Long-Range OASDI Projection

Methodology

Intermediate Assumptions of the 2013 Trustees 

Report

July 2013

Office of the Chief Actuary

Social Security Administration
A. Flow Charts
Overview of Long-Range OASDI Projection Methodology

Process 2:

Economics

Process 1:

Demography

Process 4:

Trust Fund Operations and Actuarial Status

Process 3:

Beneficiaries

Social Security Administration

Office of the Chief Actuary

July 2013

Chart 1:
Trustees ultimate assumptions

Fertility

Mortality

Legal Immigration

Other Immigration

1.2 Mortality

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

U.S. resident population; medicare deaths and enrollments

Outputs: Historical and projected death probabilities 

1.4 Historical Population

Inputs: Historical U.S. population, undercounts, 

marital status data, other immigrant population 

data, and estimates of population in other 

components of Social Security area. 

Outputs: Historical Social Security area 

population by age, sex, and marital status 

(including starting population)

Historical other immigrant population by age 

and sex 

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 

by age, sex, and marital status; other immigrant population

by age, sex and marital status; children by age of parent and 

average family size; projected deferred action for 

childhood arrivals (DACA) population by age and sex

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 Legal Immigration

Inputs: Historical legal U.S. immigration 

levels 

Outputs: Historical and projected annual

 legal immigration and emigration levels 

Demography – Process 1

Social Security Administration

Office of the Chief Actuary

July 2013

Chart 2:

1.5 Other Immigration

Outputs: Projected annual other 

immigration and emigration levels 
Trustees Ultimate Economic Assumptions

Average real wage

Productivity

Average hours worked

Inflation

Full-employment unemployment rate

 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 

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 immigrant 

population and DACA 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

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

July 2013

 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 
 3.1 Fully-insured (FI) population

Inputs: Covered workers, median earnings,

and AWI (Economics); SS area population 

(Demography); DACA population (Demography) 

earnings distribution, historical FI population 

(historical and short-range projections).

Outputs: FI population (historical and projected)

3.1 Disability-insured (DII) population

Inputs: Historical DII population 

Outputs: DII population (historical and projected)

3.2 Disabled-worker beneficiary (DIB) population

Inputs: Base period incidence, recovery, and 

mortality rates. 

Projected Data -- Assumed ultimate changes in 

incidence rates, recovery rates, and mortality 

rates (Demography) from base period 

Outputs: DIB population and conversions to OAB 

(projected) 

3.3 Old-Age beneficiary (OAB) population

Inputs: Historical OAB population, labor force 

participation rates (Economics), and scheduled 

reductions for early retirement and increases for

delayed retirement 

Outputs: OAB population (projected) 

3.3 Auxiliary Beneficiaries of Retired and Deceased Workers

Inputs: Historical auxiliary beneficiaries of retired and deceased

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

number of children with at least one 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

July 2013

 3.2 DIB Auxiliary Beneficiaries

Inputs: Historical beneficiaries by type of 

benefit, Population (Demography), other 

relationships 

Outputs: Auxiliary beneficiaries of disabled 

workers by type of benefit (projected) 

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

Trustees ultimate assumptions

 Disability incidence rates 

 Disability recovery rates 

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

Inputs: Historical and projected short-range data on 

income taxation of benefits from Office of Tax Analysis

in the Department of the Treasury and data from 

current population survey 

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

 4. 3 Taxation of benefits (TOB)

Outputs: Taxes on benefits 

 4.3 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, DIB population,

married and divorced aged population (Demography), 

Cost-of-Living Adjustments (Economics), post-entitlement factors, 

assumed benefit relationships between workers and auxiliaries, shortrange estimates of benefit payments 

Outputs: Scheduled benefit payments during year, average scheduled

benefits 

 4. 3 Railroad 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

July 2013

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), Tax Maximum; 

historical and projected fully insured rates by sex and age, 

historical and projected (Beneficiaries)

Outputs: Projected AIME distributions for new 

entitlements 
8

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. 

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

represented as being dependent in an equation, where the dependent variable is defined in 

terms of one or more independent variables. Independent variables may include previously 

calculated dependent variables or data provided from outside the subprocess. Other key 

variables are referenced by “(·)” following the variable name. This indicates that the 

calculation of this variable can not easily be communicated by an equation and, thus, requires 

a more complex discussion. 

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

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

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

from outside the Social Security Administration (e.g., estimates of the U.S. population). Data 

description includes data source and data detail (e.g., define age detail of data). In addition, 

an indication of how often additional data are expected to be received is included. 

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

level of disaggregation of the data. 
9

Process 1:

Demography
10

1. Demography

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

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

For the 2013 report, the projection period covers the years 2013 through 2087. 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, 

LEGAL IMMIGRATION, HISTORICAL POPULATION, OTHER 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

LEGAL 

IMMIGRATION

• Legal immigrants, by age and sex

• Legal emigrants, by age and sex

• Adjustments of status from other than legal (OTL) status to legal status, 

by age and sex

HISTORICAL 

POPULATION

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

year of age, sex, and marital status

• Historical estimates of the OTL population, by single year of age and sex

OTHER 

IMMIGRATION

• OTL immigrants, by age and sex

• Data (“fixed exits” and “exit rates”) used to project OTL emigration, by 

age and sex

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, developed by 

starting with the latest estimates from HISTORICAL POPULATION and 

projecting these estimates forward using outputs from all other 

subprocesses

• Projected OTL populations, by single year of age and sex, developed by 

starting with the latest OTL estimates from HISTORICAL 

POPULATION and projecting these estimates forward using values from 

MORTALITY, LEGAL IMMIGRATION, and OTHER IMMIGRATION

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

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

residents of the U.S. and its territories, citizens living abroad, and beneficiaries living abroad.
11

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 resident 

population by single year of age for females. Age-specific birth rates ( z

x b ) for a given year z are 

defined as the ratio of (1) births ( z Bx ) during the year to mothers at the specified age x to (2) the 

midyear female population ( z Px ) at that age. The total fertility rate z TFR summarizes the agespecific 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 number of children born to a woman if she were to survive her childbearing

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

The FERTILITY subprocess combines the historical values of z

x b and z TFR and assumed future 

values of the TFR to develop projections of z

x b . The primary equations of this subprocess are 

given below:

z

x b = zx b (

.

) (1.1.1)

= ∑x

z

x

z TFR b (1.1.2) 

1.1.b. Input Data

Trustees Assumptions -

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

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

intermediate assumptions underlying the 2013 Trustees Report, the ultimate TFR is 2.0 and it is 

assumed to be reached in 2037.

Other input data - 

• From the NCHS, annual numbers of births by age of mother2 (10-14, 15, 16, 17, ..., 48, 49-

54) for years 1980-2010. In general, the NCHS provides an annual update including one 

additional year of final birth data and the previous historical years are only updated if the

NCHS makes a historical revision to their data. 

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

occurred at age 14 and ages reported to mothers older than 49 are treated as having occurred at age 49.
12

• From the NCHS, preliminary TFR for 2011. In general, NCHS provides a preliminary TFR 

only for the year after the last final data year.

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

year of age for ages 14-49 for 1980-2010. In general, each year, Census provides updated 

data for years after the most recent decennial census.

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

1917-1979. No updates of these data are needed.

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 

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

x

z

z x

x P

B b = , 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 ultimate assumed total fertility rate. This process consists 

of the following steps:

1. Averaged birth rates by age group,

3 designated as z

x b5 , are calculated from the age-specific 

birth rates z

x b for each year during the period 1980-2010.

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

5 bx values from the last five 

years of historical data are averaged using weights of 5, 4, 3, 2, and 1 for years 2010, 2009, 

2008, 2007, and 2006, respectively.

3. For each z

x b5 age group series, the slope of the least squares line is calculated based on a 

regression over the period 1985-2010.

4. For 2011, each of the seven starting values of z

5 bx (from Step 2) is projected forward by 

adding 100 percent of their respective slope (from Step 3).

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

groups calculated are: 14-19, 20-24, 25-29, 30-34, 35-39, 40-44, and 45-49. 
13

5. Then, a preliminary total fertility rate for 2011, 2011 TFRp , is calculated such that, in general, it 

is equal to 5 times the sum of each 2011

5 bx . For the age group 14-19, 6 times the sum is used 

since this age group actually contains one additional age.

6. For 2011, the preliminary TFR released by NCHS was 1.8945 and thus the Trustees set

2011 TFR equal to 1.8945. 

7. To ensure the assumed total fertility rate is achieved for 2011, each value of 2011

5 bx (from 

Step 4) is now multiplied by the ratio of the assumed 2011 TFR (from Step 6) and the 

respective value of 2011 TFRp (from Step 5).

8. For 2012, each final z

x b5 for 2011 is projected forward by adding 96 percent of the respective 

slope (from Step 3). For subsequent projection years (2013-2037), an arithmetically 

decreasing portion of the slopes

4 is added to the previous year’s final values of z

5 bx to get 

preliminary values of z

5 bx . 

9. For years 2012 and later, a preliminary total fertility rate, z TFRp , is calculated from the 

preliminary values of z

5 bx in Step 8 and is calculated in the same manner as in Step 5.

10. Then, for each year, an adjustment is made so that the annual z TFR is consistent with the 

Trustees’ assumed TFRs. As mentioned in Step 6, 2011 TFR is assumed to be 1.8945. From 

2012 – 2021, z TFR is assumed to increase consistent with the economic recovery where 

greater increases in the TFR occur in the middle of the period. For years after 2021, z TFR is 

assumed to decrease linearly from 2021 TFR until reaching the ultimate value in 2037.

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

5 bx (Step 8) is multiplied 

by the ratio of the assumed z TFR (Step 10) and the respective value of z TFRp (Step 9).

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

5 bx into single age birth 

rates by multiplying the final z

5 bx values for each year (Steps 7 or 11) by the ratio of the 

single year z

x b to the z5 bx for each of the respective ages and age groups as calculated in the 

last year of complete historical data (Step 1). Then, minor adjustments correct rounding 

issues.

 4 For each year of the projection, the slope is reduced by four percentage points.
14

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.

5

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

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

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

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

the projection period ( u

y AAx ) 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 ( ) is defined as the average number of years of life remaining for people 

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

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

of overall mortality for that year. 

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

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

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

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

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

 

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

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

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

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

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

Statistics.
15

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

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

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

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

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

population.

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

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

 yMx = yMx (·) (1.2.1)

 

 yAAx = yAAx (·) (1.2.2)

qx = qx (·) (1.2.3)

 

 = (·) (1.2.4)

∑

∑ ⋅

=

x

y x

z

y x s

x

y x

z

s SP

SP M

ADR

,

(1.2.5)

∑∑

∑∑ ⋅

=

s x

y x s

s

z

y x s

x

y x s

z

SP

SP M

ASDR

,

, ,

(1.2.6)

where z

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

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

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

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

1.2.b. Input Data

Trustees Assumptions -

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

for the yAAx by sex, age group,

6 and cause of death.7

 The average annual percentage 

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

 6 Age groups are: less than 15, 15-49, 50-64, 65-84, 85+ 7 The five causes of death are: Cardiovascular Disease, Cancer, Violence, Respiratory Disease, and Other
16

ultimate rates of reduction by sex, age group, and cause of death can be found in Appendix 1.2-

1.

NCHS Data -

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

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

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

•Annual numbers of deaths by sex, age group, and cause for the period 1979-2009. Generally, 

a new year of data is received each year. In addition, revised data are often available for 

years beginning with 1999. (1999 was the starting year of the latest international 

classification of diseases – ICD10.)

•The monthly number of births, by sex, for years 1938-2009. These data are updated 

annually, when the NCHS provides an additional year of data. 

•The number of infant deaths, by age, sex, and age group,

8 for years 1938-2009. These data 

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

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

generally 5-year age groups and are as follows: 0, 1-4, 5-9, 10-14, ..., 95+). These data 

are updated as resources are available.

•The population of states in the Death Registration area by age group9 and sex, for years 1900-

1939. These data are not updated.

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

years 1900-1967. These data are not updated.

U.S. Census Bureau Data -

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

1980-2009. Each year, Census provides an additional year of data and updated data for 

years after the most recent decennial census.

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

group10 for the years 1995 and 1996. These data are updated as resources are available.

 8

 Age groups are: under 24 hours, 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, 4 years 9 Age groups are: 0, 1-4, 5-14, 15-24, ..., 75-84, 85+ 10 Age groups are: 15-17, 18-19, 20-24, 25-29,..., 40-44, 45-54, ..., 65-74, 85+
17

•The resident population by sex, marital status, and age group,

11 as of as of July 1, 1995 and 

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

incorporated.

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

intervals). These data are not updated.

•The resident population, by sex and age group,12 for 1940-2000. These data are not updated. 

CMS Data -

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

1968-2010. These data are updated annually, when the CMS provides an additional year 

of preliminary data and replaces the prior year’s preliminary with final data.

•Annual numbers of Medicare enrollments (who are insured for Social Security benefits), by 

sex and single year of age (ages 65 and over), for the period 1968-2011. These data are 

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

replaces the prior year’s preliminary with final data.

Other input data -

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

population by sex, marital status, and single year of age (5 through 100+). These data are 

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

 11 Age groups are: 15-19, 20-24, 25-29, ..., 90-94, 95+

12 Age groups for years prior to 1980 are: 0, 1-4, 5-9, ..., 80-84, 85+. For years 1980 and later, the age groups are: 0, 

1-4, 5-9, ..., 90-94, 95+.
18

1.2.c. Development of Output

Equation 1.2.2 - Average Annual Percentage Reduction in the Central Death Rates ( y AAx )

The y AAx , by sex and cause, are calculated based on the decline in the yMx for the period 1997

through 2009, and distributed by 21 age groups,

13 2 sexes, and 5 causes of death.14 The values 

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

the logarithms of the yMx.

The ultimate assumed values for the central death rates ( u

y AAx ), as set by the Board of Trustees 

of the OASI and DI Trust Funds, are assumed to be reached in the 25th year of the 75-year 

projection period. The assumed ultimate values are specified by five causes of death for the 

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

female values are set equal.

The values of y AAx , by the 21 age groups, sex, and cause, for 2010 through 2012, are assumed 

to equal the average y AAx based on the decline in the yMx for the period 1997-2009. Available 

Medicare preliminary data is used for overall levels with the last available NCHS data year cause 

of death percentages carrying forward. For years after 2012, a method of graduation is used that 

causes the absolute difference between the current y AAx and the ultimate u

y AAx to decrease 

rapidly until it reaches the Trustees’ ultimate assumed value, u

y AAx . This is accomplished by 

repeating the following steps for each of the first 25 years of the projection:

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

ultimate assumed u

y AAx is calculated.

2. If the ultimate assumed u

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

the difference is subtracted from the ultimate assumed u

y AAx . If the ultimate assumed 

u

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

ultimate assumed u

y AAx .

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

ultimate assumed values, u

y AAx . 

 13 Age groups are: 0, 1-4, 5-9, 10-14, ..., 90-94, and 95+ 14 The five causes of death are: Cardiovascular Disease, Cancer, Violence, Respiratory Disease, and Other.
19

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 5 causes of death. The starting year for the projections of the yMx is 2009, 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 value for the most recent year falling 

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

weights are 0.2, 0.4, 0.6, and 0.8 for the earliest four years of the 12 years and are 1.0 for all 

other years.

For years after 2009, yMx are projected, by sex and cause of death, by applying the respective 

y AAx to the prior year yMx. 

Equations 1.2.3 – Probabilities of death (qx)

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 accessed at the 

following internet site:

http://www.socialsecurity.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 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 
20

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: 

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 

accessed at the following internet site: 

http://www.socialsecurity.gov/OACT/NOTES/s2000s.html. (Choose study number 120; then 

section IV.A in the table of contents.)
21

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

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

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

calendar years 1995 and 1996.

Equation 1.2.4 –Life expectancy 

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

expectancy, , from the probabilities of death (qx,). This study can be accessed at the following 

internet site: http://www.socialsecurity.gov/OACT/NOTES/s2000s.html. (Choose study number 

120; then IV.A in the table of contents.)
22

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 ultimate rates are the same for males and females, the historical rates differ.

Table 2.3: Average Annual Rates of Reduction in Central Death Rates by Age Group, Sex, and Cause

Historical Alternative II* Historical Alternative II*

2012 TR 2013 TR 2012 TR 2013 TR 

1979 to 2009

1999 to 

2009

2036-

2086

2037-

2087

1979 to 

2009

1999 to 

2009

2036-

2086 2037-2087

Under Age 15 Male Female

Cardiovascular Disease 2.66 1.68 2.3 2.3 2.51 1.80 2.3 2.3

Cancer 2.55 1.84 1.5 1.5 2.05 1.31 1.5 1.5

Violence 2.91 2.44 1.0 1.0 2.34 2.09 1.0 1.0

Respiratory Disease 2.78 0.40 2.0 2.0 2.81 0.89 2.0 2.0

Other 2.39 1.00 1.7 1.7 2.28 0.90 1.7 1.7

Resulting Total ** 2.52 1.30 1.55 1.56 2.31 1.13 1.57 1.58

Ages 15 - 49 Male Female

Cardiovascular Disease 2.06 1.12 1.5 1.5 1.20 0.92 1.5 1.5

Cancer 1.80 2.24 1.5 1.5 1.62 1.66 1.5 1.5

Violence 0.86 -0.60 0.7 0.7 0.14 -1.51 0.7 0.7

Respiratory Disease 0.80 0.17 0.5 0.5 -0.28 -0.82 0.5 0.5

Other -0.01 2.65 0.8 0.8 -0.62 0.69 0.8 0.8

Resulting Total ** 1.06 0.83 0.87 0.87 0.54 0.31 0.94 0.94

Ages 50 - 64 Male Female

Cardiovascular Disease 3.17 2.78 2.2 2.2 2.62 3.16 2.2 2.2

Cancer 1.60 1.95 1.5 1.5 1.31 2.10 1.5 1.5

Violence 0.49 -2.93 0.5 0.5 -0.12 -3.75 0.5 0.5

Respiratory Disease 1.18 0.56 0.7 0.7 -0.62 0.65 0.7 0.7

Other -0.39 -1.03 0.6 0.6 -0.44 -0.34 0.6 0.6

Resulting Total ** 1.73 1.08 1.05 1.05 1.15 1.39 1.06 1.06

Ages 65 - 84 Male Female

Cardiovascular Disease 3.14 4.70 2.2 2.2 2.74 4.40 2.2 2.2

Cancer 0.67 1.86 0.9 0.9 -0.27 1.00 0.9 0.9

Violence 0.71 0.21 0.5 0.5 0.02 -0.15 0.5 0.5

Respiratory Disease 0.44 2.08 0.3 0.3 -2.44 0.63 0.3 0.3

Other -0.81 -0.44 0.3 0.3 -1.61 -0.90 0.3 0.3

Resulting Total ** 1.51 2.45 0.78 0.78 0.64 1.70 0.73 0.73

Ages 85 and older Male Female

Cardiovascular Disease 1.50 3.32 1.2 1.2 1.66 3.61 1.2 1.2

Cancer -0.50 1.31 0.5 0.5 -0.66 0.48 0.5 0.5

Violence -0.66 0.02 0.3 0.3 -1.04 -1.44 0.3 0.3

Respiratory Disease -1.02 2.66 0.2 0.2 -2.26 1.59 0.2 0.2

Other -2.36 -2.26 0.2 0.2 -3.31 -2.86 0.2 0.2

Resulting Total ** 0.15 1.53 0.53 0.51 -0.01 1.13 0.50 0.49

Total Male Female

Cardiovascular Disease 2.58 3.81 2.25 3.84

Cancer 0.75 1.80 0.27 1.23

Violence 0.75 -0.64 0.10 -1.33

Respiratory Disease 0.09 2.10 -2.04 0.88

Other -0.82 -0.63 -1.56 -1.29

Resulting Total ** 1.18 1.83 0.75 0.75 0.55 1.36 0.71 0.70

* Alternative 1 is 1/2 times Alternative 2; Alternative 3 is 5/3 times Alternative 2.

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

75 year projection period.
23

1.3. LEGAL IMMIGRATION

1.3.a. Overview

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

been granted legal permanent resident (LPR) status. Legal emigration consists of legal 

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

elsewhere. 

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

estimates of legal immigration (Lz

) and legal emigration (Ez), by age and sex, based on 

assumptions set by the Trustees for each category. In addition, the LEGAL IMMIGRATION 

subprocess disaggregates the estimates of Lz into those who have been admitted into the United 

States during the year (NEWz) and those who adjusted from the other-immigrant population to 

LPR status (AOSz).

Each fiscal year,

15 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 legal immigration and emigration estimates by age 

and sex. 

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

the 75-year projection period are summarized below:

( ) , , = ⋅ z

x s

z NEWx s NEW (1.3.1)

( ) , , = ⋅ z

x s

z AOSx s AOS (1.3.2)

z

x s

z

x s

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

( ) , , = ⋅ z

x s

z Ex s E (1.3.4)

z

x s

z

x s

z NLx,s = L , − E , (1.3.5)

1.3.b. Input Data

Trustees Assumptions -

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

values for legal immigration and legal emigration. For the 2013 Trustees Report, the ultimate 

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

specified calendar year.
24

values for legal immigration and emigration are 1,050,000 and 262,500, respectively (both 

reached in 2013). 

Office of Immigration Statistics –

• Historical legal immigration by fiscal year (1941-1995), 5-year age group (0-4, 5-9, ..., 80-

84), and sex. These data will not be updated.

• Legalizations due to IRCA by 5-year age group and sex for the years 1989-1996. These data 

will not be updated.

Department of Homeland Security –

• Historical legal immigration by fiscal year (1996-2011), single year of age (0 through 99), 

sex, 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.

• Total adjustments of status for the years 1966 to 1995 (OCACT further estimates total 

adjustments of status for 1963-1965). These data will not be updated.

U.S. Census Bureau –

• Unpublished estimates of annual legal emigration by five-year age groups (0-4, 5-9, ..., 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 -

• Legal emigration conversion factors. These estimates were developed internally by five-year 

age groups (0-4, 5-9, ..., 80-84) and sex to reflect the fact that the estimated number of 

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

Security area. These data are updated when annual legal emigration estimates are updated 

(see above).

1.3.c. Development of Output

Equations 1.3.1 and 1.3.2 – Legal Immigration

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

projection period. In order to incorporate the numbers of new immigrants into the Social 
25

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 immigrants and 

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

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

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

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

following steps: 

1. Refugee and Asylee LPR admissions are subtracted from the 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 arrival and adjustment of status, the historical data for the 

last 10 years (from 2002-2011) are combined into an average age-sex distribution.

z NEWx,s , the expected number of new arrival legal immigrants by age (x) and sex (s), is

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

new arrivals. The Trustees’ assumed number of adjustments of status is multiplied by the agesex distribution of adjustments of status to calculate z AOSx,s .

Equation 1.3.4 – Legal Emigration

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

period. This is done by setting the ratio of emigration to legal immigration. For the 2013

Trustees Report, the ratio is set at 25 percent.

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

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

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

Census that are based on changes between the 1980 and 1990 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.
26

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:

∑∑= =

=

f

s m x

x s

z

x s

z Ex s L EDIST

84

0

, , , .25( )*
27

1.4. HISTORICAL POPULATION

1.4.a. Overview

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

area population for the period 1941 through 2011. The Social Security area population consists 

of:

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

• Net census undercount plus

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

Islands, and American Samoa plus

• Federal civilian employees overseas plus

• Dependents of armed forces and federal civilian employees overseas plus

• Residual beneficiaries living abroad plus

• Other citizens overseas

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

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

publishes an estimate of the post-censal population. 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 ( z Px,s ) and other than 

legal population ( z Ox,s ). 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 ( z Px,s,m ). These estimates are then used as the basis for 

the PROJECTED POPULATION subprocess described in section 1.8. The primary equations 

for this subprocess, 1.4.1, 1.4.2, and 1.4.3, are given below:

z Px,s = z Px,s (·) (1.4.1)

z Px,s,m = z Px,s,m (·) (1.4.2)

z Ox,s = z Ox,s (·) (1.4.3)
28

1.4.b. Input Data

Long-Range OASDI Projection Data -

Demography

• Probabilities of death from MORTALITY, by age last birthday and sex, for years 1941-

2011. These data are updated every year. 

• The number of new legal immigrants by age and sex for years 1941-2010. These data 

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

• The number of legal emigrants by age and sex for years 1941-2010. These data are 

from the LEGAL IMMIGRATION subprocess and are updated each year.

• The number of adjustments of status by age and sex for years 1941-2010. These data 

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

• The number of “other immigrants” legalized under the Immigration Reform and Control 

Act of 1986 (IRCA) from LEGAL IMMIGRATION. These data are reproduced each 

year.

• Birth rates by single year of age of mother (14-49) for the years 1941-2011 from the 

FERTILITY subprocess. These data are updated each year.

U.S. Census Bureau Data -

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

July 1 (1940-1979) by sex and single-year of age through 84, and for the group aged 85 

and older. These data are generally not updated.

• Estimates of the U.S. resident population for each 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.

• Estimates of total U.S. residential population and total residential population plus Armed 

Forces overseas population for each January of each Census year from 1990 and 2010. 

New decennial Census estimates come out about every ten years.

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

overseas as of each July 1 (1980-2011) 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.
29

• Estimates of the population by age group,

16 sex, and marital status for years 1940-2010

from the CPS. These data are not updated.

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

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

• Estimates of the population by marital status, sex, and age from the American 

Community Survey (ACS) public use microdata samples (PUMS) for years 2000 –

2011. An additional year of data is available each year.

• Undercount factors by single year of age (0-85+) and sex, estimated using post-censal 

survey data. These data are updated after each decennial census.

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

Northern Marianas, and American Samoa for years 1951-2011. 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.

• Decennial Census population estimates, by varying degree of age detail and sex, for 

Censuses from 1950 – 2000 for territories and components outside the 50 states, D.C., 

and armed forces overseas. Most data is 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 all ages starting in 1980. New estimates are added as they become available.

• July populations of the territories by single year of age and sex from 2000 – 2011. An 

additional year of data is available each year.

• From American Community Survey (ACS) public use microdata samples (PUMS), 

number of existing marriages from 2000 – 2011 by age group of husband crossed with 

age group of wife. An additional year of data is available each year.

• From decennial Census public use microdata samples (PUMS) via the University of 

Minnesota’s IPUMS website, number of existing marriages for Census years 1940 –

2000 by age group of husband crossed with age group of wife. New estimates are 

added as they become available.

• Estimates of net immigration by age and sex of the U.S. residential plus armed forces 

overseas (USAF) population from 2000 through 2011. 

• 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 

 16 Age groups are: 15-17, 18-19, 20-24, 25-29, ..., 55-64, 65-74, 75-84, 85+
30

international sources are derived from different years but center around the year 2003. 

Additional data will be updated as they become available. 

Other input data -

• From the Centers for Medicare and Medicaid (CMS), Medicare enrollments by single 

year of age (85-100+) and sex for years 1968-2011. The last year of data is provisional. 

Each year, the CMS provides a final year of data to replace the prior year’s provisional 

data, and a new provisional year of data.

• 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.

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

Beneficiaries living abroad for most years 1953-2010. Age group data is also available. 

For each Trustees Report, an additional year of data is available. Age group data is 

updated for each decennial Census year.

• From the National Center for Health Statistics (NCHS), the sex ratio (number of males 

born per female) for years 1941 – 2010. Each year, NCHS provides another year of 

data. For 2011, the sex ratio is assumed to be 1.05, the same as the assumed projected 

sex ratio.

• From the Department of Homeland Security (DHS), the total number of other immigrants 

(unauthorized immigrants plus nonimmigrants) from 2005 – 2011.

• From the Office of Personnel Management (OPM), total estimates of the number of 

federal employees overseas from July 1998 – July 2009. The July 2010 and 2011

values are assumed to be equal to the July 2009 value. These estimates are updated as 

they become available on the OPM website.

• 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 – 2010 are available. These 

estimates are updated as they become available.

• From the Department of Defense, total numbers of armed forces in Puerto Rico, Virgin 

Islands, Guam, and American Samoa each Census year starting in 1990. These data are 

updated as they become available.

1.4.c. Development of Output

Equation 1.4.1 – Historical Population by age and sex ( z Px,s )
31

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

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

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

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

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

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

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

estimated using post-censal survey data from the 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 civilian residents of 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 z Px,s as of January 1st for certain “tab years” (1941, 

1951, 1957, 1961, each decennial Census year [1970 through 2000], and the last year of 

historical data [2011 for the 2013 Trustees Report]). For ages 0-84, z Px,s for each tab year is set 

equal to the averaged surrounding July 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 and years past 2010) plus an undercount adjustment plus other component 

populations. For ages 85 and over, z Px,s 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 averaged surrounding July 1 U.S. population and armed forces 

overseas counts from the Census Bureau (modified by OCACT mortality rates and Census 

USAF net immigration for years past 2010) plus an undercount adjustment plus other component 

populations for ages 85 and over for each sex. 

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 legal immigration

(or 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 ( z Px,s,m )
32

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 Census years 1940 – 2000 

from Census public use microsample data (PUMS) samples. These data are aggregated by age 

group of husband crossed with age group of wife. Additional tabulations from the American 

Community Survey from 2000 – 2011 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.

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

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

each age group and sex based on either the CPS, more detailed Census numbers, if available, or 

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

age groups, an average of the surrounding groups replaces the original value. After verifying the 

percentages are close to the original data (and adjusted if needed), 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 males equals the number of married females. Next, the marital prevalence grids are 

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

diagonal in the grid. 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.

Equation 1.4.3 – Historical Other Than Legal (OTL) Population by age and sex ( z Ox,s )

This subprocess also estimates historical levels of “other immigrants” 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, legal 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 OTL deaths (using the same death 

rates as for the total population), an initial OTL 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 OTL populations are set equal to the values that linearly 

grade from the final OCACT January 2000 total OTL population to a DHS-based January 2005 

total OTL population. From January 2005 through January 2011, the total OTL population is 
33

forced to match DHS-based total OTL population estimates. The total OTL population from the 

DHS is equal to the sum of their estimates for unauthorized immigrants and nonimmigrants. 

Nonimmigrants include categories such as students, temporary workers, and exchange visitors.
34

1.5. OTHER IMMIGRATION

1.5.a. Overview

The term “other 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 legally admitted for a limited period of time, such as 

temporary workers and foreign students) in addition to undocumented immigrants living in the 

U.S. Other emigration includes other immigrants who depart the Social Security area for another 

country, in addition to those who adjust status to become LPRs.

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

estimates of other immigration (Oz), by age and sex, based on assumptions set by the Trustees 

for each category. Estimates of projected other emigration are not developed in this subprocess, 

but rather are developed in the PROJECTED POPULATION subprocess, documented in section 

1.8.

The Census Bureau estimated the aggregate number of net other immigrants who entered the 

country during 1975-1980, by age and sex. These historical data are used as a basis for 

developing age-sex distributions that are applied to the Trustees’ aggregate other immigration 

assumptions to produce annual other immigration estimates by age and sex. 

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

the 75-year projection period are summarized below:

( ) , , = ⋅ z

x s

z Ox s O (1.5.1)

1.5.b. Input Data

Trustees Assumptions -

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

values for other immigration. The Trustees set the ultimate annual level at 1,400,000 persons per 

year for each year beginning in 2022. Due to the recent recession, they assume that the level of 

other immigration was 1,000,000 in 2011, and will gradually increase above the ultimate level to 

1,600,000 by 2018, followed by a gradual decrease until 2022 when the ultimate is reached.

Long-Range OASDI Projection Data -

Demography

• 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

1941-2101. These data are updated each year.
35

• Historical net other immigration by single year of age (0-100+) and sex for years 1961-2010. 

These data are updated each year. 

• Historical new arrivals by single year of age (0-83 and 84+) and sex for years 1941-2010. 

These data are updated each year.

• Historical adjustments of status by single year of age (0-83 and 84+) and sex for years 1941-

2010. These data are updated each year.

• Historical adjustments of status by single year of age (0-99) and sex, for years 1996-2011. 

These data are updated each year.

Department of Homeland Security –

• Components of the Unauthorized Immigrant Population by year for 2005-2011, used to 

calculate undercount factors. These data are updated each year.

• Recent arrivals by 5-year age group and sex for 2006. These data are updated occasionally 

(based on having new data from an outside source and on OCACT resource time constraints).

• An estimate of the size of the other immigrant population as of January 1, 2006. These data 

are updated occasionally (based on having new data from an outside source and on OCACT 

resource time constraints).

U.S. Census Bureau –

• From the American Community Survey (ACS), foreign-born new arrivals by ACS year 

(2000-2011), entry year (1900-2011), age (0-100) and sex. These data are updated each year.

• Unpublished tabulations of the cumulative number of net other immigrants entering the 

country during 1975-1980 by five-year age groups (0-4, 5-9, ..., 80-84) and sex. These data 

are updated occasionally (based on having new data from an outside source and on OCACT 

resource time constraints).

• Foreign born non-citizen population by 5-year age groups (0-4, 5-9, ..., 80-84, 85+) and sex

from the March 2000 Current Population Survey. These data are updated occasionally 

(based on having new data from an outside source and on OCACT resource time constraints).

Other input data -

• Internally developed total estimated number of non-immigrants in 2000. These data will not 
36

be updated.

• Internally developed persistence factors. These data will not be updated.

• Estimate of the residual immigrant population by age group (0-17, 18-49, 50-64, and 65+) 

and sex as of January 1, 2000, from Population Division Working Paper 61.

17 These data 

will not be updated.

• Internally developed age distribution factors to smooth out age 0-4 foreign born population 

into single year of age. These data will not be updated.

• Internally developed alternate estimate of the net other population during the period 2000-

2005. These data will not be updated.

1.5.c. Development of Output

Equation 1.5.1 – Other Immigration

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

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

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

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

distribution of non-adjusting other immigrants. 

The age distribution of the adjustments of status is modified to incorporate a five-year setback 

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

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

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

immigration during the period 1975-80, using internally developed levels of persistence. The 

two age distributions are then combined using the following formula:

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

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

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

immigration. For the 2013 Trustees Report, this w equals 0.417. The assumed total level of 

other immigration is denoted by z TO . Thus, for each year (z) other immigration is defined by 

the following equation:

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

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

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

status may die or return to their native country prior to doing so.
37

x s

z z Ox,s TO ODIST , = ∗

Projected other departures are calculated later in the PROJECTED POPULATION subprocess, 

using two key inputs that are calculated in the OTHER IMMIGRATION subprocess. Ideally, 

projected other departures would be modeled utilizing rates of emigration by age, sex, and year 

of entry. However due to the scarcity of available data on other immigrants, calculating rates of 

emigration by this level of detail is not feasible at this time. As an alternative, the total level of 

departures was modeled based on changes in the estimated size of the other immigration 

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

time was split into two pieces (1) a fixed component that is expressed as a percentage of recent 

arrivals and (2) a rate based component that varies by age and sex. The rate based component is 

calculated later in the PROJECTED POPULATION subprocess.

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

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

adjust status. The following equation shows the calculation:

z FDx,s x s

z Ox s Nadj 2, 2, 0.10( )* = − −

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

the percentage of new other immigrants who are not expected to have the potential to adjust 

status. Since z Ox,s is constant for each year of the long-range projection period after 2014, the 

values of z FDx,s remain fixed for each year z.

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

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

were calculated and averaged over the period 2000-05 as follows: 

( ) 















− − −

− = z

x s

z

x s

z

x s

z

x s

z

x s

z

x s

x s OP q FD AOS

OD FD

r Average

, , , ,

, ,

, * 1 for z = 2000, 2005

where z OPx,s is an alternate estimation of the historical other than legal population, which is 

calculated using the total level of the other than legal population in 2000, the Department of 

Homeland Security (DHS) estimate of the total other than legal population in 2006, probabilities 

of death, levels of other immigrants, assumed fixed levels of other emigrants, and adjustments of 

status.
38

The other than legal population, z OPx,s , for the year 2000 is calculated as the sum of the 

unauthorized population and the non-immigrant19 population for that year. The unauthorized 

population for these two years is calculated by taking the following steps: 

1. Compute the foreign born non-citizen age distribution by taking the foreign born non-citizen 

population by 5-year age groups (from the Current Population Survey) and applying the 

Beers method to get single year of age values.

2. Apply this foreign born non-citizen age distribution to the Census residual unauthorized 

population (from Technical Working Paper 61), after first grouping ages 18-49 of the 

residual unauthorized population.

3. Regroup the single age values into 5-year age groups, and smooth the data by applying the 

Beers method to get single year of ages 0-84.

4. Compute single year of age values for ages 85-100 by applying the same age distribution as 

the 85-100 SSA population for 2000.

The non-immigrant population is calculated by using the recent arrivals by 5-year age group 

(from the DHS) to break out the total estimate of non-immigrants (from the DHS) by 5-year age 

groups, then applying the Beers method to get single year of age values. Note that in both of the 

above cases where the Beers method is used, a separate method is used to break out the 0-4 age 

group, using internally developed factors, since these ages for immigrants would behave 

differently than the normal population would behave using the Beers method. 

The other than legal population by age and sex for a given year (2001-2005) is calculated as:

( ) 1

1,

1

1,

1

1,

1

1,

1

, 1, * 1 −

−

−

−

−

−

−

−

− = − − + − − z

x s

z

x s

z

x s

z

x s

z

x s

z OPx s OP q O OD AOS

where z

x s q , is the probability of death (calculated in the MORTALITY subprocess), z Ox,s is the 

other immigration, z ODx,s is the number of other departures, and z AOSx,s is the number of 

adjustments of status.

The HISTORICAL subprocess calculates the historical net other than legal immigration. In the 

OTHER IMMIGRATION subprocess, these values are further split into other than legal 

immigration and emigration by age and sex for 1999-2010. The ACS provides the number of 

foreign born new arrivals which is then used to separate the net other than legal immigration. 

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 foreign born residing in Puerto 

Rico. The estimated other than legal immigration is calculated by taking the Beers’d foreign 

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

The estimated other than legal emigration is then calculated as the difference between the net 

 19 The term non-immigrant refers to a foreign national who has entered the United States temporarily for a specific 

purpose (as defined by the DHS).
39

other than legal immigration (calculated in the HISTORICAL subprocess) and the estimated 

other than legal immigration. A series of steps are then taken to smooth the two categories.
40

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. 

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

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

1995. The American Community Survey (ACS) public use microdata samples (PUMS) started 

asking if a person was married in the last 12 months in 2008. Using this question along with 

ages of spouses, new marriages grids by age-group-of-husband crossed with age-group-of-wife 

were developed. For the years in between the NCHS and ACS data, the marriage grids were 

linearly interpolated. These NCHS and ACS data are used to adjust the more detailed age-ofhusband crossed with age-of-wife rates from the earlier years.

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

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

midyear unmarried population at those ages ( z Px, y ). The theoretical midyear population is 

defined as the geometric mean20 of the midyear unmarried males and unmarried females.

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

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

the MRA as of July 1, 1982. The first step in calculating the total age-adjusted central marriage 

rate for a particular year is to determine an expected number of marriages by applying the ageof-husband-age-of-wife specific central marriage rates for that year to the geometric mean of the 

corresponding age groups in the standard population. 

 20 The geometric mean, as used in this document, is the square root of the product of two numbers.
41

The z AMˆR is then obtained by dividing:

• The expected number of marriages by 

• The geometric mean of (a) the number of unmarried males, ages 15 and older, and (b) the 

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

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

The equations for this subprocess, 1.6.1 and 1.6.2, are given below:

z

x y

z mx, y m , ˆ = ˆ (·) (1.6.1)

∑

∑ ∗

=

x y

S

x y

z

x y

x y

S

x y

z

P

P m

AMR

,

,

,

,

, ˆ

ˆ (1.6.2)

where and x and y refer to the age of males and females, respectively, and S Px, y is the theoretical 

unmarried population in the MRA as of July 1, 1982 (the geometric mean of the corresponding 

age groups in the standard population).

1.6.b. Input Data

Long-Range OASDI Projection Data -

Demography

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

status for years 1978-2010, excluding 1980. These data are updated each year based on 

output of the HISTORICAL POPULATION subprocess.

Assumptions -

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

ultimate value in the 25th year of the 75-year projection period. For the 2013 report, the 

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

NCHS Data -

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

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

years after 1988. The data vary in detail by year. They are broken out by single year age-ofhusband crossed with single year age-of-wife for many ages (particularly younger ages).
42

• Number of unmarried males and females in the MRA for calendar years 1978 through 1988, 

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

generally broken out by single year age for ages under 40 and by age groups 40-44, 45-49, 

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

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

age-group-of-wife (age groups include 15-19, 20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 

65+), for calendar years 1989-1995. These data are updated as new data become available 

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

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

the MRA unmarried population for the period 1957-1988. These data are not updated.

• The total number of new marriages in the United States for the period 1989-2010. Normally, 

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

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

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

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

after 1988.

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

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

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

after 1988.

U.S. Census Bureau Data -

• Estimates of new marriages by age-group-of-husband crossed with age-group-of-wife from 

the American Community Survey (ACS) public use microdata samples (PUMS) occurring, 

on average, end of years 2007 – 2010. An additional year of data is available each year.

Other Input Data -

• From state officials, number of same-sex marriages from 2004 – 2010. These data are 

updated as they become available.

1.6.c. Development of Output

Equation 1.6.1 -

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 
43

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 2010. 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 agespecific marriage rate calculations for the provisional period 1989 – 2010. The projection period 

of the MARRIAGE subprocess begins one year after the last historical data year (2011).

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

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

is given below:

z

x y

z

z x y

x y P

M

m

,

,

,

ˆ

ˆ = , where

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

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

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

z.

The rates for the period 1978 through 198821 are then averaged, graduated, and loaded into an 87 

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

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

provisional years and the years in the projection period.

For the provisional period, 1989-2010, the NCHS and ACS provided data on the number of 

marriages by age-group-of-husband crossed with age-group-of-wife (age groups include 15-19, 

20-24, 25-29, 30-34, 35-44, 45-54, 55-64, and 65+). These data are used to change the 

distribution of MarGrid by these age groups. For each age-group-of-husband crossed with agegroup-of-wife, the more detailed marriage rates in MarGrid that are contained within this group 

are adjusted so that the number of marriages obtained by using the rates in MarGrid match the 

number implied in the subset. 

For each year of the entire provisional period (1989 – 2010), an expected total number of 

marriages is calculated by multiplying the rates in the MarGrid (or the adjusted MarGrid for 

years 1989-2010) by the corresponding geometric mean of the unmarried males and unmarried 

females in the Social Security area population. All rates in MarGrid (or the adjusted MarGrid for 

years 1989-2010) 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 samesex marriages reported to NCHS as we do not project same-sex marriages. The provisional 

 21 Data for 1980 is not available and is excluded from the calculations.
44

period age-specific rates are then graduated using the Whittaker-Henderson method and are used 

to calculate the age-adjusted rates for each year. 

The age-adjusted marriage rates are expected to reach their ultimate value in the 25th year of the 

75-year projection period. Rather than use the last year of provisional data to calculate the 

starting rate, the rates for the past five historical data years are averaged to derive the starting 

value. The annual rate of change in the age-adjusted marriage rate is calculated by taking the 

27th root of the ratio of the ultimate value and the starting value. Thus, to calculate the rate for a 

projected year, the rate of change is applied to the prior year’s rate (or the starting value for the 

first year of the projection period).

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

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

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

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

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

rates by prior marital status are assumed to be the same as the average of those experienced 

during 1979 and 1981-1988. 
45

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-ofhusband crossed with age-group-of-wife. In 1988, the DRA consisted of 31 States and 

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

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

for the Social Security area is based on the total number of divorces 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 ( z dx, y ˆ ) for a given year z

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

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

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

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

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

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

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

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

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

The primary equations, 1.7.1 and 1.7.2, are given below:

z

x y

z dx, y d , ˆ ˆ = (·) (1.7.1)

∑

∑ ∗

=

x y

S

x y

z

x y

x y

S

x y

z

P

P d

ADR

,

,

,

,

, ˆ

ˆ (1.7.2)

where x and y refer to the age of husband and age of wife, respectively, and S Px, y is the number of 

married couples in the Social Security area population as of July 1, 1982.
46

1.7.b. Input Data

Long-Range OASDI Projection Data -

Demography

• Social Security area population of married couples by age-of-husband crossed with age-ofwife as of January 1 for years 1979-2010. These data are updated each year from the 

HISTORICAL POPULATION subprocess.

• The total population in the Social Security area for years 1979-2009. An additional year of 

data is added for each additional year of divorce data from the NCHS.

• The total population in the residential population plus armed forces overseas for years 1979-

2009. An additional year of data is added for each additional year of divorce data from the 

NCHS.

• The total population in Puerto Rico and the Virgin Islands for years 1979-2009. An 

additional year of data is added for each additional year of divorce data from the NCHS.

Assumptions -

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

reaches its ultimate value in the 25th year of the 75-year projection period. For the 2013 report, 

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

NCHS Data -

• 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 no longer 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).

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

available.

• The total number of divorces in the United States for the period for 1989-2009. Data is 

updated when it becomes available. 

• The total number of divorces in Puerto Rico and the Virgin Islands for years 1989-2009. The 

most recent year of data was obtained in 2000; the 2000 figures are used as a proxy for 2001-

2009.

22 New data are incorporated as they become available and resources are sufficient to 

 22 Data for 1988 was used to estimate the number of Puerto Rico and Virgin Island divorces for 1989-1997. 
47

validate their use. 

1.7.c. Development of Output

Equation 1.7.1 -

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

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

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

States are used for the period 1989 through 2009. 

 

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 ( z dx, y ˆ ), for each year, z, are calculated for the 

period 1979-1988 by taking the number of divorces (inflated to represent the Social Security 

area, z Dx, y ) and dividing by the married population in the Social Security area at that age-ofhusband and age-of-wife ( z Px, y ). The formula for this calculation is given below:

z

x y

z

z x y

x y P

D

d

,

,

,

ˆ ˆ = (1.7.3)

These rates are then averaged, graduated,

23 and loaded into an 87 by 87 matrix (age-of-husband 

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

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

period.

For each year in the provisional period (1989-2009), 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 rates over the past five historical data years are averaged and used as the starting value and 

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

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

rate is calculated by taking the 28th root of the ratio of the ultimate value and the starting value. 

 23 Using the Whittaker-Henderson method of graduation.
48

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

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

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

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

that particular year.
49

1.8. PROJECTED POPULATION

1.8.a. Overview

For the 2013 Trustees Report, the starting population for the population projections is the 

January 1, 2011, 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 2011.) The Social Security area population is then projected using a

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

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

age and sex to prepare an estimated population as of January 1, 2012, and to project the 

population through the 75-year projection period (years 2013-87). There is a separate equation 

for each of the components of change as follows:

= (⋅) z

s

z Bs B (1.8.1)

where z Bs is the number of births of each sex (s) born in year z;

( ) , , = ⋅ z

x s

z Dx s D (1.8.2)

where z Dx,s is the number of deaths at age (x) and sex (s) that occurs in year z;

z

x s

z

x s

z NLx,s = L , −E ,

where z NLx,s is describe in the LEGAL IMMIGRATION section, as equation 1.3.5; and

( ) , , = ⋅ z

x s

z NOx s NO (1.8.3)

where z NOx,s is the number of net other immigrants,

24 by age (x) and sex (s), for year z.

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

They include unauthorized immigrants, temporary workers, and students.
50

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

Social Security area population by age and sex:

1

1,

1 −

−

− − z

x s

z Bs D for age = 0

z Px,s = (1.8.4)

1

1,

1

1,

1

1,

1

1,

−

−

−

−

−

−

−

− − + + zx s

z

x s

z

x s

z Px s D NL NO for ages > 0

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

0, 1

1,

−

−

z D s represents neonatal deaths.

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

( ) , , , , = ⋅ z

x s m

z Px s m P (1.8.5)

The children (ages 0-18) population is further disaggregated into the following four parent 

statuses (i.e., fates): both parents survive, only father survives, only mother survives, and both 

parents deceased. The following 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:

( ) , , , , , , = ⋅ z

x s g f

z Cx s g f C (1.8.6)

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

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

1

1,

1

1,

1

, 1,

−

−

−

−

− = − + − z

x s

z

x s

z

x s

z OPx s OP NO D (1.8.7)

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

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

for year z (see equation 1.8.2). 

1.8.b. Input Data

Long-Range OASDI Projection Data -

Demography
51

 FERTILITY

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

with 1941 and ending with the year prior to the starting year. These data are updated

each year.

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

with the starting year and ending with 2101. These data are updated each year.

 MORTALITY

• 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 year prior to the starting year. These data 

are updated each year.

• 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 starting year and ending with 2101. These data are updated each 

year.

• 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.

 LEGAL IMMIGRATION

• Projected numbers of legal immigrants who are new arrivals, by single year of age (0-

84) and sex for years beginning with the starting year and ending with 2101. These 

data are updated each year.

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

of age (0-84) and sex for years beginning with the starting year and ending with 2101. 

These data are updated each year.

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

beginning with the starting year and ending with 2101. These data are updated each 

year.

HISTORICAL POPULATION

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

marital status for the years beginning with 1941 and ending with the starting year.

These data are updated each year. 

• Married couples by single year of age of husband (ages 14-100+) crossed with single 

year of age of wife (ages 14-100+) for the years beginning with 1941 and ending with 

the starting year. These data are updated each year. 

• Other than legal population by age and sex for the years beginning with 1964 and 

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

 OTHER IMMIGRATION

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

with the starting year and ending with 2101. These data are updated each year.
52

• Fixed departures by age and sex. These data are updated each year.

• Rates of emigration by age and sex. These data are updated each year.

MARRIAGE

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

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

period. These data are updated each year.

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

year of age (ages 14-100+), sex, and prior marital status (single, divorced, and 

widowed). These data are updated each year.

• Total number of marriages for the years beginning with 1989 and ending the year 

prior to the starting date. These data are updated each year.

 DIVORCE

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

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

These data are updated each year.

U.S. Census Bureau Data -

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

group of householder (age groups 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, and 

55-64) for 1960-2011. (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.

Other Input Data -

• The number of those potentially eligible under the deferred action for childhood arrivals 

(DACAs) initiative by age group and an overall gender split, from the Migration Policy 

Institute.

• Internally developed factors of potential DACA stock attaining DACA status by sex and 

ages 5-30 for the initial and ultimate DACA years.

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:
53















 + =

+

2

z 1

x

z

z x

x

z

x

FP FP

B b

where,

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

 z

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

 z FPx = 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 gender ratio of 105 male 

births for every 100 female births.

Equation 1.8.2 – Deaths

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

each projection year by applying the death probabilities for each age and sex, z

x s q , , to the 

exposed population at the beginning of the year.

z

x s

z

x s

z Dx,s = q , P ,

Deaths for the other immigrant population are calculated in the same manner using the same 

death probabilities.

z

x s

z

x s

z ODx,s = q , OP ,

Equation 1.8.3 – Net Other Immigration

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

other emigration. Thus, we have the following equation:

z

x s

z

x s

z NOx,s = O , − OE ,

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

subprocess (1.5) for each year z of the long-range projection period. Other emigration by age

and sex, z OEx,s , consists of those who adjust status to legal permanent residents and departures 

from the Social Security area population. Therefore, other emigration can be expressed via the 

following equation:

z

x s

z

x s

z OEx,s = AOS , + OD ,
54

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

status, and z ODx,s is discussed in the next paragraph. Adjustments of status are calculated in the 

LEGAL IMMIGRATION subprocess.

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

age (x) and sex (s), as shown in the following equation:

z

x s

z

x s

z ODx,s = FD , + RD ,

where z FDx,s is the number of fixed departures (calculated in the OTHER IMMIGRATION 

subprocess) and z RDx,s is the varying number of departures based on the rates of emigration. 

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

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

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

z RDx,s is calculated by applying the rates of emigration, x s r , , to the exposed population. The 

rates of emigration, which are calculated in the OTHER IMMIGRATION subprocess, do not 

vary by year. The exposed population is calculated by subtracting deaths, fixed departures, and 

adjustments of status from the beginning of year other immigrant population.

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

z

x s x s

z

x s

z

x s x s

z RDx s = r OP − q − FD − AOS

This subprocess also projects the Deferred Action for Childhood Arrivals (DACA) population, a 

subset of the other immigrant population, by age (x) and sex (s). The DACA population 

consists of other than legal immigrants who meet the criteria for the DACA initiative and will be 

granted authorization to work.

Equation 1.8.5 – Disaggregating the population by marital status

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

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

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

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

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

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

the starting date. 

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

marital status according to the relative differences in death rates by marital status observed for 
55

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

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

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

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

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

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

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

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

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

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

population for new immigrants and marriages during the year.

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

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

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

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

The age-specific midyear unmarried male population25 is estimated from the beginning of the 

year unmarried populations. It is calculated by adjusting the number of unmarried males 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 by 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 by 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.

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

divorced).
56

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, 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 average 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, 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 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. 
57

Process 2:

Economics
58

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 four subprocesses, U.S. EMPLOYMENT, U.S. 

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

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

earnings data, respectively, while COVERED EMPLOYMENT AND EARNINGS converts 

these employment and earnings variables to OASDI covered concepts. TAXABLE PAYROLL, 

in turn, converts OASDI covered earnings to taxable concepts, which are eventually used to 

estimate future payroll tax income and future benefit payments. 

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

COVERED EMPLOYMENT AND EARNINGS is annual. TAXABLE PAYROLL produces 

both.

Two appendices are at the end of this documentation. The first appendix, 2-1, provides details 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.
59

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 non-institutional 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 groups26, 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 assume that the 

military population (M) will remain constant over the first ten years of the projection horizon 

then grow at the same rate as E. We also assume 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

 = M2010 for t < 2020

M t-1 * (E t/ E t-1) for t > 2020 (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 immigrant population (OP). Similarly, USEMP 

projects annual values for E and employed OP (EO). USEMP further separates EO to those 

whose earnings are reported and posted to the Master Earnings File (EO_MEF), those whose 

 26 Group disaggregation includes age and gender. Some groups are additionally disaggregated by marital status, 

presence of children.
60

earnings are reported posted to the Earnings Suspense File (EO_ESF), those in the underground 

economy (EO_UND), and EO_MEF who are OASDI covered (EO_MEFC). Equations 2.1.7

through 2.1.11 outline the overall structure of the subprocess used to estimate EO and its 

sub-components.

EO = E * OP / N (2.1.7)

EO_MEF = EO_MEF(·) (2.1.8)

EO_MEFC = EO_MEFC(·) (2.1.9)

EO_ESF = EO_ESF(·) (2.1.10)

EO_UND = EO_UND(·) (2.1.11)

Finally, for each age/gender group, USEMP projects total “at-any-time” employed other 

immigrant population (TEO). EO represents the average weekly employment of the other 

immigrant population during a calendar year. TEO represents the total number of individuals in 

the other immigrant population who had any employment during the calendar year. (EO can be 

roughly viewed as the average number of jobs worked by OP during a calendar year, while TEO 

represents the total number of individuals who worked those jobs.) Effectively, Equations 2.1.12 

through 2.1.16 convert every EO age-gender sub-component to an at-any-time TEO age-gender 

sub-component counterpart. 

TEO = TEO(·) (2.1.12)

TEO_MEF = TEO_MEF(·) (2.1.13)

TEO_MEFC = TEO_MEFC(·) (2.1.14)

TEO_ESF = TEO_ESF(·) (2.1.15)

TEO_UND = TEO_UND(·) (2.1.16)

2.1.b. Input Data

Long-Range OASDI Projection Data

These data are updated each year.

Demography

• Social Security area population as of year-end (1941 – 2099) by age, marital status 
61

(single, married, widowed, divorced) and gender (M, F)

• “Other immigrant” population as of year-end (1980 – 2099) by age, marital status (single, 

married, widowed, divorced) and gender (M, F)

• Number of children by age of child and age of mother (1960-2099)

• Life expectancy by age and gender (1950-2099)

• Exit rates (probability of leaving the “other immigrant” population by other than death) 

by age and gender.

• Mortality rates by age and gender (1941-2099)

Trust Fund Operations and Actuarial Status – The Trust Fund Operations and Actuarial Status 

Process provides no input to the Economic Process sections. However, the LFPRs use input from 

the Outgo Process from the prior year’s Trustees Report. That is, the projected LFPRs for the 

2011 Trustees Report use input from the 2010 Trustees Report that includes projections for the 

disability prevalence rates by age and gender (originally from the Beneficiaries subprocess), and 

the 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 assumed values for 

key economic variables:

• Real wage differential 

• Annual percentage change in total economy productivity

• Annual percentage change in average hours worked

• Ratio of wages to compensation (RWSD)

• Ratio of compensation to GDP (RWSSY)

• Annual percentage change in the price differential

• Annual percentage change in CPI

• Annual trust fund real interest rate

• Unemployment rate

These ultimate values are generally implemented during the last half of the short-range (first 10 

years) of the projection horizon. Earlier projected values are set to provide a smooth transition 

from the latest actual historical values to the assumed long-range ultimate ones. As a by-product 

of this process, values for the GDP deflator (PGDP), real GDP, and potential GDP are set. The 

ratio (RTP) of real to potential GDP is an important summary measure of the business cycle.

It is important to note that the Trustees also agree on the assumed short-range values for the 

above variables.
62

Addfactors

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 and over to reflect projected changes in life 

expectancy.

Other input data

• 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.

• 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 

October 2008) by single year of age (16 to 69) and gender. These data are updated several 

times a year.

• Data for the mobilized military reservist population, by branch of service (September 2001-

October 2010) are reported by the US Department of Defense weekly. This subprocess updates 

the data several times a year.

• Data from the March Supplement of the Joint BLS/Census Current Population Survey (CPS) 

by year (1968-2008), for levels of the civilian noninstitutional population, labor force, military, 

and unemployment. These data are available from the U.S. Census Bureau, via Data Ferrett, by 

single year of age (16 to 85+), gender, marital status (never married, married with a spouse 

present, and married with no spouse present), and presence of children. These data are updated 

by the U.S. Census Bureau for the BLS annually. This subprocess updates the data every other 

year (or more often, based on time availability). 

•Data from the March Supplement of the CPS by year (1992-2008), for levels of the civilian 

noninstitutional population. These data are available from the U.S. Census Bureau, via Data 

Ferrett, 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.

• Data from the CPS (1948-2008) 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.

•Data from the CPS by year (1994-2008), for the civilian noninstitutional population. These data 
63

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.

• Data from the Current Employment Statistics survey (CES) (1964 (varies) to 2008) 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.

•Unpublished data from the CPS (1965 - October 2010) 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. 

•The historical resident population is published annually by the Census (1980-2010). These data 

are available by gender and age group. This subprocess uses data for age groups under 16 and 

60 and over. This subprocess updates the data annually.
64

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 males and 14 for females. 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 and constrained to an expected aggregate behavior 

whereby a 2.0 percentage point increase in the RTP elicits a 1.0 percentage point decrease in the 

RU. Furthermore, projections are constrained to the ultimate age-gender-adjusted RU set by the 

Trustees. The aggregate RU is dependent on the projected distribution of the labor force by age 

and 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, married with spouse present, and 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 females with at least one child under the age of six 

and females without a child under the age of six. Thus, USEMP contains 153 LFPR equations, 

69 for males and 84 for females. 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. RD is adjusted with a

multiplicative factor defined as the group’s average historical LFPR over a 15-year period. 

This adjustment implicitly assumes that disability can strike any person in the population 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 retired-worker 

beneficiaries. To avoid these problems, RDs for ages 62-74 are set to their cohort RD at age 
65

61. For example, the RD for males age 62 in year (t) is set to the RD for males age 61 in year 

(t-1).

• The unemployment rate (RU) is a measure of the business cycle. An increase in the lagged 

and current unemployment rate leads to a decrease in the LFPR. The RU affects most LFPRs.

• 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 patterns27 who retire at ages 62 through 

69. The replacement rate is adjusted to include the reduction for early 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 education distribution of the workforce increases the LFPRs if the level of educational 

attainment increases.

• The index of females with children is approximately equal to the ratio of the number of 

children under age 6 to mothers age 20 to 44. For females aged 20 to 44 with at least one own 

child, an increase in the index lowers the LFPR. 

• A LFPR increases with its lagged cohort. Lagged cohort variables affect female LFPRs age 

55 and over, and male LFPRs age 75 and over.

• The LFPRs for males age 62 through 74 increase with spousal LFPRs.

• For those approximately age 40 and over, an increase in life expectancy leads to an increase 

in LFPRs .

Equation 2.1.7 to 2.1.16 – Employed Other Immigrant Population (EO) and At-Any-Time 

Employed Other Immigrant Population (TEO)

EO is estimated by gender and single-year of age from 16 to 100. Thus, this portion of USEMP 

contains 170 equations, 85 for males and 85 for females. We separate each age-gender EO into 

visa-status components including those authorized to work, those not authorized to work but 

previously authorized, and those never authorized to work. We separate EO who were never 

authorized to work into those who worked in 2001 and earlier and those who began working in 

2002 and later, since we believe that those who worked in 2001 and earlier are more likely to 

have OASDI covered wages. Each of these groups is then further separated into EO_MEF, 

EO_MEFC, EO_ESF, and EO_UND. 

Every age-gender EO sub-component is converted to its age-gender TEO sub-component 

counterpart using an age-gender “conversion weight.” For example, if the sub-component of EO 

 27 More details on the hypothetical scaled workers are provided in Actuarial Note #2005.3, located at the following 

internet address: www.socialsecurity.gov/OACT/NOTES/ran3/index.html.
66

is for males age 20 to 24, the conversion weight is defined as the ratio of total economy-wide 

at-any-time employed males age 20 to 24 (TEM2024) to the sum of military and CPS civilian

male employment age 20 to 24. 
67

2.2. U.S. EARNINGS (USEAR)

2.2.a. Overview

In the CPS data, E is separated by class of worker. The broad categories include wage and salary 

workers (EW), the self-employed (ES), and unpaid family workers (EU). For the nonagricultural 

sector, a self-employed participation rate (SEPR) is defined as the ratio of ES to E, the 

proportion of employed persons who are self-employed. For the agricultural sector, the SEPR is 

defined as the ratio of ES to the civilian noninstitutional population. 

USEAR projects quarterly values for these 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). PGDP is equal to the ratio of nominal to real GDP. 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.

USEAR 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. Projected real GDP is 

set equal to the product of potential GDP and RTP. RTP reaches 1.0 in the short-range period 

and remains at 1.0 thereafter. Nominal GDP is the product of real GDP and PGDP. The growth 

rate in PGDP is set by assumptions.

The BEA also publishes quarterly values for the principal components of U.S. earnings, 

including total wage worker compensation (WSS), total wage and salary disbursements (WSD), 

and total proprietor income (Y). These concepts can be aggregated and rearranged. Total 

compensation (WSSY) is defined as the sum of WSS and Y. The total compensation ratio 
68

(RWSSY) is defined as the ratio of WSSY to the GDP. The income ratio (RY) is defined as the 

ratio of Y to WSSY. The earnings ratio (RWSD) is defined as the ratio of WSD to WSS. 

USEAR projects quarterly values for these principle components of U.S. earnings using 

Equations 2.2.5 through 2.2.11.

RWSSY = RWSSY(·) (2.2.5)

WSSY = RWSSY * GDP (2.2.6)

RY = RY(·) (2.2.7)

Y = RY * WSSY (2.2.8)

WSS = WSSY - Y (2.2.9)

RWSD = RWSD(·) (2.2.10)

WSD = RWSD * WSS (2.2.11)

2.2.b. Input Data

Long-Range OASDI Projection Data

Demography- (See Section 2.1.b.)

