 25, 25-29,...,60-64), sex and 

marital status (widowed, divorced) 

s. Total parent beneficiaries

Note: We will not update this data.

23. Number of beneficiaries with benefits withheld due to receipt of a significant government 

pension by sex and marital status (married, widowed) for EOY 2019 from the 2020 

Annual Statistical Supplement 

185
24. 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 2016 

through 2020 WEP 100 percent sample

25. 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 we use for Annual Update #9, 

which calculates beneficiaries by sex. Therefore, we apply the 2003 proportions to 

estimate the breakdown of disabled adult children by sex of the child. We will not update 

this input.). Not used for SOSI.

26. 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 1970-2100 from the Social Security website (Note: these values are only 

updated when there is a Social Security law change regarding the NRA) 

27. Prevalence rate regression coefficients (slopes and y-intercept value by sex) 

28. Regressed prevalence rate by sex for the most recent historical year 

29. Adjustment factors which account for the difference between estimated and actual 

historical retired worker prevalence rates by year (EOY 2021-2100), age (63-69) and sex 

30. Adjustment factors which account for the difference between projected beneficiary values 

for the 10th 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, 65-67, 68-70, 71+) 

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 

31. Adjustment factors to auxiliary beneficiary categories for demographic assumption 

changes increasing the other-than-LPR population by sex for years 2021-2100. Factors 

are computed for: 

a. Aged spouses of deceased workers (widow(er)s) 

b. Aged spouses of retired workers 

c. Disabled adult children of retired workers 

d. Minor children of deceased workers 

186
e. Disabled adult children of deceased workers

f. Young spouses of deceased workers

Note: Starting with the 2017 TR, these factors are all set to 1 due to the change to using 

LPR fully insured rates versus total fully insured for calculating FIB factors. 

32. Number of one-earner couples by year of birth of the primary account holder where the 

primary account holder files for and suspends their retirement worker benefit and their 

spouse receives a spousal benefit for years 2008-2015 from a 1 percent MBR sample. 

Note: We will not update this data.

33. EOY 2020 male and female retired worker counts by attained age and entitlement age 

from a 100 percent MBR sample. 

34. Adjustments to the estimated historical retired worker prevalence rates to account for the 

increase in retired workers due to the elimination of the deemed filing claiming strategy.

3.3.c. Development of Output

We use several acronyms to describe the equations presented below. Acronyms not preceded by 

a subscript generally refer to the number of beneficiaries. For example, RWN refers to the 

number of retired workers. Acronyms preceded with a ‘p’ refer to probabilities. For example, 

ppppppFFFFFF refers to the probability that a person is fully insured. 

Equation 3.3.1 – Aged Spouses of Deceased Workers (ASDWN) 

Aged Spouses of Deceased Workers 

 Exposures: SSA population by age (60-95+), sex and marital status (widowed and 

 divorced) 

 Linkages: pASDWDEA = probability that the primary account holder (PAH) is 

 deceased

 pASDWFIA = probability that the PAH was fully insured at death 

 pASDWMBB = probability that the widow(er) is not receiving a young- 

 spouse benefit for the care of a child

 pASDWFIB = probability that the aged-widow(er) is or is not 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 non-covered 

 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 

We project the number of aged spouses of deceased workers (widow(er)s), along with all 

187
linkage factors, 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 (fin = 1) and uninsured (fin = 

2). Note that all variables preceded by the letter p refer to calculated probabilities. We 

calculate the projected number of insured aged spouses of deceased workers age 60 to 70, 

and uninsured aged spouses of deceased workers age 60 to 95+ as follows:

AAAAAA AA = AAAAAA PPPPPP × pp ppDDDD × pp ppFFFFFF × pp ppMMMMMM

 × pp ppFFFF × ppAAAAAA GG × pp ppRR RR (3.3.1) 

For each sex we calculate the projected number of insured aged spouses of deceased workers 

over age 70 by applying mortality rates to the population already receiving such benefits: 

AAAAAA AANN,YY = AAAA NN−1,YY −1 × (1 − qqqqNN−1,YY )

Where N is the age, and qqqqNN−1,YY is the death rate for age N-1 in the given year. 

ASDWPOP represents the subset of the population from which we draw these beneficiaries. 

We set this equal to the Social Security area population ( SSSSSSmmmm) for each possible 

marital status.

AAAAAA PPPPPP = SSSSSSmmmm

pASDWDEA represents the probability that the primary account holder (PAH) is deceased. 

For the widowed population, we set this factor equal to one. For the divorced population, we 

set this factor equal to the portion of the total widowed ( SSSSSSwwwwww) and married 

( SSSSSSmmmmmm) population who are widowed. 

pp ppDDDD = �

 1, mmmm = 1 (wwwwwwwwwwwwww)

SSSSSSwwwwww

SSSSSSmmmmmm + SSSSSSwwwwww

, mmmm = 2 ( vv vvvv )

pASDWFIA represents the probability that the PAH was fully insured at death. For a given 

age of widow, AW, we assume that the age of her deceased husband, AH, ranges from AW-6

to AW+12 with a lower and upper bound of 60 and 95+. Further, we assume that the more 

likely age of the husband is AW+3. For each age, we calculate pp ppFFFFFF as a weighted 

average of the portion of the Social Security area population who are fully insured at each 

possible age of the husband (II AA). For example, for a widow age 70, we assume that the 

age of her husband is between 64 and 82, therefore we calculate the weighted average of the 

portion of the population who are fully insured men, applying the highest weight of 10 to age 

73, and a linearly reduced weight to zero for each age above and below 73. We use the same 

concept 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. 

WW WWWWWW AA = 10 − |AA + 3 − AA |

188
 

WW WW WW = 10 − |AA − 3 − AA |

pp ppFFFFFF =

⎩

⎪

⎨

⎪

⎧ ∑ WW WWWWWW AA × II AA

+12

AA= −6

∑ WW WWWWWW AA

+12

AA= −6

, ssss = 1

∑ WW WWWWWW × II AA+6

= AA−12

∑ WW WWWWWW AA+6

= AA−12

, ssss = 2

pASDWMBB represents the probability that the widow(er) is not receiving a young-spouse 

benefit for the care of a child. A widow(er) can receive a young-spouse benefit up to age 69 

if he/she meets all other eligibility requirements. Since the minimum age requirement to 

receive a widow(er) benefit is 60, it is necessary to remove those receiving a young-spouse 

benefit (YY ), where ab represents the 5-year age bracket1. We assume a uniform 

breakdown to divide the age groups into single-age estimates.

For fin = 1 (insured):

pp ppMMMMMM = 1

For fin = 2 (uninsured): 

FF FF =

⎩

⎪

⎨

⎪

⎧

 

 1, 65 ≤ aa aa ≥ aa + 1

− aa , aa < < aa + 1

 0, ee h

pp ppMMMMMM =

⎩

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎧1 − 0.2 × YY 60−64

AAAAAA PPPPPP × pp ppDDDD × pp ppFFFFFF

, aa = 60 − 64

1 − YY 65−69

AAAAAA PPPPPP × pp ppDDDD × pp ppFFFFFF

×

FF FF aaaa

∑ FF FF aaaa

69

65

, 65 ≤ aa ≤

1, aa >

pASDWFIB represents the probability that the aged widow(er) is fully insured. For insured 

widow(er)s, pp ppFFFF is equal to the LPR fully insured rate (FILEG) at each age and sex. 

For uninsured widow(er)s, pp ppFFFF is simply one minus the probability for insured 

widow(er)s.

pp ppFFFF = �

FF FF , ff = 1

 1 − FF FF , ff = 2

Where fin represents the insured status of the account holder.

1 There are no young spouses at NRA or above.

189
pASDWGPB represents the probability that the aged-widow(er)'s benefits are not withheld or 

completely offset because of receipt of a significant government pension based on earnings 

in non-covered employment. According to the 1977 amendments, Social Security benefits 

are subject to reduction by up to two-thirds of non-covered government pension. 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, we 

do not apply a factor. 

For fin = 1 (insured): 

pp GG = 1

For fin = 2 (uninsured): 

pp ppGG = �

1, yy ≤ 1978

1 − ×

AAAAAA PPPPPP × pp ppDDDD × pp ppFFFFFF × pp ppMMMMMM × pp ppFFFF

, yy > 1978

pASDWRES represents the probability that a widow(er), who is eligible to receive 

widow(er)’s benefits actually receives the benefits. In particular, for fin = 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. This factor accounts for 

other eligibility requirements not previously mentioned. For example, in the case of an aged 

widow(er), that the widow(er) did not remarry before age 60. In the case of a divorced 

widow(er), that the marriage to the PAH lasted at least 10 years. For all historical years, we 

calculate pp ppRR RR

yy 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.

pp ppRR RR

yy = PPPPPP×pp DDDDDD×pp FFFF ×pp MMMMMM×pp FFFF ×pp GG

, year < TRYR

Where TRYR is the Trustees Report year.

For each age, sex, insured status, and marital status, we use a least squares regression over 

the last ten years of historical data to determine a starting value in TRYR-1 for 

pp ppRR RR

yy from which we project future values. In addition, for each sex, insured status, 

and marital status, we graduate the regressed values of pp ppRR RR

TT −1 over age using a 

weighted minimized third-difference formula to produce . are 

the preliminary estimates of pp ppRR RR

TT +9, the values in the 10th year of the projection 

period2. In addition, we apply adjustments to the widows (sa = 1) by age group (60-64, 65-

69 for insured; 60-64, 65+ for uninsured), SS , to the 10th year of the projection 

2 For the 2021 Trustees Report, the ten-year regression is over the period 2010-2019, and we graduate the TRYR-2 

regressed values of ppAAAAAA RR RR, excluding the 2020 data due to the Covid-19 pandemic. 

190
period in order to match the projections made by the Short-Range office. We linearly 

interpolate the values of pp ppRR RR

yy for intermediate years between pp ppRR RR

TT −1 and 

pp ppRR RR

TT +9 (equal to × SS ). After the 10th year, we linearly 

grade these adjustment factors to one over the 10 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. 

We also apply adjustments to the 70+ insured widows by age group (70-74, 75-79, 80-84, 

85+). The adjustments for the intermediate years between the TRYR and TRYR + 9 are 

applied on a cohort basis to the number of aged spouses of deceased workers (ASDWN) 

using the following formula: 

AAAAAA AANN,YY = AAAAAA AANN,YY × SS

�

1

h�

Where h is the number of years the adjustment is applied for the cohort. For age 70, we 

linearly grade these adjustment factors to one over the 10 years beyond the end of the shortrange 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)

Retired Workers

 Exposure: SSA population by age (62-95+), sex and marital status (single, married, 

 widowed and divorced) 

 Linkages: pRWFIA = probability that the primary account holder (PAH) is insured 

 pRWDBB = probability that the PAH is not receiving a disabled-worker 

 benefit

 pRWWBB = probability that the PAH is not receiving a widow(er) benefit 

 pRWRES = retirement prevalence rate; probability that a fully insured

 worker not receiving disability or widow(er)’s benefits would 

 receive a retired-worker benefit

We project the numbers of retired-worker beneficiaries, along with all linkage factors, by 

age, sex, and marital status. Age ranges from 62 to 95+, and marital status includes single, 

married, widowed, and divorced (ms = 1-4). We calculate the projected number of retiredworker beneficiaries as follows:

= PPPPPP × ppppppFFFF × ppppppDD × ppppppWW × ppppppRR RR (3.3.2) 

RWPOP represents the subset of the population from which we draw these beneficiaries. We 

set this equal to the Social Security area population ( SSSSSSmmmm) for ms = 1-4. 

PPPPPP = SSSSSSmmmm

pRWFIA represents the probability that the primary account holder (PAH) is insured. We set 

191
this factor equal to the portion of the Social Security area population that is fully insured 

(INS) for ms = 1-4. 

ppppppFFFFFF = II

PPPPPP

pRWDBB represents the probability that the PAH is not receiving a disabled-worker or 

disability-conversion benefit. We set this factor 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.

ppppppDD =

⎩

⎪

⎨

⎪

⎧1 − DD

PPPPPP × ppppppFFFFFF

, mm = 1, 2

�1 − DD + AAAAAA AA

PPPPPP × ppppppFFFFFF

�

� DD DD

DD DD + �

, mm = 3, 4

 

pRWWBB represents the probability that the PAH is not receiving a widow(er) benefit. We set 

this factor equal to the portion of fully insured workers that is not aged spouses of deceased 

workers. 

ppppppWW =

⎩

⎪

⎨

⎪

⎧1, mm = 1, 2

 

�1 − DD + AAAAAA AA

PPPPPP × ppppppFFFFFF

�

�

DD DD + �

, mm = 3, 4

pppppp RRRR

NN,yyeeeeeerepresents 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 ppppppRR RR

NN,yy . 

For each historical year and sex, we calculate ppppppRR RR

NN,yy 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. 

ppppppRR RR

NN,yy = RR

RR PPPPPP×pp FFFF ×pp DD ×pp WW

, N = 62-95+ and year < TRYR

Historical prevalence rates at age 62 follow an inverse relationship with (1) employment rates 

( EE yy ) at age 62, by sex, and (2) increases in the normal retirement age over the 

historical period. We assume this relationship holds in the projection period, and therefore we 

used it to calculate yy , the regressed prevalence rate based on the projected 

EE yy at age 62 for each year and sex, and the number of months from age 62 to the 

normal retirement age (mm mmh yy ). Note that we calculate prevalence rates on a cohort 

192
basis3

. The regression equation used to estimate the prevalence rates is:

yy = −1.35852 × EE yy + −0.00417 × mm mmh yy + 1.25532 for male 

with an R2

 value of 0.88795 

and

yy = −0.46351 × EE yy + −0.00955 × mm h yy + 1.00156 for female 

with an R2 value of 0.89175 

We then set the future prevalence rate at age 62, ppppppRR RR

62,yy , equal to the sum of the 

regressed prevalence rate ( yy ) and ERROR, the difference between the actual 

prevalence rate and the regressed prevalence rate in the most recent historical year, which we 

phase out linearly over 10 years. 

ppppppRR RR

62,yy = yy + ( ) × mm �0, TT +9−yy

10 �, N = 62 and year ≥ TRYR-1 

To compute ppppppRR RR

NN,yy for ages 63 through 69 in the projection period, we must calculate 

several preliminary variables. These include:

 NN, for N = 62-70 (same for both sexes), 

 NN

yy , for N = 63-69 and by sex, and

 NN, for N = 63-69 and by sex. 

NN 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. We base the 

calculation of NN 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. 

NN =

⎩

⎪

⎨

⎪

⎧1 + ( − ) × , ≥

1 − ( − ) × AA 3, − 3 ≤ ≤

1 − 3 × AA 3 − ( − 3 − ) × AA 3, < − 3

NN

yy , the estimated prevalence rate at age N, is then calculated as the prevalence rate 

at age 62 (ppppppRR RR

62,yy −(NN−62)

) plus an estimate on the expected portion of the remaining 

probability (1 − ppppppRR RR

62,yy −(NN−62)

), that a potential retired worker will actually retire by 

that given age. We base this estimate on NN, assuming that the retirement decision 

by a worker is totally and completely influenced by the expected change in the portion of 

3 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.

193
PIA that is payable at each age relative to the potential change after the initial eligibility.

NN

yy = ppppppRR RR

62,yy −(NN−62) + (1 − ppppppRR RR62,yy −(NN−62)

) × MMMM NN−MMMM 62

MMMM PP 70−MMMM 62

, N = 63-69 

In the first year of the projection period, an adjustment ( NN) 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 to 69, the value used beginning in TRYR is a regressed 

value based on the last 5 years’ differences between the actual and estimated prevalence rate. 

With the exception of age 66, we hold this value constant throughout the projection period. 

NN is greater during NRA transition periods. This affects 66 due to the 

scheduled increase in NRA from age 66 to 67 over the years 2017-2022. For the years 

preceding the NRA transition, we use the average from the last five historical years to 

calculate 66. We assume that the effects on age 66 prevalence rates after the NRA 

change from 66 to 67 will be similar to the effects on age 65 prevalence rates after the NRA 

change from 65 to 66. Thus we set 266 to the average difference between actual 

and estimated prevalence rates for age 65 during the five years after the NRA changed from 

65 to 66. Then after the NRA increases to age 67, we use 266 to decrease age 66 

prevalence rates to the level that age 65 prevalence rates dropped to after the NRA increase 

to 66. In the years during which the NRA transitions to age 67 we use a linear interpolation 

based on the number of months that the NRA has increased in order to phase out 66

and phase in II 266. It will remain at 266 for the rest of the projection 

period. 

ppppppRR RR

NN,yy = NN + NN

We apply additional adjustments to lower age 66 prevalence rates for the 1955 through 1960 

birth cohorts to account for the NRA transition to age 67. The target age 66 prevalence for 

the 1960 cohort (the first cohort with an NRA of 67) is set by matching the increase in 

prevalence between ages 65 and 66 to the increase between ages 64 and 65 of the 1943 

cohort (the first with an NRA of 66). The adjustment factor needed to reduce the 1960 cohort 

age 66 prevalence to the target value is graded in over the age 66 prevalence rates of the 1955 

through 1959 cohorts. 

For age 70 men, we assume that the values of the latest actual ppppppRR RR

NN,yy , change linearly to 

the ultimate level of 0.995 over the first 20 years of the projection period. For age 70 women, 

we assume an ultimate level of 0.990 through 2023 and an ultimate level of 0.995 starting in 

2024. This is due to the Bipartisan Budget Act of 2015 (BBA), which expands deemed filing 

to those at NRA or above, thus eliminating the deemed filing claiming strategy for those 

turning 62 in 2016 or later. 

For year ≥ TRYR:

194
ppppppRR RR

70,yy

=

⎩

⎪

⎨

⎪

⎧0.995 − �0.995 − ppppppRR RR

70,TT −1� × max �0,

+ 19 − yy

20 � , ssss = 1

0.990 − �0.990 − ppppppRR RR

70,TT −1� × max �0,

+ 19 − yy

20 � , ssss = 2 aa yy ≤ 2023

0.995 − �0.995 − ppppppRR RR

70,TT −1� × max �0,

+ 19 − yy

20 � , ssss = 2 aa yy > 2023

For ages 71 and older, we assume ppppppRR RR

NN,yy stays constant at the level when the age was 70 

because there is no incentive to delay applying for benefits beyond age 70. 

ppppppRR

NN,yy = ppppppRR RR

70,yy −(NN−70)

, for N = 71-95+ and year ≥ TRYR

In addition, we apply adjustments by age group (62-64, 65-69) and sex, SSRR , to the 10th

year of the projection period in order to match the projections made by the Short-Range 

office. We also apply these adjustments to ppppppRR RR

NN,yy for all years after TRYR+9. The 

values of ppppppRR RR

NN,yy for intermediate years are linearly interpolated between ppppppRR

NN,TT −1

and ppppppRR RR

NN,TT +9. 

In response to the elimination of the file and suspend and deemed filing claiming strategies 

for aged spouses by the BBA, we expect that the married and divorced retired workers who 

would have delayed receiving their worker benefits will instead file for benefits earlier. As 

such, we use the unsuspRW(69) factor to increase the projected number of age 69 married 

workers for those who would have suspended their benefits but will now begin receiving 

them at age 69. 

uu uu (69) = ss ss (69) + 69,MM,MM + 69,FF,MM

69,MM,MM + 69,FF,MM

− 1

Where suspRW(69) is the number of age 69 retired workers who would have suspended their 

benefits for the file and suspend strategy. Since the utilization of this filing strategy had been 

expected to continue to grow in popularity had it not been eliminated, we apply a behavioral 

increase factor, RWBehavioralInc(69), to unsuspRW(69) to reflect the increasing number of 

retired workers who will no longer delay their benefits now that the filing strategy is no 

longer available. 

h aa (69) = �

1.5, ff h 1947

1.03, ff h 1948

1.0, ff h 1948

We use the DFRetWrkr(ag,sx) factor to increase the number of married and divorced retired 

workers for those affected by the expansion of deemed filing. This includes both the insured 

aged spouses who will no longer be able to delay receiving their worker benefit while 

195
receiving their aged spouse benefit, and the insured aged spouses who would never claim 

their retired worker benefit because their aged spouse benefit is higher. We calculate these 

factors as:

DD ( , ss )

=

⎩

⎪

⎨

⎪

⎧ ( aa, ss ) + aa, ss,MM + aa, ss,DD DD

aa, ss,MM + aa, ss,DD DD

− 1, yy − aa ≥ 1955

aa, ss,MM + aa, ss,DD DD

aa, ss,MM + aa, ss,DD DD − ( aa, ss )

− 1, yy − aa < 1955

Where DeemdFiler(ag,sx) is the number of insured aged spouses who will now have to claim 

their retired worker benefit due to the expansion of deemed filing. We assume that all of the 

insured aged spouses who would never have claimed their retired worker benefit will file at 

NRA. We identify this group as the insured aged spouses still receiving a spouse benefit at 

age 71. For those who are delaying claiming their worker benefit, we assume that 60 percent 

will file for worker benefits earlier now that the strategy is no longer available, with 1/2 

claiming at age 66, and 1/6 at each age 67 through 69. As the NRA transitions from 66 to 67 

we reduce DFRetWrkr(66,sx) by one minus the increase in NRA expressed as a fraction of a 

year with each factor being set to zero once the NRA is 67. 

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 

II TT −1 NN to the prevalence rate at age N, 

 yy = yy ×

TTTTTTTT−1 NN

pp RR

NN,yyyyyyyy

NN NN , AE ≤ N

where we calculate the incidence rate for a given AE = N and year as the change in the 

prevalence rate at age N to the prevalence rate at age N-1 in the previous year 

II yy =

⎩

⎪

⎪

⎨

⎪

⎪

⎧ppppppRR RR

NN,yy , = AA = 62

ppppppRR RR

NN,yy − ppppppRR RRNN−1,yy −1, 63 ≤ = AA ≤ 69

1 − ppppppRR RR

NN−1,yy −1, = AA = 70

and we set the incidence rate for a given AE < N and year to the incidence rate for AE and 

age N-1 in the previous year. 

II yy NN = II yy −1 NN−1 , AA <

For the last historical year, we use the TRYR-1 male and female retired worker counts by age 

and age of entitlement from a 100 percent sample to recalculate the TRYR-1 incidence rates 

196
for all attained ages, N, and all entitlement ages, AE.

4

Additional adjustments are applied to the incidence rates in order to account for the increase 

in retired worker beneficiaries due to the elimination of the deemed filing and file and 

suspend strategies. Since many of the beneficiaries utilizing these strategies delayed 

receiving their worker benefit until age 70, we assume that the retired workers added through 

the unsuspRW(ag) and DFRetWrkr(ag,sx) factors will survive until age 70. As such, our 

incidence rate calculations are adjusted to reflect the age at which the new retired workers 

claim benefits and to ensure that they remained on the rolls until age 70. 

