Long-Range OASDI Projection 

Methodology 

Intermediate Assumptions of the 2011 Trustees 

Report 

 June 2011 

 

 Office of the Chief Actuary 

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

Process 

Econo

Process 1:

Demography

Process 4:

Trust Fund Operations and Actuarial S

Process 3:

Beneficiaries

Chart 1:
Trustees ultimate assumptions

Fertility

Mortality

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 than legal population data, and estimates of population in other components of Social Security area. Outputs: Historical Social Security area population by age, gender, and marital status (including starting population)Historical other than legal 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 P

by age, sex, and marital status; other than legal p

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

and average family size 

Economics, Beneficiaries, and Trust Fund Operati

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

1.1 Fertility 

Inputs: Historical U.S. births and female 

resident population 

Outputs: Historical and projected central birth rates

1.3 

Inputs: Histo

levels 

Outputs: His

legal immigr

Demography – Process 1

Social Security Administration

Office of the Chief Actuary

April 2011

Chart 2:

1.5 

Outputs: immigrat
Trustees Ultimate Economic Assumptions

Average real wageProductivityAverage hours workedInflationFull-employment unemployment rate

2.2 Class of Worker

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

2.3 AWI Series

Inputs: Historical AWI 

2.1 Real & Potential GDP, NInputs: Historical NIPA (BEA) Outputs: Real, potential, and n

2.3 Covered Employment

Inputs: Historical U.S. & covered employmentdata, population including illegal immigrants 

(Demography) Outputs: Covered worker rates, covered worker levels, & total employed (all by age, sex, type of worker) 

2.2 U. S. Wag

Inputs: Historical NIPA (B

(BLS) by sector 

Outputs: Wages & SE inc

2.3 Average Covered Earnings

Outputs: Projected average covered

earnings by type of worker

2.4 Taxable Earnings

Inputs: Historical distribution of earnings 

Outputs: Taxable wages, taxable SE income 

multi-employer refunds 

2.4 Average Taxable Earnings

Outputs: Average taxable earnings 

2.4 Effective taxable payroll

Outputs: Effective taxable payroll

Chart 3: Economics – Process 2

S

2.1 U. S. Employment

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

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

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

2.3 Cov

Inputs: Historical 

data by sector 

Outputs: Historica

earnings by type of 

Beneficiaries, 

Trust Fund Operations and Actuarial Status

2.3 Taxable Maximum

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

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

3.1 Disability-insured (DII) population

Inputs: Historical DII population 

Outputs: DII population (historical and projected)

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

3.3 Old-Age beneficiary (OAB) population

Inputs: Historical OAB population, labor force 

participation rates (Economics), and scheduled 

reductions for early retirement and increases for

delayed retirement 

Outputs: OAB population (projected) 

3.3 Auxiliary Beneficiaries of Retired and Deceased Workers

Inputs: Historical auxiliary beneficiaries of retired and deceased

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

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

number of children with at least one deceased parent 

(Demography), average number of children per family 

(Demography) and other relationships 

Outputs: Auxiliary beneficiaries of retired and deceased workers 

by type of benefit (projected) 

Trust Fund Operations and Actuarial Status

3.3 Widow benef

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

Chart 4: Beneficiaries – Process 3

Soci

Of

3.2 DIB Auxiliary Beneficiaries

Inputs: Historical beneficiaries by type of 

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

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

Trustees ultimate assumptions

Disability incidence rates 

Disability recovery rates 

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

4.3 Payroll 

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

4.1 Fraction benefits taxable

Inputs: Historical and projected short-range data on 

income taxation of benefits from Office of Tax Analysis

in the Department of the Treasury and data from 

current population survey 

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

4. 3 Taxation of benefits (TOB)

Outputs: Taxes on benefits

4.3 Administra

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

4.3 Benefit payments

Inputs: Starting average benefits, OAB population, DIB population,married and divorced aged population (Demography), Cost-of-Living Adjustments (Economics), post-entitlement factors, assumed benefit relationships between workers and auxiliaries, shortrange estimates of benefit payments Outputs: Scheduled benefit payments during year, average scheduled

benefits 

4. 3 Railroad inter

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

4. 3 Interest income

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

Trust Fund Operations and Actuarial Status

Output: Summarized income and cost rates and actuarial balances; 

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

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

Office of the Chief Actuary

April 2011

Trustees ultimate aReal interest rate, C

4.2 AIME Levels for newly-entitled OABs and DIBs

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

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

covered workers, average taxable earnings (Economics); 

and National Average Wage Index (AWI), Tax Maximum 

Outputs: Projected AIME distributions for new 

entitlements 
7 

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. 
8 

Process 1: 

Demography
9 

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 2011 report, the projection period covers the years 2011 through 2085. 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. As a rough overview, 

FERTILITY projects birth rates by age of mother, MORTALITY projects probabilities of death 

by age and sex, and LEGAL IMMIGRATION projects numbers of legal immigrants, legal 

emigrants, and adjustments of status from other than legal (OTL) to legal, by age and sex. 

HISTORICAL POPULATION combines population estimates from different sources to obtain 

historical estimates of the Social Security area total population by single year of age, sex and 

marital status and OTL population by single year of age and sex. OTHER IMMIGRATION 

projects OTL immigration by age and sex and, in addition, prepares data to assist the 

PROJECTED POPULATION subprocess in projecting OTL emigration by age and sex. 

MARRIAGE projects marriage rates by age-of-husband crossed with age-of-wife, and 

DIVORCE projects divorce rates by age-of-husband crossed with age-of-wife. PROJECTED 

POPULATION starts with the latest estimates of the total Social Security area population from 

HISTORICAL POPULATION and projects the total population by age, sex, and marital status 

using projected values from FERTILITY, MORTALITY, LEGAL IMMIGRATION, OTHER 

IMMIGRATION, MARRIAGE, and DIVORCE. PROJECTED POPULATION also starts with 

the latest estimates of the OTL population from the HISTORICAL POPULATION subprocess 

and projects the OTL populations and OTL emigrants by age, sex, and marital status using 

values from MORTALITY, LEGAL IMMIGRATION, and OTHER IMMIGRATION. 

 

1

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

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

consists of residents of the U.S. and its territories, citizens living abroad, and beneficiaries living abroad. 
10 

1.1. FERTILITY

1.1.a. Overview 

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

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

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

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

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

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

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

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

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

childbearing years. 

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

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

subprocess are given below: 

z bx = z bx (

.

) (1.1.1) 

 x

z

x

z TFR b (1.1.2) 

1.1.b. Input Data

Trustees Assumptions - 

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

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

Under the intermediate assumptions underlying the 2011 Trustees Report, the ultimate TFR

is 2.0 and it is assumed to be reached in 2035. 

Other input data - 

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

48, 49-54) for years 1980-2007. In general, the NCHS provides an annual update 

including one additional year of birth data and the previous historical years are only 

 

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. 
11 

updated if the NCHS makes a historical revision to their data. 

 From the NCHS, preliminary TFR for 2008. In general, NCHS provides an annual 

update including one additional year of data. 

 From the NCHS, estimated annual number of births for 2008 and 2009. In general, 

NCHS provides one additional year of birth data and the previous historical year of 

data. 

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

single year of age for ages 14-49 for 1980-2007. 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 were obtained 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

5 bx , are calculated from the agespecific birth rates z bx for each year during the period 1980-2007. 

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 2007, 

2006, 2005, 2004, and 2003, respectively. 

 

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. 
12 

3. For each z

5 bx age group series, the slope of the least squares line is calculated based on a 

regression over the period 1982-2007. 