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.

Trustees Assumptions - (See Section 2.1.b.)

Addfactors

Addfactors were included on some employment and output variables to smooth the transition 

between the latest historical data and the projected values. The need for addfactors is reviewed 

each year and they are implemented if necessary.
69

Other input data

• Data from the NIPA (1929 (varies) to 2007) 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.

• Ratio of OASDI covered to NIPA wages, and ratio of OASDI taxable to covered wages. 

NIPA wages by sector are available quarterly and annually from 1947 to 2005. They are 

published by the BEA and updated several times during the year. OASDI covered and taxable 

wages (1971 to 2004) are updated annually by the Economic process. Covered and taxable 

data for more recent historical years are estimated from preliminary tabulations of Form 941 

and W-2 data. Projected values for covered ratios are set to the latest historical year.

• OASDI employee, employer, and self-employed tax rates from 1937 to 2080. These 

contribution rates are set according to the Social Security Act of 1935 as amended through 

2005. The rates are updated when legislation mandates a change.

• The October ratio of the number of teenagers enrolled in school to the civilian 

noninstitutional population by gender and age group (16-17 and 18-19) for the period 1947 to 

2006. An additional new year of data from the Census Bureau is usually available for 

including in preparation of the next annual Trustees Report. Projected values are set to levels 

from the latest historical year.

• The historical Consumer Price Index (CPI) is published monthly by the BLS. This

subprocess updates the data several times a year.

• The historical CPI for medical services is published monthly by the BLS. Quarterly values 

are projected based on the projected growth in the aggregate CPI and an additional amount 

defined as the growth rate differential in the two price measures that was assumed in the latest 

President’s Fiscal Year Budget. The series is updated annually.

• U.S. armed forces (EDMIL) by age and 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.

• 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 October 2008) by single year of age (16 to 69) and gender. These data are updated several 

times a year.
70

• Wages for railroad workers are wages covered by the Railroad Retirement Act. The annual 

data are for the period 1971 to 2006. An additional year of data from the Railroad Retirement 

Board is usually available for including in preparation of the next annual Trustees Report.

• Unpublished data from the CPS (1988-2007) on employment by class of worker (i.e., 

agricultural, non-agricultural, 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.

• Data from the NIPA (1947-2008) for wages and compensation of households and institutions 

are published by the BEA quarterly. This subprocess updates the data several times a year.

• 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.

• Ratios of OASDI covered wages to NIPA wages are used from the prior year’s Trustees 

Report as input to the current year’s calculations, for the following sectors: Federal civilian, 

Federal military, state and local, and private industry.

• Recent historical values (2000-2010) for quarterly real potential GDP are obtained from the 

Congressional Budget Office. This subprocess updates the data annually and adjusts the series 

to create a series usable for the current Trustees Report.

• 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 (1948-2008) and 

annually (1948-2007). This subprocess updates the data several times a year.

• The Federal minimum hourly wage is based on the Fair Labor Standards Act from the 

Department of Labor for 1938 to 2007. The wage is updated when there is legislation 

mandating a change.

• Time trends (set by Economic process) are used in the agriculture sector for employment, 

real output, and compensation in the short-range period. These short-range trends are 

extended for each year’s Trustees Report, reflecting a new short-range period.

2.2.c. Development of Output

Equation 2.2.1 - Self-Employed Participation Rate (SEPR)
71

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 

non-agriculture.

For the non-agriculture sector, the SEPRs by age and gender are defined as the ratio of the nonagriculture self-employment to total employment. Thus, the aggregate non-agriculture SEPR is 

dependent on the projected distribution of employment by age and gender. All non-agriculture 

SEPRs by age and gender are dependent on the RTP. Increases in the RTP lead to decreases in 

the SEPRs. For female age groups between 20 and 64, the non-agriculture SEPRs are also 

dependent on the groups LFPRs. Increases in the LFPRs lead to increases in the SEPRs.

For the agriculture sector, the male SEPRs by age are defined as the ratio of agriculture selfemployment to the civilian noninstitutional population. Thus, the aggregate agriculture SEPR for 

males is dependent on the projected distribution of the population by age. The agriculture SEPRs 

for males by age are dependent on the ratio of total agriculture employment (EA) to the total 

civilian population aged 16 and over. (EA is projected in a farm sub-program. Real farm output 

is projected to increase with the population, while farm productivity, defined as output per 

worker, is projected to continue to follow its historical trend. EA is projected as the ratio of farm 

output to farm productivity.) An increase in the ratio of EA to the total civilian population aged 

16 and over leads to an increase in the agriculture SEPRs for males.

The female SEPRs by age for the agriculture sector are defined as the ratio of the female to male 

agriculture self-employment. Thus, the aggregate agriculture SEPR for females is dependent on 

the projected distribution of male agriculture employment by age. For female age groups 

between 18 and 64, the SEPRs are dependent on the RTP and the corresponding ratio of total 

female to male employment. Generally, an increase in the RTP leads to increases in the SEPRs. 

An increase in the total employment ratio also leads to an increase in the SEPR. 

Equation 2.2.3 - Unpaid Family Workers (EU)

EU is disaggregated by age, 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 2005, the level of EU fell from about 0.5 to 0.03 million in the agriculture sector 

and from about 0.5 to 0.09 million in the nonagriculture sector. For projections, the levels of EU 

by age and gender in the agriculture sector are assumed constant and about five thousand or less. 

The EUs by age and gender in the nonagriculture sector are projected as a constant ratio to ES. 

Equation 2.2.5 - Total Compensation Ratio (RWSSY)

The Trustees set the ultimate annual growth rate for RWSSY. For the short-range period, total 

WSS, WSD, and Y are aggregated from sector components. Total GDP, WSS, and WSD are 

divided into the farm and nonfarm sectors. The nonfarm sector is further separated into the 
72

government and government enterprises, households, non-profit institutions, and residual 

(private nonfarm business excluding government enterprises (PBNFXGE)) sectors. Total Y is 

divided into the farm and residual (i.e., PBNFXGE) sectors.

The methodology used to estimate GDP, WSS, WSD, and Y differs by sector.

Farm - Nominal GDP is the product of real GDP and the farm price deflator. Real farm GDP is 

projected from estimates of real farm per capita output. EA is projected from estimates of farm 

productivity. EAW is projected to continue its historical increase relative to EA. Farm 

compensation (WSSPF) is the product of estimates for average farm compensation (AWSSPF) 

and EAW, while farm proprietor income (YF) is the product of estimates of average farm 

proprietor income (AYF) and EAS. AYF is projected based, in part, on the growth in average 

compensation in the private sector.

Government and Government Enterprises - This sector is further disaggregated to Federal 

Civilian, Federal Military, and State and Local. In each sector, WSD is the product of estimates 

for average wages and employment. WSS is the sum of WSD and estimates for non-wage 

components of compensation. GDP is the sum of WSS and estimates of consumption of fixed 

capital.

Household - WSS is the product of estimates for average compensation and employment. WSD 

is WSS less employer contributions for the OASDHI tax. GDP is the sum of WSS and the gross 

value added of owner-occupied housing.

Nonprofit Institutions - The Nonprofit Institutions sector is further disaggregated to Health, 

Education, and Social Services sectors. In each sector, WSS is the product of estimates for 

average compensation and employment. WSD is WSS less the estimates for non-wage 

components of compensation. GDP is WSS plus a residual component of output.

Private Nonfarm Business Excluding Government Enterprises (PBNFXGE) - GDP in the 

PBNFXGE sector is total economy-wide GDP less the sum of the other sector GDPs. WSS is 

projected as a ratio to GDP less Y. The ratio is projected to be mostly stable, varying only 

temporarily with changes in RTP. Y is projected as a ratio to GDP.

Thus, total labor compensation (WSSY) is summed from sector components, while the total 

compensation ratio (RWSSY) is the ratio of total WSSY to total GDP. It is important to note that 

the pure program-generated estimate for the total RWSSY is adjusted to ensure a smooth 

transition between the latest historical data and the Trustees’ ultimate assumptions.

Equation 2.2.7 - Income Ratio (RY)

Y is disaggregated to the farm and PBNFXGE sectors. In the PBNFXGE sector, the Y is 

projected as a ratio to GDP in the sector. In the farm sector, Y is projected based in part on the 

growth in average compensation in the private sector.
73

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 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 yearby-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) and is 

consistent with new health care legislation enacted in 2010. Employer contributions to employee 

pension funds are assumed to increase as life expectancy increases.
74

2.3. OASDI COVERED EMPLOYMENT AND EARNINGS (COV)

2.3.a. Overview 

Total at-any-time employment (TE) is defined as the sum of total OASDI covered employment 

(TCE) and total noncovered employment (NCE). TCE can be decomposed to workers who only 

report OASDI covered self-employed earnings (SEO) and to wage and salary workers who 

report some OASDI covered wages (WSW). Combination workers (CMB_TOT) are those who 

have both OASDI covered wages and self-employed income. Workers with some selfemployment income (CSW) are the sum of SEO and CMB_TOT.

Some of these concepts can be rearranged. The total employed ratio (RTE) is defined as the ratio 

of TE to the sum of EW, ES, and EDMIL, while the combination employment ratio (RCMB) is 

defined as the ratio of CMB_TOT to WSW.

COV projects annual values for TE and the principle measures of OASDI covered employment. 

Equations 2.3.1 through 2.3.9 outline the overall structure and solution sequence used to project 

these concepts.

(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)
75

Total OASDI covered earnings is defined as the sum of OASDI covered wages (WSC) and total 

covered self-employed income (CSE_TOT). Both components can be expressed as ratios to their 

U.S. earnings counterparts. The covered wage ratio (RWSC) is defined as the ratio of WSC to 

WSD, while the covered self-employed ratio (RCSE) is the ratio of CSE_TOT to Y.

COV projects annual values for the principal measures of OASDI covered earnings using 

Equations 2.3.10 through 2.3.13.

RWSC = RWSC(·) (2.3.10)

WSC = RWSC * WSD (2.3.11)

RCSE = RCSE(·) (2.3.12)

CSE_TOT = RCSE * Y (2.3.13)

COV 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 from 

Forms W-2 posted to the Master Earnings File (MEF). By law, it is used to set the OASDI 

contribution and benefit base (TAXMAX).

COV projects annual values for the AWI and TAXMAX.

AWI = AWI(·) (2.3.17)

TAXMAX = TAXMAX(·) (2.3.18)

2.3.b. Input Data

Long-Range OASDI Projection Data

Demography - (See Section 2.1.b.)
76

Economics- Employment and earnings-related data from Sections 1.1 and 1.2.

Trustees Assumptions - (See Section 2.1.b.)

Addfactors

Addfactors were included on some employment variables to smooth the transition from the latest 

historical data to program estimates. The need for addfactors is reviewed each year and they are 

implemented if necessary. 

Other input data

• The ratio of maximum quarterly population within a year to the annual value for that year 

is calculated from 1959 through the year of latest available data by 5-year age group and 

gender. The population, defined as the sum of the civilian noninstitutional population and 

the military is updated quarterly from CPS and military data.

• Ratios of OASDI covered to NIPA wages by sector. NIPA wages by sector are available 

quarterly and annually from 1947 to 2008. They are published by the BEA and updated 

several times during the year. OASDI covered wages (1971 to 2005) are updated 

annually by the Economic process. Covered data for the latest historical year are 

estimated from tabulations of Form 941 and W-2 data.

• Ratio of disabled worker beneficiaries to the Social Security area population is produced 

by 5-year age group and gender for the years 1970 to 2099. The Social Security area 

population is produced by the Demography process and updated annually for the Trustees 

Report. The number of disabled worker beneficiaries are annual data from the prior 

year’s Trustees Report (Disability subprocess), and are updated annually.

• U.S. armed forces (EDMIL) by age and 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.

• 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 October 2008) by single year of age (16 to 69) and gender. These 

data are updated several times a year.

• Railroad employment is covered by the Railroad Retirement Act. The annual historical 

data are for the period 1971 to 2008. An additional new year of historical data from the 
77

Railroad Retirement Board is usually available for inclusion in preparation of the next 

annual Trustees Report.

• Data obtained from Office of Research, Evaluation, and Statistics (ORES) are tabulations 

of quarterly Form 941 data. Data currently used are the OASDI, HI, and income taxable 

wages by sector for the most recent five years. The data represent changes in reported 

wages since the prior quarterly report. The most recent data are appended to previously 

reported data. Annual totals are computed and used to derive estimates of OASDI 

covered wages by sector for the latest historical years.

• Data obtained from the most recently available 1.0% CWHS active file, maintained on 

Social Security’s mainframe and made available by ORES. The years of data are 1951 to 

the third year prior to the current Trustees Report year. The data are used for comparison 

of OASDI covered earnings from other sources.

• Data obtained from extracting information from the 1.0% Employee-Employer Files, 

maintained on Social Security’s mainframe and made available by ORES. Each year two 

files are created: a Version 1 file for the third year prior to the current Trustees Report 

and a Version 3 file for the fifth year prior to the current Trustees Report. Data currently 

being used are government and farm sector OASDI, HI, and total wages and 

employment. Data from the latest files are used to estimate OASDI covered wages for the 

years available on each file.

• Data obtained from quarterly IRS Form 941 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 previously reported data. Annual totals are 

computed and used to derive estimates of HI taxable wages, which are then used to 

develop OASDI covered wages for the most recent historical years.

• Data for the most recent ten years from the Quarterly EPOXY Report, received in hardcopy 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 selfemployment earnings. 

• 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.
78

• Data obtained from OS on amounts of OASDI taxable wages on the Earnings Suspense 

File for 1937 through the second year prior to the current Trustees Report year. The data 

are used in estimating total OASDI covered employment.

2.3.c. Development of Output

Equation 2.3.2 - Total Employment (TE)

Based on the CPS, BLS estimates the total number of persons with any work experience (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 non-institutional 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 accounts for the effect of the 2010 decennial census.

Equation 2.3.3 - Non-Covered 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 
79

hired S&L employees were covered under HI. Beginning January 1990, all S&L employees not 

under an S&L retirement system were covered under OASDHI.

By 2002, about 30 and 10 percent of S&L employment (and wages) are still not covered under 

OASDI and HI respectively. The closed group of relatively older S&L employees not covered 

under HI is projected to fall to near zero by 2020. S&L employment not covered under OASDI is 

projected to grow at about the same rate as the labor force.

Students at Public Schools - Prior to 2000, students working at S&L public schools were covered 

under OASDI and HI if the other school employees were covered. In 2000, legislation offered an 

“open season” allowing schools to remove their students from coverage. Virtually all major 

schools opted for removal. Hence, almost no students working at their public schools are covered 

under OASDI or HI. Students at public schools are projected to grow at about the same rate as 

the population aged 18 to 24.

Election Workers - Most S&L election workers are subject to an earnings test and are not 

covered under OASDHI. The earnings test was raised from $100 to $1,000 beginning January 

1995 and indexed beginning in 2000. Election workers are projected to grow at about the same 

rate as LC.

Private Household - The threshold for coverage of domestic employees’ earnings was raised 

from $50 per calendar quarter to $1,000 per calendar year (CY) per employee. Domestic workers 

are no longer covered if under age 18. Private household employment is projected to grow at 

about the same rate as E and vary with RTP. 

Students at Private Schools - All students working in private schools are not covered under 

OASDHI. Students at private schools are projected to grow at about the same rate as the 

population aged 18 to 24.

Railroad - Employers do not submit payments for payroll taxes to the IRS for railroad 

employees. Railroad employees are projected by the Railroad Retirement Board.

Other Noncovered Workers - Set at a constant amount of 0.4 million to reflect relatively small 

and shrinking groups such as paperboys. 

Underground Economy Workers - Set to the at-any-time employed in the other immigrant 

population who have no reported earnings and therefore are part of the underground economy 

(i.e., TEO_UND). 

Equation 2.3.5 - Self-Employed Only (SEO)

SEO is projected to grow at the same rate as ES.
80

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 falls.

Equation 2.3.10 - Ratio of Covered Wages (RWSC)

RWSC is disaggregated by the following sectors: Federal Civilian government, Federal Military, 

S&L government, and Private.

Federal Civilian government - Total Federal civilian employment and wages are split by 

retirement system. Those under FERS are OASDI covered, while those under CSRS are not. 

Employment and wages are projected for workers under each retirement system. Employment 

under CSRS is a closed group that is expected to fall to zero by about 2030. Employment under 

FERS is defined as total Federal employment less employment under CSRS. Total Federal 

civilian employment is projected to grow at an average annual rate of about 0.2 percent from 

2004 to the end of the short-range period, and about equal to the growth in the LC thereafter. The 

growth rates in the average wage for those under CSRS and FERS are projected based on, for the 

first five years, pay raises assumed under the most recent OMB FY Budget and on the growth 

rate in the CPI. Hence, the RWSC for the Federal civilian employment is defined as the ratio of 

wages for employment under FERS to total Federal civilian wages.

Federal Military - The RWSC for the Federal military sector is projected to remain constant at its 

latest actual historical level.

S&L government - The RWSC for the S&L government sector is projected to remain constant at 

its latest actual historical level.

Private - The private sector is separated into sub-sectors including private households, farm, 

railroad, tips, and a residual private “base”. The RWSCs for the private household and farm subsectors 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 
81

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 an economy-wide average wage 

(ACWC) defined as the ratio of WSD to total wage workers (covered and non-covered). Total 

wage workers are projected as the sum of WSW and the various groups of non-covered wage 

workers discussed above.

Equation 2.3.18 - OASDI Taxable Maximum (TAXMAX)

By law, the growth in the AWI is used to increase the TAXMAX.
82

2.4. Effective TAXABLE PAYROLL (TAXPAY)

2.4.a. Overview

TAXPAY estimates historical annual taxable earnings data including total employee OASDI 

taxable wages (WTEE), total employer taxable wages (WTER), and total self-employed taxable 

income (SET). By law, each employee is required to pay the OASDI tax on wages from all 

covered jobs up to the TAXMAX, while each employer is required to pay the OASDI tax on the 

wages of each worker up to the TAXMAX. If an employee works more than one covered wage 

job and the sum of all covered wages exceeds the TAXMAX, the employee but not the employer 

is due a refund. Hence, WTER is greater than WTEE. The difference (i.e., WTER less WTEE) is 

defined as multi-employer refund wages (MER).

TAXPAY also estimates the historical annual effective OASDI taxable payroll (ETP). ETP is the 

amount of earnings in a year which, when multiplied by the combined employee-employer tax 

rate, yields the total amount of taxes due from wages and self-employed income in the year. ETP 

is used in estimating OASDI income and in determining income and cost rates and the actuarial 

balance. ETP is defined as WTER plus SET less one-half of MER.

TAXPAY projects annual values for ETP after first estimating its components. The components 

in turn are estimated by a collection of ratios. The employee taxable ratio (RWTEE) is defined as 

the ratio of WTEE to WSC. The multi-employer refund wage ratio (RMER) is defined as the 

ratio of MER to WSC. The self-employed net income taxable ratio (RSET) is defined as the ratio 

of SET to CSE_TOT. Equations 2.4.1 through 2.4.8 outline the projection methodology.

RWTEE = RWTEE(·) (2.4.1)

WTEE = RWTEE * WSC (2.4.2)

RMER = RMER(·) (2.4.3)

MER = RMER * WSC (2.4.4)

WTER = WTEE + MER (2.4.5)

RSET = RSET(·) (2.4.6)

SET = RSET * CSE_TOT (2.4.7)

ETP = WTER + SET - 0.5 * MER (2.4.8)
83

Over the short-range projection horizon (i.e., first 10 years), TAXPAY also projects annual 

OASDI wage tax liabilities (WTL) and self-employment tax liabilities (SEL). In Equation 2.4.9, 

WTL is the product of the effective taxable wages, defined as WTER less one-half of MER, and 

the combined OASDI employee-employer tax rate (TRW). In Equation 2.4.10, SEL is the 

product of SET and the OASDI self-employed tax rate (TRSE).

WTL = WTER * TRW (2.4.9)

SEL = SET * TRSE (2.4.10)

Also over the short-range horizon, TAXPAY decomposes WTL into quarterly wage tax 

liabilities (WTLQ) then to quarterly wage tax collections (WTLQC). TAXPAY also decomposes 

SEL into quarterly self-employed net income tax collections (SELQC).

WTLQ = WTLQ(·) (2.4.11)

WTLQC = WTLQC(·) (2.4.12)

SELQC = SELQC(·) (2.4.13)

Finally, over the first two projected quarters, TAXPAY estimates of WTLQC and SELQC are 

replaced with ones from the most recent OMB FY Budget. And, over the first four projected 

quarters, TAXPAY includes estimates for appropriation adjustments (AA).

AA = AA(·) (2.4.14)

2.4.b. Input Data

Data used to obtain values input directly to model

• Data obtained from ORES by email for the amounts of single and multi-employer refunds 

for the latest 5 years. Each year, data are updated.

• Data obtained from ORES are tabulations of quarterly Form 941 data. Data currently 

used are the OASDI, HI, and income taxable wages by sector for the most recent five 

years. The data represent changes in reported wages since the prior quarterly report. The 

most recent data are appended to previously reported data. Annual totals are computed 

and used to derive estimates of OASDI taxable wages by sector for the latest historical 

years.

• Data obtained from the most recently available 1.0% CWHS active file, maintained on 

Social Security’s mainframe and made available by ORES. The years of data are 1951 to 
84

the third year prior to the current Trustees Report year. The data are used for comparison 

of OASDI taxable earnings from other sources.

• Data obtained from quarterly IRS Form 941 files, provided by OS. Data currently used

are the OASDI and HI taxable wages for 1978 to the most recent year available. The data 

represent changes in reported wages since the prior quarterly report. The most recent data 

are appended to previously reported data. Annual totals are computed and used to derive 

estimates of OASDI taxable wages for the most recent historical years.

• Data for the most recent ten years from the quarterly EPOXY Report, received in hardcopy and, more recently, electronic formats obtained from OS. The data currently used 

are the total number of workers with OASDI taxable earnings, total number of workers 

with OASDI self-employed taxable earnings, distribution of number of HI workers by 

wage intervals, distribution of number of OASDI workers by wage intervals, number of 

persons with OASDI taxable wages, number of persons with HI taxable wages, number 

of persons with OASDI taxable self-employment, number of persons with HI taxable 

self-employment, number of workers with single-employer excess wages, and number of 

workers with multi-employer excess wages.

• Data obtained from the Quarterly Trust Fund Letter, received from OFPO. Data currently 

used are OASDI and HI taxable wages accumulated from all Forms 941 and W-2 to date, 

and changes in self-employment earnings and self-reported tips since the prior Letter. 

These data are for years 1978 to the most recent year available.

Long-Range OASDI Projection Data

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 2099. Each variable is shown with starting year.

AIW Average wage for indexing ($), 1971

AWSCFM Average covered wage for farm workers ($), 1971

AWSCML Average covered wage for military ($), 1971

DMWCHI Deemed military wage credits for HI ($ millions), 1978

DMWCOD Deemed military wage credits for OASDI ($ millions), 1978

ECFCHO Number of HI-only covered Federal Civilian workers (millions), 

1983

ECFCOD Number of OASDI covered Federal Civilian workers (millions), 

1983

ECHITOT Number of HI covered workers (millions), 1971

ECSEHI Number of HI covered self-employed workers (millions), 1994

ECSENOMAX Number of covered self-employed workers if no taxable 

maximum (millions), 1983

ECSEO Number of OASDI covered self-employed only workers 

(millions), 1971
85

ECSEOD Number of OASDI covered self-employed workers (millions), 

1971

ECSLNOIS Number of non-OASDI covered State and Local workers 

including students (millions), 1983

ECSLNRP Number of OASDI covered State and Local workers with no 

retirement plan (millions), 1983

ECSLOD Number of OASDI covered State and Local workers (millions), 

1983

ECSLP91 Number of State and Local workers covered under OASDI under 

pre-1991 law (millions), 1983

ECWSHI Number of HI covered wage workers (millions), 1983

ECWSOD_MEF Number of OASDI covered wage workers on the Master 

Earnings File (MEF) in millions, 1990

ECWSODFU16_MEF Number of OASDI covered wage workers on the MEF, female 

under 16 years old (millions), 1990

ECWSODF1619_MEF Number of OASDI covered wage workers on the MEF, female 

16 to 19 years old (millions), 1990

ECWSODF2024_MEF Number of OASDI covered wage workers on the MEF, female 

20 to 24 years old (millions), 1990

ECWSODF2529_MEF Number of OASDI covered wage workers on the MEF, female 

25 to 29 years old (millions), 1990

ECWSODF3034_MEF Number of OASDI covered wage workers on the MEF, female 

30 to 34 years old (millions), 1990

ECWSODF3539_MEF Number of OASDI covered wage workers on the MEF, female 

35 to 39 years old (millions), 1990

ECWSODF4044_MEF Number of OASDI covered wage workers on the MEF, female 

40 to 44 years old (millions), 1990

ECWSODF4549_MEF Number of OASDI covered wage workers on the MEF, female 

45 to 49 years old (millions), 1990

ECWSODF5054_MEF Number of OASDI covered wage workers on the MEF, female 

50 to 54 years old (millions), 1990

ECWSODF5559_MEF Number of OASDI covered wage workers on the MEF, female 

55 to 59 years old (millions), 1990

ECWSODF6064_MEF Number of OASDI covered wage workers on the MEF, female 

60 to 64 years old (millions), 1990

ECWSODF6569_MEF Number of OASDI covered wage workers on the MEF, female 

65 to 69 years old (millions), 1990

ECWSODF70O_MEF Number of OASDI covered wage workers on the MEF, female 

70 years old and older (millions), 1990

ECWSODMU16_MEF Number of OASDI covered wage workers on the MEF, male 

under 16 years old (millions), 1990

ECWSODM1619_MEF Number of OASDI covered wage workers on the MEF, male 16 

to 19 years old (millions), 1990
86

ECWSODM2024_MEF Number of OASDI covered wage workers on the MEF, male 20 

to 24 years old (millions), 1990

ECWSODM2529_MEF Number of OASDI covered wage workers on the MEF, male 25 

to 29 years old (millions), 1990

ECWSODM3034_MEF Number of OASDI covered wage workers on the MEF, male 30 

to 34 years old (millions), 1990

ECWSODM3539_MEF Number of OASDI covered wage workers on the MEF, male 35 

to 39 years old (millions), 1990

ECWSODM4044_MEF Number of OASDI covered wage workers on the MEF, male 40 

to 44 years old (millions), 1990

ECWSODM4549_MEF Number of OASDI covered wage workers on the MEF, male 45 

to 49 years old (millions), 1990

ECWSODM5054_MEF Number of OASDI covered wage workers on the MEF, male 50 

to 54 years old (millions), 1990

ECWSODM5559_MEF Number of OASDI covered wage workers on the MEF, male 55 

to 59 years old (millions), 1990

ECWSODM6064_MEF Number of OASDI covered wage workers on the MEF, male 60 

to 64 years old (millions), 1990

ECWSODM6569_MEF Number of OASDI covered wage workers on the MEF, male 65 

to 69 years old (millions), 1990

ECWSODM70O_MEF Number of OASDI covered wage workers on the MEF, male 70 

years old and older (millions), 1990

ESLCG Number of State and Local workers not covered under HI 

(millions), 1983

ESLSTUD Number of noncovered students at public schools employed by 

their school (millions), 1983

GAPLAG Ratio of real to potential GDP lagged (units), 1971

RTP Ratio of real to potential GDP (units), 1971

RU Civilian unemployment rate (percent), 1971

SEECCMB Self-employed earnings of all SE workers who also earned wages 

in same year ($ millions), 1991

SEECHI HI covered self-employed earnings ($ millions), 1991

SEECNOMAX Covered self-employed earnings if no taxable maximum ($ 

millions), 1991

SEECOD OASDI covered self-employed earnings ($ millions), 1991

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

TAXMAXHI HI taxable maximum ($) – 0 indicates no maximum, 1971

TAXMAXOD OASDI taxable maximum ($), 1971

TCFCD Proportion of annual Federal Civilian wages earned in each 

quarter (units), 1971

TCMD Proportion of annual military wages earned in each quarter 

(units), 1971
87

TCPD Proportion of annual private sector wages earned in each quarter 

(units), 1971

TCSLD Proportion of annual State and Local wages earned in each 

quarter (units), 1971

WSCCMB Wages earned in same year by all SE workers with both types of 

earnings ($ millions), 1991

WSCFCHO HI Covered wages of Federal Civilian HI-only workers ($ 

millions), 1983

WSCFCOD OASDI Covered wages of Federal Civilian workers ($ millions),

1971

WSCFM Covered wages of farm workers ($ millions), 1971

WSCHI HI covered wages ($ millions), 1983

WSCML Covered wages of members of the Armed Forces ($ millions), 

1971

WSCOD OASDI covered wages ($ millions), 1971

WSCOD_SF OASDI covered wages on the Suspense File ($ millions), 1971

WSCPHH Covered wages of private household workers ($ millions), 1971

WSCPNF Covered wages of private nonfarm workers ($ millions), 1971

WSCSLHI HI covered State and Local wages ($ millions), 1983

WSCSLNRP Covered wages of State and Local workers with no retirement 

plan ($ millions), 1971

WSCSLOD OASDI covered State and Local wages ($ millions), 1971

WSCSLP91 Wages of State and Local workers covered under OASDI under 

pre-1991 law ($ millions), 1971

WSD Total NIPA wages ($ millions), 1971

WSP Total NIPA private sector wages ($ millions), 1971

WSS Total NIPA compensation ($ millions), 1971

WSSLCG Wages of State and Local workers not covered under HI ($ 

millions), 1983

WSSLNOIS Wages of non-OASDI covered State and Local workers 

including students ($ millions), 1983

WSSLSTUD Wages of noncovered students at public schools employed by 

their school ($ millions), 1983

WSTTIPSSR Taxable tips reported by tip earner instead of employer ($ 

millions), 1978

WTWPO Proportion of annual Postal Service wages earned in each quarter 

(units), 1971

Other direct input data

• FICA, SECA, and Federal Employer tax transfers by month from the Department of the 

Treasury for years 1984 to 2008.

• FICA, SECA, and Federal Employer tax transfers by month from the Department of the 
88

Treasury for January 2009 and estimated transfers for February 2009 to June 2009.

• FICA and SECA tax transfers by month split by liability period from the Department of 

the Treasury for 1984 to 2007.

• FICA and SECA tax transfers by month split by liability period from the Department of 

the Treasury for January 2008 to June 2008.

• Monthly OASI, DI, and HI deposits by States, received periodically throughout the year 

from the Department of the Treasury for 1984 to 2008. (This is an obsolete type of 

revenue which has had no valid non-zero amount since 2002.)

• Historical annual HI taxable self-employment earnings for 1983 to 2006.

• Historical annual OASDI taxable self-employment earnings for 1971 to 2006.

• Historical annual OASDI multi-employer refund wages for 1971 to 2007.

• Historical annual HI taxable wages for 1983 to 2007.

• Historical annual OASDI taxable wages for 1971 to 2007.

• Historical annual HI-only taxable Federal Civilian wages for 1987 to 2003.

• Historical annual OASDI taxable Federal Civilian wages for 1971 to 2003.

• Historical annual HI taxable Federal Civilian wages for 1987 to 2003.

• Historical annual OASDI taxable farm sector wages for 1971 to 2003.

• Historical annual HI taxable farm sector wages for 1991 to 2003.

• Historical annual OASDI taxable military sector wages for 1971 to 2003.

• Historical annual HI taxable military sector wages for 1991 to 2003.

• Historical annual OASDI taxable State and Local government sector wages for 1971 to 

2003.

• Historical annual HI taxable State and Local government sector wages for 1987 to 2003.

• Historical and projected annual OASDI taxable tips for employees as reported by 

employers for 1971 to 2019.
89

• Historical and projected annual OASDI taxable tips for employers as reported by 

employers for 1971 to 2019.

• Annual and quarterly OASDI and HI taxable wages for calendar year 2008.

• Estimated annual HI taxable payroll for railroad workers for 2007 to 2099.

• Historical FICA and SECA appropriation adjustments for OASI, DI, and HI by month for 

1968 to 2008.

• Historical FICA revenues for OASI, DI, and HI by quarter for 1984 to 2008.

• Historical SECA revenues for OASI, DI, and HI by quarter for 1984 to 2008.

• Historical Federal Employer revenues for OASI, DI, and HI by quarter for 1984 to 2008.

• Historical Deposits by States for OASI, DI, and HI by quarter for 1984 to 2008.

• Historical single-employer refunds of excess taxes for OASI, DI, and HI by quarter for 

1984 to 2008.

• Historical FICA credits for OASI and DI by quarter for 1984 to 2008.

• Historical SECA credits for OASI, DI, and HI by quarter for 1984 to 2008.

• Historical multi-employer refunds of excess taxes for OASI, DI, and HI by month for 

1968 to 2008.

• Data used to estimate future FICA appropriation adjustments for 2008 to 2010 – These 

adjustments are used to make sure that transfers to the Trust Funds reflect taxable wage 

amounts reported to SSA. The data input includes estimated quarterly tax liabilities 

ultimately owed the Trust Funds from President’s Budget model solutions, quarterly tax 

liabilities for 2009Q1 from IRS-941 tabulations, estimates of tax liabilities for all prior 

years for 2009Q1 to 2010Q2, and estimated ratios of quarterly liability amounts reported 

to SSA over ultimate values for 2008Q2 to 2009Q2. Values are estimated for the four 

quarters of the Trustees Report year and for the following two quarters.

• Miscellaneous historical covered employment and earnings data:

o HI Covered self-employed workers for 1986 to 1993.

o Number of OASDI covered wage workers by age group and gender for 1996.
90

o HI covered self-employment earnings for 1971 to 1993.

o Covered self-employment earnings if there were no taxable maximum for 1971 to 

1993.

o OASDI covered self-employment earnings for 1971 to 1993.

• Miscellaneous historical and fixed projected data:

o Quarterly distribution of annual OASDI taxable farm wages for 1971 to 2020.

o Quarterly OASDI covered private nonfarm sector wages for 1971 to 1977.

o Quarterly OASDI covered State and Local government sector wages for 1971 to 

1977.

o Quarterly OASDI covered military sector wages for 1971 to 1977.

o Quarterly OASDI covered Federal Civilian sector wages for 1971 to 1977.

o Quarterly OASDI taxable private nonfarm sector wages for 1971 to 1977.

o Quarterly OASDI taxable State and Local government sector wages for 1971 to 

1977.

o Quarterly OASDI taxable military sector wages for 1971 to 1977.

o Quarterly OASDI taxable Federal Civilian sector wages for 1971 to 1977.

o Quarterly OASDI taxable farm sector wages for 1971 to 1977.

o OASDI employee, employer, and self-employment tax rates from 1937 to 2100. 

These contribution rates are set according to the Social Security Act of 1935 and 

amendments to the Act through 2004. The rates are updated when legislation 

mandates a change (which hasn’t occurred since 2000).

o Annual OASDI employee credit tax rate for 1984.

o Annual OASDI self-employment credit tax rates for 1984 to 1989.

o Annual trend variable for taxable to covered wage ratio calculation for 1971 to 

2100 (no longer used)

o Annual trend variable for taxable to covered self-employment earnings ratio 
91

calculation for 1971 to 2100 (no longer used)

• Proportions of OASDI tax liabilities for self-employment earnings for the current and 

prior calendar year estimated to be collected in each quarter for 1971 to 2100. (In any 

particular quarter, some self-employed individuals are paying taxes on earnings from the 

prior year and some are paying from the current year’s earnings.) Values are derived 

from historical data from the Office of Tax Analysis (OTA) in the Department of the 

Treasury for the amount of self-employment taxes transferred to the OASDI Trust Funds 

in each month split by the calendar year (either the current or the prior) in which the selfemployment income was earned. The data are updated every year after historical 

information for a complete new year is received (usually in March).

• Average OASDI covered wages by age groups and gender for 1996.

• Ratio of OASDI taxable to covered wages by age groups and gender for 1996.

• Corrections to prior FICA appropriation adjustments made in March 2000.

• Projected single-employer refunds of excess tax by month for September 2009 to 

September 2020.

• An adjustment factor to trend variable for ratio of OASDI taxable to covered wages for 

1971 to 2100. A factor of 0.4 is input for years 2002 to 2100 and is applied to modelcomputed time trend adjustments to RWTEE. Historical analysis suggests a “trend” rate 

of decline in RWTEE of about 0.0016 per year through 2001. This trend reflects a 

movement toward greater amounts of wages being paid to workers earning above the 

taxable maximum. We expect this trend to continue to the end of the short-range 

projection horizon, but at a slower rate. Consequently, we assume an adjustment factor of 

0.4 such that the trend annual rate of decline from 2002 to the end of the short-range 

projection horizon is about 0.0006 per year (i.e., 0.0016 * 0.4). The adjustment factor has 

not been updated since first decided upon. It will be changed if and when it is deemed 

appropriate.

• Add factor for ratio of OASDI taxable to covered Federal Civilian government sector 

wages for 2002 to 2020.

• Add factor for ratio of OASDI taxable to covered State and Local government sector 

wages for 2002 to 2020.

• Add factor to adjust model-computed add factor for the ratio of OASDI taxable to 

covered self-employment earnings for 2007.
92

2.4.c. Development of Output

Equation 2.4.1 - Employee Taxable Ratio (RWTEE)

Over the short-range projection horizon, the projected value for RWTEE is the sum of the 

model’s “raw” estimate and an addfactor. The raw estimate for RWTEE is dependent on the 

distribution of workers by wage interval, the RELMAX, RTP, the age-gender distribution of 

wage workers, and a time trend adjustment. The projected distribution of workers by wage 

interval is an average (or amalgam) distribution over the 1993 through 2004 period. Holding 

other factors constant, a distribution with relatively more workers with wages over the 

TAXMAX leads to a lower RWTEE. The RELMAX is defined as the ratio of the TAXMAX to 

the ACW. A higher RELMAX leads to a higher RWTEE. An increase in the RTP also leads to a 

higher RWTEE. The change in the projected RWTEE due to the change in the age-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 addfactor is the product of a “base” adjustment and an assumed weight. The base adjustment 

is defined as the actual value for RWTEE in the latest historical (or base) year less the raw 

estimated value for the same period. The weight has an assumed value of 0.9 for the first 

projected year, then values of 0.8 in the second projected year, 0.7 in the third projected year, ..., 

and 0.0 in the tenth projected year (i.e., the end of the short-range projection horizon). The 

addfactor is necessary because we assume that the distribution of wage workers by earnings 

interval in the base year will gradually change to the amalgam distribution by the end of the 

short-range period and remain constant thereafter. 

Over the long-range projection horizon, RWTEE is assumed to remain constant.

RWTEEs are also projected for various sub-aggregates including Federal Civilian employees 

under FERS and CSRS, Federal Civilian employees under CSRS only, S&L employees covered 

under OASDI, S&L employees covered under HI only, U.S. armed forces, and agriculture. The 

RWTEE for each sub-aggregate is dependent only on its sub-aggregate RELMAX, that is, the 

ratio of the TAXMAX to the sub-aggregate’s average covered wage.

Equation 2.4.3 - Multi-Employer Refund Wage Ratio (RMER)

The RMER is functionally related to the RWTEE. As RWTEE approaches one, then RMER 

approaches zero. In between the limit values, RMER is positive. Given the present position of 

RWTEE and RMER on the function, a projected decline in RWTEE leads to an increase in 

RMER.
93

The projected RMER is also dependent on RU. An increase in RU leads to a decrease in RMER. 

Equation 2.4.6 - Self-Employed Net Income Taxable Ratio (RSET)

The RSET is disaggregated by type of self-employed worker, SEO and CMB_TOT.

SEO - The RSET is dependent on the distribution of self-employed workers by income interval 

and a RELMAX. The projected distribution of self-employed workers by income interval is set 

to the 1996 distribution. The RELMAX is defined here as the ratio of the TAXMAX to the 

average income for SEO. A higher RELMAX leads to a higher RSET. 

CMB_TOT - Taxable self-employed net income for CMB_TOT is projected in two steps. First, a 

taxable earnings (wages and self-employed income) ratio for CMB_TOT is projected based on 

the 1996 distribution and a RELMAX defined as the ratio of the TAXMAX to the average 

covered earnings. The projected level of taxable earnings for CMB_TOT is the product of the 

estimated taxable earnings ratio for CMB_TOT and their covered earnings. Second, a taxable 

wage ratio for CMB_TOT is projected based on a RELMAX defined as the ratio of the 

TAXMAX to the average covered wage for CMB_TOT. The projected level of taxable wages for 

CMB_TOT is the product of the estimated taxable wage ratio for CMB_TOT and their covered 

wages.

Taxable self-employed net income for CMB_TOT is obtained by subtracting taxable wages from 

taxable earnings for CMB_TOT.

A “combined” RSET is calculated as the ratio of taxable self-employed net income for SEO and 

CMB_TOT to CSE_TOT. As with the RWTEE, the combined RSET is adjusted over the shortrange 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 selfemployed workers decline over the long-range period while the RELMAX for wage workers is 

approximately constant. Hence, the RSETs for SEO and CMB_TOT are projected to decline 

over the long-range period while the RWTEE is held constant.

Equation 2.4.11 - Quarterly Wage Tax Liabilities (WTLQ)

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 
94

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 are also calculated for each quarter for the other 

sectors. However, these are expected to be constants over the projection horizon.

Equation 2.4.12 - Quarterly Wage Tax Collections (WTLQC)

Employers incur tax liabilities when they pay wages to their employees. These liabilities are 

required to be deposited with the U.S. Treasury by employers based on the amount of total 

payroll tax liability (income taxes plus Social Security and Medicare taxes withheld) 

accumulated. Some very large employers must deposit their tax liabilities the next banking day 

after paying their employees. Other levels of accumulated tax liabilities require depositing within 

three days, by the middle of the following month, or by the end of the month following the 

quarter. If employers follow these deposit requirements, the result is that all tax liability for a 

particular quarter is deposited by the last day of the month following the end of the quarter. 

Thus, the WTLQC for any particular quarter are the sum of the tax liabilities deposited for wages 

paid in the same quarter and the liabilities deposited for wages paid in the prior quarter.

WTLQC are summed from sector components that include the Federal Civilian, Federal Military, 

Farm, S&L, and residual Private Nonfarm (including Private Household and Self-Reported 

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 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, WTLQC are the product of WTLQ and the proportion of 

WTLQ that should be deposited in the month following the end of each quarter. This proportion 

is based on the deposit requirements and estimates of accumulated tax liabilities, which in turn 

are based on firm size (or total wages paid).

Equation 2.4.13 - Quarterly Self-Employed Net Income Tax Collections (SELQC)

For wage workers, annual liabilities (WTL) are distributed to quarterly liabilities (WTLQ),

which in turn are distributed to quarterly collections (WTLQC). However, for self-employed 

workers, annual liabilities (SEL) are distributed directly to SELQC, since the SSA only receives 

self-employed liability amounts on an annual basis (from tabulations of Form 1040 Schedule SE 

provided by IRS).

SEL for a particular calendar year 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 self-employed workers to 

deposit estimated tax liabilities four times a year (January, April, June, and September).
95

Equation 2.4.14 - Appropriation Adjustments (AA)

We estimate WTLQC and SELQC for the next two quarters based on projected levels of WSD 

and Y in the various OMB FY Budgets. The Treasury uses these estimates to make initial 

appropriations to the OASDI Trust Funds over the period. Roughly one year after an initial 

appropriation has been made for a quarter, the initial appropriation is adjusted based on certified 

taxable wages reported on Forms 941 and W-2 and taxable self-employment income reported on 

Forms 1040 Schedule SE. This appropriation adjustment occurs quarterly and includes amounts 

due to newly-reported wages and self-employment income for all earlier periods.

FICA appropriation adjustments for wages are projected for all quarters for which we know what 

the Treasury will transfer. This generally means that we make estimates for adjustments to occur 

through the second quarter of the year following the Trustees Report year. The projected 

adjustment for each quarter is composed of two parts. The first part estimates the error in the 

initial appropriation for the fourth earlier quarter. This error is defined as the difference between 

the Treasury’s initial appropriation and that portion of TAXPAY’s latest estimate for that quarter 

which is expected to be certified at the point when the adjustment is made. The second part is an 

estimate of the tax liability from additional certified wages for all previous periods and is based 

on an average of additional amounts over a recent historical period. These estimates are currently 

made in separate Excel files (generally named “EstimatedAppAdjAlt2.xls” and placed in a folder 

unique to the particular Trustees Report, e.g., \\wmpiet\usr\wmpiet\Excel\TR10), where they are 

further documented in a “Notes” sheet in the Excel file.

Appropriation adjustments for self-employment income are projected over the entire projection 

horizon based on the historical pattern of reporting. These estimates are made in TAXPAY.
96

Appendix 2-1

Equations

2.1 U.S. Employment (USEMP)

UNEMPLOYMENT RATES, PRELIMINARY

MALES

RM1617_P = RM1617_P.1 + (-36.2076 * DIFF(RTP) - 14.2816 * DIFF(RTP.1) - 26.6756 * DIFF(RTP.2) - 16.9202 * DIFF(RTP.3)) *

50.00/44.72

RM1617

Ordinary Least Squares

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rm1617)

 = - 36.2076 * diff(rtp) - 14.2816 * diff(rtp)[-1]

 (2.29349) (0.87160)

 - 26.6756 * diff(rtp)[-2] - 16.9202 * diff(rtp)[-3]

 (1.63426) (1.06303)

 + 1.64214 * minw - 0.90365 * minw[-1] + 0.06020 * minw[-2]

 (1.76311) (0.70381) (0.04365)

 - 0.77627 * minw[-3] - 0.12616

 (0.72653) (0.26611)

Sum Sq 198.967 Std Err 1.2719 LHS Mean 0.0553

R Sq 0.1483 R Bar Sq 0.0929 F 8,123 2.6769

D.W.( 1) 2.5142 D.W.( 4) 2.3291

RM1819_P = RM1819_P.1 + (-48.4227 * DIFF(RTP) - 25.8766 * DIFF(RTP.1) - 21.7466 * DIFF(RTP.2) + 1.1551 * DIFF(RTP.3)) *

50.00/44.72

RM1819

Ordinary Least Squares

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rm1819)

 = - 48.4227 * diff(rtp) - 25.8766 * diff(rtp)[-1]

 (3.45103) (1.77685)

 - 21.7466 * diff(rtp)[-2] + 1.15512 * diff(rtp)[-3]

 (1.49900) (0.08165)

 + 0.62723 * minw - 0.48738 * minw[-1] + 0.67739 * minw[-2]

 (0.75770) (0.42710) (0.55270)

 - 0.79385 * minw[-3] - 0.11294

 (0.83595) (0.26803)

Sum Sq 157.172 Std Err 1.1304 LHS Mean 0.0235

R Sq 0.1890 R Bar Sq 0.1362 F 8,123 3.5828

D.W.( 1) 2.6908 D.W.( 4) 2.4565

RM2024_P = RM2024_P.1 + (-51.6518 * DIFF(RTP) - 16.6465 * DIFF(RTP.1) - 13.1350 * DIFF(RTP.2) - 10.9309 * DIFF(RTP.3)) *

50.00/44.72

RM2024
97

Ordinary Least Squares

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rm2024)

 = - 51.6518 * diff(rtp) - 16.6465 * diff(rtp)[-1]

 (7.75482) (2.35721)

 - 13.1350 * diff(rtp)[-2] - 10.9309 * diff(rtp)[-3] + 0.00093

 (1.86731) (1.59404) (0.01922)

Sum Sq 38.7297 Std Err 0.5522 LHS Mean -0.0048

R Sq 0.4356 R Bar Sq 0.4178 F 4,127 24.5002

D.W.( 1) 2.4679 D.W.( 4) 2.2856

RM2529_P = RM2529_P.1 + (-37.9533 * DIFF(RTP) - 17.3941 * DIFF(RTP.1) - 14.9170 * DIFF(RTP.2) - 7.0513 * DIFF(RTP.3)) *

50.00/44.72

RM2529

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm2529)

 = - 37.9533 * diff(rtp) - 17.3941 * diff(rtp)[-1]

 (7.06307) (3.05222)

 - 14.9170 * diff(rtp)[-2] - 7.05126 * diff(rtp)[-3] + 0.00609

 (2.61734) (1.28703) (0.15745)

Sum Sq 23.9433 Std Err 0.4394 LHS Mean 0.0095

R Sq 0.4417 R Bar Sq 0.4237 F 4,124 24.5278

D.W.( 1) 2.1341 D.W.( 4) 2.4166

RM3034_P = RM3034_P.1 + (-23.6417 * DIFF(RTP) - 14.1284 * DIFF(RTP.1) - 7.5008 * DIFF(RTP.2) - 9.7232 * DIFF(RTP.3)) * 50.00/44.72

RM3034

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm3034)

 = - 23.6417 * diff(rtp) - 14.1286 * diff(rtp)[-1]

 (6.21241) (3.50067)

 - 7.50079 * diff(rtp)[-2] - 9.7232 * diff(rtp)[-3] + 0.01058

 (1.85832) (2.50593) (0.38580)

Sum Sq 12.0091 Std Err 0.3112 LHS Mean 0.0119

R Sq 0.4221 R Bar Sq 0.4034 F 4,124 22.6397

D.W.( 1) 2.1876 D.W.( 4) 1.8816

RM3539_P = RM3539_P.1 + (-27.6828 * DIFF(RTP) - 5.4850 * DIFF(RTP.1) - 10.8974 * DIFF(RTP.2) - 9.8932 * DIFF(RTP.3)) * 50.00/44.72

RM3539

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm3539)

 = - 27.6828 * diff(rtp) - 5.48498 * diff(rtp)[-1]

 (6.57840) (1.22901)

 - 10.8974 * diff(rtp)[-2] - 9.8932 * diff(rtp)[-3] + 0.01127

 (2.44154) (2.30580) (0.37184)

Sum Sq 14.6843 Std Err 0.3441 LHS Mean 0.0130
98

R Sq 0.3795 R Bar Sq 0.3595 F 4,124 18.9589

D.W.( 1) 2.3381 D.W.( 4) 1.9092

RM4044_P = RM4044_P.1 + (-14.6558 * DIFF(RTP) - 14.9735 * DIFF(RTP.1) - 8.2594 * DIFF(RTP.2) - 5.5023 * DIFF(RTP.3)) * 50.00/44.72

RM4044

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm4044)

 = - 14.6558 * diff(rtp) - 14.9735 * diff(rtp)[-1]

 (3.48851) (3.36064)

 - 8.25944 * diff(rtp)[-2] - 5.50233 * diff(rtp)[-3] + 0.00570

 (1.85359) (1.28455) (0.18829)

Sum Sq 14.6357 Std Err 0.3436 LHS Mean 0.0064

R Sq 0.2692 R Bar Sq 0.2456 F 4,124 11.4206

D.W.( 1) 2.6138 D.W.( 4) 2.0655

RM4549_P = RM4549_P.1 + (-20.7806 * DIFF(RTP) - 11.5121 * DIFF(RTP.1) - 9.9409 * DIFF(RTP.2) + 1.5480 * DIFF(RTP.3)) * 

50.00/44.72

RM4549

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm4549)

 = - 20.7806 * diff(rtp) - 11.5121 * diff(rtp)[-1]

 (5.31669) (2.77721)

 - 9.9409 * diff(rtp)[-2] + 1.54797 * diff(rtp)[-3] + 0.00874

 (2.39795) (0.38844) (0.31046)

Sum Sq 12.6680 Std Err 0.3196 LHS Mean 0.0114

R Sq 0.3249 R Bar Sq 0.3031 F 4,124 14.9185

D.W.( 1) 2.2355 D.W.( 4) 1.7877

RM5054_P = RM5054_P.1 + (-19.3341 * DIFF(RTP) - 9.5336 * DIFF(RTP.1) - 8.8784 * DIFF(RTP.2) - 7.6218 * DIFF(RTP.3)) * 50.00/44.72

RM5054

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm5054)

 = - 19.3341 * diff(rtp) - 9.5336 * diff(rtp)[-1]

 (4.72314) (2.19601)

 - 8.87840 * diff(rtp)[-2] - 7.62180 * diff(rtp)[-3] + 0.01083

 (2.04491) (1.82617) (0.36742)

Sum Sq 13.8950 Std Err 0.3347 LHS Mean 0.0118

R Sq 0.2957 R Bar Sq 0.2730 F 4,124 13.0163

D.W.( 1) 2.1290 D.W.( 4) 1.7836

RM5559_P = RM5559_P.1 + (-25.9031 * DIFF(RTP) - 11.4442 * DIFF(RTP.1) - 4.5421 * DIFF(RTP.2) + 0.55815 * DIFF(RTP.3)) * 

50.00/44.72

RM5559

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm5559)

 = - 25.9031 * diff(rtp) - 11.4442 * diff(rtp)[-1]
99

 (5.21572) (2.17280)

 - 4.54211 * diff(rtp)[-2] + 0.55815 * diff(rtp)[-3] + 0.00326

 (0.86229) (0.11023) (0.09111)

Sum Sq 20.4526 Std Err 0.4061 LHS Mean 0.0068

R Sq 0.2605 R Bar Sq 0.2366 F 4,124 10.9177

D.W.( 1) 2.2469 D.W.( 4) 1.7904

RM6064_P = RM6064_P.1 + (1.3133 * DIFF(RTP) - 12.9625 * DIFF(RTP.1) - 2.4816 * DIFF(RTP.2) - 14.4797 * DIFF(RTP.3)) * 50.00/44.72

RM6064

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm6064)

 = 1.31332 * diff(rtp) - 12.9625 * diff(rtp)[-1]

 (0.25208) (2.34596)

 - 2.48164 * diff(rtp)[-2] - 14.4797 * diff(rtp)[-3] + 0.00491

 (0.44909) (2.72583) (0.13091)

Sum Sq 22.5085 Std Err 0.4261 LHS Mean 0.0021

R Sq 0.1187 R Bar Sq 0.0903 F 4,124 4.1768

D.W.( 1) 2.3485 D.W.( 4) 1.9007

RM6569_P = RM6569_P.1 + (-19.5151 * DIFF(RTP) + 4.9785 * DIFF(RTP.1) -13.3449 * DIFF(RTP.2) + 2.4706 * DIFF(RTP.3)) * 

50.00/44.72

RM6569

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rm6569)

 = - 19.5151 * diff(rtp) + 4.97852 * diff(rtp)[-1]

 (2.18595) (0.52582)

 - 13.3449 * diff(rtp)[-2] + 2.47056 * diff(rtp)[-3] - 0.01208

 (1.40935) (0.27142) (0.18783)

Sum Sq 66.0895 Std Err 0.7301 LHS Mean -0.0096

R Sq 0.0551 R Bar Sq 0.0246 F 4,124 1.8065

D.W.( 1) 2.6235 D.W.( 4) 1.5080

RM7074_P = RM7074_P.1 + (4.1938 * DIFF(RTP) - 5.9012 * DIFF(RTP.1) - 27.0406 * DIFF(RTP.2) + 7.0400 * DIFF(RTP.3)) * 50.00/44.72

RM7074

Ordinary Least Squares

QUARTERLY data for 111 periods from 1981Q2 to 2008Q4

Date: 23 OCT 2009

diff(rm7074)

 = 4.19384 * diff(rtp) - 5.90117 * diff(rtp)[-1]

 (0.25776) (0.34403)

 - 27.0406 * diff(rtp)[-2] + 7.03995 * diff(rtp)[-3] + 0.02434

 (1.59539) (0.43075) (0.24587)

Sum Sq 114.781 Std Err 1.0406 LHS Mean 0.0185

R Sq 0.0282 R Bar Sq -0.0085 F 4,106 0.7684

D.W.( 1) 2.8303 D.W.( 4) 1.7482

RM75O_P = RM75O_P.1 + (-12.1042 * DIFF(RTP) - 15.6142 * DIFF(RTP.1) + 7.06185 * DIFF(RTP.2) - 2.5738 * DIFF(RTP.3)) * 50.00/44.72

RM75O

Ordinary Least Squares

QUARTERLY data for 111 periods from 1981Q2 to 2008Q4
100

Date: 23 OCT 2009

diff(rm75o)

 = - 12.1042 * diff(rtp) - 15.6142 * diff(rtp)[-1]

 (0.80507) (0.98509)

 + 7.06185 * diff(rtp)[-2] - 2.57381 * diff(rtp)[-3] + 0.00860

 (0.45088) (0.17042) (0.09395)

Sum Sq 98.0128 Std Err 0.9616 LHS Mean 0.0133

R Sq 0.0212 R Bar Sq -0.0157 F 4,106 0.5749

D.W.( 1) 2.6726 D.W.( 4) 1.8788

FEMALES

RF1617_P = RF1617_P.1 + (-27.3243 * DIFF(RTP) + 13.4173 * DIFF(RTP.1) - 50.4583 * DIFF(RTP.2) - 0.3678 * DIFF(RTP.3))*50.00/44.72

RF1617

Ordinary Least Squares

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rf1617)

 = - 27.3243 * diff(rtp) + 13.4173 * diff(rtp)[-1]

 (1.81297) (0.85773)

 - 50.4583 * diff(rtp)[-2] - 0.36782 * diff(rtp)[-3]

 (3.23806) (0.02421)

 + 0.33050 * minw + 0.19356 * minw[-1] + 0.18090 * minw[-2]

 (0.37169) (0.15791) (0.13742)

 - 0.68394 * minw[-3] - 0.13675

 (0.67051) (0.30213)

Sum Sq 181.339 Std Err 1.2142 LHS Mean -0.0136

R Sq 0.1227 R Bar Sq 0.0656 F 8,123 2.1501

D.W.( 1) 2.9150 D.W.( 4) 2.4862

RF1819_P = RF1819_P.1 + (-42.6358 * DIFF(RTP) - 13.6261 * DIFF(RTP.1) + 9.5650 * DIFF(RTP.2) - 31.4798 * DIFF(RTP.3))*50.00/44.72

RF1819

Ordinary Least Squares

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rf1819)

 = - 42.6358 * diff(rtp) - 13.6261 * diff(rtp)[-1]

 (3.54124) (1.09043)

 + 9.5650 * diff(rtp)[-2] - 31.4798 * diff(rtp)[-3]

 (0.76838) (2.59333)

 + 0.27394 * minw - 0.95221 * minw[-1] + 1.01588 * minw[-2]

 (0.38566) (0.97247) (0.96600)

 - 0.32609 * minw[-3] - 0.05888

 (0.40019) (0.16286)

Sum Sq 115.721 Std Err 0.9700 LHS Mean -0.0217

R Sq 0.1706 R Bar Sq 0.1167 F 8,123 3.1631

D.W.( 1) 2.7048 D.W.( 4) 2.3991

RF2024_P = RF2024_P.1 + (-16.9400 * DIFF(RTP) - 13.2669 * DIFF(RTP.1) - 7.8323 * DIFF(RTP.2) - 8.6887 * DIFF(RTP.3))*50.00/44.72

RF2024

Ordinary Least Squares
101

QUARTERLY data for 132 periods from 1976Q1 to 2008Q4

Date: 23 OCT 2009

diff(rf2024)

 = - 16.9400 * diff(rtp) - 13.2669 * diff(rtp)[-1]

 (3.09139) (2.28348)

 - 7.83232 * diff(rtp)[-2] - 8.68870 * diff(rtp)[-3] - 0.02226

 (1.35342) (1.54010) (0.56228)

Sum Sq 26.2142 Std Err 0.4543 LHS Mean -0.0275

R Sq 0.1917 R Bar Sq 0.1663 F 4,127 7.5310

D.W.( 1) 2.5252 D.W.( 4) 2.1988

RF2529_P = RF2529_P.1 + (-15.5798 * DIFF(RTP) - 11.9097 * DIFF(RTP.1) - 9.8424 * DIFF(RTP.2) - 2.7555 * DIFF(RTP.3))*50.00/44.72

RF2529

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf2529)

 = - 15.5798 * diff(rtp) - 11.9097 * diff(rtp)[-1]

 (3.32423) (2.39607)

 - 9.8424 * diff(rtp)[-2] - 2.75548 * diff(rtp)[-3] - 0.01837

 (1.97999) (0.57663) (0.54398)

Sum Sq 18.2145 Std Err 0.3833 LHS Mean -0.0172

R Sq 0.2094 R Bar Sq 0.1839 F 4,124 8.2130

D.W.( 1) 2.3764 D.W.( 4) 2.0455

RF3034_P = RF3034_P.1 + (-12.5396 * DIFF(RTP) - 1.6601 * DIFF(RTP.1) - 21.0289 * DIFF(RTP.2) + 0.0881 * DIFF(RTP.3))*50.00/44.72

RF3034

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf3034)

 = - 12.5396 * diff(rtp) - 1.66005 * diff(rtp)[-1]

 (2.58233) (0.32234)

 - 21.0289 * diff(rtp)[-2] + 0.08813 * diff(rtp)[-3] - 0.01851

 (4.08297) (0.01780) (0.52910)

Sum Sq 19.5533 Std Err 0.3971 LHS Mean -0.0179

R Sq 0.1929 R Bar Sq 0.1669 F 4,124 7.4100

D.W.( 1) 2.5217 D.W.( 4) 2.0509

RF3539_P = RF3539_P.1 + (-21.9314 * DIFF(RTP) - 3.0139 * DIFF(RTP.1) - 7.8723 * DIFF(RTP.2) - 6.4785 * DIFF(RTP.3))*50.00/44.72;

RF3539

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf3539)

 = - 21.9314 * diff(rtp) - 3.01391 * diff(rtp)[-1]

 (5.04991) (0.65436)

 - 7.87232 * diff(rtp)[-2] - 6.47846 * diff(rtp)[-3] - 0.00217

 (1.70904) (1.46307) (0.06942)

Sum Sq 15.6401 Std Err 0.3551 LHS Mean -0.0005

R Sq 0.2453 R Bar Sq 0.2210 F 4,124 10.0778

D.W.( 1) 2.3835 D.W.( 4) 1.7499
102

RF4044_P = RF4044_P.1 + (-7.7893 * DIFF(RTP) - 7.7152 * DIFF(RTP.1) - 5.7849 * DIFF(RTP.2) - 2.7298 * DIFF(RTP.3))*50.00/44.72

RF4044

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf4044)

 = - 7.78933 * diff(rtp) - 7.71518 * diff(rtp)[-1]

 (1.61580) (1.50905)

 - 5.78494 * diff(rtp)[-2] - 2.72977 * diff(rtp)[-3] - 0.00986

 (1.13141) (0.55538) (0.28389)

Sum Sq 19.2707 Std Err 0.3942 LHS Mean -0.0095

R Sq 0.0780 R Bar Sq 0.0483 F 4,124 2.6232

D.W.( 1) 2.2897 D.W.( 4) 2.2106

RF4549_P = RF4549_P.1 + (-7.8747 * DIFF(RTP) -12.5212 * DIFF(RTP.1) + 3.56675 * DIFF(RTP.2) - 5.4812 * DIFF(RTP.3))*50.00/44.72

RF4549

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf4549)

 = - 7.87468 * diff(rtp) - 12.5212 * diff(rtp)[-1]

 (1.73362) (2.59919)

 + 3.56675 * diff(rtp)[-2] - 5.48119 * diff(rtp)[-3] - 0.00968

 (0.74033) (1.18351) (0.29587)