Equation 3.3.3 – Aged Spouses of Retired Workers (ASRWN) 

 Aged Spouses of Retired Workers 

 Exposures: SSA population by age (62-95+, sex, and marital status (married and 

 divorced)) 

 Linkages: pASRWDEA = probability that the primary account holder (PAH) is not 

 deceased

 pASRWAGA = probability that the PAH is of the required age 

 pASRWFIA = probability that the PAH is fully insured 

 pASRWCPA = probability that the PAH is receiving benefits

 pASRWMBB = probability that the beneficiary is not receiving a young-spouse 

 benefit

 pASRWFIB = probability that the aged-spouse is not fully insured 

 pASRWGPB = probability that the aged-spouse’s benefits are not withheld 

 because of receipt of a significant government pension based 

 on earnings in non-covered employment

 pASRWRES = probability that a person who is eligible to receive aged-spouse 

 benefits actually receives the benefits

 pASRWFS2 = probability that a couple will engage in a filing 

 strategy in which the PAH files for and may or may not 

 suspend their benefit and the fully insured spouse files only for 

 their aged-spouse benefit. 

We project the number of aged spouses of retired workers, along with all linkage factors, 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). We 

calculate the projected number of aged spouses of retired workers as follows: 

AAAA AA = AAAA PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFFFF × pp pppp ×

pp ppppMMMMMM × pp ppppFFFF × pp ppppGG × pp ppppRR RR × pp ppppFF 2 

 (3.3.3) 

ASRWPOP represents the subset of the population from which these beneficiaries are drawn, 

4 For the oaicp.1992+ file produced for the Trust Fund Operations and Actuarial Status/Awards area, TRYR-1 

incidence rates are not recalculated from the 100 percent sample and instead are calculated as described in the 

previous paragraph.

197
and we set it equal to the Social Security area population (SSAPOPmb) for mb = 1, 2. 

AAAA PPPPPP = SSSSSSmmmm

pASRWDEA represents the probability that the PAH is not deceased. For the married 

population, we do not apply a factor. For the divorced population, we set the factor equal to 

the portion of the total married and widowed population who are married. 

pp ppppDDDD = �

1, mmmm = 1 (mm )

SSSSSSmmmmmm

SSSSSSmm + SSSSSSwwwwww

, mmmm = 2 ( )

pASRWAGA represents the probability that the PAH is of the required age, and we set it equal 

to the portion of the married population with a spouse (PAH) at least age 62. 

pp pppp = ∑ mm (AAAA, AAAA) 95 =62

SSSSSS ,mmmmmm

Where mar(AA, AS) is the number of married couples where the age of the account holder is 

AA and the spouse of the account holder is age AS. 

 

pASRWFIA represents the probability that the PAH is fully insured, and we set it equal to the 

portion of married couples of the required age where the PAH is fully insured (FI_PAH). 

For example, when the program estimates the number of female aged spouse of retired 

workers, this factor will find the portion where their spouse, the male PAH, is fully insured. 

pp ppppFFFFFF = ∑ [mm (AAAA, AAAA) × FF _ ,mmmmmm] 95 =62

∑ mm (AAAA, AAAA) 95 =62

pASRWCPA represents the probability that the PAH is receiving benefits. We set this factor 

equal to the portion of eligible married couples where the PAH is receiving benefits 

(RETIRED). If the beneficiary is divorced, we do not apply a factor, since it is not required 

for the retired worker to be receiving benefits for the divorced aged spouse to receive 

benefits.

pp pppp =

⎩

⎪

⎨

⎪

⎧

 1, yy ≥ 1985 aa

 mmmm = 2

 

∑ [mm (AAAA, AAAA) × FF _ ,mmmmmm × 95 =62 ]

∑ mm (AAAA, AAAA) × FF _ ,mmmmmm 95 =62

, ee h

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, we do not apply 

a factor. Otherwise, we set this factor equal to the portion of potentially eligible widow(er)s 

198
where the spouse of the PAH is not receiving a young-spouse benefit (YY ), where ab

represents the 5-year age group.5

For mb = 1 (married):

FF FF = �

 1, 65 ≤ aa aa ≥ aa + 1

 − aa , aa < < aa + 1

 0, ee h

pp pp MMMMMM =

⎩

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎧1 − 0.2 × YY 60−64

AAAA PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFF × pp pppp , aa = 62 − 64

1 − YY 65−69

AAAA PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFFFF × pp pppp × 

 FFAA

∑ FF FF aa

69

65

, 65 ≤ aa ≤

1, ee h

For mb = 2 (divorced): 

pp ppppMMMMMM = 1

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. We set this 

factor equal to one minus the LPR fully insured rate (FILEG) at each age and sex.

pp ppppFFFF = 1 − FF FF

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 non-covered 

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. 

pp ppppGG

= �

1, yy ≤ 1978

1 − ×

AAAA PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFFFF × pp pppp × pp ppppMMMMMM × pp ppppFFFF

, ee h

pASRWRES represents the probability that a person who is eligible to receive aged-spouse 

benefits actually receives the benefits. This factor accounts for other eligibility requirements 

not previously mentioned. For example, that the aged spouse has been married to the PAH 

for at least one year and in the case of a divorced aged spouse that the spouse was married to 

5 There are no young spouses at NRA or above.

199
the PAH for at least 10 years. For all historical years, we calculate pp ppppRR RR

yy as the ratio 

of uninsured aged-spouse beneficiaries receiving benefits to the number of persons meeting 

all previously mentioned requirements by age, sex, and marital status. We calculate the 

number of uninsured aged-spouse beneficiaries as the actual number of aged spouses 

receiving benefits (ASRWN), both insured and uninsured, less couples ages NRA and above 

where the PAH has filed for benefits and their fully insured spouse is receiving only a 

spousal benefit (FSCouple2(ag, sa, mb)). 

For year < TRYR:

pp ppppRR RR

yy =

AAAA AA aa, ,mmmm − FF FF 2( aa, ssss, mmmm)

AAAA PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFFFF × pp pppp × pp ppppMMMMMM × pp ppppFFFF × pp ppppGG

For each age, sex, and marital status, we use a least squares regression over the last ten years 

of historical data to determine a starting value in TRYR-1 for pp ppppRR RR

yy from which we 

project future values. In addition, for each sex and marital status, we graduate the regressed

values of pp ppppRR RR

TT −1 over age using a weighted minimized third-difference formula to 

compute . are the preliminary estimates of pp ppppRR RR

TT +9, the 

values in the 10th year of the projection period6

. For female spouses, we apply additional 

adjustments by age group (62-64, 65+), SS , to the 10th year of the projection period 

in order to match the projections made by the Short-Range office. We linearly interpolate the 

values of pp ppppRR RR

yy for intermediate years interpolated between pp ppppRR RR

TT −1 and 

pp ppppRR RR

TT +9 (equal to × SS ). After the 10th year of the projection 

period, we linearly grade these adjustment factors to one over the 10 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. 

pASRWFS2 represents the probability that a couple engages in the deemed filing claiming 

strategy or that the insured spouse has a spouse benefit that is higher than their retired worker 

benefit. The deemed filing claiming strategy is a strategy in which the PAH files for and may 

or may not suspend their worker benefit and their fully insured spouse receives only a 

spousal benefit thus delaying receiving their worker benefit. For historical years 2006 to 

TRYR-1, we set pASRWFS2 equal to the ratio of ASRWN to the number of uninsured aged 

spouses. Due to the BBA, those turning 62 in 2016 or later will no longer be able to use the 

filing strategy. For the projection period prior to the elimination of the filing strategy, we set 

pp ppppFF 2

yy equal to pp ppppFF 2yy −1 multiplied by a behavioral increase factor 

(BehaviorInc(ag, sa)). This factor accounts for the increase in the number of couples 

engaging in the filing strategy due to knowledge of the strategy becoming more widespread 

as well as the growth in the age 62 LPR fully insured married and divorced population 

(filpop62). We set pp ppppFF 2 to 1 in the projection period as those age 62 in 2016 reach 

NRA and above. 

6 For the 2021 Trustees Report, the ten-year regression is over the period 2010-2019, and we graduate the TRYR-2 

regressed values of ppAAAA RR RR, excluding the 2020 data due to the Covid-19 pandemic.

200
For year < TRYR:

pp ppppFF 2

yy

= �

AAAA AA

AAAA PPPPPP × AAAA DDDD × AAAA × AAAA FFFFFF × AAAA × AAAA MMMMMM × AAAA FFFF × AAAA GG × AAAA RR RR

, 2006 ≤ yy aa ≤ aa

1, ee h

For year ≥TRYR: 

h aa ( aa, ssss) = �

1.00 × ff 62, ff h 1950 − 1951

1.05 × ff 62, ff h 1952

1.15 × ff 62, ff h 1953

1.00 × ff 62, ff h 1953

pp ppppFF 2

yy =

⎩

⎨

⎧ 1 + �pp ppppFF 2

yy −1 − 1� × h aa ( aa, ssss), ≤ aa aa

 yy − 2016 + 62 < aa

1, ee h

Equation 3.3.4 – Disabled Spouses of Deceased Workers (DSDWN) 

 Disabled Spouses of Deceased Workers 

 Exposure: SSA population by age (50-69), sex and marital status (widowed and 

divorced) 

 Linkages: pDSDWDEA = probability that the primary account holder (PAH) is 

 deceased

 pDADWFIA = probability that the PAH was fully insured at death 

 pDSDWSSB = probability that the spouse is indeed disabled 

 pDSDWDEB = probability that the disabled spouse is not receiving another 

 type of benefit 

 pDSDWRES = probability that a person who is eligible to receive disabled- 

 spouse benefits actually receives the benefits

We project the number of disabled spouses of deceased workers, along with all linkage 

factors, 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). We calculate the projected number of disabled spouses of deceased workers as 

follows: 

= PPPPPP × pp ppDDDD × pp ppFFFFFF

× pp pp × pp ppDDDD × pp ppRR RR (3.3.4) 

DSDWPOP represents the subset of the population from which we draw these beneficiaries, 

and we set it equal to the Social Security area population ( SSSSSSmmmm) for mb = 1, 2. 

PPPPPP = SSSSSSmmmm

201
pDSDWDEA represents the probability that the primary account holder is deceased. For the 

widowed population, we do not apply a factor. For the divorced population, we set this 

factor equal to the portion of the total widowed and married population that is widowed. 

pp ppDDDD = �

1, mmmm = 1 (wwwwwwwwwwwwww)

SSSSSSwwwwww

SSSSSSwwwwww + SSSSSSmmmmmm

, mmmm = 2 ( )

pDSDWFIA represents the probability that the PAH was fully insured at death. Given the age 

of the widow, AW, we assume 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, we assume that the more 

likely age of the husband is AW+3. For each age, we calculate pp ppFFFFFF as a weighted 

average of the portion of the Social Security area population that is fully insured (INS), at 

each possible age of the husband. For example, if the widow is age 65, we assume that the 

age of the husband is between 59 and 77. Therefore, when we calculate the weighted 

average of the portion of the population who are fully insured men, we apply the highest 

weight of ten to age 68 and linearly reduce the weight to zero for each age above and below 

68. We use the same concept 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. 

WW WWWWWW AA = 10 − |AA + 3 − AA |

WW WWWWWW = 10 − |AA − 3 − AA |

pp ppFFFFFF =

⎩

⎪

⎨

⎪

⎧∑ WW WWWWWW AA × II AA

+12

AA= −6

∑ WW WWWWWW AA

+12

AA= −6

, ssss = 1

∑ WW WWWWWW × II AA+6

= AA−12

∑ WW WWWWWW AA+6

= AA−12

, ssss = 2

pDSDWSSB represents the probability that the spouse is indeed disabled. We set this factor 

equal to the disability prevalence rates (DISPREV) by age and sex received from the 

DISABILITY subprocess. 

pp pp = DD

pDSDWDEB represents the probability that the disabled spouse is not dually eligible for

another type of benefit. We assume this factor remains at a constant level by sex.

pp ppDDDD = �

0.85, ss = 1

0.06, ssss = 2

pDSDWRES represents the probability that a person who is eligible to receive disabled-spouse 

benefits actually receives the benefits. This factor accounts for other eligibility requirements 

not previously mentioned. For example, that the disabled widow met the seven-year deadline 

202
for surviving spouses to qualify for benefits on the basis of disability. For all historical years, 

we calculate pp ppRR RR

yy 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. 

pp ppRR RR

yy = DD DD

DD DD PPPPPP×pp DDDDDD×pp FFFF ×pp ×pp DDDD

, year < TRYR

For ages 50 to 64, and each sex, and marital status, we use the average pp ppRR RR

yy over the 

last five years of historical data to determine starting values for pp ppRR RR

yy from which we 

project future values. We phase in these averages over five years using a linear interpolation 

between the five-year averages and pp ppRR RR

TT −17. For female disabled spouses, we apply 

an adjustment, SSDD DD , to the 10th year of the projection period in order to match the 

projections made by the Short-Range office. We exponentially interpolate the values of 

pp ppRR RR

yy for intermediate years between pp ppRR RR

TT −1 and pp ppRR RR

TT +9 (equal to 

pp ppRR RR

yy × SSDD DD ). After the 10th year of the projection period, we linearly grade 

the adjustment factors to one over the 10 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 the NRA when the 

beneficiary was age 60, pp ppRR RR

yy is equal to pp ppRR RRyy at age 64 times an adjustment 

that accounts for the additional ages as NRA changes.

FF FF aaaa = �

1, aa 60 ≥ aa + 1

aa 60 − aa , aa < aa 60 < aa + 1

pp ppRR RR

yy = pp ppRR RRyy ,64 × �

pp RR

yyyyyyyy,64

pp RR

yyyyyyyy,63�

( aaaa−64)

× FF FF aaaa, 65 ≤ age ≤ 69 and 

 age < NRA at age 60 

Equation 3.3.5 – Minor Children of Retired Workers (MCRWN) 

We project the number of minor children of retired workers, MCRWN, by age of the minor 

(am = 0-17) and sex of the account holder (sa = 1 for male, sa = 2 for female). 

For children of male retired workers: 

MM,

yy = mm h MM,yy × _ ss yyyyyyyy

pppppp_ ss yyyyyyyy

× pp ppppRR RR

yy (3.3.5.1) 

For the number of minor children of male retired workers, we multiply the number of 

7 For the 2021 Trustees Report, the five-year average is over the period 2015-2019, and we phase between the fiveyear averages and pp RR RR TT −2, excluding the 2020 data due to the Covid-19 pandemic.

203
children under the age of 18 with a father who is at least 62 years old and who’s other parent 

is not deceased (mm h MM,

yy ) by the total number of male retired workers ages 62 to 71 

( _ss yy ) divided by the total number of men in the population ages 62 to 71 

(pp pp_ss yy ).

pMCRWRES represents the probability that a child who is eligible to receive minor-child 

benefits actually receives the benefits. This factor accounts for other eligibility requirements 

not previously mentioned. For example, the marital status of the child or the dependency 

status of the child. In the historical period, we calculate this as the ratio of the total number of 

minor children of retired workers actually receiving benefits to the total eligible to receive 

benefits.

pp ppppRR RR

yy = MM

yy

mm h MM,

yy × _ss yy

pp pp_ss yy

For the projection period, we take the average of these ratios over the last ten historical years 

and phase it in using a linear interpolation between the average and pp ppppRR RR

TT −18. We 

apply an adjustment, SSMM , to the 10th year of the projection period in order to match 

the projections made by the Short-Range office. The adjustment factor is phased in over the 

first 10 years of the projection period with the full factor applied in the 10th year. After the 

10th year of the projection period, we linearly grade these adjustment factors to one over the 

10 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 children of female retired workers: 

FF,

yy = MM TTTTTT TT,MM

yyyyyyyy ×mmmmmm mmmmmmmm mm

1−mmmmmmww ×

MM mm,FF

TTTTTTTT−1

MM TTTTTT TT,FF

TTTTTTTT−1 (3.3.5.2) 

mcrwPrcntFem represents the average over the last five historical years9 of the percentage of 

the total number of minor children of female retired workers, ages 0 to 17, to the total 

number of minor children for both male and female retired workers. 

mm mm mm = TT TT,FF

yy

TT TT,FF

yy + TT TT,MMyy

We maintain the total 0−17,FF

YY at this percentage over the entire projection period by 

multiplying our estimate of 0−17,MM

YY by mcrwPrcntFem divided by its complement. 

8 For the 2021 Trustees Report, the ten-year average is over the period 2010-2019, and we phase between the tenyear average and pp RR RR TT −2, excluding the 2020 data due to the Covid-19 pandemic. 9 For the 2021 Trustees Report, the five-year average is over the period 2015-2019, excluding the 2020 data due to 

the Covid-19 pandemic.

204
0−17,FF

YY = 0−17,MM

YY × mm mm mm

1 − mm mm mm

In order to distribute 0−17,FF

YY among the ages 0 to 17, we multiply 0−17,FFYY by 

the proportion of beneficiaries at each age in the last historical year10. 

Equation 3.3.6 – Minor Children of Deceased Workers (MCDWN ) 

 Minor Children of Deceased Workers 

 Exposure: SSA population by age (0-17) and sex of the account holder 

 Linkages: pMCDWDEA = probability that the parent is deceased

 pMCDWFIA = probability that the primary account holder (PAH) is fully 

 insured 

 pMCDWRES = probability that a child who is eligible to receive minor- 

 child benefits actually receives the benefits

We project the number of minor children of deceased workers, along with all linkage factors, 

by age of the minor (am = 0-17) and sex of the account holder (sa = 1 for male, sa = 2 for 

female). We calculate it as follows: 

= PPPPPP × pp ppDDDD × pp ppFFFFFF × pp ppRR RR (3.3.6) 

MCDWPOP represents the subset of the population from which we draw these beneficiaries, 

and we set it equal to the Social Security area population (SSAPOP).

PPPPPP = SSSSSS

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. 

pp ppDDDD = _

PPPPPP

pMCDWFIA represents the probability that the parent (PAH) is fully insured. We set this 

equal to the portion of the population aged 25+am to 35+am where the PAH is fully insured 

(FI_PAH).

pp ppFFFFFF = ∑ [ SSSSSS × FF _ ] 35+

25+

∑ SSSSSS 35+

25+

pMCDWRES represents the probability that a child who is eligible to receive minor-child 

benefits actually receives the benefits. This factor accounts for other eligibility requirements 

not previously mentioned. For example, the marital status of the child or the dependency 

status of the child. For all historical years, we calculate pp ppRR RR

yy as the ratio of MCDWN, 

10 For the 2021 Trustees Report, we use TRYR-2.

205
the actual number of minor children of deceased workers receiving benefits, to the number of 

persons meeting all previously mentioned requirements by age and sex of the parent. 

pp ppRR RR

yy = MM

MM PPPPPP×pp DDDDDD×pp FFFF

, year < TRYR

For each age and sex of parent, we use a least squares regression over the last ten years11 of 

historical data to determine a starting value in TRYR-1 for pp ppRR RR

yy from which we 

project future values. We apply an adjustment, SSMM , to the 10th year of the 

projection period in order to match the projections made by the Short-Range office. We 

linearly interpolate the values of pp ppRR RR

yy for intermediate years between the regressed 

values for pp ppRR RR

TT −1 and pp ppRR RR

TT +9 × SSMM . After the 10th year of the 

projection period, we linearly grade the adjustment factors to one over the 10 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. 

Equations 3.3.7-8 – Student Children of Retired and Deceased Workers (SCRWN and SCDWN) 

 Student Children of Retired Workers 

 Exposure: SSA population by age of the student (18-21) and sex of the account holder 

 Linkages: pSCRWDEA = probability that at least one parent is retired

 pSCRWAGA = probability that the primary account holder (PAH) is age 62 

 or older 

 pSCRWFIA = probability that the PAH is fully insured 

 pSCRWCPA = probability that the PAH is receiving benefits

 pSCRWSSB = probability that the child is indeed attending school 

 pSCRWRES = probability that a child who is eligible to receive student- 

 child benefits actually receives the benefits

 Student Children of Deceased Workers 

 Exposure: SSA population by age of the student (18-21) and sex of the account holder 

 Linkages: pSCDWDEA = probability that at least one parent is deceased

 pSCDWAGA = probability that the PAH is age 62 or older (set to 1) 

 pSCDWFIA = probability that the PAH is fully insured 

 pSCDWCPA = probability that the PAH is receiving benefits (set to 1)

 pSCDWSSB = probability that the child is indeed attending school 

 pSCDWRES = probability that a child who is eligible to receive student- 

 child benefits actually receives the benefits

We project the number of student children of retired and deceased workers, along with all 

linkage factors, by age of the student (as = 18, 19) and sex of the account holder (sa = 1 for 

male, sa = 2 for female). We calculate the projected number of student children of retired 

and deceased workers as follows:

11 For the 2021 Trustees Report, the ten-year regression is over the period 2010-2019, excluding the 2020 data due 

to the Covid-19 pandemic.

206
= PP × pp ppppDDDD × pp pppp × pp ppppFFFFFF

× pp pppp × pp pppp × pp ppppRR RR (3.3.7) 

= PPPPPP × pp ppDDDD × pp pp × pp ppFFFFFF

× pp pp × pp pp × pp ppRR RR (3.3.8) 

SCRWPOP and SCDWPOP represent the subset of the population from which these 

beneficiaries are drawn, and we set them equal to the Social Security area population 

(SSAPOP).