4. For 2008, 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). 

5. Then, a preliminary total fertility rate for 2008, 2008 TFRp , is calculated such that, in 

general, it is equal to 5 times the sum of each 2008

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

the sum is actually used since this age group contains one additional age. 

6. For 2008, the preliminary TFR released by NCHS was 2.0855 and thus the Trustees set 

2008 TFR equal to 2.0855. 

7. To ensure the assumed total fertility rate is achieved for 2008, each value of 2008

5 bx (from 

Step 4) is now multiplied by the ratio of the assumed 2008 TFR (from Step 6) and the 

respective value of 2008 TFRp (from Step 5).

8. For 2009, each final z

5 bx for 2008 is projected forward by adding 96 percent of the 

respective slope (from Step 3). For subsequent projection years (2010-2035), an 

arithmetically decreasing portion of the slopes4 is added to the previous year’s final 

values of z

5 bx to get preliminary values of z5 bx . 

9. For years 2009 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 ultimate level. For the preliminary period (2008-2010), the values of z TFR are set equal to values consistent with expectations and the preliminary and 

provisional data from the NCHS. As mentioned in Step 6, 2008 TFR is assumed to be 

2.0855. 2009 TFR is assumed to be 2.0324, and 2010 TFR is assumed to be approximately 

2.0756. For years after 2010, z TFR is assumed to decrease linearly from 2010 TFR until 

reaching the ultimate value in 2035. 

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 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 

 

4

 For each year of the projection, the slope is reduced by four percentage points. 
13 

of the single year z bx to the z

5 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 

are made to correct rounding issues. 
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 

 

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 

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

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

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

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

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

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

population. 

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

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

 yMx = yMx (·) (1.2.1) 

 

 yAAx = yAAx (·) (1.2.2) 

 qx = qx (·) (1.2.3) 

 

 = (·) (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 

 

6

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

7

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

Mellitus, and Other 
16 

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

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

1.2-1. 

NCHS Data -

 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 1979-2007. 

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 1938-2007. 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 1938-2007. 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 1980-2007. 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 

 

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 

9

 Age groups are: 0, 1-4, 5-14, 15-24, ..., 75-84, 85+ 
17 

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

available. 

 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 1968-2007. These data are updated annually, when the CMS provides an 

additional year of data. 

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

benefits), by sex and single year of age (ages 65 and over), for the period 1968-2008. 

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

Other input data - 

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

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

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

 

10 Age groups are: 15-17, 18-19, 20-24, 25-29,..., 40-44, 45-54, ..., 65-74, 85+ 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 2007, and distributed by 21 age groups,13 2 sexes, and 7 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 ( u

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

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

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

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

The values of y AAx , by the 21 age groups, sex, and cause, for 2008 through 2010, are assumed 

to equal the average y AAx based on the decline in the yMx for the period 1997-2007. For years 

after 2010, a method of graduation is used that causes the absolute difference between the current 

y AAx and the ultimate u

y AAx to decrease rapidly until it reaches the Trustees’ ultimate assumed 

value, u

y AAx . This is accomplished by repeating the following steps for each year of the 

projection: 

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

ultimate assumed u

y AAx is calculated. 

2. If the ultimate assumed u

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

difference is subtracted from the ultimate assumed u

y AAx . If the ultimate assumed 

u

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

the ultimate assumed u

y AAx . 

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

their ultimate assumed values, u

y AAx . 

 

13 Age groups are: 0, 1-4, 5-9, 10-14, ..., 90-94, and 95+ 14 The seven causes of death are: Heart Disease, Vascular Disease, Violence, Cancer, Respiratory Disease, Diabetes 

Mellitus, 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 7 causes of death. The starting year for the projections of the yMx is 2007, 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 2007, 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, ..., 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. 
20 

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

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

thereafter. 

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

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

detail in Actuarial Study number 120. 

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

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

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

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

percent per year for women. For men, probabilities of death at each ages 95 and older are 

calculated as follows: 

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

current and prior Trustees Reports. For comparison purposes, rates are also presented for an 

historical period. 

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

 Historical Alternative II Historical Alternative II 

 2010TR 2011TR 2010TR 2011TR 

 1979 to 2007 2034-2084 2035-2085 1979 to 2007 2034-2084 2035-2085 

Under Age 15 Male Female 

Heart Disease 3.19 2.2 2.2 2.98 2.2 2.2 

Cancer 2.61 1.5 1.5 2.15 1.5 1.5 

Vascular Disease 1.26 2.5 2.5 1.25 2.5 2.5 

Violence 2.95 1.0 1.0 2.33 1.0 1.0 

Respiratory Disease 3.02 2.0 2.0 3.11 2.0 2.0 

Diabetes Mellitus 1.08 1.0 1.0 2.58 1.0 1.0 

Other 2.56 1.7 1.7 2.46 1.7 1.7 

Total 2.66 1.55 1.55 2.45 1.56 1.57 

Ages 15 - 49 Male Female 

Heart Disease 2.23 1.5 1.5 1.00 1.5 1.5 

Cancer 1.78 1.5 1.5 1.59 1.5 1.5 

Vascular Disease 1.58 1.8 1.8 1.80 1.8 1.8 

Violence 0.93 0.7 0.7 0.21 0.6 0.6 

Respiratory Disease 0.94 0.5 0.5 -0.11 0.5 0.5 

Diabetes Mellitus -1.48 0.3 0.3 -0.79 0.3 0.3 

Other -0.28 0.8 0.8 -0.72 0.8 0.8 

Total 1.02 0.88 0.86 0.54 0.91 0.89 

Ages 50 - 64 Male Female 

Heart Disease 3.31 2.2 2.2 2.69 2.2 2.2 

Cancer 1.51 1.5 1.5 1.18 1.5 1.5 

Vascular Disease 2.30 2.0 2.0 2.12 2.0 2.0 

Violence 0.72 0.5 0.5 0.15 0.5 0.5 

Respiratory Disease 1.22 0.7 0.7 -0.72 0.7 0.7 

Diabetes Mellitus -2.45 0.3 0.3 -1.05 0.3 0.3 

Other -0.05 0.6 0.6 -0.32 0.6 0.6 

Total 1.75 1.07 1.03 1.10 1.08 1.05 

Ages 65 - 84 Male Female 

Heart Disease 3.05 2.2 2.2 2.77 2.2 2.2 

Cancer 0.55 0.8 0.8 -0.40 1.0 1.0 

Vascular Disease 2.90 2.0 2.0 2.21 2.0 2.0 

Violence 0.76 0.5 0.5 0.07 0.5 0.5 

Respiratory Disease 0.33 0.3 0.3 -2.69 0.3 0.3 
23 

Diabetes Mellitus -2.23 0.3 0.3 -1.16 0.3 0.3 

Other -0.59 0.3 0.3 -1.75 0.3 0.3 

Total 1.44 0.79 0.76 0.57 0.80 0.76 

Ages 85 and 

older Male Female 

Heart Disease 1.18 1.2 1.2 1.37 1.2 1.2 

Cancer -0.67 0.5 0.5 -0.75 0.5 0.5 

Vascular Disease 1.95 1.8 1.8 1.88 1.8 1.8 

Violence -0.70 0.3 0.3 -0.95 0.3 0.3 

Respiratory Disease -1.32 0.2 0.2 -2.57 0.2 0.2 

Diabetes Mellitus -2.94 0.2 0.2 -1.72 0.2 0.2 

Other -2.34 0.2 0.2 -3.52 0.2 0.2 

Total 0.04 0.59 0.55 -0.08 0.58 0.53 

Total Male Female 

Heart Disease 2.50 2.16 

Cancer 0.64 0.16 

Vascular Disease 2.46 2.05 

Violence 0.84 0.20 

Respiratory Disease -0.06 -2.27 

Diabetes Mellitus -2.34 -1.23 

Other -0.67 -1.62 

Total 1.12 0.77 0.75 0.49 0.76 0.73 
24 

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 2011 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. 
25 

values for legal immigration and emigration are 1,000,000 and 250,000, respectively (both 

reached in 2012). 