Sum Sq 17.1092 Std Err 0.3715 LHS Mean -0.0093

R Sq 0.1055 R Bar Sq 0.0767 F 4,124 3.6575

D.W.( 1) 2.5032 D.W.( 4) 2.1339

RF5054_P = RF5054_P.1 + (-9.7818 * DIFF(RTP) - 3.1242 * DIFF(RTP.1) - 14.0327 * DIFF(RTP.2) - 4.0364 * DIFF(RTP.3))*50.00/44.72

RF5054

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf5054)

 = - 9.7818 * diff(rtp) - 3.12420 * diff(rtp)[-1]

 (2.25978) (0.68055)

 - 14.0327 * diff(rtp)[-2] - 4.03638 * diff(rtp)[-3] - 0.00195

 (3.05649) (0.91457) (0.06247)

Sum Sq 15.5373 Std Err 0.3540 LHS Mean -0.0021

R Sq 0.1556 R Bar Sq 0.1283 F 4,124 5.7111

D.W.( 1) 2.3211 D.W.( 4) 1.9891

RF5559_P = RF5559_P.1 + (-2.4665 * DIFF(RTP) - 4.8191 * DIFF(RTP.1) - 11.4418 * DIFF(RTP.2) - 3.5854 * DIFF(RTP.3))*50.00/44.72

RF5559

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf5559)

 = - 2.46651 * diff(rtp) - 4.81906 * diff(rtp)[-1]

 (0.39811) (0.73342)
103

 - 11.4418 * diff(rtp)[-2] - 3.58538 * diff(rtp)[-3] - 0.00784

 (1.74120) (0.56759) (0.17561)

Sum Sq 31.8294 Std Err 0.5066 LHS Mean -0.0088

R Sq 0.0474 R Bar Sq 0.0166 F 4,124 1.5416

D.W.( 1) 2.8260 D.W.( 4) 1.3743

RF6064_P = RF6064_P.1 + (-22.1139 * DIFF(RTP) + 4.5539 * DIFF(RTP.1) - 6.2406 * DIFF(RTP.2) - 7.0337 * DIFF(RTP.3))*50.00/44.72

RF6064

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf6064)

 = - 22.1139 * diff(rtp) + 4.55389 * diff(rtp)[-1]

 (2.75662) (0.53526)

 - 6.24055 * diff(rtp)[-2] - 7.03372 * diff(rtp)[-3] - 0.00247

 (0.73345) (0.85995) (0.04266)

Sum Sq 53.3640 Std Err 0.6560 LHS Mean -0.0008

R Sq 0.0732 R Bar Sq 0.0433 F 4,124 2.4497

D.W.( 1) 3.0445 D.W.( 4) 1.3297

RF6569_P = RF6569_P.1 + (9.2541 * DIFF(RTP) + 7.6281 * DIFF(RTP.1) - 22.5230 * DIFF(RTP.2) + 0.2738 * DIFF(RTP.3))*50.00/44.72

RF6569

Ordinary Least Squares

QUARTERLY data for 129 periods from 1976Q4 to 2008Q4

Date: 23 OCT 2009

diff(rf6569)

 = 9.25410 * diff(rtp) + 7.62811 * diff(rtp)[-1]

 (0.80440) (0.62521)

 - 22.5230 * diff(rtp)[-2] + 0.27380 * diff(rtp)[-3] - 0.01724

 (1.84584) (0.02334) (0.20808)

Sum Sq 109.749 Std Err 0.9408 LHS Mean -0.0199

R Sq 0.0329 R Bar Sq 0.0017 F 4,124 1.0547

D.W.( 1) 3.0050 D.W.( 4) 1.0241

RF7074_P = RF7074_P.1 + (24.2237 * DIFF(RTP) + 8.3386 * DIFF(RTP.1) - 13.5317 * DIFF(RTP.2) - 8.1855 * DIFF(RTP.3))*50.00/44.72

RF7074

Ordinary Least Squares

QUARTERLY data for 111 periods from 1981Q2 to 2008Q4

Date: 23 OCT 2009

diff(rf7074)

 = 24.2237 * diff(rtp) + 8.33858 * diff(rtp)[-1]

 (1.28864) (0.42077)

 - 13.5317 * diff(rtp)[-2] - 8.18546 * diff(rtp)[-3] + 0.01891

 (0.69102) (0.43349) (0.16535)

Sum Sq 153.213 Std Err 1.2023 LHS Mean 0.0075

R Sq 0.0218 R Bar Sq -0.0151 F 4,106 0.5903

D.W.( 1) 2.6506 D.W.( 4) 1.6645

RF75O_P = RF75O_P.1 + (-28.8294 * DIFF(RTP) + 55.5911 * DIFF(RTP.1) - 31.0676 * DIFF(RTP.2) - 15.8580 * DIFF(RTP.3))*50.00/44.72

RF75O

Ordinary Least Squares

QUARTERLY data for 111 periods from 1981Q2 to 2008Q4

Date: 23 OCT 2009
104

diff(rf75o)

 = - 28.8294 * diff(rtp) + 55.5911 * diff(rtp)[-1]

 (1.09028) (1.99419)

 - 31.0676 * diff(rtp)[-2] - 15.8580 * diff(rtp)[-3] + 0.03090

 (1.12786) (0.59703) (0.19206)

Sum Sq 303.162 Std Err 1.6912 LHS Mean 0.0324

R Sq 0.0508 R Bar Sq 0.0149 F 4,106 1.4170

D.W.( 1) 2.6248 D.W.( 4) 1.5572

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

MALES

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) 

FEMALES

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) 

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) 
105

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

MALES

DRM1617_FE = (-36.2076 * (1 - RTP) - 14.2816 * (1 - RTP.1) - 26.6756 * (1 - RTP.2) - 16.9202 * (1 - RTP.3))*50.00/44.72

DRM1819_FE = (-48.4227 * (1 - RTP) - 25.8766 * (1 - RTP.1) - 21.7466 * (1 - RTP.2) + 1.1551 * (1 - RTP.3))*50.00/44.72

DRM2024_FE = (-51.6518 * (1 - RTP) - 16.6465 * (1 - RTP.1) - 13.1350 * (1 - RTP.2) - 10.9309 * (1 - RTP.3))*50.00/44.72

DRM2529_FE = (-37.9533 * (1 - RTP) - 17.3941 * (1 - RTP.1) - 14.9170 * (1 - RTP.2) - 7.0513 * (1 - RTP.3))*50.00/44.72

DRM3034_FE = (-23.6417 * (1 - RTP) - 14.1284 * (1 - RTP.1) - 7.5008 * (1 - RTP.2) - 9.7232 * (1 - RTP.3))*50.00/44.72

DRM3539_FE = (-27.6828 * (1 - RTP) - 5.4850 * (1 - RTP.1) - 10.8974 * (1 - RTP.2) - 9.8932 * (1 - RTP.3))*50.00/44.72

DRM4044_FE = (-14.6558 * (1 - RTP) - 14.9735 * (1 - RTP.1) - 8.2594 * (1 - RTP.2) - 5.5023 * (1 - RTP.3))*50.00/44.72

DRM4549_FE = (-20.7806 * (1 - RTP) - 11.5121 * (1 - RTP.1) - 9.9409 * (1 - RTP.2) + 1.5480 * (1 - RTP.3))*50.00/44.72

DRM5054_FE = (-19.3341 * (1 - RTP) - 9.5336 * (1 - RTP.1) - 8.8784 * (1 - RTP.2) - 7.6218 * (1 - RTP.3))*50.00/44.72

DRM5559_FE = (-25.9031 * (1 - RTP) - 11.4442 * (1 - RTP.1) - 4.5421 * (1 - RTP.2) + 0.55815 * (1 - RTP.3))*50.00/44.72

DRM6064_FE = (1.3133 * (1 - RTP) - 12.9625 * (1 - RTP.1) - 2.4816 * (1 - RTP.2) - 14.4797 * (1 - RTP.3))*50.00/44.72

DRM6569_FE = (-19.5151 * (1 - RTP) + 4.9785 * (1 - RTP.1) - 13.3449 * (1 - RTP.2) + 2.4706 * (1 - RTP.3))*50.00/44.72

DRM7074_FE = 4.1938 * (1 - RTP) - 5.9012 * (1 - RTP.1) - 27.0406 * (1 - RTP.2) + 7.0400 * (1 - RTP.3))*50.00/44.72

DRM75O_FE = (-12.1042 * (1 - RTP) - 15.6142 * (1 - RTP.1) + 7.06185 * (1 - RTP.2) - 2.5738 * (1 - RTP.3))*50.00/44.72

FEMALES

DRF1617_FE = (-27.3243 * (1 - RTP) + 13.4173 * (1 - RTP.1) - 50.4583 * (1 - RTP.2) - 0.3678 * (1 - RTP.3))*50.00/44.72

DRF1819_FE = (-42.6358 * (1 - RTP) - 13.6261 * (1 - RTP.1) + 9.5650 * (1 - RTP.2) - 31.4798 * (1 - RTP.3))*50.00/44.72

DRF2024_FE = (-16.9400 * (1 - RTP) - 13.2669 * (1 - RTP.1) - 7.8323 * (1 - RTP.2) - 8.6887 * (1 - RTP.3))*50.00/44.72

DRF2529_FE = (-15.5798 * (1 - RTP) - 11.9097 * (1 - RTP.1) - 9.8424 * (1 - RTP.2) - 2.7555 * (1 - RTP.3))*50.00/44.72

DRF3034_FE = (-12.5396 * (1 - RTP) - 1.6601 * (1 - RTP.1) - 21.0289 * (1 - RTP.2) + 0.0881 * (1 - RTP.3))*50.00/44.72

DRF3539_FE = (-21.9314 * (1 - RTP) - 3.0139 * (1 - RTP.1) - 7.8723 * (1 - RTP.2) - 6.4785 * (1 - RTP.3))*50.00/44.72

DRF4044_FE = (- 7.7893 * (1 - RTP) - 7.7152 * (1 - RTP.1) - 5.7849 * (1 - RTP.2) - 2.7298 * (1 - RTP.3))*50.00/44.72

DRF4549_FE = (- 7.8747 * (1 - RTP) - 12.5212 * (1 - RTP.1) + 3.56675 * (1 - RTP.2) - 5.4812 * (1 - RTP.3))*50.00/44.72

DRF5054_FE = (- 9.7818 * (1 - RTP) - 3.1242 * (1 - RTP.1) - 14.0327 * (1 - RTP.2) - 4.0364 * (1 - RTP.3))*50.00/44.72

DRF5559_FE = (- 2.4665 * (1 - RTP) - 4.8191 * (1 - RTP.1) - 11.4418 * (1 - RTP.2) - 3.5854 * (1 - RTP.3))*50.00/44.72

DRF6064_FE = (-22.1139 * (1 - RTP) + 4.5539 * (1 - RTP.1) - 6.2406 * (1 - RTP.2) - 7.0337 * (1 - RTP.3))*50.00/44.72

DRF6569_FE = (9.2541 * (1 - RTP) + 7.6281 * (1 - RTP.1) - 22.5230 * (1 - RTP.2) + 0.2738 * (1 - RTP.3))*50.00/44.72

DRF7074_FE = (24.2237 * (1 - RTP) + 8.3386 * (1 - RTP.1) - 13.5317 * (1 - RTP.2) - 8.1855 * (1 - RTP.3))*50.00/44.72

DRF75O_FE = (-28.8294 * (1 - RTP) + 55.5911 * (1 - RTP.1) - 31.0676 * (1 - RTP.2) - 15.8580 * (1 - RTP.3))*50.00/44.72
106

UNEMPLOYMENT RATES, FULL EMPLOYMENT DIFFERENTIALS

TOTALS

MALES

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

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)

MALE LFPR EQUATIONS

AGE 16 TO 19

PM1617_P = 0.98298 - 0.000026

 - 0.368046 * RM1617DI 

 - (- 0.78720 + 0.01330 * TR_PM1617 + 0.00158 * RM1617 + 0.00180 * RM1617.1 + 0.00115 * RM1617.2 + 0.00014 * RM1617.3 - 0.00072 

* RM1617.4 - 0.00094 * RM1617.5);

PM1819_P = 0.97979 - 0.000070

 - 0.614469 * RM1819DI 

 - (- 0.50476 + 0.00764 * TR_PM1819 + 0.00626 * MOVAVG(5,RM1819));

PM1617 = PM1617_P;

PM1819 = PM1819_P;
107

AGE 20 TO 54

NEVER MARRIED

PM2024NM_P = 1.04005 - 0.00523 - 0.000143 - 0.00225 * TR_PM2024 

 - 0.00063 * RM2024 - 0.00077 * RM2024.1 - 0.00059 * RM2024.2 - 0.00027 * RM2024.3 + 0.00005 * RM2024.4 + 0.00020 * RM2024.5

 - 0.788895 * RM2024DI;

PM2529NM_P = 0.97919 - 0.00809 + 0.000424 - 0.00070 * TR_PM2529 

 - 0.00028 * RM2529 - 0.00044 * RM2529.1 - 0.00050 * RM2529.2 - 0.00047 * RM2529.3 - 0.00037 * RM2529.4 - 0.00021 * RM2529.5

 - 0.887239 * RM2529DI;

PM3034NM_P = 0.90427 + 0.000567 

 - 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 - 0.00014 * RM3034.4 + 0.00001 * RM3034.5

 - 0.883076 * RM3034DI;

PM3539NM_P = 0.86825 - 0.000105 

 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 0.00015 * RM3539.5

 - 0.846107 * RM3539DI;

PM4044NM_P = 0.83977 - 0.001481 

 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 0.00031 * RM4044.5

 - 0.807518 * RM4044DI;

PM4549NM_P = 0.81116 - 0.004005

 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 0.00040 * RM4549.5

 - 0.765856 * RM4549DI;

 

PM5054NM_P = 0.77540 - 0.010316

 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 0.00139 * RM5054.5

 - 0.715161 * RM5054DI;

AGE 20 TO 54

MARRIED, SPOUSE PRESENT

PM2024MS_P = 1.03184 - 0.00733 + 0.000543 - 0.00069 * TR_PM2024 

 - 0.00063 * RM2024 - 0.00077 * RM2024.1 - 0.00059 * RM2024.2 - 0.00027 * RM2024.3 + 0.00005 * RM2024.4 + 0.00020 * RM2024.5 

 - 0.937270 * RM2024DI;

PM2529MS_P = 1.00110 - 0.00498 + 0.001239 - 0.00025 * TR_PM2529 

 - 0.00028 * RM2529 - 0.00044 * RM2529.1 - 0.00050 * RM2529.2 - 0.00047 * RM2529.3 - 0.00037 * RM2529.4 - 0.00021 * RM2529.5

 - 0.956095 * RM2529DI;

PM3034MS_P = 0.97120 + 0.001964 + 0.16457 * 1/(TR_PM3034 - 85) 

 - 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 - 0.00014 * RM3034.4 + 0.00001 * RM3034.5

 - 0.961197 * RM3034DI;

PM3539MS_P = 0.98068 + 0.002566

 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 0.00015 * RM3539.5

 - 0.958567 * RM3539DI;

PM4044MS_P = 0.98250 + 0.003434

 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 0.00031 * RM4044.5

 - 0.950227 * RM4044DI;

PM4549MS_P = 0.98115 + 0.004829

 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 0.00040 * RM4549.5

 - 0.935691 * RM4549DI;

PM5054MS_P = 0.94484 + 0.004732

 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 0.00139 * RM5054.5
108

 + 0.09796 * (RF5054CU6+RF5054C6O) - 0.901430 * RM5054DI;

AGE 20 TO 54

MARRIED, SPOUSE ABSENT

PM2024MA_P = 1.14087 - 0.01412 + 0.000270 - 0.00232 * TR_PM2024 

 - 0.00063 * RM2024 - 0.00077 * RM2024.1 - 0.00059 * RM2024.2 - 0.00027 * RM2024.3 + 0.00005 * RM2024.4 + 0.00020 * RM2024.5 

 - 0.878382 * RM2024DI;

PM2529MA_P = 0.98602 - 0.00788 + 0.000733 - 0.00051 * TR_PM2529 

 - 0.00028 * RM2529 - 0.00044 * RM2529.1 - 0.00050 * RM2529.2 - 0.00047 * RM2529.3 - 0.00037 * RM2529.4 - 0.00021 * RM2529.5

 - 0.913332 * RM2529DI;

PM3034MA_P = 0.93933 + 0.001197

 - 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 - 0.00014 * RM3034.4 + 0.00001 * RM3034.5

 - 0.918267 * RM3034DI;

PM3539MA_P = 0.92354 + 0.001209

 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 0.00015 * RM3539.5

 - 0.901443 * RM3539DI;

PM4044MA_P = 0.91512 + 0.001111

 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 0.00031 * RM4044.5

 - 0.882777 * RM4044DI;

PM4549MA_P = 0.89473 + 0.000334

 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 0.00040 * RM4549.5 

 - 0.849283 * RM4549DI;

 

PM5054MA_P = 0.84912 - 0.004345

 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 0.00139 * RM5054.5

 - 0.789075 * RM5054DI;

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;
109

PM2529MS = PM2529MS_P * PM2529 / PM2529_P;

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;

AGE 55 TO 61

PM55_P = - 0.76902 + 0.000142 - 0.818694 * RM55DI + PM55E_DE + PM55_DM

 + 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 - 0.00147 * RM5559.4 - 0.00126 * 

RM5559.5;

PM56_P = - 0.76098 - 0.002143 - 0.798138 * RM56DI + PM56E_DE + PM56_DM

 + 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 - 0.00147 * RM5559.4 - 0.00126 * 

RM5559.5;

PM57_P = - 0.71065 - 0.004979 - 0.776220 * RM57DI + PM57E_DE + PM57_DM

 + 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 - 0.00147 * RM5559.4 - 0.00126 * 

RM5559.5; 

PM58_P = - 0.69412 - 0.007970 - 0.755977 * RM58DI + PM58E_DE + PM58_DM

 + 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 - 0.00147 * RM5559.4 - 0.00126 * 

RM5559.5; 

PM59_P = - 0.60153 - 0.012123 - 0.730720 * RM59DI + PM59E_DE + PM59_DM

 + 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 - 0.00147 * RM5559.4 - 0.00126 * 

RM5559.5; 

PM60_P = - 0.58858 - 0.011072 + 0.000362 - 0.682175 * RM60DI + PM60E_DE + PM60_DM

 + 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * 

RM6064.5

 + 0.01566 * PF58;

PM61_P = - 0.55646 - 0.019672 + 0.002517 - 0.647667 * RM61DI + PM61E_DE + PM61_DM

 + 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * 

RM6064.5

 + 0.08544 * PF59;

AGE 62 TO 74

PM62_P = 0.26329 * PF60 - 0.29161 - 0.544582 * RM61DI.4 + PM62E_DE + PM62_DM - 0.056836 + 0.008814

 + 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * 

RM6064.5

 - 0.60 * RRADJ_M62 - 0.02 * POT_ET_TXRT_62; 

PM63_P = 0.40940 * PF61 - 0.29495 - 0.480592 * RM61DI.8 + PM63E_DE + PM63_DM - 0.085295 + 0.017121

 + 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * 

RM6064.5

 - 0.55 * RRADJ_M63 - 0.02 * POT_ET_TXRT_63; 

PM64_P = 0.47933 * PF62 - 0.22665 - 0.435189 * RM61DI.12 + PM64E_DE + PM64_DM - 0.113466 + 0.030849
110

 + 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * 

RM6064.5

 - 0.50 * RRADJ_M64 - 0.02 * POT_ET_TXRT_64; 

PM65_P = 0.72722 * PF63 - 0.35819 - 0.368105 * RM61DI.16 + PM65E_DE + PM65_DM - 0.016932 + 0.059764

 + 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 - 0.00178 * RM6569.4 - 0.00151 * 

RM6569.5

 - 0.45 * RRADJ_M65 - 0.02 * POT_ET_TXRT_65;

PM66_P = 0.38684 * PF64 - 0.20883 - 0.330352 * RM61DI.20 + PM66E_DE + PM66_DM + 0.000194 + 0.036539

 + 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 - 0.00178 * RM6569.4 - 0.00151 * 

RM6569.5

 - 0.40 * RRADJ_M66 - 0.02 * POT_ET_TXRT_66;

PM67_P = 0.35012 * PF65 - 0.15975 - 0.294277 * RM61DI.24 + PM67E_DE + PM67_DM + 0.042362 - 0.012475

 + 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 - 0.00178 * RM6569.4 - 0.00151 * 

RM6569.5

 - 0.35 * RRADJ_M67 - 0.02 * POT_ET_TXRT_67; 

PM68_P = 0.95984 * PF66 - 0.26305 - 0.269452 * RM61DI.28 + PM68E_DE + PM68_DM + 0.057835 - 0.027492

 + 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 - 0.00178 * RM6569.4 - 0.00151 * 

RM6569.5

 - 0.30 * RRADJ_M68 - 0.02 * POT_ET_TXRT_68; 

PM69_P = 0.74113 * PF67 - 0.22589 - 0.246975 * RM61DI.32 + PM69E_DE + PM69_DM + 0.047260 - 0.018867

 + 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 - 0.00178 * RM6569.4 - 0.00151 * 

RM6569.5

 - 0.30 * RRADJ_M69 - 0.02 * POT_ET_TXRT_69;

PM70_P = 0.46445 * PF68 - 0.23451 - 0.220464 * RM61DI.36 + PM70E_DE + PM70_DM + 0.037323 - 0.010528

 - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * 

RM7074.5;

PM71_P = 0.27684 * PF69 - 0.20679 - 0.202537 * RM61DI.40 + PM71E_DE + PM71_DM + 0.030867 - 0.005653

 - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * 

RM7074.5;

PM72_P = 0.77240 * PF70 - 0.25289 - 0.186071 * RM61DI.44 + PM72E_DE + PM72_DM + 0.040290 - 0.012330

 - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * 

RM7074.5;

PM73_P = 0.65971 * PF71 - 0.19394 - 0.167545 * RM61DI.48 + PM73E_DE + PM73_DM + 0.036021 - 0.009631

 - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * 

RM7074.5;

PM74_P = 0.78464 * PF72 - 0.17649 - 0.147134 * RM61DI.52 + PM74E_DE + PM74_DM + 0.033451 - 0.010839

 - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * 

RM7074.5;

AGE 75 TO 79

PM75_P = PM74.4 * 0.920 + DPM75O_FE;

PM76_P = PM75.4 * 0.920 + DPM75O_FE;

PM77_P = PM76.4 * 0.920 + DPM75O_FE;

PM78_P = PM77.4 * 0.920 + DPM75O_FE;

PM79_P = PM78.4 * 0.920 + DPM75O_FE;

AGE 55 TO 79

PM55 = PM55_P;

PM56 = PM56_P;
111

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;

AGE 80 AND OVER

PM80_P = PM79.4 * 0.965**( 1) + DPM75O_FE;

PM81_P = PM79.8 * 0.965**( 2) + DPM75O_FE;

PM82_P = PM79.12 * 0.965**( 3) + DPM75O_FE;

PM83_P = PM79.16 * 0.965**( 4) + DPM75O_FE;

PM84_P = PM79.20 * 0.965**( 5) + DPM75O_FE;

PM85_P = MOVAVG(8,PM79.24) * 0.965**( 6) + DPM75O_FE;

PM86_P = MOVAVG(8,PM79.28) * 0.965**( 7) + DPM75O_FE;

PM87_P = MOVAVG(8,PM79.32) * 0.965**( 8) + DPM75O_FE;

PM88_P = MOVAVG(8,PM79.36) * 0.965**( 9) + DPM75O_FE;

PM89_P = MOVAVG(8,PM79.40) * 0.965**(10) + DPM75O_FE;

PM90_P = MOVAVG(8,PM79.44) * 0.965**(11) + DPM75O_FE;

PM91_P = MOVAVG(8,PM79.48) * 0.965**(12) + DPM75O_FE;

PM92_P = MOVAVG(8,PM79.52) * 0.965**(13) + DPM75O_FE;

PM93_P = MOVAVG(8,PM79.56) * 0.965**(14) + DPM75O_FE;

PM94_P = MOVAVG(8,PM79.60) * 0.965**(15) + DPM75O_FE;

 

PM95_P = PM94_P * 0.965 + DPM75O_FE;

PM96_P = PM95_P * 0.965 + DPM75O_FE;

PM97_P = PM96_P * 0.965 + DPM75O_FE;

PM98_P = PM97_P * 0.965 + DPM75O_FE;

PM99_P = PM98_P * 0.965 + DPM75O_FE;

PM100_P = PM99_P * 0.965 + DPM75O_FE;

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;
112

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;

PM98 = PM98_P * PM80O / PM80O_P;

PM99 = PM99_P * PM80O / PM80O_P;

PM100 = PM100_P * PM80O / PM80O_P; 

FEMALE LFPR EQUATIONS

AGE 16 TO 19

PF1617_P = 0.98681 - 0.000047 - (0.377204 * RF1617DI) 

 - (- 0.00741 + 0.23393 * RF1617CU6 + 0.00051 * MOVAVG(5,RF1617))

 - (- 0.69608 + 0.01166 * TR_PF1617 + 0.00616 * MOVAVG(5,RF1617));

 

PF1819_P = 0.98200 - 0.000069

 - (0.584930 * RF1819DI) 

 - (-0.00080 + 0.22814 * RF1819CU6 + 0.00318 * MOVAVG(5,RF1819))

 - (- 0.53433+ 0.00764 * TR_PF1819 + 0.00667 * MOVAVG(5,RF1819));

PF1617 = PF1617_P;

PF1819 = PF1819_P;

AGE 20 TO 44

FEMALES - NEVER MARRIED WITH AT LEAST 1 OWN CHILD UNDER AGE 6

 

PF2024NMC6U_P = ( 0.70868 - 0.000477

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.661872 * RF2024DI)

 * 1.0160;

PF2529NMC6U_P = ( 0.74861 - 0.000966

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.700572 * RF2529DI)

 * 0.9981;

PF3034NMC6U_P = ( 0.73944 - 0.001998

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.690741 * RF3034DI)

 * 0.9980;

PF3539NMC6U_P = ( 0.75363 - 0.003230

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.701148 * RF3539DI)

 * 0.9989;

PF4044NMC6U_P = ( 0.73920 - 0.005589

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.677955 * RF4044DI)

 * 0.9989;
113

 

 

FEMALES - NEVER MARRIED NO OWN CHILDREN UNDER AGE 6

PF2024NMNC6_P = ( 1.13654 - 0.000206 - 0.00366 * TR_PF2024NMNC6

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.742995 * RF2024DI)

 * 1.0160;

PF2529NMNC6_P = ( 0.98148 + 0.000457 - 0.00111 * TR_PF2529NMNC6

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.853721 * RF2529DI)

 * 0.9981;

PF3034NMNC6_P = ( 0.84901 + 0.000598 

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.838634 * RF3034DI)

 * 0.9980;

PF3539NMNC6_P = ( 0.84953 + 0.000015 

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.822121 * RF3539DI)

 * 0.9989;

PF4044NMNC6_P = ( 0.83790 - 0.000878 

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.799021 * RF4044DI)

 * 0.9989;

FEMALES - MARRIED SPOUSE PRESENT WITH AT LEAST 1 OWN CHILD UNDER AGE 6

PF2024MSC6U_P = ( 0.69043 - 0.000935 + 0.000015

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.524765 * RF2024DI - 0.1*IF2024MSC6U)

 * 1.0160;

PF2529MSC6U_P = ( 0.76218 - 0.001821 - 0.000004

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.608428 * RF2529DI - 0.1*IF2529MSC6U)

 * 0.9981;

PF3034MSC6U_P = ( 0.78186 - 0.002891 - 0.000006

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.639819 * RF3034DI - 0.1*IF3034MSC6U)

 * 0.9980;

PF3539MSC6U_P = ( 0.79072 - 0.004987 - 0.000005

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.635646 * RF3539DI - 0.1*IF3539MSC6U)

 * 0.9989;

PF4044MSC6U_P = ( 0.79356 - 0.007041 - 0.000008

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.640644 * RF4044DI - 0.1*IF4044MSC6U)

 * 0.9989;

FEMALES - MARRIED SPOUSE PRESENT NO OWN CHILDREN UNDER AGE 6

PF2024MSNC6_P = ( 0.79421 - 0.000075
114

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.781956 * RF2024DI)

 * 1.0160;

PF2529MSNC6_P = ( 0.83502 + 0.000186

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.824520 * RF2529DI)

 * 0.9981;

PF3034MSNC6_P = ( 0.80379 - 0.000056

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.801357 * RF3034DI)

 * 0.9980;

PF3539MSNC6_P = ( 0.80906 - 0.000984

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.784868 * RF3539DI)

 * 0.9989; 

PF4044MSNC6_P = ( 0.82602 - 0.001249

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.789470 * RF4044DI)

 * 0.9989;

FEMALES - MARRIED SPOUSE ABSENT WITH AT LEAST 1 OWN CHILD UNDER AGE 6

PF2024MAC6U_P = ( 0.95787 - 0.000403 + 0.000007

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.683999 * RF2024DI - 0.16722 * IF2024MAC6U)

 * 1.0160; 

PF2529MAC6U_P = ( 0.90653 - 0.000676

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.731798 * RF2529DI - 0.10000 * IF2529MAC6U)

 * 0.9981;

PF3034MAC6U_P = ( 0.88071 - 0.001042

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.745172 * RF3034DI - 0.10000 * IF3034MAC6U)

 * 0.9980;

PF3539MAC6U_P = ( 0.90258 - 0.002058

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.744846 * RF3539DI - 0.10000 * IF3539MAC6U)

 * 0.9989;

PF4044MAC6U_P = ( 0.89876 - 0.003975 - 0.000005

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.719419 * RF4044DI - 0.10000 * IF4044MAC6U)

 * 0.9989;

FEMALES - MARRIED SPOUSE ABSENT NO OWN CHILDREN UNDER AGE 6

PF2024MANC6_P = ( 0.75174 - 0.000258 + 0.000005

 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 0.00052 * RF2024.5

 - 0.727427 * RF2024DI)

 * 1.0160;

PF2529MANC6_P = ( 0.82060 - 0.000015

 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 0.00013 * RF2529.5

 - 0.802962 * RF2529DI)
115

 * 0.9981;

PF3034MANC6_P = ( 0.83806 + 0.000442

 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 + 0.00128 * RF3034.5

 - 0.829717 * RF3034DI)

 * 0.9980;

PF3539MANC6_P = ( 0.86613 + 0.000458

 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 0.00132 * RF3539.5

 - 0.838637 * RF3539DI)

 * 0.9989;

PF4044MANC6_P = ( 0.85937 + 0.000112

 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 0.00046 * RF4044.5

 - 0.824438 * RF4044DI)

 * 0.9989;

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;

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;

AGE 45 TO 54

FEMALES - NEVER MARRIED 45 TO 54

PF4549NM_P = 0.03650 - 0.003349 + PF4549E_DE

 - 0.00076 * RF4549 - 0.00070 * RF4549.1 - 0.00018 * RF4549.2 + 0.00049 * RF4549.3 + 0.00096 * RF4549.4 + 0.00091 * RF4549.5

 - 0.774819 * RF4549DI;

PF5054NM_P = 0.05788 - 0.008250 + PF5054E_DE 

 + 0.00003 * RF5054 - 0.00011 * RF5054.1 - 0.00032 * RF5054.2 - 0.00051 * RF5054.3 - 0.00059 * RF5054.4 - 0.00045 * RF5054.5

 - 0.732696 * RF5054DI;

FEMALES - MARRIED SPOUSE PRESENT 45 TO 54

PF4549MS_P = 0.03842 - 0.003545 + PF4549E_DE 

 - 0.00076 * RF4549 - 0.00070 * RF4549.1 - 0.00018 * RF4549.2 + 0.00049 * RF4549.3 + 0.00096 * RF4549.4 + 0.00091 * RF4549.5

 - 0.771341 * RF4549DI - 0.15 * RF4549MSCU6;

PF5054MS_P = - 0.40180 - 0.008735 + PF5054E_DE

 + 0.00003 * RF5054 - 0.00011 * RF5054.1 - 0.00032 * RF5054.2 - 0.00051 * RF5054.3 - 0.00059 * RF5054.4 - 0.00045 * RF5054.5

 + 0.00454 * TR_PF5054MS - 0.726715 * RF5054DI - 0.12 * RF5054MSCU6;
116

FEMALES - MARRIED SPOUSE ABSENT 45 TO 54

PF4549MA_P = 0.06830 - 0.001541 + PF4549E_DE 

 - 0.00076 * RF4549 - 0.00070 * RF4549.1 - 0.00018 * RF4549.2 + 0.00049 * RF4549.3 + 0.00096 * RF4549.4 + 0.00091 * RF4549.5

 - 0.806961 * RF4549DI - 0.1 * RF4549MACU6; 

PF5054MA_P = 0.08983 - 0.006021 + PF5054E_DE 

 + 0.00003 * RF5054 - 0.00011 * RF5054.1 - 0.00032 * RF5054.2 - 0.00051 * RF5054.3 - 0.00059 * RF5054.4 - 0.00045 * RF5054.5

 - 0.760157 * RF5054DI - 0.2 * RF5054MACU6; 

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;

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; 
117

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; 

AGE 55 TO 61

PF55_P = - 0.678427 * RF55DI - 0.011198

 + 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * RF5559.4 - 0.00132 * RF5559.5

 + PF55E_DE + PF55_DM + 0.00368 * PF55COH48 - 0.90941; 

PF56_P = - 0.651951 * RF56DI - 0.014942

 + 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * RF5559.4 - 0.00132 * RF5559.5

 + PF56E_DE + PF56_DM + 0.00486 * PF56COH48 - 0.96865; 

PF57_P = - 0.634496 * RF57DI - 0.018113

 + 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * RF5559.4 - 0.00132 * RF5559.5

 + PF57E_DE + PF57_DM + 0.00344 * PF57COH48 - 0.85033; 

PF58_P = - 0.604503 * RF58DI - 0.023096

 + 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * RF5559.4 - 0.00132 * RF5559.5

 + PF58E_DE + PF58_DM + 0.00362 * PF58COH48 - 0.83081; 

PF59_P = - 0.571801 * RF59DI - 0.029463

 + 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * RF5559.4 - 0.00132 * RF5559.5

 + PF59E_DE + PF59_DM + 0.00470 * PF59COH48 - 0.85665; 

PF60_P = - 0.526008 * RF60DI - 0.033474

 + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * RF6064.4 - 0.00066 * RF6064.5

 + PF60E_DE + PF60_DM + 0.00819 * PF60COH48 - 1.18744; 

PF61_P = - 0.487750 * RF61DI - 0.041036

 + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * RF6064.4 - 0.00066 * RF6064.5

 + PF61E_DE + PF61_DM + 0.00520 * PF61COH48 - 0.87850; 

AGE 62 TO 74

PF62_P = - 0.412411 * RF61DI.4 - 0.063463 

 + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * RF6064.4 - 0.00066 * RF6064.5
118

 + PF62E_DE + PF62_DM + 0.00523 * PF62COH48 - 0.56287 - 0.5100 * RRADJ_F62 - 0.02 * POT_ET_TXRT_62; 

PF63_P = - 0.359185 * RF61DI.8 - 0.082104 

 + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * RF6064.4 - 0.00066 * RF6064.5

 + PF63E_DE + PF63_DM + 0.00659 * PF63COH48 - 0.68289 - 0.4675 * RRADJ_F63 - 0.02 * POT_ET_TXRT_63; 

PF64_P = - 0.323866 * RF61DI.12 - 0.094477 

 + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * RF6064.4 - 0.00066 * RF6064.5

 + PF64E_DE + PF64_DM + 0.00745 * PF64COH48 - 0.72813 - 0.4250 * RRADJ_F64 - 0.02 * POT_ET_TXRT_64;

PF65_P = - 0.256938 * RF61DI.16 + 0.035143

 + 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5

 + PF65E_DE + PF65_DM + 0.00348 * PF65COH48 - 0.37490 - 0.3825 * RRADJ_F65 - 0.02 * POT_ET_TXRT_65;

PF66_P = - 0.226911 * RF61DI.20 + 0.028402

 + 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5

 + PF66E_DE + PF66_DM + 0.00512 * PF66COH48 - 0.52851 - 0.3400 * RRADJ_F66 - 0.02 * POT_ET_TXRT_66;

PF67_P = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5

 - 0.206835 * RF61DI.24 + 0.025203 + PF67E_DE + PF67_DM + 0.00518 * PF67COH48 - 0.53735 - 0.2975 * RRADJ_F67 - 0.02 * 

POT_ET_TXRT_67;

PF68_P = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5

 - 0.180608 * RF61DI.28 + 0.020367 + PF68E_DE + PF68_DM + 0.00400 * PF68COH48 - 0.41046 - 0.2550 * RRADJ_F68 - 0.02 * 

POT_ET_TXRT_68;

PF69_P = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5

 - 0.162386 * RF61DI.32 + 0.017869 + PF69E_DE + PF69_DM + 0.00400 * PF69COH48 - 0.36706 - 0.2550 * RRADJ_F69 - 0.02 * 

POT_ET_TXRT_69;

PF70_P = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5

 - 0.136965 * RF61DI.36 + 0.015491 + PF70E_DE + PF70_DM + 0.00424 * PF70COH48 - 0.49282;

PF71_P = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5

 - 0.123245 * RF61DI.40 + 0.014381 + PF71E_DE + PF71_DM + 0.00300 * PF71COH48 - 0.37390;

PF72_P = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5

 - 0.107978 * RF61DI.44 + 0.013644 + PF72E_DE + PF72_DM + 0.00286 * PF72COH48 - 0.34670;

PF73_P = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5

 - 0.094426 * RF61DI.48 + 0.012196 + PF73E_DE + PF73_DM + 0.00370 * PF73COH48 - 0.41058;

PF74_P = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5

 - 0.082404 * RF61DI.52 + 0.010762 + PF74E_DE + PF74_DM + 0.00304 * PF74COH48 - 0.35113;

AGE 75 TO 79

PF75_P = PF74.4 * 0.900 + DPF75O_FE;

PF76_P = PF75.4 * 0.900 + DPF75O_FE;

PF77_P = PF76.4 * 0.900 + DPF75O_FE;

PF78_P = PF77.4 * 0.900 + DPF75O_FE;

PF79_P = PF78.4 * 0.900 + DPF75O_FE;

AGE 55 TO 79

PF55 = PF55_P;

PF56 = PF56_P;

PF57 = PF57_P;

PF58 = PF58_P;

PF59 = PF59_P;

PF60 = PF60_P;
119

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;

AGE 80 AND OVER

PF80_P = PF79.4 * 0.965**( 1) + DPF75O_FE;

PF81_P = PF79.8 * 0.965**( 2) + DPF75O_FE;

PF82_P = PF79.12 * 0.965**( 3) + DPF75O_FE;

PF83_P = PF79.16 * 0.965**( 4) + DPF75O_FE;

PF84_P = PF79.20 * 0.965**( 5) + DPF75O_FE;

PF85_P = MOVAVG(8,PF79.24) * 0.965**( 6) + DPF75O_FE;

PF86_P = MOVAVG(8,PF79.28) * 0.965**( 7) + DPF75O_FE;

PF87_P = MOVAVG(8,PF79.32) * 0.965**( 8) + DPF75O_FE;

PF88_P = MOVAVG(8,PF79.36) * 0.965**( 9) + DPF75O_FE;

PF89_P = MOVAVG(8,PF79.40) * 0.965**(10) + DPF75O_FE;

PF90_P = MOVAVG(8,PF79.44) * 0.965**(11) + DPF75O_FE;

PF91_P = MOVAVG(8,PF79.48) * 0.965**(12) + DPF75O_FE;

PF92_P = MOVAVG(8,PF79.52) * 0.965**(13) + DPF75O_FE;

PF93_P = MOVAVG(8,PF79.56) * 0.965**(14) + DPF75O_FE;

PF94_P = MOVAVG(8,PF79.60) * 0.965**(15) + DPF75O_FE;

PF95_P = PF94_P * 0.965 + DPF75O_FE;

PF96_P = PF95_P * 0.965 + DPF75O_FE;

PF97_P = PF96_P * 0.965 + DPF75O_FE;

PF98_P = PF97_P * 0.965 + DPF75O_FE;

PF99_P = PF98_P * 0.965 + DPF75O_FE;

PF100_P = PF99_P * 0.965 + DPF75O_FE;

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;
120

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 + 

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 +
121

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;

P16O_P = (PM16O_P * NM16O + PF16O_P * NF16O) / (NM16O + NF16O);

LCM_P = PM16O_P * NM16O;

LCF_P = PF16O_P * NF16O;

LC_P = LCM_P + LCF_P;

LABOR FORCE PARTICIPATION RATES, FULL EMPLOYMENT

MALE LFPR EQUATIONS, FULL EMPLOYMENT

DPM1617_FE = (- 0.00158 * RM1617_FE - 0.00180 * RM1617_FE.1 - 0.00115 * RM1617_FE.2 - 0.00014 * RM1617_FE.3 + 0.00072 * 

RM1617_FE.4 + 0.00094 * RM1617_FE.5) - (- 0.00158 * RM1617 - 0.00180 * RM1617.1 - 0.00115 * RM1617.2 - 0.00014 * RM1617.3 + 

0.00072 * RM1617.4 + 0.00094 * RM1617.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pm1617_dpk

 = - 0.00158 * rm1617_dpk - 0.00180 * rm1617_dpk[-1]

 (5.56270) (6.13183)

 - 0.00115 * rm1617_dpk[-2] - 0.00014 * rm1617_dpk[-3]

 (7.49261) (0.94429)

 + 0.00072 * rm1617_dpk[-4] + 0.00094 * rm1617_dpk[-5]

 (2.47378) (3.30450)

Polynomial lags:

 rm1617_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0343 Std Err 0.0149 LHS Mean -0.0011 Res Mean 0.0037

R Sq 0.2826 R Bar Sq 0.2777 F 2,146 28.7598 %RMSE 46265.0
122

D.W.( 1) 0.3942 D.W.( 4) 0.9128

DPM1819_FE = (- 0.00108 * RM1819_FE - 0.00127 * RM1819_FE.1 - 0.00088 * RM1819_FE.2 - 0.00023 * RM1819_FE.3 + 0.00034 * 

RM1819_FE.4 + 0.00053 * RM1819_FE.5) - (- 0.00108 * RM1819 - 0.00127 * RM1819.1 - 0.00088 * RM1819.2 - 0.00023 * RM1819.3 + 

0.00034 * RM1819.4 + 0.00053 * RM1819.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pm1819_dpk

 = - 0.00108 * rm1819_dpk - 0.00127 * rm1819_dpk[-1]

 (5.22267) (5.94236)

 - 0.00088 * rm1819_dpk[-2] - 0.00023 * rm1819_dpk[-3]

 (7.96365) (2.16526)

 + 0.00034 * rm1819_dpk[-4] + 0.00053 * rm1819_dpk[-5]

 (1.61951) (2.56002)

Polynomial lags:

 rm1819_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0192 Std Err 0.0114 LHS Mean -0.0040 Res Mean 0.0008

R Sq 0.2729 R Bar Sq 0.2679 F 2,146 27.3976 %RMSE 17596.7

D.W.( 1) 0.7981 D.W.( 4) 1.2825

DPM2024_FE = (- 0.00063 * RM2024_FE - 0.00077 * RM2024_FE.1 - 0.00059 * RM2024_FE.2 - 0.00027 * RM2024_FE.3 + 0.00005 * 

RM2024_FE.4 + 0.00020 * RM2024_FE.5) - (- 0.00063 * RM2024 - 0.00077 * RM2024.1 - 0.00059 * RM2024.2 - 0.00027 * RM2024.3 + 

0.00005 * RM2024.4 + 0.00020 * RM2024.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pm2024_dpk

 = - 0.00063 * rm2024_dpk - 0.00077 * rm2024_dpk[-1]

 (4.32837) (5.14659)

 - 0.00059 * rm2024_dpk[-2] - 0.00027 * rm2024_dpk[-3]

 (7.47597) (3.39844)

 + 0.00005 * rm2024_dpk[-4] + 0.00020 * rm2024_dpk[-5]

 (0.35674) (1.36468)

Polynomial lags:

 rm2024_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0067 Std Err 0.0068 LHS Mean -0.0028 Res Mean -0.0002

R Sq 0.2336 R Bar Sq 0.2284 F 2,146 22.2560 %RMSE 32980.5

D.W.( 1) 0.5915 D.W.( 4) 1.0423

DPM2529_FE = (- 0.00028 * RM2529_FE - 0.00044 * RM2529_FE.1 - 0.00050 * RM2529_FE.2 - 0.00047 * RM2529_FE.3 - 0.00037 * 

RM2529_FE.4 - 0.00021 * RM2529_FE.5) - (- 0.00028 * RM2529 - 0.00044 * RM2529.1 - 0.00050 * RM2529.2 - 0.00047 * RM2529.3 -

0.00037 * RM2529.4 - 0.00021 * RM2529.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009
123

pm2529_dpk

 = - 0.00028 * rm2529_dpk - 0.00044 * rm2529_dpk[-1]

 (1.40609) (2.14232)

 - 0.00050 * rm2529_dpk[-2] - 0.00047 * rm2529_dpk[-3]

 (4.60340) (4.70117)

 - 0.00037 * rm2529_dpk[-4] - 0.00021 * rm2529_dpk[-5]

 (1.87119) (1.06920)

Polynomial lags:

 rm2529_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0026 Std Err 0.0049 LHS Mean -0.0033 Res Mean -0.0016

R Sq 0.0492 R Bar Sq 0.0396 F 2, 99 2.5598 %RMSE 48872.7

D.W.( 1) 0.7362 D.W.( 4) 1.0116

DPM3034_FE = (- 0.00046 * RM3034_FE - 0.00061 * RM3034_FE.1 - 0.00054 * RM3034_FE.2 - 0.00036 * RM3034_FE.3 - 0.00014 * 

RM3034_FE.4 + 0.00001 * RM3034_FE.5) - (- 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 -

0.00014 * RM3034.4 + 0.00001 * RM3034.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm3034_dpk

 = - 0.00046 * rm3034_dpk - 0.00061 * rm3034_dpk[-1]

 (1.81713) (2.34240)

 - 0.00054 * rm3034_dpk[-2] - 0.00036 * rm3034_dpk[-3]

 (4.05252) (2.76527)

 - 0.00014 * rm3034_dpk[-4] + 0.00001 * rm3034_dpk[-5]

 (0.56353) (0.02760)

Polynomial lags:

 rm3034_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0024 Std Err 0.0049 LHS Mean -0.0015 Res Mean -0.0001

R Sq 0.1497 R Bar Sq 0.1411 F 2, 99 8.7134 %RMSE 50015.8

D.W.( 1) 0.6227 D.W.( 4) 0.8678

DPM3539_FE = (- 0.00004 * RM3539_FE - 0.00010 * RM3539_FE.1 - 0.00016 * RM3539_FE.2 - 0.00021 * RM3539_FE.3 - 0.00021 * 

RM3539_FE.4 - 0.00015 * RM3539_FE.5) - (- 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 -

0.00021 * RM3539.4 - 0.00015 * RM3539.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm3539_dpk

 = - 0.00004 * rm3539_dpk - 0.00010 * rm3539_dpk[-1]

 (0.12650) (0.32986)

 - 0.00016 * rm3539_dpk[-2] - 0.00021 * rm3539_dpk[-3]

 (1.10007) (1.48792)

 - 0.00021 * rm3539_dpk[-4] - 0.00015 * rm3539_dpk[-5]
124

 (0.72412) (0.51868)

Polynomial lags:

 rm3539_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0028 Std Err 0.0052 LHS Mean -0.0017 Res Mean -0.0010

R Sq -0.0664 R Bar Sq -0.0772 F 2, 99 NC %RMSE 1817.43

D.W.( 1) 0.4246 D.W.( 4) 0.5372

DPM4044_FE = (- 0.00057 * RM4044_FE - 0.00066 * RM4044_FE.1 - 0.00044 * RM4044_FE.2 - 0.00009 * RM4044_FE.3 + 0.00022 * 

RM4044_FE.4 + 0.00031 * RM4044_FE.5) - (- 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 

0.00022 * RM4044.4 + 0.00031 * RM4044.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm4044_dpk

 = - 0.00057 * rm4044_dpk - 0.00066 * rm4044_dpk[-1]

 (1.75853) (1.97180)

 - 0.00044 * rm4044_dpk[-2] - 0.00009 * rm4044_dpk[-3]

 (2.56550) (0.54915)

 + 0.00022 * rm4044_dpk[-4] + 0.00031 * rm4044_dpk[-5]

 (0.66426) (0.95499)

Polynomial lags:

 rm4044_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0029 Std Err 0.0054 LHS Mean -0.0012 Res Mean -0.0004

R Sq 0.0268 R Bar Sq 0.0170 F 2, 99 1.3647 %RMSE 310.335

D.W.( 1) 0.5028 D.W.( 4) 0.7333

DPM4549_FE = (- 0.00002 * RM4549_FE - 0.00016 * RM4549_FE.1 - 0.00034 * RM4549_FE.2 - 0.00049 * RM4549_FE.3 - 0.00054 * 

RM4549_FE.4 - 0.00040 * RM4549_FE.5) - (- 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 -

0.00054 * RM4549.4 - 0.00040 * RM4549.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm4549_dpk

 = - 0.00002 * rm4549_dpk - 0.00016 * rm4549_dpk[-1]

 (0.06650) (0.55897)

 - 0.00034 * rm4549_dpk[-2] - 0.00049 * rm4549_dpk[-3]

 (2.31789) (3.39192)

 - 0.00054 * rm4549_dpk[-4] - 0.00040 * rm4549_dpk[-5]

 (1.92566) (1.46813)

Polynomial lags:

 rm4549_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0015 Std Err 0.0039 LHS Mean -0.0013 Res Mean -0.0003

R Sq 0.0719 R Bar Sq 0.0625 F 2, 99 3.8350 %RMSE 4821.60
125

D.W.( 1) 0.7819 D.W.( 4) 1.0968

DPM5054_FE = ( 0.00112 * RM5054_FE + 0.00103 * RM5054_FE.1 + 0.00023 * RM5054_FE.2 - 0.00078 * RM5054_FE.3 - 0.00149 * 

RM5054_FE.4 - 0.00139 * RM5054_FE.5) - ( 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 -

0.00149 * RM5054.4 - 0.00139 * RM5054.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm5054_dpk

 = 0.00112 * rm5054_dpk + 0.00103 * rm5054_dpk[-1]

 (3.16181) (2.84569)

 + 0.00023 * rm5054_dpk[-2] - 0.00078 * rm5054_dpk[-3]

 (1.30991) (4.52791)

 - 0.00149 * rm5054_dpk[-4] - 0.00139 * rm5054_dpk[-5]

 (4.15166) (3.96094)

Polynomial lags:

 rm5054_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0037 Std Err 0.0061 LHS Mean -0.0012 Res Mean 0.0001

R Sq 0.1417 R Bar Sq 0.1330 F 2, 99 8.1732 %RMSE 42597.0

D.W.( 1) 1.0445 D.W.( 4) 1.5173

DPM5559_FE = ( 0.00062 * RM5559_FE + 0.00041 * RM5559_FE.1 - 0.00026 * RM5559_FE.2 - 0.00101 * RM5559_FE.3 - 0.00147 * 

RM5559_FE.4 - 0.00126 * RM5559_FE.5) - ( 0.00062 * RM5559 + 0.00041 * RM5559.1 - 0.00026 * RM5559.2 - 0.00101 * RM5559.3 -

0.00147 * RM5559.4 - 0.00126 * RM5559.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm5559_dpk

 = 0.00062 * rm5559_dpk + 0.00041 * rm5559_dpk[-1]

 (1.23508) (0.79452)

 - 0.00026 * rm5559_dpk[-2] - 0.00101 * rm5559_dpk[-3]

 (1.02810) (4.16786)

 - 0.00147 * rm5559_dpk[-4] - 0.00126 * rm5559_dpk[-5]

 (2.91432) (2.53301)

Polynomial lags:

 rm5559_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0066 Std Err 0.0080 LHS Mean -0.0037 Res Mean -0.0014

R Sq 0.0164 R Bar Sq 0.0065 F 2, 99 0.8277 %RMSE 256947

D.W.( 1) 0.8793 D.W.( 4) 1.2992

DPM6064_FE = ( 0.00203 * RM6064_FE + 0.00160 * RM6064_FE.1 - 0.00021 * RM6064_FE.2 - 0.00235 * RM6064_FE.3 - 0.00374 * 

RM6064_FE.4 - 0.00331 * RM6064_FE.5) - ( 0.00203 * RM6064 + 0.00160 * RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 -

0.00374 * RM6064.4 - 0.00331 * RM6064.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009
126

pm6064_dpk

 = 0.00203 * rm6064_dpk + 0.00160 * rm6064_dpk[-1]

 (2.66008) (2.03611)

 - 0.00021 * rm6064_dpk[-2] - 0.00235 * rm6064_dpk[-3]

 (0.51861) (5.71949)

 - 0.00374 * rm6064_dpk[-4] - 0.00331 * rm6064_dpk[-5]

 (4.77362) (4.35298)

Polynomial lags:

 rm6064_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0165 Std Err 0.0110 LHS Mean -0.0095 Res Mean -0.0067

R Sq -0.2740 R Bar Sq -0.2869 F 2, 99 NC %RMSE 21316.0

D.W.( 1) 0.5297 D.W.( 4) 0.7821

DPM6569_FE = ( 0.00067 * RM6569_FE + 0.00040 * RM6569_FE.1 - 0.00040 * RM6569_FE.2 - 0.00127 * RM6569_FE.3 - 0.00178 * 

RM6569_FE.4 - 0.00151 * RM6569_FE.5) - ( 0.00067 * RM6569 + 0.00040 * RM6569.1 - 0.00040 * RM6569.2 - 0.00127 * RM6569.3 -

0.00178 * RM6569.4 - 0.00151 * RM6569.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm6569_dpk

 = 0.00067 * rm6569_dpk + 0.00040 * rm6569_dpk[-1]

 (0.93838) (0.52443)

 - 0.00040 * rm6569_dpk[-2] - 0.00127 * rm6569_dpk[-3]

 (0.89477) (2.96224)

 - 0.00178 * rm6569_dpk[-4] - 0.00151 * rm6569_dpk[-5]

 (2.41737) (2.13109)

Polynomial lags:

 rm6569_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0210 Std Err 0.0138 LHS Mean -0.0059 Res Mean -0.0047

R Sq -0.0832 R Bar Sq -0.0942 F 2, 99 NC %RMSE 36465.0

D.W.( 1) 0.5122 D.W.( 4) 0.7034

DPM7074_FE = (- 0.00013 * RM7074_FE - 0.00016 * RM7074_FE.1 - 0.00013 * RM7074_FE.2 - 0.00006 * RM7074_FE.3 + 0.00000 * 

RM7074_FE.4 + 0.00003 * RM7074_FE.5) - (- 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * RM7074.3 + 

0.00000 * RM7074.4 + 0.00003 * RM7074.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm7074_dpk

 = - 0.00013 * rm7074_dpk - 0.00016 * rm7074_dpk[-1]

 (0.30689) (0.35702)

 - 0.00013 * rm7074_dpk[-2] - 0.00006 * rm7074_dpk[-3]

 (0.44247) (0.21289)

 + 0.00000 * rm7074_dpk[-4] + 0.00003 * rm7074_dpk[-5]

 (0.00874) (0.08371)
127

Polynomial lags:

 rm7074_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0114 Std Err 0.0080 LHS Mean -0.0073 Res Mean -0.0071

R Sq -0.8795 R Bar Sq -0.8984 F 2, 99 NC %RMSE 1540.73

D.W.( 1) 0.5068 D.W.( 4) 0.7160

DPM75O_FE = (- 0.00043 * RM75O_FE - 0.00051 * RM75O_FE.1 - 0.00036 * RM75O_FE.2 - 0.00010 * RM75O_FE.3 + 0.00013 * 

RM75O_FE.4 + 0.00021 * RM75O_FE.5) - (- 0.00043 * RM75O - 0.00051 * RM75O.1 - 0.00036 * RM75O.2 - 0.00010 * RM75O.3 + 0.00013 

* RM75O.4 + 0.00021 * RM75O.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pm75o_dpk

 = - 0.00043 * rm75o_dpk - 0.00051 * rm75o_dpk[-1]

 (1.82379) (2.03996)

 - 0.00036 * rm75o_dpk[-2] - 0.00010 * rm75o_dpk[-3]

 (2.39851) (0.66247)

 + 0.00013 * rm75o_dpk[-4] + 0.00021 * rm75o_dpk[-5]

 (0.51659) (0.86124)

Polynomial lags:

 rm75o_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0039 Std Err 0.0058 LHS Mean -0.0031 Res Mean -0.0025

R Sq -0.2424 R Bar Sq -0.2549 F 2, 99 NC %RMSE 19877.0

D.W.( 1) 0.8382 D.W.( 4) 1.0542

FEMALE LFPR EQUATIONS, FULL EMPLOYMENT DIFFERENTIALS

DPF1617_FE = (- 0.00224 * RF1617_FE - 0.00239 * RF1617_FE.1 - 0.00126 * RF1617_FE.2 + 0.00035 * RF1617_FE.3 + 0.00163 * 

RF1617_FE.4 + 0.00178 * RF1617_FE.5) - (- 0.00224 * RF1617 - 0.00239 * RF1617.1 - 0.00126 * RF1617.2 + 0.00035 * RF1617.3 + 0.00163 

* RF1617.4 + 0.00178 * RF1617.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pf1617_dpk

 = - 0.00224 * rf1617_dpk - 0.00239 * rf1617_dpk[-1]

 (5.90261) (6.13505)

 - 0.00126 * rf1617_dpk[-2] + 0.00035 * rf1617_dpk[-3]

 (6.26010) (1.72973)

 + 0.00163 * rf1617_dpk[-4] + 0.00178 * rf1617_dpk[-5]

 (4.17464) (4.69274)
128

Polynomial lags:

 rf1617_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0354 Std Err 0.0153 LHS Mean 0.0006 Res Mean 0.0030

R Sq 0.2161 R Bar Sq 0.2107 F 2,146 20.1227 %RMSE 28883.0

D.W.( 1) 0.4141 D.W.( 4) 0.9322

DPF1819_FE = (- 0.00124 * RF1819_FE - 0.00147 * RF1819_FE.1 - 0.00106 * RF1819_FE.2 - 0.00035 * RF1819_FE.3 + 0.00030 * 

RF1819_FE.4 + 0.00053 * RF1819_FE.5) - (- 0.00124 * RF1819 - 0.00147 * RF1819.1 - 0.00106 * RF1819.2 - 0.00035 * RF1819.3 + 0.00030 * 

RF1819.4 + 0.00053 * RF1819.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pf1819_dpk

 = - 0.00124 * rf1819_dpk - 0.00147 * rf1819_dpk[-1]

 (4.35316) (5.03839)

 - 0.00106 * rf1819_dpk[-2] - 0.00035 * rf1819_dpk[-3]

 (7.08785) (2.38461)

 + 0.00030 * rf1819_dpk[-4] + 0.00053 * rf1819_dpk[-5]

 (1.03892) (1.89331)

Polynomial lags:

 rf1819_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0217 Std Err 0.0120 LHS Mean -0.0031 Res Mean 0.0021

R Sq 0.2645 R Bar Sq 0.2594 F 2,146 26.2493 %RMSE 53411.9

D.W.( 1) 0.8392 D.W.( 4) 1.3288

DPF2024_FE = (- 0.00087 * RF2024_FE - 0.00099 * RF2024_FE.1 - 0.00063 * RF2024_FE.2 - 0.00007 * RF2024_FE.3 + 0.00041 * 

RF2024_FE.4 + 0.00052 * RF2024_FE.5) - (- 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 

* RF2024.4 + 0.00052 * RF2024.5)

Restricted Ordinary Least Squares

QUARTERLY data for 148 periods from 1971Q1 to 2007Q4

Date: 2 SEP 2009

pf2024_dpk

 = - 0.00087 * rf2024_dpk - 0.00099 * rf2024_dpk[-1]

 (1.95040) (2.16369)

 - 0.00063 * rf2024_dpk[-2] - 0.00007 * rf2024_dpk[-3]

 (2.80524) (0.30336)

 + 0.00041 * rf2024_dpk[-4] + 0.00052 * rf2024_dpk[-5]

 (0.90125) (1.17782)

Polynomial lags:

 rf2024_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0212 Std Err 0.0120 LHS Mean -0.0017 Res Mean 0.0002

R Sq 0.0408 R Bar Sq 0.0343 F 2,146 3.1076 %RMSE 51970.8

D.W.( 1) 0.2424 D.W.( 4) 0.5144
129

DPF2529_FE = (- 0.00056 * RF2529_FE - 0.00070 * RF2529_FE.1 - 0.00057 * RF2529_FE.2 - 0.00029 * RF2529_FE.3 - 0.00002 * 

RF2529_FE.4 + 0.00013 * RF2529_FE.5) - (- 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * 

RF2529.4 + 0.00013 * RF2529.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf2529_dpk

 = - 0.00056 * rf2529_dpk - 0.00070 * rf2529_dpk[-1]

 (0.83571) (1.02414)

 - 0.00057 * rf2529_dpk[-2] - 0.00029 * rf2529_dpk[-3]

 (1.64524) (0.87576)

 - 0.00002 * rf2529_dpk[-4] + 0.00013 * rf2529_dpk[-5]

 (0.02505) (0.19165)

Polynomial lags:

 rf2529_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0129 Std Err 0.0110 LHS Mean 0.0014 Res Mean 0.0030

R Sq 0.0265 R Bar Sq 0.0167 F 2, 99 1.3467 %RMSE 1908.57

D.W.( 1) 0.2611 D.W.( 4) 0.6593

DPF3034_FE = (- 0.00081 * RF3034_FE - 0.00065 * RF3034_FE.1 + 0.00005 * RF3034_FE.2 + 0.00089 * RF3034_FE.3 + 0.00143 * 

RF3034_FE.4 + 0.00128 * RF3034_FE.5) - (- 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 

* RF3034.4 + 0.00128 * RF3034.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf3034_dpk

 = - 0.00081 * rf3034_dpk - 0.00065 * rf3034_dpk[-1]

 (1.30466) (1.02194)

 + 0.00005 * rf3034_dpk[-2] + 0.00089 * rf3034_dpk[-3]

 (0.16121) (2.80112)

 + 0.00143 * rf3034_dpk[-4] + 0.00128 * rf3034_dpk[-5]

 (2.29055) (2.08640)

Polynomial lags:

 rf3034_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0083 Std Err 0.0088 LHS Mean 0.0040 Res Mean 0.0026

R Sq -0.1326 R Bar Sq -0.1440 F 2, 99 NC %RMSE 29049.2

D.W.( 1) 0.3221 D.W.( 4) 0.8675

DPF3539_FE = (- 0.00195 * RF3539_FE - 0.00216 * RF3539_FE.1 - 0.00128 * RF3539_FE.2 + 0.00002 * RF3539_FE.3 + 0.00111 * 

RF3539_FE.4 + 0.00132 * RF3539_FE.5) - (- 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 

* RF3539.4 + 0.00132 * RF3539.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf3539_dpk
130