PP = PPPPPP = SSSSSS

pSCRWDEA and pSCDWDEA represent the status of the parent (PAH). For student children of 

retired workers, we set this equal to the proportion of the subset of the population where 

neither parents are deceased. For student children of deceased workers, we set this 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. 

pp ppppDDDD = 1 − _

PPPPPP

pp ppDDDD = _

PPPPPP

pSCRWAGA and pSCDWAGA represent the probability that the PAH is age 62 or older. For 

student children of retired workers, we set this equal to the proportion of the student 

population that has one parent age 62 or older, CHI_62+. For student children of deceased 

workers, we set the factor equal to one.

pp pppp = _62 +

PPPPPP

pp pp = 1

pSCRWFIA and pSCDWFIA represent the probability that the PAH is fully insured. For 

student children of retired workers, we set this 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, we calculate the factor similarly with the population being aged 25+as to 35+as. 

pp ppppFFFFFF = ∑ [ SSSSSS × FF _ ] 64+

62

∑ SSSSSS 64+

62

pp ppFFFFFF = ∑ [ SSSSSS × FF _ ] 35+

25+

∑ SSSSSS 35+

25+

pSCRWCPA and pSCDWCPA represent the probability that the PAH is receiving benefits. For 

student children of retired workers, we set this factor equal to the portion of the population 

207
aged 62 to 64+as where the PAH is receiving benefits (RETIRED). For student children of 

deceased workers, we set this factor equal to one. 

pp pppp = ∑ [ SSSSSS × FF _ × ] 64+

62

∑ [ SSSSSS × FF _ ] 64+

62

pp pp = 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 we calculate it as follows. 

pp pppp = pp pp =

⎩

⎪

⎨

⎪

⎧ 1

− 16 , yy ≤ 1981

0.5

− 16 , yy > 1981

pSCRWRES and pSCDWRES represent the probability that a child who is eligible to receive 

student-child benefits actually receives the benefits. This factor accounts for other eligibility 

requirements not previously mentioned. For example, the marital status of the child or the 

dependency status of the child. For all historical years, we calculate pp ppppRR RR

yy and 

pp ppRR RR

yy as the ratio of SCRWN and SCDWN, the actual number of student children 

receiving benefits, to the number of persons meeting all previously mentioned requirements 

by age and sex of the parent. 

pp ppppRR RR

yy = PPPPPP×pp DDDDDD×pp ×pp FFFF ×pp CC ×pp , year < TRYR

pp ppRR RR

yy = PPPPPP×pp DDDDDD×pp ×pp FFFF ×pp CC ×pp , year < TRYR

For each age and sex of parent, we use a least squares regression over the last ten years12 of 

historical data to determine a starting value in TRYR-1 for pp ppppRR RR

yy from which we 

project future values. We apply an adjustment, SS , to the 10th year of the 

projection period in order to match the projections made by the Short-Range office. We 

linearly interpolate the values of pp ppppRR RR

yy for intermediate years between the regressed 

values for pp ppppRR RR

TT −1 and pp ppppRR RR

TT +9 × SS . After the 10th year of the 

projection period, we linearly grade the adjustment factors to one over the 10 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. We calculate 

the values of pp ppRR RR

yy similarly.

Equations 3.3.9-10 – Disabled Adult Children of Retired and Deceased Workers (DCRWN and 

12 For the 2021 Trustees Report, the ten-year regression is over the period 2010-2019, excluding the 2020 data due 

to the Covid-19 pandemic.

208
DCDWN)

 Disabled Adult Children of Retired Workers 

 Exposure: SSA population by age of the adult child (18-95) 

 Linkages: pDCRWAGA = probability that the primary account holder (PAH) is age 62 

 or older 

 pDCRWDEA = probability that the parent is retired

 pDCRWFIA = probability that the PAH is fully insured 

 pDCRWCPA = probability that the PAH is receiving benefits

 pDCRWSSB = probability that the child is indeed disabled 

 pDCRWRES = probability that a child who is eligible to receive disabled- 

 child benefits actually receives benefits

 Disabled Adult Children of Deceased Workers

 Exposure: SSA population by age of the adult child (18-95) 

 Linkages: pDCDWAGA = probability that the PAH is age 62 or older (set to 1) 

 pDCDWDEA = probability that the parent is deceased

 pDCDWFIA = probability that the PAH is fully insured 

 pDCDWCPA = probability that the PAH is receiving benefits (set to 1)

 pDCDWSSB = probability that the child is indeed disabled 

 pDCDWRES = probability that a child who is eligible to receive disabled- 

 child benefits actually receives the benefits

We project the number of disabled adult children of retired and deceased workers, along with 

all linkage factors, 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+. We calculate the projected number of disabled adult children of retired and 

deceased workers as follows:

DCRWN = DCRWPOP × pDCRWAGA × pDCRWDEA × pDCRWFIA

× pp pppp × pp pppp × pp ppppRR RR (3.3.9) 

 

= PPPPPP × pp pp × pp ppDDDD × pp ppFFFFFF

× pp pp × pp pp × pp ppRR RR (3.3.10) 

 

We calculate all factors similarly 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). We calculate pp ppDDDD similarly for disabled children of deceased 

workers.

209
pp ppppDDDD =

⎩

⎪

⎨

⎪

⎧ SSSSSSmmmmmm

SSSSSSmmmmmm + SSSSSSwwwwww

, = 1 − 9

0.25 × SSSSSSmmmmmm

SSSSSSmmmmmm + SSSSSSwwwwww

, = 10

pp ppDDDD =

⎩

⎪

⎨

⎪

⎧ SSSSSSwwwwww

SSSSSSmmmmmm + SSSSSSwwwwww

, = 1 − 9

0.25 × SSSSSSwwwwww

SSSSSSmmmmmm + SSSSSSwwwwww

+ 0.75, = 10

pDCRWSSB and pDCDWSSB represent the probability that the adult child is indeed disabled. 

DCPREM is the preliminary calculation of this factor and we assume it to remain constant. 

For the projection period, for ad = 6-10, we set pp pppp and pp pp 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 

pp pppp = pp pp = �

mm [0.005, + 0.0001 × (yy − )], = 7 − 10 aa

 yy > + 1

, ee h

pDCRWRES and pDCDWRES represent the probability that a child who is eligible to receive 

disabled-child benefits actually receives the benefits. This factor accounts for other 

eligibility requirements not previously mentioned. For example, the marital status of the child 

or the dependency status of the child. For all historical years, we calculate pp ppppRR RR

yy and 

pp ppRR RR

yy as the ratio of DCRWN and DCDWN, the actual number of disabled children 

receiving benefits, to the number of persons meeting all previously mentioned requirements 

by age and sex of the parent. 

For year < TRYR:

pp RR RR

yy = PPPPPP × pp ppppDDDD × pp pppp × pp ppppFFFFFF × pp pppp × pp pppp

pp ppRR RR

yy = PPPPPP × pp ppDDDD × pp pp × pp ppFFFFFF × pp pp × pp pp

DCPREM =

210
For each age and sex of parent, we use a least squares regression over the last ten years13 of 

historical data to determine a starting value in TRYR-1 for pp ppppRR RR

yy from which we 

project future values. We apply an adjustment, SSDDDD , to the 10th year of the projection 

period in order to match the projections made by the Short-Range office. We linearly 

interpolate the values of pp ppppRR RR

yy for intermediate years between pp ppppRR RR

TT −1 and 

pp ppppRR RR

TT +9 × SSDDDD . After the 10th year of the projection period, we linearly 

grade the adjustment factors to one over the 10 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. We calculate the values of 

pp ppRR RR

yy similarly.

Equations 3.3.11-12 – Young Spouses of Retired and Deceased Workers (YSRWN and YSDWN) 

 Young Spouses of Retired Workers 

 Exposure: SSA population by age (15-69), sex of account holder, and marital status 

 (married)

 Linkages: pYSRWAGA = probability that the primary account holder (PAH) is of the 

 required age.

 pYSRWECB = probability that the young spouse has an entitled child in their 

 care

 pYSRWFSB = probability that the young spouse is not already receiving 

 benefits based on another child in their care 

 pYSRWRES = probability that a person who is eligible to receive young- 

 spouse benefits actually receives the benefits

 Young Spouses of Deceased Workers 

 Exposure: SSA population by age (15-69), sex of the account holder and marital status 

 (widowed and divorced) 

 Linkages: pYSDWDEA = probability that the PAH is deceased

 pYSDWECB = probability that the young spouse has an entitled child in their 

 care

 pYSDWFSB = probability that the young spouse is not already receiving 

 benefits based on another child in their care 

 pYSDWRMB = probability that the young spouse is not remarried 

 pYSDWRES = probability that a person who is eligible to receive young- 

 spouse benefits actually receives the benefits

We project the number of young spouses of retired and deceased-workers, along with all 

linkage factors, by age group (ab = 1-10) of the young spouse and sex of the account holder 

(sa = 1 for male, sa = 2 for female). We also project young spouses of deceased workers 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. We calculate the projected number of young spouses 

of retired and deceased-workers as follows: 

13 For the 2021 Trustees Report, the ten-year regression is over the period 2010-2019, excluding the 2020 data due 

to the Covid-19 pandemic.

211
YY = YY PPPPPP × pp pppp × pp pppp × pp ppppFF × pp ppppRR RR (3.3.11) 

YY = YY PPPPPP × pp ppDDDD × pp pp × pp ppFF

× pp ppRR × pp ppRR RR (3.3.12) 

YSRWPOP and YSDWPOP represent the subset of the population from which we draw these 

beneficiaries. We set YY PPPPPP equal to the married Social Security area population 

( SSSSSSmmmmmm) and we set YY PPPPPP equal to SSSSSSmmmm for mb = 1, 2. 

YY PPPPPP = SSSSSSmmmmmm

YY PPPPPP = SSSSSSmmmm

pYSRWAGA represents the probability that the PAH is of the required age. We set pp pppp

equal to the portion of the married population who has an aged spouse (AGSP). 

pp pppp = AA AA

YY PPPPPP

pYSDWDEA represents the probability that the PAH is deceased. For mb = 1, we do not apply 

any factor. For mb = 2, we set this factor equal to the portion of young spouses that is 

widowed. 

pp ppDDDD = �

1, mmmm = 1 (wwwwwwwwwwww )

SSSSSSwwwwww

SSSSSSwwwwww + SSSSSSmmmmmm

, mmmm = 2 ( )

pYSRWECB and pYSDWECB represent the probability that the young spouse has an entitled 

child in their care. We set YY equal to the portion of persons meeting the previously 

mentioned requirements who have a minor or disabled adult child in their care. We set 

YY , by marital status, equal to the portion of persons meeting the previously 

mentioned requirements who have a minor or disabled adult child in their care. 

and 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. 

pp pppp = +

YY PPPP × pp pppp

pp ppmmmm =

( + ) × � YY PPPPPP

mmmm × pp ppDDDD

mmmm × pp ppmmmm

YY PPPPPP × pp ppDDDD × pp pp �

YY PPPPPP × pp ppDDDD

pYSRWFSB and pYSDWFSB represent the probability that the young spouse is not already 

receiving benefits based on another child in their care. We set this factor equal to one 

divided by the number of children in the average family (AAAA ) for the given age bracket 

212
of the spouse. For young spouses of retired workers, we do not apply a factor for sa = 2. 

pp ppppFF =

⎩

⎪

⎨

⎪

⎧ 1

AAAA , ssss = 1

1, ssss = 2

pp ppFF = 1

AAAA

pYSDWRMB represents the probability that the spouse is not remarried. We assume this 

factor remains constant at 0.600. 

pp ppRR = 0.600

pYSRWRES and pYSDWRES represent the probability that a person who is eligible to receive 

young-spouse benefits actually receives the benefits. This factor accounts for other 

eligibility requirements not previously mentioned. For example, that the young spouse is not 

entitled to a widow(er) benefit. For all historical years, we calculate pp ppppRR RR

yy 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. We calculate pp ppRR RR

yy similarly, using the number of young spouses of deceased 

workers.

pp ppppRR RR = YY

YY PPPPPP × pp pppp × pp pppp × pp ppppFF

, yy <

pp ppRR RR = YY

YY PPPPPP × pp ppDDDD × pp pp × pp ppFF × pp ppRR

, yy <

For each age, sex, and marital status, we hold pp ppppRR RR

yy constant based on the value for 

the last historical year. For female young spouses, we apply an adjustment, SSYY , to 

the 10th year of the projection period in order to match the projections made by the ShortRange office. We exponentially interpolate the values of pp ppppRR RR

yy for intermediate years

between pp ppppRR RR

TT −1 and pp ppppRR RR

TT +914. After the 10th year of the projection period, 

we linearly grade the adjustment factors to one over the 10 years beyond the end of the shortrange period, thus gradually eliminating the effect of the short-range adjustment factors, so 

that we ultimately return to the long-range projections. We calculate the values 

of pp ppRR RR

yy similarly.

Equation 3.3.13 – Number of Deaths of Insured Workers (LUMSUMab) 

14 For the 2021 Trustees Report, we hold pp ppppRR RR

yy constant based on the value for TRYR-2 and interpolate 

between pp ppppRR RR TT −2 and pp ppppRR RR TT +9, excluding the 2020 data due to the Covid-19 pandemic.

213
We project the number of deaths of insured workers by sex and 5-year age group (ab = 1-14). 

Age groups include 20-24, 25-29,...,80-84, 85+. We calculate EE EE , the estimated 

number of lump-sum payments paid during the year for age group ab, as the number of total 

deaths during the year times the probability that the deceased was fully insured and has a 

surviving spouse or child. We calculate BASE 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. We then calculate for each year in the projection 

period. 

= EE EE × (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 non-covered 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 ..., 60-64) 

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: 

ASRWPOP : population of potential aged spouse of retired worker beneficiaries 

DEA pASRW : probability that the primary account holder (PAH) is not deceased

pASRWAGA : probability that the PAH is of the required age 

FIA pASRW : probability that the PAH is fully insured 

pASRWCPA : probability that the PAH is receiving benefits

214
MBB pASRW : probability that the beneficiary is not receiving a young-spouse benefit 

FIB pASRW : probability that the aged spouse is not fully insured 

pASRWGPB : probability that the aged-spouse's benefits are not withheld because of 

 receipt of a significant government pension based on earnings in 

 non-covered employment

pASRWFS2: probability that a couple will engage in a filing strategy in which the PAH 

 files for and may or may not suspend their benefit and the fully insured for 

 their aged spouse benefit. 

pASRWRES : probability that a person who is eligible to receive aged-spouse benefits 

 actually receives 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 

BBA: Bipartisan Budget Act of 2015. A provision of this act closes unintended loopholes by 

eliminating (1) the ability to receive only a retired-worker benefit or an aged-spouse benefit 

when eligible for both, for those attaining age 62 in 2016 and later, and (2) the ability of a family 

member other than a divorced spouse to receive a benefit based on the earnings of a worker with 

a voluntarily suspended benefit, for voluntary suspensions requested after April 29, 2016. 

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. 

DCDWPOP : population of potential disabled children 

pDCDWAGA : 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 

pDCDWCPA : probability that the PAH is receiving benefits

pDCDWSSB : probability that the child is indeed disabled 

pDCDWRES : probability that a child who is eligible to receive disabled-child benefits 

 actually receives 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 that 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: 

215
DSDWPOP : 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

pDSDWSSB : probability that the spouse is indeed disabled 

DEB pDSDW : probability that the disabled spouse is not receiving another type of benefit 

pDSDWRES : probability that a person who is eligible to receive disabled-spouse 

 benefits actually receives the benefits

DSDWN: final number of disabled spouse of deceased workers (product of all linkage factors) 

EMPRATE: employment rates for age 62, by sex 

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

ESTRES: preliminary estimate of the RES factor for the 10th 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 

FI_PAH: portion of married population where one spouse is fully insured 

FILEG: fraction of the LPR SSA population that is fully insured 

FIN: insured status of the beneficiary 

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 

INS: portion of the SSA population that is fully insured 

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: 

MCDWPOP : 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 

pMCDWRES : probability that a child who is eligible to receive minor-child benefits 

 actually receives 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 

216
REGPR: regressed prevalence rate for retired workers

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: 

RWPOP : 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 

pRWWBB : probability that the PAH is not receiving a widow(er) benefit 

pRWRES : 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: 

SCDWPOP : population of potential student children 

DEA pSCDW : probability that the parent is either retired or deceased

pSCDWAGA : probability that the PAH is age 62 or older 

FIA pSCDW : probability that the PAH is fully insured 

pSCDWCPA : probability that the PAH is receiving benefits

pSCDWSSB : probability that the child is indeed attending school 

pSCDWRES : probability that a child who is eligible to receive student-child benefits 

 actually receives 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: 

YSDWPOP : population of potential young spouse of deceased workers 

DEA pYSDW : probability that the primary account holder (PAH) is of the required age

pYSDWECB : probability that the young spouse has an entitled child in their care 

pYSDWFSB : probability that the young spouse is not already receiving benefits based 

 on another child in their care

pYSDWRMB: probability that the young spouse is not remarried 

217
pYSDWRES : probability that a person who is eligible to receive young-spouse benefits 

 actually receives 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: 

YSRWPOP : population of potential young spouse of retired workers

pYSRWAGA : probability that the primary account holder (PAH) is of the required age 

pYSRWECB : probability that the young spouse has an entitled child in their care 

FSB pYSRW : probability that the young spouse is not already receiving benefits based 

 on another child in their care 

pYSRWRES : probability that a person who is eligible to receive young-spouse benefits 

 actually receives the benefits

YSRWN: final number of young spouse of retired workers (product of all linkage factors) 

218
Process 4: 

Trust Fund 

Operations & 

Actuarial Status 

219
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. 

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4.1. TAXATION OF BENEFITS

4.1.a. Overview

The Social Security Amendments of 1983 (P.L. 98-21) amended the Internal Revenue 

Code to establish taxation of Social Security benefits. The 1983 law specifies including 

up to 50 percent of the Social Security benefits in a tax return filer’s adjusted gross 

income (AGI) for tax liability if a tax return filer’s “income”, defined as the sum of 

modified adjusted gross income1 and one-half of Social Security and Tier 1 Railroad 

Retirement benefits, is above the specified income threshold amount of $25,000 as a 

single filer (or $32,000 as a joint filer). Subsequently, the 1993 OBRA (Omnibus Budget 

Reconciliation Act—P.L. 103-66) further amended the Internal Revenue Code to provide 

for taxation of up to 85 percent of Social Security benefits if a tax return filer’s “income” 

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 

law, are credited to the OASI and DI Trust Funds, while additional taxes on the OASDI 

benefits, as a result of the 1993 law, are credited to the HI Trust Fund. 

Income to the Trust Funds from such taxation is estimated by using ratios of taxes on 

benefits to benefits for the OASI and DI programs separately. These ratios, called 

“RTBs”, are applied to projected OASI and DI benefit amounts to estimate tax revenues 

to the OASI and DI Trust Funds. 

Initially we rely on the Department of the Treasury Office of Tax Analysis’s (OTA)

estimates of the percent of benefits taxable for OASI and DI benefits separately and the 

average marginal tax rates applicable to those taxable OASI and DI benefits. These 

estimates are based on Internal Revenue Service (IRS) tax returns data.

For the short range period (first 10 years of the projection), the Cost sub-process (4.3) 

uses OTA’s projected estimates for (1) the percent of benefits taxable and (2) the average 

marginal tax rates applicable to those taxable OASI and DI benefits. The multiplication 

of (1) and (2) produces projected RTBs under the 1983 law (up to 50 percent of benefits 

taxable) and the 1993 OBRA (additional up to 35 percent of benefits taxable). 

For the long range period (11th through 75th year of the projection period), we compute 

the RTB ratios for OASI benefits and those for DI benefits under the 1983 law and the 

combined 1983 and 1993 laws 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

1 Modified adjusted gross income equals adjusted gross income (before Social Security and Railroad 

Retirement benefits are considered) plus nontaxable interest income.

221
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. 

After initial estimates of projected ratios of taxes on benefits to benefits by Trust Fund, 

based on the OTA’s data, we include nonresident alien withholding tax revenue 

projections by our Short Range office since the OTA does not include nonresident 

withholding tax revenues. We add estimated nonresident tax revenues, as a ratio of taxes 

on benefits to benefits by Trust Fund, to the above projected ratios of taxes on benefits to 

benefits based on OTA data, to arrive at the final RTB ratios.

Finally, the Cost sub-process (4.3) applies the projected RTB ratios to our own estimates 

of the projected OASI and DI benefit payments to produce taxation of benefit revenues to 

the OASI and DI Trust Funds. 

4.1.b. Input Data

OCACT Data

Economics—process 2

1a. Projected SSA wage index series by year, updated yearly 

1b. Projected COLAs and average wage index levels under the intermediate 

assumptions of the prior Trustees Report 

Beneficiaries—process 3 

2a. Projected OASI beneficiaries by age and sex under the intermediate 

assumptions of the prior Trustees Report 

2b. Projected DI beneficiaries by age and sex under the intermediate 

assumptions of the prior Trustees Report 

Trust Fund Operations—process 4 

3. Aggregate OASI and DI benefit ratios (as a ratio of total OASDI benefits)

under the intermediate assumptions of the prior Trustees Report

OCACT Short-Range Office Data

4a. Nonresident alien withholding taxes for the OASI and DI benefits for the 

short range period

222
4b. Total OASI and DI benefits respectively for the short range period

Other input Data 

5. OTA’s projected percent of benefits taxable and average marginal tax 

rates by type of benefit (OASI and DI) for the short range period (updated 

yearly). 

6. OTA’s ultimate ratios of taxes on benefits to benefits (i.e., with income 

thresholds, assumed equal to 0). Such ultimate ratios are provided on a 

combined OASDI benefit basis, and are expected to be updated annually 

based on OTA’s update. 

7. Current Population Survey (CPS) data for year 2018 

8. Marginal income tax bracket amounts for tax years 2018 - 2020 

9. Marginal income tax rates for tax years 2018 - 2020 

10. General filing requirement amounts (standard deduction amounts) for 

personal income tax purposes for tax years 2018 - 2020 

11. Ratios of taxable income to adjusted gross income by income level (IRS 

data) for tax year 2018 

12. Treasury’s aggregate taxable benefit amount (IRS data) for tax year 2018 

13. OTA’s estimated taxes on benefits for the OASDI and HI Trust Funds for 

tax year 2018 

14. Aggregate OASDI benefit payment for calendar year 2018 

4.1.c. Development of Output

For the short range period, the Cost sub-process (4.3) uses OTA’s projected RTBs for 

OASI and DI benefits under the 1983 law, to project taxation of benefit revenues to the 

OASI and DI Trust Funds. 

For the long 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 law (up to 50 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 

223
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 0.99 and 0.99 to project smooth transitional RTB ratios for OASI and 

DI benefits, respectively.

The ultimate RTB ratios used in the projection are based on OTA’s ultimate ratios, 

reduced by about 2.6 percent. This reduction reflects estimates of the effect of the higher 

proportion of “old elderly” beneficiaries at about the 75th projection year OASDI 

beneficiary population distribution relative to the 2030 OASDI beneficiary population 

distribution, due to improved mortality.

For the 2021 Trustees Report, the ultimate RTB ratios for up to 50 percent of OASI and 

DI benefits taxable were set at 0.0604 and 0.0201, as compared to 0.0630 and 0.0210 for 

the 2020 Trustees Report. These decreases in the ultimate RTB ratios reflect OTA’s 

updated zero threshold estimates. 

Lastly, the Cost sub-process (4.3) applies these projected RTB ratios to projected OASI 

and DI benefit payments to develop estimated taxation of benefit revenues to the OASI 

and DI Trust Funds. 