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 (1996-2009), 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 fiveyear age groups (0-4, 5-9, ..., 80-84) and sex to reflect the fact that the estimated number 

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

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

updated (see above). 

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 
26 

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 2000-2009) 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 2011 

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. 
27 

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 x m

x s

z

x s

z Ex s L EDIST

84

0

, , * , . 25( )
28 

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 2009. The Social Security area population consists 

of: 

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

 Net census undercount plus 

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

Islands, and American Samoa plus 

 Federal civilian employees overseas plus 

 Dependents of armed forces and federal civilian employees overseas plus 

 Residual beneficiaries living abroad plus 

 Other citizens overseas 

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

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

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

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

these 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 smoothed 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 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) 
29 

1.4.b. Input Data 

Long-Range OASDI Projection Data - 

Demography 

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

1941-2009. These data are updated every year. 

 The number of new legal immigrants by age and sex for years 1941-2008. These 

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

 The number of legal emigrants by age and sex for years 1941-2008. 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 1941-2008. 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 1941-2009 from the 

FERTILITY subprocess. These data are updated each year. 

U.S. Census Bureau Data - 

 Decennial census population estimates, by single year of age and sex, for 1970, 

1980, 1990 and 2000, and total residential and residential plus armed forces 

overseas populations for January 1 of each Census year. These figures, along with 

the undercounts mentioned below, are used to create a total January 1 residential 

plus armed forces overseas population, including residential undercounts. A new 

estimate is created about every ten years. 

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

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

aged 85 and older. These data are not updated. 

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

each July 1 (1980-2009) by sex and single-year of age 0 through 99, and ages 100 

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

recent decennial census and includes one additional year of data. 
30 

 Estimates of the population by age group,16 sex, and marital status for years 1940-

2009. An additional year of data is added for each Trustees Report. 

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

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

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

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

Guam, Northern Marianas, and American Samoa for years 1940-2009. 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 

each Census starting in 1940 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. As of 2000, single year of age and sex data was available for Puerto Rico, 

Virgin Islands, Guam, and American Samoa. New estimates are available about 

every ten years. 

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

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

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

 Estimates of total net immigration of the U.S. residential plus armed forces overseas 

(USAF) population from 2000 through 2008. A regression from 2000 through 2008 

estimates the net immigration for 2009. 

Other input data - 

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

single year of age (85-100+) and sex for years 1968-2009. 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. 

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

OASDI Beneficiaries living abroad for years 1987-2009. For each Trustees Report, 

an additional year of data is available. 

 

16 Age groups are: 15-17, 18-19, 20-24, 25-29, ..., 55-64, 65-74, 75-84, 85+ 
31 

 Output from the Urban Institute’s microsimulation model, Polisim, regarding 

marriage prevalence for the period 1980-2009 by age of husband and age of wife. 

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

may be added.

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

males born per female) for years 1941 – 2007. Each year, NCHS provides another 

year of data. For years 2008 and 2009, the sex ratio is assumed to be the average of 

the latest 5 years of actual data.

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

immigrants (unauthorized immigrants plus nonimmigrants) from 2005 – 2009.

1.4.c. Development of Output

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

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

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

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

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

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

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

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

estimated using post-censal survey data from the 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, dependents of these Federal civilian employees, dependents of Armed Forces overseas, 

and other citizens overseas covered by Social Security are also based on estimates used by the 

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 from 1970 through 2000, and the last year of historical 

data [2009 for the 2011 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 2000) plus an undercount adjustment plus other component populations. 
32 

For ages 85 and over, z Px,s for each tab year is set equal to [Built Up Pops Age x, Sex s] * [Total 

USAF 85+]/[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 USAF 85+] 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 2000) plus an undercount adjustment plus other component 

populations for ages 85 and over. 

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 legal immigration 

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 )

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 for 1980 and later is based on the 1980 

Census Marital Status Report, which contains the number of married couples in 1980 by age 

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

for 1980 through 2009 are incorporated to adjust these marital prevalence grids for changes since 

1980. Multiplying the previous year values by the ratio of the current year Polisim values to the 

previous year Polisim values ensures that the 1980 and later grids are consistent with the pre1980 grids. The grids are transformed from age grouped numbers to single year of age figures 

from ages 14 to 100+ for husband and wife using the two dimensional H.S. Beers method of 

interpolation. 

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

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

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

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

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

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

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

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

diagonal in the grid. Then, the number of married persons for each age and sex is set equal to the 
33 

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 input to the Economics process. For each year, an initial net other 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. Then, a preliminary 

OTL population by single year of age and sex is built up using these net other estimates, along 

with adjustments of status and OTL deaths (using the same death rates as the total population). 

These stocks are then modified to ensure reasonableness. 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 the DHS January 2005 total OTL population. 

From January 2005 through January 2009, the total OTL population is forced to match the DHS 

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 1,500,000 persons 

per year for each year beginning in 2015. Due to the recent recession, they assume that the 

level of other immigration was 1,000,000 in 2010, and will increase by 100,000 each year until 

2015 when the ultimate is reached. 

Long-Range OASDI Projection Data - 

Demography 

 Historical 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-
35 

2008. These data are updated each year. 

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

status, for years 1941-2008. These data are updated each year. 

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

2009. These data are updated each year. 

Department of Homeland Security – 

 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 – 

 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 1990 and 2000. These 

data will not 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, 1990 and 2000, from Population Division Working Paper 

61.17 These data will not be updated. 

 

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. 
36 

 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 set back 

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

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

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

immigration during the period 1975-80, using 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 2011 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: 

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 

 

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 

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. 

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

applying the Beers method to get single year of age values. 

 

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). 
38 

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. 
39 

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

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

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

these years. 

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

marriages for 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. 

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: 

 

20 The geometric mean, as used in this document, is the square root of the product of two numbers. 
40 

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 1978-2009, 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 2011, the intermediate 

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

NCHS Data - 

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

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

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

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

ages). 

 

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

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

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

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

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

with age-group-of-wife (age groups include 15-19, 20-24, 25-29, 30-34, 35-44, 45-54, 
41 

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 1989-2009. 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. 

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 

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 total number of marriages is used for the period 1996 

through 2009. The provisional period refers to years 1989 – 2009. The projection period of the 

MARRIAGE subprocess begins one year after the last historical data year (2010). 

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 
42 

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

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

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

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

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

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

MarGrid match the number implied by the MRA subset. 

For each year of the entire provisional period (1989 – 2009), an expected total number of 

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

years 1989-1995) by the corresponding geometric mean of the unmarried males and unmarried 

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

years 1989-1995) are then proportionally adjusted to correspond to the total number of marriages 

estimated in the year for the Social Security area population. This estimate is obtained by 

increasing the number of marriages reported in the U.S. to reflect the difference between the 

Social Security area population and the U.S. population. The provisional 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 years are averaged to derive the starting value. The annual 

rate of change in the age-adjusted marriage rate is calculated by taking the 26th root of the ratio 

of the ultimate value and the starting value. Thus, to calculate the rate for a projected year, the 

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

projection period). 

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

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

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

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

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

 

21 Data for 1980 is not available and is excluded from the calculations. 
43 

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

during 1979 and 1981-1988. 
44 

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

year. 