 = - 0.00195 * rf3539_dpk - 0.00216 * rf3539_dpk[-1]

 (2.96355) (3.19201)

 - 0.00128 * rf3539_dpk[-2] + 0.00002 * rf3539_dpk[-3]

 (3.74105) (0.06643)

 + 0.00111 * rf3539_dpk[-4] + 0.00132 * rf3539_dpk[-5]

 (1.67998) (2.03681)

Polynomial lags:

 rf3539_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0079 Std Err 0.0089 LHS Mean -0.0021 Res Mean -0.0007

R Sq 0.0801 R Bar Sq 0.0708 F 2, 99 4.3116 %RMSE 6918.68

D.W.( 1) 0.3914 D.W.( 4) 0.5620

DPF4044_FE = (- 0.00026 * RF4044_FE - 0.00050 * RF4044_FE.1 - 0.00068 * RF4044_FE.2 - 0.00076 * RF4044_FE.3 - 0.00070 * 

RF4044_FE.4 - 0.00046 * RF4044_FE.5) - (- 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * 

RF4044.4 - 0.00046 * RF4044.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf4044_dpk

 = - 0.00026 * rf4044_dpk - 0.00050 * rf4044_dpk[-1]

 (0.53052) (0.99291)

 - 0.00068 * rf4044_dpk[-2] - 0.00076 * rf4044_dpk[-3]

 (2.55091) (2.90760)

 - 0.00070 * rf4044_dpk[-4] - 0.00046 * rf4044_dpk[-5]

 (1.41817) (0.96194)

Polynomial lags:

 rf4044_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0041 Std Err 0.0061 LHS Mean 0.0005 Res Mean 0.0021

R Sq 0.1306 R Bar Sq 0.1218 F 2, 99 7.4378 %RMSE 4872.89

D.W.( 1) 0.5681 D.W.( 4) 0.8422

DPF4549_FE = (- 0.00076 * RF4549_FE - 0.00070 * RF4549_FE.1 - 0.00018 * RF4549_FE.2 + 0.00049 * RF4549_FE.3 + 0.00096 * 

RF4549_FE.4 + 0.00091 * RF4549_FE.5) - (- 0.00076 * RF4549 - 0.00070 * RF4549.1 - 0.00018 * RF4549.2 + 0.00049 * RF4549.3 + 0.00096 

* RF4549.4 + 0.00091 * RF4549.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf4549_dpk

 = - 0.00076 * rf4549_dpk - 0.00070 * rf4549_dpk[-1]

 (1.20345) (1.08117)

 - 0.00018 * rf4549_dpk[-2] + 0.00049 * rf4549_dpk[-3]

 (0.50034) (1.36204)

 + 0.00096 * rf4549_dpk[-4] + 0.00091 * rf4549_dpk[-5]

 (1.47572) (1.44905)

Polynomial lags:
131

 rf4549_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0046 Std Err 0.0063 LHS Mean 0.0028 Res Mean 0.0027

R Sq -0.1835 R Bar Sq -0.1954 F 2, 99 NC %RMSE 316691

D.W.( 1) 0.7137 D.W.( 4) 0.9879

DPF5054_FE = ( 0.00003 * RF5054_FE - 0.00011 * RF5054_FE.1 - 0.00032 * RF5054_FE.2 - 0.00051 * RF5054_FE.3 - 0.00059 * 

RF5054_FE.4 - 0.00045 * RF5054_FE.5) - ( 0.00003 * RF5054 - 0.00011 * RF5054.1 - 0.00032 * RF5054.2 - 0.00051 * RF5054.3 - 0.00059 * 

RF5054.4 - 0.00045 * RF5054.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf5054_dpk

 = 0.00003 * rf5054_dpk - 0.00011 * rf5054_dpk[-1]

 (0.05929) (0.18046)

 - 0.00032 * rf5054_dpk[-2] - 0.00051 * rf5054_dpk[-3]

 (1.13804) (1.96823)

 - 0.00059 * rf5054_dpk[-4] - 0.00045 * rf5054_dpk[-5]

 (1.04732) (0.80816)

Polynomial lags:

 rf5054_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0054 Std Err 0.0073 LHS Mean -0.0004 Res Mean 0.0010

R Sq 0.0704 R Bar Sq 0.0611 F 2, 99 3.7511 %RMSE 66278.7

D.W.( 1) 0.8578 D.W.( 4) 1.1467

DPF5559_FE = ( 0.00064 * RF5559_FE + 0.00041 * RF5559_FE.1 - 0.00029 * RF5559_FE.2 - 0.00107 * RF5559_FE.3 - 0.00155 * 

RF5559_FE.4 - 0.00132 * RF5559_FE.5) - ( 0.00064 * RF5559 + 0.00041 * RF5559.1 - 0.00029 * RF5559.2 - 0.00107 * RF5559.3 - 0.00155 * 

RF5559.4 - 0.00132 * RF5559.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf5559_dpk

 = 0.00064 * rf5559_dpk + 0.00041 * rf5559_dpk[-1]

 (0.89335) (0.55546)

 - 0.00029 * rf5559_dpk[-2] - 0.00107 * rf5559_dpk[-3]

 (0.75840) (2.90227)

 - 0.00155 * rf5559_dpk[-4] - 0.00132 * rf5559_dpk[-5]

 (2.15075) (1.87882)

Polynomial lags:

 rf5559_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0102 Std Err 0.0102 LHS Mean -0.0011 Res Mean 0.0005

R Sq 0.0769 R Bar Sq 0.0676 F 2, 99 4.1224 %RMSE 4599.06

D.W.( 1) 0.8791 D.W.( 4) 0.8944
132

DPF6064_FE = ( 0.00141 * RF6064_FE + 0.00166 * RF6064_FE.1 + 0.00116 * RF6064_FE.2 + 0.00033 * RF6064_FE.3 - 0.00041 * 

RF6064_FE.4 - 0.00066 * RF6064_FE.5) - ( 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 0.00041 * 

RF6064.4 - 0.00066 * RF6064.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf6064_dpk

 = 0.00141 * rf6064_dpk + 0.00166 * rf6064_dpk[-1]

 (1.84124) (2.11172)

 + 0.00116 * rf6064_dpk[-2] + 0.00033 * rf6064_dpk[-3]

 (2.99557) (0.93319)

 - 0.00041 * rf6064_dpk[-4] - 0.00066 * rf6064_dpk[-5]

 (0.54220) (0.88278)

Polynomial lags:

 rf6064_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0113 Std Err 0.0105 LHS Mean 0.0007 Res Mean -0.0017

R Sq 0.1074 R Bar Sq 0.0984 F 2, 99 5.9541 %RMSE 8386.58

D.W.( 1) 0.6636 D.W.( 4) 0.8453

DPF6569_FE = ( 0.00029 * RF6569_FE + 0.00014 * RF6569_FE.1 - 0.00023 * RF6569_FE.2 - 0.00063 * RF6569_FE.3 - 0.00086 * 

RF6569_FE.4 - 0.00072 * RF6569_FE.5) - ( 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * 

RF6569.4 - 0.00072 * RF6569.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf6569_dpk

 = 0.00029 * rf6569_dpk + 0.00014 * rf6569_dpk[-1]

 (0.39369) (0.18572)

 - 0.00023 * rf6569_dpk[-2] - 0.00063 * rf6569_dpk[-3]

 (0.46891) (1.29792)

 - 0.00086 * rf6569_dpk[-4] - 0.00072 * rf6569_dpk[-5]

 (1.10980) (0.98371)

Polynomial lags:

 rf6569_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0161 Std Err 0.0097 LHS Mean -0.0088 Res Mean -0.0083

R Sq -0.8729 R Bar Sq -0.8918 F 2, 99 NC %RMSE 5935.52

D.W.( 1) 0.3864 D.W.( 4) 0.3951

DPF7074_FE = (- 0.00009 * RF7074_FE - 0.00028 * RF7074_FE.1 - 0.00048 * RF7074_FE.2 - 0.00063 * RF7074_FE.3 - 0.00064 * 

RF7074_FE.4 - 0.00046 * RF7074_FE.5) - (- 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * 

RF7074.4 - 0.00046 * RF7074.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf7074_dpk

 = - 0.00009 * rf7074_dpk - 0.00028 * rf7074_dpk[-1]
133

 (0.41200) (1.18982)

 - 0.00048 * rf7074_dpk[-2] - 0.00063 * rf7074_dpk[-3]

 (3.71663) (4.89240)

 - 0.00064 * rf7074_dpk[-4] - 0.00046 * rf7074_dpk[-5]

 (2.78954) (2.06896)

Polynomial lags:

 rf7074_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0038 Std Err 0.0059 LHS Mean -0.0043 Res Mean -0.0018

R Sq -0.1504 R Bar Sq -0.1620 F 2, 99 NC %RMSE 14566.3

D.W.( 1) 0.7462 D.W.( 4) 1.0245

DPF75O_FE = (- 0.00007 * RF75O_FE - 0.00012 * RF75O_FE.1 - 0.00015 * RF75O_FE.2 - 0.00014 * RF75O_FE.3 - 0.00012 * RF75O_FE.4 -

0.00007 * RF75O_FE.5) - (- 0.00007 * RF75O - 0.00012 * RF75O.1 - 0.00015 * RF75O.2 - 0.00014 * RF75O.3 - 0.00012 * RF75O.4 - 0.00007 

* RF75O.5)

Restricted Ordinary Least Squares

QUARTERLY data for 101 periods from 1982Q4 to 2007Q4

Date: 2 SEP 2009

pf75o_dpk

 = - 0.00007 * rf75o_dpk - 0.00012 * rf75o_dpk[-1]

 (0.83244) (1.28137)

 - 0.00015 * rf75o_dpk[-2] - 0.00014 * rf75o_dpk[-3]

 (2.41595) (2.48652)

 - 0.00012 * rf75o_dpk[-4] - 0.00007 * rf75o_dpk[-5]

 (1.27553) (0.79882)

Polynomial lags:

 rf75o_dpk

 from 0 to 5 degree 3 near far

Sum Sq 0.0008 Std Err 0.0028 LHS Mean 0.0001 Res Mean 0.0004

R Sq 0.0818 R Bar Sq 0.0725 F 2, 99 4.4079 %RMSE 43067.0

D.W.( 1) 0.7531 D.W.( 4) 1.3841
134

2.2 U.S. Earnings (USEAR)

Annual Employment Equations

NonagriculturalWage Workers, Private Household Workers

EF1617NAWPH = MAX (0.001, -0.20802 * RTP - 0.40988 * RTP.1 + 0.01015 + 61.2465 * 1/YEAR - 0.00965 * MINW/CPIW_U + 0.01561 * 

NU10/NF1617 - 0.13398) * EF1617

EF1819NAWPH = MAX (0.001, -0.03363 * RTP - 0.12989 * RTP.1 - 0.00661 + 8.44701 * 1/YEAR - 0.00539 * MINW/CPIW_U + 0.00345 * 

NU10/NF1819 + 0.07597) * EF1819

EF2024NAWPH = MAX (0.001, -0.18707 * MOVAVG (5, RTP) - 0.00223 + 2.12060 * 1/YEAR + 0.00820 * NU10/NF2024 + 0.14537) * EF2024

EF2534NAWPH = MAX (0.001, 0.01874 * RTP - 0.04167 * MOVAVG (5, RTP.1) - 0.00090 + 1.55167 * 1/YEAR + 0.01021 * NU10/NF2534 -

0.00170) * EF2534

EF3544NAWPH = (0.00622 * RTP - 0.06062 * MOVAVG (5, RTP.1) + 0.00008 + 0.29372 * MOVAVG (3, EF2534NAWPH.9/EF2534.9) + 

0.06187) * EF3544

EF4554NAWPH = (0.02788 * RTP - 0.10996 * MOVAVG (5, RTP.1) - 0.00349 + 0.53068 * MOVAVG (3, EF3544NAWPH.9/EF3544.9) + 

0.08883) * EF4554

EF5564NAWPH = (0.05939 * RTP - 0.10618 * MOVAVG (2, RTP.1) - 0.00579 + 0.66195 * MOVAVG (3, EF4554NAWPH.9/EF4554.9) + 

0.05966) * EF5564

EF65ONAWPH = (0.22642 * RTP - 0.02069 + 0.33505 * MOVAVG (3, EF5564NAWPH.9) - 0.19707)

EM1617NAWPH = MAX (0.001, -0.05284 * RTP - 0.17833 * RTP.1 - 0.00768 + 9.19738 * 1/YEAR - 0.00588 * MINW/CPIW_U + 0.16862) * 

EM1617

EM1819NAWPH = MAX (0.001, -0.07122 * RTP - 0.03737 * RTP.1 - 0.00282 + 3.76796 * 1/YEAR - 0.00499 * MINW/CPIW_U + 0.08727) * 

EM1819

EM2024NAWPH = MAX (0.001, -0.00450 * RTP - 0.02345 * RTP.1 - 0.00113 - 0.00057 * MINW/CPIW_U + 0.03265) * EM2024

EM2534NAWPH = MAX (0.001, -0.00490 * RTP.1 - 0.00054 - 0.00051 * MINW/CPIW_U + 0.00789) * EM2534

EM3544NAWPH = (-0.00446 * RTP.1 - 0.00041 - 0.00053 * MINW/CPIW_U + 0.00726) * EM3544

EM4554NAWPH = (-0.00039 + 0.00129) * EM4554

EM5564NAWPH = (-0.00015 + 0.00200) * EM5564

EM65ONAWPH = (-0.00679 + 0.64405 * MOVAVG (3, EM5564NAWPH.9) + 0.00231)

Nonagricultural Self-employed workers

EF1617NAS = (0.12015 * RTP.1 - 0.10551) * EF1617

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef1617nas/ef1617 = 0.12015 * rtp.1 - 0.10551

 (1.96868) (1.73441)

Sum Sq 0.0000 

Std Error 0.0030 

LHS Mean 0.0142

R-Squared 0.5637 

R Bar Squared 0.4182 

F-stat 1, 3 3.8757

D.W. (1) 1.5620 

D.W. (2) 2.3626

EF1819NAS = (0.11184 * RTP.1 - 0.10241) * EF1819

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

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 
135

D.W. (2) 0.9766

EF2024NAS = (0.08908 * RTP.1 - 0.07176) * EF2024

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef2024nas/ef2024 = 0.08908 * rtp.1 - 0.07176

 (2.54605) (2.05763)

Sum Sq 0.0000 

Std Error 0.0017 

LHS Mean 0.0170

R-Squared 0.6836 

R Bar Squared 0.5782 

F-STAT 1, 3 6.4824

D.W. (1) 2.6600 

D.W. (2) 1.5247

EF2534NAS = (0.00906 * RTP.1 + 0.03539) * EF2534

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef2534nas/ef2534 = 0.00906 * rtp.1 + 0.03539

 (0.34277) (1.34366)

Sum Sq 0.0000 

Std Error 0.0013 

LHS Mean 0.0444

R-Squared 0.0377 

R Bar Squared 0.2831 

F-STAT 1, 3 0.1175

D.W. (1) 3.0818 

D.W. (2) 1.1094

EF3544NAS = (-0.01869 * RTP.1 + 0.08087) * EF3544

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef3544nas/ef3544 = -0.01869 * rtp.1 + 0.08087

 (0.70565) (3.06320)

Sum Sq 0.0000 

Std Error 0.0013 

LHS Mean 0.0622

R-Squared 0.1424 

R Bar Squared 0.1435 

F-STAT 1, 3 0.4979

D.W. (1) 2.2440 

D.W. (2) 2.1852

EF4554NAS = (0.07232 * RTP.1 - 0.00701) * EF4554

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
136

D.W. (1) 1.7821 

D.W. (2) 2.7029

EF5564NAS = (0.07872 * RTP.1 + 0.00466) * EF5564

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef5564nas/ef5564 = 0.07872 * rtp.1 + 0.00466

 (1.38159) (0.08196)

Sum Sq 0.0000 

Std Error 0.0028 

LHS Mean 0.0831

R-Squared 0.3889 

R Bar Squared 0.1851 

F-STAT 1, 3 1.9088

D.W. (1) 2.6092 

D.W. (2) 2.2686

EF65ONAS = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O)

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef6569nas/ef6569 = 0.10940

 (37.7493)

Sum Sq 0.0002 

Std Error 0.0065 

LHS Mean 0.1094

R-Squared 0.0000 

R Bar Squared 0.0000 

F 0, 4 NC

D.W. (1) 3.0431 

D.W. (2) 1.2204

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

ef7074nas/ef7074 = 0.12265

 (16.4939)

Sum Sq 0.0011 

Std Error 0.0166 

LHS Mean 0.1226

R-Squared 0.0000 

R Bar Squared 0.0000 

F 0, 4 NC

D.W. (1) 1.0289 

D.W. (2) 1.7188

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 
137

D.W. (2) 1.2345

EM1617NAS = (-0.23035 * RTP.1 + 0.24985) * EM1617

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em1617nas/em1617 = -0.23035 * rtp.1 + 0.24985

 (5.08538) (5.53372)

Sum Sq 0.0000 

Std Error 0.0022 

LHS Mean 0.0203

R-Squared 0.8961 

R Bar Squared 0.8614 

F-STAT 1, 3 25.8611

D.W. (1) 2.4658 

D.W. (2) 1.6839

EM1819NAS = (-0.05782 * RTP.1 + 0.07265) * EM1819

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em1819nas/em1819 = -0.05782 * rtp.1 + 0.07265

 (3.43044) (4.32458)

Sum Sq 0.0000 

Std Error 0.0008 

LHS Mean 0.0150

R-Squared 0.7969 

R Bar Squared 0.7291 

F-STAT 1, 3 11.7679

D.W. (1) 3.3262 

D.W. (2) 1.0399

EM2024NAS = (-0.09206 * RTP.1 + 0.11567) * EM2024

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em2024nas/em2024 = -0.09206 * rtp.1 + 0.11567

 (2.44839) (3.08618)

Sum Sq 0.0000 

Std Error 0.0018 

LHS Mean 0.0239

R-Squared 0.6665 

R Bar Squared 0.5553 

F-STAT 1, 3 5.9946

D.W. (1) 2.1493 

D.W. (2) 1.7046

EM2534NAS = (-0.09661 * RTP.1 + 0.14843) * EM2534

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em2534nas/em2534 = -0.09661 * rtp.1 + 0.14843

 (2.81478) (4.33847)

Sum Sq 0.0000 

Std Error 0.0017 

LHS Mean 0.0522

R-Squared 0.7254 

R Bar Squared 0.6338 

F-STAT 1, 3 7.9230
138

D.W. (1) 1.8300 

D.W. (2) 2.9632

EM3544NAS = (0.02739 * RTP.1 + 0.05236) * EM3544

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em3544nas/em3544 = 0.02739 * rtp.1 + 0.05236

 (0.61129) (1.17241)

Sum Sq 0.0000 

Std Error 0.0022 

LHS Mean 0.0797

R-Squared 0.1108 

R Bar Squared 0.1857 

F-STAT 1, 3 0.3737

D.W. (1) 2.5508 

D.W. (2) 2.2676

EM4554NAS = (0.06217 * RTP.1 + 0.03411) * EM4554

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em4554nas/em4554 = 0.06217 * rtp.1 + 0.03411

 (1.91738) (1.05544)

Sum Sq 0.0000 

Std Error 0.0016 

LHS Mean 0.0961

R-Squared 0.5507 

R Bar Squared 0.4009 

F-STAT 1, 3 3.6764

D.W. (1) 2.5497 

D.W. (2) 1.5554

EM5564NAS = (-0.04776 * RTP.1 + 0.16626) * EM5564

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em5564nas/em5564 = -0.04776 * rtp.1 + 0.16626

 (0.60480) (2.11226)

Sum Sq 0.0000 

Std Error 0.0039 

LHS Mean 0.1187

R-Squared 0.1087 

R Bar Squared 0.1884 

F-STAT 1, 3 0.3658

D.W. (1) 2.9234 

D.W. (2) 1.9432

EM65ONAS = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O)

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em6569nas/em6569 = 0.16527

 (53.9126)

Sum Sq 0.0002 

Std Error 0.0069 

LHS Mean 0.1653

R-Squared 0.0000 

R Bar Squared 0.0000 

F-stat 0, 4 NC
139

D.W. (1) 1.7716 

D.W. (2) 2.9645

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em7074nas/em7074 = 0.17798

 (22.9265)

Sum Sq 0.0012 

Std Error 0.0174 

LHS Mean 0.1780

R-Squared 0.0000 

R Bar Squared 0.0000 

F-stat 0, 4 NC

D.W. (1) 1.7116 

D.W. (2) 2.1991

Ordinary Least Squares

ANNUAL data for 5 periods from 2000 to 2004

Date: 9 NOV 2005

em75onas/em75o = 0.19058

 (20.1892)

Sum Sq 0.0018 

Std Error 0.0211 

LHS Mean 0.1906

R-Squared 0.0000 

R Bar Squared 0.0000 

F-stat 0, 4 NC

D.W. (1) 2.7330 

D.W. (2) 0.9992

Nonagricultural Unpaid Family Workers

EF1617NAU = 0.00012 * ENAS

EF1819NAU = 0.00025 * ENAS

EF2024NAU = 0.00024 * ENAS

EF2534NAU = 0.00117 * ENAS

EF3544NAU = 0.00218 * ENAS

EF4554NAU = 0.00226 * ENAS

EF5564NAU = 0.00083 * ENAS

EF65ONAU = (0.00027 + 0.00021 + 0.00008) * ENAS

EM1617NAU = 0.00028 * ENAS

EM1819NAU = 0.00033 * ENAS

EM2024NAU = 0.00050 * ENAS

EM2534NAU = 0.00044 * ENAS

EM3544NAU = 0.00043 * ENAS

EM4554NAU = 0.00052 * ENAS

EM5564NAU = 0.00037 * ENAS

EM65ONAU = (0.00023 + 0.00010 + 0.00011) * ENAS

Agricultural Wage Workers

EM1617AW = EAW * (-0.00594 - 0.09353 * RTP + 5.28754 * EM1617/E + 0.08116)

EM1819AW = EAW * (-0.00131 - 0.18120 * RTP + 3.87151 * EM1819/E + 0.16636)

EM2024AW = EAW * (-0.00664 + 0.10493 * RTP + 2.00153 * EM2024/E - 0.08191)

EM2534AW = EAW * (-0.02065 + 0.38358 * RTP - 0.98380 * EM2534/E + 0.00751)

EM3544AW = EAW * (0.00402 - 0.15663 * RTP + 1.72119 * EM3544/E + 0.05679)

EM4554AW = EAW * (0.00834 + 0.03746 * RTP + 0.46522 * EM4554/E + 0.00144)

EM5564AW = EAW * (-0.00655 + 0.03521 * RTP + 0.46852 * EM5564/E - 0.00037)

EM65OAW = EAW * (-0.00114 + 0.07640 * RTP + 3.25911 * EM65O/E - 0.10058)
140

EF1617AW = EAW * (-0.00055 - 0.05470 * RTP + 1.41760 * EF1617/E + 0.04979)

EF1819AW = EAW * (0.00102 - 0.07375 * RTP + 0.78394 * EF1819/E + 0.07226)

EF2024AW = EAW * (0.00112 - 0.05971 * RTP + 0.57256 * EF2024/E + 0.05907)

EF2534AW = EAW * (0.00623 + 0.08868 * RTP + 1.00897 * EF2534/E - 0.15142)

EF3544AW = EAW * (0.00687 - 0.00259 * RTP + 0.51319 * EF3544/E - 0.00937)

EF4554AW = EAW * (0.00185 + 0.08747 * RTP + 0.28022 * EF4554/E - 0.08053)

EF5564AW = EAW * (-0.00140 - 0.03001 * RTP - 0.59383 * EF5564/E + 0.07088)

EF65OAW = EAW * (0.00096 + 0.06768 * RTP + 1.04213 * EF65O/E - 0.07359)

Agricultural Self-employed Workers

EM1617AS = NM1617 * (0.00528 + 0.00404)

EM1819AS = NM1819 * (0.00309 + 0.28448 * EA / (NM16O+ NF16O) - 0.00165)

EM2024AS = NM2024 * (-0.00181 + 0.97958 * EA / (NM16O+ NF16O) - 0.01093)

EM2534AS = NM2534 * (-0.00263 + 1.23186 * EA / (NM16O+ NF16O) - 0.01021)

EM3544AS = NM3544 * (-0.00151 + 1.66765 * EA / (NM16O+ NF16O) - 0.01450)

EM4554AS = NM4554 * (-0.00381 + 2.86654 * EA / (NM16O+ NF16O) - 0.03175)

EM5564AS = NM5564 * (-0.00460 + 2.78817 * EA / (NM16O+ NF16O) - 0.02398)

EM65OAS = NM65O * (0.00079 + 1.76904 * EA / (NM16O+ NF16O) - 0.01437)

EF1617AS = NF1617 * (0.00181 + 0.00030)

EF1819AS = EM1819AS * (-0.02393 + 0.63672 * RTP + 0.98791 * EF1819/EM1819 - 1.43926)

EF2024AS = EM2024AS * (0.07353 - 0.40207 * RTP + 0.57572 * EF2024/EM2024 - 0.01117)

EF2534AS = EM2534AS * (0.16575 + 0.16967 * RTP + 0.55503 * EF2534/EM2534 - 0.43412)

EF3544AS = EM3544AS * (0.15848 + 0.37839 * RTP + 0.37764 * EF3544/EM3544 - 0.45362)

EF4554AS = EM4554AS * (0.21947 + 0.29497 * RTP + 0.58974 * EF4554/EM4554 - 0.51966)

EF5564AS = EM5564AS * (0.20892 + 0.36294 * RTP + 0.65320 * EF5564/EM5564 - 0.66626)

EF65OAS = EM65OAS * (0.16242 + 0.54916 * RTP + 0.06199 * EF65O/EM65O - 0.47556)

Agricultural Unpaid Family Workers

EF1617AU = 0.002

EF1819AU = 0.001

EF2024AU = 0.001

EF2534AU = 0.003

EF3544AU = 0.004

EF4554AU = 0.005

EF5564AU = 0.003

EF65OAU = 0.001

EM1617AU = 0.006

EM1819AU = 0.005

EM2024AU = 0.005

EM2534AU = 0.002

EM3544AU = 0.002

EM4554AU = 0.001

EM5564AU = 0.001

EM65OAU = 0.002

Quarterly Employment Equations

ENA = E - EA

Nonagricultural Wage Workers, Private Household Workers:

EF1617NAWPH_R = MAX (0.001, -0.20802 * MOVAVG (4, RTP.1) - 0.40988 * MOVAVG (4, RTP.5) + 0.01015 + 61.2465 * 1/YEAR -

0.00965 * MINW/CPIW_U + 0.01561 * NU10/NF1617 - 0.13398) * EF1617 + EF1617NAWPH.ADJ

EF1819NAWPH_R = MAX (0.001, -0.03363 * MOVAVG (4, RTP.1) - 0.12989 * MOVAVG (4, RTP.5) - 0.00661 + 8.44701 * 1/YEAR -

0.00539 * MINW/CPIW_U + 0.00345 * NU10/NF1819 + 0.07597) * EF1819 + EF1819NAWPH.ADJ

EF2024NAWPH_R = MAX (0.001, -0.18707 * MOVAVG (20, RTP.1) - 0.00223 + 2.12060 * 1/YEAR + 0.00820 * NU10/NF2024 + 0.14537) * 

EF2024 + EF2024NAWPH.ADJ

EF2534NAWPH_R = MAX (0.001, 0.01874 * MOVAVG (4, RTP.1) - 0.04167 * MOVAVG (20, RTP.5) - 0.00090 + 1.55167 * 1/YEAR + 

0.01021 * NU10/NF2534 - 0.00170) * EF2534 + EF2534NAWPH.ADJ

EF3544NAWPH_R = (0.00622 * MOVAVG (4, RTP.1) - 0.06062 * MOVAVG (20, RTP.5) + 0.00008 + 0.29372 * MOVAVG (12, 

EF2534NAWPH.36/EF2534.36) + 0.06187) * EF3544 + EF3544NAWPH.ADJ
141

EF4554NAWPH_R = (0.02788 * MOVAVG (4, RTP.1) - 0.10996 * MOVAVG (20, RTP.5) - 0.00349 + 0.53068 * MOVAVG (12, 

EF3544NAWPH.36/EF3544.36) + 0.08883) * EF4554 + EF4554NAWPH.ADJ

EF5564NAWPH_R = (0.05939 * MOVAVG (4, RTP.1) - 0.10618 * MOVAVG (8, RTP.5) - 0.00579 + 0.66195 * MOVAVG (12,

EF4554NAWPH.36/EF4554.36) + 0.05966) * EF5564 + EF5564NAWPH.ADJ

EF65ONAWPH_R = (0.22642 * MOVAVG (4, RTP.1) - 0.02069 + 0.33505 * MOVAVG (12, EF5564NAWPH.36) - 0.19707) + 

EF65ONAWPH.ADJ

EM1617NAWPH_R = MAX (0.001, -0.05284 * MOVAVG (4, RTP.1) - 0.17833 * MOVAVG (4, RTP.5) - 0.00768 + 9.19738 * 1/YEAR -

0.00588 * MINW/CPIW_U + 0.16862) * EM1617+ EM1617NAWPH.ADJ

EM1819NAWPH_R = MAX (0.001, -0.07122 * MOVAVG (4, RTP.1) - 0.03737 * MOVAVG (4, RTP.5) - 0.00282 + 3.76796 * 1/YEAR -

0.00499 * MINW/CPIW_U + 0.08727) * EM1819+ EM1819NAWPH.ADJ

EM2024NAWPH_R = MAX (0.001, -0.00450 * MOVAVG (4, RTP.1) - 0.02345 * MOVAVG (4, RTP.5) - 0.00113 - 0.00057 * MINW/CPIW_U 

+ 0.03265) * EM2024 + EM2024NAWPH.ADJ

EM2534NAWPH_R = MAX (0.001, - 0.00490 * MOVAVG (4, RTP.5) - 0.00054 - 0.00051 * MINW/CPIW_U + 0.00789) * EM2534 + 

EM2534NAWPH.ADJ

EM3544NAWPH_R = (-0.00446 * MOVAVG (4, RTP.5) - 0.00041 - 0.00053 * MINW/CPIW_U + 0.00726) * EM3544 + EM3544NAWPH.ADJ

EM4554NAWPH_R = (-0.00039 + 0.00129) * EM4554 + EM4554NAWPH.ADJ

EM5564NAWPH_R = (-0.00015 + 0.00200) * EM5564 + EM5564NAWPH.ADJ

EM65ONAWPH_R = (-0.00679 + 0.64405 * MOVAVG (12, EM5564NAWPH.36) + 0.00231) + EM65ONAWPH.ADJ

ENAWPH_R = EF1617NAWPH_R + EF1819NAWPH_R + EF2024NAWPH_R + EF2534NAWPH_R + EF3544NAWPH_R + 

EF4554NAWPH_R + EF5564NAWPH_R + EF65ONAWPH_R + EM1617NAWPH_R + EM1819NAWPH_R + 

EM2024NAWPH_R + EM2534NAWPH_R + EM3544NAWPH_R + EM4554NAWPH_R 

+ EM5564NAWPH_R + EM65ONAWPH_R

ENAWPH = IF LONGRANGE = 0 

THEN ENAWPH_R 

ELSE ENAWPH.1 * (E_FE/E_FE.1)

EM1617NAWPH = EM1617NAWPH_R * (ENAWPH/ENAWPH_R)

EM1819NAWPH = EM1819NAWPH_R * (ENAWPH/ENAWPH_R)

EM2024NAWPH = EM2024NAWPH_R * (ENAWPH/ENAWPH_R)

EM2534NAWPH = EM2534NAWPH_R * (ENAWPH/ENAWPH_R)

EM3544NAWPH = EM3544NAWPH_R * (ENAWPH/ENAWPH_R)

EM4554NAWPH = EM4554NAWPH_R * (ENAWPH/ENAWPH_R)

EM5564NAWPH = EM5564NAWPH_R * (ENAWPH/ENAWPH_R)

EM65ONAWPH = EM65ONAWPH_R * (ENAWPH/ENAWPH_R)

EF1617NAWPH = EF1617NAWPH_R * (ENAWPH/ENAWPH_R)

EF1819NAWPH = EF1819NAWPH_R * (ENAWPH/ENAWPH_R)

EF2024NAWPH = EF2024NAWPH_R * (ENAWPH/ENAWPH_R)

EF2534NAWPH = EF2534NAWPH_R * (ENAWPH/ENAWPH_R)

EF3544NAWPH = EF3544NAWPH_R * (ENAWPH/ENAWPH_R)

EF4554NAWPH = EF4554NAWPH_R * (ENAWPH/ENAWPH_R)

EF5564NAWPH = EF5564NAWPH_R * (ENAWPH/ENAWPH_R)

EF65ONAWPH = EF65ONAWPH_R * (ENAWPH/ENAWPH_R)

EFNAWPH = EF1617NAWPH + EF1819NAWPH + EF2024NAWPH + EF2534NAWPH + EF3544NAWPH + EF4554NAWPH + 

EF5564NAWPH + EF65ONAWPH

EMNAWPH = EM1617NAWPH + EM1819NAWPH + EM2024NAWPH + EM2534NAWPH + EM3544NAWPH + EM4554NAWPH + 

EM5564NAWPH + EM65ONAWPH

Nonagricultural Self-employed Workers:

EF1617NAS_R = (0.12015 * RTP.1 - 0.10551) * EF1617 + EF1617NAS.ADJ

EF1819NAS_R = (0.11184 * RTP.1 - 0.10241) * EF1819 + EF1819NAS.ADJ

EF2024NAS_R = (0.08908 * RTP.1 - 0.07176) * EF2024 + EF2024NAS.ADJ

EF2534NAS_R = (0.00906 * RTP.1 + 0.03539) * EF2534 + EF2534NAS.ADJ

EF3544NAS_R = (-0.01869 * RTP.1 + 0.08087) * EF3544 + EF3544NAS.ADJ

EF4554NAS_R = (0.07232 * RTP.1 - 0.00701) * EF4554 + EF4554NAS.ADJ

EF5564NAS_R = (0.07872 * RTP.1 + 0.00466) * EF5564 + EF5564NAS.ADJ

EF65ONAS_R = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) + EF65ONAS.ADJ

EM1617NAS_R = (-0.23035 * RTP.1 + 0.24985) * EM1617 + EM1617NAS.ADJ

EM1819NAS_R = (-0.05782 * RTP.1 + 0.07265) * EM1819 + EM1819NAS.ADJ

EM2024NAS_R = (-0.09206 * RTP.1 + 0.11567) * EM2024 + EM2024NAS.ADJ

EM2534NAS_R = (-0.09661 * RTP.1 + 0.14843) * EM2534 + EM2534NAS.ADJ

EM3544NAS_R = (0.02739 * RTP.1 + 0.05236) * EM3544 + EM3544NAS.ADJ
142

EM4554NAS_R = (0.06217 * RTP.1 + 0.03411) * EM4554 + EM4554NAS.ADJ

EM5564NAS_R = (-0.04776 * RTP.1 + 0.16626) * EM5564 + EM5564NAS.ADJ

EM65ONAS_R = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O) + EM65ONAS.ADJ

ENAS_R = EF1617NAS_R + EF1819NAS_R + EF2024NAS_R + EF2534NAS_R + EF3544NAS_R + EF4554NAS_R + EF5564NAS_R +

EF65ONAS_R + EM1617NAS_R + EM1819NAS_R + EM2024NAS_R + EM2534NAS_R + EM3544NAS_R + EM4554NAS_R + 

EM5564NAS_R + EM65ONAS_R

ENAS = IF LONGRANGE = 0 

THEN ENAS_R 

ELSE ENA * (ENAS.1/ENA.1)

EM1617NAS = EM1617NAS_R * (ENAS/ENAS_R)

EM1819NAS = EM1819NAS_R * (ENAS/ENAS_R)

EM2024NAS = EM2024NAS_R * (ENAS/ENAS_R)

EM2534NAS = EM2534NAS_R * (ENAS/ENAS_R)

EM3544NAS = EM3544NAS_R * (ENAS/ENAS_R)

EM4554NAS = EM4554NAS_R * (ENAS/ENAS_R)

EM5564NAS = EM5564NAS_R * (ENAS/ENAS_R)

EM65ONAS = EM65ONAS_R * (ENAS/ENAS_R)

EF1617NAS = EF1617NAS_R * (ENAS/ENAS_R)

EF1819NAS = EF1819NAS_R * (ENAS/ENAS_R)

EF2024NAS = EF2024NAS_R * (ENAS/ENAS_R)

EF2534NAS = EF2534NAS_R * (ENAS/ENAS_R)

EF3544NAS = EF3544NAS_R * (ENAS/ENAS_R)

EF4554NAS = EF4554NAS_R * (ENAS/ENAS_R)

EF5564NAS = EF5564NAS_R * (ENAS/ENAS_R)

EF65ONAS = EF65ONAS_R * (ENAS/ENAS_R)

EFNAS = EF1617NAS + EF1819NAS + EF2024NAS + EF2534NAS + EF3544NAS + EF4554NAS + EF5564NAS + EF65ONAS

EMNAS = EM1617NAS + EM1819NAS + EM2024NAS + EM2534NAS + EM3544NAS + EM4554NAS + EM5564NAS + EM65ONAS

Nonagricultural Unpaid Family Workers

EF1617NAU_R = 0.00012 * ENAS + EF1617NAU.ADJ

EF1819NAU_R = 0.00025 * ENAS + EF1819NAU.ADJ

EF2024NAU_R = 0.00024 * ENAS + EF2024NAU.ADJ

EF2534NAU_R = 0.00117 * ENAS + EF2534NAU.ADJ

EF3544NAU_R = 0.00218 * ENAS + EF3544NAU.ADJ

EF4554NAU_R = 0.00226 * ENAS + EF4554NAU.ADJ

EF5564NAU_R = 0.00083 * ENAS + EF5564NAU.ADJ

EF65ONAU_R = (0.00027 + 0.00021 + 0.00008) * ENAS + EF65ONAU.ADJ

EM1617NAU_R = 0.00028 * ENAS + EM1617NAU.ADJ

EM1819NAU_R = 0.00033 * ENAS + EM1819NAU.ADJ

EM2024NAU_R = 0.00050 * ENAS + EM2024NAU.ADJ

EM2534NAU_R = 0.00044 * ENAS + EM2534NAU.ADJ

EM3544NAU_R = 0.00043 * ENAS + EM3544NAU.ADJ

EM4554NAU_R = 0.00052 * ENAS + EM4554NAU.ADJ

EM5564NAU_R = 0.00037 * ENAS + EM5564NAU.ADJ

EM65ONAU_R = (0.00023 + 0.00010 + 0.00011) * ENAS + EM65ONAU.ADJ

ENAU_R = EF1617NAU_R + EF1819NAU_R + EF2024NAU_R + EF2534NAU_R + EF3544NAU_R + EF4554NAU_R + 

EF5564NAU_R + EF65ONAU_R + EM1617NAU_R + EM1819NAU_R + EM2024NAU_R + EM2534NAU_R + 

EM3544NAU_R + EM4554NAU_R + EM5564NAU_R + EM65ONAU_R

ENAU = ENAU_R

EM1617NAU = EM1617NAU_R * (ENAU/ENAU_R)

EM1819NAU = EM1819NAU_R * (ENAU/ENAU_R)

EM2024NAU = EM2024NAU_R * (ENAU/ENAU_R)

EM2534NAU = EM2534NAU_R * (ENAU/ENAU_R)

EM3544NAU = EM3544NAU_R * (ENAU/ENAU_R)

EM4554NAU = EM4554NAU_R * (ENAU/ENAU_R)
143

EM5564NAU = EM5564NAU_R * (ENAU/ENAU_R)

EM65ONAU = EM65ONAU_R * (ENAU/ENAU_R)

EF1617NAU = EF1617NAU_R * (ENAU/ENAU_R)

EF1819NAU = EF1819NAU_R * (ENAU/ENAU_R)

EF2024NAU = EF2024NAU_R * (ENAU/ENAU_R)

EF2534NAU = EF2534NAU_R * (ENAU/ENAU_R)

EF3544NAU = EF3544NAU_R * (ENAU/ENAU_R)

EF4554NAU = EF4554NAU_R * (ENAU/ENAU_R)

EF5564NAU = EF5564NAU_R * (ENAU/ENAU_R)

EF65ONAU = EF65ONAU_R * (ENAU/ENAU_R)

EFNAU = EF1617NAU + EF1819NAU + EF2024NAU + EF2534NAU + EF3544NAU + EF4554NAU + EF5564NAU + EF65ONAU

EMNAU = EM1617NAU + EM1819NAU + EM2024NAU + EM2534NAU + EM3544NAU + EM4554NAU + EM5564NAU + EM65ONAU

Agricultural Workers

EA = IF LONGRANGE = 0 

THEN GDPPF00 / (EXP (-0.20541 + 0.03254 * YEAR - 0.07829 + 0.37854)) 

ELSE E * EA.1/E.1

Agricultural Wage Workers

EAW = IF LONGRANGE = 0 

THEN EA * (0.00893 * YEAR + 0.33159 * RTP - 0.67943) 

ELSE EA * (EAW.1/EA.1)

EM1617AW_R = MAX (0, EAW * (-0.00594 - 0.09353 * MOVAVG (2, RTP.1) + 5.28754 * EM1617/E + 0.08116) + EM1617AW.ADJ)

EM1819AW_R = MAX (0, EAW * (-0.00131 - 0.18120 * MOVAVG (2, RTP.1) + 3.87151 * EM1819/E + 0.16636) + EM1819AW.ADJ)

EM2024AW_R = MAX (0, EAW * (-0.00664 + 0.10493 * MOVAVG (2, RTP.1) + 2.00153 * EM2024/E - 0.08191) + EM2024AW.ADJ)

EM2534AW_R = MAX (0, EAW * (-0.02065 + 0.38358 * MOVAVG (2, RTP.1) - 0.98380 * EM2534/E + 0.00751) + EM2534AW.ADJ)

EM3544AW_R = MAX (0, EAW * (0.00402 - 0.15663 * MOVAVG (2, RTP.1) + 1.72119 * EM3544/E + 0.05679) + EM3544AW.ADJ)

EM4554AW_R = MAX (0, EAW * (0.00834 + 0.03746 * MOVAVG (2, RTP.1) + 0.46522 * EM4554/E + 0.00144) + EM4554AW.ADJ)

EM5564AW_R = MAX (0, EAW * (-0.00655 + 0.03521 * MOVAVG (2, RTP.1) + 0.46852 * EM5564/E - 0.00037) + EM5564AW.ADJ)

EM65OAW_R = MAX (0, EAW * (-0.00114 + 0.07640 * MOVAVG (2, RTP.1) + 3.25911 * EM65O/E - 0.10058) + EM65OAW.ADJ)

EF1617AW_R = MAX (0, EAW * (-0.00055 - 0.05470 * MOVAVG (2, RTP.1) + 1.41760 * EF1617/E + 0.04979) + EF1617AW.ADJ)

EF1819AW_R = MAX (0, EAW * (0.00102 - 0.07375 * MOVAVG (2, RTP.1) + 0.78394 * EF1819/E + 0.07226) + EF1819AW.ADJ)

EF2024AW_R = MAX (0, EAW * (0.00112 - 0.05971 * MOVAVG (2, RTP.1) + 0.57256 * EF2024/E + 0.05907) + EF2024AW.ADJ)

EF2534AW_R = MAX (0, EAW * (0.00623 + 0.08868 * MOVAVG (2, RTP.1) + 1.00897 * EF2534/E - 0.15142) + EF2534AW.ADJ)

EF3544AW_R = MAX (0, EAW * (0.00687 - 0.00259 * MOVAVG (2, RTP.1) + 0.51319 * EF3544/E - 0.00937) + EF3544AW.ADJ)

EF4554AW_R = MAX (0, EAW * (0.00185 + 0.08747 * MOVAVG (2, RTP.1) + 0.28022 * EF4554/E - 0.08053) + EF4554AW.ADJ)

EF5564AW_R = MAX (0, EAW * (-0.00140 - 0.03001 * MOVAVG (2, RTP.1) - 0.59383 * EF5564/E + 0.07088) + EF5564AW.ADJ)

EF65OAW_R = MAX (0, EAW * (0.00096 + 0.06768 * MOVAVG (2, RTP.1) + 1.04213 * EF65O/E - 0.07359) + EF65OAW.ADJ)

EAW_R = EF1617AW_R + EF1819AW_R + EF2024AW_R + EF2534AW_R + EF3544AW_R + EF4554AW_R + EF5564AW_R + 

EF65OAW_R + EM1617AW_R + EM1819AW_R+ EM2024AW_R + EM2534AW_R + EM3544AW_R + EM4554AW_R + 

EM5564AW_R + EM65OAW_R

EM1617AW = EM1617AW_R * (EAW/EAW_R)

EM1819AW = EM1819AW_R * (EAW/EAW_R)

EM2024AW = EM2024AW_R * (EAW/EAW_R)

EM2534AW = EM2534AW_R * (EAW/EAW_R)

EM3544AW = EM3544AW_R * (EAW/EAW_R)

EM4554AW = EM4554AW_R * (EAW/EAW_R)

EM5564AW = EM5564AW_R * (EAW/EAW_R)

EM65OAW = EM65OAW_R * (EAW/EAW_R)

EF1617AW = EF1617AW_R * (EAW/EAW_R)

EF1819AW = EF1819AW_R * (EAW/EAW_R)

EF2024AW = EF2024AW_R * (EAW/EAW_R)

EF2534AW = EF2534AW_R * (EAW/EAW_R)

EF3544AW = EF3544AW_R * (EAW/EAW_R)

EF4554AW = EF4554AW_R * (EAW/EAW_R)

EF5564AW = EF5564AW_R * (EAW/EAW_R)

EF65OAW = EF65OAW_R * (EAW/EAW_R)
144

EFAW = EF1617AW+ EF1819AW+ EF2024AW+ EF2534AW+ EF3544AW+ EF4554AW+ EF5564AW+ EF65OAW

EMAW = EM1617AW+ EM1819AW+ EM2024AW+ EM2534AW+ EM3544AW+ EM4554AW+ EM5564AW+ EM65OAW

Self-employed Agricultural Workers

EAS = EA - EAU - EAW

EM1617AS_R = MAX (0, NM1617 * (0.00528 + 0.00404) + EM1617AS.ADJ)

EM1819AS_R = MAX (0, NM1819 * (0.00309 + 0.28448 * EA / (NM16O+ NF16O) - 0.00165) + EM1819AS.ADJ)

EM2024AS_R = MAX (0, NM2024 * (-0.00181 + 0.97958 * EA / (NM16O+ NF16O) - 0.01093) + EM2024AS.ADJ)

EM2534AS_R = MAX (0, NM2534 * (-0.00263 + 1.23186 * EA / (NM16O+ NF16O) - 0.01021) + EM2534AS.ADJ)

EM3544AS_R = MAX (0, NM3544 * (-0.00151 + 1.66765 * EA / (NM16O+ NF16O) - 0.01450) + EM3544AS.ADJ)

EM4554AS_R = MAX (0, NM4554 * (-0.00381 + 2.86654 * EA / (NM16O+ NF16O) - 0.03175) + EM4554AS.ADJ)

EM5564AS_R = MAX (0, NM5564 * (-0.00460 + 2.78817 * EA / (NM16O+ NF16O) - 0.02398) + EM5564AS.ADJ)

EM65OAS_R = MAX (0, NM65O * (0.00079 + 1.76904 * EA / (NM16O+ NF16O) - 0.01437) + EM65OAS.ADJ)

EF1617AS_R = MAX (0, NF1617 * (0.00181 + 0.00030) + EF1617AS.ADJ)

EF1819AS_R = MAX (0, EM1819AS.1 * (-0.02393 + 0.63672 * MOVAVG (2, RTP.1) + 0.98791 * EF1819/EM1819 - 4.43926) + 

EF1819AS.ADJ)

EF2024AS_R = MAX (0, EM2024AS.1 * (0.07353 - 0.40207 * MOVAVG (2, RTP.1) + 0.57572 * EF2024/EM2024 - 0.01117) +

EF2024AS.ADJ)

EF2534AS_R = MAX (0, EM2534AS.1 * (0.16575 + 0.16967 * MOVAVG (2, RTP.1) + 0.55503 * EF2534/EM2534 - 0.43412) + 

EF2534AS.ADJ)

EF3544AS_R = MAX (0, EM3544AS.1 * (0.15848 + 0.37839 * MOVAVG (2, RTP.1) + 0.37764 * EF3544/EM3544 - 0.45362) + 

EF3544AS.ADJ)

EF4554AS_R = MAX (0, EM4554AS.1 * (0.21947 + 0.29497 * MOVAVG (2, RTP.1) + 0.58974 * EF4554/EM4554 - 0.51966) + 

EF4554AS.ADJ)

EF5564AS_R = MAX (0, EM5564AS.1 * (0.20892 + 0.36294 * MOVAVG (2, RTP.1) + 0.65320 * EF5564/EM5564 - 0.66626) + 

EF5564AS.ADJ)

EF65OAS_R = MAX (0, EM65OAS.1 * (0.16242 + 0.54916 * MOVAVG (2, RTP.1) + 0.06199 * EF65O/EM65O- 0.47556) + EF65OAS.ADJ)

EAS_R = EF1617AS_R + EF1819AS_R + EF2024AS_R + EF2534AS_R + EF3544AS_R + EF4554AS_R + EF5564AS_R + 

EF65OAS_R + EM1617AS_R + EM1819AS_R+ EM2024AS_R + EM2534AS_R + EM3544AS_R + EM4554AS_R + 

EM5564AS_R + EM65OAS_R

EM1617AS = EM1617AS_R * (EAS/EAS_R)

EM1819AS = EM1819AS_R * (EAS/EAS_R)

EM2024AS = EM2024AS_R * (EAS/EAS_R)

EM2534AS = EM2534AS_R * (EAS/EAS_R)

EM3544AS = EM3544AS_R * (EAS/EAS_R)

EM4554AS = EM4554AS_R * (EAS/EAS_R)

EM5564AS = EM5564AS_R * (EAS/EAS_R)

EM65OAS = EM65OAS_R * (EAS/EAS_R)

EF1617AS = EF1617AS_R * (EAS/EAS_R)

EF1819AS = EF1819AS_R * (EAS/EAS_R)

EF2024AS = EF2024AS_R * (EAS/EAS_R)

EF2534AS = EF2534AS_R * (EAS/EAS_R)

EF3544AS = EF3544AS_R * (EAS/EAS_R)

EF4554AS = EF4554AS_R * (EAS/EAS_R)

EF5564AS = EF5564AS_R * (EAS/EAS_R)

EF65OAS = EF65OAS_R * (EAS/EAS_R)

EFAS = EF1617AS + EF1819AS + EF2024AS + EF2534AS + EF3544AS + EF4554AS + EF5564AS + EF65OAS

EMAS = EM1617AS + EM1819AS + EM2024AS + EM2534AS + EM3544AS + EM4554AS + EM5564AS + EM65OAS

Unpaid Agricultural Family Workers

EM1617AU_R = MAX (0, 0.002 + EM1617AU.ADJ)

EM1819AU_R = MAX (0, 0.001 + EM1819AU.ADJ)

EM2024AU_R = MAX (0, 0.001 + EM2024AU.ADJ)

EM2534AU_R = MAX (0, 0.003 + EM2534AU.ADJ)

EM3544AU_R = MAX (0, 0.004 + EM3544AU.ADJ)

EM4554AU_R = MAX (0, 0.005 + EM4554AU.ADJ)

EM5564AU_R = MAX (0, 0.003 + EM5564AU.ADJ)

EM65OAU_R = MAX (0, 0.001 + EM65OAU.ADJ)
145

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

EAU = IF LONGRANGE = 0 

THEN EAU_R 

ELSE EAU.1/EA.1 * EA

EM1617AU = EM1617AU_R * (EAU/EAU_R)

EM1819AU = EM1819AU_R * (EAU/EAU_R)

EM2024AU = EM2024AU_R * (EAU/EAU_R)

EM2534AU = EM2534AU_R * (EAU/EAU_R)

EM3544AU = EM3544AU_R * (EAU/EAU_R)

EM4554AU = EM4554AU_R * (EAU/EAU_R)

EM5564AU = EM5564AU_R * (EAU/EAU_R)

EM65OAU = EM65OAU_R * (EAU/EAU_R)

EF1617AU = EF1617AU_R * (EAU/EAU_R)

EF1819AU = EF1819AU_R * (EAU/EAU_R)

EF2024AU = EF2024AU_R * (EAU/EAU_R)

EF2534AU = EF2534AU_R * (EAU/EAU_R)

EF3544AU = EF3544AU_R * (EAU/EAU_R)

EF4554AU = EF4554AU_R * (EAU/EAU_R)

EF5564AU = EF5564AU_R * (EAU/EAU_R)

EF65OAU = EF65OAU_R * (EAU/EAU_R)

EFAU = EF1617AU + EF1819AU + EF2024AU + EF2534AU + EF3544AU + EF4554AU + EF5564AU + EF65OAU

EMAU = EM1617AU + EM1819AU + EM2024AU + EM2534AU + EM3544AU + EM4554AU + EM5564AU + EM65OAU

ANNUAL "AVERAGE HOURS WORKED" EQUATIONS

Total Nonagricultural Wage Workers

Males

AHWM1617NAW = 34.4953 * RTP + 1.03247 * MINW/CPIW_U - 31.4229 * RNM1617S- 0.12369 * 1 + 12.1981

AHWM1819NAW = 32.4361 * RTP + 12.8742 * RTP.1 + 1.28624 * MINW/CPIW_U- 16.0989 * RNM1819S - 0.27834 * 1 - 8.58664

AHWM2024NAW = 20.1161 * RTP - 10.2292 * RNM2024S - 2.28628 * (PM2024NM * NM2024NM / (PM2024NM * NM2024NM + 

PM2024MS * NM2024MS + PM2024MA * NM2024MA)) + 23.2252

AHWM2534NAW = 17.0559 * RTP - 0.29076 * 1 + 0.04542 *YEAR + 22.5121

AHWM3544NAW = 18.3314 * RTP - 0.30475 * 1 + 0.04409 *YEAR + 22.3275

AHWM4554NAW = 16.0678 * RTP - 0.12289 * 1 + 0.07446 *YEAR + 21.4366

AHWM5564NAW = 10.8277 * RTP + 0.23715 * 1 + 30.8975

AHWM65ONAW = -0.28038 * 1 + 5.40682 * RTP + 25.4797

Females

AHWF1617NAW = 17.2598 * RTP + 7.31262 * RTP.1 - 24.9241 * RNF1617S + 16.9218

AHWF1819NAW = 18.7922 * RTP + 13.1066 * RTP.1 - 18.9417 * RNF1819S- 16.2182 * PF1819 + 0.81920 * 1 + 16.7826

AHWF2024NAW = -219.154 * PF2024 + 12.4226 * RTP - 0.98470 * 1 + 158.354 * (PF2024)

2 + 98.6034

AHWF2534NAW = -39.2904 * PF2534 + 39.6515 * (PF2534)

2 + 9.10839 * RTP- 0.33503 * 1 + 35.8525

AHWF3544NAW = -39.2904 * PF3544 + 39.6515 * (PF3544)

2 + 7.40115 * RTP- 0.38214 * 1 + 36.9133

AHWF4554NAW = 8.64511 * RTP - 63.8042 * PF4554 + 59.9107 * (PF4554)

2 - 0.58355 * 1 + 44.0723
146

AHWF5564NAW = 6.61506 * RTP - 0.28969 * 1 + 8.36882 * PF5564 + 24.8288

AHWF65ONAW = -0.43916 * 1 + 26.5228 + (8.36882/2) * (PF65O- 0.086)

Nonagricultural Self-employed Workers

AHWNAS = 24.9592 * RTP - 17.2194 * EFNAS/ENAS + 22.0120

Nonagricultural Unpaid Family Workers

AHWNAU = 25.5124 * (EF2534NAU + EF3544NAU + EF4554NAU)/ENAU + 19.2730

Agricultural Wage Workers

AHWAW = 6.58073 * RTP + 14.9130 * RTP.1 + 19.7800

Agricultural Self-employed Workers

AHWAS = 2.45830 * PGDPAF/PGDP - 3.61107 * 1 + 44.5318

Agricultural Unpaid Family Workers

AHWAU = 39.3563

QUARTERLY "AVERAGE HOURS WORKED" EQUATIONS

Total

AHW = (AHWNA * ENA + AHWA * EA) / E

Nonagricultural sector

AHWNA = (AHWNAW * (E-ENAS-ENAU-EA) + AHWNAS * ENAS + AHWNAU * ENAU) / ENA

Nonagricultural Wage Workers

AHWNAW = (AHWMNAW * (EM – EMNAS - EMNAU – EMAW - EMAS - EMAU) + AHWFNAW * (EF - EFNAS - EFNAU – EFAW -

EFAS – EFAU))/ (E – ENAS – ENAU – EA)

Males

AHWMNAW1 = AHWM1617NAW * (EM1617 - EM1617NAS - EM1617NAU - EM1617AW - EM1617AS - EM1617AU)

AHWMNAW2 = AHWM1819NAW * (EM1819 - EM1819NAS - EM1819NAU - EM1819AW - EM1819AS - EM1819AU)

AHWMNAW3 = AHWM2024NAW * (EM2024 - EM2024NAS - EM2024NAU - EM2024AW - EM2024AS - EM2024AU)

AHWMNAW4 = AHWM2534NAW * (EM2534 - EM2534NAS - EM2534NAU - EM2534AW - EM2534AS - EM2534AU)

AHWMNAW5 = AHWM3544NAW * (EM3544 - EM3544NAS - EM3544NAU - EM3544AW - EM3544AS - EM3544AU)

AHWMNAW6 = AHWM4554NAW * (EM4554 - EM4554NAS - EM4554NAU - EM4554AW - EM4554AS - EM4554AU)

AHWMNAW7 = AHWM5564NAW * (EM5564 - EM5564NAS - EM5564NAU - EM5564AW - EM5564AS - EM5564AU)

AHWMNAW8 = AHWM65ONAW * (EM65O - EM65ONAS - EM65ONAU - EM65OAW - EM65OAS - EM65OAU)

AHWMNAW = (AHWMNAW1 + AHWMNAW2 + AHWMNAW3 + AHWMNAW4 + AHWMNAW5 + AHWMNAW6 + AHWMNAW7 + 

AHWMNAW8) / (EM - EMNAS - EMNAU- EMAW - EMAS - EMAU)

AHWM1617NAW = 34.4953 * MOVAVG (2, RTP.1) + 1.03247 * MINW/CPIW_U - 31.4229 * RNM1617S - 0.12369 * 1 + 12.1981 + 

AHWM1617NAW.ADJ

AHWM1819NAW = 32.4361 * MOVAVG (2, RTP.1) + 12.8742 * MOVAVG (2, RTP.5) + 1.28624 * MINW/CPIW_U - 16.0989 * RNM1819S -

0.27834 * 1 - 8.58664 + AHWM1819NAW.ADJ

AHWM2024NAW = 20.1161 * MOVAVG (2, RTP.1) - 10.2292 * RNM2024S - 2.28628 * (PM2024NM * NM2024NM/ (PM2024NM * 

NM2024NM + PM2024MS * NM2024MS + PM2024MA * NM2024MA)) + 23.2252 + AHWM2024NAW.ADJ

AHWM2534NAW = MIN (45, 17.0559 * MOVAVG (2, RTP.1) - 0.29076 * 1 + 0.04542 *YEAR + 22.5121) + AHWM2534NAW.ADJ

AHWM3544NAW = MIN (45, 18.3314 * MOVAVG (2, RTP.1) - 0.30475 * 1 + 0.04409 *YEAR + 22.3275) + AHWM3544NAW.ADJ

AHWM4554NAW = MIN (45, 16.0678 * MOVAVG (2, RTP.1) - 0.12289 * 1 + 0.07446 *YEAR + 21.4366) + AHWM4554NAW.ADJ

AHWM5564NAW = 10.8277 * MOVAVG (2, RTP.1) + 0.23715 * 1 + 30.8975 + AHWM5564NAW.ADJ

AHWM65ONAW = -0.28038 * 1 + 5.40682 * MOVAVG (2, RTP.1) + 25.4797 + AHWM65ONAW.ADJ

Females

AHWFNAW1 = AHWF1617NAW* (EF1617 -EF1617NAS-EF1617NAU-EF1617AW-EF1617AS-EF1617AU)

AHWFNAW2 = AHWF1819NAW* (EF1819 -EF1819NAS-EF1819NAU-EF1819AW-EF1819AS-EF1819AU)

AHWFNAW3 = AHWF2024NAW* (EF2024 -EF2024NAS-EF2024NAU-EF2024AW-EF2024AS-EF2024AU)

AHWFNAW4 = AHWF2534NAW* (EF2534 -EF2534NAS-EF2534NAU-EF2534AW-EF2534AS-EF2534AU)

AHWFNAW5 = AHWF3544NAW* (EF3544 -EF3544NAS-EF3544NAU-EF3544AW-EF3544AS-EF3544AU)

AHWFNAW6 = AHWF4554NAW* (EF4554 -EF4554NAS-EF4554NAU-EF4554AW-EF4554AS-EF4554AU)
147

AHWFNAW7 = AHWF5564NAW* (EF5564 -EF5564NAS-EF5564NAU-EF5564AW-EF5564AS-EF5564AU)

AHWFNAW8 = AHWF65ONAW * (EF65O -EF65ONAS-EF65ONAU-EF65OAW-EF65OAS-EF65OAU)

AHWFNAW = (AHWFNAW1 + AHWFNAW2 + AHWFNAW3 + AHWFNAW4 + AHWFNAW5 + AHWFNAW6 + AHWFNAW7 

+ AHWFNAW8) / (EF – EFNAS – EFNAU – EFAW – EFAS – EFAU)

AHWF1617NAW = 17.2598 * MOVAVG (2, RTP.1) + 7.31262 * MOVAVG (2, RTP.5) - 24.9241 * RNF1617S + 16.9218 + 

AHWF1617NAW.ADJ

AHWF1819NAW = 18.7922 * MOVAVG (2, RTP.1) + 13.1066 * MOVAVG (2, RTP.5) - 18.9417 * RNF1819S - 16.2182 * PF1819 + 0.81920 * 1 

+ 16.7826 + AHWF1819NAW.ADJ

AHWF2024NAW = -219.154 * PF2024 + 12.4226 * MOVAVG (2, RTP.1) - 0.98470 * 1 + 158.354 * (PF2024)

2 + 98.6034 + 

AHWF2024NAW.ADJ

AHWF2534NAW = -39.2904 * PF2534 + 39.6515 * (PF2534)

2 + 9.10839 * MOVAVG (2, RTP.1) - 0.33503 * 1 + 35.8525 + 

AHWF2534NAW.ADJ

AHWF3544NAW = -39.2904 * PF3544 + 39.6515 * (PF3544)

2 + 7.40115 * MOVAVG (2, RTP.1) - 0.38214 * 1 + 36.9133 + 

AHWF3544NAW.ADJ

AHWF4554NAW = 8.64511 * MOVAVG (2, RTP.1) - 63.8042 * PF4554 + 59.9107 * (PF4554)