224
4.2. AWARDS

Each year over 3 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 (PIA). The PIA is computed using the average indexed monthly earnings (AIME) and 

the PIA benefit formula as specified in the 1977 amendments. The AIME depends on the 

worker’s number of computation years, Y, and the earnings in each year. For retired-worker 

beneficiaries who have attained or will attain age 62 in 1991 or later, Y = 35. 

The AWARDS subprocess (AWARDS) selects records from a 10 percent sample of newly 

entitled worker beneficiaries obtained from the Master Beneficiary Record (MBR).1

 The 

selected sample, referred to as “sample”, contains 293,416 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 entitled worker beneficiaries, 

AWARDS modifies the earnings records in the sample to reflect the expected work histories 

and earnings levels of future beneficiaries (equation 4.2.1). After the modifications, 

AWARDS computes an AIME for each record in the future sample of beneficiaries (equation 

4.2.2). AWARDS subdivides the AIME value of each record into bend point subintervals2

(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 )(Earnings Indexed 

∗

∑

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, 

Y is the number of computation years, and 

AIMEn (r) is the AIME amount contained within the nth interval for record r. 

1 A record is selected if the year of initial entitlement equals 2017 as of the December 2019 MBR extract file date, 

and the beneficiary is not in death status as of the December 2017 MBR extract file date. Retired beneficiaries 

over age 70 and disability beneficiaries under age 20 are excluded. 2 The current law PIA formula has two bend points. For the purposes of PAP, the Awards subprocess instead uses 

30 subintervals.

225
4.2.b. Input Data

Long-Range OCACT Projection Data

Demography– 

1. Total Social Security area population (as of July) by sex and age.

o From 1941 to 2100 (1951 to 2100 used in SOSI)

o Updated annually

2. Other-than-lawful permanent resident (“other-than-LPR”) population (as of July) by

sex and age

o From 1964 to 2100 (1964 to 2100 used in SOSI)

o Updated annually

3. Deferred Action for Childhood Arrivals (DACA) population (as of July) by sex and

age.

o From 2012 to 2100 (2012 to 2100 used in SOSI)

o Updated annually

Economics – 

4. 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 1937 to 2100 (1951 to 2100 used in SOSI)

o Updated annually

5. Covered workers not in the other-than-LPR population by sex and age —with

earnings posted to the Master Earnings File (MEF) only

o From 1937 to 2100 (1951 to 2100 used in SOSI)

o Updated annually

6. Average Wage Index (AWI), projected values.

o From 2020 to 2100

o Updated annually

7. Total taxable earnings and number of workers with taxable earnings by age, sex,

and year from the Continuous Work History Sample (CWHS).

o From 1951 to 2018

o Updated annually

8. Historical 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 1937 to 2019 (only 2014- 2019 data used in SOSI)

o Updated annually

9. Projected 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 2020 to 2100

o Updated annually

10. Projected Covered Worker Rate based on total covered workers/total population

(not used in SOSI)

o From 2020 to 2100

226
o Updated annually

11. COLA (Cost of Living Adjustment) – not used in SOSI

o From 2020 to 2100

o Updated annually

12. Projected Wage Base (current law)

o From 2022 to 2100

o Updated annually

Fully Insured – 

13. Historical and projected fully insured rates by sex and single year of age 14-95

o From 1969 to 2100

o Updated annually

Beneficiaries – 

14. Distribution of number of in-current-pay retired beneficiaries by age at retirement

from age 62 to 70 by year, sex and age

o From 2020 to 2100

o Updated annually

Other input data

15. 10% Awards Sample from the MBR and Master Earnings File

o Newly entitled OASI / DI beneficiaries, whose initial entitlement year was

2017 as of the December 2019 MBR extract file date, and the beneficiary is

not in death status as of the December 2017 MBR extract file date.

 SSN

 Type of benefit

 Type of claim (retirement or disability)

 Sex

 Date of birth

 Date of initial entitlement

 Date of disability onset

 PIA amount

 Type of dual entitlement

 Dual entitlement status code

 PIFC

 LAF

 Eligibility year

 Trust fund

 Earnings histories for each worker from 1951 to 2016

o Generally updated annually, pending validation of the sample

16. AWI, Average Wage Index, historical values

o From 1951 to 2019

o Data obtained from OCACT internet site.

o Updated annually

17. Wage base, historical values

o From 1951 to 2021

o Data obtained from OCACT internet site.

o Updated annually

227
18. COLA, cost of living adjustment (historical values) – not used in SOSI

o From 1975 to 2020

o Data obtained from OCACT internet site.

o Updated annually

19. Amount of earnings needed to earn one quarter of coverage

o From 1951 to 2021

o 1978-2021 data obtained from OCACT internet site. 1951-1977 values

estimated by applying projection methodology backwards from 1978.

o Updated annually

20. Windfall Elimination Provision (WEP) factors, the percent of sample cases affected

by the WEP which will no longer be affected by the WEP, by sex and projection

year

o From 2020 to 2100

o Data obtained from OCACT internal calculations

o Updated annually

21. PIA bend points – not used in SOSI (except for 1979 bend points)

o From 1979 to 2021

o Data obtained from OCACT internet site.

o Updated annually

22. Hypothetical Wage Base (to reflect relative changes in relative taxable maximum

levels over time)

o From 1951 to 2021

o Updated annually

o

23. HI scaled factors, scaled factors computed using HI earnings instead of taxable

earnings

o From age 16 to 100.

o Data obtained from OCACT internal calculations.

o Updated periodically.

24. Bucket earnings file

o Detail earnings for years 1978 and later for each worker in Awards Sample

with at least one year of earnings at the taxable maximum during those years.

• SSN

• Tax year

• Total Compensation (W-2 box #1)

• Social Security taxable wages and tips (W-2 boxes #3 and #7)

• Medicare taxable wages and tips (W-2 box #5)

• Social Security taxable self-employment income

• Medicare taxable self-employment income

• Deferred Compensation Distributions (W-2 box 11)

• Deferred Compensation Contributions (W-2 box 12)

o Updated when changing the initial entitlement sample.

25. Taxable ratio goals for OASI and DI

o Data obtained from OCACT internal calculations

o Updated annually.

228
26. CWHS Median earnings / ratios of average earnings to average taxable earnings

(MEF only) below and above median

o Data obtained from OCACT internal calculations

o Updated as needed.

27. Distribution of number of in-current-pay retired beneficiaries from 1992 to 2100 –

only use the data from sample year 2017

o Data obtained from Beneficiaries area

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 entitled in future years. Three distinct modifications are 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 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 obtains or imputes his/her covered earnings. See

below section “Change in Wage Bases” and appendix 4.2-1 for more information.

• 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 “legal” covered workers (from Economics subprocess) to the

Social Security area “legal” population (from Demography subprocess). See the below

detailed section “Changes in Covered Worker Rates” for more information.

• Earnings Experience in the CWHS3.

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 

3 This file is a 1% sample of individuals who had covered earnings at some point in their work histories.

229
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, AWARDS uses an 

additional data source to obtain covered earnings for 1994 and later, and to impute as best as 

possible covered earnings for years before 1994. This is done in order to reflect higher 

maximum taxable amounts imposed on future newly entitled beneficiaries. Then, these 

projected covered earnings are capped at the wage base values that would be in effect for 

future samples of retired workers (using the “projected wage base” input file) to determine the 

taxable earnings to use in the benefit calculations. Please refer to appendix 4.2-1 for more 

details on this method. 

Change in Covered Worker Rates

The sample 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 men and women, 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 economywide 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 “legal” workers in the economy in this group that have some earnings in this period, 

to (2) the total midyear “legal” population in this group in this period.4 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, Demography, and Fully Insured 

subprocesses.

In projecting sample covered worker rates, examination is done for the change in adjusted

economy-wide covered worker rates, by age-sex 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). The adjusted economy-wide covered 

4 For this purpose, we define the “legal” population as the total SSA area population minus the other-than-lawful 

permanent resident (“other-than-LPR”) population (those in the U.S. illegally and those in the U.S. on a 

temporary basis, e.g., individuals with specific non-immigrant worker or student visas) plus the DACA population 

(DACA individuals are included in the other-than-LPR data but had been effectively made legal, for Social 

Security purposes, by policy directive or executive action). 

230
worker rates in the base year take into account 100% (for men) and 40% (for women) of the 

change in projected age-62 fully insured rates relative to the base year. These two percentages 

are based on analyses of different cohorts of historical data. For each projection year, the 

method estimates what the base year economy wide covered worker rates would have been if 

100% (for men) and 40% (for women) of the increase in the covered worker rates were 

attributable to those individuals becoming newly fully insured (or losing insured status if the 

change in covered worker rates is negative). 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, are given below. The method used is the same for men and women in projecting 

sample covered worker rates. For additional explanation of this calculation, refer to example 

1.1 in appendix 4.2-2 of this subprocess. 

 

Projected sample covered worker rate equals (for increasing economy-wide rates): 

• The ratio of (1) the potential difference in the economy-wide male (or female) 

covered worker rate in the projection year to (2) the potential difference in the 

adjusted economy-wide male (or female) covered worker rate in the sample year 

(i.e., 1 – adjusted economy-wide male (or female) covered worker rate), 

multiplied by 

• The corresponding potential difference in the sample’s male (or female) covered 

worker rates (i.e,. 1 – sample male (or female) covered worker rate)). 

• The above result is subtracted from 1 to get the projected sample covered worker 

rate. 

This presentation above presumes that economy-wide covered rates increase over time, which 

is very common for women but not always true for men. The calculation of the change in 

covered worker rate differs if there is a reduction in relevant economy-wide covered worker 

rates. Example 1.2 shows the calculations done for men and women if economy-wide covered 

worker rates decline.

A similar procedure exists for projecting sample covered worker rates for disabled workers, 

except that the calculations are further broken down by entitlement age group. For disabled 

workers, years used to determine disability insured status do not have earnings added or 

removed (the last 10 years for disabled workers initially entitled after age 31). See Example 

1.3 for an illustration of the method. 

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.5

 For men, the procedure is to select records randomly 

with no other restrictions or criteria. However, for women, an additional selection criterion is 

included in order to achieve a specified 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 after the sample year, the distribution limit for women is equal to the 

5 Individuals in the sample affected by the Windfall Elimination Provision are less likely to have earnings 

removed or added by this process.

231
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 women’s years of earnings distribution for those with 11 to 25 years of 

earnings is adjusted to approach that of the men. 

If a record is selected to remove the earnings in a particular year, the full amount of earnings 

will be taken away. 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, AIE(r)

6

, 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 and earnings year. Then, the 

preliminary amount of earnings7 in year t that is added to the record is

Earnings(r, t) = SATE( tf ,sex, t, a) * AIE( )

AIE( )

w

r , 

where SATE(tf, sex, t, a) is the average taxable earnings in year t, for those in the 

sample with the same sex as that of the record for year of birth a by trust fund tf. 

For additional explanation of this calculation, refer to example 2 in appendix 4.2-2 of this 

subprocess. Note that all earnings levels get further adjusted by earnings experience in the 

CWHS for recent workers, as discussed in the below section. 

Once the earnings are added or taken away for some records, the earnings are further adjusted 

to reflect the dispersion in historical taxable earnings observed from 1970 to 2010 in the 

model’s earnings projections, using a 1% sample of workers likely to be eligible for retirement 

benefits. Over this period, increases in taxable earnings were generally higher for workers 

with taxable earnings over the median than for workers with taxable earnings under the 

median. A side model computes changes in average taxable earnings (ATE) levels above and 

below the median, as a ratio to the overall ATE level, for each earnings year, age, and sex 

combination from the 1% earnings sample. In the Awards program, the changes in these ratios 

(above and below median) in the projection year relative to the sample year were used to 

project taxable earnings from historical to projected years. The changes in these ratios (above 

and below median) are then applied to the earnings after coverage loads. See example 2.1 for 

an illustration. 

The overall targeted projected ATE level for each projection year, earnings year, sex, and age 

combination, as explained in the next section, is unaffected by this dispersion adjustment. 

6 AIE is the average indexed annual earnings, average over the highest Y years of earnings (similar to AIME, but 

an annual amount). Y is 35 for retired workers and is based on years of non-disability for disabled workers 

(resulting in a low of 2 and a high of 35).

7 In this subprocess, earnings histories of projected beneficiaries are all reflected as wage-indexed earnings 

histories in the 2017 sample.

232
Earnings Experience in the CWHS 

For historical years beginning with 1951, AWARDS 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 file8. To estimate ATE levels for the first projection year, 

AWARDS uses the average values of normalized average taxable earnings calculated from the 

last five historical years of the most recent CWHS file. These computed normalized values 

take into account changes in aggregate ATEs from the Economics subprocess between each of 

the five historical years and the first projection year; this allows the comparison of 

corresponding values from different years in a way that reduces time series effects. 

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 

aggregate annual average taxable earnings (ATE) from the Economics process9 attributable to 

ages 15-80. The first step is to determine preliminary CWHSATE'as (preliminary average 

taxable earnings by age and sex) by using the annual growth rate in the total economy-wide 

ATE and projected number of covered workers from the Economics process. 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 covered workers from the 

Economics process and CWHSATEas for the year, produces the same aggregate ATE level for 

that year as projected by the Economics process. A small constant adjustment is also made, 

based on historical data, to reflect the difference between aggregate ATE levels for ages 15-80 

(as used here) and aggregate ATE levels for all ages produced by the Economics subprocess. 

For additional explanation of this calculation, refer to example 3 in appendix 4.2-2 of this 

subprocess.

The historical and projected CWHSATEas are then used to change the earnings histories of the 

sample of newly entitled beneficiaries so that the earnings better represent newly entitled 

beneficiaries in future years. For a given sex, year of birth, trust fund, and earnings year, the 

expected annual average taxable earnings of a future sample is denoted as ATEf'. ATEf' equals 

the sample’s average taxable earnings for a specific earnings year, multiplied by the 

comparable changes in the CWHSATEas, that is, the wage-indexed changes in the CWHSATEas

between the year of earnings in the sample of new beneficiaries and the year of earnings in the 

projected sample. Refer to example 3.1 in appendix 4.2-2 for additional explanation. 

ATEf' is then compared to the average taxable earnings of the sample (after adjustments to the 

records’ earnings levels for changes in wage bases and covered worker rates), denoted as ATEf 

and computed by sex, trust fund, earnings year, and year of birth. The difference between 

these values is the amount by which the average annual earnings levels are adjusted. Let

8 These historical values are tabulated by the Economic subprocess.

9 Aggregate ATE values for all ages are based on earnings posted to the Master Earnings File (MEF), excluding 

earnings posted to the suspense file. Historical experience from the CWHS sample is used to estimate the ATE 

for the large age 15-80 subgroup, and is used throughout this part of the model. 

233
f ATEf δ(t) ATE ' −= , 

for a specific age (or year of birth in the sample) in the projection year t. Denote the total 

workers in the sample in year t as TotalWorkers(t). Then, (δ(t) * TotalWorkers(t)) is the total 

amount of earnings which the model distributes for a given sex and single age 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 4.2-2. 

When δ(t) is negative, earnings for the year are decreased. To achieve ATEf' for the given sex, 

age, trust fund, earnings year, and year of birth, AWARDS multiplies CoveredEarnings(r, t) by 

a ratio, 

α

δ

+= +

ATE )(

)( ratio 1)(

f t

t

t . 

The term, α, is a necessary additional adjustment because covered earnings near or above the 

wage base, may have either a partial effect or no effect on modifying ATEf to ATEf'. These α 

values vary by sex, trust fund, and whether earnings increase or decrease. For OASI, the 

adjustment, α, is further broken down by year of birth to better match the targeted ATE levels. 

Otherwise, the determination process for OASI and DI is the same. These α values are set to 

best target ATEf' while making adjustments throughout as many of the sample records as 

possible. 

As AWARDS applies a ratio(t) to CoveredEarnings(r, t) by each record, it makes sure that the 

total earnings adjustment in a given earnings year and single age 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. 

Shuttling Method 

The change in distribution of the retired worker beneficiaries in projection years, as compared 

to the sample year, is another element in projecting earnings. To account for the general 

projected shifting of retirement by workers to later ages relative to the initial entitlement 

sample, the “forward shuttling” method facilitates the shift and estimates the additional 

earnings for the corresponding years before later retirement. Records are randomly chosen for 

additional earnings in the later retirement years. The amount of earnings for these shuttled 

records with delayed retirement are assumed to be the projected sample average taxable 

earnings. The number of shuttled records with additional earnings depends on the projected 

sample covered worker rates by sex and age. In the case of “backwards shuttling”, which is 

also possible in projected years, workers could retire at younger ages than in the Awards initial 

entitlement sample. When this happens, the worker will have fewer years of earnings. The 

earnings are removed in the appropriate age(s) for backwards shuttling. Since backwards 

shuttling rarely occurs, this condition does not have a major effect. 

234
Due to slightly different methodologies, the age distribution of newly entitled retired workers 

in the awards sample is slightly different than the corresponding age distribution from the 

OASI beneficiaries program for the sample year (2017). Therefore, an adjustment was made to

align the OASI beneficiaries area distribution of newly retired workers by age to the 

distribution from the Awards area. This alignment process, applicable to beneficiary age 

distributions in projection years, occurs for the sample year used by the Awards area and 

effectively eliminates the differences in the two sample year distributions in projecting average 

retired worker benefit levels by age. This alignment restores the procedure in place before the 

2010 Trustees Report.

For each age in a given projection year, the result of the shuttling method (forward or 

backward) is a weighted average of the PAPs that correspond to retirement at that age. As 

mentioned in the preceding paragraph, when the sample retirement age is earlier than the age in 

question (that is, individuals who delay retirement in the projection year), this calculation

includes potential additional earnings in the AIME calculation for the additional years before 

retirement. Refer to example 7 in appendix 4.2-3 for additional explanation and illustration. 

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 is set to be 2 years before the sample year. Thus, 











≥

∗ < =

i

i

t

i

tr

 t),,Earnings(r if t

 , if t

AverageWag )( e

AverageWag )( e ),Earnings( IndexedEarnings(r,t)

Step 2: Determine Computation Years 

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 1951 or the year the

disabled worker turned age 22.

Elapsed Years min Year of disability onset, Year attained age 62 max 1951,Year att = { } { − ained age 22 }

•Divide the elapsed years by five and truncate. Subtract this number (cannot exceed five)

235
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, 

12Y

Highest (r) Earnings Indexed Y 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 

$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) n r bp)(bp n ∗=

Next the record’s AIME amount, AIME (r), is compared to the indexed intervals. If

ElapsedYears Y Elapsed Y ears min int ,5 5    = −        

236
∑

−

=

1

1

)(bp 

k

n

n r < AIME (r) ≤ ∑=

k

1n

r)(bpn , 

then AIME (r) falls within the kth interval. And for n = 1 to 30, 

r)(bpn , 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 for 

all projection years by sex, age (20-65 for disabled workers, and 62-70 for retired workers), 

and trust fund. The ratio of these values gives the average potential AIME percentages (PAPS): 

PAPn = 

)(bp

AIME )(

r

n

r

n

r

r

∑

∑ . 

For an example of this calculation, refer to example 6 in appendix 4.2-2 of this subprocess. 

237
Appendix 4.2-1 

This appendix provides additional details on how the AWARDS process imputes covered 

earnings above the historical wage base. The taxable earnings in the Awards sample are less 

than or equal to the historical wage base. 

The Hospital Insurance (HI) wage base was phased out from 1991 to 1993 and eliminated in 

1994. For years 1994 and later, HI earnings are a good proxy for Social Security covered 

earnings. For years 1991 to 1993, HI earnings are a good proxy for Social Security covered 

earnings if they are under the HI wage base. Otherwise they give a lower bound for Social 

Security covered earnings. Total compensation (TC) earnings, available starting in 1978, are 

earnings subject to federal income tax. TC can differ from Social Security covered earnings 

but, where other data is lacking, gives a reasonable estimate of Social Security covered 

earnings. The program uses Hospital Insurance (HI) covered earnings for years 1991 and later 

and Total Compensation (TC) earnings for years 1978 and later to estimate covered earnings 

for those years. For years in which no good HI or TC estimate is available, including all years 

before 1978, the program estimates covered earnings based on available data from later years 

or from the application of HI “scaled” earning factors by age. The program then adjusts 

covered earnings estimates for years 1993 and earlier in order to align taxable ratios to taxable 

ratio “targets” based on CWHS, Economics, and sample data. 

To start with, the covered earnings methodology determines which workers in the Awards 

sample had taxable earnings at the wage base in years 1978 and later. For these individuals we 

obtained ORES “bucket” file records. These records contain individual HI earnings, total 

compensation (TC) earnings, and deferred compensation, and are only available for years 1978 

and later. Program module HI_EarningsMod.f90 in the AwardsPart1 program reads the bucket 

file and makes the earnings available to module CoveredEarningsMod.90. 

The program estimates covered earnings in three phases. In phase one, the program makes a 

best estimate of covered earnings in each year, for each record. In phase two, taxable ratio

“targets” (the ratio of taxable to covered earnings) are computed by trust fund, sex, and year. 

These targets, for years 1993 and earlier, are externally computed based on economics data, 

Continuous Work History Sample data, and sample covered earnings after 1993. Finally, for 

phase 3, in an iterative process, the program adjusts covered earnings for years 1993 and 

earlier until the computed taxable ratios match the taxable ratio targets.

More details of each phase follow. 

Phase 1 

Phase 1 makes a best estimate of covered earnings in each year for each worker using sample 

taxable earnings, bucket earnings, and scaled factors based on HI earnings.10 For years with 

10 HI scaled factors are computed using the same methodology as regular scaled factors [see actuarial note 2021.3 

at http://www.ssa.gov/OACT/NOTES/ran3/an2021-3.pdf except that HI taxable earnings are used in the 

calculations instead of Social Security taxable earnings. We discovered that the method worked better when HI 

scaled factors for ages under 22 were set equal to the age 22 factor so the factors hold steady under age 22.

238
sample taxable earnings under the wage base, covered earnings are simply set equal to taxable 

earnings. If taxable earnings are equal to the wage base then the program estimates covered 

earnings using the following data sources, in order of perceived accuracy: 1) HI earnings over 

the wage base in the year, 2) TC over the wage base in the year, 3) HI or TC earnings over the 

wage base in a later year combined with adjustments for AWI and HI scaled factors, 4) 

estimated lower bounds for covered earnings in earlier years with adjustments for AWI and HI 

scaled factors. In some cases, the program will choose the results from data source 4) over 

other sources if that results in a higher covered earnings amount. Note that comparing TC to HI 

in years 1994 and later, we observed that HI tends to be slightly higher than TC. When using 

TC to estimate covered earnings prior to 1994, we apply an adjustment factor to the TC 

earnings to account for this. TC, as used in the program, includes deferred compensation 

contributions but not distributions. 