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

The primary equations, 1.7.1 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) 
45 

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. 

1.7.b. Input Data

Long-Range OASDI Projection Data - 

Demography 

 Social Security area population of married couples by age-of-husband crossed with ageof-wife as of January 1 for years 1979-2009. These data are updated each year from the 

HISTORICAL POPULATION subprocess. 

 Social Security area population of married couples by age-of-husband crossed with ageof-wife for projected years, if needed. These data are updated each year from 

PROJECTED POPULATION subprocess of the prior year’s Trustees Report. Normally, 

these data are not used but are necessary if the last HISTORICAL subprocess data year is 

less than the last DIVORCE subprocess data year. 

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

of data is added each Trustees Report. 

Assumptions - 

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

rate reaches its ultimate value in the 25th year of the 75-year projection period. For 2011, the 

ultimate assumed z ADˆR is 2,000 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. 

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

every year. If no new data is available, data for the most recent year is used as a proxy. 
46 

 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 validate their use. 

Other Input Data- 

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

new data are needed. 

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

Virgin Islands for years 1989-2009. The most recent year of data was obtained in 2000; 

the 2000 figures are used as a proxy for 2001-2009.23 New data are incorporated as they 

become available and resources are sufficient to 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,24 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. 

 

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

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

24 Using the Whittaker-Henderson method of graduation. 
47 

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 years are averaged and used as the starting value for 2009 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 26th root of the ratio of the ultimate value and the starting value. 

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

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

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

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

that particular year. 
48 

1.8. PROJECTED POPULATION

1.8.a. Overview 

For the 2011 Trustees Report, the starting population for the population projections is the 

January 1, 2009, Social Security area population, by age, sex, and marital status, produced by the 

HISTORICAL POPULATION subprocess. The Social Security area population is then 

projected using the component method. The components of change include births, deaths, net 

legal immigration, and net other immigration. The components of change are applied to the 

starting population by age and sex to prepare an estimated population as of January 1, 2010, and 

to project the population through the 75-year projection period (years 2011-85). 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 are expected to occur 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,25 by age (x) and sex (s), for year z. 

 

25 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. 
49 

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,















    z

x 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 - 
50 

Demography 

 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 year prior to 

the starting date. These data are updated each year. 

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

of wife for the years beginning with 1941 and ending with the year prior to the 

starting date. These data are updated each year. 

 Other than legal population by age and sex for the years beginning with 1980 and 

ending with the year prior to the starting date. These data are updated each year. 
51 

 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. 

 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. 

 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 1960-2009. (Note that the program splits the last age group, which is a 

10-year age group, into two 5-year age groups.) An additional year of data is added 

each year.

1.8.c. Development of Output

Equation 1.8.1 - Births 

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

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

14 to 49 as follows: 















  



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 bx = birth rate of mothers age x in year z; and
52 

 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 , 

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. 
53 

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 

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 

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 
54 

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 population26 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. 

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), 

 

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

divorced). 
55 

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. 
56 

Process 2: 

Economics
57 

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. 
58 

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 groups27, 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 

 

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

presence of children. 
59 

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

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

economy (EO_UND), 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 / P (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 
60 

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

(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. 
61 

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

above variables. 

Addfactors 

Addfactors are adjustments that move an estimate closer to an expected value. 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 and hypothetical disability prevalence rates for those at the NRA 

through age 72. 

 Addfactors are reviewed each year and implemented if necessary. 

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. 
62 

 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 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. 
63 

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 and is only dependent on one input, the distributed 

lag in the change in the ratio of real to potential GDP (RTP). 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. The RD affects the 

LFPRs for males and females below the NRA. The RD is adjusted for the number of 

weeks worked per year, and for the difference between the number of disability 

beneficiaries and the number of people self-reporting disability in the Current Population 

Survey. 

 Hypothetical disability prevalence ratios (HRD) are constructed by gender and singleyear-of-age for those at the NRA and up to age 72. The HRD are estimates of what the RD 

would be if there were no NRA, or the NRA were much higher (age 73 or above), or there 
64 

were no conversion of disability to retirement benefits at NRA. The projected HRD values 

for a particular age-gender cohort are based on actual RD values for the cohort at an 

earlier age. They also assume that there is a natural tendency for the RD values to increase 

with age, as is observed for ages below the NRA. An increase in the HRD lowers the 

LFPR. However, the degree to which increasing HRDs lower the LFPR is assumed to 

decrease with age, reflecting the belief that, as people age, their tendency to retire and 

leave the labor force increases regardless of disability. Thus, weights applied to HRDs to 

compute their effect on LFPRs vary with age. The weights are 1.0 for males and females 

age 67, 0.9 for those age 68, 0.7 for 69, 0.5 for 70, 0.3 for 71, and 0.1 for those age 72. For 

example, we only take 50 percent of the estimated effect of an increase in the HRD on the 

LFPRs of males and females age 70. 

 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 patterns28 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) 

 

28 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. 
65 

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 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. However, TEM2024 is by definition the 

sum of at-any-time employment posted and not posted to the MEF, of which, the latter group 

includes the portion of TEO who are male age 20 to 24 in the underground economy. Thus, 

we must use proxies for the conversion weights. For males age 20 to 24, our proxy 

conversion rate is defined as the ratio of the sum of OASDI covered employment posted to 

the MEF, EO_ESF, and EO_UND to the sum of military and CPS civilian employment. 

Effectively, this method assumes that the conversion weight for each age-gender 

sub-component of EO is approximately equal to the conversion rate for each age-gender 

sub-component of E. 
66 

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 (1) full-employment values for E (including U.S. armed forces), (2) average hours 

worked per week, and (3) productivity. Full-employment values for E are derived by solving 

USEMP under full-employment conditions, while the full-employment values for the other 

variables (average hours worked and productivity) are set by assumption. Projected real GDP is 

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

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

rate in PGDP is set by assumptions. 

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

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

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

compensation (WSSY) is defined as the sum of WSS and Y. The total compensation ratio 
67 

(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. 
68 

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. 
69 

 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: the ratio of 

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) 
70 

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 

non-agriculture self-employment to total employment. Thus, the aggregate non-agriculture 

SEPR is dependent on the projected distribution of employment by age and gender. All nonagriculture SEPRs by age and gender are dependent on the RTP. Increases in the RTP lead to 

decreases in the SEPRs. For 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 

non-agriculture. 

From 1970 to 2005, the level of EU fell from about 0.5 to 0.03 million in the agriculture 

sector and from about 0.5 to 0.09 million in the nonagriculture sector. For projections, the 

levels of EU by age and 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) 
71 

The Trustees set the ultimate annual growth rate for RWSSY. For the short-range period, 

total WSS, WSD, and Y are aggregated from sector components. Total GDP, WSS, and 

WSD are divided into the farm and nonfarm sectors. The nonfarm sector is further separated 

into the government and government enterprises, households, non-profit institutions, and 

residual (private nonfarm business excluding government enterprises (PBNFXGE)) sectors. 

Total Y is divided into the farm and residual (i.e., PBNFXGE) sectors. 

The methodology used to estimate GDP, WSS, WSD, and Y differs by sector. 

Farm - Nominal GDP is the product of real GDP and the farm price deflator. Real farm GDP 

is projected from estimates of real farm per capita output. EA is projected from estimates of 

farm productivity. EAW is projected to continue its historical increase relative to EA. Farm 

compensation (WSSPF) is the product of estimates for average farm compensation 

(AWSSPF) and EAW, while farm proprietor income (YF) is the product of estimates of 

average farm proprietor income (AYF) and EAS. AYF is projected based, in part, on the 

growth in average compensation in the private sector. 