2 - 0.58355 * 1 + 44.0723 + AHWF4554NAW.ADJ

AHWF5564NAW = 6.61506 * MOVAVG (2, RTP.1) - 0.28969 * 1 + 8.36882 * PF5564 + 24.8288 + AHWF5564NAW.ADJ

AHWF65ONAW = -0.43916 * 1 + 26.5228 + (8.36882/2) * (PF65O- 0.086) + AHWF65ONAW.ADJ

Nonagricultural Self-employed

AHWNAS = 24.9592 * MOVAVG (2, RTP.1) - 17.2194 * EFNAS/ENAS + 22.0120 + AHWNAS.ADJ

Nonagricultural Unpaid Family Workers

AHWNAU = 25.5124 * (EF2534NAU + EF3544NAU + EF4554NAU)/ ENAU + 19.2730 + AHWNAU.ADJ

Agricultural sector

AHWA = (AHWAW * EAW + AHWAS * EAS + AHWAU * EAU) / EA

Agricultural Wage Workers

AHWAW = 6.58073 * MOVAVG (2, RTP.1) + 14.9130 * MOVAVG (2, RTP.5) + 19.7800 + AHWAW.ADJ

Agricultural Self-employed

AHWAS = 2.45830 * PGDPAF/PGDP - 3.61107 * 1 + 44.5318 + AHWAS.ADJ

Agricultural Unpaid Family Workers

AHWAU = 39.3563 + AHWAU.ADJ

OTHER EMPLOYMENT MEASURES

Federal Civilian Government and Government Enterprises

EGFC = IF LONGRANGE = 0 

THEN (EGFC.1 * 1.00940.25) 

ELSE (EGFC.1 * (E_FE/E_FE.1))

EGEFCPS = IF LONGRANGE = 0 

THEN (EGEFCPS.1 * 1.00750.25) 

ELSE (EGEFCPS.1 * (E_FE/E_FE.1))

EGGEFC = EGFC + EGEFCPS

State and Local Government and Government Enterprises

EGGESL = IF LONGRANGE = 0 

THEN EGGESL.1 * (LC_FE/LC_FE.4)0.25

ELSE EGGESL.1 * (E_FE/E_FE.1)

Military

DNEDMIL = IF (EDMIL-EDMIL.4) < 0 

THEN (EDMIL-EDMIL.4) 

ELSE 0

EP = E-EGGESL - EGGEFC – EAS - ENAS

Compensation and Output Sectors

Price Deflator for Medical Services

CPIWMS = CPIWMS.1 * (1 + ((CPIW_U/CPIW_U.4)0.25 - 1) * CPIWMSWT)
148

Unemployment Insurance and Workers Compensation Effective Tax Rates

TMAXUI_SL = TMAXUI_SL.1 *AWSUI.1/AWSUI.2

RELMAX_UI = TMAXUI_SL/AWSUI.1/1000

CR_UI = 0.775

TRATIO_UI = 0.96996 * RELMAX_UI-0.13744 * MOVAVG (4, RTP.1) + 0.10368 * MOVAVG (4, RTP.5) + 0.04887

TRATE_UI = 0.00143 * MOVAVG (4, RU.5) + 0.00128 * MOVAVG (4, RU.9) + 0.00057 * MOVAVG (4, RU.13) + 0.00356

RUIWS1 = CR_UI * TRATIO_UI * TRATE_UI

RUIWS2 = 0.32476 * MOVAVG (4, RUIWS1.8 * (WSP.8 -WSPRRB.8 +WSGGESL.8)) / (WSP.1 -WSPRR2.1 +WSGGESL.1)

Workers' Compensation

RWCWS = RWCWS.1 - (RWCWS.1 - 0.0144)/12

State and Local Government and Government Enterprises TAXMAXQ = IF QTR = 1 

THEN 300.* ROUND (MOVAVG (4, AWSE.5)/MOVAVG (4, AWSE.9) * 1000.* TAXMAX.1/300 +0.5)/1000 

ELSE TAXMAX.1

Wages

AWSPL = MOVAVG (8, AWSP.1)

AWSSPL = MOVAVG (8, AWSSP.1)

AWSGGESL = IF LONGRANGE = 0 

THEN AWSGGESL.1 * AWSPL/AWSPL.1 

ELSE AWSGGESL.1 * AVG_GDP/AVG_GDP.1 * (1 + WS_TO_WSS_D/100)0.25

WSGGESL = AWSGGESL * EGGESL

Employer Contribution for Government Social Insurance

OASDISL_L = (EMPTROASI + EMPTRDI) * 0.978 * CSLA * WSGGESL

HISL_L = EMPTRHI * 1.0 * CSLHI * WSGGESL

SOC_UISL = (-0.02821 * MOVAVG (4, RTP.2) + 0.03145) * WSGGESL

RSOCSL_WC = RSOCSL_WC.1 - (RSOCSL_WC.1 - 0.176)/12

SOC_WCSL = RSOCSL_WC * RWCWS * WSGGESL

SOC_SL = (OASDISL_L + HISL_L + SOC_UISL + SOC_WCSL)

Employer Contributions for Employee Pension and Insurance funds

Workers' Compensation - employees and annuitants

OLI_WCSL = (1 - RSOCSL_WC) * RWCWS * WSGGESL

Pensions

OLI_RETSL = WSGGESL * (OLI_RETSL.1/WSGGESL.1)

Life Insurance - employees and annuitants

OLI_GLI_SL = 2.0 * EGGESL * ((WSGGESL/EGGESL) +2.0) * 0.075 * 26/1000

Health Insurance - employees and annuitants

OLI_GHI_SL = (OLI_GHI_SL.1 / EGGESL.1) * CPIWMS/CPIWMS.1 * EGGESL * RGR_GHI

Total

OLI_SL = (OLI_GLI_SL + OLI_GHI_SL + OLI_WCSL + OLI_RETSL)

RCWSSL = (1 + (SOC_SL + OLI_SL)/WSGGESL)

WSSGGESL = IF LONGRANGE = 0 

THEN RCWSSL*WSGGESL 

ELSE (WSSGGESL.1/EGGESL.1) * AVG_GDP/AVG_GDP.1 * EGGESL

WSSGSL = WSSGGESL * WSSGSL.1/WSSGGESL.1

WSSGESL = WSSGGESL - WSSGSL

CFCGSL = IF LONGRANGE = 0 

THEN WSSGSL * RCFCGSL 

ELSE CFCGSL.1 * WSSGGESL/WSSGGESL.1

GDPGSL = WSSGSL + CFCGSL

CFCGESL = IF LONGRANGE = 0 

THEN WSSGESL * RCFCGESL 

ELSE CFCGESL.1 * WSSGGESL/WSSGGESL.1

GDPGESL = WSSGESL + CFCGESL
149

GDPGGESL = GDPGSL + GDPGESL

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)

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)

AWSGGEFC = IF LONGRANGE = 0 

THEN (AWSGGEFC.1 * (1 +1.0 *CRAZ1 +0.0015)) 

ELSE AWSGGEFC.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100)0.25

WSGGEFC = AWSGGEFC * EGGEFC

CSRS workers

AWEFC_N = IF LONGRANGE = 0 

THEN (AWEFC_N.1 * (1 +1.0 *CRAZ1 +0.00082)) 

ELSE AWEFC_N.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100)0.25

WEFC_N = AWEFC_N * TEFC_N

Government Enterprises (Mostly U.S. Postal Service)

AWSGEFC = IF LONGRANGE = 0 

THEN (AWSGEFC.1 * (1 +1.0 *CRAZ1 +0.0015)) 

ELSE AWSGEFC.1 * AVG_GDP/AVG_GDP.1 * (1 +WS_TO_WSS_D/100) 0.25

WSGEFC = AWSGEFC * EGEFCPS

General Government

WSGFC = WSGGEFC -WSGEFC

AWSGFC = WSGFC/EGFC

Employer Contribution for Government Social Insurance

General Government and Government Enterprises

OASDIFC_L = (EMPTROASI + EMPTRDI) * 1.04 * (WSGGEFC - WEFC_N) * ADJ_FSA_FC

HIFC_L = EMPTRHI* 1.055 * WSGGEFC * ADJ_FSA_FC

SOCF_UIFC = (-0.05934 * RTP + 0.06165) * WSGGEFC

SOCF_WC = 0.0159 * WSGGEFC

SOC_FC = (SOCF_UIFC + SOCF_WC + OASDIFC_L + HIFC_L)

Employer Contributions for Employee Pension and Insurance funds

General Government and Government Enterprises

Pensions

OLI_CSRS1 = ((0.174 * WSGEFC + 0.07 * WSGFC) / WSGGEFC) * WEFC_N

OLI_FERS1 = 0.107 * (WSGGEFC * 0.9 -WEFC_N) 

OLI_FERSFC = 0.048 * (WSGGEFC * 0.9 -WEFC_N)

OLI_RETFC = OLI_CSRS1 + OLI_FERS1 + OLI_FERSFC + OLIF_RETFCO

Life Insurance - employees and annuitants

OLI_GLI_FC = 2.0 * EGGEFC * ((WSGGEFC/EGGEFC) + 2.0) * 0.075 * 26/1000
150

Health Insurance - employees and annuitants

OLI_GHI_FC = (OLI_GHI_FC.1 / EGGEFC.1) * CPIWMS/CPIWMS.1 * EGGEFC * RGR_GHI

OLI_FC = (OLI_GHI_FC + OLI_GLI_FC + OLI_RETFC)

Compensation

General Government and Government Enterprises

RCWSF = (1 + (SOC_FC + OLI_FC)/WSGGEFC)

WSSGGEFC = IF LONGRANGE = 0 

THEN RCWSF * WSGGEFC 

ELSE (WSSGGEFC.1/EGGEFC.1) * AVG_GDP/AVG_GDP.1 * EGGEFC

WSSGFC = IF LONGRANGE = 0 

THEN RCWSF * WSGFC 

ELSE (WSSGFC.1 / (EGGEFC.1 - EGEFCPS.1)) * AVG_GDP/AVG_GDP.1 * (EGGEFC - EGEFCPS)

WSSGEFC = IF LONGRANGE = 0 

THEN RCWSF * WSGEFC 

ELSE (WSSGEFC.1/EGEFCPS.1) * AVG_GDP/AVG_GDP.1 * EGEFCPS

Consumption of Fixed Capital

General Government and Government Enterprises

CFCGFC = IF LONGRANGE = 0 

THEN WSSGFC * RCFCGFC 

ELSE CFCGFC.1 * WSSGGEFC / WSSGGEFC.1

CFCGEFC = IF LONGRANGE = 0 

THEN WSSGEFC * RCFCGEFC 

ELSE CFCGEFC.1 * WSSGGEFC / WSSGGEFC.1

Gross Domestic Product

General Government and Government Enterprises

GDPGFC = WSSGFC + CFCGFC

GDPGEFC = WSSGEFC + CFCGEFC

GDPGGEFC = GDPGFC + GDPGEFC

Federal Government Military

Wages

AWSGFM = IF LONGRANGE = 0 

THEN (AWSGFM.1 * (1.0027 +1.0 * MRAZ)) 

ELSE AWSGFM.1 * AVG_GDP/AVG_GDP.1 * (1 + WS_TO_WSS_D/100) 0.25

WSGFM = AWSGFM * (EDMIL+ EDMIL_R)

Employer Contribution for Government Social Insurance

OASDIFM_L = (EMPTROASI + EMPTRDI) * 0.9975 * CML * WSGFM

HIFM_L = EMPTRHI* 1.0 *CML * WSGFM

SOCF_UIFM = MAX (0.001, (-0.05263 * DIFF (EDMIL + EDMIL_R) - 0.03079 * RTP + 0.03310)) * WSGFM

SOCF_MIFM = 0.30 * CPIWMS * (EDMIL + EDMIL_R)

SOC_FM = (SOCF_UIFM + SOCF_MIFM + OASDIFM_L + HIFM_L)

Employer Contributions for Employee Pension and Insurance funds

OLI_RETFM = (OLI_RETFM.1/WSGFM.1 - (OLI_RETFM.1/WSGFM.1 - 0.472)/12) * WSGFM

Compensation

RCWSM = (1 + (OLI_RETFM + SOC_FM)/WSGFM)

WSSGFM = IF LONGRANGE = 0 

THEN RCWSM * WSGFM 

ELSE (WSSGFM.1/EDMIL.1) * AVG_GDP/AVG_GDP.1 * EDMIL

Consumption of Fixed Capital
151

CFCGFM = IF LONGRANGE = 0 

THEN WSSGFM * RCFCGFM 

ELSE CFCGFM.1 * WSSGFM/WSSGFM.1

Gross Domestic Product

GDPGFM = WSSGFM + CFCGFM

GDPGF = GDPGFC + GDPGFM

GDPGGE = GDPGGEFC + GDPGGESL + GDPGFM

Total (Civilian and Military) Federal General Government and Government Enterprises

WSSGF = WSSGFC + WSSGFM

WSSGE = WSSGEFC + WSSGESL

WSSG = WSSGF + WSSGSL

GDPGE = GDPGEFC + GDPGESL

GDPG = GDPGF + GDPGSL

NIPA Farm Output and Earnings

GDPPF00 = IF LONGRANGE = 0 

THEN EXP (- 3.52340 + 0.02055 * YEAR) * N_SSA 

ELSE GDPPF00.1 * GDP00/GDP00.1

PGDPAF = IF LONGRANGE = 0 

THEN PGDPAF.1 * ((PGDP/PGDP.1)4 - 0.01) 0.25

ELSE PGDPAF.1 * ((PGDP/PGDP.1)4

) 0.25

GDPPF = GDPPF00 * PGDPAF

AYF_K = ((YF.1 /EAS.1) / (WSSPF.1/EAW.1) - 1.594) * 0.8 + 1.594

WSSPF = IF LONGRANGE = 0 

THEN EAW * MOVAVG (4, WSSP.2/EP.2) * (3.15749 / (YEAR- 65) - 0.43419 * RTP + 0.68725) 

ELSE (WSSPF.1/EAW.1) * AVG_GDP/AVG_GDP.1 * EAW

WSPF = IF LONGRANGE = 0 

THEN WSSPF * (MOVAVG (12, (WSP.1/WSSP.1)) + 0.015) 

ELSE (WSPF.1 /WSSPF.1) * (WSP.1/WSSP.1) / (WSP.2/WSSP.2) * WSSPF

AWSPF = WSPF/EAW

YF = AYF_K * (WSSPF/EAW) * EAS

GDP, WSS and WS, Private Households & Nonprofit Institutions

Private Households

Compensation & Wages

WSSPH = IF LONGRANGE = 0 

THEN (((WSSPH.1/ENAWPH.1)/MOVAVG (4, WSSP.3/EP.3) - 0.41) * 0.875 + 0.41) * MOVAVG (4, WSSP.2/EP.2) * 

ENAWPH 

ELSE (AVG_GDP/AVG_GDP.1) * ENAWPH * (WSSPH.1/ENAWPH.1)

WSPH = IF LONGRANGE = 0 

THEN WSSPH / (1 +CPH* 1 * (EMPTROASI + EMPTRDI + EMPTRHI)) 

ELSE (AWSPH.1 * ENAWPH.1/WSSPH.1) * (1 + WS_TO_WSS_D/100) 0.25 * WSSPH

AWSPH = WSPH / ENAWPH

Owner Occupied Housing

OOH = OOH.1 * (KGDP00 * PGDP) / (KGDP00.1 * PGDP.1)

Gross Value Added

GDPPH = IF LONGRANGE = 0 

THEN WSSPH + OOH 

ELSE (AVG_GDP/AVG_GDP.1) * ENAWPH * (GDPPH.1/ENAWPH.1)

Nonprofit Institutions

Health Services
152

EPHS_EST = IF LONGRANGE = 0 

THEN EPHS_EST.1 + 0.275/4 

ELSE EPHS_EST.1 * (E_FE/E_FE.1)

AWSSPHS = IF LONGRANGE = 0 

THEN AWSSPHS.1 * AWSSPL/AWSSPL.1 

ELSE AWSSPHS.1 * AVG_GDP/AVG_GDP.1

WSSPHS = AWSSPHS* EPHS_EST

Educational Services

EPES_EST = IF LONGRANGE = 0 

THEN EPES_EST.1 + 0.075/4 

ELSE EPES_EST.1 * (E_FE/E_FE.1)

AWSSPES = IF LONGRANGE = 0 

THEN AWSSPES.1 * AWSSPL/AWSSPL.1 

ELSE AWSSPES.1 * AVG_GDP/AVG_GDP.1

WSSPES = AWSSPES* EPES_EST

Social Services

EPSS_EST = IF LONGRANGE = 0 

THEN EPSS_EST.1 + 0.075/4 

ELSE EPSS_EST.1 * (E_FE/E_FE.1)

AWSSPSS = IF LONGRANGE = 0 

THEN AWSSPSS.1 * AWSSPL/AWSSPL.1 

ELSE AWSSPSS.1 * AVG_GDP/AVG_GDP.1

WSSPSS = AWSSPSS* EPSS_EST

Gross Value Added

WSSPNI = WSSPNI.1 * (WSSPHS + WSSPES + WSSPSS) / (WSSPHS.1 + WSSPES.1 + WSSPSS.1)

WSPNI = IF LONGRANGE = 0 

THEN WSSPNI * (WSPNI.1/WSSPNI.1) * ((WSP.1/WSSP.1) / (WSP.9/WSSP.9))(1/8)

ELSE WSSPNI * (WSPNI.1/WSSPNI.1) * (1 +WS_TO_WSS_D/100) 0.25

GDPPNI = IF LONGRANGE = 0 

THEN WSSPNI / ((WSSPNI.1/GDPPNI.1 - 0.866) * 0.8 + 0.866) 

ELSE WSSPNI /0.866

Private Output and Compensation

ROASDIP_L = (EMPTROASI + EMPTRDI) * TXRP * CP

RHIP_L = EMPTRHI * 1.0 * CP

RSOC_UIP = 0.00109 * MOVAVG (4, RU.2) + 0.00045 * MOVAVG (4, RU.10) + 0.00048 * MOVAVG (4, RU.18) - 0.00331

RSOC_WCP = RWCWS * RSOCSL_WC

RSOCF_PBG = 0.00022

OLI

ROLI_WCP = RWCWS * (1 - RSOCSL_WC)

ROLI_SU = 0.0005

OLI_GLI_P = 0.0025 * EP * AWSP.1

OLI_GHI_P = (OLI_GHI_P.1 / EP.1) * CPIWMS/CPIWMS.1 * EP * RGR_GHI

ROLI_PPPS = MAX (ROLI_PPPS.1, 0.00031 * YEAR + 0.00866)

Employee Compensation and Non-Farm Proprietor Income (WSS and YNF)

WSSGGE = (WSSGGESL + WSSGGEFC + WSSGFM)

GDPPBNFXGE = (GDP – GDPGGE – GDPPF – GDPPH – GDPPNI)

RWSSPBNFXGE = (-0.35334 * DRTPP - 0.16925 * DRTPP.1 + 0.20074 * DRTPN.1 + 0.16114 * DRTPN.2 + 0.59442)

ENAW = ENA-ENAS-ENAU

ENAWPBXGE = ENAW - (ENAWPH + EGGEFC + EGGESL + WSSPNI / (WSSPHS + WSSPES + WSSPSS) * (EPHS_EST + 

EPES_EST + EPSS_EST))

ENAWSPBXGE = ENAWPBXGE + ENAS

AYNF_K = ((YNF.1/ENAS.1 / (WSSPBNFXGE.1/ENAWPBXGE.1)) - 1.65) * 0.9 + 1.65

AYF = YF/EAS

AWSSPF = WSSPF/EAW

AYNF = YNF/ENAS

AWSSPBNFXGE = WSSPBNFXGE/ENAWPBXGE
153

YNF = YNF.1 * (GDPPBNFXGE / GDPPBNFXGE.1) * (ENAS / (ENAS + ENAWPBXGE)) / (ENAS.1 / (ENAS.1 + 

ENAWPBXGE.1))

WSSPBNFXGE = (GDPPBNFXGE - YNF) * ((WSSPBNFXGE.1 / (GDPPBNFXGE.1 - YNF.1) - 0.621) * (0.8) + 0.621)

WSSP = WSSPBNFXGE+WSSPF+WSSPH +WSSPNI

RCWSP = WSSP / (WSSP - SOCF_RETRR - OLI_GLI_P - OLI_GHI_P) * (1 + ROASDIP_L + RHIP_L + RSOC_UIP + 

RSOC_WCP + RSOCF_PBG + ROLI_WCP + ROLI_SU+ ROLI_PPPS)

WS = IF WS_TO_WSS_DYR = 0 

THEN (WSGGESL + WSGGEFC + WSGFM + WSSP/RCWSP) 

ELSE WSS * WS.1/WSS.1 * (1 + WS_TO_WSS_D/100) 0.25

WSP = (WS - WSGGESL - WSGGEFC - WSGFM)

AWSP = WSP/EP

AWSSP = WSSP/EP

Other Variables

WSD = WS

WSDP = (WSD –WSGGESL – WSGGEFC – WSGFM)

AWSE = WS / (E + EDMIL – EAS – ENAS)

AWSUI = (WS -WSGGEFC -WSGFM) / (E – EGGEFC – EAS – ENAS)

WSS = (WSSP + WSSGGE)

OLI = OLI_GGE + OLI_P

SOC = SOC_GGE + SOC_P

OLI_GGE = OLI_FC + OLI_SL + OLI_RETFM

SOC_GGE = SOC_FC + SOC_FM + SOC_SL

SOC_UIP = RSOC_UIP * WSP

SOC_WCP = RSOC_WCP * WSP

OASDIP_L = ROASDIP_L * WSP

HIP_L = RHIP_L * WSP

SOCF_PBG = RSOCF_PBG * WSP

SOCF_RETRR = 0.20 * WSPRRB

SOC_P = SOC_UIP + SOC_WCP + OASDIP_L + HIP_L + SOCF_PBG + SOCF_RETRR

OLI_WCP = ROLI_WCP * WSP

OLI_SU = ROLI_SU * WSP

OLI_PPPS = ROLI_PPPS * WSP

OLI_P = OLI_WCP + OLI_SU + OLI_GHI_P + OLI_GLI_P + OLI_PPPS

OLI_PPS = OLI_PPPS + OLI_RETFC + OLI_RETFM + OLI_RETSL

OLI_GHI = OLI_GHI_P + OLI_GHI_FC + OLI_GHI_SL

OLI_GLI = OLI_GLI_P + OLI_GLI_FC + OLI_GLI_SL

OLI_WC = OLI_WCP + OLI_WCSL

SOCSL_WC = SOC_WCSL + SOC_WCP

SOCF_UIFED = SOCF_UIFC + SOCF_UIFM

SOCF_UIS = (SOC_UIP + SOC_UISL) * RUIWS1 / (RUIWS1 + RUIWS2)

SOCF_UIF = (SOC_UIP + SOC_UISL) - SOCF_UIS

SOCF_OASDI = OASDIP_L + OASDISL_L + OASDIFC_L + OASDIFM_L

SOCF_HI = HIP_L + HISL_L + HIFC_L + HIFM_L
154

2.3 OASDI Covered Employment and Earnings (COV)

Total At-Any-Time Employment

Males

Aged 1 through 9

CEM1 = 0.00026 * NM1 

CEM2 = 0.00031 * NM2 

CEM3 = 0.00025 * NM3 

CEM4 = 0.00019 * NM4 

CEM5 = 0.00036 * NM5 

CEM6 = 0.00042 * NM6 

CEM7 = 0.00165 * NM7 

CEM8 = 0.00239 * NM8 

CEM9 = 0.00279 * NM9 

Aged 10 through 15

TEM1013 = 0.01969 * (NM10 + NM11 + NM12 + NM13 + NM10[+1] + NM11[+1] + NM12[+1] + NM13[+1])/2

TEM1415 = (0.42767 * RTP - 1.02624 * NM1415 / (NM1415 + NM1617) + 0.23102) * ((NM14 + NM15 + NM14[+1] + NM15[+1])/2)

Females

Aged 1 through 9

CEF1 = 0.00028 * NF1 

CEF2 = 0.00023 * NF2 

CEF3 = 0.00020 * NF3 

CEF4 = 0.00031 * NF4 

CEF5 = 0.00041 * NF5 

CEF6 = 0.00055 * NF6 

CEF7 = 0.00129 * NF7 

CEF8 = 0.00156 * NF8 

CEF9 = 0.00212 * NF9 

Aged 10 through 15

TEF1013 = IF YEAR < = 110 

THEN (0.04615 * RTP - 0.00014 * YEAR - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] + 

NF13[+1])/2 

ELSE (0.04615 * RTP - 0.00014 * 110 - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] + 

NF13[+1])/2

TEF1415 = (0.48500 * RTP - 0.79002 * NF1415 / (NF1415 + NF1617) + 0.02205) * ((NF14 + NF15 + NF14[+1] + NF15[+1])/2)

Total Males, Total Females and Combined Total

TEM = CEM1 + CEM2 + CEM3 + CEM4 + CEM5 + CEM6 + CEM7 + CEM8 + CEM9 + TEM1013 + TEM1415 + TEM16O

TEF = CEF1 + CEF2 + CEF3 + CEF4 + CEF5 + CEF6 + CEF7 + CEF8 + CEF9 + TEF1013 + TEF1415 + TEF16O

TE = TEM + TEF

Male Disaggregates Aged 16 and Over

Preliminary

Average Weeks Worked

AWWM1617_P = 0.35417 * TREND_TE - 0.17568 * RM1617 + 8.80229;

AWWM1819_P = 0.28021 * TREND_TE - 0.16633 * RM1819 + 15.4522;

AWWM2024_P = 0.17338 * TREND_TE - 0.32843 * RM2024 + 31.4779;

AWWM2529_P = 0.04353 * TREND_TE - 0.32898 * RM2529 + 46.8304; 

AWWM3034_P = 0.04353 * TREND_TE - 0.32898 * RM3034 + 46.8304;

AWWM3539_P = 0.03256 * TREND_TE - 0.26573 * RM3539 + 47.9512;

AWWM4044_P = 0.03256 * TREND_TE - 0.26573 * RM4044 + 47.9512; 

AWWM4549_P = 0.03923 * TREND_TE - 0.23146 * RM4549 + 46.8025; 
155

AWWM5054_P = 0.03923 * TREND_TE - 0.23146 * RM5054 + 46.8025; 

AWWM5559_P = 0.04481 * TREND_TE - 0.28537 * RM5559 + 45.0196;

AWWM6064_P = 0.14488 * TREND_TE + 0.01910 * RM6064 + 29.5797;

AWWM6569_P = 0.21483 * TREND_TE - 0.23366 * RM6569 + 21.1343;

AWWM70O_P = 0.09069 * TREND_TE + 0.43206 * RM70O + 28.6903;

AWWM1617_PL = 0.35417 * TREND_TE.1 - 0.17568 * RM1617.1 + 8.80229;

AWWM1819_PL = 0.28021 * TREND_TE.1 - 0.16633 * RM1819.1 + 15.4522;

AWWM2024_PL = 0.17338 * TREND_TE.1 - 0.32843 * RM2024.1 + 31.4779;

AWWM2529_PL = 0.04353 * TREND_TE.1 - 0.32898 * RM2529.1 + 46.8304; 

AWWM3034_PL = 0.04353 * TREND_TE.1 - 0.32898 * RM3034.1 + 46.8304;

AWWM3539_PL = 0.03256 * TREND_TE.1 - 0.26573 * RM3539.1 + 47.9512;

AWWM4044_PL = 0.03256 * TREND_TE.1 - 0.26573 * RM4044.1 + 47.9512; 

AWWM4549_PL = 0.03923 * TREND_TE.1 - 0.23146 * RM4549.1 + 46.8025; 

AWWM5054_PL = 0.03923 * TREND_TE.1 - 0.23146 * RM5054.1 + 46.8025; 

AWWM5559_PL = 0.04481 * TREND_TE.1 - 0.28537 * RM5559.1 + 45.0196;

AWWM6064_PL = 0.14488 * TREND_TE.1 + 0.01910 * RM6064.1 + 29.5797;

AWWM6569_PL = 0.21483 * TREND_TE.1 - 0.23366 * RM6569.1 + 21.1343;

AWWM70O_PL = 0.09069 * TREND_TE.1 + 0.43206 * RM70O.1 + 28.6903;

Work Experience

WEM1617_3_P = EM1617 * 52 / AWWM1617_P;

WEM1819_3_P = EM1819 * 52 / AWWM1819_P;

WEM2024_3_P = EM2024 * 52 / AWWM2024_P;

WEM2529_3_P = EM2529 * 52 / AWWM2529_P;

WEM3034_3_P = EM3034 * 52 / AWWM3034_P;

WEM3539_3_P = EM3539 * 52 / AWWM3539_P;

WEM4044_3_P = EM4044 * 52 / AWWM4044_P;

WEM4549_3_P = EM4549 * 52 / AWWM4549_P;

WEM5054_3_P = EM5054 * 52 / AWWM5054_P;

WEM5559_3_P = EM5559 * 52 / AWWM5559_P;

WEM6064_3_P = EM6064 * 52 / AWWM6064_P;

WEM6569_3_P = EM6569 * 52 / AWWM6569_P;

WEM70O_3_P = EM70O * 52 / AWWM70O_P ;

WEM1617_3_PL = EM1617.1 * 52 / AWWM1617_PL;

WEM1819_3_PL = EM1819.1 * 52 / AWWM1819_PL;

WEM2024_3_PL = EM2024.1 * 52 / AWWM2024_PL;

WEM2529_3_PL = EM2529.1 * 52 / AWWM2529_PL;

WEM3034_3_PL = EM3034.1 * 52 / AWWM3034_PL;

WEM3539_3_PL = EM3539.1 * 52 / AWWM3539_PL;

WEM4044_3_PL = EM4044.1 * 52 / AWWM4044_PL;

WEM4549_3_PL = EM4549.1 * 52 / AWWM4549_PL;

WEM5054_3_PL = EM5054.1 * 52 / AWWM5054_PL;

WEM5559_3_PL = EM5559.1 * 52 / AWWM5559_PL;

WEM6064_3_PL = EM6064.1 * 52 / AWWM6064_PL;

WEM6569_3_PL = EM6569.1 * 52 / AWWM6569_PL;

WEM70O_3_PL = EM70O.1 * 52 / AWWM70O_PL ;

Total Employed

TEM1617_P = ((WEM1617_3_P / WEM1617_3_PL) * (TEM1617.1 - NM1617M.1) + NM1617M) * MULT1_TEM1617 * MULT2_TEM1617;

TEM1819_P = ((WEM1819_3_P / WEM1819_3_PL) * (TEM1819.1 - NM1819M.1) + NM1819M) * MULT1_TEM1819 * MULT2_TEM1819;

TEM2024_P = ((WEM2024_3_P / WEM2024_3_PL) * (TEM2024.1 - NM2024M.1) + NM2024M) * MULT1_TEM2024 * MULT2_TEM2024;
156

TEM2529_P = ((WEM2529_3_P / WEM2529_3_PL) * (TEM2529.1 - NM2529M.1) + NM2529M) * MULT1_TEM2529 * MULT2_TEM2529;

TEM3034_P = ((WEM3034_3_P / WEM3034_3_PL) * (TEM3034.1 - NM3034M.1) + NM3034M) * MULT1_TEM3034 * MULT2_TEM3034;

TEM3539_P = ((WEM3539_3_P / WEM3539_3_PL) * (TEM3539.1 - NM3539M.1) + NM3539M) * MULT1_TEM3539 * MULT2_TEM3539;

TEM4044_P = ((WEM4044_3_P / WEM4044_3_PL) * (TEM4044.1 - NM4044M.1) + NM4044M) * MULT1_TEM4044 * MULT2_TEM4044;

TEM4549_P = ((WEM4549_3_P / WEM4549_3_PL) * (TEM4549.1 - NM4549M.1) + NM4549M) * MULT1_TEM4549 * MULT2_TEM4549;

TEM5054_P = ((WEM5054_3_P / WEM5054_3_PL) * (TEM5054.1 - NM5054M.1) + NM5054M) * MULT1_TEM5054 * MULT2_TEM5054;

TEM5559_P = ((WEM5559_3_P / WEM5559_3_PL) * (TEM5559.1 - NM5559M.1) + NM5559M) * MULT1_TEM5559 * MULT2_TEM5559;

TEM6064_P = ((WEM6064_3_P / WEM6064_3_PL) * (TEM6064.1)) * MULT1_TEM6064 * MULT2_TEM6064;

TEM6569_P = ((WEM6569_3_P / WEM6569_3_PL) * (TEM6569.1)) * MULT1_TEM6569 * MULT2_TEM6569;

TEM70O_P = ((WEM70O_3_P / WEM70O_3_PL ) * (TEM70O.1 )) * MULT1_TEM70O * MULT2_TEM70O;

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; 

AWWM16O_P = EM16O * 52 / WEM16O_3_P;

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;

Final (Pre-TE.ADD)

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;
157

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;

AWWM16O = AWWM16O_P ;

TEM16O = TEM16O_P ; 

Female Disaggregates Aged 16 and Over

Preliminary

Average Weeks Worked

AWWF1617_P = 0.44829 * TREND_TE - 0.06786 * RF1617 + 0.37331;

AWWF1819_P = 0.24262 * TREND_TE - 0.00950 * RF1819 + 17.0791;

AWWF2024_P = 0.18291 * TREND_TE - 0.06453 * RF2024 + 26.6823;

AWWF2529_P = 0.07674 * TREND_TE - 0.10131 * RF2529 + 40.0210; 

AWWF3034_P = 0.07674 * TREND_TE - 0.10131 * RF3034 + 40.0210;

AWWF3539_P = 0.05004 * TREND_TE - 0.10322 * RF3539 + 43.9974;

AWWF4044_P = 0.05004 * TREND_TE - 0.10322 * RF4044 + 43.9974; 

AWWF4549_P = 0.08209 * TREND_TE - 0.17307 * RF4549 + 41.1649; 

AWWF5054_P = 0.08209 * TREND_TE - 0.17307 * RF5054 + 41.1649; 

AWWF5559_P = 0.04868 * TREND_TE + 0.17072 * RF5559 + 41.9580;

AWWF6064_P = 0.14339 * TREND_TE + 0.01918 * RF6064 + 29.1567;

AWWF6569_P = 0.01857 * TREND_TE + 0.64199 * RF6569 + 36.1193;

AWWF70O_P = 0.20193 * TREND_TE + 0.92866 * RF70O + 14.2412;

AWWF1617_PL = 0.44829 * TREND_TE.1 - 0.06786 * RF1617.1 + 0.37331;

AWWF1819_PL = 0.24262 * TREND_TE.1 - 0.00950 * RF1819.1 + 17.0791;

AWWF2024_PL = 0.18291 * TREND_TE.1 - 0.06453 * RF2024.1 + 26.6823;

AWWF2529_PL = 0.07674 * TREND_TE.1 - 0.10131 * RF2529.1 + 40.0210; 

AWWF3034_PL = 0.07674 * TREND_TE.1 - 0.10131 * RF3034.1 + 40.0210;

AWWF3539_PL = 0.05004 * TREND_TE.1 - 0.10322 * RF3539.1 + 43.9974;

AWWF4044_PL = 0.05004 * TREND_TE.1 - 0.10322 * RF4044.1 + 43.9974; 

AWWF4549_PL = 0.08209 * TREND_TE.1 - 0.17307 * RF4549.1 + 41.1649; 

AWWF5054_PL = 0.08209 * TREND_TE.1 - 0.17307 * RF5054.1 + 41.1649; 

AWWF5559_PL = 0.04868 * TREND_TE.1 + 0.17072 * RF5559.1 + 41.9580;

AWWF6064_PL = 0.14339 * TREND_TE.1 + 0.01918 * RF6064.1 + 29.1567;

AWWF6569_PL = 0.01857 * TREND_TE.1 + 0.64199 * RF6569.1 + 36.1193;

AWWF70O_PL = 0.20193 * TREND_TE.1 + 0.92866 * RF70O.1 + 14.2412;

Work Experience

WEF1617_3_P = EF1617 * 52 / AWWF1617_P;

WEF1819_3_P = EF1819 * 52 / AWWF1819_P;

WEF2024_3_P = EF2024 * 52 / AWWF2024_P;
158

WEF2529_3_P = EF2529 * 52 / AWWF2529_P;

WEF3034_3_P = EF3034 * 52 / AWWF3034_P;

WEF3539_3_P = EF3539 * 52 / AWWF3539_P;

WEF4044_3_P = EF4044 * 52 / AWWF4044_P;

WEF4549_3_P = EF4549 * 52 / AWWF4549_P;

WEF5054_3_P = EF5054 * 52 / AWWF5054_P;

WEF5559_3_P = EF5559 * 52 / AWWF5559_P;

WEF6064_3_P = EF6064 * 52 / AWWF6064_P;

WEF6569_3_P = EF6569 * 52 / AWWF6569_P;

WEF70O_3_P = EF70O * 52 / AWWF70O_P ;

WEF1617_3_PL = EF1617.1 * 52 / AWWF1617_PL;

WEF1819_3_PL = EF1819.1 * 52 / AWWF1819_PL;

WEF2024_3_PL = EF2024.1 * 52 / AWWF2024_PL;

WEF2529_3_PL = EF2529.1 * 52 / AWWF2529_PL;

WEF3034_3_PL = EF3034.1 * 52 / AWWF3034_PL;

WEF3539_3_PL = EF3539.1 * 52 / AWWF3539_PL;

WEF4044_3_PL = EF4044.1 * 52 / AWWF4044_PL;

WEF4549_3_PL = EF4549.1 * 52 / AWWF4549_PL;

WEF5054_3_PL = EF5054.1 * 52 / AWWF5054_PL;

WEF5559_3_PL = EF5559.1 * 52 / AWWF5559_PL;

WEF6064_3_PL = EF6064.1 * 52 / AWWF6064_PL;

WEF6569_3_PL = EF6569.1 * 52 / AWWF6569_PL;

WEF70O_3_PL = EF70O.1 * 52 / AWWF70O_PL ;

Total Employed

TEF1617_P = ((WEF1617_3_P / WEF1617_3_PL) * (TEF1617.1 - NF1617M.1) + NF1617M) * MULT1_TEF1617 * MULT2_TEF1617;

TEF1819_P = ((WEF1819_3_P / WEF1819_3_PL) * (TEF1819.1 - NF1819M.1) + NF1819M) * MULT1_TEF1819 * MULT2_TEF1819;

TEF2024_P = ((WEF2024_3_P / WEF2024_3_PL) * (TEF2024.1 - NF2024M.1) + NF2024M) * MULT1_TEF2024 * MULT2_TEF2024;

TEF2529_P = ((WEF2529_3_P / WEF2529_3_PL) * (TEF2529.1 - NF2529M.1) + NF2529M) * MULT1_TEF2529 * MULT2_TEF2529;

TEF3034_P = ((WEF3034_3_P / WEF3034_3_PL) * (TEF3034.1 - NF3034M.1) + NF3034M) * MULT1_TEF3034 * MULT2_TEF3034;

TEF3539_P = ((WEF3539_3_P / WEF3539_3_PL) * (TEF3539.1 - NF3539M.1) + NF3539M) * MULT1_TEF3539 * MULT2_TEF3539;

TEF4044_P = ((WEF4044_3_P / WEF4044_3_PL) * (TEF4044.1 - NF4044M.1) + NF4044M) * MULT1_TEF4044 * MULT2_TEF4044;

TEF4549_P = ((WEF4549_3_P / WEF4549_3_PL) * (TEF4549.1 - NF4549M.1) + NF4549M) * MULT1_TEF4549 * MULT2_TEF4549;

TEF5054_P = ((WEF5054_3_P / WEF5054_3_PL) * (TEF5054.1 - NF5054M.1) + NF5054M) * MULT1_TEF5054 * MULT2_TEF5054;

TEF5559_P = ((WEF5559_3_P / WEF5559_3_PL) * (TEF5559.1 - NF5559M.1) + NF5559M) * MULT1_TEF5559 * MULT2_TEF5559;

TEF6064_P = ((WEF6064_3_P / WEF6064_3_PL) * (TEF6064.1)) * MULT1_TEF6064 * MULT2_TEF6064;

TEF6569_P = ((WEF6569_3_P / WEF6569_3_PL) * (TEF6569.1)) * MULT1_TEF6569 * MULT2_TEF6569;

TEF70O_P = ((WEF70O_3_P / WEF70O_3_PL ) * (TEF70O.1 )) * MULT1_TEF70O * MULT2_TEF70O;

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; 

AWWF16O_P = EF16O * 52 / WEF16O_3_P;

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;

Final (Pre-TE.ADD)

Average Weeks Worked

AWWF1617 = AWWF1617_P;

AWWF1819 = AWWF1819_P;

AWWF2024 = AWWF2024_P;
159

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 ;

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;

AWWF16O = AWWF16O_P ;

TEF16O = TEF16O_P ; 

Combined, Age 16 and Over

WE16O_3_P = WEM16O_3_P + WEF16O_3_P;

AWW16O_P = E16O * 52 / WE16O_3_P;

WE16O_3 = WE16O_3_P ;

AWW16O = AWW16O_P ;
160

Self-Employed Only

SEOCMB = 0.039 * (TEFC_N_N + TESL_N_N + EPRRB)

SEOCMBL1 = 0.039 * (TEFC_N_N.1 + TESL_N_N.1 + EPRRB.1)

SEO = (SEO.1 * (EAS + ENAS) / (EAS.1 + ENAS.1) + (SEOCMB - SEOCMBL1)) * MULTSEO

Combination Workers

CMB_TOT = ((-0.01468 + 0.06227 * RTP.1 -0.0008) * WSWA - SEOCMB) * MULTCMB

CSW_TOT = SEO + CMB_TOT

AW_CMBTOT = 1.4953 * ACWA

W_CMBTOT = AW_CMBTOT * CMB_TOT

CMB_WRELMAX = TAXMAX/AW_CMBTOT

CMB Wage Andover Curve

CMB_WAO1 = IF (CMB_WRELMAX < 0.0543009)

THEN 1 - 0.722659 * CMB_WRELMAX0.65 - 0.461913 * CMB_WRELMAX0.8

ELSE IF (CMB_WRELMAX<0.1086018)

THEN -1.02884 * CMB_WRELMAX0.6 + 0.324761 * CMB_WRELMAX1.6 + 1.02015

ELSE IF (CMB_WRELMAX < 0.1629027)

THEN -0.906607 * CMB_WRELMAX0.7 + 0.947662

ELSE IF (CMB_WRELMAX < 0.2172037)

THEN -0.813951 * CMB_WRELMAX0.55 + 0.991722

ELSE IF (CMB_WRELMAX < 0.3258055)

THEN -0.755135 * CMB_WRELMAX0.55 + 0.964593

ELSE 0

CMB_WAO2 = IF (CMB_WRELMAX < 0.5430091)

THEN -0.649755 * CMB_WRELMAX0.6 + 0.886467

ELSE IF (CMB_WRELMAX < 0.7059119)

THEN -0.573205 * CMB_WRELMAX0.7 + 0.810122

ELSE IF (CMB_WRELMAX < 0.9231155)

THEN - 5.22264 * CMB_WRELMAX0.06 + 5.47514

ELSE IF (CMB_WRELMAX < 1.0860183)

THEN - 2.02619 * CMB_WRELMAX0.15 + 2.27963

ELSE IF (CMB_WRELMAX < 1.5204256)

THEN 0.605192 * EXP (-0.2 * CMB_WRELMAX) - 0.827158 * EXP (-0.8 * CMB_WRELMAX) +

1.52918 * EXP (- 1.5 * CMB_WRELMAX) - 0.212269

ELSE 0

CMB_WAO3 = IF (CMB_WRELMAX < 1.8462311)

THEN 0.19139 * EXP (-0.6 * CMB_WRELMAX) + 0.764408 * EXP (- 1.8 * CMB_WRELMAX) + 0.0194903

ELSE IF (CMB_WRELMAX < 2.3077888)

THEN 0.12964 * EXP (-0.5 * CMB_WRELMAX) + 0.644861 * EXP (- 1.5 * CMB_WRELMAX) + 0.0183343

ELSE IF (CMB_WRELMAX < 2.9865502)

THEN 0.361318 * EXP (-0.8 * CMB_WRELMAX) + 0.0219491

ELSE IF (CMB_WRELMAX < 4.3440731)

THEN 0.193202 * EXP (-0.45 * CMB_WRELMAX) + 0.00425171

ELSE IF (CMB_WRELMAX<5.4300913)

THEN 0.0560412 * EXP (-0.25 * CMB_WRELMAX) +0.311286 * EXP (-0.8 * CMB_WRELMAX) +

0.00297316

ELSE 0

CMB_WAO4 = IF (CMB_WRELMAX < 13.5752283)

THEN 0.0995677 * EXP (-0.32 * CMB_WRELMAX) + 0.00355234

ELSE IF (CMB_WRELMAX < 21.7203653)

THEN 0.041159 * EXP (-0.19 * CMB_WRELMAX) + 0.00156765

ELSE IF (CMB_WRELMAX < 678.7614168)

THEN 0.265022 * CMB_WRELMAX (-1.555)

ELSE 0

CMB_WAO = IF (CMB_WRELMAX < 0.3258055) 

THEN CMB_WAO1

ELSE IF (CMB_WRELMAX < 1.5204256) 

THEN CMB_WAO2

ELSE IF (CMB_WRELMAX < 5.4300913) 

THEN CMB_WAO3

ELSE CMB_WAO4
161

CMB = (1 - (CMB_WAO - 0.019)) * CMB_TOT

CSW = SEO + CMB

SEOCMB_HI = 0.039 * (TEFC_N_N + TESL_N_N_HI)

SEO_HI = SEO - SEOCMB_HI

CMB_HI = CMB_TOT + SEOCMB_HI

CSW_HI = SEO_HI + CMB_HI

NIPA Wages

Private Residual Sector

WSDPB = WSDP – WSPH – WSPF – WSPRRB – TIPS_SR

TIPS_SR = (0.000508328 * RTP - 0.000481700) * GDP * 1.26393

OASDI Wages

Covered Employment and Wages – Federal Civilian Government

TEFC = (TEFC.1 / EGGEFC.1) * EGGEFC

TEFC_N = IF (CSRS.1 > 0) THEN TEFC_N.1/CSRS.1 * CSRS - TEFC_N_SW ELSE 0

TEFC_N_N = TEFC_N * 0.86

TEFC_N_O = (TEFC_N - TEFC_N_N)

TEFC_O = (TEFC - TEFC_N)

WEFC = (WEFC.1 / WSGGEFC.1) * WSGGEFC

WEFC_O = (WEFC -WEFC_N) * ADJ_FSA_FC

Covered Employment and Wages - State and Local Govt.

TESL = (TESL.1/EGGESLMAX.1) * EGGESLMAX

TESL_O = (TESL_O.1/TESL.1) * TESL

TESL_N = (TESL-TESL_O)

TESL_N_O = (TESL_N_O_HI + TESL_N_O_NHI)

TESL_N_O_HI = (TESL_N - TESL_N_O_NHI - TESL_N_N_NHI) * CER_MQGE_O

TESL_N_O_NHI = (TESL_N_O_NHI_S + TESL_N_O_NHI_E + TESL_N_O_NHI_NS)

TESL_N_S = TESL_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + NM2024.1)

TESL_N_E = TESL_N_E.1 * (TESL / TESL.1)

TESL_N_O_NHI_S = TESL_N_S * (TESL_N_O_NHI_S.1/TESL_N_S.1)

TESL_N_O_NHI_E = TESL_N_E * 0.6

TESL_N_O_NHI_NS = TESL_N_O_NHI_NS.1 * ESR_NS

TESL_N_N = (TESL_N - TESL_N_O)

TESL_N_N_HI = (TESL_N_N - TESL_N_N_NHI)

TESL_N_N_NHI = (TESL_N_N_NHI_S + TESL_N_N_NHI_E + TESL_N_N_NHI_NS)

TESL_N_N_NHI_S = (TESL_N_S - TESL_N_O_NHI_S)

TESL_N_N_NHI_E = (TESL_N_E - TESL_N_O_NHI_E)

TESL_N_N_NHI_NS = TESL_N_N_NHI_NS.1 * ESR_NS

WESL = (WESL.1/WSGGESL.1) * WSGGESL

WESL_O = (WESL_O.1/WSGGESL.1) * WSGGESL

WESL_N = (WESL - WESL_O)

WESL_N_HI = (WESL_N - WESL_N_NHI)

WESL_N_NHI = (WESL_N_NHI_S + WESL_N_NHI_E + WESL_N_NHI_NS)

WESL_N_NHI_S = WESL_N_NHI_S.1 * (TESL_N_S/TESL_N_S.1) * (AWSGGESL/AWSGGESL.1)

WESL_N_NHI_E = WESL_N_NHI_E.1 * (TESL_N_E/TESL_N_E.1) * (AWSGGESL/AWSGGESL.1)

RAWR_NS = IF (AWR_NS = 0) THEN 0 ELSE AWR_NS/AWR_NS.1

WESL_N_NHI_NS = IF (ESR_NS = 0) THEN 0 ELSE WESL_N_NHI_NS.1 * (TESL_N_O_NHI_NS + TESL_N_N_NHI_NS) / 

(TESL_N_O_NHI_NS.1 + TESL_N_N_NHI_NS.1) * (AWSGGESL/AWSGGESL.1) * RAWR_NS

Self-Employed Earnings Sector

Covered SENE

CSE_TOT = (YF +YNF) / (YF.1 + YNF.1) * CSE_TOT.1

CSE_CMB_N = (CSE_TOT / (CMB_TOT + SEO)) / (CSE_TOT.1 / (CMB_TOT.1 + SEO.1)) * (CSE_CMB_N.1 / (CMB_TOT.1 -

CMB.1)) * (CMB_TOT - CMB)
162

CSE = CSE_TOT - CSE_CMB_N

ACSE_SEO = (CSE_TOT / (SEO + 0.416488 * CMB_TOT))

ACSE_CMB_TOT = 0.416488 * ACSE_SEO

CSE_SEO = ACSE_SEO * SEO

CSE_CMB_TOT = ACSE_CMB_TOT * CMB_TOT

CSE_CMB = CSE_CMB_TOT - CSE_CMB_N

ACSE_CMB = CSE_CMB/CMB

Present Law OASDI and HI Covered Wages and Earnings

WSGMLC = CML * WSGFM

WSGFCA = WEFC_O

CFCA = WSGFCA/WSGGEFC

CSLHI = (WESL_O+WESL_N_HI)/WSGGESL

WSGSLCA = WESL_O

WSPH_O = CPH * WSPH

WSPF_O = WSPF_O.1 * WSPF/WSPF.1

CPF = WSPF_O/WSPF

WSPRR_O = CPRR * WSPRRB

CPB_ILL = (CPB) * (WSWA* 0.86 - LOST_MF) / (WSWA * 0.86 + LOST_MF) + (1.5 * 0.5) * (2.0 * LOST_MF) / (WSWA * 0.86 + 

LOST_MF)

CPB_ADJ = IF REAL_ACW_DYR = 0 

THEN CPB_ILL 

ELSE (((REAL_ACW_D + PCH (CPIW_U))/100 *ACWA.1 + ACWA.1) * WSWA - WSPH_O - WSPF_O - WSPRR_O -

TIPS_SR - WSGSLCA – WSGFCA - WSGMLC)/WSDPB

WSPB_O = CPB_ADJ * WSDPB

WSPC = WSPH_O + WSPF_O + WSPRR_O + TIPS_SR + WSPB_O

CP = WSPC/WSDP

WSCA = (WSPC + WSGSLCA + WSGFCA + WSGMLC)

COVERNA = (WSCA + CSE)

ACWA = WSCA/WSWA

ASE = CSE/CSW

ASEHI = CSE_TOT/CSW_HI

ACEA = COVERNA/TCEA

ACSLW = WESL_O/TESL_O * MULTACSLW

ACMW = ACMW.1 * AWSGFM/AWSGFM.1 * CML/CML.1

ACFCW = WEFC_O/TEFC_O

ACFMW = ACFMW.1 * (AIW.1/AIW.3)0.5

TEPH_N = ENAWPH * (1 -CPH)

TEP_N_N_S = TEP_N_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + NM2024.1)

TCEA = (TE - TEPH_N – EPRRB - TEP_N_N_S - TEPO_N - TESL_N_N_NHI_S - TESL_N_N_NHI_E - TESL_N_N_NHI_NS -

TESL_N_N_HI - TEFC_N_N)

WSWA = (TCEA-SEO)

Present Law HI Covered Wages and Earnings

WSCAHI_ADD = WSCA * WSCAHI_ADD.1/WSCA.1 

TCEAHI = (TCEA + TEFC_N_N + TESL_N_N_HI)

WSWAHI = TCEAHI - SEO_HI

WSCAHI = WSCA + WEFC_N + WESL_N_HI + WSCAHI_ADD

ACWAHI = WSCAHI/WSWAHI

COVERNHI = WSCAHI + CSE_TOT

ACEAHI = COVERNHI/TCEAHI

Complete Coverage concepts

WSWC = (WSWAHI + TEPH_N + EPRRB + TEP_N_N_S + TEPO_N + TESL_N_N_NHI) + LOST_MF

ACWC = WSD/WSWC

AIW = IF AIW_GR_YR = 0 

THEN AIW.1 *ACWC/ACWC.1 * MULTAIW 

ELSE AIW.1 * (1 +AIW_GR/100)

Taxable Maximums

RAIW = AIW.2/AIWBASE
163

TAXMAXB1 = RAIW * TMAXBASE * 1000/300

TAXMAXB2 = IF TAXMAXB1 - ROUND (TAXMAXB1) >= 0.5 

THEN ROUND (TAXMAXB1) +1 

ELSE ROUND (TAXMAXB1)

TAXMAXB3 = IF TAXMAXB2 < TAXMAX.1 

THEN TAXMAX.1 * 1000/300 

ELSE TAXMAXB2

TAXMAX = IF BENINC.1 <= 0.001 

THEN TAXMAX.1 

ELSE 300 * TAXMAXB3/1000

Deemed Military Wage Credits

EDMILAF = EDMIL * 1.1

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
164

2-4 Effective Taxable Payroll (TAXPAY)

2-4.1 Ratio of taxable employee to total covered OASDI wages (RWTEE)

IF(RM.LT.0.439103091)THEN

 RWTEE=RM-(0.26651/1.5)*RM**1.5-(0.388274/1.9)*RM**1.9

ELSE IF(RM.LT.1.313896269)THEN

 RWTEE=(1.17877/1.5)*RM**1.5-(2.9291/0.68)*DEXP(-0.68*RM)-2.31401*RM+4.327630386

ELSE IF(RM.LT.2.570433485)THEN

 RWTEE=-(0.0202216/0.25)*DEXP(-0.25*RM)-(1.329/1.4)*DEXP(-1.4*RM)+0.00944271*RM+0.904661863

ELSE IF(RM.LT.4.418783378)THEN

 RWTEE=-(0.0654817/0.35)*DEXP(-0.35*RM)-(1.415/1.51)*DEXP(-1.51*RM)+0.000676576*RM+0.954098019

ELSE IF(RM.LT.14.73231225)THEN

 RWTEE=-(0.0110626/0.15)*DEXP(-0.15*RM)-(0.0472319/0.45)*DEXP(-0.45*RM)-(0.257195/0.95)*DEXP(-

0.95*RM)+0.000367645*RM+0.970880621

ELSE

 RWTEE=-(0.179935/0.75)*RM**(-0.75)+0.999970738

END IF

Where

RM = OASDI taxable maximum / average covered OASDI wage

RWTEE = Ratio if OASDI taxable employee to covered wages 

2-4.2Taxable 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

2-4.4Multi-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

2-4.5Taxable employer OASDI wages (WTER)

WTER = WTEE + MER

Where

MER = OASDI multi-employer refund wages

WTEE = OASDI taxable employee wages

WTER = OASDI taxable employer wages

2-4.6 Ratio of taxable to covered self-employment earnings (RSET)

Preliminary
165

BASECT = 47831.98

BASECW = 36831.79

BASEO = 23448.56

Self-employed only

SECSEO = CSE - SECCMB

ASESEO = SECSEO / SEO

ASEO96 = ASESEO(1996)

ASESEO = ASESEO * BASEO / ASEO96

O = TAXMAX / ASESEO

IF(O.LT.0.021323273)THEN

 OTR=O-(401.8/3.8)*O**3.8

ELSE IF(O.LT.0.170586184)THEN

 OTR=(12.6861/1.1)*O**1.1-(10.7855/1.15)*O**1.15-(.208585/1.9)*O**1.9-1.58102*O-.0000212479

ELSE IF(O.LT.0.938224014)THEN

 OTR=-(2.03924/2.5)*DEXP(-2.5*O)+(2.52113/1.6)*O**1.6-(1.11979/2.2)*O**2.2-1.33547*O+.825500132

ELSE IF(O.LT.1.705861843)THEN

 OTR=-(.375957/.3)*DEXP(-.3*O)-(.642976/2.3)*DEXP(-2.3*O)-.108863*O+1.555087525

ELSE IF(O.LT.2.302913488)THEN

 OTR=-(.248596/.25)*DEXP(-.25*O)-(1.003/2.2)*DEXP(-2.2*O)-.0565126*O+1.368881905

ELSE IF(O.LT.3.624956417)THEN

 OTR=-(.207896/.15)*DEXP(-.15*O)-(3.99112/2.5)*DEXP(-2.5*O)-.0699402*O+1.823982598

ELSE IF(O.LT.5.970516451)THEN

 OTR=-(.110423/.2)*DEXP(-.2*O)-(.571353/1.25)*DEXP(-1.25*O)-.00842494*O+1.068478626

ELSE IF(O.LT.12.79396382)THEN

 OTR=-(.0631844/.2)*DEXP(-.2*O)-(.242063/.65)*DEXP(-.65*O)+.0011163*O+.947373543

ELSE IF(O.LT.21.32327304)THEN

 OTR=-(.0218297/.13)*DEXP(-.13*O)-(.0876571/.32)*DEXP(-.32*O)+.000522742*O+.966817185

ELSE IF(O.LT.213.2327304)THEN

 OTR=-(2.86725/1.36)*O**(-1.36)+1.00002612

ELSE

 OTR=1D0

END IF

SETSEO=OTR*SECSEO

OASDI taxable wages of workers with both wages and self-employment earnings

AWSCMB=WSCCMB/CMBNT

AWSCMB96=AWSCMB(1996)

AWSCMB=AWSCMB*BASECW/AWSCMB96

CW=TAXMAX/AWSCMB

IF(CW.LT.0.0543009)THEN

 CWTR=CW-(.722659/1.65)*CW**1.65-(.461913/1.8)*CW**1.8

ELSE IF(CW.LT.0.1086018)THEN

 CWTR=-(1.02884/1.6)*CW**1.6+(.324761/2.6)*CW**2.6+1.02015*CW-.0000130669

ELSE IF(CW.LT.0.1629027)THEN

 CWTR=-(.906607/1.7)*CW**1.7+.947662*CW+.002059472

ELSE IF(CW.LT.0.2172037)THEN

 CWTR=-(.813951/1.55)*CW**1.55+.991722*CW+.002022215

ELSE IF(CW.LT.0.3258055)THEN

 CWTR=-(.755135/1.55)*CW**1.55+.964593*CW+.004355898

ELSE IF(CW.LT.0.5430091)THEN

 CWTR=-(.649755/1.6)*CW**1.6+.886467*CW+.011658928

ELSE IF(CW.LT.0.7059119)THEN

 CWTR=-(.573205/1.7)*CW**1.7+.810122*CW+.019653316

ELSE IF(CW.LT.0.9231155)THEN

 CWTR=-(5.22264/1.06)*CW**1.06+5.47514*CW-.053844798

ELSE IF(CW.LT.1.0860183)THEN

 CWTR=-(2.02619/1.15)*CW**1.15+2.27963*CW-.023407805

ELSE IF(CW.LT.1.5204256)THEN

 CWTR=-(.605192/.2)*DEXP(-.2*CW)+(.827158/.8)*DEXP(-.8*CW)-(1.52918/1.5)*DEXP(-1.5*CW)-.212269*CW+2.946985922

ELSE IF(CW.LT.1.8462311)THEN

 CWTR=-(.191389/.6)*DEXP(-.6*CW)-(.764408/1.8)*DEXP(-1.8*CW)+.0194903*CW+.719848486

ELSE IF(CW.LT.2.3077888)THEN

 CWTR=-(.12964/.5)*DEXP(-.5*CW)-(.644861/1.5)*DEXP(-1.5*CW)+.0183343*CW+.731280763
166

ELSE IF(CW.LT.2.9865502)THEN

 CWTR=-(.361318/.8)*DEXP(-.8*CW)+.0219491*CW+.698954858

ELSE IF(CW.LT.4.3440731)THEN

 CWTR=-(.193202/.45)*DEXP(-.45*CW)+.00425171*CW+.82237055

ELSE IF(CW.LT.5.4300913)THEN

 CWTR=-(.0560412/.25)*DEXP(-.25*CW)-(.311286/.8)*DEXP(-.8*CW)+.00297316*CW+.854848493

ELSE IF(CW.LT.13.5752283)THEN

 CWTR=-(.0995677/.32)*DEXP(-.32*CW)+.00355234*CW+.843717127

ELSE IF(CW.LT.21.7203653)THEN

 CWTR=-(.041159/.19)*DEXP(-.19*CW)+.00156765*CW+.883046178

ELSE IF(CW.LT.678.7614168)THEN

 CWTR=-(.265022/.555)*CW**(-.555)+1.000103517

ELSE

 CWTR=1D0

END IF

WSTCMB=CWTR*WSCCMB

OASDI taxable earnings of workers with both wages and self-employment earnings

TECCMB=SECCMB+WSCCMB

ATECMB=TECCMB/CMBNT

ATECMB96=ATECMB(1996)

ATECMB=ATECMB*BASECT/ATECMB96

CT=TAXMAX/ATECMB

IF(CT.LT.0.0209065)THEN

 CTTR=CT-(58.6063/3.5)*CT**3.5

ELSE IF(CT.LT.0.1254391)THEN

 CTTR=(.320825/1.4)*CT**1.4-(1.90732/2)*CT**2+.967979*CT+.000050526-.00000622

ELSE IF(CT.LT.0.3345042)THEN

 CTTR=-(1.77251/1.9)*CT**1.9+(1.18333/2.8)*CT**2.8+1.11299*CT-.003813108-.00000622

ELSE IF(CT.LT.0.7108215)THEN

 CTTR=-(.246427/1.35)*CT**1.35-(1.24155/1.8)*CT**1.8+(.55025/2.3)*CT**2.3+1.16953*CT-.001078375-.00000622

ELSE IF(CT.LT.0.7944476)THEN

 CTTR=(3.15997/1.4)*CT**1.4-(4.21829/1D0)*DEXP(-1*CT)-4.46998*CT+4.300993015-.00000622

ELSE IF(CT.LT.1.0453257)THEN

 CTTR=(.55343/1.6)*CT**1.6-(1.76791/1.2)*DEXP(-1.2*CT)-.845578*CT+1.479639989-.00000622

ELSE IF(CT.LT.1.8815863)THEN

 CTTR=-(.360108/.3)*DEXP(-.3*CT)-(1.24485/2.7)*DEXP(-2.7*CT)-.110244*CT+1.566702582-.00000622

ELSE IF(CT.LT.3.7631726)THEN

 CTTR=-(.262138/.6)*DEXP(-.6*CT)+(.208323/1.9)*DEXP(-1.9*CT)-(2.27562/2.7)*DEXP(-2.7*CT)+.00933849*CT+

 .799685739-.00000622

ELSE IF(CT.LT.4.1813029)THEN

 CTTR=-(.26942/.6)*DEXP(-.6*CT)+(.266252/1.7)*DEXP(-1.7*CT)+.00905196*CT+.80182568-.00000622

ELSE IF(CT.LT.10.4532574)THEN

 CTTR=-(.0592625/.25)*EXP(-.25*CT)-(.541514/1)*DEXP(-1*CT)+.00174723*CT+.88757547-.00000622

ELSE IF(CT.LT.18.8158632)THEN

 CTTR=-(.0610012/.25)*DEXP(-.25*CT)+.00174344*CT+.888109189-.00000622

ELSE IF(CT.LT.522.6628676)THEN

 CTTR=-(.21993/.5455)*CT**(-.5455)+1.000030393-.00000622

ELSE

 CTTR=1D0

END IF

TETCMB=CTTR*TECCMB

SETCMB=TETCMB-WSTCMB

Ratio OASDI taxable to covered self-employment earnings

RSET = (SETCMB+SETSEO)/CSE

Where

ASEO96 = Average self-employment earnings of workers with no OASDI taxable wages in 1996