The program computes two estimates of covered earnings for each applicable record in the 

sample and takes the one judged to be the best estimate. The two estimates are 

“Covered_Earnings_1” and “Covered_Earnings_2.” 

Covered_Earnings_1 is an estimate of covered earnings based on earnings in the current and 

later years. The program computes some intermediate values that will be used to estimate 

covered earnings.

For each worker iii in the sample and for each earnings year (iyear) from 1978 through 

SAMPLE_YEAR-1 

HIearnings(iyear,iii), if iyear 1994 HIplusAdjEarnings(iyear,iii) max(HIearnings(iyear,iii),TC(iyear,iii)), if 1978 iyear 1993

 ≥ = 

 ≤ ≤

For each worker iii in the sample and for each earnings year (iyear) from SAMPLE_YEAR-1 

through 1951 (stepping backwards), a variable ratioYearToUse is created for each earnings 

year:

0, if ( , ) ( )

, if ( , ) ( )

( , ) 1, 

earnings iyear iii wagebase iyear

iyear HIplusadjearnings iyear iii wagebase iyear

ratioYearToUse iyear iii iyear

<

>

= + if ( 1) 1

earliest for which ( , ) ( )

1, if none of the above conditions are met

ratioYearToUse iyear iyear

iyear HIplusadjearnings iyear iii wagebase iyear









 += +

 > 

−

 

This will yield a value other than “-1” if an individual has HI or TC earnings over the wage 

base in any year 1978 or later. 

Then, for each worker iii in the sample with at least one year of earnings at the wage base, for

each earnings year (iyear) 1951 to SAMPLE_YEAR-1: 

239
0, if ( , )

( ,) ( ( ,)

ratioYearToUse iyear iii iyear

ratio iyear iii HIplusAdjEarnings ratioYearToUse iyear iii

≤

= ) , otherwise averageWage ratioYearToUse iyear iii HIscaledFactor iage ( ( , )* ( ))











where - iage iyear yearOfBirth iii = ( )

If there is a year, 1978 or later, with HI or TC earnings over the wage base, then 

Covered_Earnings_1 in that year will be set to the HIplusAdjEarnings value computed above. 

Otherwise, if the ratio is above zero, Covered_Earnings_1 will be set to the product of the ratio 

times the HIscaledFactor times the averageWage for the year, or to the wage base + $1 if 

higher. If neither of these methods applies, then the variable is set to the wage base + $1 and 

may be overwritten by Covered_Earnings_2 below. 

Covered_Earnings_2 is an estimate of covered earnings in the current year based on estimates 

for earlier years. To set values for Covered_Earnings_2(year,iii) the program starts by setting 

the 1951 estimate to the taxable earnings value and using AWI increases and changes to HI 

scaled factors to estimate covered earnings in following years. For each consecutive year, the 

estimate will be the higher of the HI scaled factor and cumulative AWI increase applied to the 

prior year Covered_Earnings_2, or the taxable earnings of the current year. 

The program then decides whether to use the value for Covered_Earnings_1 or 

Covered_Earnings_2 for the phase 1 estimate of covered earnings. Generally, 

Covered_Earnings_2 will be used if higher than Covered_Earnings_1, and if the 

Covered_Earnings_1 estimate is based on earnings at least 2 years different than the earnings 

year in question. In general, Covered_Earnings_2 ends up being used less often overall.

Phase 2 

The program uses the covered earnings from Phase 1 to compute taxable ratios by trust fund, 

year, and sex. Taxable ratio targets are developed for OASI and DI outside of the Awards 

program. These target values are produced by age and sex for years 1954-1993 for OASI and 

years 1971-1993 for DI for those aged 20-64 in those years. The program also takes weighted 

averages of these single age targets to obtain annual goals in aggregate by sex and trust fund. 

The program reads in the taxable ratio targets from input files. Below is a summary of the 

process used to generate these taxable ratio targets:

1) Obtain data from the CWHS for years 2004-2018 of taxable and covered earnings by 

age and sex for individuals fully insured as of the end of each year, and compute 

taxable ratios for each cell

2) In a side FORTRAN program, for each year 1953-1993, match to the aggregate taxable 

ratio from the Economics group, separately revising each of year 2004-2018 CWHS 

data for this purpose. From this exercise, the resulting output is 15 sets of individual 

taxable ratios modeled to fit the aggregate 1953-1993 taxable ratios. Average these 15 

years’ worth of data to establish individual age/sex taxable ratios for each year 1953-

1993. 

240
3) By age and sex for OASI, adjust the taxable ratios in step 2 by a) a constant factor to 

align from Economic group’s taxable ratio for each year 2004-2018 to that of the data 

in step 1, and b) a second constant factor by birth cohort to align from the 2004-2018 

CWHS data developed in step 1 to the taxable ratio for the 2017 initial entitlement 

sample; this is done for birth cohorts 1947-1955 for the 2017 sample.

4) By age and sex for DI, adjust DI taxable ratios from the levels in step 2 by the relative 

percentage closer to 1.000 of the taxable ratios between the CWHS data and that of the 

2017 sample at that age/sex. This attempts to reflect the relative difference of taxable 

ratios for the smaller subset of DI cases (usually higher, that is, less earnings over the 

taxable maximum)

5) Aggregate these taxable ratio targets by year, sex, and Trust Fund, using the number of 

individuals in the 2017 sample at the appropriate age as the weights to derive one 

taxable ratio by trust fund, year, and sex. 

Phase 3 

For this final phase, the program starts an iterative process to match the overall targeted taxable 

ratio for that year, sex, and Trust Fund. If, for a given combination, the computed taxable ratio 

is within epsilon (.001 for OASI, .002 for DI) of the taxable ratio target then the covered 

earnings for that combination are accepted and taxable ratios by single age result from the 

analysis. If the computed taxable ratio is not within epsilon of the target, then all records with 

corresponding covered earnings over the wage base are either increased or decreased to move 

the computed taxable ratio closer to the taxable ratio target, and the two ratios are compared 

again. This is repeated until the computed taxable ratio is within epsilon of the taxable ratio 

target. If, in rare instances, all covered earnings are less than or equal to the wage base then no 

more iterations are done and those covered earnings are accepted. 

241
Appendix 4.2-2 

This appendix provides examples to help understand the calculations described in the 

model documentation of the AWARDS subprocess. These examples do not 

necessarily reflect values actually used in the projections.

Example 1.1: (OASI-Women with increasing economy-wide covered 

worker rates)—same method applies for men

Task: In projecting the 2017 sample of newly entitled female beneficiaries to 

represent newly entitled female beneficiaries in 2035, an adjustment to the earnings 

histories for those women age 30-34 is needed to reflect higher covered worker rates 

expected for women in this age group. 

This example illustrates the calculation of the projected covered worker rate for women

who are age 30-34 in the projection period. We will be comparing the group of women

age 30-34 in the base period with its counterpart group of women age 30-34 in the 

projection period. 

Information given: 

• Newly entitled retired female beneficiaries represented in the 2017 

sample are age 30-34 in the base period, 1977-1989, and the counterpart 

group of women retiring in 2035 is age 30-34 in the projection period, 

1995-2007. 

• Based on the 2017 sample, the covered worker rate for women age 30-34 

in the base period = 71.05%. 

• Fully insured rate for women age 62 in 2016 (SampleYear -1) = 89.33% 

• Fully insured rate for women age 62 in 2035 = 91.55% 

• Fully insured adjustment factor for women = 40% 

• Unadjusted economy-wide covered worker rate in year 2016 for women

age 30-34 = 67.38% in the base period 1977-1989. 

• Economy-wide covered worker rate in year 2034 for women age 30-34 = 

79.32% in the projection period 1995-2007. 

Calculations: 

1. Adjusted economy wide covered worker rate for women in the base 

period = Unadjusted economy-wide covered worker rate for women in 

the base period * (1+ (Fully insured rate for women in 2035/Fully 

insured rate for women in 2016 - 1) * fully insured adjustment factor) 

=68.05% 

2. The potential difference in the economy-wide covered worker rate for 

women age 30-34 in the projection period is 100.0% - 79.32% or

20.68%. 

242
3. The potential difference in the adjusted economy-wide covered worker 

rate for women age 30-34 in the base period is 100.0% -68.05% or 

31.95%. 

4. The ratio from steps 2 and 3 is 64.73%. 

5. The potential difference in the sample covered worker rate for the 

women age 30-34 in the base period is 100.0% - 71.05% or 28.95%.

6. The ratio from step 4 is multiplied by the potential difference in the 

sample’s covered worker rate for women age 30-34 in the base period to 

yield 18.74% (64. 73% * 28.95%).

7. The amount in step 6 (18.74%) would be subtracted from 1 to yield the 

sample’s covered worker rate for women who are age 30-34 in the 

projection period (81.26%).

Example 1.2: (OASI-Men with decreasing economy-wide covered 

worker rates)—same method applies for women

Task: In projecting the 2017 sample of newly entitled male beneficiaries to represent 

newly entitled male beneficiaries in 2050, an adjustment to the earnings histories for 

those men age 40-44 is needed to reflect lower covered worker rates expected for men

in this age group. 

This example illustrates the calculation of the projected covered worker rate for men

who are age 40-44 in the projection period. We will be comparing the group of men age 

40-44 in the base period with its counterpart group of men age 40-44 in the projection 

period. 

Information given: 

• Newly entitled retired male beneficiaries represented in the 2017 sample 

are age 40-44 in the base period, 1987-1999, and the counterpart group of 

men retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

• Based on the 2017 sample, the covered worker rate for men age 40-44 in 

the base period = 86.92%. 

• Fully insured rate for men age 62 in 2016 (Sample Year - 1) = 95.63% 

• Fully insured rate for men age 62 in 2050 = 95.26% 

• Fully insured adjustment factor for men = 100 % 

• Unadjusted economy-wide covered worker rate in year 2016 for men age 

40-44 = 85.27% in the base period 1987-1999. 

• Economy-wide covered worker rate in year 2049 for men age 40-44 = 

84.81% in the projection period 2020-2032. 

Calculations: 

1. Adjusted economy wide covered worker rate in the base period = 

Unadjusted economy-wide covered worker rate in the base period * 

243
(1+ (Fully insured rate 2050/Fully insured rate 2016 - 1) * fully 

insured adjustment factor for men) =84.94% 

2. The economy-wide covered worker rate for men age 40-44 in the 

projection period is 84.81%. 

3. The ratio from steps 2 and 1 is .8481/.8494 or 99.85 %. 

4. The ratio from step 3 is multiplied by the sample’s covered worker 

rate for men age 40-44 in the base period to yield 86.79% (99.85 % 

*86.92% = 86.79%).

The amount in step 4 (86.79%) would be the sample covered worker rate for men who 

are age 40-44 in the projection period.

Example 1.3: (DI-Men with decreasing economy-wide covered worker 

rates) – same method applies for women

Task: In projecting the 2017 sample of newly entitled male DI beneficiaries age 60-64 

to represent newly entitled male beneficiaries in 2050, an adjustment to the earnings 

histories for those men age 40-44 is needed to reflect lower covered worker rates 

expected for men in this age group. 

This example illustrates the calculation of the projected covered worker rate for men

who are newly entitled at age 60-64 in 2050 and are age 40-44 in the projection period. 

We will be comparing the group of men age 40-44 in the base period with its 

counterpart group of men age 40-44 in the projection period. The formulas are similar 

to Example 1.2 in relating the age-group of earnings to a specific entitlement agegroup, but with no fully insured adjustment to economy-wide covered worker rates in 

the base year. 

Information given: 

• Newly entitled male DI beneficiaries who are age 60-64 represented in 

the 2017 sample are age 40-44 in the base period, 1993-2001, and the 

counterpart group of male DI beneficiaries who are age 60-64 in 2050 is 

age 40-44 in the projection period, 2026-2034. 

• Based on the 2017 sample, the covered worker rate for male DI

beneficiaries age 40-44 in the base period = 92.09%. 

• The economy-wide covered worker rate in year 2016 for men age 40-44 

in the base period 1993-2001 is 87.11%.

• The economy-wide covered worker rate in year 2049 for men age 40-44 

in the projection period 2026-2034 is 85.5%.

Calculations: 

244
1. The economy wide covered worker rate for men age 40-44 in the base

period is 87.11%

2. The economy wide covered worker rate for men age 40-44 in the

projection period is 85.5%.

3. The sample covered worker rate for male DI beneficiaries age 40-44 is

92.09%.

4. The ratio from steps 2 and 1 is 98.15 %.

5. The ratio from step 4 is multiplied by the sample’s covered worker rate

for men age 40-44 in the base period to yield 90.39% (98.15 % *

92.09%).

Example 2: 

Task: In projecting the 2017 sample of newly entitled male OASI beneficiaries to 

represent newly entitled male OASI beneficiaries in 2050, an adjustment to the 

earnings histories for those men age 30 is needed to reflect higher covered worker rates 

expected for men in this age group. To achieve this target, the desired numbers 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 age 66 represented in the 2017

sample are age 30 in the base period 1981.

• Based on the 2017 sample, a male record, r = 30, has been randomly

selected to replace his zero taxable earnings reported in the base year

1981 at age 30 with an amount based on his career earnings pattern. His

year of birth is 1951.

• The Average Indexed Earnings for this record, AIE (30), is computed to

be $20,417. Note: This value is calculated by (1) using the record’s

annual taxable earnings reported each year through 2016, (2) converting

them to 2016 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 1951 is $67,770. This value is calculated as above given

the hypothetical worker earned the average taxable earnings in each of

the base years for men retiring at age 66 in the 2017 sample.

• The sample Average Taxable Earnings of men at age 30 in 1981 is

S

ATE(OASI, male, 1981, 1951) = $17,388.

Calculations: 

1. The ratio of the Average Indexed Earnings for record number 30,

AIE(30) to the Average Indexed Earnings of a hypothetical male worker

245
born in 1951 and retiring at age 66, AIE(w) is $20,417/$67,770 or 

0.3017. 

2. The amount in step 1 (0.3017) would be multiplied by S

ATE(OASI,

male, 1981, 1951), which is given as $17,388. This yields the amount of

earnings assigned to record number. Thus, Earnings(30, 1981) = .3017 *

$17,388 which equals $5,246.

Note that, at this stage of the process, the average taxable earnings are modified to 

reflect the higher covered worker rates expected in the economy-wide labor force, but 

have not accounted for the dispersion effect. The next example 2.1 will illustrate the 

dispersion effect. 

Example 2.1: 

Task: In the example 2, an adjustment was made to the earnings to reflect higher 

covered worker rates for men in that age group. A further step is to reflect the 

dispersion effect by giving the different weights to the earnings below or above the 

median earnings in the same age group. 

This example illustrates the calculation of earnings to be further modified for dispersion 

effect after the earnings were assigned to a newly entitled retired male record with zero 

taxable earnings in the base year. 

Information given:

• Newly entitled retired male beneficiaries age 66 represented in the 2017

sample are age 30 in the base period 1981. His year of birth is 1951.

• Worker retires at age 66 in 2050 (year of birth 1984). Age 30, earnings

would occur in 2014

• Earnings for record #30 for 1981 = $5,246.

• Median earnings for men age 30 in 1981 = $15,293.

• Dispersion factor for earnings below median (DFB,male,1981,1951) =

0.6587. This reflects dispersion from 1981 to 2010 (the last year of

measured dispersion) since the projected worker born in 1984 would be

age 30 in 2014, later than 2010.

• Dispersion factor for earnings above median (DFA,male,1981,1951) =

0.8473. Again this reflects dispersion from 1981 to 2010.

Calculations: 

1. The earnings for this record number #30 after being assigned earnings

(from example 2) is $5,246.

2. Compare the earnings ($5,246) of this record with median earnings

($15,293) from the same age group in the base earnings year 1981. The

dispersion factor for earnings below median (DFB) is chosen.

246
3. The amount in step 1 ($5,246) would be multiplied by dispersion factor

(DFB,male,1981,1951), which is given as 0.6587. This yields the

amount of earnings adjusted to record number 44897. Thus,

Earnings(30, 1981) = .6587 * $5,246 which equals $3,455.

Note that, at this stage of the process, the average taxable earnings have been computed using 

projected earnings after dispersion and after adjustment for changes in the wage base. 

Adjustments to earnings for the earnings experience in the CWHS have not yet been applied. 

See the earlier section “Earnings Experience in the CWHS” and example 4 below for a 

description of this adjustment process. 

Example 3: 

Task: The AWARDS subprocess estimates projected values of Average Taxable 

Earnings by age and sex using the values11 in the 2018 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 2022 for 42 year old women, CWHSATE42,female(2022). We will be using 

the number of female covered workers age 42 and the total taxable earnings for women

age 42 as given the in 2018 CWHS data.

Information given: 

• The average taxable earnings calculated from last 5 historical years in the

CWHS for women age 42 are:

ATE_cwhs(2014) = 38,682.48

ATE_cwhs(2015) = 40,693.53

ATE_cwhs(2016) = 41,259.98

ATE_cwhs(2017) = 43,158.24

ATE_cwhs(2018) = 44,478.19

• The economy-wide average taxable earnings for women age 42 (after

adjustment for bias factor = 1.0018 for TR2021) are:

ATE_econ(2014) = 37,119.14

ATE_econ(2015) = 38,205.67

ATE_econ(2016) = 38,751.94

ATE_econ(2017) = 40,234.46

ATE_econ(2018) = 41,502.87

11 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 2018 CWHS, 

adjustment factors were applied to data in years 2014 through 2018.

247
ATE_econ(2019) = 43,136.68 

ATE_econ(2020) = 43,963.34 

ATE_econ(2021) = 46,261.22 

ATE_econ(2022) = 47,958.43 

Note: The above ATE values reflect an adjustment from the aggregate 

values supplied by the Economics group for all ages, to make them 

consistent with the historical CWHS ATE values for ages 15-80. 

Calculations: 

1. The normalized ATE for women age 42 in 2022, using 2014-2018

CWHS data brought forward to 2022 ATE levels. The calculation is

shown in 2 steps:

Step a

ATE_cwhs(2014)*ATE_econ(2022)/ATE_econ(2014) +

ATE_cwhs(2015)*ATE_econ(2022)/ATE_econ(2015) + ... +

ATE_cwhs(2018)*ATE_econ(2022)/ATE_econ(2018) 

Step b

Sum of Step a ($254,962), then take the average ($254,962 / 5 

=$50,992) 

2. Repeat the same steps in (1) to calculate the normalized ATE for each

age (15 to 80). Multiply the normalized ATE by number of econ-wide

covered workers by age and sex in year 2022. This gives us the taxable

earnings. Sum up the taxable earnings for all ages and sex (both male

and female). Then divide the total taxable earnings (age and sex

combined) by total number of economy-wide covered workers in 2022

(age and sex combined). The resulting ATE for 2022 using economywide covered workers and 2014-2018 CWHS data brought forward to

2022 ATE levels is $47,698.

3. The value from step 1 ($50,992) is multiplied by a final multiplicative

adjustment factor to match the aggregate ATE level produced by the

Economic subprocess. The adjustment is a ratio of economy-wide ATE

to CWHS projected aggregate average taxable earnings ($47,958 /

$47,698 from step 2 above) yielding for women age 42 in 2022 an ATE

value of $51,270.33.

Example 3.1: 

This example illustrates the calculation of the projected Average Taxable Earnings in 

2005 for 40-year old women who retire at age 65 in 2030. We will be using the 

248
historical and projected ATE and distribution of retired workers in the projection year 

to calculate the weighted CWHS ATE for that year.

 

Information given: 

• The historical ATE from CWHS sample for women age 40 in 1992, who 

retire at age 65 in sample year 2017, is listed as follows: 

ATE(female,1992,40) = 18,968 

• The projected ATE, using historical CWHS sample data as a guide and 

projected covered worker data from the Economics group for age 40 in 

2005, who retire at age 65 in sample year 2030, is listed as follows: 

ATE (female,2005,40) = 29,826 

• Average wage index in 1992 = $22,935.42 

• Average wage index in 2005 = $36,952.94 

• Sample average taxable earnings for age 40 in 1992 = $19,157 

Calculations: 

1. The ratio of AWI (1992) to AWI (2005) = .6207 ($22,935/$36,953) 

2. Calculate the projected ATE (CWHS sample) for women age 40 in 2005 

(in 1992 dollars). Multiply the projected ATE by the ratio in step (1) = 

$18,512 ($29,826*.6207) 

3. The adjusted sample ATE in 2005 (in 1992 dollar) = sample ATE in 

1992 * projected ATE (CWHS sample) in 2005 in 1992 dollars from 

step (2) / historical ATE (CWHS sample) in 1992 = 19,157 * 18,512 / 

18,968 = $18,696. 

Example 4: 

Task: In projecting the 2017 sample of newly entitled female beneficiaries to 

represent newly entitled female beneficiaries in 2030, the projected Average Taxable 

Earnings of women age 40 (year of birth 1952) in the sample (ATEf)12 for year t = 2005 

must be adjusted by an amount, δ(2005), to meet a targeted Average Taxable 

Earnings(ATEf'') for 2005. 

This example illustrates the calculation of δ(2005) for the female cohort retiring at age 

65 in the projection year 2030. The value δ(2005) is the dollar amount in which the 

average annual earnings levels are adjusted for women age 40 in the year 2005 and 

12 The average taxable earnings have been computed using projected earnings adjusted for changes in the wage 

base and for changes in covered worker rates.

249
retiring in 2030. We will be comparing this group of women age 40 in the projection 

2005 year with its counterpart of women age 40 in the base year 1992. 

 

Information given: 

• A cohort of newly entitled retired female beneficiaries retiring at ages 65 

represented in the 2017 sample is age 40 in the base year, 1992, and the 

counterpart group of women retiring in 2030 is age 40 in the year 2005. 

• Based on the 2017 sample, the average taxable earnings for women age 

40 in the base year 1992 is $18,696. 

• For a sample projected to be retiring in 2030, the average taxable 

earnings (ATEf) for women age 40 in the year 2005 is $18,94113, after 

applying adjustments to the records’ earning levels for changes in the 

wage base, covered worker rates, and dispersion effect. 

• The average taxable earnings (ATEf'') of future sample (2030) for women

age 40 in 2005 as shown in Example 3.1 is $18,696. 

Calculations: 

• The difference in ATEf'' ($18,696) and ATEf' ($18,941) yields the 

δ(2005) value -$245 ($18,696 - $18,941).