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) 
72 

Y is disaggregated to the farm and PBNFXGE sectors. In the PBNFXGE sector, the Y is 

projected as a ratio to GDP in the sector. In the farm sector, Y is projected based in part on 

the growth in average compensation in the private sector. 

Equation 2.2.10 - Earnings Ratio (RWSD) 

In the NIPA, the difference between 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 

year-by-year basis over the entire 75-year projection horizon due to projected increases in 

employer contributions to employee group health insurance premiums (ECEGHIP) and 

pensions. ECEGHIP is projected by the Center for Medicare and Medicaid Services (CMS) 

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. 
73 

2.3. OASDI COVERED EMPLOYMENT AND EARNINGS (COV) 

2.3.a. Overview 

Total at-any-time employment (TE) is defined as the sum of total OASDI covered employment 

(TCE) and total noncovered employment (NCE). TCE can be decomposed to workers who only 

report OASDI covered self-employed earnings (SEO) and to wage and salary workers who 

report some OASDI covered wages (WSW). Combination workers (CMB_TOT) are those who 

have both OASDI covered wages and self-employed income. Workers with some selfemployment income (CSW) are the sum of SEO and CMB_TOT. 

Some of these concepts can be rearranged. The total employed ratio (RTE) is defined as the ratio 

of TE to the sum of EW, ES, and EDMIL, while the combination employment ratio (RCMB) is 

defined as the ratio of CMB_TOT to WSW. 

COV projects annual values for TE and the principle measures of OASDI covered employment. 

Equations 2.3.1 through 2.3.9 outline the overall structure and solution sequence used to project 

these concepts. 

RTE = RTE(·) (2.3.1) 

TE = RTE * (EW + ES + EDMIL) (2.3.2) 

NCE = NCE(·) (2.3.3) 

TCE = TE - NCE (2.3.4) 

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) 
74 

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.) 
75 

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. 
76 

 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 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 

hard-copy and, more recently, electronic formats obtained from OS. The data 

currently used are the total number of workers with OASDI taxable earnings, total 

number of workers with OASDI self-employed taxable earnings, distribution of 

number of HI workers by wage intervals, distribution of number of OASDI workers 

by wage intervals, number of persons with OASDI taxable wages, number of persons 

with HI taxable wages, number of persons with OASDI taxable self-employment, and 

number of persons with HI taxable self-employment. 

 Data obtained from the Quarterly Trust Fund Letter, received from Office of 

Financial Policy and Operations (OFPO). Data currently used are OASDI and HI 
77 

taxable wages accumulated from all Forms 941 and W-2 to date, and changes in selfemployment earnings and self-reported tips since the prior Letter. These data are for 

years 1978 to the most recent year available. 

 Data obtained from OS on amounts of OASDI taxable wages on the Earnings 

Suspense File for 1937 through the second year prior to the current Trustees Report 

year. The data are used in estimating total OASDI covered employment. 

2.3.c. Development of Output

Equation 2.3.1 - Ratio of Total Employment (RTE) 

Since CPS data are only available for those aged 16 and over, RTEs could not be constructed 

or projected. For those aged 9 and under, we used covered population ratios (CPR), defined 

as the ratio of OASDI covered employment to the Social Security area population. CPRs for 

those aged 9 and younger are disaggregated by single-year of age and gender. Projected 

values for CPRs by age and gender are set to their latest historical levels. Thus, the aggregate 

CPR for those aged 9 and under is dependent on the projected age-gender distribution of the 

population. For those aged 10-15, we used total population ratios (TPR), defined as the ratio 

of TE to the Social Security area population. The TPRs are disaggregated by gender and age, 

including those aged 10-13 and 14-15. The TPR for males aged 10-13 is projected to remain 

constant at its latest historical level. The TPR for females aged 10-13, and the TPRs for 

males and females aged 14-15, are dependent on the RTP. An increase in the RTP leads to an 

increase in the TPRs. 

The RTE for those aged 16 and over is defined as the ratio of TE to the sum of EW and ES 

(or alternatively, E less EU) and EDMIL. The RTE is disaggregated by gender and age, 

including those aged 16-17, 18-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 

60-64, 65-69, and 70 and over. Thus, COV contains 26 RTE equations, 13 for males, and 13 

for females. 

The aggregate RTE for those aged 16 and over is dependent on the projected age-gender 

distribution of employment. Each disaggregated RTE is dependent on its corresponding 

age-gender employment ratio. The employment ratio is roughly defined as the ratio of E to 

N. Increases in the employment ratio lead to decreases in the RTEs. 

Equation 2.3.3 - Non-Covered Employment (NCE) 

NCE is disaggregated by age and 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. 
78 

Federal Civilian Government - All Federal civilian employees are HI (i.e., Medicare) 

covered. All Federal Civilian employees hired in January 1984 and later are covered under 

the Federal Employees Retirement System (FERS) and are OASDI covered. Employees hired 

before January 1984 are covered under the Civil Service Retirement System (CSRS) and are 

not OASDI covered. This “closed group” of relatively older CSRS employees is projected to 

fall to near zero by 2030. 

State and Local Government - In 1983, about 70 percent of State and Local Government 

(S&L) employment and wages were covered under OASDI and HI. Beginning April 1986, 

all newly hired S&L employees were covered under HI. Beginning January 1990, all S&L 

employees not under an S&L retirement system were covered under OASDHI. 

By 2002, about 30 and 10 percent of S&L employment (and 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. 
79 

Underground Economy Workers - Set to the at-any-time employed in the other immigrant 

population who have no reported earnings and therefore are part of the underground 

economy (i.e., TEO_UND). 

Equation 2.3.5 - Self-Employed Only (SEO) 

SEO is projected to grow at the same rate as ES. 

Equation 2.3.7 - Ratio of Combination Workers (RCMB) 

Total CMB_TOT can be separated into two groups depending on whether they have OASDI 

covered wages under or over the TAXMAX. CMB_TOT with covered wages under the 

TAXMAX have taxable wages and self-employed income. CMB_TOT with covered wages 

over the TAXMAX have taxable wages only. CMB_TOT with covered wages over the 

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. 
80 

S&L government - The RWSC for the S&L government sector is projected to remain 

constant at its latest actual historical level. 

Private - The private sector is separated into sub-sectors including private households, farm, 

railroad, tips, and a residual private “base”. The RWSCs for the private household and farm 

sub-sectors are projected to remain constant at their latest actual historical levels. By 

definition, the RWSCs for the railroad and tips sub-sectors are projected to remain constant 

at 0.0 and 1.0, respectively. The projected RWSC for the private base sub-sector is dependent 

on the ratio of EO wage workers in the private base sub-sector who are covered under the 

OASDI program to all EO wage workers in the private base sub-sector. We assume that all of 

EO will be wage workers employed in the private residual base sub-sector of the economy 

and that the proportion of EO that is covered under the OASDI program will decrease. 

Therefore, we assume that the RWSC for the private residual base sector will also decrease. 

Equation 2.3.12 - Ratio of Covered Self-Employed Earnings (RCSE) 

The RCSE is projected to remain constant at its latest actual historical level. 

Equation 2.3.17 - Average Wage Index (AWI) 

The growth in the AWI is projected to be equal to the growth in an economy-wide average 

wage (ACWC) defined as the ratio of WSD to total wage workers (covered and noncovered). Total wage workers are projected as the sum of WSW and the various groups of 

non-covered wage workers discussed above. 

Equation 2.3.18 - OASDI Taxable Maximum (TAXMAX) 

By law, the growth in the AWI is used to increase the TAXMAX. 
81 

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) 
82 

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 
83 

1951 to the third year prior to the current Trustees Report year. The data are used for 

comparison of OASDI taxable earnings from other sources. 