ATECMB = Average OASDI covered earnings of workers with both OASDI covered wages and self-employment earnings

ATECMB96 = Average OASDI covered earnings of workers with both OASDI covered wages and self-employment earnings in 1996

AWSCMB = Average OASDI covered wage of workers with both wages and self-employment earnings

AWSCMB96 = Average OASDI covered wage of workers with both wages and self-employment earnings in 1996

ASESEO = Average self-employment earnings of workers with no OASDI taxable wages

AWSCMB = Average OASDI covered wage of workers with both wages and self-employment earnings
167

BASECT = Average total earnings of workers with both self-employment earnings and wages in 1% sample data for 1996 used to

produce equations

BASECW = Average OASDI covered wages of workers with both self-employment earnings and wages in 1% sample data for 

1996 used to produce equations

BASEO = Average self-employment earnings of workers with no OASDI taxable wages in 1% sample data for 1996 used to

produce equations

CMBNT = Number or workers with both OASDI taxable wages and self-employment earnings

CSE = OASDI covered self-employment earnings

CT = Ratio OASDI taxable maximum to average earnings of workers with both self-employment earnings and OASDI

taxable wages

CW = Ratio OASDI taxable maximum to average self-employment earnings of workers with both self-employment earnings

and OASDI taxable wages

CTTR = Ratio of OASDI taxable to covered earnings for workers with both wages and self-employment earnings

CWTR = Ratio of OASDI taxable to covered wages for workers with both wages and self-employment earnings

O = Ratio OASDI taxable maximum to average self-employment earnings of workers with no OASDI taxable wages

OTR = Ratio of OASDI taxable self-employment to covered earnings for workers with no OASDI taxable wages

SECCMB = OASDI covered self-employment earnings of workers with both 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 = SETR * CSE

Where

CSE = OASDI covered self-employment earnings

SET = OASDI taxable self-employment earnings

SETR = Ratio of OASDI taxable to covered self-employment earnings

2-4.8 OASDI effective taxable payroll (ETP)

ETP=WTER+SET-0.5*MER

Where

ETP = OASDI effective taxable payroll

MER = OASDI multi-employer refund wages

SET = OASDI taxable self-employment earnings

WTER = Annual OASDI taxable employer wages

2-4.9 OASDI taxable wage liability (WTL)

WTL = WTER * TRW

Where

TRW = OASDI combined employee-employer tax rate

WTL = Annual OASDI taxable wage liabilities

WTER = Annual OASDI taxable employer wages

2-4.10 OASDI taxable self-employment liability (SEL)

SEL = SET * TRSE

Where

SEL = OASDI taxable self-employment earnings liabilities

SET = OASDI taxable self-employment earnings

TRSE = OASDI self-employment tax rate

2-4.11 OASDI quarterly taxable wage liability (WTLQ)
168

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)

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
169

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

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
170

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

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
171

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)

 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
172

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

 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
173

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

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
174

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

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
175

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 non-farm OASDI taxable wages and liabilities

Annual

WTPNF = WTER – WTFC – WTML – WTSL – TFMW – WTTIPSEE – WTTIPSSR

Where

TFMW = Annual OASDI taxable farm wages

WTSL = Annual OASDI taxable State and Local wages

WTFC = Annual OASDI taxable Federal Civilian wages

WTPNF = Annual OASDI taxable private non-farm wages excluding tips

WTTIPSEE = Annual OASDI taxable tips received by employees reported by employers

WTTIPSSR = Annual OASDI taxable tips received by employees self-reported on income tax returns

WTER = Annual OASDI taxable employer wages

Quarterly

BACW93 = 21912.00

NACW = BACW93 / ACW93 * AWC

X = MAX / NACW

IF(X.LT.0.91274)THEN

 TWTR=1D0+.990751*DEXP(X)**(-1)/(-1)-.013904602

ELSE IF(X.LT.2.05367)THEN

 TWTR=1D0+(-.003129*X+(1.167562*DEXP(X)**(-1.17)/(-1.17)))-.065747345

ELSE IF(X.LT.4.791895)THEN

 TWTR=1D0+(.003962*X+(.770093*X**(-1.85053))/(-1.85053))-.06071106

ELSE

 TWTR=1D0+(.267708*X**(-.94))/(-.94)+.00066

END IF

IF(TWTR.LT.0.70)THEN

 QP(1)=-(-0.000575+0.18692*DLOG(TWTR)-0.23133*DLOG(TWTR)**2-

0.10453*DLOG(TWTR)**3+0.04306*DLOG(TWTR)**4+0.01906*DLOG(TWTR)**5)-0.0325201+PD(1)+TCPD(I,1)

 QP(2)=-(0.00657+1.7015*TWTR-8.60615*TWTR**2+14.444*TWTR**3-9.97171*TWTR**4+2.42519*TWTR**5)-

0.0080956+PD(2)+TCPD(I,2)

 QP(3)=-(0.12167+1.31142*TWTR**3-6.31672*TWTR**4+8.03785*TWTR**5-3.15412*TWTR**6)+0.019325+PD(3)+TCPD(I,3)

 QP(4)=-(0.1548-0.41354*TWTR**5+0.25874*TWTR**7)+0.0197767+PD(4)+TCPD(I,4)

ELSE IF(TWTR.LT.0.88)THEN

 QP(1)=0.224763-0.237056*TWTR+PD(1)+TCPD(I,1)

 QP(2)=0.190385-0.209676*TWTR+0.00176*(TWTR-0.7)/(0.88-0.7)+PD(2)+TCPD(I,2)

 QP(3)=-0.052523+0.05309*TWTR+PD(3)+TCPD(I,3)

 QP(4)=-0.354571+0.38249*TWTR+PD(4)+TCPD(I,4)

ELSE

 QP(1)=0.968092-1.877574*TWTR+0.904348*TWTR**2+PD(1)+TCPD(I,1)

 QP(2)=-0.468266+1.148107*TWTR-0.690132*TWTR**2+PD(2)+TCPD(I,2)

 QP(3)=-0.850885+1.824094*TWTR-0.981557*TWTR**2+PD(3)+TCPD(I,3)

 QP(4)=0.350767-1.093966*TWTR+0.766972*TWTR**2+PD(4)+TCPD(I,4)

END IF

IF(PTR.LT.0.86)THEN

 QP(J)=QP(J)+ADJTP(J)

ELSE

 IF((ADJCP(J)-ADJTP(J)).NE.0D0)QP(J)=QP(J)+ADJTP(J)+((PTR-BPTR)/(1.-BPTR))**4*(ADJCP(J)-ADJTP(J))

END IF

QWTPNF(I, J) = QP(J) * WTPNF(I) + QWTTIPSEE(I, J) + QWTPHH(I, J)

QWTPNF(I, 2) = QWTPNF(I, 2) + WTTIPSSR(I)

Where

ACW93 = Annual average OASDI covered wage for 1993
176

AWC = Annual average OASDI covered wage for current year

BACW93 = Annual average OASDI covered wage for 1993 from actual data used to determine taxable to covered wage equations

I = Calendar year

J = Quarter

MAX = Annual OASDI taxable maximum

NACW = Annual average OASDI covered wage for current year adjusted for average from actual data used to determine equations

PD = Payday variable for private non-farm based on calendar

QP = Proportion of annual OASDI taxable private non-farm wages excluding taxable tips paid in each quarter

QWTPNF = Quarterly OASDI taxable private non-farm wages including tips

TCPD = Proportion of annual NIPA private wages paid in each quarter

TWTR = Ratio of OASDI taxable to covered wages computed using equations based on data for 1993

X = Ratio of annual OASDI taxable maximum to adjusted annual average OASDI covered wage (NACW)

Quarterly OASDI wage liabilities

WTLQPNF(I,J) = (QWTPNF(I,J) – QWTPHH(I,J)) * TRW(I)

Where

QWTPHH = Quarterly OASDI taxable private household wages

QWTPNF = Quarterly OASDI taxable private non-farm wages including tips

TRW = OASDI combined employee-employer tax rate

WTLQPNF = Quarterly OASDI tax liabilities from taxable private non-farm wages including tips, excluding private household 

taxable wages

Total quarterly OASDI taxable wages and wage liabilities

QWT(I,J) = QWTPNF(I,J) + QWTF(I,J) + QWTSL(I,J) + QWTFM(I,J)

WTLQ(I,J) = QWT(I,J) * TRW(I)

Where

I = Calendar year

J = Quarter

QWT = Quarterly OASDI taxable wages

QWTF = Quarterly OASDI taxable Federal wages

QWTFM = Quarterly OASDI taxable farm wages

QWTPNF = Quarterly OASDI taxable private non-farm wages including tips

QWTSL = Quarterly OASDI taxable State and Local wages

WTLQ = Quarterly OASDI taxable wage liabilities

2-4.12 OASDI quarterly taxable wage liability collections (WTLQC)

OASDI taxable private non-farm wages by sub-quarterly periods

PTR =WTP/WCP

MR =MAR(I)-.04346*(1.-PTR)+.08497*(1.-PTR)**2

JR =JUN(I)-.02627*(1.-PTR)-.26844*(1.-PTR)**2

SR =SEP(I)-.12321*(1.-PTR)-.02344*(1.-PTR)**2

DR =DEC(I)-.12468*(1.-PTR)-.20710*(1.-PTR)**2

MWTP(1)=QWTP(I,1)*MR

MWTP(2)=QWTP(I,1)-MWTP(1)

MWTP(3)=QWTP(I,2)*JR

MWTP(4)=QWTP(I,2)-MWTP(3)

MWTP(5)=QWTP(I,3)*SR

MWTP(6)=QWTP(I,3)-MWTP(5)

MWTP(7)=QWTP(I,4)*DR

MWTP(8)=QWTP(I,4)-MWTP(7)

Where

DEC = Proportion of fourth quarter OASDI covered private non-farm wages (excluding tips and household) paid in December

DR = Proportion of fourth quarter OASDI taxable private non-farm wages (excluding tips and household) paid in December

I = Calendar year

JR = Proportion of second quarter OASDI taxable private non-farm wages (excluding tips and household) paid in June

JUN = Proportion of second quarter OASDI covered private non-farm wages (excluding tips and household) paid in June

MAR = Proportion of first quarter OASDI covered private non-farm wages (excluding tips and household) paid in March

MR = Proportion of first quarter OASDI taxable private non-farm wages (excluding tips and household) paid in March

MWTP = OASDI taxable private non-farm wages (excluding tips and household) paid in last month and in first two months of quarter

PTR = Ratio of annual OASDI taxable private non-farm wages (excluding tips and household) to covered private non-farm wages
177

QWTP = Quarterly OASDI taxable private non-farm wages (excluding tips and household)

SEP = Proportion of third quarter OASDI covered private non-farm wages (excluding tips and household) paid in September

SR = Proportion of third quarter OASDI taxable private non-farm wages (excluding tips and household) paid in September

WCP = Annual OASDI covered private non-farm wages

WTP = Annual OASDI taxable private non-farm wages (excluding tips and household)

OASDI taxable private non-farm wages collected on in same quarter wages are paid

TRAT =RATEE(I,5)

CA =.95

MWCP(1)=QWSCPNF(I,1)*MAR(I)

MWCP(2)=QWSCPNF(I,1)-MWCP(1)

MWCP(3)=QWSCPNF(I,2)*JUN(I)

MWCP(4)=QWSCPNF(I,2)-MWCP(3)

MWCP(5)=QWSCPNF(I,3)*SEP(I)

MWCP(6)=QWSCPNF(I,3)-MWCP(5)

MWCP(7)=QWSCPNF(I,4)*DEC(I)

MWCP(8)=QWSCPNF(I,4)-MWCP(7)

RCSM =.80

QRMREQ=750.

QRWREQ=11250.

RMF=70786.*WSP(I)/1001400.

CALL ITERNU(QRMREQ,MWTP(2),MWCP(2),TRAT,RMF,PWCS(1))

CALL ITERNU(QRWREQ,MWTP(1),MWCP(1),TRAT,RMF,PWCE(1))

CALL ITERNU(QRMREQ,MWTP(4),MWCP(4),TRAT,RMF,PWCS(2))

CALL ITERNU(QRWREQ,MWTP(3),MWCP(3),TRAT,RMF,PWCE(2))

CALL ITERNU(QRMREQ,MWTP(6),MWCP(6),TRAT,RMF,PWCS(3))

CALL ITERNU(QRWREQ,MWTP(5),MWCP(5),TRAT,RMF,PWCE(3))

CALL ITERNU(QRMREQ,MWTP(8),MWCP(8),TRAT,RMF,PWCS(4))

CALL ITERNU(QRWREQ,MWTP(7),MWCP(7),TRAT,RMF,PWCE(4))

DO J=1,4

 QWTPC(I,J)=PWCS(J)+PWCE(J)*RCSM*CA

 QWTPF(I,J)=QWSTXPHH(I,J)-QWTPC(I,J)

END DO

Where

AWSCODXSRT = Annual average OASDI covered private non-farm wages (excluding household)

CA = Compliance allowance

DEC = Proportion of fourth quarter OASDI covered private non-farm wages (excluding tips and household) paid in 

December

I = Calendar year

J = Quarter

JUN = Proportion of second quarter OASDI covered private non-farm wages (excluding tips and household) paid in June

MAR = Proportion of first quarter OASDI covered private non-farm wages (excluding tips and household) paid in March

MWCP = OASDI covered private non-farm wages paid in third month and in first two months of each quarter

MWTP = OASDI taxable private non-farm wages paid in third month and in first two months of each quarter

PWCE = OASDI taxable private non-farm wages paid in the third month of each quarter

PWCS = OASDI taxable private non-farm wages paid in the first two months of each quarter on which taxes are collected in 

that quarter

QWSCPNF = Quarterly OASDI covered private non-farm wages

QRMREQ = Monthly deposit requirement

QRWREQ = Quarterly deposit requirement

QWSTXPHH = Quarterly OASDI taxable private non-farm wages (excluding household)

QWTPC = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in the quarter the wages were 

paid

QWTPF = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in the quarter after the wages 

were paid

RATEE(I,5) = OASDHI employee tax rate

RCSM = Proportion of OASDI taxable private non-farm wages wages paid in same quarter in which taxes are collected

RMF = Current year average wage size of firm

SEP = Proportion of third quarter OASDI covered private non-farm wages (excluding tips and household) paid in September

TRAT = OASDHI employee tax rate

WSP = Economy-wide (NIPA) private wages

SUBROUTINE ITERNU(A11,QPAR,QTOT,T,RMF,AMTOUT)

 R=QPAR/QTOT

 X=A11/(T*2.+.10)
178

 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 non-farm wages paid in sub-quarterly period and collected on in same quarter

D = Ratio of deposit requirement to total taxes withheld

FWH = FICA taxes withheld

IWH = Income taxes withheld

N1 = Ratio of deposit requirement to total taxes withheld times 1000 (used to see how close we are to target)

QPAR = OASDI taxable private non-farm wages paid in sub-quarterly period

QTOT = OASDI covered private non-farm wages paid in sub-quarterly period

R = Initial ratio of OASDI taxable to covered private non-farm wages paid in sub-quarterly period

RMF = Current year average wage size of firm

RTAX = Ratio of OASDI taxable to covered private non-farm 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

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
179

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

2-4.13 Quarterly Self-Employed Net Income Tax Collections (SELQC)

DO J = 1, 4

 SELQC(I,J) = SECRCY(I,J) * SEL(I) + SECRPY(I,J) * SEL(I-1)

END DO

Where

I = Calendar year

J = Quarter

SECRCY = Proportion of OASDI taxable self-employment earnings collected on in same year earned

SECRPY = Proportion of OASDI taxable self-employment earnings collected on in year following that in which earned

SEL = OASDI taxable self-employment earnings liabilities

SELQC = Quarterly OASDI self-employed net income tax collections

2-4.14 SECA Appropriation Adjustments (MSECAAA)

MSECAAA = 0

DO L = I-2, I-9, -1

 MSECAAA = MSECAAA + SEAACO(I,J) * SELIAC(L)

END DO

Where

I = Calendar year

J = Quarter

L = Liability year

MSECAAA = OASDI SECA appropriation adjustment for quarter (assigned to last month in quarter)

SEAACO = Proportion of past year’s OASDI self-employment tax liability which will be reported in current quarter

SELIAC = Prior years’ OASDI self-employment tax liability
180

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

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 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
181

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 

business 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

Total number serving in the US Armed Forces estimated by the 

Department of Defense and published by the Census Bureau

Federal civilian government employment
182

EGEFCPS

EGGEFC

EGGESL

EMPTRDI

EMPTRHI

EMPTROASI

ENA

ENAS

ENAU

ENAW

ENAWPBXGE

ENAWPH

ENAWSPBXGE

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 

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 immigrant population

EO_ESF Total employment in the other immigrant population whose reported 

earnings are posted to the Earnings Suspense File

EO_MEF Total employment in the other immigrant population whose earnings are 

reported and posted to the Master Earnings File

EO_MEFC Total employment in the other immigrant population whose earnings are 

reported and posted to the Master Earnings File and are OASDI-covered

EO_UND

EP

EPES_EST

EPHS_EST

EPSS_EST

Total employment in the other immigrant 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

Gross domestic product

GDP, 2005$

GDP, General Government

GDP, Federal and State & local government enterprises
183

GDPGEFC

GDPGESL

GDPGF

GDPGFC

GDPGFM

GDPGGE

GDPGGEFC

GDPGGESL

GDPGSL

GDPPBNFXGE

GDPPF

GDPPH

GDPPNI

GDP, Federal civilian government enterprises

GDP, State & local government enterprises

GDP, General Government, Federal

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

Employer contributions for employee pension and insurance funds

Contributions for CSRS employees’ pay

Other labor income, Federal civilian

Contributions for FERS employees’ pay
184

OLI_FERSFC

OLI_GGE

OLI_GHI

OLI_GHI_FC

OLI_GHI_P

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

PGDP

PGDPAF

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 

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

Gross Domestic Product Price Index, Units: 2005=100

Deflator for farm output
185

PIA Primary insurance amount

PIARR PIA replacement rate, defined as the ratio of a hypothetical medium 

scale worker’s PIA to his/her career average indexed earnings.

PGDP GDP price deflator

PBNFXGE Private nonfarm business excluding government enterprises

RCMB Proportion of wage workers who are also self-employed 

(CMB_TOT/WSW)

RCSE

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

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
186

RSOCSL_WC 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))

RTP A summary measure of the business 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

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, 
187

SOC_WCP

SOC_WCSL

SOCF_HI

SOCF_MIFM

SOCF_OASDI

SOCF_PBG

SOCF_RETRR

SOCF_UIF

SOCF_UIFC

SOCF_UIFED

SOCF_UIFM

SOCF_UIS

SOCF_WC

SOCSL_WC

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 

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
188

TEO Total “at any time” employment in the other immigrant population

TEO_ESF Total “at any time” employment in the other immigrant population 

whose reported earnings are posted to the Earnings Suspense File

TEO_MEF Total “at any time” employment in the other immigrant population 

whose earnings are reported and posted to the Master Earnings File

TEO_MEFC Total “at any time” employment in the other immigrant population 

whose earnings are reported and posted to the Master Earnings File and 

are OASDI-covered

TEO_UND

TMAXUI_SL

TRATE_UI

TRATIO_UI

Total “at any time” employment in the other immigrant population that 

is strictly in the underground economy (i.e., with no earnings reported)

Taxable maximum for State & local unemployment insurance

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

USEAR 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

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

WSS

WSSG

WSSGE

WSSGEFC

WSSGESL

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
189

WSSGF

WSSGFC

WSSGFM

WSSGGE

WSSGGESL

WSSGSL

WSSP

WSSPBNFXGE

WSSPES

WSSPF

WSSPH

WSSPHS

WSSPNI

WSSPSS

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

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 Wage and salary workers that report some OASDI covered earnings

WTEE Total employee OASDI taxable wages

WTER Total employer OASDI taxable wages

WTL Annual OASDI wage tax liabilities

WTLQ Quarterly OASDI wage tax liabilities

WTLQC Quarterly OASDI wage tax collections

Y

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
190

Process 3:

Beneficiaries
191

3. Beneficiaries

OCACT uses the Beneficiaries process to project the fully insured and disability insured 

population, the number of disabled worker and their dependent beneficiaries, the number of 

retired worker and their dependent beneficiaries, and the number of dependent beneficiaries of 

deceased workers. The Beneficiaries process receives input data from the Demography and 

Economics sections 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.
192

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 

(SSAPRO) 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 nonother immigration population (LEGPOP). These histories are constructed from past and 

projected cover worker rates of the non-other immigration population, median earnings, and 

amounts required for crediting QC. 

The equations for this subprocess are given below: 

FPRO = FPRO(·) (3.1.1)

DPRO = DPRO(·) (3.1.2)

FINPOP = FPRO * SSAPOP (3.1.3)

DINPOP = DPRO * SSAPOP (3.1.4)

3.1.b. Input Data

All data are updated annually, except those that are noted.

Long-Range OCACT Data

Demography 

• Social Security area population as end of year (1940 – 2090) by age (0 -100, age 100 
193

including age 100 and older), marital status (single, married, widowed, divorced) and sex 

(M, F). (Workflow 3.a)

• “Other immigrant” population as end of year (1963 – 2090) by age (0 -100, age 100 

including age 100 and older) and sex (M, F). (Workflow 3.c)

• Number of new “net legal immigrants” (legal immigrants – estimated legal 

emigrants) entering the Social Security area each year (1940 – 2090) by age (14 – 69) and

sex (M, F). (Workflow 3.d)

• The population granted deferred action for childhood arrivals (DACAs) as end of year 

(2011-2090) by age (0 -100, age 100 including age 100 and older) and sex (M, F). 

(Workflow 3.e)

Economics

• Annual estimates of covered workers posted to the Master Earnings File (MEF) by sex 

(M, F) and age (15 – 74) for years (1937 – 2090). (Workflow 3.b)

• Annual projection (2009 – 2090) of average wage index and median covered earnings. 

(Workflow 3.g)

• “Other immigrant” workers with earnings posted to the (MEF) by sex (M, F), age (16 – 95), 

and for years (1964 – 2090). (Workflow 3.h)

Beneficiaries

• Disabled-worker beneficiaries at year end (2011 – 2090) 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 the 

Beneficiaries/DISABILITY (#3.2) area. (Workflow 3.f)

Short-Range OCACT data

• 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 (2022). (Workflow 2.f)

(MKS-2013.2)

DINPOP by age (15 – 66) and sex (M, F) from the end of year 1969 to the end of ShortRange projection period (2022). (Workflow 2.g) (MKS-2013.2)

Other input data

• Historical series of annual median earnings of covered workers by age group (<20, 

20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-61, 62-64, 65-69) and sex (M, 

F) for years 1937-2009. Data are updated using the data in the most recent Social 

Security Annual Statistical Supplement Table 4.B6. (Workflow 2.b) (MKS-2013.2)

• Number of disabled workers by age (20-69) and sex (M, F) for years 1958-2011. 

Ages 66-69 are zeros. Data are updated using the data from the historical disability file 
194

“wkrben”. (Workflow 2.e) (MKS-2013.2)

• The amount required for crediting one quarter of coverage for years 1937-2009 from 

a OCACT web site. (Workflow 2.d) (MKS-2013.2)

• Historical series of annual median earnings of all covered workers for years 1937-

2009. Data are updated using the data in the most recent Social Security Annual 

Statistical Supplement Table 4.B6. (Workflow 2.c) (MKS-2013.2)

• The number of all covered workers (wage/salary workers, self-employed workers) by 

sex and amount of earnings for 2009 in the most recent Social Security Annual Statistical 

Supplement Table 4.B7 & 4.B9. These are used to produce the input data for the 

distribution of earnings (FRAC.f90). (Workflow 2.a) (MKS-2013.2) (Did not change 

for the 2013 TR)

• ANNUAL factor (comparability factor between quarterly and annual reporting of 

earnings) by age (13-69) and sex (M, F) for years prior to 1978. These data are not 

updated. (Workflow 4.d) (MKS-2013.1)

• SLCT factor (adjustment factor to bring simulated fully insured rate in line with 

historical fully insured rate) by age (13-69) and sex (M, F). These data are updated when 

needed. (Workflow 4.b) (MKS-2013.2) Updated for 2013 TR

• SRCH factor (adjustment factor to bring simulated fully insured rate in line with 

historical fully insured rate) by age (13-69) and sex (M, F). These data are updated when 

needed. (Workflow 4.c) (MKS-2013.2) Updated for 2013 TR

• 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 are updated 

when needed. (Workflow 4.e) (MKS-2013.2) Updated for 2013 TR

3.1.c. Development of Output

Equation 3.1.1 & 3.1.2 -

Determining the QC distribution 

There are three variables playing important roles in the simulation process starting from age 13 

through 69 of a birth cohort by sex. They include historical and projected covered worker rates 

of the non-other population28 by age and sex, the amounts required for crediting QC, and a 

cumulative worker distribution by earnings level.

Covered worker rates of the non-other population (CPRO) are the ratio of the non-other covered 

workers to the non-other Social Security area population. A non-other population is its total 

population minus its other immigrant population. Historical and projected (total and other 

immigrant) numbers of covered workers and the Social Security area population, which are 

 28 The insured model treats the DACA population (those granted deferred action for childhood arrivals) like legal 

permanent resident immigrants.
195

provided by the Economics and Demography sections respectively, are used to calculate the rates

for ages 15 through 69. For ages, 13 and 14, INSURED estimates covered worker rates based on 

the covered worker rates at age 15. 

The 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 69, INSURED begins the simulation process by randomly selecting records to 

represent new net legal immigrants from the covered worker portion of 30,000 records. For each 

record, a number of QC (1, 2, 3 or 4) is assigned on a uniform basis. Once a record is assigned a 

number of QC, INSURED nullifies the previous earnings of the record. 

After the records for new immigrants are selected, the rest of the records for ages 14 to 69 are 

either non-covered workers or covered workers. The total number of records assigned as noncovered workers is set equal to (1-covered worker rate) * 30,000. These records receive no QC. 

To identify records as non-covered workers, INSURED uses two parameters (SRCH, SLCT), 

which vary by age and sex. 

SRCH sets a limit on the number of consecutive records to be searched for a non-covered 

worker. In general, the younger age groups have lower SRCH values. SLCT is the number of 

consecutive prior years in which no QC were earned that is required in order for a simulated 

record to be assigned as a non-covered worker. Lower SLCT values are set for the very young 

and older age groups. Sensitivity analyses show that insured percentages are negatively 

correlated with these two parameters. When the female covered worker rates approach the male 
196

rates, the female SRCH and SLCT values are graded toward the male values29.

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 legal 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 legal immigrants, for ages 14-

69.

Determining Insured Status

Once the simulation process is complete, the insured status for each record at any age can be 

determined based on the total QC assigned up to that age. The simulated non-other 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). 

For each sex and cohort, FSIM_LEG and DSIM_LEG are 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 situation30. Thus, DINADD is 

 29 This occurs when the female covered worker rate is greater than 80 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 80 and 100 

percent of the male rate.

30 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.
197

# of workers on the disability rolls morethan3 years

Social Security Area population by age, sex, and cohort.

A small proportion of the other immigrant population, OTLPOP, is added to calculate the 

simulated fully insured rate of the Social Security Area population, FSIM. We assume that other 

immigrants who have their earnings posted to the MEF will have the same insurability as the 

non-other population. We project FSIM as

SSAPRO

FSIM _ LEG *(LEGPOP + CW _ OTHER /CPRO) by age, sex, and cohort.

Hence, the simulated fully insured rate of the other immigrant population FSIM _OTL is

OTLPOP

FSIM _ LEG *CW _ OTHER /CPRO by age, sex, and cohort.

FSIM_LEG and FSIM_OTL are assumed to remain the same beyond age 69. For ages 70 and 

older, FSIM is projected by multiplying the non-other and other 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 set equal to Short-Range estimates. The difference in terms of the 

percentage between the Long-Range and Short-Range projections at the end of 10th year is 

linearly phased out during the next ten years by cohort and sex. 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 martial status. 
198

DISABILITY 

3.2.a. Overview

The Social Security Administration pays monthly disability benefits to disability-insured workers 

who meet the 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 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 DIB EOY = Exposures EOY × Linkages EOY (3.2.4)

 

3.2.b. Input Data

Trustees Assumptions

Each year, the Trustees set the assumption for the ultimate age-sex-adjusted incidence rate and 
199

the ultimate age-sex-adjusted recovery rate. We achieve this by setting the age-adjusted 

incidence rate and the age-adjusted recovery rate for each sex. The ultimate level for the age-sexadjusted incidence rate and for the age-sex-adjusted recovery rate is set for the twentieth year of 

the projection period. Then for each age group and sex, we adjust the ultimate incidence rate to 

match a “target” incidence rate. The following chart shows these “target” incidence rates by age 

group and sex. 

Using a standard population of disability insured who are not in current pay as of December 

1999, the age-sex-adjusted incidence rate for the 2013 Trustees Report was 5.8 per 1,000. Using 

a standard population of DIBs as of December 1999, the age-sex-adjusted recovery rate for the 

2013 Trustees Report was 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. 

Workflow reference is bolded in parenthesis after each item.

Demography

• January Social Security area population by age, sex, and marital status31 (dimensioned 

(0:100,1:2,1:4)) for beginning of years 1971-2091. (3a)

• Probabilities of death by sex, age and year (1:2,15:148,2011:2090). (3b)

• Total children by sex of parent, age of parent and age of child (dimensioned (1:2,19:71,0:18)) 

for beginning of years 1971-2091. (3c)

• Total married lives by age of husband crossed with age of wife (dimensioned 

(14:100,14:100)) for beginning of years 1971-2091. (3d)

• Average number of children under 16 per couple with children by age group (<25, 25-

29,...,60-64) of head of household (dimensioned (1:9)) for beginning of years 1971-2091. 

(3e)

Economics

• Unemployment rates by age group (16-19, 20-24,...,60-64), sex and year (1991:2023). (3h)

 31 Single, married, widowed, divorced.

Target Incidence Rates by Age Group

<19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 

Male 2.46 2.58 1.66 2.49 3.34 4.52 5.96 9.89 15.72 19.02 9.00 Female 1.90 1.02 2 1.62 2.82 3.54 4.78 6.39 10.10 14.16 14.72 8.34 

Age Group
200

Beneficiaries

INSURED subprocess #3.1

• Disability-insured population by age, sex and year (15:69,1:2,1969:2090) from the 2013 

Trustees Report. (3g)

• Disability-insured population by age, sex and year (15:69,1:2,1969:2090) from the 2012 

Trustees Report. (2j)

• Fully insured population by age, sex and marital status (14:95,1:2,1:4) for years 1970-

2090. (3f)

2012 Trustees Report DISABILITY subprocess #3.2

• Death rate projection factors from the 2012 Trustees Report by age group (15-19,20-

24,...,60-64), sex and year (1:2,1:10,2012:2090). (3i)

• Recovery rate projection factors and recovery rates from the 2012 Trustees Report by age 

group (15-19,20-24,...,60-64), sex and year (1:2,1:10,2012:2090). (3j) and (3k)

Other input data

We update only the most recent year data annually for this category except as noted otherwise 

below:

• The December 2012 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). (2b)

• December 2012 and December 2011 data from the MBR containing the number of 

disabled workers in current-payment status by age, sex and year [(15:66,1:2,1969:2012). 

(2a) and (2j)

• December 2012 data from the MBR containing the number of disabled workers in 

withheld or suspended status by age, sex and year [(15:66,1:2,1969:2012). (2a) 

• 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. (2a)

1) Minor child (0:17,1:2,1970:2012) 

2) Student child (18:21,1:2,1970:2012)

3) Disabled adult child (age group1:932,1:2,1970:2012)

4) Young spouse (19:64,1:2,1970:2012) 

5) Married aged spouse (62:100,1:2,1970:2012) 

6) Divorced aged spouse (62:100,1:2,1970:2012)

 We also read totals for each category.

• December data from the MBR containing the number of DIB awards by age, sex and year 

(15:67,1:2,1970:2012). (2c)

• December data from the MBR containing (1) the number of DIB total terminations 

(recoveries and deaths) and (2) the number of conversions33. These data are by sex and 

 32 Age groups 1 through 9 are 18-19, 20-24, 25-29,..., 55-59. 33 Conversions are DIB beneficiaries who become eligible for old-age benefits due to reaching the normal retirement 

age.
201

year (1:2,1970:2012). (2d)

• December data from the MBR containing the number of DIB deaths by age, sex and year 

(15:67,1:2,1975:2012). (2d)

• December data from the MBR containing the number of estimated DIB recoveries by 

age, sex and year (15:67,1:2,1975:2012). (2d)

• 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: (65:95+,1:2,1970:2012) (2b)

• 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 

(2:11,1:2,1973:2012). (2e)

• December data from the MBR containing the number of DIB awards by duration, age, 

sex and year (0:5,0:65,1:2,1993:2011). 2011 Awards were retrieved for this year’s TR, 

1993-2010 Awards have not been updated. (2j)

• Retroactive factors34 by year (1969:2011). These values are estimated using OCACT 

beneficiary data. (2h)

All numbers in the following categories are updated annually unless otherwise noted.

• Average incidence rates by age and sex (15:65,1:2) for the base period 1997-2006 based 

on awards data from 1997-2011 (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. (2j)

• 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 2001-2005. These numbers (also known as 

the base probabilities of death) are from Actuarial Study No. 122. We update these 

values when time and data are available. (2f)

• 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 2001-2005. These numbers (also known as 

the base probabilities of recovery) are from are from Actuarial Study No. 122. We 

update these values when time and data are available. (2g)

• Initial Incurred but not reported (IBNR)35 factors by duration, age and sex (0:10, 15: 69, 

1:2) based on 2002 entitlements (awards data from 2002-2007). (2j) (Not Updated)

• Ultimate IBNR factors by duration, age and sex (0:10, 15: 69, 1:2) based on 1997-2006 

entitlements (awards data from 1996-2011). We update these values when time and data 

are available. The IBNR calculation linearly grades between the initial and ultimate 

IBNR factors during the ten years from 2008-2017. The ultimate IBNR factor table 

applies for all years after 2017. (2j)

 34 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. 35 IBNR factors reflect the proportion of DIBs entitled to benefits who have been awarded since the year of their 

entitlement.
202

• For each year 2000-2090, (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. (2k)

• For the years 2016-2026, weights for ages 61-66 for linear interpolating between one set 

of incidence rates at a particular NRA and another set of incidence rates at the next higher 

NRA. We update these values only when there is a change in the NRA or in the present 

law. (4b)

• 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.

(4a)

• Short-Range/Long-Range adjustment (APROJ) factors by auxiliary beneficiary category 

(1:7) for years 2013-2032. 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. (2i)

• 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. 

IPROJG (1:11, 2, 2013-2090) and DPROJG (1:10, 2, 2013-2090) adjustment factors are 

by age group, sex and year. RPROJG (2, 2013-2022) adjustment factors are by sex and 

year. (2l),(4i), and (4d) 

• Ultimate RPROJG values by sex and age group (1:2, 1:10) calculated to reach a target 

value. Updated when the probabilities of recovery for DIB’s are updated. (4d)

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 and independent variables of unemployment rates 

and previous years’ incidence rates. We describe the regression equations in detail in Appendix 

3.2-1. 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” incidence rates were 

determined based on a recent review of historical and projected award rates by age group and 

sex. 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-
203

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 

2013 Trustees Report, we made IPROJG adjustments in the short-range period to better project 

the drop in disability claims as we recover from the current economic recession. 

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 ) qx ) and ( (r) qx ), respectively. Projected ( (d ) qx ) 

and ( (r) qx ) by age, sex, and duration are calculated by multiplying the base probabilities by the 

respective projection factors by age group and sex for that year.

For the first ten years, 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 

calculate the starting RPROJGs the following way:

 RPROJGTR13(2012) = RPROJGTR12 (2012) × actual recovery rate(2012) / estimated 

 recovery rate TR12(2012)

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 (2022). Then, for each age group 

and sex, we calculate the tenth year’s RPROJGs as follows:

 RPROJGTR13(2022) = RPROJGTR13 (2012) ×target value recovery rate (2022) / 

 actual recovery rate (2012)

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 (2022). We assume 

attainment of ultimate recovery rates in the twentieth year of the projection period. 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 (see Appendix 3.2-1). 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: 
204

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, 

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
205

Disabled Adult Child 

Exposure: Single SSA population by age groups 18-19, 20-24, 25-29,

 30-34, 35-39, 40-44, 45-49, 50-54, 55-59

Linkages: pDCAGA = Probability that parent is under NRA

pDCDIA = Probability that parent is disability insured given 

that the parent is under NRA

pDCDPA = Probability that disability insured parent under 

NRA is disabled

pDCDPC = Probability that adult child is disabled

DCRES = Residual Factor

Young Spouse 

Exposure: Married SSA population by sex and by single ages 20-64 

Linkages: pYSAGA = Probability that account holder is under NRA

pYSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA

pYSDPA = Probability that disability insured account holder 

under NRA is disabled

pYSETB = Probability that young spouse is not subject to

 earnings test 

pYSMCB = Probability that young spouse has a minor child

 beneficiary in his/her care

pYSDCB = Probability that young spouse has a disabled child 

 beneficiary in his/her care 

YSRES = Residual Factor

Married Aged Spouse 

Exposure: Married SSA population by sex and by single ages 62-100

Linkages: pMSAGA = Probability that account holder is under NRA

pMSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA

pMSDPA = Probability that disability insured account holder 

under NRA is disabled

pMSFIB = Probability that beneficiary is not insured

MSRES = Residual Factor

Divorced Aged Spouse 

Exposure: Divorced SSA population by sex and by single ages 62-100

Linkages: pDSDEA = Probability that account holder is living

pDSAGA = Probability that account holder is under NRA

pDSDIA = Probability that account holder is disability 

insured given that the account holder is under 
206

 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.

We develop APROJ 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.
207

Appendix: 3.2-1

The following information provides details about the regression equations used in determining 

incidence rates and IPROJG values by age group and sex for the first ten years of the projection 

period.

Male

Independent Variable: 16-19 unemployment rates

Independent Variable: 15-19 incidence rates

Dependent Variable: 15-19 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.86176177

Standard Deviation: 0.28831856

Coefficient Intercept: 0.43267500

Coefficient Slope1: 0.05380243

Coefficient Slope2: 0.85540124

Independent Variable: 20-24 unemployment rates

Independent Variable: 20-24 incidence rates

Dependent Variable: 20-24 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.89286691

Standard Deviation: 0.20031160

Coefficient Intercept: 0.40888896

Coefficient Slope1: 0.11409142

Coefficient Slope2: 0.84514054

Independent Variable: 25-29 unemployment rates

Independent Variable: 25-29 incidence rates

Dependent Variable: 25-29 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.80497678

Standard Deviation: 0.14529689

Coefficient Intercept: 0.10576024

Coefficient Slope1: 0.10512317

Coefficient Slope2: 0.94645805

Independent Variable: 30-34 unemployment rates

Independent Variable: 30-34 incidence rates

Dependent Variable: 30-34 incidence rates

Observation Period: 1994-2009
208

Adjusted R square: 0.68071757

Standard Deviation: 0.15067803

Coefficient Intercept: 0.56462912

Coefficient Slope1: 0.08824472

Coefficient Slope2: 0.76218879

Independent Variable: 35-39 unemployment rates

Independent Variable: 35-39 incidence rates

Dependent Variable: 35-39 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.57777394

Standard Deviation: 0.20491685

Coefficient Intercept: 0.73594111

Coefficient Slope1: 0.10885162

Coefficient Slope2: 0.76883721

Independent Variable: 40-44 unemployment rates

Independent Variable: 40-44 incidence rates

Dependent Variable: 40-44 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.54187111

Standard Deviation: 0.26386681

Coefficient Intercept: 0.76102922

Coefficient Slope1: 0.12635317

Coefficient Slope2: 0.82283727

Independent Variable: 45-49 unemployment rates

Independent Variable: 45-49 incidence rates

Dependent Variable: 45-49 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.58811862

Standard Deviation: 0.32352175

Coefficient Intercept: 0.23954798

Coefficient Slope1: 0.18960018

Coefficient Slope2: 0.95697005

Independent Variable: 50-54 unemployment rates

Independent Variable: 50-54 incidence rates

Dependent Variable: 50-54 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.56445957
209

Standard Deviation: 0.59348621

Coefficient Intercept: -0.59267373

Coefficient Slope1: 0.31876689

Coefficient Slope2: 1.06320963

Independent Variable: 55-59 unemployment rates

Independent Variable: 55-59 incidence rates

Dependent Variable: 55-59 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.38228937

Standard Deviation: 0.85182132

Coefficient Intercept: 1.85162332

Coefficient Slope1: 0.42349768

Coefficient Slope2: 0.87815297

Independent Variable: 60-64 unemployment rates

Independent Variable: 60-64 incidence rates

Dependent Variable: 60-64 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.39980910

Standard Deviation: 0.68304488

Coefficient Intercept: 2.47288951

Coefficient Slope1: 0.27557787

Coefficient Slope2: 0.84619445

Female

Independent Variable: 16-19 unemployment rates

Independent Variable: 15-19 incidence rates

Dependent Variable: 15-19 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.90720091

Standard Deviation: 0.14726975

Coefficient Intercept: 0.35758410

Coefficient Slope1: 0.06334315

Coefficient Slope2: 0.80301379

Independent Variable: 20-24 unemployment rates

Independent Variable: 20-24 incidence rates

Dependent Variable: 20-24 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.87599282
210

Standard Deviation: 0.15608240

Coefficient Intercept: 0.34140041

Coefficient Slope1: 0.11215547

Coefficient Slope2: 0.83033052

Independent Variable: 25-29 unemployment rates

Independent Variable: 25-29 incidence rates

Dependent Variable: 25-29 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.90374798

Standard Deviation: 0.10585696

Coefficient Intercept: 0.23393434

Coefficient Slope1: 0.11620672

Coefficient Slope2: 0.88785064

Independent Variable: 30-34 unemployment rates

Independent Variable: 30-34 incidence rates

Dependent Variable: 30-34 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.86330777

Standard Deviation: 0.12591742

Coefficient Intercept: 0.14655864

Coefficient Slope1: 0.12875875

Coefficient Slope2: 0.95436733

Independent Variable: 35-39 unemployment rates

Independent Variable: 35-39 incidence rates

Dependent Variable: 35-39 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.81926655

Standard Deviation: 0.17796500

Coefficient Intercept: 0.22390831

Coefficient Slope1: 0.15765990

Coefficient Slope2: 0.94972354

Independent Variable: 40-44 unemployment rates

Independent Variable: 40-44 incidence rates

Dependent Variable: 40-44 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.90497395

Standard Deviation: 0.16152667
211

Coefficient Intercept: 0.54410795

Coefficient Slope1: 0.20398475

Coefficient Slope2: 0.89871424

Independent Variable: 45-49 unemployment rates

Independent Variable: 45-49 incidence rates

Dependent Variable: 45-49 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.88492881

Standard Deviation: 0.19279291

Coefficient Intercept: 0.30411800

Coefficient Slope1: 0.33104569

Coefficient Slope2: 0.95743943

Independent Variable: 50-54 unemployment rates

Independent Variable: 50-54 incidence rates

Dependent Variable: 50-54 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.67828990

Standard Deviation: 0.37658822

Coefficient Intercept: -1.61878908

Coefficient Slope1: 0.31951663

Coefficient Slope2: 1.17008373

Independent Variable: 55-59 unemployment rates

Independent Variable: 55-59 incidence rates

Dependent Variable: 55-59 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.33290384

Standard Deviation: 0.56314490

Coefficient Intercept: 2.74775516

Coefficient Slope1: 0.26163299

Coefficient Slope2: 0.80759763

Independent Variable: 60-64 unemployment rates

Independent Variable: 60-64 incidence rates

Dependent Variable: 60-64 incidence rates

Observation Period: 1994-2009

Adjusted R square: 0.47821417

Standard Deviation: 0.41167446

Coefficient Intercept: 3.19374145
212

Coefficient Slope1: 0.03867550

Coefficient Slope2: 0.75887820

The following information provides details about the exponentially fitted equations used in 

determining death rates by age group and sex for the first year of the projection period.

Male

Independent Variable: Year

Independent Variable: 15-19 death rates

Observation Period: 2003-2012

Adjusted R square: 0.25988

Standard Deviation: 0.81184

Coefficient Intercept: 368.50980

Coefficient Slope1: -0.18231

Independent Variable: Year

Independent Variable: 20-24 death rates

Observation Period: 2003-2012

Adjusted R square: 0.61490

Standard Deviation: 0.06840

Coefficient Intercept: 61.84702

Coefficient Slope1: -0.02952

Independent Variable: Year

Independent Variable: 25-29 death rates

Observation Period: 2003-2012

Adjusted R square: 0.72107

Standard Deviation: 0.04192

Coefficient Intercept: 48.09743

Coefficient Slope1: -0.02273

Independent Variable: Year

Independent Variable: 30-34 death rates

Observation Period: 2003-2012

Adjusted R square: 0.90419

Standard Deviation: 0.03253

Coefficient Intercept: 69.25600

Coefficient Slope1: -0.03320

Independent Variable: Year

Independent Variable: 35-39 death rates
213

Observation Period: 2003-2012

Adjusted R square: 0.93024

Standard Deviation: 0.02504

Coefficient Intercept: 63.72011

Coefficient Slope1: -0.03033

Independent Variable: Year

Independent Variable: 40-44 death rates

Observation Period: 2003-2012

Adjusted R square: 0.91428

Standard Deviation: 0.02776

Coefficient Intercept: 63.48219

Coefficient Slope1: -0.03010

Independent Variable: Year

Independent Variable: 45-49 death rates

Observation Period: 2003-2012

Adjusted R square: 0.96874

Standard Deviation: 0.01307

Coefficient Intercept: 51.61456

Coefficient Slope1: -0.02407

Independent Variable: Year

Independent Variable: 50-54 death rates

Observation Period: 2003-2012

Adjusted R square: 0.88262

Standard Deviation: 0.01954

Coefficient Intercept: 39.30540

Coefficient Slope1: -0.01783

Independent Variable: Year

Independent Variable: 55-59 death rates

Observation Period: 2003-2012

Adjusted R square: 0.90770

Standard Deviation: 0.00813

Coefficient Intercept: 20.63736

Coefficient Slope1: -0.00847

Independent Variable: Year

Independent Variable: 60-64 death rates

Observation Period: 2003-2012
214

Adjusted R square: 0.90652

Standard Deviation: 0.01719

Coefficient Intercept: 39.46082

Coefficient Slope1: -0.01778

Female

Independent Variable: Year

Independent Variable: 15-19 death rates

Observation Period: 2003-2012

Adjusted R square: 0.02302

Standard Deviation: 0.45564

Coefficient Intercept: 113.39950

Coefficient Slope1: -0.05523

Independent Variable: Year

Independent Variable: 20-24 death rates

Observation Period: 2003-2012

Adjusted R square: 0.25264

Standard Deviation: 0.07085

Coefficient Intercept: 33.92129

Coefficient Slope1: -0.01568

Independent Variable: Year

Independent Variable: 25-29 death rates

Observation Period: 2003-2012

Adjusted R square: 0.26289

Standard Deviation: 0.08044

Coefficient Intercept: 38.78742

Coefficient Slope1: -0.01817

Independent Variable: Year

Independent Variable: 30-34 death rates

Observation Period: 2003-2012

Adjusted R square: 0.56142

Standard Deviation: 0.05465

Coefficient Intercept: 45.16787

Coefficient Slope1: -0.02129

Independent Variable: Year

Independent Variable: 35-39 death rates

Observation Period: 2003-2012
215

Adjusted R square: 0.81668

Standard Deviation: 0.02105

Coefficient Intercept: 32.41930

Coefficient Slope1: -0.01486

Independent Variable: Year

Independent Variable: 40-44 death rates

Observation Period: 2003-2012

Adjusted R square: 0.82989

Standard Deviation: 0.02670

Coefficient Intercept: 42.33441

Coefficient Slope1: -0.01970

Independent Variable: Year

Independent Variable: 45-49 death rates

Observation Period: 2003-2012

Adjusted R square: 0.89897

Standard Deviation: 0.01848

Coefficient Intercept: 39.76632

Coefficient Slope1: -0.01832

Independent Variable: Year

Independent Variable: 50-54 death rates

Observation Period: 2003-2012

Adjusted R square: 0.89701

Standard Deviation: 0.01609

Coefficient Intercept: 34.85991

Coefficient Slope1: -0.01579

Independent Variable: Year

Independent Variable: 55-59 death rates

Observation Period: 2003-2012

Adjusted R square: 0.92870

Standard Deviation: 0.01616

Coefficient Intercept: 42.12561

Coefficient Slope1: -0.01935

Independent Variable: Year

Independent Variable: 60-64 death rates

Observation Period: 2003-2012

Adjusted R square: 0.93481
216

Standard Deviation: 0.01593

Coefficient Intercept: 43.56734

Coefficient Slope1: -0.01999
217

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, 18-19 for student, age groups 18-

19, 20-24, ..., 55-59, 60+ for disabled adult) and sex of the account holder

Dependent beneficiaries of deceased workers include:

• aged spouses of deceased workers, ASDWN, by age (60-95+), sex of the account holder, 

marital status (widowed, divorced) and insured status (insured, uninsured)

• disabled spouses of deceased workers (DSDWN) by age (50-69), sex of the account holder 

and marital status (widowed, divorced)

• young spouses of deceased workers (YSDWN) by age-group (under 25, 25-29,..., 65-69), sex 

of the account holder and marital status of the beneficiary (widowed, divorced)

• minor, student, and disabled adult children of deceased workers (MCDWN, SCDWN, and 

DCDWN, respectively) by age of the child (0-17 for minor, 18-19 for student, age groups 18-

19, 20-24,..., 55-59, 60+ for disabled adult) and sex of the account holder

Lastly, we estimate the number of deaths of insured workers (LUMSUM) by 5-year age group 

(20-24, 25-29,..., 80-84, 85+) and sex.

Equations 3.3.1-13 indicates the flow of calculations of beneficiaries.

ASDWN = ASDWN(⋅) (3.3.1)

RWN = RWN(⋅) (3.3.2)
218

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

• Social Security area population by year (EOY 1970-2090), single year of age (0-100+), 

sex, and marital status (single, married, widowed, divorced)

• Deaths by year (during years 2012-2090), age group (20-24,...,80-84, 85+) and sex

• Average number of children per family by year (EOY 1970-2090), and age group of the 

householder (20-24,...,60-64)

• Children by year (EOY 1970-2090), 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)

• Married couples by year (EOY 1970-2090), age of husband (62-95+) and age of wife 

(62-95+)

• Persons with an aged spouse by year (EOY 1970-2090), age group (15-24, 25-29,...,65-

69) and sex

• Probabilities of death by year (EOY 1941-2100), single year of age (-1,100), and sex

Economics

• Covered wages and employment in the Federal Civilian and State and Local Sectors 

(during years 1998-2090)
219

• Labor force participation rates for age 62 by year (during years 1970-2090) and sex

Beneficiaries

• Fully insured persons by year (EOY 1969-2090), age (14-95+), sex, and marital status 

(single, married, widowed, divorced)

• Disabled-worker beneficiaries in current pay by year (EOY 1970-2090), age (62-66) 

and sex

• Converted DI to OAI beneficiaries by year (EOY 1970-2090), age(65-95+) and sex

• Disability prevalence rates by year (EOY 1970-2090), age (50-66) and sex

Short-Range OCACT Data

• Insured aged spouses of deceased workers by year (EOY 1974-2012), age (60-95+) 

and sex

• Retired worker beneficiaries in-current-pay status by age (62-70, 70+) and sex for 

EOY 2011-2022

• We receive the following for EOY 2012:

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 (50-65), sex and marital status (widowed, divorced)

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased)

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased)

g. Disabled adult children by age (20-60+), sex of parent and status of parent (retired, 

deceased)

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64, 65-69) and 

sex

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced)

j. Total parent beneficiaries

Note: Each year, we append data for the most recent historical year.

• We receive the following for EOY 2022:

a. Retired workers by age group (62-64, 65-69) and sex

b. Insured widows by age group (60-64,...,80-84,85+)

c. Uninsured widows by age group (60-64, 65+)

d. Total disabled widows

e. Female young spouses of deceased workers

f. Female aged spouses of retired workers by age group (62-64, 65+)

g. Female young spouses of retired workers
220

h. Minor children by status of parent

i. Student children by status of parent

j. Disabled adult children by status of parent

• Total amount of lump-sum death payments during 2011

Other Input Data

• For EOY 1970-2004, obtained from the MBR10PER dataset on the mainframe:

a. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced)

b. Retired workers by age (62-95+) and sex

c. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced)

d. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced)

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased)

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased)

g. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased)

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced)

j. Total parent beneficiaries

Note: We will not update this data.

• Number of beneficiaries with benefits withheld due to receipt of a significant 

government pension by sex and marital status (married, widowed) for EOY 2011 from 

the 2012 Annual Statistical Supplement

• Age distribution of beneficiaries with benefits withheld due to receipt of a significant 

government pension by age (60-95+) and sex, computed as an average from the 2007 

through 2011 WEP 100-percent sample

• 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.

• 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 1970-2090 from the Social Security website (Note: these values are only 
221

updated when there is a Social Security law change regarding the NRA)

• Prevalence rate regression coefficients (slopes and y-intercept value by sex)

• Regressed prevalence rate by sex for the most recent historical year

• Adjustment factors which account for the difference between estimated and actual 

historical retired worker prevalence rates by year (EOY 1970-2090), age (63-69) and sex

• Adjustment factors which account for the difference between projected beneficiary 

values for the tenth year of the projection period made by the Long-Range and ShortRange offices. Factors are computed for:

a. Retired workers by age group (62-64, 65-69) and sex

b. Insured widows by age group (60-64,...,80-84,85+)

c. Uninsured widows by age group (60-64, 65+)

d. Total disabled widows

e. Female young spouses of deceased workers

f. Female aged spouses of retired workers by age group (62-64, 65+)

g. Female young spouses of retired workers

h. Minor children by status of parent

i. Student children by status of parent

j. Disabled adult children by status of parent

3.3.c. Development of Output

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, 

FIA pRW 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

pASDWDEA = probability that the 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 fully insured
222

pASDWGPB =probability that the aged-widow(er)’s 

benefits are

not withheld or offset totally because of receipt of a 

significant government pension based on earnings in 

noncovered employment

pASDWRES=probability that a widow(er) eligible to receive 

his/her own retired-worker benefits would instead apply for 

and receive widow(er) benefits

We project the number of aged spouses of deceased workers (widow(er)s), along with all 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 (in=1) and uninsured (in=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:

POP DEA FIA MBB

FIB GPB RES

ASDWN ASDW pASDW pASDW pASDW

pASDW pASDW pASDW

=× × ×

×× × (3.3.1)

We calculate the projected number of insured aged spouses of deceased workers over age 70 by 

applying termination rates to the population already receiving such benefits:

ASDWPOP represents the subset of the population from which we draw these beneficiaries. We 

set this equal to the Social Security area population (SSAPOPmb) for each possible marital status.

ASDWPOP = SSAPOPmb

pASDWDEA represents the probability that the primary account holder (PAH) is deceased. For 

the widowed population, we set this factor equal to one. For the divorced population, we set this 

factor equal to the portion of the total widowed (SSAPOPwid) and married (SSAPOPmar) 

population who are widowed.

 1, mb = 1 (widowed)

 , wid

mar wid

SSAPOP

SSAPOP SSAPOP + mb = 2 (divorced)

pASDWFIA represents the probability that the PAH was fully insured at death. For a given age 

of widow, AW, 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 pASDWFIA as a weighted average of the 

portion of the Social Security area population who are fully insured at each possible age of the 

husband (FINSAH). For example, for a widow age 70, we assume that the age of her husband is 

pASDWDEA =
223

between 64 and 82, therefore we calculate the weighted average of the portion of the population 

who are fully insured males, 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. 

WEIGHTAH =10 − AW + 3− AH

WEIGHTAW =10 − AH − 3− AW

 

12

6

12

6

AW

AH AH

AH AW

AW

AH

AH AW

WEIGHT FINS

WEIGHT

+

= −

+

= −

∑ ×

∑

, sa = 1

 pASDWFIA =

 

6

12

6

12

AH

AW AW

AW AH

AH

AW

AW AH

WEIGHT FINS

WEIGHT

+

= −

+

= −

∑ ×

∑

, sa = 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 

( ab YSDWN ), where ab represents the 5-year age bracket36. We assume a uniform breakdown to 

divide the age groups into single-age estimates.

 1, 65 ≤ age < NRA and in = 2

 0, elsewhere

 36 There are no young spouses at NRA or above.

FACTORage =
224

 60 64 0.2 1 ,

POP DEA FIA

YSDWN

ASDW pASDW pASDW

− × − × × 

 65 69

69

65

1 , age

POP DEA FIA age

YSDWN FACTOR

ASDW pASDW pASDW FACTOR

−

− ∗ × × ∑

 

 1, 

pASDWFIB represents the probability that the aged widow(er) is fully insured. For insured 

widow(er)s, pASDWFIB is the portion of the Social Security area population that is fully insured 

(FINS) at each age, sex, and marital status. For uninsured widow(er)s, pASDWFIB is simply one 

minus the probability for insured widow(er)s.

 ,

mb

FINS

SSAPOP in = 1

 pASDWFIB =

 1 ,

mb

FINS

SSAPOP − in = 2

pASDWGPB represents the probability that the aged-widow(er)'s benefits are not withheld or not 

offset totally because of receipt of a significant government pension based on earnings in 

noncovered employment. According to the 1977 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. 

 1 

 1 ,

POP DEA FIA MBB FIB

rGPOAGE GPWHLD

ASDW pASDW pASDW pASDW pASDW

× − × ×× × in = 2

pASDWRES represents the probability that a widow(er), who is eligible to receive widow(er)’s 

benefits, will actually receive benefits. In particular, for in = 1, this factor is equivalent to the 

probability that a widow(er) eligible to receive his/her own retired-worker benefits would instead 

apply for and receive widow(er) benefits. For all historical years, we calculate year pASDWRES 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.

pASDWMBB = 65≤ age <NRA 

and in = 2

pASDWGPB =

age = 60-64 

and in = 2

age = 60-69 

and in = 1

in = 1 OR 

year ≤ 1978
225

, year

RES

POP DEA FIA MBB FIB GPB

ASDWN pASDW ASDW pASDW pASDW pASDW pASDW pASDW = × ×× ××

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 year pASDWRES from 

which we project future values. In addition, for each sex, insured status, and marital status, we 

graduate the regressed values of TRYR−1 pASDWRES over age using a weighted minimized thirddifference formula to produce ASDW ESTRES . ASDW ESTRES are the preliminary estimates of 

TRYR+9 pASDWRES , the values in the tenth year of the projection period. In addition, we apply 

adjustments by age group (60-64, 65-69, 70-74, 75-79, 80-84, 85+ for insured; 60-64, 65+ for 

uninsured), ASDW SRADJ , to the tenth year of the projection period in order to match the 

projections made by the Short-Range office. We linearly interpolate the values of year pASDWRES for 

intermediate years between TRYR−1 pASDWRES and N,TRYR+9 pRWRES (equal 

to ) ASDW ASDW ESTRES SRADJ ∗ . 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. 

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 to 4). We calculate the projected number of retired-worker 

beneficiaries as follows:

RWN RW pRW pRW pRW pRW =× × × × POP FIA DBB WBB RES (3.3.2)

RWPOP represents the subset of the population from which we draw these beneficiaries. We set 

year < TRYR,
226

this equal to the Social Security area population (SSAPOPms) for ms = 1 to 4.

POP ms RW = SSAPOP

pRWFIA represents the probability that the primary account holder (PAH) is insured. We set this 

factor equal to the portion of the Social Security area population that is fully insured (FINS) for 

ms=1 to 4.

POP

FIA RW

FINS pRW =

pRWDBB represents the probability that the PAH is not receiving a disabled-worker or disabilityconversion 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.

 

 1 ,

POP FIA

DIBCON

RW pRW − × ms = 1-2

 1 ,

DIBCON

DIBCON ASDWN

POP FIA

DIBCON ASDWN

RW pRW

      +   +   −

  × ms = 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. 

 1, ms = 1-2

 1 ,

ASDWN

DIBCON ASDWN

POP FIA

DIBCON ASDWN

RW pRW

      +   +   −

  × ms =3-4

pRWRESN,year represents the retirement prevalence rate, which is the probability that a fully 

insured worker not receiving disability or widow(er)’s benefits would receive retired-worker 

benefits as of the given age, N, for the given year. In order to estimate the future prevalence rate, 

the program first calculates the historical values of N year

RES pRW , .

For each historical year and sex, we calculate N year pRWRES

, 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.

pRWDBB =

pRWWBB =
227

N year ,

RES

POP FIA DBB WBB

RWN pRW RW pRW pRW pRW = ×× × , N = 62-95+ and year < TRYR 

Historical prevalence rates at age 62 follow an inverse relationship with (1) labor force 

participation rates (LFPRyear) 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 REGPRyear, the regressed prevalence rate based on the projected 

LFPRyear at age 62 for each year and sex, and the number of months from age 62 to the normal 

retirement age (monthNRAyear). Note that we calculate prevalence rates on a cohort basis37. The 

regression equation used to estimate the prevalence rates is:

REGPR year = -1.01306 × LFPR year + -0.00246 × monthNRAyear +1.03602 for male with an R2

value of 0.91956,

and

REGPR year = -0.39868 × LFPR year + -0.00675 × monthNRAyear + 0.88741 for female with an R2

value of 0.94722

We then set the future prevalence rate at age 62, year pRWRES

62, , equal to the sum of the regressed 

prevalence rate (REGPRyear) and ERROR, the difference between the actual prevalence rate and 

the regressed prevalence rate in the most recent historical year, which we phase out linearly. 