Example 5: 

Task: In projecting the 2017 sample of newly entitled female OAB beneficiaries to 

represent newly entitled female OAB beneficiaries in 2030, for year t = 2005, δ(2005) 

is negative indicating an adjustment to earnings histories is needed to reflect lower

average taxable earnings for women age 40 for the year 2005. 

This example illustrates the calculation of the ratio (2005) in projection year 2005 for 

the women retiring at age 65 in the projection year 2030. The value, ratio (2005), is the 

adjustment ratio that will be applied to women age 40 projected covered earnings in 

2005 in order to achieve the targeted Average Taxable Earnings of this cohort for 2005. 

Information given: 

• Earnings in the year 2005 for the newly entitled female beneficiaries 

retiring at age 65 in 2030 is the counterpart corresponding to earnings in 

the base year 1992 for the newly entitled female beneficiaries retiring at 

age 65 in the 2017 sample.

• The targeted average taxable earnings ATE2005' for the year 2005 is 

$18,696 (shown in Example 4). 

13 Amount is in 1992 dollars, ‘sample year dollars’.

250
• For newly entitled women retiring at age 65 in 2030, the average taxable

earnings (ATE2005) for the year 2005 is $18,94114 (shown in Example 4).

• δ(2005), the difference in the targeted average taxable earnings ATE2005'

and ATE2005, is calculated to be -$245 ($18,696 - $18,941).

• α is an subtractive constant to the ratio(2005). For women age 40 (1952

birth cohort in the 2017 sample) OABs, when δ(t) is negative, the

constant α (birth cohort 1952, age 40 in 1992) is .003.

Calculations: 

• The ratio(2005) multiplied to the covered earnings in 2005 for women

age 40 retiring in 2030 is 1 + δ(2005) /ATE2005 + α = ( 1 + (-

$245/$18,941) - 0.003), or .9841.

Example 6: 

Task: The AWARDS subprocess calculates the Average Indexed Monthly Earnings 

(AIME) of each beneficiary in the sample. The AIME values are then divided into 30 

intervals.

This example illustrates the division of a possible AIME value into intervals. 

Information given: 

• An OAB beneficiary retired at age 64 in 2017

• This OAB beneficiary is record #150000 in the sample (r = 150000)

• The AIME for this individual is $3,000

• The initial eligibility year is 2015, the year the individual turned age 62.

• The length of each interval (bpn) in 1979 dollars is given in Equation

4.2.3. The length of each interval in 2015 dollars is given by the

equation

bpn (r) = bpn * AWI (2013) / AWI (1977) 

where bpn is the length of interval n in 1979 dollars 

• The average wage index (AWI) for year 2013 is $44,888.16

• The AWI for year 1977 is $9,779.44

• When converting the intervals from 1979 dollars to 2015 dollars, there is

a 2-year lag in AWI values.

• AIMEn (150000) is the AIME value in interval n for Record #150000

14 Amount is in 1992 dollars, ‘sample year dollars’.

251
Calculations: 

• The AIME for this individual ($3,000) is compared to the indexed 

intervals. It falls within the 14th interval.

• The AIME15 is the residual of $3,000 subtracting the cumulative indexed

bend points up to 13th interval ($2,685.15). The AIME for this individual 

in 14th interval is $314.85 

• AIMEn (150000) for interval 1 through 13 equals bpn (150000) for the 

corresponding intervals, such that PAPn = AIMEn / bpn = 1 for these 

intervals

• AIME14(150000) = $348.71, such that PAP14 = $314.85 / $459.01 = 

0.6859 

• AIMEn (150000) for interval 15 through 30 equals 0, such that PAPn = 0 

for these intervals.

• The following table details these results. 

n 

bpn in 

1979 

dollars

bpn (r) in 

2015 

dollars

)(bp 

1

n r

n

k

∑=

in 2015 

dollars

AIMEn (r) 

in 2015 

dollars

PAPn 

in 2015 

dollars

1 $45 $206.55 $206.55 $206.55 1

2 45 206.55 413.10 206.55 1

3 45 206.55 619.65 206.55 1

4 45 206.55 826.20 206.55 1

5 45 206.55 1,032.75 206.55 1

6 45 206.55 1,239.30 206.55 1

7 45 206.55 1,445.85 206.55 1

8 45 206.55 1,652.40 206.55 1

9 45 206.55 1,858.95 206.55 1

10 45 206.55 2,065.50 206.55 1

11 45 206.55 2,272.05 206.55 1

12 45 206.55 2,478.60 206.55 1

13 45 206.55 2,685.15 206.55 1

14 100 459.01 3,144.16 314.85 0.6859

15 100 459.01 3,603.17 0 0

16 100 459.01 4,062.18 0 0

17 100 459.01 4,521.19 0 0

18 100 459.01 4,980.20 0 0

19 200 918.01 5,898.21 0 0

20 200 918.01 6,816.22 0 0

252
21 200 918.01 7,734.23 0 0

22 200 918.01 8,652.24 0 0

23 200 918.01 9,570.25 0 0

24 200 918.01 10,488.26 0 0

25 200 918.01 11,406.27 0 0

26 200 918.01 12,324.28 0 0

27 200 918.01 13,242.29 0 0

28 200 918.01 14,160.30 0 0

29 1000 4,590.05 18,750.50 0 0

30 1000 4,590.05 23,340.40 0 0

Appendix 4.2-3 Shuttling Method

The Awards program works with a sample of workers newly entitled in the sample year of 

2016. The sample contains the age-sex distribution of newly entitled worker beneficiaries in 

the sample year. The beneficiaries area (subprocess 3.3) projects that the age-sex distribution 

of newly entitled worker beneficiaries will vary throughout the long-range period. In past 

years, the “Cost” area (subprocess 4.3) adjusted the Awards output to align it with the age-sex 

distribution from subprocess 3.3. Starting with the 2017 Trustees Report, the alignment 

adjustment occurs in the Awards program. This alignment adjustment is referred to as the 

“shuttling method” as it “shuttles” some workers retiring at one age in the sample to different 

ages in the projection years. 

The shuttling method consists of determining an array for each projection year, which 

determines what proportion of retirees at each age will “shuttle” to retirement at older ages, or 

in some rare instances, to retirement at younger ages. For example, it allocates the proportion 

of sample year 2017 age 62 retirees into later retirement ages 63 through 70 in the projection 

year. The same process applies to allocate the proportion of age 63 retirees into revised 

retirement ages 64 through 70, and so on, through age 70. Shuttling backward to the earlier 

retirement age is rare but possible. For example, when appropriate, the method would allocate 

the proportion of sample year 2017 age 66 retirees into earlier retirement ages 62 through 65. 

For a specific age, then, the final PAPs equal a weighted average of these shuttled PAPs, with 

the PAPs for revised retirement ages potentially reflecting additional earnings when the revised 

retirement age is later. 

The frequency of earnings in the additional years is set to match projected covered worker 

rates by age group/sex/projection year, using randomization to achieve this match. Earnings 

amounts are based on cohort average taxable earnings and the individual’s relative earnings 

level. PAPs values are computed for each shuttling year and averaged using similar weighting 

factors, as previously existed in the Cost program before the 2017 Trustees Report, to obtain 

shuttled PAPs values. 

253
Example 7: 

Task: The AWARDS subprocess illustrates the process in determining the matrix of 

shuttling at age 62 to 70 in the 2017 sample and how the matrix is used in providing 

adjusted PAPs values by single retirement age. 

Information given: 

Consider the following example. In this example, the projection year is 2024, for male 

retired workers. 

 We start with the age distribution from the OASI retired worker beneficiary and the 

 distribution from Awards in the sample year 2017. 

The oasi_age_dist_samp vector (initial sex-age distribution in 2017 from sample) is as 

follows. 

62 63 64 65 66 67 68 69 70 . Male 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0170 0.0515

The oasi_age_dist_rsb vector in sample year 2017, is as follows. 

62 63 64 65 66 67 68 69 70

Male 0.2662 0.1134 0.0561 0.0955 0.2986 0.0591 0.0254 0.0159 0.0698

This alignment, applicable to beneficiary age distributions in projection years, is processed 

by the following steps.

a) Take the difference between two distributions (oasi_age_dist_rsb vector – 

oasi_age_dist_samp vector) in the sample year. 

62 63 64 65 66 67 68 69 70

Male 0.0046 0.0017 0.0060 0.0086 0.0189 0.0162 0.0030 0.0011 0.0183 − −−− −

The original projected OASI beneficiary distribution (oasi_age_dist_rsb) in year 2024 is: 

62 63 64 65 66 67 68 69 70

Male 0.1692 0.1058 0.0724 0.1041 0.1691 0.1977 0.0445 0.0355 0.1017

b) To align the projected OASI beneficiary distribution (oasi_age_dist_rsb) with the 

254
Awards sample distribution (oasi_age_dist_samp), we subtract the differences in Step 

a) from the oasi_age_dist_samp vector. The aligned age-sex distribution

(oasi_age_dist_rsb) for projection year 2024 is as follows.

62 63 64 65 66 67 68 69 70

Male 0.1738 0.1040 0.0784 0.1127 0.1880 0.1815 0.0415 0.0366 0.0835

The matrix oads, computed in this subprocess (4.2) is as follows. An explanation of how 

this matrix is generated appears below. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0074 0.0000 0.0000 0.0366

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0150 0.0170 0.0515 0.0835

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0170 0.0515 1.0000

Note that the column total is oasi_age_dist_samp and the row total is oasi_age_dist_rsb. 

The oads matrix is determined using these row and column sum constraints. The nonzero 

entries of the oads matrix zigzag down and to the right. To demonstrate the process of 

determining the values for the elements of the matrix oads, the irrelevant cells are zeroed 

out for simplicity. 

1. Starting at the upper left hand corner, the lesser of oasi_age_dist_samp and 

oasi_age_dist_rsb is placed there. So oads(62,62) 0.1738. = 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

ageentRSB ageentAWD

2. Move one spot down to oads(63,62) . By the column sum constraint, we are forced to 

have oads(63,62) 0.2708 0.1738 0.0970 =−= to meet age 62 column sum constraint. 

Since the difference (0.0970) is less than the row sum constraint (0.1040) for age 63, 

we want the row sum to equal 0.1040, the difference will be set for

oads(63,63) 0.1040 .0970 0.0070 = −= 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

Total 0.2708 0.1117 0.0000 0.0000 0.000

ageentRSB ageentAWD

0 0.0000 0.0000 0.0000 0.0000 0.0000

255
3. With the row sum constraint for age 63 met, we move one spot down to oads(64,63) .

Since oasi_age_dist_rsb (64) = 0.0784 < 0.1117 (oasi_age_dist_samp (63)), we are

forced to have the entry oads(64,63) 0.0784 =

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

Total 0.2708 0.1117 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

4. The row sum constraint for age 64 is now met, we move one spot down to oads(65,63).

Since 0.1117- 0.0070 – 0.0784 = 0.0263, which is less than 0.1127 ( oasi_age_dist_rsb

(65)), we are forced to have oads(65,63) 0.0263 = to meet the age 63 column sum

constraint.

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

Total 0.2708 0.1117 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

5. The column sum constraint for age 63 is now met, we move one spot to the right

oads(65,64) . Since oasi_age_dist_samp (64) = 0.0621 < 0.1127 (oasi_age_dist_rsb

(65)), the entry oads(65,64) 0.0621 = to meet the age 64 column sum constraint.

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

Total 0.2708 0.1117 0.0621 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

6. The column sum constraint for age 64 is met, we move one spot to the right

oads(65,65) . Since oasi_age_dist_rsb (65) = 0.1127 > 0.1041 (oasi_age_dist_samp

(65)), we are forced to have the entry oads(65,65) 0.1127 0.0263 0.0621 0.0243 =−−= to

meet the age 64 row sum constraint.

256
\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

Total 0.2708 0.1117 0.0621 0.1041 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7. The row sum constraint for age 65 is now met, but not the column constraint for age 65, 

we move down one spot to oads(66,65) . Since oasi_age_dist_samp (65) = 0.1041 < 

0.1880 (oasi_age_dist_rsb (66)), the entry oads(65,66) 0.1041 0.0243 0.0798 =−= to 

meet the age 64 column sum constraint. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.0000 0.0000 0.0000 0.0000 0.0000 0.1880

Total 0.2708 0.1117 0.0621 0.1041 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

8. The column sum constraint for age 65 is met, but not the row constraint for age 66, we 

move one spot to the right to oads(66,66) . Since oasi_age_dist_rsb (66) = 0.1880 < 

0.3175 (oasi_age_dist_samp (65)), the entry oads(66,66) 0.1880 0.0798 0.1082 =−= is 

forced to meet the age 66 row sum constraint. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0000 0.0000 0.0000 0.0000 0.0000

9. The row sum constraint for age 66 is now met, we move one spot down to oads(67,66) . 

Since oasi_age_dist_rsb (67) = 0.1815 < 0.3175 (oasi_age_dist_samp (66) – 0.1082), 

the entry is forced to meet the row constraint oads(66,66) 0.1815 =

257
\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0000 0.0000 0.0000 0.0000 0.0000

10. The row sum constraint for age 67 is now met, but not the column sum constraint for 

age 66. We move down one spot to oads(68,66) . The entry 

oads(68,66) 0.3175 0.1082 0.1815 0.0278 =−−= is forced to meet the age 66 column 

sum constraint. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0000 0.0000 0.0000 0.0000 0.0415

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0000 0.0000 0.0000 0.0000 0.0000

11. The column sum constraint for age 66 is now met, but not the row sum constraint for 

age 68. We move one spot to the right oads(68,67) . By setting 

oads(68,67) 0.0415 0.0278 0.0137 =−= to meet the row sum constraint 0.0415. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0000 0.0000 0.0000 0.0000

12. Now the age 68 row sum constraint is met, we move one spot down to oads(69,67) to 

meet the column sum constraint (0.0429) by setting 

oads(69,67) 0.0429 0.0137 0.0292 =−=

258
\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0000 0.0000 0.0000 0.0366

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0000 0.0000 0.0000 0.0000

13. The column sum constraint for age 67 is now met, we move one spot to the right

oads(69,68) to meet the row constraint for age 69 by setting

oads(69,68) 0.0366 0.0292 0.0074 =−=

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0074 0.0000 0.0000 0.0366

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0000 0.0000 0.0000

14. The row sum constraint for age 69 is now met, we move one spot down to oads(70,68)

to meet the column sum constraint (0.0224) by setting

oads(70,68) 0.0224 0.0074 0.0150 =−=

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0074 0.0000 0.0000 0.0366

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0150 0.0000 0.0000 0.0835

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0000 0.0000 0.0000

15. The column sum constraint is now met, we move one spot to the right oads(70,69) to

259
meet the row constraint (0.0835). Since oasi_age_dist_samp (69) 0.0170 < 

oasi_age_dist_samp (70) 0.0835, we are forced to have oads(70,69) 0.0170 = to meet 

the column sum constraint for age 69. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0074 0.0000 0.0000 0.0366

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0150 0.0170 0.0000 0.0835

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0170 0.0000 0.0000

16. The column sum constraint for age 69 is now met, we move one spot to the right 

oads(70,70) to meet the row sum constraint (0.0835) by setting the last entry 

oads(70,70) 0.0835 0.0150 0.0170 0.0515 =−−=

\ 62 63 64 65 66 67 68 69 70 Total

62 0.1738 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1738

63 0.0970 0.0070 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1040

64 0.0000 0.0784 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0784

65 0.0000 0.0263 0.0621 0.0243 0.0000 0.0000 0.0000 0.0000 0.0000 0.1127

66 0.0000 0.0000 0.0000 0.0798 0.1082 0.0000 0.0000 0.0000 0.0000 0.1880

67 0.0000 0.0000 0.0000 0.0000 0.1815 0.0000 0.0000 0.0000 0.0000 0.1815

68 0.0000 0.0000 0.0000 0.0000 0.0278 0.0137 0.0000 0.0000 0.0000 0.0415

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.0292 0.0074 0.0000 0.0000 0.0366

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0150 0.0170 0.0515 0.0835

Total 0.2708 0.1117 0.0621 0.1041 0.3175 0.0429 0.0224 0.0170 0.0515 1.0000

To obtain the normalized shuttle weight w matrix, normalize the rows from step (16) by 

dividing by the row sum. 

260
\ 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 0.9327 0.0673 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 0.2334 0.5510 0.2156 0.0000 0.0000 0.0000 0.0000 0.0000

66 0.0000 0.0000 0.0000 0.4245 0.5775 0.0000 0.0000 0.0000 0.0000

67 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000

68 0.0000 0.0000 0.0000 0.0000 0.6699 0.3301 0.0000 0.0000 0.0000

69 0.0000 0.0000 0.0000 0.0000 0.0000 0.7978 0.2022 0.0000 0.0000

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1796 0.2036 0.6168

With these normalized weights, final PAPs are computed for each age (row) as a weighted 

average of the PAPs, shuttled and non-shuttled, for the applicable individual ages with nonzero values in each row. Going down the row of the above matrix, then: 

• Age 62 final PAPs = age 62 original (unshuttled) PAPs

• Age 63 final PAPs = .9327 * age 62 PAPs shuttled to age 63 + .0673*age 63 original

PAPs 

• Age 64 final PAPs = age 63 PAPs shuttled to age 64

• Age 65 final PAPs = 0.2334 * age 63 PAPs shuttled to age 65 + 0.5510 * age 64 PAPs

shuttled to age 65 + 0.2156 * age 65 original PAPs 

• Age 66 final PAPs = + .4245 * age 65 PAPs shuttled to age 66 + .5775 * age 66

original PAPs

• Age 67 final PAPs = age 66 original PAPs

• Age 68 final PAPs = .6699 * age 66 PAPs shuttled to age 68 + .3301 * age 67 PAPs

shuttled to age 68

• Age 69 final PAPs = .7978 * age 67 PAPs shuttled to age 69 + .2022 * age 68 PAPs

shuttled to age 69 

• Age 70 final PAPs = .1796 * age 68 PAPs shuttled to age 70 + .2036 *age 69 PAPs

shuttled to age 70 + .6168 * age 70 original PAPs 

When PAPs are shuttled from a given age to age + x, all sample cases at the given original 

age have their AIME recalculated for retirement at age + x, with potential x additional 

earnings years included. 

261
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 payroll tax contributions

and taxation of benefits.1 The other component of income is interest earned on the trust

fund asset reserves. 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 beginningof-year assets (ASSETS), adding payroll 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 that 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 

1

 As noted throughout the Trustees Report a third component of non-interest income is reimbursements 

from the General Fund of the Treasury. In the cost program such reimbursements are simply treated as 

payroll tax contributions. 

262
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). 

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-2021 for the 2021 TR

 ni+74 represents the final year of the projection period-2095 for the 2021 TR

 nf represents the last year the cost program will project-2100 for the 2021 TR

 nim1 is equal to ni-1

 nim2 is equal to ni-2

 ns is equal to ni+9

 nbase, the year of the awards sample, is equal to 2017

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 

1) Estimates for the first ten years of the projection period for the first six

equations (4.3.1 through 4.3.6) mentioned above, including bond holdings by

Trust Fund as of 12/31/(ni+10).

2) 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

3) Projected effective taxable payroll for years nim1 through nf, updated yearly

Other 

4) 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) 

263
ii. Equation 4.3.2 – Scheduled Benefits (BEN)

Demography-Process 1 

5) Projected number of married and divorced people in the Social Security area 

population by age for end of years nim2 through 2100, updated yearly 

Economics -Process 2 

6) Historical COLA for years 1975 through nim2, with nim2 updated yearly, 

years ni-8 through ni-2 used in SOSI. 

7) Projected cost of living adjustment (COLA) for years nim1 through nf, 

updated yearly 

8) Historical SSA average wage index for years 1951 through nim2, with nim2 

updated yearly, years 1977 through ni-2 used in SOSI 

9) Projected percent increases in the average wage index for years nim1 through 

nf, updated yearly 

Beneficiaries-Process 3 

10) Projected number of disabled workers newly awarded by sex, attained age, 

and duration from entitlement (0 through 9 and 10+) for years ni through nf, 

updated yearly from subprocess 3.2 

11) 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 

12) 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 

13) Projected number of auxiliary beneficiaries (by benefit category) of retiredworker, deceased-worker, and disabled-worker beneficiaries for years nim1

through nf, updated yearly from subprocesses 3.2 and 3.3 

14) 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 

3.2 and 3.3 

15) Retired Workers 65+ by sex, and marital status (single, married, widowed, 

and divorced) for years nim1 through nf

16) Retired Workers 62+ by sex, and marital status (single, married, widowed, 

and divorced) for years nim1 through nf

17) Male widowed retired workers by age band (62-64, 65-69, 70-74, 75-79, 80-

84, 85-89, 90-95, 95+) for years nim1 through nf

18) Female widowed retired workers by age band (62-64, 65-69, 70-74, 75-79, 

80-84, 85-89, 90-95, 95+) for years nim1 through nf

 Other 

19) Adjustment factor, applied to DI worker retroactive benefit payments to align 

to historical data, updated yearly 

20) Total (aggregate) PIA and MBA, not actuarially reduced, of DI male and 

264
female workers in current payment status for years 2000 through nim1, with 

nim1 updated yearly from the Table 1-A Supplement, years 2010 through 

nim1 used in SOSI 

21) Total (aggregate) PIA and MBA, actuarially reduced, of DI male and female 

workers in current payment status for years 2000 through nim1, with nim1

updated yearly from the Table 1-A Supplement, years 2010 through nim1 

used in SOSI 

22) Total (aggregate) PIA and MBA, not actuarially reduced, of newly awarded 

DI male and female workers for years 2000 through nim1, updated yearly 

from the Table 1-A Supplement, years 2010 through nim1 used in SOSI 

23) 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 

24) Cumulative distribution of AIME dollars for newly entitled disabled-worker 

beneficiaries by age (20 through 65) and sex, for years nim1 through nf, 

updated yearly from subprocess 4.2. Ages 15 through 19 are assumed to have 

the same distribution of dollars as does age 20. Future age 66 disabled 

workers are assumed to have the same distribution of dollars as age 65 

workers have 

25) Starting average PIA matrix for retired-worker benefits for the year nim1, by 

age at entitlement, age in current-pay and sex, updated yearly 

26) Starting average PIA matrix for disabled-worker benefits, for the year nim1, 

by age in current-pay, duration and sex, updated yearly 

27) 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 

28) Starting average MBA matrix for retired-worker benefits for the year nim1, by 

age at entitlement, age in current-pay and sex, updated yearly 

29) Starting average MBA 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 

30) 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 qlink21.xls 

31) Benefit relationships between workers and aged spouses for years nim1

through nf with the effect of the ‘Bipartisan Budget Act of 2015’ on “claiming 

strategies” taken into account 

32) Retroactive payment loading factors for auxiliary beneficiary categories for all 

years, for each benefit category and both sexes, updated yearly 

33) Initial and ultimate post entitlement factors for retired workers by sex and 

duration updated yearly. Factors are read in such that there is a twenty-year 

linear phase-in from initial factors to ultimate factors. 