 Data obtained from quarterly IRS Form 941 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 

hard-copy and, more recently, electronic formats obtained from OS. The data 

currently used are the total number of workers with OASDI taxable earnings, total 

number of workers with OASDI self-employed taxable earnings, distribution of 

number of HI workers by wage intervals, distribution of number of OASDI workers 

by wage intervals, number of persons with OASDI taxable wages, number of persons 

with HI taxable wages, number of persons with OASDI taxable self-employment, 

number of persons with HI taxable self-employment, number of workers with singleemployer excess wages, and number of workers with multi-employer excess wages. 

 Data obtained from the Quarterly Trust Fund Letter, received from OFPO. Data 

currently used are OASDI and HI taxable wages accumulated from all Forms 941 and 

W-2 to date, and changes in self-employment earnings and self-reported tips since the 

prior Letter. These data are for 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 
84 

ECSEO Number of OASDI covered self-employed only workers 

(millions), 1971 

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 
85 

ECWSODM1619_MEF Number of OASDI covered wage workers on the MEF, male 

16 to 19 years old (millions), 1990 

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 selfemployed 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 
86 

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 

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 
87 

 

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 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. 
88 

 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. 

 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 
89 

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. 

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 
90 

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 

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 self-employment 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 

model-computed 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 shortrange 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). 
91 

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. 

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. 
92 

RWTEEs are also projected for various sub-aggregates including Federal Civilian employees 

under FERS and CSRS, Federal Civilian employees under CSRS only, S&L employees 

covered under OASDI, S&L employees covered under HI only, U.S. armed forces, and 

agriculture. The RWTEE for each sub-aggregate is dependent only on its sub-aggregate 

RELMAX, that is, the ratio of the TAXMAX to the sub-aggregate’s average covered wage. 

Equation 2.4.3 - Multi-Employer Refund Wage Ratio (RMER) 

The RMER is functionally related to the RWTEE. As RWTEE approaches one, then RMER 

approaches zero. In between the limit values, RMER is positive. Given the present position 

of RWTEE and RMER on the function, a projected decline in RWTEE leads to an increase in 

RMER. 

The projected RMER is also dependent on RU. An increase in RU leads to a decrease in 

RMER. 

Equation 2.4.6 - Self-Employed Net Income Taxable Ratio (RSET) 

The RSET is disaggregated by type of self-employed worker, SEO and CMB_TOT. 

SEO - The RSET is dependent on the distribution of self-employed workers by income 

interval and a RELMAX. The projected distribution of self-employed workers by income 

interval is set to the 1996 distribution. The RELMAX is defined here as the ratio of the 

TAXMAX to the average income for SEO. A higher RELMAX leads to a higher RSET. 

CMB_TOT - Taxable self-employed net income for CMB_TOT is projected in two steps. 

First, a taxable earnings (wages and self-employed income) ratio for CMB_TOT is projected 

based on the 1996 distribution and a RELMAX defined as the ratio of the TAXMAX to the 

average covered earnings. The projected level of taxable earnings for CMB_TOT is the 

product of the estimated taxable earnings ratio for CMB_TOT and their covered earnings. 

Second, a taxable wage ratio for CMB_TOT is projected based on a RELMAX defined as the 

ratio of the TAXMAX to the average covered wage for CMB_TOT. The projected level of 

taxable wages for CMB_TOT is the product of the estimated taxable wage ratio for 

CMB_TOT and their covered wages. 

Taxable self-employed net income for CMB_TOT is obtained by subtracting taxable wages 

from taxable earnings for CMB_TOT. 

A “combined” RSET is calculated as the ratio of taxable self-employed net income for SEO 

and CMB_TOT to CSE_TOT. As with the RWTEE, the combined RSET is adjusted over the 

short-range period due to other factors (i.e., RTP, the age-gender distribution of workers, and 

a trend). The effect of the other factors are taken from RWTEE and “scaled.” That is, RSET 
93 

is adjusted by a percent effect (as opposed to percentage point) that is equal to the percent 

change in RWTEE due to changes in these other factors. 

It is important to note that while the RWTEE is held constant after the short-range period, the 

RSETs for self-employed workers are not. After the short-range period, the projected RSETs 

for SEO and CMB_TOT continue to be dependent on their respective RELMAXs. Since by 

law the TAXMAX grows at the rate of the AWI and since ACSE is assumed to grow faster 

than the ACW (since only ACW declines with the growth in fringe benefits), the RELMAXs 

for self-employed workers decline over the long-range period while the RELMAX for wage 

workers is approximately constant. Hence, the RSETs for SEO and CMB_TOT are projected 

to decline over the long-range period while the RWTEE is held constant. 

Equation 2.4.11 - Quarterly Wage Tax Liabilities (WTLQ) 

Total WTLQ is summed from sector components that include Federal Civilian, Federal 

Military, S&L, Private Household, Farm, Self-reported Tips, and residual Private Nonfarm. 

Sector WTLQs are determined by computing ratios of quarterly to annual liabilities for each 

quarter. These are calculated for the Private Nonfarm, S&L, Federal Civilian and Military 

sectors. Each is dependent on the quarterly distribution of WSD and the RWTEE for the 

relevant sector, and on a payday adjustment that takes into account the actual number of 

paydays that fall into a particular calendar quarter. WTLQ ratios 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 SelfReported Tips). For the Federal Civilian and Military sectors, the WTLQC are set equal to 

their respective WTLQ since tax liabilities for the two sectors are 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 
94 

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 selfemployed workers to deposit estimated tax liabilities four times a year (January, April, June, 

and September). 

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. 
95 

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 
97 

RM2024 

 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) 
98 

 Sum Sq 14.6843 Std Err 0.3441 LHS Mean 0.0130 

 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 
99 

 diff(rm5559) 

 = - 25.9031 * diff(rtp) - 11.4442 * diff(rtp)[-1] 

 (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 
100 

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 

 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 
101 

 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 

 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) 
102 

 - 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 

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 
103 

 Date: 23 OCT 2009 

 diff(rf5559) 

 = - 2.46651 * diff(rtp) - 4.81906 * diff(rtp)[-1] 

 (0.39811) (0.73342) 

 - 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 
104 

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 

 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 
105 

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) 

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 
106 

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 

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) 

 (NOTE: "RNLM" OR "RNLF" IN SOME EQUATIONS BELOW REFERS TO "NOT IN THE LABOR FORCE RATE" FOR 

 MALES OR FEMALES. THE LETTER FOLLOWING REFERS TO THE REASON FOR NOT BEING IN THE LABOR 

 FORCE.) 