62, 9 ( ) max 0, 10

year year

RES

TRYR year pRW REGPR ERROR   + −

= +×    

To compute N year pRWRES

, for ages 63 to 69 in the projection period, we must calculate several 

preliminary variables. These include:

 MBAPIAN, for N = 62,70 (same for both sexes),

 year ESTPRN , for N = 63,69 and by sex,

 DIFFADJN, for N = 63,69 and by sex, 

 year ESTPR2N for N = 63,69 and by sex, and

MBAPIAN is the ratio of the monthly benefit amount (MBA) to the primary insurance amount 

(PIA) at age N and is calculated on a cohort basis for N = 62,70. We base the calculation of 

MBAPIAN 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.

 37 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.

, N = 62 and year ≥ TRYR-1 
228

 1( ) , +− × N NRA DRC N ≥ NRA

 1 ( ) 3, − −× NRA N ARFLE NRA-3 ≤ N < NRA

 1 3 3 ( 3 ) 3, −× − −− × ARFLE NRA N ARFGT N < NRA-3

year ESTPRN , the estimated prevalence rate at age N, is then calculated as the prevalence rate at 

age 62 ( 62, year−(N−62) pRWRES ) plus an estimate on the expected portion of the remaining probability 

( 62, ( 62) 1 − − − year N pRWRES ), that a potential retired worker will actually retire by that given age. We 

base this estimate on MBAPIAN, assuming that the retirement decision by a worker is totally and 

completely influenced by the expected change in the portion of PIA that is payable at each age 

relative to the potential change after the initial eligibility.

62, ( 62) 62, ( 62) 62

70 62

(1 ) , year year N year N N

N RES RES

MBAPIA MBAPIA ESTPR pRW pRW MBAPIA MBAPIA

− − − − − = + − × −

In the first year of the projection period, an adjustment (DIFFADJN) is made which accounts for 

the difference between the actual and estimated prevalence rate at each age in the most recent 

historical years. For ages 63 to 69, the value used beginning in TRYR is the average of the last 5 

years’ differences between the actual and estimated PR. With the exception of age 66, we hold 

this value constant throughout the projection period. 

For years in which the NRA increases, DIFFADJN is greater for a period of time both before and 

after the NRA transitions to a new age. This affects DIFFADJ66 due to the increase in NRA from 

age 65 to age 66 between the years 2000-2005, and the scheduled increase from age 66 to 67 

over the years 2017-2022. Thus for the years preceding the change in NRA from age 66 to 67, 

we use the average from the last five historical years, which includes the increase in the 

difference between actual and estimated prevalence rates from when the NRA changed from age 

65 to 66, in order to calculate DIFFADJ66 . After the NRA increases to age 67 in 2026, we use 

DIFFADJ266 which is the average difference between actual and estimated prevalence rates 

from the years 1995-1999 since at that time it is expected to decrease to the level it was prior to 

the increase in NRA to age 66 in the year 2000. In the years during which the NRA transitions 

to age 67 (2021-2026) we use a linear interpolation based on the number of months that the 

NRA has increased in order to phase out DIFFADJ66 and phase in DIFFADJ266. It will remain 

at DIFFADJ266 for the rest of the projection period. 

ESTPR2N = ESTPRN + DIFFADJ N

For age 70, we assume that the values of the latest actual N year pRWRES

, by sex change linearly to 

the ultimate level of 0.995 for male and 0.99 for female over the first 20 years of the projection 

period.

MBAPIAN =

N = 63-69
229

 70, 1 19 0.995 0.995 max 0, , 20

TRYR

RES

TRYR year pRW −   + −

−− ×        

= year pRWRES

70,

 70, 1 19 0.99 0.99 max 0, , 20

TRYR

RES

TRYR year pRW −   + −

−− ×        

For ages 71 and older, we assume N year pRWRES

, stays constant at the level when the age was 70 

because there is no incentive to delay applying for benefits beyond age 70.

, 70, −( −70) = year N

RES

N year pRWRES pRW , for N = 71-95+ and year ≥ TRYR

In addition, we apply adjustments by age group (62-64, 65-69) and sex, RW SRADJ , to the tenth 

year of the projection period in order to match the projections made by the Short-Range office. 

We also apply these adjustments to N year pRWRES

, for all years after TRYR+9. The values 

of N year pRWRES

, for intermediate years are linearly interpolated between N,TRYR−1 pRWRES and 

N,TRYR+9 pRWRES .

For each age, retired workers are further broken down by age at entitlement, AE, by multiplying 

the number of retired workers at age N by the ratio of the incidence rate at AE ( N AE − years 

prior) to the prevalence rate at age N.

( )

,

year N AE

N year N year AE

AE N year

RES

INCRATE RWN RWN

pRW

− −

= × , 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.

 , , N year

RES pRW for N = AE = 62

= year

AE INCRATE , 1, 1, N year N year

RES RES pRW pRW − − − for 63 ≤ N = AE ≤69

 1, 1 1 , N year

RES pRW − − − for N = AE=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 

 sa = 1 and 

 year ≥ TRYR

sa = 2 and 

year ≥ TRYR
230

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 youngspouse 

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 noncovered employment

pASRWRES = probability that a person who is eligible to receive aged-spouse 

benefits actually receives the benefits

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:

POP DEA AGA FIA CPA

MBB FIB GPB RES

ASRWN ASRW pASRW pASRW pASRW pASRW

pASRW pASRW pASRW pASRW

=× × × × ×

×× × (3.3.3) 

ASRWPOP represents the subset of the population from which these beneficiaries are drawn, and 

we set it equal to the Social Security area population (SSAPOPmb) for mb = 1,2.

ASRWPOP = SSAPOPmb

pASRWDEA represents the probability that the PAH is not deceased. For the married population, 

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.

 1, mb = 1 (married)

 , mar

mar wid

SSAPOP

SSAPOP SSAPOP + mb = 2 (divorced)

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 (MAR62PLUS).

pASRWAGA = 

SSAPOPmar

MAR62PLUS

 

pASRWDEA =
231

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.

[ 62 _ ]

62 FIA

MAR PLUS FI PAH

pASRW MAR PLUS

× = ∑

∑

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.

 

 1, year ≥ 1985 and mb = 2

 [ ]

[ ]

62 _

62 _

MAR PLUS FI PAH RETIRED

MAR PLUS FI PAH

× ×

×

∑

∑ , elsewhere

pASRWMBB represents the probability that the beneficiary is not receiving a young-spouse 

benefit. If the beneficiary is age 70 or older or if the beneficiary is divorced, we do not apply a 

factor. Otherwise, we set this factor equal to the portion of potentially eligible widow(er)s where 

the spouse of the PAH is not receiving a young-spouse benefit ( ab YSRWN ), where ab represents 

the 5-year age group.38

 1, 65 ≤ age < NRA

 0, elsewhere

 38 There are no young spouses at NRA or above.

pASRWCPA =

FACTORage =
232

 60 64 0.2 1 ,

POP DEA AGA FIA CPA

YSRWN

ASRW pASRW pASRW pASRW pASRW

− × − × × ×× 

 

65 69

69

65

1

,

POP DEA AGA FIA CPA

ag

ag

YSRWN

ASRW ASRW pASRW pASRW pASRW

FACTOR

FACTOR

−

− ×× × ×

×

∑

 1, elsewhere 

pASRWFIB represents the probability that the aged spouse is not fully insured, and is therefore 

not receiving a retired-worker benefit based on his/her own earnings. We set this factor equal to 

the portion of the married and divorced population that is not fully insured. For example, when 

the program estimates the number of female aged spouse of retired workers, this factor will find 

the portion of female beneficiaries that is fully insured. 

1 , FIB

FINS pASRW SSAPOP = − mb = 1-2

pASRWGPB represents the probability that the aged-spouse's benefits are not withheld because of 

receipt of a significant government pension based on earnings in noncovered employment. 

GPWHLD represents the total number of aged spouse of retired-worker beneficiaries (for all 

ages) expected to receive a significant government pension. rGPOAGE represents the ratio of 

the total for each given age. 

 1, year ≤ 1978

 1 ,

POP DEA AGA FIA CPA FIB

rGPOAGE GPWHLD

ASRW pASRW pASRW pASRW pASRW pASRW

× − ∗ × ×× × elsewhere

pASRWRES represents the probability that a person who is eligible to receive aged-spouse 

benefits actually receive the benefits. For all historical years, we calculate year

RES pASRW as the 

ratio of ASRWN, the actual number of aged spouses receiving benefits, to the number of persons 

meeting all previously mentioned requirements by age, sex, and marital status.

, year

RES

POP DEA AGA FIA CPA FIB

ASRWN pASRW ASRW pASRW pASRW pASRW pASRW pASRW = ∗ × ×× ×

pASRWMBB =

age = 62-64 

 and mb = 1

 65 ≤ age < NRA 

 and mb = 1

pASRWGPB =

year < TRYR
233

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 TR-1 for year pASRWRES from which we project 

future values. In addition, for each sex and marital status, we graduate the regressed values of 

TRYR−1 pASRWRES over age using a weighted minimized third-difference formula to compute 

ASRW ESTRES . ASRW ESTRES are the preliminary estimates of TRYR+9 pASRWRES , the values in the 

tenth year of the projection period. For female spouses, we apply additional adjustments by age 

group (62-64, 65+), ASRW SRADJ , to the tenth year of the projection period in order to match the 

projections made by the Short-Range office. We linearly interpolate the values of year pASRWRES

for intermediate years interpolated between TRYR−1 pASRWRES and TRYR+9 pASRWRES (equal 

to ASRW ASRW ESTRES SRADJ × ). 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.

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 

disabledspouse benefits actually receive 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:

 POP DEA FIA

SSB DEB RES

DSDWN DSDW pDSDW pDSDW

pDSDW pDSDW pDSDW

=× × ×

× × (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 (SSAPOPmb) for mb = 1,2.

DSDWPOP = SSAPOPmb
234

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.

 1, mb = 1 (widowed)

 , wid

wid mar

SSAPOP

SSAPOP SSAPOP + mb = 2 (divorced)

pDSDWFIA represents the probability that the PAH was fully insured at death. Given the age of 

the widow, AW, 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 pDSDWFIA as a weighted average of the 

portion of the Social Security area population that is fully insured (FINS), at each possible age of 

the husband. For example, if the widow is age 65, 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 males, 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. 

WEIGHTAH =10 − AW + 3− AH

WEIGHTAW =10 − AH − 3− AW

 

12

6

12

6

,

AW

AH AH

AH AW

AW

AH AW

WEIGHT FINS

WEIGHT

+

= −

+

= −

∑ ×

∑

sa = 1

 pDSDWFIA =

 

6

12

6

12

,

AH

AW AW

AW AH

AH

AW AH

WEIGHT FINS

WEIGHT

+

= −

+

= −

∑ ×

∑

 sa = 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.

pDSDWSSB = DISPREV

pDSDWDEA =
235

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.

 0.85, sa = 1

 pDSDWDEB =

 0.06, sa = 2

pDSDWRES represents the probability that a person who is eligible to receive disabled-spouse 

benefits actually receive the benefits. For all historical years, we calculate year pDSDWRES 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.

, year

RES

POP DEA FIA DEB

DSDWN pDSDW DSDW pDSDW pDSDW pDSDW = × ×× year < TRYR

For ages 50 to 64, and each sex, and marital status, we use the average over the last 

five years of historical data to determine starting values for from which we project 

future values. We phase in these averages over five years using a linear interpolation between 

the five-year averages and . For female disabled spouses, we apply an 

adjustment, , to the tenth year of the projection period in order to match the 

projections made by the Short-Range office. We exponentially interpolate the values of 

for intermediate years between and (equal to 

). 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 NRA, year

RES pDSDW is equal to 

year pDSDWRES at age 64 times an adjustment that accounts for the additional ages as NRA 

changes.

 1, NRA ≥ age + 1

 NRA – age, age < NRA < age + 1

 

( 64) ,64

,64

,63 ,

age year

year year RES

RES RES year age

RES

pDSDW pDSDW pDSDW FACTOR

pDSDW

−

 

=× ×    

FACTORage =

 age = 65-69 and 

 age < NRA
236

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 to 17) and sex of the account holder (sa = 1 for male, sa = 2 for female). 

For children of male retired workers:

 (3.3.5.1)

For the number of minor children of male retired workers, we multiply the number of children 

under the age of 18 with a father who is at least 62 years old and who’s other parent is not 

deceased ( ) by the total number of male retired workers ages 62 to 71 

( ) divided by the total number of males in the population ages 62 to 71 

( ).

represents the probability that a child who is eligible to receive minor-child benefits 

actually receives them. 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.

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 . We apply an 

adjustment, MCRW SRADJ , to the tenth 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 tenth 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:

(3.3.5.2)

mcrwPrcntFem represents the average over the last five historical years 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.

We maintain the total at this percentage over the entire projection period by 
237

multiplying our estimate of by mcrwPrcntFem divided by its complement. 

In order to distribute among the ages 0 to 17, we multiply by the 

proportion of beneficiaries at each age in the last historical year. 

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 either retired or deceased

pMCDWFIA = probability that the primary account holder (PAH) is fully 

insured

pMCDWRES = probability that a child who is eligible to receive minorchild benefits actually receive the benefits

We project the number of minor children of deceased workers, along with all linkage factors, by 

age of the minor (am = 0 to 17) and sex of the account holder (sa = 1 for male, sa = 2 for 

female). We calculate it as follows:

MCDWN MCDW pMCDW pMCDW pMCDW =× × × POP DEA FIA RES (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).

MCDWPOP = SSAPOP

pMCDWDEA represents the status of the parent (PAH). This is set equal to the portion of the 

minor population where at least one parent is deceased. CHI_DEA represents the number of 

children having at least one deceased parent. 

POP

DEA MCDW

CHI DEA pMCDW _ =

pMCDWFIA represents the probability that the parent (PAH) is fully insured. We set this equal 

to the portion of the population aged 25 + am to 35 + am where the PAH is fully insured 

(FI_PAH).
238

[ ]

35

25

35

25

_

am

am

FIA am

am

SSAPOP FI PAH

pMCDW

SSAPOP

+

+

+

+

×

=

∑

∑

pMCDWRES represents the probability that a child who is eligible to receive minor-child benefits 

actually receive the benefits. For all historical years, we calculate year pMCDWRES as the ratio of 

MCDWN, the actual number of minor children of deceased workers receiving benefits, to the 

number of number of persons meeting all previously mentioned requirements by age and sex of 

the parent.

, year

RES

POP DEA FIA

MCDWN pMCDW MCDW pMCDW pMCDW = × × year < TRYR

For each age and sex of parent, we use a least squares regression over the last ten years of 

historical data to determine a starting value in TR-1 for year pMCDWRES from which we project 

future values. We apply an adjustment, MCDW SRADJ , to the tenth year of the projection period 

in order to match the projections made by the Short-Range office. We linearly interpolate the 

values of year pMCDWRES for intermediate years between the regressed values for TRYR−1 pMCDWRES

and TRYR 9 MCDW

RES pMCDW SRADJ + × . 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.

Equation 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 studentchild 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)
239

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 studentchild 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 to 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:

POP DEA AGA FIA

CPA SSB RES

SCRWN SCRW pSCRW pSCRW pSCRW

pSCRW pSCRW pSCRW

=× × × ×

× × (3.3.7)

POP DEA AGA FIA

CPA SSB RES

SCDWN SCDW pSCDW pSCDW pSCDW

pSCDW pSCDW pSCDW

=× × × ×

× × (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).

SCRWPOP = SCDWPOP = SSAPOP

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. 

POP

DEA SCRW

CHI DEA pSCRW _ = 1−

POP

DEA SCRW

CHI DEA pSCDW _ =

pSCRWAGA and pSCDWAGA represent the probability that the PAH is age 62 or older. For 

student children of retired workers, 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.

POP

AGA SCRW

CHI pSCRW + = _ 62

 

= 1 AGA pSCDW
240

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.

[ ]

64

62

64

62

_

as

FIA as

SSAPOP FI PAH

pSCRW

SSAPOP

+

+

×

=

∑

∑

[ ]

35

25

35

25

_

as

as

FIA as

as

SSAPOP FI PAH

pSCDW

SSAPOP

+

+

+

+

×

=

∑

∑

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 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.

[ ]

[ ]

64

62

64

62

_

_

as

CPA as

SSAPOP FI PAH RETIRED

pSCRW

SSAPOP FI PAH

+

+

× ×

=

×

∑

∑

pSCDWCPA = 1

pSCRWSSB and pSCDWSSB represent the probability that the child is indeed attending school 

(full-time elementary or secondary school). This factor is dependent upon the age of the child, 

and we calculate it as follows.

 1 , as −16 year ≤ 1981

 0.5 , as −16 year > 1981

pSCRWRES and pSCDWRES represent the probability that a child who is eligible to receive 

student-child benefits actually receive the benefits. For all historical years, we calculate 

year pSCRWRES and year pSCDWRES as the ratio of SCRWN and SCDWN, the actual number of student 

children receiving benefits, to the number of number of persons meeting all previously 

mentioned requirements by age and sex of the parent.

pSCRWSSB =pSCDWSSB =
241

, year

RES

POP DEA AGA FIA CPA SSB

SCRWN pSCRW SCRW pSCRW pSCRW pSCRW pSCRW pSCRW = × × ×× ×

year

RES

POP DEA AGA FIA CPA SSB

SCDWN pSCDW SCDW pSCDW pSCDW pSCDW pSCDW pSCDW = × × ×× ×

For each age and sex of parent, we use a least squares regression over the last ten years of 

historical data to determine a starting value in TR-1 for year pSCRWRES from which we project 

future values. We apply an adjustment, SCRW SRADJ , to the tenth year of the projection period 

in order to match the projections made by the Short-Range office. We linearly interpolate the 

values of year pSCRWRES for intermediate years between the regressed values for TRYR−1 pSCRWRES and 

TRYR 9 SCRW

RES pSCRW SRADJ + × . 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 year pSCDWRES similarly.

Equation 3.3.9-10 – Disabled Adult Children of Retired and Deceased Workers (DCRWN and 

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 

disabledchild benefits actually receive 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 disabledchild benefits actually receive the benefits

We project the number of disabled adult children of retired and deceased workers, along with all 

year < TRYR

year < TRYR
242

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:

 POP AGA DEA FIA

CPA SSB RES

DCRWN DCRW pDCRW pDCRW pDCRW

pDCRW pDCRW pDCRW

=× × ×

××× (3.3.9)

 POP AGA DEA FIA

CPA SSB RES

DCDWN DCDW pDCDW pDCDW pDCDW

pDCDW pDCDW pDCDW

=× × ×

× ×× (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 pDCDWDEA similarly for disabled children of deceased workers.

mar wid

mar

SSAPOP SSAPOP

SSAPOP

+ , ad = 1-9

 pDCRWDEA =

0.25 mar

mar wid

SSAPOP

SSAPOP SSAPOP

×

+ , ad = 10

 , wid

mar wid

SSAPOP

SSAPOP SSAPOP + ad = 1-9

 pDCDWDEA =

0.25 0.75, wid

mar wid

SSAPOP

SSAPOP SSAPOP

×

+

+

ad = 10

pDCRWSSB and pDCDWSSB represent the probability that the adult child is indeed disabled. 

DCPREM is the preliminary calculation of this factor and we assume it to remain constant. For 

the projection period, for ad=6-10, we set pDCRWSSB and pDCDWSSB 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

DCPREM =
243

0.004, ad = 7-10

 min 0.005,   DCPREM year TRYR + ×− 0.0001 ( ) ,  

 DCPREM, elsewhere 

pDCRWRES and pDCDWRES represent the probability that a child who is eligible to receive 

disabled-child benefits actually receive the benefits. For all historical years, we calculate 

year pDCRWRES and year pDCDWRES as the ratio of DCRWN and DCDWN, the actual number of 

disabled children receiving benefits, to the number of number of persons meeting all previously 

mentioned requirements by age and sex of the parent.

, year

RES

POP DEA AGA FIA CPA SSB

DCRWN pDCRW DCRW pDCRW pDCRW pDCRW pDCRW pDCRW = ∗ × ×× ×

, year

RES

POP DEA AGA FIA CPA SSB

DCDWN pDCDW DCDW pDCDW pDCDW pDCDW pDCDW pDCDW = ∗ × ×× ×

We apply an adjustment, DCRW SRADJ , to the tenth year of the projection period in order to match 

the projections made by the Short-Range office. We linearly interpolate the values of 

year pDCRWRES for intermediate years between TRYR−1 pDCRWRES and TRYR 9 DCRW

RES pDCRW SRADJ + × . 

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 year pDCDWRES similarly.

Equation 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 youngspouse benefits actually receive the benefits

Young Spouses of Deceased Workers

pDCRWSSB

=pDCDWSBB=

 ad = 7-10 and 

 year > TRYR+1

,year < TRYR

year < TRYR
244

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 youngspouse benefits actually receive 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:

YSRWN YSRW pYSRW pYSRW pYSRW pYSRW =× × × × POP AGA ECB FSB RES (3.3.11)

YSDWN YSDW pYSDW pYSDW pYSDW pYSDW pYSDW =× × × × × POP DEA ECB FSB RMB RES (3.3.12)

YSRWPOP and YSDWPOP represent the subset of the population from which we draw these 

beneficiaries. We set YSRWPOP equal to the married Social Security area population 

(SSAPOPmar) and we set YSDWPOP equal to SSAPOPmb for mb = 1-2.

YSRWPOP = SSAPOPmar

YSDWPOP = SSAPOPmb

pYSDWDEA represent 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.

 1, mb = 1 (widowed)

 , wid

wid mar

SSAPOP

SSAPOP SSAPOP + mb = 2 (divorced)

pYSRWAGA and represent the probability that the PAH is of the required age. We set pYSRWAGA

equal to the portion of the married population who has an aged spouse (AGSP). 

pYSDWDEA =
245

POP

AGA YSRW

AGSP pYSRW =

pYSRWECB and pYSDWECB represent the probability that the young spouse has an entitled child 

in their care. We set pYSRWECB equal to the portion of persons meeting the previously mentioned 

requirements who have a minor or disabled adult child in their care. We set pYSDWECB ,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. ab MCRWN and ab DCRWN represent the 

total number of minor and disabled adult children of retired workers where the other parent 

(young spouse) is in the age bracket ab.

ab ab

ab

ECB

POT AGA

MCRWN DCRWN pYSRW YSRW pYSRW+ = ×

( )

mb mb mb

ab ab POP DEA AGA

total total total

mb POP DEA AGA

ECB

POP DEA

YSDW pYSDW pYSDW MCDWN DCDWN

YSDW pYSDW pYSDW pYSDW YSDW pYSDW

  × ×

+ ×     × × = ×

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 (ASOFab) for the given age bracket of the spouse. 

For young spouses of retired workers, we do not apply a factor for sa=2.

 1 , ASOFab

 sa = 1

 1, sa = 2

ab

FSB ASOF pYSDW 1 =

pYSDWRMB represents the probability that the spouse is not remarried. We assume this factor 

remains constant at 0.600.

pYSDWRMB = 0.600

pYSRWRES and pYSDWRES represent the probability that a person who is eligible to receive 

young-spouse benefits actually receive the benefits. For all historical years, we calculate 

year

RES pYSRW 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 

pYSRWFSB =
246

age, sex, and marital status. We calculate year pYSDWRES similarly, using the number of young 

spouses of deceased workers.

, RES

POP AGA ECB FSB

YSRWN pYSRW YSRW pYSRW pYSRW pYSRW = ××× year < TRYR

, RES

POP DEA ECB FSB RMB

YSDWN pYSDW YSDW pYSDW pYSDW pYSDW pYSDW = ××××

year < TRYR

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 TR-1 for year pYSRWRES . In addition, for each sex 

and marital status we graduate the regressed values of TRYR−1 pYSRWRES over age using a weighted 

minimized third-difference formula to compute YSRW ESTRES . YSRW ESTRES are the preliminary 

estimates of TRYR+9 pYSRWRES , the values in the tenth year of the projection period. For female 

young spouses, we apply an adjustment, YSRW SRADJ , to the tenth year of the projection period in 

order to match the projections made by the Short-Range office. We exponentially interpolate the 

values of year pYSRWRES for intermediate years between TRYR−1 pYSRWRES and TRYR+9 pYSRWRES (equal to 

YSRW YSRW ESTRES SRADJ × ). 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 year pYSDWRES similarly.

Equation 3.3.13 – Number of Deaths of Insured Workers (LUMSUMab)

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 EXPOSUREab, 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 lumpsum death payments paid in TRYR-1 to the estimated total amount of lump-sum payments paid 

in TRYR-1. We then calculate LUMSUM ab for each year in the projection period.

LUMSUM EXPOSURE BASE ab = ab × (3.3.13)
247

Appendix 3.3-1

Glossary

AB: age group of the beneficiary

AD: age of the disabled child

AGSP: married population where at least one spouse is age 62 or older

AM: age of the minor child

ARFGT3: actuarial reduction factor for ages more than 3 years below normal retirement age

ARFLE3: actuarial reduction factor for ages less than 3 years below normal retirement age

AS: age of the student child

ASDW: aged spouse of deceased worker by linkage factor, age (60-95+), sex of the account 

holder, marital status (widowed, divorced) and insured status (insured, uninsured). Linkage 

factors are:

ASDWPOP : population of potential aged spouse of retired workers

DEA pASDW : probability that the primary account holder (PAH) is deceased

FIA pASDW : probability that the PAH was fully insured at death

MBB pASDW : probability that the widow(er) is not receiving a young-spouse benefit for 

the care of a child

FIB pASDW : probability that the aged widow(er) is fully insured

pASDWGPB : probability that the aged-widow(er)'s benefits are not withheld or offset 

totally because of receipt of a significant government pension based on 

earnings in noncovered employment

pASDWRES : probability that a widow(er) eligible to receive his/her own retired-worker 

benefits would instead apply for and receive widow(er) benefits

ASDWN: final number of aged spouse of deceased workers (product of all linkage factors)

ASOF: average number of children in a family, by age group (under 25, 25-29 ..., 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

pASRWDEA : 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

CPA pASRW : probability that the PAH is receiving benefits

MBB pASRW : 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 

noncovered employment

RES pASRW : probability that a person who is eligible to receive aged-spouse benefits 
248

actually receive the benefits

ASRWN: final number of aged spouse of retired workers (product of all linkage factors)

AH: age of husband

AW: age of wife

BASE: ratio of actual to estimated total amount of lump-sum death payments paid in TRYR-1

CHI_62+: number of children having at least one parent aged 62 or older

CHI_DEA: number of children having at least one deceased parent

CON: number of persons converted from disabled-worker beneficiaries

DCDW: disabled child of deceased workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as SCDW.

DCDWPOP : population of potential disabled children

AGA pDCDW : 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

SSB pDCDW : probability that the child is indeed disabled

pDCDWRES : probability that a child who is eligible to receive disabled-child benefits 

actually receive the benefits

DCDWN: final number of disabled children of deceased workers (product of all linkage factors)

DCPREM: preliminary calculation of the probability that a child is disabled, by age

DCRW: disabled child of retired workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as those for DCDW.

DCRWN: final number of disabled children of retired workers (product of all linkage factors)

DIB: number of disabled-worker beneficiaries

DIFFADJ: adjustment 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:

DSDWPOP : population of potential beneficiaries

DEA pDSDW : probability that the primary account holder (PAH) is deceased

pDSDWFIA : 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

RES pDSDW : probability that a person who is eligible to receive disabled-spouse 

Benefits actually receive the benefits

DSDWN: final number of disabled spouse of deceased workers (product of all linkage factors)

ERROR: actual prevalence rate minus the regressed prevalence rate in the most recent historical 

year

ESTPR: preliminary estimate of the prevalence rate for retired workers
249

ESTPR2: secondary estimate of the prevalence rate for retired workers

ESTRES: preliminary estimate of the RES factor for the tenth year of the projection period

EXPOSURE: estimated number of lump-sum payments by age group (20-24, 25-29,...,80-84, 

85+)

FACTOR: adjustment for calculation of MBB factor of aged spouse of deceased worker

FINS: portion of the SSA population that is fully insured

FI_PAH: portion of married population where one spouse is fully insured

FP: status of the parent (retired, deceased)

GPOAGE: portion, by age, of the total beneficiaries expected to receive a significant 

government pension

GPWHLD: total number of beneficiaries (for all ages) expected to receive a significant 

government pension

IN: insured status of the beneficiary

LFPR: labor force participation rates for age 62, by sex

LUMSUM: number of deaths of insured workers by sex and age group (20-24,...,80-84,85+)

MAR62PLUS: number of couples where both husband and wife are age 62 and over

MS: marital status of the primary account holder

MB: marital status of the beneficiary

MBAPIA: ratio of the monthly benefit amount (MBA) to the primary insurance amount (PIA) 

by age (62-70) and sex

MCDW: minor children of deceased workers by linkage factor, age of the child (0-17) and sex 

of the account holder. Linkage factors are:

MCDWPOP : population of potential minor children

pMCDWDEA : probability that the parent is either retired or deceased

FIA pMCDW : probability that the PAH is fully insured

RES pMCDW : probability that a child who is eligible to receive minor-child benefits 

actually receive the benefits

MCDWN: final number of minor children of deceased workers (product of all linkage factors)

MCRW: minor children of retired workers by linkage factor, age of the child (0-17) and sex of 

the account holder.

MCRWN: final number of minor children of retired workers (product of all linkage factors)

NRA: normal retirement age

PAH: primary account holder

REGPR: regressed prevalence rate for retired workers

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

WBB pRW : probability that the PAH is not receiving a widow(er) benefit

pRWRES : retirement prevalence rate; probability that a fully insured worker (not 
250

receiving disability or widow(er)’s benefits) would receive a retiredworker 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

AGA pSCDW : 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 receive the benefits

SCDWN: final number of student children of deceased workers (product of all linkage factors)

SCRW: student children of retired workers by linkage factor, age of the student (18-21) and sex 

of the account holder. Linkage factors are same as SCDW.

SCRWN: final number of student children of retired workers (product of all linkage factors)

SRADJ: adjustment to match short-range projections in 10th year of projection period

SSAPOP: Social Security area population by age (0:100), sex, and marital status (single, 

married, widowed, divorced)

SX: sex of the beneficiary

TRYR: first year of the projection period

WEIGHT: estimated probability applied to each possible age of the spouse, given the age of the 

primary account holder

YSDW: young spouse of deceased worker by linkage factor, age group (under 25, 25-29,...,65-

69), sex of the account holder and marital status (widowed, divorced). Linkage factors are:

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

FSB pYSDW : 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

RES pYSDW : probability that a person who is eligible to receive young-spouse benefits 

actually receive the benefits

YSDWN: final number of young spouse of deceased workers (product of all linkage factors)

YSRW: young spouse of retired worker by linkage factor, age group (under 25, 25-29,...,65-69) 

and sex of the account holder. Linkage factors are:

YSRWPOP : population of potential young spouse of retired workers

AGA pYSRW : probability that the primary account holder (PAH) is of the required age
251

ECB pYSRW : 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 receive the benefits

YSRWN: final number of young spouse of retired workers (product of all linkage factors)
252

Process 4:

Trust Fund

Operations &

Actuarial Status
253

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 net

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 assess 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, including selected summarized information used

to prepare the Statement of Social Insurance.
254

4.1. TAXATION OF BENEFITS

4.1.a. Overview

The 1983 Social Security Act specifies including up to 50 percent of the Social Security benefits 

to tax return filer’s adjusted gross income (AGI) for tax liability if tax return filer’s adjusted 

gross income plus half of his (or her) Social Security benefits is above the specified income 

threshold amount of $25,000 as a single filer (or $32,000 as a joint filer). Subsequently, the 1993 

OBRA (Omnibus Budget Reconciliation Act) provided for taxation of up to 85 percent if a tax 

return filer’s adjusted gross income plus half of his (or her) Social Security benefits is above the 

specified income threshold amount of $34,000 as a single filer (or $44,000 as a joint filer). 

The proceeds from taxing up to 50 percent of the OASDI benefits, as a result of the 1983 Act, 

are credited to the OASI and DI Trust Funds, while additional taxes on the OASDI benefits, as a 

result of the 1993 Act, are credited to the HI Trust Fund.

Income to the Trust Funds from such taxation is estimated by using ratios of taxes on benefits to 

benefits for the OASI and DI programs separately. These ratios, called “RTBs”, are applied to 

the projected OASI and DI benefit amounts to estimate tax revenues to the OASI and DI Trust 

Funds. 

For the short range period (first 10 years of the projection), the Cost sub-process (4.3) uses OTA 

(Office of Tax Analysis)’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 the projected RTBs under the 1983 Act (up to 50 percent of benefits 

taxable).

For the long range period (11th through 75th year of the projection period), the RTB ratios for 

OASI benefits and those for DI benefits under the 1983 Act are computed with the following 

formula for each projection year.

RTB(yr) = RTB(tryr+9) * {AWI(tryr+9)/AWI(yr)}^P + 

 RTB(ultimate)*{1- AWI(tryr+9)/AWI(yr)}^P, (4.1.1) 

where

 tryr = first year of the projection period (year of the Trustees Report) 

 

 RTB(ultimate) = ratio of taxes on benefits to benefits assuming income 

 threshold amounts equal zero.

 

 AWI = SSA average wage index series

 P = exponential parameter for a trend curve line.
255

Finally, the Cost sub-process (4.3) applies the projected RTB ratios to its own estimates of the 

projected OASI and DI benefit payments to produce taxation of benefit revenues to the OASI 

and DI Trust Funds.

4.1.b. Input Data

OCACT Data

Economics--process 2

- Projected SSA wage index series by year, updated yearly

- Projected COLAs and average wage index levels under the intermediate 

assumptions of the prior Trustees Report

Beneficiaries--process 3

- Projected OASI beneficiaries by age and sex under the intermediate assumptions 

of the prior Trustees Report

- Projected DI beneficiaries by age and sex under the intermediate assumptions of 

the prior Trustees Report

Trust Fund Operations--process 4

- Aggregate OASI and DI benefit ratios (as a ratio of total OASDI benefits) under 

the intermediate assumptions of the prior Trustees Report

Other

- Aggregate OASDI benefit payments for calendar year ni-3 (ni = initial projection 

year, e.g, 2013 for the 2013 Trustees Report)

Other input Data

- 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). 

- 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 periodically based on 

OTA’s update.

- Current Population Survey (CPS) data for year ni-3

- Personal income tax brackets for year ni-3 and tax year 2013
256

- Marginal personal income tax rates for year ni-3 and tax year 2013

- General filing requirement amounts for personal income tax purposes for year ni3

- Ratios of taxable income to adjusted gross income by income level (IRS data) for 

tax year ni-3

- Treasury’s aggregate taxable benefit amount (IRS data) for tax year ni-3

- OTA’s estimated taxes on benefits for the OASDI and HI Trust Funds for tax year 

ni-3

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 Act, 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 Act (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 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 0.97 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 4.5 percent. The 4.5 percent reduction reflects estimates of the effect of the higher 

proportion of “old elderly” beneficiaries in the 2090 OASDI beneficiary population distribution 

relative to the 2022 OASDI beneficiary population distribution, due to improved mortality. 

For the 2013 Trustees Report, the ultimate RTB ratios for up to 50 percent of OASI and DI 

benefits taxable were set at 0.052 and 0.026, as compared to 0.058 and 0.029 for the 2012 TR 

ultimate ratios. This net reduction results from the enactment of the American Taxpayer Relief 

Act of 2012 (ATRA) , which extended marginal tax rates at 2012 levels for individuals having 

under $400,000 of taxable income as a single tax return filer ($450,000 for joint tax return filers) 

in tax years 2013 and later.
257

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.
258

4.2. AWARDS

Each year over 2 million workers begin receiving either retired-worker or disabled-worker 

benefits. The monthly benefits for these new awards are based on their primary insurance 

amount (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).39 The 

selected sample, referred to as “sample”, contains 261,931 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 subintervals40 (equation 4.2.3). As input to the Cost 

subprocess, the AIME values are used to calculate aggregate percentages of AIME in each bend 

point subinterval for each age at entitlement, sex and trust fund (equation 4.2.4). Equations 4.2.1 

through 4.2.4 outline the overall structure and solution sequence. The subscript n refers to the 

bend point subinterval and r refers to the sample record.

 Projected Earnings = Projected Earnings (∙) (4.2.1)

 AIME(r) = 12

Highest Indexed Earnings( )

∗

∑

Y

Y r (4.2.2)

 AIME (r) n = AIME n (∙) (4.2.3)

 PAPn = ∑

∑

r

n

r

n r

bp

AIME ( )

 (4.2.4)

where bpn is the length of the nth bend point subinterval,

Y is the number of computation years, and

AIMEn (r) is the AIME amount contained within the nth interval for record r.

 39 A record is selected if the year of initial entitlement equals 2008 and the beneficiary is in current pay status as of 

Dec. 2008, 2009 or 2010. Retired beneficiaries over age 70 and disability beneficiaries under age 20 are excluded.

40 The current law PIA formula has two bend points. For the purposes of PAP, the Awards subprocess instead uses 

30 subintervals.
259

4.2.b. Input Data

Long-Range OCACT Projection Data

Demography–

• Total Social Security area population by sex and age.

o From 1951 to 2090

o Updated annually

• Other-than-legal population by sex and age

o From 1964 to 2090

o Updated annually

• Deferred Action for Childhoold Arrivals (DACA) population by sex and age.

o From 2012 to 2090

o Updated annually

Economics –

• Covered workers by sex and age—with earnings posted to the Master Earnings File 

(MEF) only. - used with CWHS data to project future earnings levels

o From 1951 to 2090 

o Updated annually

• Covered workers not in the other-than-legal population by sex and age —with 

earnings posted to the Master Earnings File (MEF) only

o From 1951 to 2090 

o Updated annually

• Average Wage Index (AWI), projected values.

o From 2012 to 2090

o Updated annually

• 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 1951 to 2011 (only 2010-2011 data used in SOSI) 

o Updated annually

• 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 2012 to 2090 

o Updated annually

• Projected Covered Worker Rate based on total covered workers/total population (not 

used in SOSI) 

o From 2012 to 2090

o Updated annually

• COLA (Cost Of Living Adjustment) – not used in SOSI

o From 2012 to 2090

o Updated annually

• Projected Wage Base (to reflect relative changes in relative taxable maximum levels 

over time)
260

o From 1951 to 2015

o Updated annually

Fully Insured –

• Historical and projected fully insured rates by sex and single year of age 14-95

o From 1969 to 2090

o Updated annually

Other input data

• 10% Awards Sample from the MBR and Master Earnings File

o Newly entitled OASI / DI beneficiaries, whose initial entitlement year was 

2008, and are in current pay status as of Dec. 2008, 2009 or 2010.

 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 2007

o Generally updated annually, pending validation of the sample

• Total taxable earnings and number of workers with taxable earnings by age, sex, and 

year from the 2010 Continuous Work History Sample (CWHS).

o From 1951 to 2010

o Updated annually

• AWI, Average Wage Index, historical values

o From 1951 to 2011

o Data obtained from OCACT internet site.

o Updated annually

• Wage base

o From 1951 to 2013 

o Data obtained from OCACT internet site.

o Updated annually

• COLA, cost of living adjustment – not used in SOSI

o From 1975 to 2012

o Data obtained from OCACT internet site.

o Updated annually

• Amount of earnings needed to earn one quarter of coverage
261

o From 1951 to 2013

o 1978-2013 data obtained from OCACT internet site. 1951-1977 values 

estimated by applying projection methodology backwards from 1978.

o Updated annually

• Windfall Elimination Provision (WEP) factors, the % of sample cases affected by the 

WEP which will no longer be affected by the WEP, by sex and projection year 

o From 2012 to 2090

o Data obtained from OCACT internal calculations

o Updated annually 

• PIA bend points – not used in SOSI (expect for 1979 bend points)

o From 1979 to 2013

o Data obtained from OCACT internet site.

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 may need to include covered earnings above the reported historical 

wage base. Thus, for each record with reported taxable earnings at the wage base in a 

given year, AWARDS imputes his/her covered earnings.

• Changes in Covered Worker Rates. 

Adjustments are made to work histories to be consistent with the projected changes in the 

economy-wide covered worker rates. Economy-wide covered worker rates are defined as 

the ratio of covered workers (from Economics subprocess) to the Social Security area 

population (from Demography subprocess).

• Earnings Experience in the CWHS41. 

 41 This file is a 1% sample of individuals who had covered earnings at some point in their work histories.
262

Earning levels are modified to capture the changes to date that are reflected in the 

average taxable earnings reported in the CWHS by age and sex and the changes expected 

in the future.

Change in Wage Bases

The earnings posted in the sample are limited by the historical wage base (contribution and 

benefit base). Prior to 1975, the maximum annual amount of earnings on which OASDI taxes 

were paid was determined by ad hoc legislation. After 1974, however, the annual maximum 

level was legislated to be determined automatically, based on the increase in the Social Security 

Average Wage Index (AWI). Prior to these automatic wage base increases, a relatively large 

portion of workers earned amounts above the base. Additional legislation raising the annual 

maximum taxable amount occurred in 1979, 1980, and 1981 to improve the financial future of 

the OASDI Trust Funds. In addition, the AWI used in the automatic calculation of the annual 

taxable maximum was modified in the early 1990s to include deferred compensation amounts. 

Therefore, for each record in the sample with earnings at the wage base, AWARDS imputes 

covered earnings above the historical wage base in order to reflect higher maximum taxable 

amounts imposed on future newly entitled beneficiaries. Please refer to appendix 4.2-1 at the 

end of this subprocess for details of this imputation. Then, these projected covered earnings are 

compared to 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. 

Change in Covered Worker Rates

The sample’s covered worker rate by age group and sex is defined as the ratio of (1) the number 

of those beneficiaries with covered earnings in the sample to (2) the total number of beneficiaries 

in the sample. For both males and females, the work histories are modified to reflect changes in 

the covered worker rates that would apply to a future sample of beneficiaries. These changes in 

the covered worker rates are based on changes in the economy-wide covered worker rates. The 

economy-wide covered worker rate is defined for an age-sex group in a particular period which 

represents a future sample cohort as the ratio of (1) the number of “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.42 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.

 42 For this purpose, we define the “legal” population as the total SSA area population minus the other-than-legal 

population (those in the U.S. illegally and those in the U.S. on a temporary basis, e.g., individuals with specific nonimmigrant worker or student visas) plus the DACA population (DACA individuals are included in the other-thanlegal data but are effectively made legal, for Social Security purposes, by recent legislation ).
263

In projecting sample covered worker rates, examination is done of the change in adjusted

economy-wide covered worker rates, by age group, between the “base period” (representing 

individuals retiring in the sample year) and the “projection period” (representing individuals 

retiring in a year later than the sample year). The adjusted economy-wide covered worker rates 

in the base year takes into account 60% of the change in projected age-62 fully insured rates 

relative to the base year, based on analyses of historical data. That is, for each projection year, 

the method estimates what the base year economy wide covered worker rates would have been if 

the fully insured rates in the base year matched those in the projection year. Details of how this 

change is used to estimate the change in a covered worker rate for retired workers from a current 

period in the sample to a future period are given below. The method used is the same for males 

and females 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.

• 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

This presentation above presumes that economy-wide covered rates increase over time, which is 

very common for females but not always true for males, based on 2013 TR data. The calculation 

of the change in covered worker rate changes if there is a reduction in relevant economy-wide 

covered worker rates. Example 1.2 gives an example of the calculations done for males and 

females if economy-wide covered worker rates decline.

A similar procedure exists for projecting sample covered worker rates for disabled workers. See 

Example 1.3 for an example, for male disabled workers. 

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.

43 For males, the procedure is to select records randomly. 

However, for females, 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 females is equal to the male distribution plus 97% of the difference between 

the initial male and female distributions within the sample. In each subsequent year, the 

 43 Individuals in the sample affected by the Windfall Elimination Provision are less likely to have earnings removed 

or added by this process.
264

percentage decreases by three percent until it reaches 0%. Thus, the females’ years of earnings 

distribution for those with 11 to 25 years of earnings is adjusted to approach that of the males. 

If a record is selected for adding earnings in a particular year, the amount of earnings added is 

based on the career earnings pattern of the selected record. When earnings are added to a record, 

AWARDS calculates the ratio of (1) the record’s Average Indexed Earnings, AIE44, to (2) the 

AIE of a hypothetical worker, w, whose year of birth and sex are the same as the record and 

whose annual earnings are set equal to average taxable earnings. For this purpose, average 

taxable earnings are determined by averaging the earnings over all records in the sample with 

the same sex and year of birth. Then, the amount of earnings45 in year t that is added to the 

record is

 Earnings(r, t) = PreATEf(sex, t) * AIE( )

AIE( )

w

r ,

where PreATEf(sex, t) is the average taxable earnings in year t, for those in the sample 

with the same sex as that of the record, for those retiring in year f. 

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.

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 file46. AWARDS then projects these values from the base year (the last 

historical year in the CWHS file). Projections are made for each year after the base year through 

the end of the 75-year projection period using projected economy-wide number of covered 

workers by age and sex and annual average taxable earnings (ATE) from the Economics 

process47. 

After the base year, the numbers of covered workers by age and sex (CWHSCWas) are projected 

by applying the annual growth rates by age and sex in the numbers of economy-wide covered 

workers produced by the Economics subprocess. In addition, CWHSATEas are projected. The 

first step is to determine preliminary CWHSATE'as by using the annual growth rate in the total 

 44 AIE is the average indexed annual earnings, average over the highest Y years of earnings (similar to AIME, but an 

annual amount).

45 In this subprocess, earnings histories of projected beneficiaries are all reflected as wage-indexed earnings histories 

in the 2008 sample.

46 These historical values are tabulated by the Economic subprocess. 47 These values are based on earnings posted to the Master Earnings File (MEF), excluding earnings posted to the 

suspense file.
265

economy-wide ATE. A further multiplicative adjustment is made to each CWHSATE'as such that 

the resulting aggregate average taxable earnings, determined by combining the projected values 

of CWHSCWas and CWHSATEas for the year, produces the same growth rate as the growth in total 

taxable earnings from the Economic process. 

For additional explanation of this calculation, refer to example 3 in appendix 4.2-2 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 represent newly entitled beneficiaries 

in future years. For a given sex and age group, the expected annual average taxable earnings of a 

future sample is denoted as ATEf'. ATEf' is computed by using the comparable changes48 in the 

CWHSATEas. In addition, the annual average taxable earnings of the sample (after adjustments to 

the records’ earnings levels for changes in wage bases and covered worker rates) are computed 

by sex and age group and denoted as ATEf. The difference between these values is the amount 

by which the average annual earnings levels are adjusted. Let

f ATEf δ(t) = ATE ' − ,

for each 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 age group in a way so that the average taxable earnings after distribution is ATEf'. 

For additional explanation of the calculation δ(t), refer to example 4 in the appendix 4.2-2.

When δ(t) is negative, earnings for the year are decreased. To achieve ATEf' for the given sex 

and age-group, AWARDS multiplies CoveredEarnings(r, t) by a ratio, 

α

δ = + +

ATE ( )

( ) ratio( ) 1

f t

t

t .

The term, α, is an additional adjustment necessary because covered earnings above the wage 

base, have either no effect or only a partial effect on modifying ATEf to ATEf'. In the 2013 

Trustees Report, α was set equal to -0.08 for both sexes and trust funds (OASI and DI).

When δ(t) is positive, earnings for the year are increased. However, the method of increasing 

earnings differs between disabled beneficiaries (DIBs) and retired worker beneficiaries (OABs).

For earnings increases for DIBs, the adjustment is done similarly to the adjustment for when δ(t)

is negative, where the ratio is multiplied by covered earnings to raise each record’s earnings for 

year t. If the resulting value exceeds the future wage base in year t, taxable earnings would equal 

 48 The comparable changes reflect the wage-indexed changes in the CWHS ATEas between the year of earnings in the 

sample of new beneficiaries and the year of earnings in the projected sample.
266

the wage base. Hence, again, a constant α is added to account for the fact that increasing covered 

earnings which are greater or equal to the future wage base has no effect and covered earnings 

slightly below the future wage base have only a partial effect on modifying ATEf'' to ATEf . For 

the 2013 Trustees Report, α = 0.03 for females and α = 0.03 for males. 

However, when earnings for the year are increased for OABs, the ratio takes into account that 

among OABs, there are many more workers with earnings near or above the future wage base. 

In order to account for this, AWARDS first computes z, such that 

∑

∑ ∑

=

= = 















+ ∗ 















∗

= 20

1

20

n j

20

n 1

NumberWorkers( , )

2

( ) NumberWorkers( , ) * ( )

( ) ( ) NumberWorkers( , )

( )

n

n t

t n t

h t

t

t n t

z t

δ δ δ

,

where

(1) NumberWorkers(n, t) equals the number of workers whose earnings in year t fall within the 

nth interval, that is the number of workers whose earnings are greater or equal to IntervalLength 

(t)*(n-1) and less than IntervalLength (t)*n. For this calculation, 

20

WageBase(t) IntervalLength(t) = . Also, TotalWorkers(t) = ∑=

20

1

NumberWorkers( , )

n

n t .

(2) j(t) is the interval, such that 



 



 = − IntervalLength( )

( ) 20

t

t j(t) δ .

(3) h(t) is the dollar amount from interval j(t) to the wage base,

h t( ) IntervaLength(t) (21- ( )) = ∗ j t .

Now the covered earnings of OAB records are multiplied by the ratio

= + +α

ATE ( )

z(t) ratio(t) 1

f t ,

where α =0.03 for males and α = 0.03 for females. 

As AWARDS applies ratio(t) to Earnings(r, t) by each record, it makes sure that the total 

earnings adjustment in a year does not exceed δ(t)*TotalWorkers(t).

For additional explanation of this calculation, refer to example 5 in appendix 4.2-1 of this 

subprocess.
267

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

r t

Earnings(r, t), if t

, if t

AverageWage ( )

AverageWage ( ) 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 attained age 22}

•Divide the elapsed years by five and truncate. Subtract this number (cannot exceed five) 

from the number of elapsed years. 

•Y must be at least 2.

Step 3: Determine AIME

Finally, an individual’s AIME is computed by summing the highest Y indexed earnings and 

dividing by the number of months in those years. Hence, for each record, 

Y 12

Highest Y Indexed Earnings(r) AIME(r)

∗ = ∑ .

















 



 = − ,5

5

ElapsedYears Y Elapsed Years min
268

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) bpn (r) = bpn ∗

Next the record’s AIME amount, AIME (r), is compared to the indexed intervals. If

∑

−

=

1

1

 bp ( )

k

n

n r < AIME (r) ≤ ∑=

k

n 1

bp (r) n ,

then AIME (r) falls within the kth interval. And for n = 1 to 30,

 bp (r) n , if n < k

 AIMEn (r) = AIME (r) - ∑=

k

n

n r

1

bp ( ), if n = k

 0, if n > k
269

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 

years 2012 to 2090 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. 
270

Appendix 4.2-1

This appendix provides additional details on how the AWARDS process imputes covered 

earnings above the historical wage base.

 

To do this, AWARDS first computes the cumulative distribution, F, of the workers in the sample 

by their earnings level. Each historical wage base is divided into 20 equal intervals, n, and each 

interval length in year t is

20

WageBase(t) IntervalLength(t) = .

The cumulative distribution F(n, t) is the proportion of workers whose earnings are less than 

IntervalLength(t)*n, for n = 1 to 20. Let NumberWorkers(n, t) be the number of workers whose 

earnings in year t fall within the nth interval, that is the earnings are greater or equal to 

IntervalLength (t)*(n-1) and less than IntervalLength (t)*n. Also, let TotalWorkers(t) be the total 

number of workers in the sample with earnings in year t. Then for any n, 1 ≤ n ≤ 20,

TotalWorkers( )

NumberWorkers( , )

F ( , ) 1

t

m t

n t

n

m

∑= = .

Once F(n, t) is computed for n = 1 to 20, AWARDS extends the function for those who had 

earnings at the wage base. To extrapolate F past the historical base (define F(n, t) for n > 20), 

AWARDS groups the maximum earners in each year in the sample based on the number of years 

they had earnings at the wage base during the next four years (0, 1, 2, 3, 4). Under the 

assumption of uniform distribution within each group, AWARDS assigns an F(nr, t) value to 

each record with earnings at the tax maximum beginning with the group that has no other 

earnings at the tax maximum during the next four years and ending with the group that has 

maximum earnings in each of the next four years. Note that for these beneficiaries F(nr, t) > 

F(20,t). Once F(nr, t) is computed for these beneficiaries, values for F(n, t), where n>20 are 

estimated.

To find F(n, t), where n>20, the log odds transformation is utilized. The odds ratio, 

n,t)

n,t n,t 1- F(F( ) T( ) = , where n < 20

is the ratio of (1) the proportion of beneficiaries with earnings levels below the nth interval to (2) 

the proportion of beneficiaries with earnings levels above the nth interval. Next, the natural 

logarithm of the odds ratio is computed, giving the log odds transformation,
271

[ ] 













 = = 1- F( )

F( ) Y( ) ln T( ) ln

n,t

n,t n,t n,t , where n < 20

Utilizing the most linear portion of the function at the upper values of n, AWARDS regresses Y 

on those values. The regression line of Y has the form 

Y(n,t) * n ˆ = β 0 + β1

Finally, the amount of covered earnings of a record that has earnings at the taxable maximum is 

determined based on the F(nr, t) value assigned to the record. The F(nr, t) value for this record is 

used in the above equations to determine T(nr, t), Y(nr, t), and then nr, the non-integer value for 

n in the regression equation of Yˆ above. Thus, if earnings(r, t) = wage base in year t then

CoveredEarnings(r, t) = IntervalLength(t) r n ∗ + error49,

where nr is the record’s non-integer value for n in the regression equation of Yˆ above.

If earnings(r, t) < wage base in year t, then CoveredEarnings (r, t) = earnings(r, t)

At this point, AWARDS defines the expected taxable earnings of a future sample as,







≥

< = future wage base (t), CoveredEarnings(r,t) future wage base (t)

CoveredEarnings(r,t) , CoveredEarnings(r,t) future wage base (t) Earnings(r,t)

 49 The difference between Y(20,t) and Y(20 ) ˆ ,t .
272

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 reflect 

actual values.

Example 1.1: (OASI-Male with increasing economy-wide covered 

worker rates)—same method applies for females

Task: In projecting the 2008 sample of newly entitled male beneficiaries to represent 

newly entitled male beneficiaries in 2050, an adjustment to the earnings histories for 

those males age 40-44 is needed to reflect higher covered worker rates expected for males 

in this age group. 

This example illustrates the calculation of the projected covered worker rate for males 

who are age 40-44 in the projection period. We will be comparing the group of males age 

40-44 in the base period with its counterpart group of males age 40-44 in the projection 

period.

Information given:

• Newly entitled retired male beneficiaries represented in the 2008 sample 

are age 40-44 in the base period, 1978-1990, and the counterpart group of 

males retiring in 2050 is age 40-44 in the projection period, 2020-2032.

• Based on the 2008 sample, the covered worker rate for males age 40-44 in 

the base period = 88.0%. 

• Fully insured rate for age 62 in 2007 = 92.0%

• Fully insured rate for age 62 in 2049 = 88.5%

• Unadjusted economy-wide covered worker rate for males age 40-44 = 

87.0% in the base period. 

• Economy-wide covered worker rate for males age 40-44 = 91.0% in the 

projection period.

Calculations: 

1. Adjusted economy wide covered worker rate in the base period = 

Unadjusted economy-wide covered worker rate in the base period * (1+ 

(Fully insured rate 2049/Fully insured rate 2007 - 1) * .6 ) = 85.0%

2. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the projection period is 100.0% - 91.0% or 9.0%. 

3. The potential difference in the adjusted economy-wide covered worker 

rate for males age 40-44 in the base period is 100.0% - 85.0% or 15.0%. 

4. The ratio from steps 2 and 3 is 9/15 or 60.0 %. 
273

5. The potential difference in the sample’s covered worker rate for the males 

age 40-44 in the base period is 100.0% - 88.0% or 12.0%.

6. The ratio from step 4 is multiplied by the potential difference in the 

sample’s covered worker rate for males age 40-44 in the base period to 

yield 7.2% (60.0 % * 12.0% = 7.2% ).

7. The amount in step 6 (7.2%) would be subtracted from 1 to yield the 

sample’s covered worker rate for males who are age 40-44 in the 

projection period (92.8%).

Example 1.2: (OASI-Male with decreasing economy-wide covered 

worker rates)—same method applies for females

Task: In projecting the 2008 sample of newly entitled male beneficiaries to represent 

newly entitled male beneficiaries in 2050, an adjustment to the earnings histories for 

those males age 40-44 is needed to reflect lower covered worker rates expected for males 

in this age group. 

This example illustrates the calculation of the projected covered worker rate for males 

who are age 40-44 in the projection period. We will be comparing the group of males age 

40-44 in the base period with its counterpart group of males age 40-44 in the projection 

period.

Information given:

• Newly entitled retired male beneficiaries represented in the 2008 sample 

are age 40-44 in the base period, 1978-1990, and the counterpart group of 

males retiring in 2050 is age 40-44 in the projection period, 2020-2032.

• Based on the 2008 sample, the covered worker rate for males age 40-44 in 

the base period = 88.0%. 

• Fully insured rate for age 62 in 2007 = 82.0% 

• Fully insured rate for age 62 in 2049 = 92.0%

• Unadjusted economy-wide covered worker rate for males age 40-44 = 

79.2% in the base period. 

• Economy-wide covered worker rate for males age 40-44 = 75.0% in the 

projection period.

Calculations: 

1. Adjusted economy wide covered worker rate in the base period = 

Unadjusted economy-wide covered worker rate in the base period * (1+ 

(Fully insured rate 2049/Fully insured rate 2007 - 1) * .6 ) = 85.0%

2. The economy-wide covered worker rate for males age 40-44 in the 

projection period is 75.0%. 

3. The ratio from steps 2 and 1 is 75/85 or 88.2 %. 
274

4. The ratio from step 3 is multiplied by the sample’s covered worker rate 

for males age 40-44 in the base period to yield 77.6% (88.2 % * 88% = 

77.6% ).

The amount in step 4 (77.6%) would be the sample covered worker rate for males who 

are age 40-44 in the projection period.

Example 1.3: (DI-Male with decreasing economy-wide covered worker 

rates)

Task: In projecting the 2008 sample of newly entitled male DI beneficiaries to represent 

newly entitled male beneficiaries in 2040, an adjustment to the earnings histories for 

those males age 40-44 is needed to reflect lower covered worker rates expected for males 

in this age group. 

This example illustrates the calculation of the projected covered worker rate for males 

who are age 40-44 in the projection period. We will be comparing the group of males age 

40-44 in the base period with its counterpart group of males age 40-44 in the projection 

period. If the projection period is less than 40 years from the sample year, the following 

calculations would apply; otherwise, the projected sample covered worker rate for DI 

males would be the same as the economy-wide covered worker rate for DI males age 40-

44, adjusted in a manner similar to that described below.

Information given:

• Newly entitled retired male beneficiaries represented in the 2008 sample 

are age 40-44 in the base period, 1978-1990, and the counterpart group of 

males retiring in 2040 is age 40-44 in the projection period, 2010-2022.

• Based on the 2008 sample, the covered worker rate for males age 40-44 in 

the base period = 88.0%. 

• Adjusted economy-wide covered worker rate for males age 40-44 = 85.0% 

in the base period. This rate is the average of the most recent x years of 

“adjusted covered worker rates”, where x = the number of years with 

earnings in the sample for that age group. For each of the previous x years, 

the “adjusted covered worker rate” equals the economy-wide covered 

worker rate plus the difference between the sample covered worker rate for 

that age group and the economy-wide rate, limited by the maximum sample 

covered worker rate. 

• Adjusted economy-wide covered worker rate for males age 40-44 = 75.0% 

in the projection period. This rate is the average of the most recent x years 

of “adjusted covered worker rates”, where x = the number of years with 

earnings in the sample for that age group. For each of the previous x years, 

the “adjusted covered worker rate” equals the economy-wide covered 

worker rate plus the difference between the sample covered worker rate for 

that age group and the economy-wide rate, limited by the maximum sample 
275

covered worker rate. For projection years after (sample year -1), the 

difference is phased in from the difference in sample year – 1 to the 

average difference for all historical earnings years. 

• Weighting factor 1 is 0.8 or (2040-2008)/40. 

• Weighting factor 2 is 0.20 or (1-0.8).

Calculations: 

1. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the projection period is 100.0% - 75.0% or 25.0%. 

2. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the base period is 100.0% - 85.0% or 15.0%. 

3. The ratio from steps 1 and 2 is 25/15 or 166 2/3 %. 

4. The potential difference in the sample’s covered worker rate for the males 

age 40-44 in the base period is 100.0% - 88.0% or 12.0%.

5. The ratio from step 3 is multiplied by the potential difference in the 

sample’s covered worker rate for males age 40-44 in the base period to 

yield 20.0% (166 2/3 % * 12.0% = 20.0% ).

6. The ratio from step 5 (20.0%) then is subtracted from 100% to yield 

80.0%.

7. Multiply weighting factor 1 (0.80) by the economy-wide covered worker 

rate for males age 40-44 in the projection period (0.75) to yield 60.0% 

(0.80*0.75)

8. Multiply weighting factor 2 (0.175) by the amount in step 6 (0.8) to yield 

16% (0.20*0.8)

9. Sum up the amounts in step 7 and 8 to yield the sample covered worker 

rate for DI males who are age 40-44 in the projection period (76.0%).

Example 2:

Task: In projecting the 2008 sample of newly entitled male OASI beneficiaries to 

represent newly entitled male OASI beneficiaries in 2020, an adjustment to the earnings 

histories for those males age 40-44 is needed to reflect higher covered worker rates 

expected for males in this age group. The amount of increase in the covered worker rates 

is computed as 4 percent. To achieve this target, the desired number of records with zero 

reported earnings in this age group are randomly selected and assigned earnings.

This example illustrates the calculation of earnings to be assigned to a randomly chosen 

newly entitled retired male record with zero taxable earnings in the base year. 

Information given:

• Newly entitled retired male beneficiaries represented in the 2008 sample 

are age 40-44 in the base period, 1978-1990, and the counterpart group of 
276

males retiring in 2020 will be age 40-44 in the projection period, 1990-

2002.

• Based on the 2008 sample, a male record, r = 60,000, has been randomly 

selected to replace his zero taxable earnings reported in the base year 1985 

with an amount based on his career earnings pattern. This record is age 63 

in 2008, and his year of birth is 1945.

• A beneficiary retiring at age 63 in 2020 will have a year of birth of 1957. 

And, the corresponding projection year to the base year of 1985 is the 

projection year 1997.

• The Average Indexed Earnings for this record, AIE (60,000), is computed 

to be $43,465. Note: This value is calculated by (1) using the record’s 

annual taxable earnings reported each year through 2007, (2) converting 

them to 2007 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 1945 is $41,995. This value is calculated as above given 

the hypothetical worker earned the average taxable earnings in each of the 

base years for males retiring at age 63 in the 2008 sample.

• The projected Average Taxable Earnings50 of males retiring in 2020 for the 

projection year 1997 (converted to 1985 dollars51) is 

PreATE2020(male,1997) = $18,718.

Calculations: 

1. The ratio of the Average Indexed Earnings for record number 60,000, 

AIE(60,000) to the Average Indexed Earnings of a hypothetical male 

worker born in 1944 and retiring at age 63, AIE(w) is $43,465/$41,995 or 

1.035. 

2. The amount in step 1 (1.035) would be multiplied by 

PreATE2020(male,1997), which is given as $18,718. This yields the amount 

of earnings assigned to record number 60,000 in the projection year 1997 

representing a sample retiring in 2020, Thus, Earnings(60,000,1997) = 

1.035 * $18,718 which equals $19,373.