34) Initial and ultimate post entitlement factors for disabled workers by sex and 

duration updated yearly. Factors are read in such that there is a twenty-year 

linear phase-in from initial factors to ultimate factors. 

35) Initial and ultimate post entitlement factors for DI conversion workers by sex 

265
and duration updated yearly. Factors are read in such that there is a twentyyear linear phase-in from initial factors to ultimate factors. 

36) Initial Windfall Elimination Provision (WEP) factors by sex and age for

attributed year, updated every 2 years

37) Ultimate WEP factors by sex read in as a percentage of the way from initial

factors to one, updated every 2 years

38) Year in which ultimate WEP factor is reached by age at initial entitlement

(62-70), updated every 2 years

39) Trendline by which WEP factors are phased-in from initial value to ultimate

value, updated yearly

40) Workers’ Compensation cumulative factors by duration that adjust benefits to

account for decreasing offsets (i.e. – Workers Comp offsets decrease as

duration increases), updated yearly

41) Workers’ Compensation reduction factors (used in retroactive category) to

reflect offsets starting and stopping in the year of DI entitlement, updated

yearly

42) Workers’ Compensation parameter to account for offsets that begin and end in

the year of entitlement, updated yearly

43) Dual entitlement regression coefficients for the 12 dual entitlement equations

(3 each for number of widows, number of widowers and the average excess

amount for widows, and, 1 each for number of wives, number of husbands and

the average excess amount for wives), updated yearly

44) Dual entitlement widower excess amount as a percent of widow excess

amount, by age band and year, updated yearly

45) Dual entitlement husband excess amount as a percent of wife excess amount,

by year, updated yearly

46) Dual entitlement average excess amounts and percentages of exposure

population for December, year ni-1 for wives, husbands, widows, and

widowers, updated yearly

47) Average retired worker PIA in the last year of the projection period, by age

band and sex, updated yearly

48) Target values for ratios relating to the twelve dual entitlement categories,

updated yearly

49) Number of years in which the difference between the results from the

regression coefficients and targeted values are phased in for the twelve dual

entitlement categories, updated yearly

50) Historical adjustment factor for each of the twelve dual-entitlement categories,

updated yearly

51) Adjustment factors for average retired and disabled worker benefit amounts

(PIA and MBA) in current-pay at durations 0 through 5+, by sex and age,

updated yearly

52) Number of months retroactive benefits are received by a worker who is paid

retroactively in their year of entitlement, by trust fund, with retired workers

further broken out by age less-than normal retirement age (NRA) or above

NRA

53) Adjustment factors for average retired worker retroactive benefit amounts by

266
sex, updated yearly 

54) Adjustment factors for disabled worker retroactive benefit amounts in currentpay at durations 0 through 5+, by sex and age, updated yearly

55) Retired worker actuarial reduction factors and delayed retirement credit levels

based on year of birth, based on current law (generally not updated)

56) Adjustment factor applied to all newly entitled DI workers to account for

shifting distribution of awards by DI adjudicative level, updated yearly

iii. Equation 4.3.3 – Taxation of Benefits

Trust Fund Operations and Actuarial Status

57) 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

58) Average wage indexes for years nim1 through nf, updated yearly

59) Ultimate value of productivity factor for the period ni through nf updated

yearly

Beneficiaries-Process 3 

60) Total number of beneficiaries in current-pay status by trust fund for years

nim1 through nf, updated yearly

v. Equation 4.3.5 – Railroad Interchange

Economics-Process 2

61) Increase in the average wage index for years nim1 through nf, updated yearly

62) Ultimate value of productivity factor for the period ni through nf updated

yearly

Trust Fund Operations and Actuarial Status 

63) Taxation of benefits as a percent of the amount of benefits scheduled to be

paid, by trust fund for years nim1 through nf, updated yearly (use same factors

as in equation 4.3.3)

Other input data 

64) Nominal annual yield rate on the combined OASDI trust fund for year nim1

65) Regression coefficients to project annual prescribed interest rates, related to

railroad interchange, updated annually

66) Ratio of railroad retirement OASI and DI average benefits to overall OASI

and DI average benefits, updated yearly

67) Number of railroad beneficiaries (retirement and disability) for December of

year nim3, updated yearly

68) Average taxable earnings in railroad employment for year nim2, updated

267
yearly 

69) Expected railroad new awards as a percent of the average of historical

employment data, updated yearly

70) Historical data on average railroad employment, 1960 through nim2

71) Average worker benefit by sex and trust fund for December nim1 and

December nim2, updated yearly

72) Auxiliary loading factor by trust fund, updated yearly using 10 years of

historical financial interchange benefit data

73) Railroad initial mortality rate by trust fund for year nim2, updated yearly

using 10 years of historical financial interchange benefit data

74) Railroad mortality improvement rate by trust fund, updated yearly using 10

years of historical financial interchange benefit data

75) Fiscal Year Railroad transfer amount in millions of dollars for year nim2

76) Short-Range estimates for railroad administrative costs, military service

adjustments, and prescribed interest rates.

vi. Equation 4.3.6 – Interest Income

Economics-Process 2

77) Annual increase in the CPI for years ni through nf, updated yearly

 Trustees assumptions 

78) Ultimate real interest rate, updated annually

 Other input data 

79) Factors for exposure to interest rate for benefits, payroll, and taxation of

benefits, updated yearly

80) Factors for exposure to railroad interchange and administrative expenses,

updated periodically

81) Annual effective interest rates for years ns+1 through nf, by trust fund,

updated yearly

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 

82) Single year population and mortality rate data for years 1941 through 2101,

updated yearly

Economics-Process 2 

83) Historical and projected single-year COLA data and average wage indexing

series (AWI) data for years 1975 through 2100 (for COLA) and 1951 through

2100 (AWI), updated yearly as applicable

268
84) Historical and projected number of covered workers by single year of age 0-

99 and 100+ from year ni-23 through 2100, updated yearly 

85) Ultimate assumed annual average wage increase, wg_ult, updated yearly 

Beneficiaries-Process 3 

86) Total projected disabled workers by age for years nim1 to 2100, updated 

yearly 

87) Total projected aged spouses, divorced aged spouses, surviving aged spouses 

and divorced surviving aged spouses by sex, single year of age (up to 95+) 

and for years nim1 to 2100. 

 Awards-Process 4 

88) Projected number of workers and total taxable earnings by single year of age 

(15-80) and sex from nim1 to 2100, updated yearly 

 Other 

89) 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 2020 Master Beneficiary Record 

(MBR)2

—updated yearly 

90) 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 2020 MBR—updated yearly 

91) Consumer Price Index data from 1951-1974 from Bureau of Labor Statistics 

(not updated) 

92) Number of covered workers and average taxable earnings by single year of 

age 1-14 for years 1998-2017 from 1 percent Continuous Work History 

Sample (CWHS), updated yearly to include year ni-4 

93) Number of covered workers and average taxable earnings by single year of 

age 81-99 for years 1998-2017 from 1 percent CWHS, updated yearly to 

include year ni-4 

94) Distribution of assumed age differentials between aged spouses and workers 

ranging from -12 years to 15 years seniority for the worker by sex of the 

beneficiary, age of the beneficiary 62-74, and marital status obtained from the 

December 2018 MBR—updated every 3 years 

95) Distribution of assumed age differentials between widow(er)s and workers 

ranging from -6 years to 12 years seniority for the man (generally not 

updated) 

96) Factors to apply to the 95+ “in current pay” counts of retired workers, aged 

spouses, surviving aged spouses, divorced spouses, and dually entitled 

 

2

 For disabled adult children of deceased workers and lump-sum beneficiaries, data were extracted from a 

1- percent sample of the December 2020 MBR, mainframe dataset ACT.TAPEL.CAN1220. For the other 

18 auxiliary beneficiary categories, data was extracted from the 100 percent December 2020 MBR, 

mainframe dataset ACT.TAPEH.MBR100.D2012.CANSORT. 

269
spouses expanding the single age counts through 119, updated yearly 

4.3.c. Development of Output 

i. Equation 4.3.1 – Payroll Tax Contributions (CONTRIB)

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 is provided 

from subprocess 3.2. For each projection year, two matrices are provided – one for 

men and one for women. The structure of each matrix is as follows: 

 11 columns. The columns are indexed by duration of disability (0-9 and 

10+). 

270
 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+ 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 diagonals of the matrix 

provided by the DISABILITY subprocess are “combined with” the diagonal directly 

below it and then zeroed out.) 

Building the Average PIA Matrix for Disabled Workers

In each projection year, the COST subprocess produces an average PIA matrix for 

each sex. Each matrix is a 47 by 10 matrix whose entries are the average PIA 

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 100 percent Master Beneficiary Record (100% MBR) extract is processed by a 

side model. The final product of the side model is two matrices of average PIA 

levels, one for men and one for women, for December nim1 (2020 for the 2021 TR). 

For a given year of the projection period, a new average PIA matrix is obtained by 

moving the average PIA 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 and a post-entitlement 

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 PEadj yr sex dur

   

 

A more careful explanation of the factors, wkcomp yr sx dur (,, ) and 

271
PEadj yr sex 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 PIAs to duration 9+ average PIAs, both average PIAs are given a cost of 

living adjustment and a post-entitlement adjustment (see section “Post-Entitlement 

Adjustments”). The resulting duration 9+ average PIA is the weighted average of the 

adjusted prior year duration 8 and 9+ average PIAs, weighted by the prior year’s 

numbers of beneficiaries in current-pay status for durations 8 and 9+ respectively. 

The only column that does not follow this procedure is the duration 0 column. The 

duration 0 column corresponds to newly entitled disabled-worker beneficiaries. The 

following sections describe how average PIAs are determined for this group of 

beneficiaries. 

 

Average PIAs 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 current year disability onset and j = 2 signifies prior 

year disability onset. 

Let: 

 ( max( 60,1 )) _ (, , ) (1977) j

avgwg yr ag j Wage Idx sx ag yr

avgwg

   for j=1,2. 

 1

62

(1 ( 1)) (1 ( )) 64

_ (,) (1 ( ( 62)) 64 66.

ag

k

COLA yr COLA yr ag

Cum COLA ag yr COLA yr k ag



    

       

 

2

63

1 ( ) 63

_ (,) (1 ( ( 62)) 63 66.

ag

k

COLA yr ag

Cum COLA ag yr COLA yr k ag



  

       





272
 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 table 1-A supplement, for each month in a given historical year, 

contains total award PIA and MBA data for disabled workers, 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 annual MBA and 

PIA respectively for DIBs that are not actuarially reduced as found in the table 1-A 

data. In the historical period 2000-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 totpia DIB nar yr sx 

In the period ni through ns+9, facm p yr sx 2( , ) is defined as follows. Let 

y facm p nim sex 1 2 ( 1, ) 

y y 2 (1.0 1) / 3.0  

1/20

2 ( 1, ) 2 ( , ) max( 1 2,min( 1 2, 2 ( 1, ) )). 2 ( 11, )facm p yr sx facm p yr sx y y y y facm p yr sx facm p yr sx

          

Projected values of facm2p are therefore held within a delta of y2 from the last 

historical year of facm2p. 

This value is further adjusted by the variable facm2p_param to reflect the offset 

amounts that end within the first entitlement year. For the 2021 TR the data suggests 

this factor should be 0.39. As a result, for yr = ni, ... , ns+9, 

2 ( , ) (1 ) 0.39

0.39 0.61 .

facm p yr sx x x

x

  

 

The factor reaches its ultimate value in years ns+10 and later. 

Another factor used in the development of average PIAs for newly entitled disabled 

worker beneficiaries is DIB adjudication _ . This factor adjusts for expected 

distributions of awards by disability adjudicative level. A side model shows that 

expected future distributions will have a higher share of disabled workers coming on 

the rolls at the Administrative Law Judge level than currently shown in the Awards 

sample. This leads to a 0.48% expected reduction in newly entitled DI worker 

benefits. Therefore, DIB adjudication _  0.9952 . 

273
The preliminary average PIA for newly entitled disabled worker beneficiaries may 

now be defined. It is equal to 

30

1

2

1

_ (, , ) _ _ (,, )

_ (, , ) _ ( , )

2( , ) _ .

i i i

i

j j 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 DIB adjudication







 

     

 





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 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 

current-payment 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 that 

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. There is an additional adjustment to the 

weighted average disabled worker PIA and MBA amounts in current pay applied by 

duration from entitlement to award in order to account for benefit level differences 

that mature by duration 5. 

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 

274
way between original facm2p and 1 

1 0.523588 

2 0.699937 

3 0.773501 

4 0.818732 

5 0.852705 

6 0.871823 

7 0.886439 

8+ 0.901639 

Then wkcomp yr sx dur (,, )is defined so that 

1

2 _ ( ) 2 ( , ) (1 ( , , )).

dur

j

facm p pct dur facm p yr dur sx wkcomp yr sx j    

This is an iterative process that 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 

This trend is captured in a factor denoted Fam p yr sx 2 ( , ). The table 1-A supplement 

as of the end of December of each historical year contains total in-current pay 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 table 1-A data. 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 2000-nim1 we define fam p yr sx 2( , ) to be the ratio of the total MBA to the 

total annual 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+10, facm p yr sx 2( , ) is defined as follows: 

 y fam p nim sex 1 2 ( 1, ) 

 y y 2 (1.0 1) / 3.0   

1/20

2 ( 1, ) 2 ( , ) max( 1 2,min( 1 2, 2 ( 1, ) )). 2 ( 11, )fam p yr sx fam p yr sx y y y y 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 retroactive 

benefits to reflect offsets starting and stopping in the year of DI entitlement that are 

not captured by the current method. Based on historical administrative data, we set 

these factors by duration as follows: 

275
Duration Percentage Reduction 

0 0.2311% 

1 0.2095% 

2 0.0697% 

3 0.0316% 

4 0.0076% 

5+ 0% 

We define wkcomp_red(dur) to be 1 minus these percentage reductions. 

By law, disabled workers are no longer subject to the workers’ compensation offset at 

the attainment of a defined age. For those born prior to 1951, the defined age is 65. 

For those born in 1951 and later, the defined age is the Normal Retirement Age 

(NRA).3

 Therefore, all DI worker benefit levels are adjusted at either age 65 (for 

those born prior to 1951) or at conversion to a retired worker benefit (for those born 

1951 and later) to eliminate the effect of the offset. 

Adjustment to Average Benefit Levels by Duration

Average disabled worker PIA and MBAs are adjusted further at each duration by a 

factor, DI_RI_facs, designed to account for average benefit level changes that occur 

when beneficiaries come on the rolls retroactively. This is different than projected 

retroactive payments discussed elsewhere in the documentation. These adjustments 

mature at duration 5, when the vast majority of disabled workers have started 

receiving benefits. 

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 ( , , , ) 2 ( , , ), avgpia yr ag sx dur Fam p yr sx dur  the weights being the 

number of DI workers in current payment status by age, sex, and duration. 

Post-Entitlement Adjustments 

As cohorts of beneficiaries age, their average benefit level will likely change for 

reasons other than just the COLA increase. The two primary reasons for this are postentitlement work, which could lead to a re-calculation of one’s benefit, and a known 

correlation between greater lifetime earnings and lower mortality rates. The Cost 

process uses post-entitlement factors by sex and duration to account for the expected 

 

3

 The NRA was 65 for individuals born before 1938. It increased to 66 at the rate of 2 months per year for 

individuals born 1938-1943. Under current law, the NRA will increase to 67 for individuals born from 

1955-1960, again at the rate of 2 months per year. 

276
dynamic benefit levels. Consecutive-year comparisons of one percent December 

MBR data from 2009-2010 to 2018-2019 are used to calculate post-entitlement 

factors. 

For disabled workers we calculate separate factors for those in current pay (ICP) who 

are younger than 50 and those ICP who are age 50 or older. We use separate factors 

for each sex and each duration (0-9+

). Initial and Ultimate factors are calculated 

before being read into the cost program with initial factors set to the most recent 3-

year historical average and ultimate factors at the most recent 10-year average. 

All initial factors are phased-in linearly to the ultimate factors over the first 20 years 

of the projection period (reaching the ultimate values in ni+19). 

(2) Retired-Worker Benefits

Retired-Worker Beneficiary Matrix

The number of retired-worker beneficiaries for a given year and sex is provided from 

subprocess 3.3. Two matrices are provided – one for men and one for women. 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 at ages 62 through 70 (where age in current-pay 

equals age at entitlement) are 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 age at initial 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 100% 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. Aggregate MBAs and PIAs for the 

starting matrix are calculated, by sex, by multiplying each cell in the benefit matrix 

277
by its counterpart in the beneficiary matrix and then summing the total benefit. The 

aggregate MBAs and PIAs are compared to data in the Table 1-A supplement for year 

ni-1 (with appropriate exclusion of excess benefit for dually entitled workers) and all 

individual MBAs and PIAs in the starting benefit matrices are proportionally adjusted 

so that the new aggregate MBAs and PIAs match the values in the supplement. 

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) and by the 

appropriate post entitlement factor (see section “Post-entitlement adjustments”) for 

men and women. Adjusted age 94 benefits and age 95+ benefits are averaged, based 

on the respective number of beneficiaries in current pay in the prior year, to get the 

new average benefit for age 95+. DI conversion benefits are handled similarly, 

except the average conversion benefit for each age 66 through 67 is combined (as a 

weighted average) between the number of DI worker beneficiaries at age NRA-1 in 

the prior year (computed in subprocess 3.2) and the number of DI conversions of age 

NRA-1 already receiving benefits as a DI conversion case, if any (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 4.24

. Average benefits for newly entitled 

retired-worker beneficiaries are calculated by sex and single years of age 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 eighteen intervals (thirteen 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 OPAP values for 

each interval of AIME dollars are 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=5,...,18, and 0.15 for intervals i=19,...,30),

4

 Prior to the 2017TR, the raw OPAP values from subprocess 4.2 needed to be altered by the cost 

subprocess in order to account for projected changes from the static age distribution for newly entitled 

retired workers used by Awards subprocess 4.2. The method for doing this was referred to as the 

“Shuttling Method”. As of the 2017 TR, the shuttling method has been moved to subprocess 4.2. 

278
AIME_dollarsi be the length of subinterval i, 

 opapi (yr,sx,ag) be the OPAP value from subprocess 4.2 for retired workers

newly entitled in year yr whose sex is sx and whose age is ag.

 wff(yr,sx,age) be a reduction factor to account for the Windfall Elimination

Provision.5

 ( ( 62)) _ (,) ( 2)

avgwg yr ag Wage Idx ag yr avgwg nbase

   

 62_ ( , ) (1 ( ( 62)))

ag

k

COLA Idx ag yr COLA yr k



   

Then the average PIA for these newly entitled retired worker beneficiaries is equal to 

30

1

_ (, , ) _ ( , ) _ ( , ) (,, )

_ _ ( , , ). i i i

i

LR awdpia sx ag yr Wage Idx ag yr COLA IDX ag yr wff yr sx age

PIA factor 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 newly entitled PIA multiplied by the appropriate actuarial reduction 

factors and delayed retirement credits, arfdrc(ag,yr), based on age at initial 

entitlement. 

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. 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. Similarly, 

average PIA and MBA for all retired worker beneficiaries in current pay are 

computed, by sex. 

DI Conversions

Disabled-worker beneficiaries convert to retired-worker beneficiary status (called DI 

conversions) at normal retirement age (NRA). The average new DI conversion 

benefit for a given sex at age NRA is the weighted average of the average DI worker 

benefits from the prior year for that sex and age NRA-1, weighted by the number of 

people in current pay in each duration and then increased by the current year COLA 

and adjusted by the appropriate Post-Entitlement factor. The average DI conversion 

5

 The Windfall Elimination Provision (WEP) reduces the first PIA formula factor from 90% to as low as 

40% for individuals who receive a pension based on specified categories of non-covered employment, 

primarily non-covered state and local government employees and federal workers receiving a pension 

under the Civil Service Retirement System. The cost process uses initial factors by sex and age, ultimate 

factors, years in which ultimate factors are reached and phase-in trend lines to the ultimate factor, all 

supplied by a side model. 

279
benefit for a given sex and single age NRA+1 through 95+ is the average DI 

conversion benefit from the previous year for the same sex and age cohort increased 

by the current year COLA and adjusted by the appropriate Post-Entitlement factor. 

Both the average conversion benefit for each sex and single age NRA through 95+, 

and the number of people in current pay for these ages, are used in the computation of 

average retired worker benefits. 

Post-Entitlement Adjustments 

As discussed in the previous section, the Cost process uses post-entitlement factors by 

sex and duration to account for changes in benefit levels aside from the cost-of-living 

adjustment. For retired workers we calculate separate factors for those ICP who 

converted from DI status and those ICP who came on the rolls as a retired worker. 

We use separate factors for each sex and each duration (0-12+). Initial and ultimate 

factors are calculated before being read into the cost program with initial factors set to 

the most recent 3-year historical average and ultimate factors at a 10-year average. 

For women the ultimate post-entitlement factors are adjusted further to reflect the 

trend that female retired workers are starting to have earnings and benefit levels more 

similar to men. Therefore, female ultimate post-entitlement factors are calculated in 

the program as 90% of the male 10-year average plus 10% of the female 10-year 

average. 

All initial factors are phased-in linearly to the ultimate factors over the first 20 years 

of the projection period (reaching the ultimate values in ni+19). 

Adjustment to Average Benefit Levels by Duration

Average retired worker PIA and MBAs are adjusted at each duration by a factor, 

OA_RI_facs, designed to account for average benefit level changes that occur when 

beneficiaries come on the rolls retroactively. This is different than projected 

retroactive payments discussed elsewhere in the documentation. These adjustments 

mature at duration 5, when the vast majority of retired workers have started receiving 

benefits. 

(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 applies to all benefit amounts except the “dual entitlement excess amount.” 

If a retired worker beneficiary is also entitled to auxiliary spouse or widow(er) benefits 

and these auxiliary benefits are greater, then 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). 

280
The first step is to determine average benefits by category. A list of the beneficiary 

categories 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 

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 adult child 

55 & 56 Lump sum death benefit ($255) 

For the worker categories, the prior sections describe the computation of average benefit 

levels at the end of each year. For a specific auxiliary beneficiary category, the average 

monthly benefit at the end of each year (avgben) is determined by multiplying: 

 The linkage factor (the assumed relationship between an auxiliary beneficiary’s 

benefit level and the corresponding worker benefit level) by 

 The relevant average PIA or the average monthly benefit of the primary account 

holder (the worker beneficiary account on which the auxiliary beneficiary is 

entitled to receive the benefit). 