MALE LFPR EQUATIONS 
107 

AGE 16 TO 19 

RNLM1617_S+RNLM1617_O2+RNLM1617_H = - 0.78720 + 0.01330 * YEAR + 0.00301 * (RM1617 + RM1617.1)/2 

 RNLM1617_S 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm1617_s+rnlm1617_o2+rnlm1617_h-(0.00301*(rm1617+rm1617.1)/2) 

 = 0.01330 * year - 0.78720 

 (17.2413) (10.0980)

 Sum Sq 0.0022 Std Err 0.0129 LHS Mean 0.5556 

 R Sq 0.9581 R Bar Sq 0.9549 F 1, 13 297.261 

 D.W.( 1) 0.8599 D.W.( 2) 1.9420 

PM1617= 0.98298 - B2_2064DI * B1_M1617D * 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) 

 PM1617_AADJ 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 8 NOV 2009 

 pm1617_aadj+b2_2064di*b1_m1617d*rm1617di+rnlm1617_s+rnlm1617_h+ 

 rnlm1617_o2 

 = 0.98298 

 (1624.33) 

 Sum Sq 0.0001 Std Err 0.0023 LHS Mean 0.9830 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 0.8018 D.W.( 2) 0.9743 

RNLM1819_S+RNLM1819_O2+RNLM1819_H = - 0.50476 + 0.00764 * YEAR + 0.00626 * (RM1819 + RM1819.1)/2 

RNLM1819_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm1819_s+rnlm1819_o2+rnlm1819_h 

 = 0.00626 * (rm1819+rm1819.1)/2 + 0.00764 * year - 0.50476 

 (4.95266) (16.0633) (10.0266) 

 Sum Sq 0.0008 Std Err 0.0079 LHS Mean 0.3660 

 R Sq 0.9615 R Bar Sq 0.9551 F 2, 12 149.923 

 D.W.( 1) 2.7528 D.W.( 2) 1.5413 

PM1819= 0.97979 - B2_2064DI * B1_M1819D * RM1819DI - (- 0.50476 + 0.00764 * TR_PM1819 + 0.00626 * MOVAVG(5,RM1819)) 

 PM1819_AADJ 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 8 NOV 2009 

 pm1819_aadj+b2_2064di*b1_m1819d*rm1819di+rnlm1819_s+rnlm1819_h+ 

 rnlm1819_o2 

 = 0.97979 

 (1394.51) 
108 

 Sum Sq 0.0001 Std Err 0.0027 LHS Mean 0.9798 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 0.9376 D.W.( 2) 1.8283

AGE 20 TO 54 

NEVER MARRIED 

RNLM2024NM_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2024nm_s 

 = 0.00225 * year - 0.08557 

 (9.38645) (3.52616) 

 Sum Sq 0.0002 Std Err 0.0040 LHS Mean 0.1420 

 R Sq 0.8714 R Bar Sq 0.8615 F 1, 13 88.1054 

 D.W.( 1) 1.8852 D.W.( 2) 2.0274 

 

PM2024NM_P = 1.04005 - 0.00523 - 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 - B2_2064DI * B1_M2024D * RM2024DI 

PLM2024NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm2024nm+b2_2064di*b1_m2024d*rm2024di+0.00225*year + (0.00201*(rm2024 

 +rm2024.1)/2) 

 = - 0.00523 * dum102108 + 1.04005 

 (2.84172) (827.809) 

 Sum Sq 0.0002 Std Err 0.0036 LHS Mean 1.0376 

 R Sq 0.3832 R Bar Sq 0.3357 F 1, 13 8.0754 

 D.W.( 1) 2.6188 D.W.( 2) 1.4507 

RNLM2529NM_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2529nm_s 

 = 0.00070 * year - 0.02955 

 (3.84846) (1.60457) 

 Sum Sq 0.0001 Std Err 0.0030 LHS Mean 0.0413 

 R Sq 0.5326 R Bar Sq 0.4966 F 1, 13 14.8107 

 D.W.( 1) 1.9279 D.W.( 2) 1.5364 

PM2529NM_P = 0.97919 - 0.00809 - 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 - B2_2064DI * B1_M2534D * RM2529DI 

 PLM2529NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 
109 

 plm2529nm+b2_2064di*b1_m2534d*rm2529di+0.00070*year+(0.00185*(rm2529 

 +rm2529.1)/2) 

 = - 0.00809 * dum102108 + 0.97919 

 (3.46642) (614.240) 

 Sum Sq 0.0003 Std Err 0.0045 LHS Mean 0.9754 

 R Sq 0.4803 R Bar Sq 0.4404 F 1, 13 12.0161 

 D.W.( 1) 2.0763 D.W.( 2) 1.7656 

 

PM3034NM_P = 0.90427 - 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 - 0.00014 * RM3034.4 + 

0.00001 * RM3034.5 - B2_2064DI * B1_M2534D * RM3034DI 

PLM3034NM 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm3034nm+b2_2064di*b1_m2534d*rm3034di+(0.00210*(rm3034+rm3034.1)/2) 

 = 0.90427 

 (775.187) 

 Sum Sq 0.0003 Std Err 0.0045 LHS Mean 0.9043 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.1558 D.W.( 2) 1.7778 

 

PM3539NM_P = 0.86825 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 

0.00015 * RM3539.5 - B2_2064DI * B1_M3544D * RM3539DI 

PLM3539NM 

 ANNUAL data for 15 periods from 1994 to 2008 

Date: 7 NOV 2009 

 plm3539nm+b2_2064di*b1_m3544d*rm3539di+(0.00087*(rm3539+rm3539.1)/2) 

 = 0.86825 

 (332.008) 

 Sum Sq 0.0014 Std Err 0.0101 LHS Mean 0.8683 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 0.6401 D.W.( 2) 0.6952 

 

PM4044NM_P = 0.83977 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 

0.00031 * RM4044.5 - B2_2064DI * B1_M3544D * RM4044DI 

 PLM4044NM 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm4044nm+b2_2064di*b1_m3544d*rm4044di+(0.00123*(rm4044+rm4044.1)/2) 

 = 0.83977 

 (335.553) 

 Sum Sq 0.0013 Std Err 0.0097 LHS Mean 0.8398 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.4785 D.W.( 2) 1.6384 

 

PM4549NM_P = 0.81116 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 

0.00040 * RM4549.5 - B2_2064DI * B1_M4554D * RM4549DI 

PLM4549NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 
110 

 Date: 7 NOV 2009 

 plm4549nm+b2_2064di*b1_m4554d*rm4549di+(0.00195*(rm4549+rm4549.1)/2) 

 = 0.81116 

 (257.658) 

 Sum Sq 0.0021 Std Err 0.0122 LHS Mean 0.8112 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.5984 D.W.( 2) 2.0633 

 

PM5054NM_P = 0.77540 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 

0.00139 * RM5054.5 - B2_2064DI * B1_M4554D * RM5054DI 

PLM5054NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm5054nm+b2_2064di*b1_m4554d*rm5054di+(0.00128*(rm5054+rm5054.1)/2) 

 = 0.77540 

 (166.942) 

 Sum Sq 0.0045 Std Err 0.0180 LHS Mean 0.7754 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.1198 D.W.( 2) 2.1480 

 

AGE 20 TO 54 

MARRIED, SPOUSE PRESENT 

RNLM2024MS_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2024ms_s 

 = 0.00069 * year - 0.04629 

 (3.01675) (2.00334) 

 Sum Sq 0.0002 Std Err 0.0038 LHS Mean 0.0234 

 R Sq 0.4118 R Bar Sq 0.3665 F 1, 13 9.1008 

 D.W.( 1) 2.3964 D.W.( 2) 1.7089 

 

PM2024MS_P = 1.03184 - 0.00733 - 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 - B2_2064DI * B1_M2024D * RM2024DI 

PLM2024MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm2024ms+b2_2064di*b1_m2024d*rm2024di+0.00069*year+(0.00201*(rm2024 

 +rm2024.1)/2) 

 = - 0.00733 * dum102108 + 1.03184 

 (3.07932) (634.159) 

 Sum Sq 0.0003 Std Err 0.0046 LHS Mean 1.0284 

 R Sq 0.4218 R Bar Sq 0.3773 F 1, 13 9.4822 

 D.W.( 1) 1.5789 D.W.( 2) 2.1030 
111 

 

 RNLM2529MS_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2529ms_s 

 = 0.00025 * year - 0.01064 

 (1.99841) (0.85842) 