Example 3:

Task: The AWARDS subprocess estimates projected values of Average Taxable 

Earnings by age and sex using the values52 in the 2010 CWHS file supplied by the 

Economic subprocess as the base year on which to build our projections.

 50 The average taxable earnings have been computed using projected earnings adjusted for changes in the wage base. 

Adjustments to earnings for the earnings experience in the CWHS have not been applied at this stage in the process.

51 All projection year dollars are converted back to ‘sample year’ dollar amounts, using the Average Wage Index. 52 Because not all earnings are posted for the most recent years for a given CWHS file, adjustment factors, based on 
277

This example illustrates the calculation of the projected Average Taxable Earnings of the 

CWHS in 2011 for 42 year old females, CWHSATE42,female(2011). We will be using the 

number of female covered workers age 42 and the total taxable earnings for females age 

42 as given the in 2010 CWHS data.

Information given:

• The total number of female covered workers age 42 in 2010 reported in the 

CWHS, CWHSCW42,female(2010) is 15,125.

• The total taxable earnings for females age 42 in 2010 reported in the 

CWHS is $525,447,603. 

• The economy-wide number of covered workers for females age 42 in 2010 

is 1,529,204.

• The economy-wide number of covered workers for females age 42 in 2011 

is 1,603,865.

• The economy-wide Average Taxable Earnings (ATE) in 2010 is $33,549.

• The economy-wide ATE in 2011 is $33,345.

Calculations: 

1. The growth in the economy-wide covered workers for females age 42 

from 2010 to 2011 is 1,603,865/1,529,204 or 1.049. 

2. The growth rate in the economy-wide covered workers for females age 42 

from step 1 is applied to the CWHS female covered workers age 42 in 

2010, CWHSCW42,female(2010) to yield the projected covered workers for 

females who are age 42 in 2011, CWHSCW42,female(2011), 1.049*15,125 or 

15,866 

3. The CWHS Average Taxable Earnings for females age 42 in 2010, 

CWHSATE42,female(2010) is computed using the given CWHS total taxable 

earnings and total covered workers for females age 42 in 2010 

($525,447,603 / 15,125 = $34,740).

4. The economy-wide growth rate in the average taxable earnings from 2010 

to 2011 is $33,345 / ($33,549)or 0.9939

5. The growth rate in step 4 (0.9939) is applied to the amount in 

step3($34,740) to estimate the preliminaryCWHS Average Taxable 

Earnings for females age 42 in 2011, CWHSATE’42,female(2011) = $34,528 

(0.9939*$34,740)

6. The value from step 5 ($34,528) is multiplied by the value in step 2 

(15,866) to yield the preliminary CWHS projected total taxable earnings 

for females age 42 in 2011 ($547,821,248).

 

historical trends, are applied by the Economic subprocess to complete these earnings. For the 2010 CWHS, 

adjustment factors were applied to data in years 2007 through 2010. 
278

7. Note a final multiplicative adjustment is made to CWHSATE’42,female(2011) 

to obtain CWHSATE42,female(2011). This adjustment is made once the 

preliminary taxable earnings have been computed for each age and sex in 

2011 in order to ensure the growth rate in the aggregate average taxable 

earnings between 2010 and 2011 matches the growth rate in the ATE from 

the Economic process.

Example 4:

Task: In projecting the 2008 sample of newly entitled female beneficiaries to represent 

newly entitled female beneficiaries in 2050, the projected Average Taxable Earnings of 

females in the sample (ATEf)

53 for year t = 2020 must be adjusted by an amount,

δ(2020), to meet a targeted Average Taxable Earnings(ATEf'') for 2020. 

This example illustrates the calculation of δ(2020) for the female cohort retiring at ages 

62 to 70 in the projection year 2050. The cohort is age 32 to 40 in the projection year 

2020. The value δ(2020) is the dollar amount in which the average annual earnings levels 

are adjusted for females in this age-group in the year 2020 and retiring in 2050. We will 

be comparing this group of females age 32-40 in the projection 2020 year with its 

counterpart group of females age 32-40 in the base year 1978.

Information given:

• A cohort of newly entitled retired female beneficiaries retiring at ages 62 to 

70 represented in the 2008 sample are ages 32-40 in the base year, 1977, 

and the counterpart group of females retiring in 2050 are ages 32-40 in the 

projection year, 2020.

• Based on the 2008 sample, the average taxable earnings for females in the 

base year 1978 is $4,536. 

• For a sample projected to be retiring in 2050, the average taxable earnings 

(ATEf) for females in the projection year 2020 is $4,56454, after applying 

adjustments to the records’ earning levels for changes in the wage base and 

in covered worker rates. 

• Based on the 2010 CWHS data, the average taxable earnings for females 

ages 32-40 in the base year 1977 is $4,218.

• The projected average taxable earnings in the CWHS for females ages 32-

40 in the projection year 2020 (in 1978 dollar amounts) is $4,640.

 53 The average taxable earnings have been computed using projected earnings adjusted for changes in the wage base 

and for changes in covered worker rates.

54 Amount is in 1978 dollars, ‘sample year dollars’.
279

Calculations: 

1. The increase in the average taxable earnings for females ages 32-40 in the 

CWHS from the base year 1978 ($4,218) to the projection year 2020 

($4,640)12 is 10 percent.

2. Based on the value from step 1 the expected annual average taxable 

earnings (ATEf'') of females ages 32-40 in 2020 and retiring in 2050 is 

$4,536*1.10 or $4,990 

3. The difference in ATEf'' ($4,990) and ATEf' ($4,564) yields the δ(2020) 

value $426 ($4,990 - $4,564 = $426).

Example 5:

Task: In projecting the 2008 sample of newly entitled female OAB beneficiaries to 

represent newly entitled female OAB beneficiaries in 2033, for year t = 2023, δ(2023) is 

positive indicating an adjustment to earnings histories is needed to reflect higher average 

taxable earnings by this cohort for the projection year 2023. 

This example illustrates the calculation of the ratio(2023) in projection year 2023 for the 

female cohort retiring at ages 62 to 70 in the projection year 2033. The value, 

ratio(2023), is the adjustment ratio that will be applied to this cohort projected covered 

earnings in 2023 in order to achieve the targeted Average Taxable Earnings of this cohort 

for 2023.

Information given:

• Earnings in the projection year 2023 for a group of newly entitled female 

beneficiaries retiring in 2033 is the counterpart corresponding to earnings 

in the base year 1997 for the group of newly entitled female beneficiaries 

in the 2008 sample.

• For newly entitled females retiring in 2033, the average taxable earnings 

(ATE2023) for the projection year 2023 is $19,97055. 

• δ(2023) , the difference in the targeted average taxable earnings ATE2023' 

and ATE2023, is given to be $1,590. 

• The wage base for the projection year 2023 (in 1998 dollar amounts) is 

$57,600

• The number of females in the projected 2033 sample with earnings below 

the wage base in 2023 is 52,800.

• The dollar amounts below the wage base in 2023 are divided into 20 equal 

intervals, IntervalLength(2023), of $2,880 each.

• The number of females in the 2033 sample who in 2023 have earnings 

falling in the 20th interval (their earnings are between $54,720 and 

$57,600) is 465

 55 Amount is in 1998 dollars, ‘sample year dollars’.
280

• For female OABs the constant α when δ(t) is positive is 0.02.

Calculations: 

• The interval in which $56,010 (the wage base in 2023 minus δ(2023) or 

$57,600-$1,590) falls within is interval j(2023) and is found by rounding 

δ(2023)/ IntervalLength(2023) or ($1,590/$2,880) to the lowest integer and 

subtracting this value from 20. This yields interval 20.

• The dollar amount from interval 20 to the wage base is h(2023), and is 

$2,880*(21-20) or $2,880

• Using the equation given for z(t) yields,

( ) ( )

52,800

2

$1,590 465 *

$2,880

$1,590 $1,590 52,800

(2023)

∗ + ∗

z = = $1,594

Note, the value for z(2023) is higher than δ(2023) in order to adjust for 

those records above or close to the wage base.

• The ratio multiplied to the covered earnings in 2023 for females retiring in 

2033 is 1 + ($1,594/$19,970) + 0.02, or 1.10. 

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 2008

• This OAB beneficiary is record #150000 in the sample (r = 150000)

• The AIME for this individual is $3,000

• The initial eligibility year is 2006, 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 2006 dollars is given by the equation 

bpn (r) = bpn * AWI (2004) / AWI (1977) 

where bpn is the length of interval n in 1979 dollars

• The average wage index (AWI) for year 2004 is $35,648.55

• The AWI for year 1977 is $9,779.44
281

• When converting the intervals from 1979 dollars to 2006 dollars, there is a 

2-year lag in AWI values.

• AIMEn (150000) is the AIME value in interval n for Record #150000

Calculations: 

• The AIME for this individual ($3,000) is compared to the indexed 

intervals. It falls within the 16th interval.

• The AIME16 is the residual of $3,000 subtracting the cumulative indexed 

bend points up to 15th interval ($2861.58). The AIME for this individual in 

16th interval is $138.42

• AIMEn (150000) for interval 1 through15 equals bpn (150000) for the 

corresponding intervals, such that PAPn = AIMEn / bpn = 1 for these 

intervals

• AIME16(150000) = $138.42, such that PAP16 = $138.42 / $364.53 = 

0.3797

• AIMEn (150000) for interval 17 through 30 equals 0, such that PAPn = 0 

for these intervals.

• The following table details these results.
282

n 

bpn in 

1979 

dollars

bpn (r) in 

2006 

dollars

 bp ( )

1

n r

n

k

∑= i

n 2006 

dollars

AIMEn (r) 

in 2006 

dollars

PAPn 

in 2006 

dollars

1 $45 $164.04 $164.04 $164.04 1

2 45 164.04 328.08 164.04 1

3 45 164.04 492.12 164.04 1

4 45 164.04 656.16 164.04 1

5 45 164.04 820.20 164.04 1

6 45 164.04 984.24 164.04 1

7 45 164.04 1,148.28 164.04 1

8 45 164.04 1,312.32 164.04 1

9 45 164.04 1,476.36 164.04 1

10 45 164.04 1,640.40 164.04 1

11 45 164.04 1,804.44 164.04 1

12 45 164.04 1,968.48 164.04 1

13 45 164.04 2,132.52 164.04 1

14 100 364.53 2,497.05 364.53 1

15 100 364.53 2,861.58 364.53 1

16 100 364.53 3,226.11 138.42 0.3797

17 100 364.53 3,590.64 0 0

18 100 364.53 3,955.17 0 0

19 200 729.05 4,684.22 0 0

20 200 729.05 5,413.27 0 0

21 200 729.05 6,142.32 0 0

22 200 729.05 6,871.37 0 0

23 200 729.05 7,600.42 0 0

24 200 729.05 8,329.47 0 0

25 200 729.05 9,058.52 0 0

26 200 729.05 9,787.57 0 0

27 200 729.05 10,516.62 0 0

28 200 729.05 11,245.67 0 0

29 1000 3,645.25 14,890.92 0 0

30 1000 3,645.25 18,536.17 0 0
283

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 

benefits56. The other component of income is interest earned on the trust fund assets. The three 

components of cost are scheduled benefits, administrative expenses, and the railroad interchange. 

Each of these components is projected for each trust fund (OASI and DI). The end-of-year 

assets is computed by taking the beginning-of-year assets (ASSETS), adding 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 

 56 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.
284

entire 75-year projection periods, as well as 25- and 50-year periods. These include the actuarial 

balance (ACT_BAL), unfunded obligation (UNF_OBL), summarized income rate 

(SUMM_INC_RT), summarized cost rate (SUMM_COST_RT), and closed group unfunded 

obligation (CLOSEDGRP_UNFOBL). 

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-2013 for the 2013 TR

• ni+74 represents the final year of the projection period-2087 for the 2013 TR

• nf represents the last year the cost program will project-2090 for the 2013 TR

• nim1 is equal to ni-1

• nim2 is equal to ni-2

• ns is equal to ni+9

• nbase, the year of the sample, is equal to 2008

4.3.b. Input Data

Data received as input from the short-range office are presented first. Then data from long range 

and all other sources are identified separately for each equation.

Short-range OCACT Data

• Estimates for the first ten years of the projection period for the first six equations 

mentioned above. 

• Assets at the beginning of year ni.

All of this information is updated annually.

Long-range OCACT and other Data

i. Equation 4.3.1 – Tax Contributions (CONTRIB)

Economics-Process 2

• Projected effective taxable payroll for years nim1 through nf, updated yearly 

Other

• Projected employee/employer payroll tax rate, by trust fund and year, for years 

1981 through nf, updated as needed (e.g., as required due to legislative changes)
285

ii. Equation 4.3.2 – Scheduled Benefits (BEN)

Demography-Process 1

• Projected number of married and divorced people in the Social Security area 

population age 65 and above for beginning of years nim1 through 2101, updated 

yearly

Economics-Process 2 

• Historical COLA for years 1975 through nim2, updated yearly

• Historical CPI for years 1990 through nim1, updated yearly

• Projected cost of living adjustment (COLA) for years nim1 through nf, updated yearly

• Historical SSA average wage index for year nim2, updated yearly

• Projected percent increases in the average wage index for years nim1 through nf, 

updated yearly

Beneficiaries-Process 3

• Initial and ultimate incurred but not reported (IBNR) DI beneficiary distribution by 

age, duration of disability (0 through 9 years and 10+ years) and sex, updated every 

few years (subprocess #3.2). Factors are read in such that there is a ten-year linear 

phase-in from initial factors to ultimate factors. The number of DI beneficiaries in 

current-payment status is equal to the number of currently entitled DI workers times 

the IBNR factor.

• Projected number of disabled workers in current-pay status by sex, age in current-pay, 

and duration of disability (0 through 9 and 10+) for years nim1 through nf, updated 

yearly from subprocess 3.2

• Projected number of retired worker beneficiaries in current-pay status by sex, age in 

current-pay, and age at entitlement for years nim1 through nf, updated yearly from 

subprocess 3.3

• Projected number of auxiliary beneficiaries (by benefit category) of retired-worker, 

deceased-worker, and disabled-worker beneficiaries for years nim1 through nf, 

updated yearly from subprocess 3.3

• Projected number of disability insurance beneficiaries who convert to retirement 

insurance status upon the attainment of normal retirement age by age in current pay, 

for years nim1 through nf, updated yearly from subprocess 3.2 and 3.3

• Retired Workers 65+ by sex, and marital status (single, married, widowed, and 

divorced)

• Retired Workers 62+ by sex, and marital status (single, married, widowed, and 

divorced)

Other

• Total (aggregate) PIA and MBA, not actuarially reduced, of DI male and female 

workers in current payment status, updated yearly from the Table 1-A Supplement

• Total (aggregate) PIA and MBA, actuarially reduced, of DI male and female workers 
286

in current payment status, updated yearly from the Table 1-A Supplement

• Cumulative distribution of AIME dollars for newly entitled retired-worker 

beneficiaries by age (62 through 70) and sex, for years nim1 through nf, updated 

yearly from subprocess 4.2

• Cumulative distribution of AIME dollars for newly entitled disabled-worker 

beneficiaries by age (20 through 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. Age 66 is assumed to have the same 

distribution of dollars as does age 65

• Age distribution of newly entitled retired-worker beneficiaries in the AIME awards 

sample by sex, updated in years that the sample changes, from subprocess 4.2

• Starting average PIA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly

• Starting average PIA matrix for disabled-worker benefits, for the year nim1, by age in 

current-pay, duration and sex, updated yearly

• Starting average PIA matrix for beneficiaries who convert from disabled worker to 

retirement worker status for the year nim1, by age in current-pay and sex, updated 

yearly

• Starting average MBA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly

• 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

• 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 qlink13.xls

• Retroactive payment loading factors for auxiliary beneficiary categories for all years, 

for each benefit category and both sexes, updated yearly

• 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. 

• 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. 

• Initial and ultimate post entitlement factors for DI conversion 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. 

• Average excess MBA amounts for dually entitled wives and widows, updated yearly 

from Statistical Supplement

• Initial Windfall Elimination Provision (WEP) factors by sex and age for attributed 

year, updated every 2 years

• Ultimate WEP factors by sex read in as a percentage of the way from initial factors to 

one, updated every 2 years
287

• Year in which ultimate WEP factor is reached by age at initial entitlement (62-70), 

updated every 2 years

• Trendline by which WEP factors are phased-in from initial value to ultimate value, 

updated every 2 years

• 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

• Workers’ Compensation reduction factors (used in retroactive category) to reflect 

offsets starting and stopping in the year of DI entitlement

• Workers’ Compensation parameter to account for offsets that begin and end in the 

year of entitlement, updated yearly

• Dual Entitlement regression coefficients for the number of wives, widows, and 

widowers, and the average excess amounts for wives and widows, updated yearly

• Dual Entitlement widower excess amount as a percent of widow excess amount

• Dual entitlement average excess amounts and percentages of exposure population for 

December, year ni-1 for wives, widows, and widowers, updated yearly

• Target values for ratios relating to the five above dual entitlement categories, updated 

yearly

• Number of years in which the difference between the results from the regression 

coefficients and targeted values are phased in for the five above dual entitlement 

categories, updated yearly

• Adjustment factors for average retired and disabled worker benefit amounts (PIA and 

MBA) in current-pay at durations 0 and 1, by sex and age, updated yearly 

• Adjustment factors for average retired worker retroactive benefit amounts by sex, 

updated yearly 

• Adjustment factors for disabled worker retroactive benefit amounts in current-pay at 

durations 0, 1 and 2+, by sex and age, updated yearly 

iii. Equation 4.3.3 – Taxation of Benefits

Trust Fund Operations and Actuarial Status

• Taxation of benefits as a percentage of scheduled benefits by trust fund for years 

nim1 through nf, updated yearly from subprocess #4.1

iv. Equation 4.3.4 – Administrative Expenses

Economics-Process 2

• Average wage indexes for years nim1 through nf, updated yearly

• Ultimate value of productivity factor for the period ni through nf updated yearly

Beneficiaries-Process 3

• Total number of beneficiaries in current-pay status by trust fund for years nim1 

through nf, updated yearly
288

v. Equation 4.3.5 – Railroad Interchange

Economics-Process 2

• Increase in the average wage index for years nim1 through nf, updated yearly

• Ultimate value of productivity factor for the period ni through nf updated yearly

Trust Fund Operations and Actuarial Status

• Taxation of benefits as a percent of the amount of benefits scheduled to be paid, by 

trust fund for years nim1 through nf, updated yearly (use same factors as in equation 

4.3.3)

Other input data

• Nominal annual yield rate on the combined OASDI trust fund for years ni through nf, 

updated as the ultimate real interest rate and ultimate CPI are changed by the 

Trustees. 

• Ratio of railroad retirement OASI and DI average benefits to overall OASI and DI 

average benefits, updated yearly

• Number of railroad beneficiaries (retirement and disability) for December of year 

nim3, updated yearly

• Average taxable earnings in railroad employment for year nim2, updated yearly

• Average worker benefit by sex and trust fund, updated yearly from the December 

nim1 Table I-A Supplement

• Ratio of railroad worker benefit to worker benefit by trust fund, updated yearly using 

10 years of historical financial interchange benefit data

• Expected railroad new awards as a percent of the average of historical employment 

data

• Auxiliary loading factor by trust fund, updated yearly using 10 years of historical 

financial interchange benefit data

• Railroad initial mortality rate by trust fund for year nim2, updated yearly using 10 

years of historical financial interchange benefit data

• Railroad mortality improvement rate by trust fund, updated yearly using 10 years of 

historical financial interchange benefit data

vi. Equation 4.3.6 – Interest Income

Economics-Process 2

• Annual increase in the CPI for years ni through nf, updated yearly

Trustees assumptions

• Ultimate real interest rate, updated annually
289

Other input data

• Factors for exposure to interest rate for benefits, payroll, and taxation of benefits, 

updated yearly

• Factors for exposure to railroad interchange and administrative expenses, updated 

periodically

vii. Equations 4.3.7 through 4.3.13 – Annual Values and Summarized Values

All inputs for equations 4.3.7 through 4.3.13 are estimated internally in the Cost program.

viii. Equation 4.3.14 – Closed Group Unfunded Obligation

Demographics-Process 1

• Single year population and mortality rate data for years 1941 through 2101, updated 

yearly

• Population projections by single year of age, 75-99, from nim2 to 2101, updated 

yearly

Economics-Process 2

• Historical and projected single-year COLA data and average wage indexing series 

(AWI) data for years 1975 through 2090 (for COLA) and 1951 through 2090 (AWI), 

updated yearly

• Projected number of covered workers by single year of age 15-74 from year ni 

through 2088, updated yearly

• Aggregate number of covered workers aged less than 15, and aged 75 and over, from 

years ni through 2088, updated yearly

• Ultimate assumed annual average wage increase, wg_ult, updated yearly

Beneficiaries-Process 3

• Total projected disabled workers by age for years 2012 to 2090, updated yearly

• 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 

2012 to 2090.

Awards-Process 4

• Projected number of workers and total taxable earnings by single year of age (15-74) 

and sex from 2012 to 2090, updated yearly

 Other

• Total count of beneficiaries in 20 of the 28 beneficiary categories (excluding retired 

workers, disabled workers, aged spouses (married, divorced, and dually entitled 

excess), and aged widow(er)s (married, divorced, and dually entitled excess) from the 
290

December 2012 Master Beneficiary Record (MBR)57—updated yearly

• Total benefits paid in 20 of the 28 beneficiary categories (excluding retired workers, 

disabled workers, aged spouses (married, divorced, and dually entitled excess), and 

aged widow(er)s (married, divorced, and dually entitled excess) from the December 

2012 MBR—updated yearly

• Consumer Price Index data from 1951-1974 from Bureau of Labor Statistics

• Number of covered workers and average taxable earnings by single year of age 1-14 

for years 1991-2009 from 1 percent Continuous Work History Sample (CWHS), 

updated yearly to include year ni-4

• Number of covered workers and average taxable earnings by single year of age 75-99 

for years 1991-2009 from 1 percent CWHS, updated yearly to include year ni-4

• 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 2010 MBR—

updated every 3 years

• Distribution of assumed age differentials between widow(er)s and workers ranging 

from -6 years to 12 years seniority for the male

• Factors to apply to the 95+ “in current pay” counts of retired workers, aged spouses, 

surviving aged spouses, divorced spouses, and dually entitled 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 ≥ .

 57 For disabled adult children of deceased workers and lump-sum beneficiaries, data were extracted from a 1-

percent sample of the December 2012 MBR, mainframe dataset ACT.TAPEL.CAN1212. For the other 18 auxiliary 

beneficiary categories, data was extracted from the 100 percent December 2012 MBR, mainframe dataset 

ACT.TAPEH.MBR100.D1212.CANSORT.
291

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 the 

subprocess 3.2. For each projection year, two matrices are provided – one for males and one 

for females. The structure of each matrix is as follows:

• 11 columns. The columns are indexed by duration of disability (0-9 and 10+).

• 52 rows. These rows correspond to the age in current pay, ages 15 through 66.

 

The COST subprocess, however, only uses 10 durations (0-8 and 9+), and 47 ages (ages 20 

through 66). This requires a manipulation of the matrix of DI beneficiaries in current-pay 

status from subprocess 3.2. For ages in current pay greater than or equal to 30, the duration 9 

and 10+ columns of this matrix are added to give the total number of duration 9+ 

beneficiaries. For ages (ag) between 20 and 30 inclusive, the number of beneficiaries in 

current-pay aged ag and duration ag-20 is the value provided by the DISABILITY 

subprocess added to the number of people in current pay aged ag-j and duration ag-20 for 

j=1,..,5. (For example, the number of people aged 20 of duration 0 is combined with the 

number of people aged 15, 16, 17, 18 and 19 of duration 0; the number of people aged 21 of 

duration 1 is combined with the number of beneficiaries in current-payment status aged 16, 

17, 18, 19, and 20 of duration 1, and so on. In other words, the five nonzero diagonal of the 

matrix provided by the DISABILITY subprocess is “combined with” the diagonal directly 

below it and then zeroed out.) 

Building the Average Benefit Matrix for Disabled Workers

In each projection year, the COST subprocess produces an average benefit matrix for each 

sex. Each matrix is a 47 by 10 matrix whose entries are the average benefit amounts of 

disabled worker beneficiaries whose age in current pay is indexed by the rows (ages 20 
292

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 benefit levels, one for 

males and one for females, for December nim1 (2012 for the 2013 TR). 

For a given year of the projection period, a new average benefit matrix is obtained by moving 

the average benefit matrix from the previous year one year forward. The next few 

paragraphs describe this procedure.

In general, for each age in current-pay, the age and duration are incremented by 1 and the 

previous PIA amount is given a cost of living adjustment. In addition, the beneficiaries are 

given a workers’ compensation adjustment and a post-entitlement adjustment. For each 

duration j = 0,1,...,7, and 8+ and sex, let the workers’ compensation offset factor be 

denoted wkcomp 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 PEadj yr sex dur ( , , ), is 

given later in this document. See the section titled Average PIAs and MBAs for DisabledWorker Beneficiaries, below. To move duration 8 average benefits to duration 9+ average 

benefits, both average benefits are given a cost of living adjustment and a post-entitlement 

adjustment (see section “Post-Entitlement Adjustments”). The resulting duration 9+ average 

benefit is the weighted average of the adjusted prior year duration 8 and 9+ average benefits, 

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 benefits are determined for this group of beneficiaries. 

Average Benefits for Newly Entitled Disabled-Worker Beneficiaries

The potential AIME percentage values for newly entitled disabled-worker benefits (DPAPs) 

are obtained from the AWARDS subprocess. The two bendpoints of the PIA formula, BP1 

and BP2, are indexed by the increase in the average wage index. In 1979 dollars, the values 

of BP1 and BP2 are $180 and $1,085 respectively. The AIME dollars between 0 and BP1 

are divided into four intervals (each of length $45 in 1979 dollars). The AIME dollars 

between BP1 and BP2 are divided into fourteen intervals (nine of length $45 and five of 

length $100, in 1979 dollars). Twelve additional intervals are added beyond BP2 (ten of 

length $200 and two of length $1,000, in 1979 dollars). 
293

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

=

 + <

 =  + −− ≤ ≤ 



∏

• 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 2012, 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, ) =
294

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 2013 TR the data suggests this factor should be 

.31. As a result, for yr = ni, ... , ns+9,

2 ( , ) (1 ) 0.31

0.31 0.69 .

facm p yr sx x x

x

=+ − ×

=+×

The factor reaches its ultimate value in years ns+10 and later.

The preliminary average PIA for newly entitled disabled worker beneficiaries may now be 

defined. It is equal to 

30

1

2

1

_ (, , ) _ _ (,, )

_ (, , ) _ ( , )

2 ( , ).

i 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

=

=

=××

 

× ×   ×

 

×

∑

∑

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 currentpayment status is computed by finding the weighted average of the average PIAs for each 

age in current-pay and duration with the number of people in current pay for each of these 

ages and durations. The average PIAs were already reduced by a workers’ compensation 

offset factor, as briefly described above; a more careful description is given in this section. 

To get the average MBAs, we apply a factor 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 
295

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 at 

durations 0 and 1 to account for benefit level differences that are phased out by duration 2. 

Workers’ Compensation Offset Factors

For each duration j =1,...,7, 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 facm p pct dur 2_ ( ) be defined as in the following table. 

Duration Cumulative product above set at x% of 

way between original facm2p and 1

1 0.459753

2 0.647513

3 0.730408

4 0.782230

5 0.832050

6 0.857336

7 0.877231

8+ 0.898551

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 2012 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:
296

 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: 

Duration Percentage Reduction

0 0.2427%

1 0.1795%

2 0.0678%

3 0.0314%

4 0.0081%

5+ 0%

We define wkcomp_red(dur) to be 1 minus these percentage reductions. 

By law, disabled workers attaining age 65 are no longer subject to the workers’ 

compensation offset. Therefore, all DI worker benefit levels are adjusted at age 65 to 

eliminate the effect of the offset.

Adjustment to Average Benefit Levels at Durations 0 and 1

Average disabled worker PIA and MBAs are adjusted further at durations 0 and 1 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 are phased out by 

duration 2, when the vast majority of disabled workers have started receiving benefits.

Adjustment to Short-Range Average Benefit Levels

Average PIAs are further adjusted by a factor, icp_adj, designed to adjust the long-range 

aggregate average disabled worker in current pay monthly benefit amount (MBA) to the 

value projected by short range in the short-range period. This is done for each year of the 

short-range period and for each sex with the adjustment in year ns linearly phased down to 0 

by year ns+10.
297

Computation of Average MBA for DI Workers

The disabled worker PIA as presented in the average benefit matrix was already incremented 

by age and duration using a COLA and a workers’ compensation adjustment. The average 

PIA by year, age and duration, is denoted avgpia yr ag sx dur ( , , , ). The overall average MBA 

by year and sex is the weighted average of avgpia yr ag sx dur Fam p yr sx dur ( , , , ) 2 ( , , ), × the 

weights being the number of DI workers in current payment status by age, sex, and duration.

DI Conversions

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 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 (see subsection (2) below).

Post-Entitlement Adjustments

As a cohort 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 post-entitlement 

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 dynamic benefit levels. One percent 

December MBR data from the most recent 10 historical years are used to calculate postentitlement 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.

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 females 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 
298

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).

(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 males and one for females. The 

structure of each matrix is as follows:

• 10 columns. The first 9 columns are the age at entitlement, ages 62 through 70. 

The last column is the number of disabled workers who are projected to convert to 

retired-worker beneficiary status (DI conversions) at normal retirement age.

• 34 rows. These rows correspond to the age in current pay, ages 62 through 94 and 

ages 95+. 

Note that the entries on the diagonal 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 original age at entitlement is indexed by the columns. The final 

column simply gives the average benefits for DI conversions at the various ages in current 

pay. 

The 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. 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 males and females. 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 65 through 66 is combined (as a weighted average) between 
299

the DI conversion average benefits computed in subprocess 3.2 and the DI conversions of the 

corresponding age already receiving benefits (provided by subprocess 3.3).

The entries along the diagonal, the average benefits of newly entitled beneficiaries by age, 

must still be computed. The remainder of this section will explain how these average 

benefits are computed. Once these are computed, all entries are computed and the average 

benefit matrix for the year is complete.

Average Benefits for Newly Entitled Retired Worker Beneficiaries

The potential AIME percentage (OPAPs) values for newly entitled retired-worker benefits 

are obtained from subprocess 4.2. The OPAPs for the projection of average benefits for 

newly entitled retired-worker beneficiaries are modified by the COST subprocess. The 

reason is that the age distribution of newly entitled retired worker beneficiaries as determined 

in the awards sample is used for each projection year, i.e., the age-sex distribution matches 

that of the sample. These new potential AIME percentages are denoted OPAP1. To 

incorporate the projected change in the age distribution of projected newly entitled retiredworker beneficiaries for determining their average benefits, we use a “shuttling method.” 

Additional details about the shuttling method are given in Appendix 4.3-1.

Average benefits for newly 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 fourteen intervals (nine of length $45 and five of 

length $100, in 1979 dollars). Twelve additional intervals are added beyond BP2 (ten of 

length $200 and two of length $1,000, in 1979 dollars). 

To determine the average PIA for newly entitled beneficiaries, the OPAP1 values for each 

interval of AIME dollars 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=4,...,18, and 0.15 for intervals i=19,...,30), AIME_dollarsi be the 

length of subinterval i,

• opap1i (yr,sx,ag) be the modified PAP value for retired workers newly entitled in 

year yr whose sex is sx and whose age is ag. 

• wff(yr,sx,age) be a reduction factor to account for the Windfall Elimination 

Provision.58

 58 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.
300

• ( ( 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

_ (, , ) _ ( , ) _ ( , ) (,, )

_ _ 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. 

Adjustment to Average Benefit Levels at Durations 0 and 1

Average retired worker PIA and MBAs are adjusted at durations 0 and 1 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 are phased out by 

duration 2, when the vast majority of retired workers have started receiving benefits.

Adjustment to Short-Range Average Benefit Levels

Average PIAs are further adjusted by a factor, icp_adj, designed to be the factor that adjusts 

the long-range aggregate average retired worker in current pay monthly benefit amount 

(MBA) to the value projected by short range in the short-range period. This is done for each 

year of the short-range period and for each sex with the adjustment in year ns linearly phased 

down to 0 by year ns+10.

(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. 
301

This section applies to all benefit amounts except the “dual entitlement excess amount.” If a 

retired worker beneficiary is also entitled to spouse or widow(er) benefits and the auxiliary 

benefits are greater, than the amount by which the auxiliary benefit exceeds the worker’s MBA is 

the dual entitlement excess amount. The four categories of excess amounts (dually entitled 

wives, widows, husbands, and widowers) are projected separately. More information is found in 

subsection (4).

The first step is to 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 student child

55 & 56 Lump sum death benefit ($255)
302

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 

and the corresponding worker benefit) 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).

In order to annualize benefits for each beneficiary category, two values are used. The beginningof-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. Since the new COLA takes effect in December of the year, the 

new COLA must be reflected in the December benefits. If cp(cat,yr) is the number of 

beneficiaries in category cat for year yr, and avgben(cat,yr) is the average 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 expect 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 categories of dually entitled beneficiaries. They are the dually entitled wives (1), 

widows (2), widowers (3), and husbands (4). The number of dually entitled husbands is very 

small (currently less than 0.05% of all dually entitled beneficiaries and are expected to remain at 

this level in the future). As a result, the number of dually entitled husbands and their benefits are 

not projected. To project the number of dually entitled beneficiaries for the other three 

categories we use a regression equation with one coefficient each, ( )

1

k

a :
303

( ) ( ) ( )

1

PIA(yr,M) PIA(yr,F) PctExp ( ) ( ) PIA(yr,M)

k k k

yr a c yr − = +

(k=1,2,3) project the percentage of the exposed population entitled to wife (1), widow (2), and 

widower (3) benefits. 

PIA(yr,sex) is the average PIA of all retired worker beneficiaries in current pay by sex, wageindexed to the year of the sample and PctExp(yr) is the percentage of the entitled population in 

the category that is dually entitled. The regression alone, however, does not take into account 

expected future comparative work history changes that will affect dual entitlement populations. 

We use an “add factoring” method with variable ( ) ( ) k

c yr to account for this.

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. The regression yields a slope of ( )

1

k

a and 

a y-intercept of ( ) k b . Only the dually entitled widower regression equation warrants the usage of 

a non-zero y-intercept. 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( 2011, ) .

k k

k targ ult c yr yr phaseyrs phaseyrs

− =− ×

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 0.86265 0.0 0.20 40

2 Widow 1.86594 0.0 0.57 35

3 Widower -0.39888 0.20145 0.10 37

In the above equations, the average PIA of newly entitled beneficiaries by sex has already been 

computed (see subsection (2) above). 

Average Excess Amount for Dually Entitled Beneficiaries
304

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.

The equations used to project the average excess amount each have two terms. Each equation k 

has one coefficient, ( )

1 , k b calculated in a side model for the cost process based on historical series 

of the other terms in the equations and an add factor adjustment (denoted “c

(k)”) similar to the 

process for the number of dually entitled beneficiaries. A target value in the 75th year of the 

projection period is used in deriving the “add-factor” adjustment. The two equations

( ) ( ) ( )

1

PIA(yr,M) PIA(yr,F) AvgExcPct ( ) ( ) PIA(yr,M)

k k k yr b c yr − = +

( k =1,2 ) project the average excess benefit amounts of wife (1) and widow (2) beneficiaries as 

a percentage of the male retired worker benefit. 

The derivation of ( ) ( ) k

c yr is similar to the case of the exposure percentages as described above. 

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 ult 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( 2011, ) .

k k

k targ ult c yr yr phaseyrs phaseyrs

− =− ×

The table below shows the regression coefficients and other relevant adjustments in the 2013 

Trustees Report.

k Type ( )

1

k b Targeted Value (2087) in 

Nominal Dollars

( ) k targ

Add-factoring 

Phase-in Years

phaseyrs

1 Wife 0.43282 3,771 38

2 Widow 1.20530 9,806 35

The average excess amount of widower beneficiaries is estimated to be a fixed percentage (50%) 

of the average excess amount of widow beneficiaries. That is, 

(3) (2) AvgExcPct ( ) 0.50 AvgExcPct ( ). yr = × yr
305

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. This section discusses how retroactive benefit payments are projected for 

all beneficiary categories. 

Disabled Workers

For each age and sex the DI area (subprocess 3.2) provides two cumulative distributions (one 

initial and one ultimate), by duration, of incurred but not reported cases. Denote this by 

ibnr yr sex age dur (, , , ) where for years ni-10 to 2008 ibnr factors are set to the initial distribution, 

for years 2018 and after ibnr factors are set to the ultimate distribution, and for years 2009 to 

2017 we linearly interpolate. The number of disability beneficiaries who will eventually receive 

benefits (by age, sex, and duration) is 

dibce yr sex age dur dibcp yr sex age dur ibnr yr du ( , , , ) ( , , , ) / ( , , max(15, ), ). = −− r sex age dur dur

The associated frequency distribution of incurred but not reported cases is 

ibnr freq yr sex age dur _ ( , , , ). In other words, we have 

ibnr freq yr sex age ibnr yr sex age _ ( , , ,0) ( , , ,0) = for duration 0 and 

ibnr freq yr sex age dur ibnr yr dur sex age dur ibn _ ( , , , ) ( , , , ) ( , , , 1) =− −− − r yr dur sex age dur for 

higher durations, 1 9 ≤ ≤ dur and 10+.

Let dur be a duration, 0 through 9 or 10+. Define
306

• 0

_ ( ) (1 ( )).

dur

j

Cum COLA dur COLA yr j ==+ − ∏

• For i = 0,...,10,

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)

66 10

20 0 0

6

( , , , 0) _ ( ) _ ( , , )

(,, ) _ ()

_ ()

.

10

dur

age dur i

dibce yr dur sex age Num Months i ibnr freq sex age dur

dibpia age sex dur wkcomp red dur

= = = Cum COLA dur

− ×

= ∑∑∑ ×× ×

dibpia sex age dur (, , ) is further altered in this formula by the adjustment factors in array: 

DI RI facs sex age dur _ _ ( , , , 2)

These adjustments to dibpia are designed to account for the small differences between average 

benefit levels for all beneficiaries and levels for those receiving retroactive credit.

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, 0.7 months of retroactive 

payments. Hence 

70

62

(, , , ) 0.7 ( , , , ) 1000 _ ( ,) . 1 () ageoabicp yr sex age age oabmba yr sex age age

retro OAB sex yr = COLA yr

× ×

= + ∑

In the above formula, oabicp yr sex age age (, , , ) is the number of newly entitled beneficiaries at 

age equal to age (age in current pay equals age at entitlement equals age) and 

oabmba yr sex age age (, , , )is the corresponding average benefit. 

oabmba year sex age age ( ,, , ) in the above formula is further altered by the adjustment factors:

retrom adj sex _ ( ) {0.8975,1.0106} =

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.
307

The aggregate retroactive benefits for retired worker beneficiaries are simply added to the retired 

worker benefit category by year and sex.

Auxiliary Beneficiary Categories

Retroactive payments for auxiliary beneficiaries 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 the annual scheduled benefit levels by 

trust fund. In the short-range period, the long-range values are overridden by the values 

estimated by the short-range office. The difference between long-range scheduled benefits and 

short-range benefits in the 10th year of the short-range period is called the scheduled benefits 

adjustment. In the 10 years after the end of the short-range period, the long-range scheduled 

benefits are adjusted by linearly grading the scheduled benefits adjustment to zero. From the 20th

year forward, the projection is the pure long-range 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 longrange 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 funds, estimated to be collected as taxation on benefits, 

then

TAXBEN tf yr taxben factor tf yr BEN tf yr (, ) _ (, ) (, ) = ×

for yr ns ≥ +10.

iv. Equation 4.3.4 – Administrative Expenses (ADM)

Administrative expenses are estimated separately by trust fund. In the short-range period, the 

short-range office provides the estimates of administrative expenses by trust fund. Thereafter, 

administrative expenses are computed by multiplying the previous year’s administrative 

expenses by three factors: annual changes in total beneficiaries, annual changes in AWI, and one 
308

minus annual productivity growth. As a formula, if ticp(tf,yr) is the total estimated number of 

beneficiaries in current-pay status by trust fund and year, AWI(yr) is the average wage index in 

year yr, and prod is the ultimate assumed annual growth in productivity, then

( , ) ( , 1) [ ( , ) / ( , 1)] [ ( ) / ( 1)]

(1 )

ADM tf yr ADM tf yr ticp tf yr ticp tf yr AWI yr AWI yr

prod

= −× − × −

× −

for yr ns > .

v. Equation 4.3.5 – Railroad Interchange (RR)

Railroad interchange is disaggregated by trust fund and projection year. The long-range office 

does a projection for each year in the 75-year period. In the short-range period (first 10 years of 

the 75-year projection period), the short-range office provides the estimates of railroad 

interchange by trust fund and the long-range projection is overridden in these years. Over the 

next five years of the projection period, the estimate of the railroad interchange is a linear 

interpolation between the short-range projection at the end of the short-range period and the 

long-range projection five years hence. During the final 60 years of the projection period, the 

projection is as estimated by the long-range office.

By trust fund, the total cost in calendar year yr, rr_cost(tf,yr) is the sum of railroad benefits and 

railroad administrative expenses, less the sum of railroad contributions and railroad taxation of 

benefits. By trust fund, the railroad interchange component of total cost is then equal to 

RR tf yr rr tf yr ( , ) [0.25 _ cost( , 2) 0.75 _ cost( , 1)] [1 1.25 = × − + × −× rr tf yr + yield yr ( )].

Note that the railroad cost is increased by the yield rate on the combined OASDI trust funds for 

year yr. This formula takes into account the fact that that there is a delay from the end of the 

fiscal year to the time of valuation.

The total cost in year yr is broken down in to four components: railroad benefits in year yr, 

railroad administrative expenses in year yr, railroad contributions in year yr, and railroad 

taxation of benefits in year yr. 

Projections of numbers of newly entitled retired workers are determined by analyzing the ratio of 

new entitlements to previous levels of railroad employment using 1997-2010 new entitlement 

data in the analysis. After initial entitlement, a mortality rate of 5.8% for 2011 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 
309

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 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. 

Railroad earnings 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.

vi. Equation 4.3.6 – Interest Income (INT)

In the short-range period, the projection of interest income by trust fund is provided by the shortrange office. In each year of the short-range period, the annual yield rate is defined as the ratio 

of interest earned by a fund to the average level of assets held by the fund during the year. 

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 inflati = + (1 ) (1 ×+ − on rate) 1.

To get the yield rate for each year between the end of the short-range period (ns) and 5 years 

later, ns+5, when the ultimate yield rate is assumed to be reached, the program linearly 

interpolates between the values for years ns and ns+5. 

The projection of interest income in a given year is the yield rate for that year multiplied by the 

average level of assets. As a formula,

INT tf yr yield tf yr avg assets tf yr ( , ) ( , ) _ ( , ). = ×

The 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:
310

• 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 0.517, 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 cycling59) 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

_ ( , ) ( , ) 0.517 ( , )

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

= + ×

+× − ×

− × −×

vii. Equations 4.3.7, 4.3.8 and 4.3.9 – Annual Values

The annual income rate for a trust fund is computed as the 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

 59 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. In the past, benefits were always paid on the 3rd day of each month.
311

(, ) _ _ (, ) . ( )

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 0.517 ( )) ( , ) ( ),

_ ( , ) (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 

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 _ ( ) (1 0.5 ( )) ( ) ( ). =+ × × × yield yr payroll yr v yr

We also define

PV INC tf yr PV TAX tf yr PV TAXBEN tf yr _ (, ) _ (, ) _ (, ) = +

and
312

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 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 
313

projection period (ni). The Statement of Social Insurance displays unfunded obligations for 

closed groups (1) attaining 15 or later in 2013, (2) attaining 62 or older in 2013, and (3) attaining 

15 to 61 in 2013. For each year of the projection period, closed group calculations attribute a 

portion of the items in equations 4.3.1 through 4.3.6 to individuals falling in the defined closed 

group. The calculation of the closed-group unfunded obligation, then, uses the equation above 

but only considering the present values of cost and income attributable to the closed group. 

The following information, developed elsewhere in the “Cost” process, is used for developing 

closed group unfunded obligation amounts:

• Total number of workers and total taxable earnings by single year of age 15-74 and 

sex, years 1951 through nf, updated yearly 

• Taxable payroll, years ni through nf, updated yearly

• Payroll tax income, years ni through nf, updated yearly

• Income from taxation of benefits, years ni through nf, updated yearly

• Scheduled benefits by beneficiary category, years ni through nf, updated yearly

• Railroad interchange, years ni through nf, updated yearly

• Administrative expenses, years ni through nf, updated yearly

• Yield rate on the combined OASDI trust funds, years ni through nf, updated yearly

• 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 closed group. For 

instance, if the closed group were defined as individuals attaining age 15 or later in 2013, a 3-

year-old minor child receiving benefits in 2013 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 2013. 

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 2013 through 2112, is used by the cost program to compute payroll tax 

contributions attributable to the closed group. For each year, the closed group payroll factors are 

determined as follows:

• The number of projected workers by single year of age (ages 1-99) and sex are 

multiplied by the associated average earnings by age/sex.
314

• 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 15-74, the number of projected workers comes directly from Economics group 

projections, and the average earnings by age and sex comes directly from the AWARDS 

subprocess. 

• For ages 1-14, the number of projected workers is obtained by averaging the percentage 

of workers at each age relative to the total 1-14 age group, using 19 years of earnings data 

(1991-2009) in the averaging calculations. Average taxable earnings for ages 1-14 are 

obtained by analyzing historical 1991-2009 data of the average earnings at each age 

relative to the age 15 average earnings, and judgmentally assigning a ratio (to age 15 

average earnings) for each age. 

• For each single year of age from 75 through 99 and sex, the number of workers is 

projected each year by multiplying (1) the ratio of those workers in 2009 to the projected 

population of that group in 2009 and (2) the projected population of that group. Then, the 

resulting estimated workers are adjusted by an equivalent percentage to match the total 

number of projected workers aged 75 and later, as provided by the Economics group. 

This process is done separately by sex. To obtain the average taxable earnings for single 

years of age 75-99, ratios of average earnings by age 75-99 to overall average earnings 

for all ages are computed for each age 75-99, for earnings years 1991 through 2009. 

These ratios by age are then averaged for all 19 years, from which earnings ratios to 

overall average earnings are developed judgmentally. This process is done separately by 

sex.

Benefits

Methodologies for computing benefits attributable to the closed groups differs among benefit 

categories, as described below:

Retired Workers

For each age in current pay, the number of beneficiaries is multiplied by the corresponding 

average benefit amount across all ages of entitlement. The same applies for DI conversion 

cases. Retroactive benefits for the current year, by age, are then calculated. The closed-group 

factors for old-age benefits for each year are found by summing the benefit amounts 

attributable to the specified closed group, as a proportion of total retired worker benefits for 

all ages. This process is done separately by sex. 

Disabled Workers

For each age from 20 to the year before normal retirement age, the program adds the 
315

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. 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 category-specific 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).

For aged spouses in dual entitlement status (i.e. aged spouses 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 spouses and aged divorced spouses. The 

calculations are done separately for male and female beneficiaries.

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 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 _ 1.028) 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. 
316

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

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).
317

Appendix 4.3-1

Shuttling Method

In this appendix, we discuss the “shuttling method”. 

The shuttling method as presented in the COST model attempts to reorganize the PAPs 

obtained from subprocess 4.2, which maintains a static age-sex distribution of newly entitled 

beneficiaries, in such a way that captures the changing age-sex distribution of newly entitled 

beneficiaries provided by subprocess 3.3. The age-sex distribution of the sample (subprocess 

4.2) and those newly entitled from subprocess 3.3 are aligned in the sample year. This 

alignment persists throughout all years in the long-range period. When we refer to the agesex distribution from subprocess 3.3 in what follows below, we refer to the aligned age-sex 

distribution. 

Let oadsrs be the age/sex distribution of the sample from subprocess 4.2. Let oabicp be the 

number of newly entitled beneficiaries by age and sex from subprocess 3.3. Let total be the 

total number of newly entitled beneficiaries by sex. The ratio 

(, ) , ( )oabicp sex age

total sex

for age = 62, ... , 70 gives the age-sex distribution from subprocess 3.3. 

The array rsb_oadscp_sampleyr is the age-sex distribution from subprocess 3.3 from the 

sample year (2008 for the 2013 Trustees Report).

The value of oadscp is defined, by age and sex, to be:

(, ) (, ) ( , ) _ _ ( , ). ( )oabicp sex age oadscp sex age oadsrs sex age rsb oadscp sampleyr sex age total sex

= +− St

arting with the 2010 Trustees Report, we set all values of rsb_oadscp_sampleyr to the 

corresponding value of oadsrs. Therefore, the value of oadscp is now defined to be:

(, ) (, ) . ( )oabicp sex age oadscp sex age total sex = Despite the fact that we eliminated the actual alignment 

we will still refer to this as the aligned age-sex distribution as obtained from subprocess 3.3 

(with the assumption that the alignment left the age-sex distribution unchanged).

For each sex, we construct a matrix oads. Construction of this matrix uses two different agesex distributions: the age-sex distribution of the awards sample and the aligned age-sex 

distribution of newly entitled beneficiaries from subprocess 3.3. The matrix oads is a 9 9 ×

matrix whose rows and columns are indexed consecutively by the ages 62,..., 70. We index 

the rows of this matrix by the age of entitlement of a worker in the projection (ageentRSB) 

and the columns of this matrix by the age of entitlement of a worker in the Awards sample 

(ageentAWD). 

More precisely, for a given sex, let oadsrs be the age distribution of the sample; oadscp be 

the aligned age distribution of newly entitled beneficiaries from subprocess 3.3. Both arrays 

oadsrs and oadscp are indexed by age, ages = 62, ..., 70. For a given sex, the matrix oads is 
318

constructed with the following properties:

70

62

() (, )

ageentAWD

oadscp ageentRSB oads ageentRSB ageentAWD == ∑

and

70

62

( ) ( , ).

ageentRSB

oadsrs ageentAWD oads ageentRSB ageentAWD =

= ∑

In other words, the matrix oads has the following properties:

• The sum of the entries in any row of the matrix is the value of the distribution of the 

projection for the age corresponding to the row.

• The sum of the entries in any column of the matrix is the value of the distribution of 

the Awards sample for the age corresponding to the column.

Let opap be the original potential AIME percentages (PAPs) passed to subprocess 4.3 from 

subprocess 4.2. This is a 9 30 × matrix whose rows are indexed by ages at entitlement 62, 

..., 70 and whose columns are indexed by benefit interval 1, ..., 30 (represented by the 

variable i in the formulas below). The values of opap are modified and the results are the 

PAPs used by process 4.3, called opap1. As a formula, 

70

62

70

62

1( , )

( ,) ( , )

.

(, )

ageentAWD

ageentAWD

opap ageentRSB i

opap ageentAWD i oads ageentRSB ageentAWD

oads ageentRSB ageentAWD

=

=

×

=

∑

∑

This formula may be rewritten as follows.

70

70

62

62

1( , )

(, ) ( ,) .

(, ) =

=

= ∑ ×

∑ ageentAWD

ageentAWD

opap ageentRSB i

oads ageentRSB ageentAWD opap ageentAWD i

oads ageentRSB ageentAWD

It follows that opap1 may be interpreted as a reweighting of opap. We have 

70

,

62

1( , ) ( ,) ageentRSB ageentAWD

ageentAWD

opap ageentRSB i w opap ageentAWD i == ∑ ×

with weights ,

(, ). ( ) ageentRSB ageentAWD

oads ageentRSB ageentAWD w

oadscp ageentRSB = 

As matrices, opap w opap 1= × (and is another 9 10 × matrix). 

Consider the following example. In this example, the projection year is 2040, and the sex is 

males. 

The oadsrs vector (from subprocess 4.2) is as follows.
319

62 63 64 65 66 67 68 69 70

Male 0.3989 0.1267 0.0703 0.1118 0.2668 0.0119 0.0058 0.0040 0.0040

The unaligned age-sex distribution (from subprocess 3.3) is as follows.

62 63 64 65 66 67 68 69 70

Male 0.2722 0.1405 0.0576 0.1111 0.1461 0.1710 0.0284 0.0297 0.0436

The age-sex distribution (from subprocess 3.3) in 2008, the year of the sample is assumed the 

same as the oadsrs vector and therefore is as follows.

62 63 64 65 66 67 68 69 70

Male 0.3989 0.1267 0.0703 0.1118 0.2668 0.0119 0.0058 0.0040 0.0040

Hence the aligned age-sex distribution (from subprocess 3.3), that is, the oadscp vector, is as 

follows.

62 63 64 65 66 67 68 69 70

Male 0.2722 0.1405 0.0576 0.1111 0.1461 0.1710 0.0284 0.0297 0.0436

The matrix oads, computed in this subprocess (4.3) is as follows. An explanation of how this 

matrix is generated appears below. 

\ 62 63 64 65 66 67 68 69 70 Total

62 0.2722 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2722

63 0.1267 0.0138 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1405

64 0.0000 0.0576 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0576

65 0.0000 0.0553 0.0558 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1111

66 0.0000 0.0000 0.0145 0.1118 0.0198 0.0000 0.0000 0.0000 0.0000 0.1461

67 0.0000 0.0000 0.0000 0.0000 0.1710 0.0000 0.0000 0.0000 0.0000 0.1710

68 0.0000 0.0000 0.0000 0.0000 0.0284 0.0000 0.0000 0.0000 0.0000 0.0284

69 0.0000 0.0000 0.0000 0.0000 0.0297 0.0000 0.0000 0.0000 0.0000 0.0297

70 0.0000 0.0000 0.0000 0.0000 0.0179 0.0119 0.0058 0.0040 0.0040 0.0436

Total 0.3989 0.1267 0.0703 0.1118 0.2668 0.0119 0.0058 0.0040 0.0040 1.0000

Note that the column total is oadsrs and the row total is oadscp. The oads matrix is 

determined using these row and column sum constraints. The nonzero entries of the oads

matrix zigzag down and to the right. Starting at the upper left hand corner, the lesser of 

oadsrs and oadscp is put there. So oads(62,62) 0.2722. =

In this case (as is usually the case), oadscp is less. The difference 

oadsrs oadscp (62) (62) 0.3989 0.2722 0.1267 − =−= is placed one lower, in oads(63,62).

Since the sum of the first column is oadsrs(62) and the sum of the first row is oadscp(62), we 

move to the next entry on the right. The difference 

oadscp oads (63) (63,62) 0.1405 0.1267 0.0138, − =−= is oads(63,63). 

Now we have that the row sum is oadscp(63). We want the column sum to be oadsrs(63). 

We move down to oads(64,63). Since 
320

oadsrs oads (63) (63,63) 0.1267 0.0138 0.1129 0.0576 (64), − =−=>= oadscp by the row sum 

constraint we are forced to have oads(64,63) 0.0576. = 

Now move one lower. Since 0.1267 0.0576 0.0138 0.0553 (65) 0.1111, −−=< = oadscp the entry 

oads(65,63) 0.0553. = 

The column sum is now oadsrs(63), and we move one over to the right. We want to fill in 

this entry. Since 

oadscp oads (65) (65,63) 0.1111 0.0553 0.0558 0.0703 (64), − =−=<= oadsrs by the row sum 

constraint we are forced to have oads(65,64) 0.0558. =

The row constraint is now met, and we move down to oads(66,64). For the column sum to 

be oadsrs(64) we have oads(66,64) 0.0703 0.0558 0.0145. =−= 

Since the column constraint is now met, we move right to oads(66,65). 

oadsrs(65) 0.1118 (66) (66,64) .1461 .0145 .1316, = < − =−= oadscp oads so by the column 

constraint oads(66,65) 0.1118. =

Now we can get the row total to match oadscp(66) by setting 

oads(66,66) 0.1461 0.1118 0.0145 0.0198. =−−=

Now that this row constraint is met, we move one row down to oads(67,66). Since 

oadsrs oads (66) (66,66) 0.2668 0.0198 0.2470 0.1710 (67), − =−=>= oadscp by the row sum 

constraint we are forced to have oads(67,66) 0.1710. = 

Now that this row constraint is met, we move one row down to oads(68,66). Since 

oadsrs oads oads (66) (67,66) (66,66) 0.2668 0.1710 0.0198 0.07 − − =−−= > = 60 0.0284 (68), oadscp

by the row sum constraint we are forced to have oads(68,66) 0.0284. = 

Continuing with this logic, oads(69,66) is set to oadscp(69) 0.0297, = and we move one row 

down to oads(70,66). By the column sum constraint we are forced to have

oads(66,66) 0.2668 0.0297 0.0284 0.1710 0.0198 0.0 =−−−−= 179.

Now the column constraint is satisfied and we move right to oads(70,67). By the column 

constraint, this entry is forced to be 0.0119.

Moving to column 68, again, by the column constraint, the entry oads(70,68) is forced to be 

0.0058. 

Moving to column 69, again, by the column constraint, the entry oads(70,69) is forced to be 
321

0.0040. 

Finally, by the row and column constraints, the last entry, oads(70,70), is 0.0040.

To obtain the w matrix, normalize the rows by dividing by the row sum. 

\ 62 63 64 65 66 67 68 69 70

62 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

63 0.9018 0.0982 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 0.4977 0.5023 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

66 0.0000 0.0000 0.0992 0.7652 0.1355 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 1.0000 0.0000 0.0000 0.0000 0.0000

69 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000

70 0.0000 0.0000 0.0000 0.0000 0.4106 0.2729 0.1330 0.0917 0.0917
322

Then, as matrices, opap w opap 1 , = × as one may verify. For display purposes the transposes 

of opap and opap1 are shown.

opap 62 63 64 65 66 67 68 69 70

1 0.9996 0.9996 0.9992 0.9991 0.9987 0.9994 0.9994 0.9994 0.9972

2 0.9891 0.9889 0.9866 0.9850 0.9844 0.9934 0.9934 0.9934 0.9694

3 0.9610 0.9608 0.9586 0.9572 0.9551 0.9810 0.9810 0.9810 0.9126

4 0.9277 0.9274 0.9246 0.9255 0.9251 0.9658 0.9658 0.9658 0.8657

5 0.8951 0.8948 0.8923 0.8955 0.8995 0.9497 0.9497 0.9497 0.8321

6 0.8640 0.8640 0.8636 0.8700 0.8749 0.9342 0.9342 0.9342 0.8038

7 0.8350 0.8352 0.8369 0.8449 0.8512 0.9193 0.9193 0.9193 0.7791

8 0.8064 0.8068 0.8106 0.8189 0.8267 0.9047 0.9047 0.9047 0.7573

9 0.7783 0.7786 0.7811 0.7915 0.8029 0.8884 0.8884 0.8884 0.7344

10 0.7496 0.7498 0.7520 0.7644 0.7791 0.8718 0.8718 0.8718 0.7136

11 0.7203 0.7205 0.7221 0.7359 0.7526 0.8542 0.8542 0.8542 0.6948

12 0.6910 0.6912 0.6926 0.7070 0.7260 0.8363 0.8363 0.8363 0.6754

13 0.6607 0.6608 0.6616 0.6751 0.6966 0.8172 0.8172 0.8172 0.6573

14 0.6094 0.6093 0.6086 0.6232 0.6507 0.7801 0.7801 0.7801 0.6211

15 0.5380 0.5374 0.5318 0.5481 0.5822 0.7199 0.7199 0.7199 0.5734

16 0.4640 0.4631 0.4552 0.4714 0.5097 0.6528 0.6528 0.6528 0.5233

17 0.3900 0.3893 0.3829 0.3971 0.4414 0.5867 0.5867 0.5867 0.4745

18 0.3198 0.3192 0.3141 0.3298 0.3781 0.5219 0.5219 0.5219 0.4288

19 0.2271 0.2270 0.2259 0.2447 0.2963 0.4323 0.4323 0.4323 0.3646

20 0.1314 0.1320 0.1375 0.1561 0.2040 0.3234 0.3234 0.3234 0.2863

21 0.0645 0.0652 0.0721 0.0869 0.1262 0.2227 0.2227 0.2227 0.2098

22 0.0213 0.0217 0.0255 0.0333 0.0573 0.1118 0.1118 0.1118 0.1158

23 0.0035 0.0036 0.0046 0.0070 0.0151 0.0307 0.0307 0.0307 0.0369

24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0002 0.0002 0.0017

25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

26 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

27 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

30 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
323

opap1 62 63 64 65 66 67 68 69 70

1 0.9993 0.9992 0.9988 0.9986 0.9989 0.9988 0.9988 0.9986 0.9985

2 0.9870 0.9868 0.9854 0.9826 0.9854 0.9915 0.9915 0.9880 0.9330

3 0.9564 0.9569 0.9567 0.9535 0.9606 0.9779 0.9779 0.9679 0.8236

4 0.9229 0.9254 0.9264 0.9231 0.9349 0.9616 0.9616 0.9460 0.7315

5 0.8900 0.8951 0.8989 0.8976 0.9121 0.9453 0.9453 0.9266 0.6757

6 0.8592 0.8656 0.8716 0.8740 0.8914 0.9291 0.9291 0.9082 0.6375

7 0.8294 0.8367 0.8443 0.8509 0.8714 0.9121 0.9121 0.8905 0.6080

8 0.8000 0.8078 0.8175 0.8269 0.8502 0.8973 0.8973 0.8741 0.5763

9 0.7716 0.7805 0.7922 0.8049 0.8307 0.8815 0.8815 0.8570 0.5489

10 0.7419 0.7538 0.7667 0.7814 0.8105 0.8649 0.8649 0.8395 0.5259

11 0.7134 0.7250 0.7393 0.7579 0.7891 0.8459 0.8459 0.8199 0.5024

12 0.6840 0.6963 0.7120 0.7325 0.7657 0.8264 0.8264 0.8002 0.4852

13 0.6535 0.6646 0.6802 0.7032 0.7398 0.8051 0.8051 0.7794 0.4696

14 0.6024 0.6118 0.6270 0.6555 0.6966 0.7645 0.7645 0.7402 0.4477

15 0.5284 0.5354 0.5516 0.5857 0.6306 0.7030 0.7030 0.6809 0.4135

16 0.4534 0.4576 0.4739 0.5142 0.5629 0.6388 0.6388 0.6200 0.3848

17 0.3785 0.3824 0.3985 0.4407 0.4921 0.5698 0.5698 0.5546 0.3566

18 0.3086 0.3152 0.3321 0.3769 0.4285 0.5019 0.5019 0.4899 0.3280

19 0.2179 0.2273 0.2468 0.2953 0.3428 0.4064 0.4064 0.3983 0.2879

20 0.1239 0.1360 0.1547 0.2007 0.2447 0.2999 0.2999 0.2963 0.2390

21 0.0582 0.0689 0.0845 0.1211 0.1558 0.1997 0.1997 0.1988 0.1801

22 0.0187 0.0235 0.0316 0.0499 0.0674 0.0907 0.0907 0.0918 0.1067

23 0.0029 0.0040 0.0060 0.0125 0.0184 0.0246 0.0246 0.0256 0.0376

24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0024

25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

26 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

27 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

28 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

29 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

30 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000