281
 

Starting with the 2016 Trustees Report, the linkage factor for aged spouse categories 

comes not from the qlink workbook, but from file ‘BAsps’. This file is created by a side 

model with the purpose of accounting for the expected changes to average aged spouse 

benefit levels due to the Bipartisan Budget Act of 2015. 

In order to annualize benefits for each beneficiary category, two values are used. The 

beginning-of-year average benefit equals the average monthly benefit in December of the 

prior year. The end-of-year benefit equals the monthly average benefit of the worker 

beneficiary for December of the current year without the cost of living adjustment 

(COLA). 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. If 

cp(cat,yr) is the number of beneficiaries in category cat for year yr, and avgben(cat,yr) is 

the average monthly 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             

For all beneficiary categories except for the lump-sum benefit, the aggregate benefit 

amount is increased by the retroactive payments that were projected to be paid during the 

year. See section (5), below. 

(4) Dually Entitled Beneficiaries and Benefits 

Number of Dually Entitled Beneficiaries 

There are four primary categories of dually entitled beneficiaries. They are the dually 

entitled wives, widows, widowers, and husbands. To project the number of dually 

entitled beneficiaries for each category we combine a series of regression equations (1 

each for wives and husbands and 3 each, by age bands, for widows and widowers) with 

two coefficients each, a slope of ( )

1

k a and a y-intercept of ( ) k b , with a third factor, ( ) ( ) k c yr

derived from a process we describe as “add factoring”, and a fourth factor, ( ) ( ) k d yr

derived from an adjustment to the most recent historical data point: 

 

( ) ( ) () () ( )

1

PIA(yr,M) PIA(yr,F) PctExp ( ) ( ) ( ) PIA(yr,M)

k k kk k

yr a b c yr d yr    

(k=1,2,3,4,5,6,7,8) project the percentage of the exposed population entitled to wife (1), 

widow aged 62-74 (2), widow aged 75-84 (3), widow aged 85+ (4), widower aged 62-74 

(5), widower aged 75-84 (6), widower aged 85+ (7), and husband (8) benefits. 

PIA(yr,sex) is the average PIA of all retired worker beneficiaries in current pay by sex, 

282
and PctExp(yr) is the percentage of the entitled population in the category that is dually 

entitled. We use the “add factoring” method with variable ( ) ( ) k c yr to account for the 

expected future comparative work history changes that will affect dual entitlement 

populations. 

To derive ( ) ( ) k c yr , suppose that ( ) k ult is the value obtained from the regression equation 

without add-factoring in the final year of the projection period. Therefore 

() () ( )

1

PIA( 74,M) PIA( 74,F) . PIA( 74,M)

k k ni ni k ult a b

ni

 

 



Let ( ) k targ be the target value we estimate for the final year of the projection period. Let 

phaseyrs be the number of years it takes to fully phase in the target value. Then we 

have 

() ()

( ) ( ) min( 2019, ) .

k k

k targ ult c yr yr phaseyrs

phaseyrs

  

To derive ( ) ( ) k d yr , suppose that b1 is the measured difference between the most recent 

historical dual-entitlement percentage and the corresponding post-add-factoring 

regression value. We phase out this adjustment linearly over 20 years, thus: 

( ) ( ) 1 (1.0 min( 2020,20.0) / 20.0). k d yr b yr   

The following table displays the coefficients, target values, and phase-in years for each 

type of beneficiary. 

k Type ( )

1

k a ( ) k b Target Value 

( ) k targ

Add-factoring 

Phase-in Years 

phaseyrs 

1 Wife 0.82064 0.0 0.195 34 

2 Widow 62-74 0.18480 0.47775 0.520 31 

3 Widow 75-84 0.82691 0.41523 0.590 30 

4 Widow 85+ 0.50758 0.59192 0.615 37 

5 Widower 62-74 -0.36223 0.17228 0.10 30 

6 Widower 75-84 -0.45981 0.23001 0.085 33 

7 Widower 85+ -0.14138 0.10547 0.08 76 

 8 Husband -0.05516 0.02435 0.0090 36 

In the above equations, the average PIA of newly entitled retired worker beneficiaries by 

283
sex has already been computed (see subsection (2) above). 

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 and, as is the case with the 

percentage exposures, we use 1 regression for wives and 3 for widows (1 for each of 3 

age bands). 

The equations used to project the average excess amount each have two terms and two 

adjustment factors, similar to the process for the number of dually entitled beneficiaries. 

Each equation k has two coefficients, a slope of ( )

1

k

a and a y-intercept of ( ) k b , with a third 

factor, ( ) ( ) k

c yr derived from add factoring, and a fourth factor, ( ) ( ) k d yr derived from an 

adjustment to the most recent historical data. A target value in the 75th year of the 

projection period is used in deriving the “add-factor” adjustment. The four equations 

( ) ( ) () () ( )

1 1

PIA(yr,M) PIA(yr,F) AvgExcPct ( ) ( ) ( ) PIA(yr,M)

k k kk k

yr a b c yr d yr    

( 1,4 k  ) project the average excess benefit amounts of wives (1), widows aged 62-74 

(2), widows aged 75-84 (3), and widows aged 85+ (4). The derivations of ( ) ( ) k

c yr and 

( ) ( ) k d yr are completed in the same manner as for the number of dually entitled 

beneficiaries above. 

The table below shows the regression coefficients and other relevant adjustments in the 

2021 Trustees Report. 

k Type ( )

1

k a ( ) k b Target Value (2095) 

in Nominal Dollars 

( ) k targ

Add-factoring 

Phase-in Years 

phaseyrs 

1 Wife 0.47477 0.0 3,672.36 22 

2 Widow 62-74 -0.54954 0.60479 10,190.25 40 

3 Widow 75-84 0.99254 0.08848 9,443.60 22 

4 Widow 85+ 0.30784 0.36750 9,746.73 38 

The average excess amount of widowers and husbands is estimated to be a fixed 

percentage of the average excess amounts of widows and wives, respectively. The 

average excess amount of husband beneficiaries is measured to be 79.22% of wives in 

2020 and is assumed to linearly phase to 80% in the 13th year of the projection period 

(2033 for 2021TR). Widowers are broken down into the three age bands, such that the 

average excess amount for widowers aged 62-74 is based on the average excess amount 

284
for widows aged 62-74, etc. Similar to husbands, the factor is linearly interpolated from 

the measured historical value in 2020 to an ultimate factor in 2033. Below are the initial 

and ultimate factors: 

Type Average Benefit Level 

Relative to Widow (2020) 

Average Benefit Level 

Relative to Widow (2033) 

Widowers 62-74 58.97% 60.5% 

Widowers 75-84 53.77% 55.5% 

Widowers 85+ 45.92% 47.5% 

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             

(5) Retroactive Payments 

Frequently, beneficiaries start receiving payments later than their actual entitlement date, 

such that they receive a “catch-up” lump-sum amount for the time delay, in addition to 

regular monthly benefits going forward. These lump-sum amounts, which we call 

retroactive payments, apply for all beneficiary categories (except for the one-time $255 

death benefit) but are more significant for disabled workers because of the frequent and 

sometimes lengthy time lag in getting an allowance on their application, as well as the 12 

months of retroactivity allowed at the time of benefit filing.6

 This section discusses how 

retroactive benefit payments are projected for all beneficiary categories. 

Disabled Workers

The number of disabled-worker newly awarded beneficiaries for a given year and sex 

is provided from subprocess 3.2. For each projection year, two matrices are provided 

– one for men and one for women. The structure of each matrix is as follows: 

 

6

 In contrast, retired workers retiring before NRA have no months allowed at the time of benefit filing, 

while retired workers retiring after NRA have up to 6 months of retroactively allowed. 

285
 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 67. 

 

The COST subprocess, however, only uses 10 durations7

 (0 through 9), and 48 ages 

(ages 20 through 67). This requires a manipulation of the matrix of newly awarded 

DI beneficiaries 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 beneficiaries. For ages (ag) between 20 and 30 inclusive, the number of 

newly awarded beneficiaries aged ag and duration ag-20 is the value provided by the 

DISABILITY subprocess added to the number of new awards 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 newly 

awarded beneficiaries aged 16, 17, 18, 19, and 20 of duration 1, and so on. In other 

words, the five nonzero diagonals of the matrix provided by the DISABILITY 

subprocess are “combined with” the diagonal directly below it and then zeroed out.) 

Newly awarded disabled worker beneficiaries are denoted by year, sex, age and duration 

as dibaw(year,sex,age,dur). 

Let dur be a duration, 0 through 9. Define 

 0

_ ( ) (1 ( )).

dur

j

Cum COLA dur COLA yr j   

 For 0,...,10, i 

2 0

5 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 

Retro_DIB(sex,yr) 

67 9

20 0 0

6

( , , , ) _ ()

( , , min( , 66), ) _ ( )

_ ( )

.

10

dur

age dur i

dibaw yr sex age dur Num Months i

dibpia yr sex age dur wkcomp red dur

  Cum COLA dur

   

dibpia is further altered in this formula by the adjustment factors in array: 

 

7

 While the DI Awards file from subprocess 3.2 displays durations 0 through 9 and 10+, there are no new 

awards after duration 5 for the 2021 TR. Therefore, durations 6+ show zeros for all ages and years. 

286
DI RI facs sex age dur _ _ ( , , ,2) 8

These adjustments to dibpia are designed to account for the differences between average 

benefit levels for all beneficiaries and levels for those receiving retroactive credit. 

Retro_DIB(sex,yr) is then further adjusted to account for differences between projected 

retroactive benefits and observed retroactive benefits paid in the historical period. This 

adjustment, denoted ret_hist, is calculated to be 0.8662 for the 2021TR. After this 

adjustment Retro_DIB(sex,yr) is simply added to the disabled worker benefit category by 

year and sex.

Retired Worker Beneficiaries

Retired worker beneficiaries are assumed to have, on average, 0.4 months of retroactive 

payments if they begin receiving benefits prior to their NRA and 1.5 months of 

retroactive payments if they begin receiving benefits at or after NRA. The number of 

months for the two age groups (denoted ‘retrom’ in the below equation) is determined 

annually by a side model. Hence 

70

62

(, , , ) (, , , ) 1000 _ ( ,) . 1 () ageoabicp yr sex age age retrom 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. 

oabmba year sex age age ( ,, , ) in the above formula is further altered by the adjustment 

factors: 

retrom adj sex _ ( ) {0.993538,1.045963} 

These adjustments to oabmba are designed to account for the small differences between 

average benefit levels for all beneficiaries and levels for those receiving retroactive 

credit. 

The aggregate retroactive benefits for retired worker beneficiaries are simply added to the 

retired worker benefit category by and sex. 

Auxiliary Beneficiary Categories 

Retroactive payments for auxiliary beneficiaries (determined by a side model using 

 

8

 The fourth index of the 4-dimensional DI_RI_facs array is a binary flag to denote the ICP duration 

adjustment factor for a subscript of 1 and the retro adjustment factor for a subscript of 2. 

287
historical experience) are treated as a loading of the aggregate annual benefits by 

auxiliary category. That is, each auxiliary benefit category has a loading factor to 

represent retroactive payments on top of regular monthly benefits, and the aggregate 

annual 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 total annual scheduled 

benefits 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 are adjusted by linearly grading the scheduled 

benefits adjustment to zero. From the 20th year forward, the projection is the pure longrange value. 

iii. Equation 4.3.3 – Taxation of Benefits (TAXBEN)

The short-range office provides taxation of benefits levels by trust fund in the short-range 

period. 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 between the two 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 fund, 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 

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( , ) ( , 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. 

By trust fund, the total cashflow in year yr, rr_cashflow(tf,yr), is broken down into two 

positive components; railroad benefits in year yr and railroad administrative expenses in 

year yr, and two negative components; railroad contributions in year yr and railroad 

taxation of benefits in year yr. A positive cashflow in this calculation represents a net 

cost to the trust fund. Cashflows are calculated on a fiscal year basis. 

Projections of numbers of newly entitled retired workers are determined by analyzing the 

ratio of new entitlements to previous levels of railroad employment using 2001-2018 new 

entitlement data in the analysis. After initial entitlement, a mortality rate of 5.2% for 

2019 is assumed based on analysis of recent Railroad Retirement Board financial 

interchange data, with mortality assumed to improve thereafter. For projections of newly 

entitled disabled workers a similar trend analysis based on prior employment is used. A 

“mortality” rate (deaths plus recoveries plus conversions to retired worker benefits) is 

determined using Railroad Retirement Board (RRB) data, with the rate assumed constant 

thereafter. 

Assuming a 90/10 male/female split, the average benefit level for an OASI railroad 

worker is calculated as a ratio to the average OASI retired worker benefit. This ratio is 

constant throughout the projection period and is derived by comparing MBR and 

Railroad Board data. Additionally, a constant loading factor based on the same data is 

applied to aggregate worker benefits to determine the aggregate benefit amounts for 

auxiliary OASI beneficiaries. This same approach is used to determine similar constants 

for DI railroad benefits. 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 for railroad are computed separately by trust fund. They are set 

at levels determined by short range in the short-range period. For years ni+10 to nf, they 

289
are computed similarly to OASDI administrative expenses. Administrative expenses in 

yr-1 are multiplied by (a) the change in the total number of worker beneficiaries, (b) the 

annual change in average wage, and (c) one minus the ultimate productivity growth. 

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. Average railroad earnings levels are assumed to grow with 

the increase in the average wage index, and railroad employment is assumed to decrease 

over time, both of which are in line with the Railroad Retirement Board’s own “most 

likely” projections. 

The interchange amount is calculated both on a fiscal year basis and at the date of the 

actual transfer from SSA to the Railroad Retirement Board (usually in the first week of 

June in the following year). These interchange amounts can be represented by 

RR_Transfer_FY(tf,yr) and RR_Transfer_CY(tf,yr+1). RR_Transfer_FY(tf,yr) is 

calculated by adding the cashflow amount to an interest amount, rr_interest(tf,yr), which 

includes interest accrued by the cashflow components along with a reconciliation of 

interest amounts from the previous fiscal year calculated transfer amount and the current 

year June interchange. If irate_presc(tf,year) is the prescribed interest rate used by the 

Railroad Retirement Board the interchange amount in June is: 

RR Transfer CY tf yr RR Transfer FY tf yr Irate esc yf yr _ _ ( , ) _ _ ( , 1) (1.0 (2.0 / 3.0) _ Pr ( , ))    

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 short-range 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. 

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.

A side model is used to determine the year in which the ultimate rate is achieved and to 

get the yield rate for each year between the end of the short-range period (ns) and the 

ultimate year by trust fund. The primary input to this model is a daily bond transaction 

log from the short-range office which is used to determine a monthly exposure to interest 

for the various cash flow items in addition to the expected duration of time various types 

of bonds are held. This calculation, and the bond holdings in December of the last year 

of the short-range projection period from the log, are then used to model a monthly longrange version of a bond transaction log. This model ultimately produces annual effective 

yield rates for OASI and DI which are read directly into the main cost model. 

The projection of interest income in a given year is the yield rate for that year multiplied 

290
by the average level of assets. As a formula, 

INT tf yr yield tf yr avg assets tf yr ( , ) ( , ) _ ( , ).  

The amount of assets in a trust fund at the end of a given year is estimated from the level 

of assets at the beginning of the year by: 

 Increasing the level for the tax contributions and taxation of benefits income 

received during the year (each exposed to the point in the year in which they are 

estimated to be received, on average), and 

 Decreasing the level for scheduled benefits, railroad interchange, and 

administrative expenses paid during the year (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 0.519, 

taxation of benefits are given an exposure of 0.625, railroad interchange is given an 

exposure of 0.583, and administrative expenses are given an exposure of 0.5. For 

scheduled benefits, separate OASI and DI exposures are determined through a side 

model. The exposure, ben_exp(yr), is larger than 0.5 in the early years of the projection 

period for both trust funds, whereas in later years OASI benefit exposures fall below 0.5 

with DI remaining above 0.5. The reason is that in the past, benefits were always paid on 

the 3rd of each month. Now benefits are paid out throughout the month, based on the 

birth date of the beneficiary. The reason for the differences between trust funds is that 

benefits are paid on the third of the month (exempting check cycling9

) for a higher 

proportion of DI beneficiaries due primarily to (1) concurrent receipt of SSI benefits, or 

(2) state payment of Medicare premiums. The average assets held by the trust funds for a 

given year is estimated by the formula 

_ ( , ) ( , ) 0.519 ( , )

0.625 ( , ) ( , ) ( , )

0.583 ( , ) 0.5 ( , ).

BOY avg assets tf yr ASSETS tf yr CONTRB tf yr

TAXBEN tf yr ben_exp tf yr BEN tf yr

RR tf yr ADM tf yr

  

  

  

Finally, the effective interest rate for the hypothetical combined OASDI fund is 

calculated as the sum of the magnitude of the individual fund interest amounts divided by 

the magnitude of the average level of assets of the individual funds: 

( ) ( ( ( , )) ( ( , ))) /

( ( _ ( , )) ( _ ( , )))

irate yr ABS INT OASI yr ABS INT DI yr

ABS avg assets OASI yr ABS avg assets DI yr

 



vii. Equations 4.3.7, 4.3.8 and 4.3.9 – Annual Values 

 

9

 Under check cycling many Social Security beneficiaries filing for benefits after April 1997 are paid on 

either the 2nd, 3rd, or 4th Wednesday of each month. 

291
The annual income rate for a trust fund is computed as the sum of payroll tax 

contributions plus taxation of benefits as a percentage of taxable payroll. 

 

(, ) (, ) _ _ (, ) . ( )

CONTRB tf yr TAXBEN tf yr ANN INC RT tf yr payroll yr

 

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 total cost. It is expressed as a percentage: 

(, ) (, ) . (, )ASSETS tf yr BOY TFR tf yr COST 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(tf,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 0.519 ( )) ( , ) ( ),

_ ( , ) (1 0.625 ( )) ( , ) ( ),

_ ( , ) (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 tf yr yield yr BEN tf yr v yr

PV RR tf yr yield yr

   

   

    

  ( , ) ( ),

and _ ( , ) (1 0.5 ( )) ( , ) ( ).

RR tf 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 

292
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 ( )) ( ) ( ).    

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. Let 

yr1 = the first year of the valuation period and yr2 = the ending year of the valuation. 

Then the summarized income rate is: 

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 

293
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   

Note that the unfunded obligation excludes the target fund. 

ix. Equation 4.3.14—Closed Group Unfunded Obligation 

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 2021, (2) attaining 62 or older in 

2021, and (3) attaining 15 to 61 in 2021. 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 0-

119 and sex, years 1951 through nf, updated yearly (years 1998 through nf

used in the SOSI) 

 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 

 Population counts for all retired workers, spouses, divorced spouses, and 

widow(er)s by year, sex, and age 95-119 (read in as a percentage of 95+ 

counts) 

 Distribution of assumed age differentials between aged spouses and workers 

ranging from -12 years to 15 years seniority for the worker by sex of the 

beneficiary, age of the beneficiary 62-74, and marital status 

 Distribution of assumed age differentials between aged widow(er)s and 

deceased workers from -6 years to +12 years 

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 

294
closed group. For instance, if the closed group were defined as individuals attaining age 

15 or later in 2021, a 3-year-old minor child receiving benefits in 2021 on the account of 

a retired worker aged 63 would be considered part of this closed group because the 

account holder was at least age 15 in 2021. 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 2021 through 2120, 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 0-119) 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. 

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 0-99, the number of projected workers comes directly from 

Economics group projections. 

 For ages 100-119, the total age 100+ amounts from Economics are distributed 

among ages 100 through 119 for each projection year using mortality rates 

derived by looking back 10 years and multiplying these populations by 10 

years of mortality increases by sex. 

 For ages 0-14, the average taxable earnings are obtained by analyzing 

historical 1998-2017 data of the average earnings at each age relative to age 

15 average earnings, and judgmentally assigning a ratio (to age 15 average 

earnings) for each age. 

 For ages 15-80, the average taxable earnings by age and sex come directly 

from the AWARDS subprocess. 

 For ages 81-99, the average taxable earnings are calculated as a weighted 

average of the average earnings for ages 76-80, weighted by the ratios of 

earnings between these ages and each age 81 through 99 for earnings years 

1998 through 2017. This is similar to the method to calculate average 

earnings for ages 0 through 14, though here we are using five anchor years 

instead of one. For ages 100-119, average taxable earnings are set equal to the 

average earnings calculated for age 99. 

Benefits 

Methodologies for computing benefits attributable to the closed groups differ among 

benefit categories, as described below: 

295
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 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 and Divorced Aged Spouses 

Closed Group calculations are done separately (although in the same manner) for 

aged wives, aged divorced wives, aged husbands and aged divorced husbands 

(combined), dually entitled aged wives, and dually entitled aged husbands. The 

number of aged spouse beneficiaries in each beneficiary category in current pay status 

(no dual entitlement) is provided by single year of age (up through 119). Then, for 

each single year of age, the program allocates total numbers of workers by age, from 

12 years younger to 15 years older than the aged spouse using an assumed categoryspecific distribution. Next, for each age of worker in current pay, the number of 

workers is multiplied by the weighted average retired worker benefit for that age; this 

is done for all ages. The closed group factors, then, are obtained by determining the 

proportion of total benefit amounts attributable to the given closed group (based on 

the worker’s age). 

Aged Widows and Divorced Aged Widows 

Closed Group calculations are done separately (although in the same manner) for 

aged widows, aged divorced widows, aged widowers, and aged divorced widowers. 

The number of aged widow(er) beneficiaries in current pay status (no dual 

entitlement) is provided by age from 60 to 119. 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 6 years younger to 12 years 

older than the aged widow using an assumed distribution. The same distribution is 

used in reverse order for aged widowers leading to an age range of 12 years younger 

to 6 years older for the deceased wife. For each age of deceased spouses aged 119 or 

296
younger, a real wage growth factor is applied to reflect ultimate real wage growth 

taken to the power of the number of years younger than age 119. 

(119 ker ) (1 _ 1.024) deceased wor age Benefitadj wg ult   

This exponent is intended to reflect differences in average levels of benefits, with 

younger deceased spouses 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. 

For aged widow(er)s in dual entitlement status (i.e. aged widow(er)s with a smaller 

worker benefit) we do similar calculations with the assumption that the age 

distributions are equal to the combined distribution of non-dually entitled aged 

widow(er)s and aged divorced widow(er)s. 

Other Beneficiary Categories 

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 

297
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). 

298