 Sum Sq 0.0001 Std Err 0.0021 LHS Mean 0.0141 

 R Sq 0.2350 R Bar Sq 0.1762 F 1, 13 3.9937 

 D.W.( 1) 2.3603 D.W.( 2) 1.0595 

 

PM2529MS_P = 1.00110 - 0.00498 - 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 - B2_2064DI * B1_M2534D * RM2529DI 

PLM2529MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm2529ms+b2_2064di*b1_m2534d*rm2529di+0.00025*year+(0.00185*(rm2529 

 +rm2529.1)/2) 

 = - 0.00498 * dum102108 + 1.00110 

 (2.59558) (764.261) 

 Sum Sq 0.0002 Std Err 0.0037 LHS Mean 0.9988 

 R Sq 0.3413 R Bar Sq 0.2907 F 1, 13 6.7370 

 D.W.( 1) 2.3980 D.W.( 2) 1.9950 

 

PM3034MS_P = 0.97120 + 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 - B2_2064DI * B1_M2534D * RM3034DI 

PLM3034MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm3034ms+b2_2064di*b1_m2534d*rm3034di+(0.00210*(rm3034+rm3034.1)/2) 

 = 0.16457 * 1/(year-85) + 0.97120 

 (5.86039) (489.209) 

 Sum Sq 0.0001 Std Err 0.0022 LHS Mean 0.9824 

 R Sq 0.7254 R Bar Sq 0.7043 F 1, 13 34.3441 

 D.W.( 1) 1.8302 D.W.( 2) 2.8385 

 

PM3539MS_P = 0.98068 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 

0.00015 * RM3539.5 - B2_2064DI * B1_M3544D * RM3539DI 

PLM3539MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 
112 

 plm3539ms+b2_2064di*b1_m3544d*rm3539di+(0.00087*(rm3539+rm3539.1)/2) 

 = 0.98068 

 (929.829) 

 Sum Sq 0.0002 Std Err 0.0041 LHS Mean 0.9807 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 0.2877 D.W.( 2) 0.5705 

 

PM4044MS_P = 0.98250 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 

0.00031 * RM4044.5 - B2_2064DI * B1_M3544D * RM4044DI 

PLM4044MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm4044ms+b2_2064di*b1_m3544d*rm4044di+(0.00123*(rm4044+rm4044.1)/2) 

 = 0.98250 

 (1655.38) 

 Sum Sq 0.0001 Std Err 0.0023 LHS Mean 0.9825 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 0.8575 D.W.( 2) 1.5758 

 

PM4549MS_P = 0.98115 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 

0.00040 * RM4549.5 - B2_2064DI * B1_M4554D * RM4549DI 

PLM4549MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm4549ms+b2_2064di*b1_m4554d*rm4549di+(0.00195*(rm4549+rm4549.1)/2) 

 = 0.98115 

 (1530.80) 

 Sum Sq 0.0001 Std Err 0.0025 LHS Mean 0.9811 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.0766 D.W.( 2) 2.1919 

 

PM5054MS_P = 0.94484 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 

0.00139 * RM5054.5 + 0.09796 * (RF5054CU6+RF5054C6O) - B2_2064DI * B1_M4554D * RM5054DI 

PLM5054MS 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm5054ms+b2_2064di*b1_m4554d*rm5054di+(0.00128*(rm5054+rm5054.1)/2) 

 = 0.09796 * rf5054cu6+rf5054c617 + 0.94484 

 (2.44491) (136.906) 

 Sum Sq 0.0002 Std Err 0.0039 LHS Mean 0.9615 

 R Sq 0.3150 R Bar Sq 0.2623 F 1, 13 5.9776 

 D.W.( 1) 1.5461 D.W.( 2) 2.4174 
113 

 

AGE 20 TO 54 

MARRIED, SPOUSE ABSENT 

RNLM2024MA_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2024ma_s 

 = 0.00232 * year - 0.19022 

 (3.44223) (2.78908) 

 Sum Sq 0.0017 Std Err 0.0113 LHS Mean 0.0443 

 R Sq 0.4768 R Bar Sq 0.4366 F 1, 13 11.8489 

 D.W.( 1) 2.1390 D.W.( 2) 2.0340 

 

PM2024MA_P = 1.14087 - 0.01412 - 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 - B2_2064DI * B1_M2024D * RM2024DI 

PLM2024MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm2024ma+b2_2064di*b1_m2024d*rm2024di+0.00232*year+(0.00201*(rm2024 

 +rm2024.1)/2) 

 = - 0.01412 * dum102108 + 1.14087 

 (1.46970) (173.836) 

 Sum Sq 0.0045 Std Err 0.0186 LHS Mean 1.1343 

 R Sq 0.1425 R Bar Sq 0.0765 F 1, 13 2.1600 

 D.W.( 1) 1.4227 D.W.( 2) 1.9550 

 

RNLM2529MA_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlm2529ma_s 

 = 0.00051 * year - 0.03080 

 (1.65087) (0.98569) 

 Sum Sq 0.0003 Std Err 0.0052 LHS Mean 0.0207 

 R Sq 0.1733 R Bar Sq 0.1097 F 1, 13 2.7254 

 D.W.( 1) 1.5349 D.W.( 2) 2.1177 

 

PM2529MA_P = 0.98602 - 0.00788 - 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- B2_2064DI * B1_M2534D * RM2529DI 

PLM2529MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 
114 

 plm2529ma+b2_2064di*b1_m2534d*rm2529di+0.00051*year+(0.00185*(rm2529 

 +rm2529.1)/2) 

 = - 0.00788 * dum102108 + 0.98602 

 (1.97520) (361.786) 

 Sum Sq 0.0008 Std Err 0.0077 LHS Mean 0.9823 

 R Sq 0.2308 R Bar Sq 0.1717 F 1, 13 3.9014 

 D.W.( 1) 1.4431 D.W.( 2) 2.2441 

 

PM3034MA_P = 0.93933 - 0.00046 * RM3034 - 0.00061 * RM3034.1 - 0.00054 * RM3034.2 - 0.00036 * RM3034.3 - 0.00014 * RM3034.4 + 

0.00001 * RM3034.5 - B2_2064DI * B1_M2534D * RM3034DI 

PLM3034MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm3034ma+b2_2064di*b1_m2534d*rm3034di+(0.00210*(rm3034+rm3034.1)/2) 

 = 0.93933 

 (449.774) 

 Sum Sq 0.0009 Std Err 0.0081 LHS Mean 0.9393 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 0.9470 D.W.( 2) 1.2630 

 

PM3539MA_P = 0.92354 - 0.00004 * RM3539 - 0.00010 * RM3539.1 - 0.00016 * RM3539.2 - 0.00021 * RM3539.3 - 0.00021 * RM3539.4 - 

0.00015 * RM3539.5 - B2_2064DI * B1_M3544D * RM3539DI 

PLM3539MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm3539ma+b2_2064di*b1_m3544d*rm3539di+(0.00087*(rm3539+rm3539.1)/2) 

 = 0.92354 

 (538.814) 

 Sum Sq 0.0006 Std Err 0.0066 LHS Mean 0.9235 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.6678 D.W.( 2) 1.7279 

 

PM4044MA_P = 0.91512 - 0.00057 * RM4044 - 0.00066 * RM4044.1 - 0.00044 * RM4044.2 - 0.00009 * RM4044.3 + 0.00022 * RM4044.4 + 

0.00031 * RM4044.5 - B2_2064DI * B1_M3544D * RM4044DI 

PLM4044MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm4044ma+b2_2064di*b1_m3544d*rm4044di+(0.00123*(rm4044+rm4044.1)/2) 

 = 0.91512 

 (721.479) 

 Sum Sq 0.0003 Std Err 0.0049 LHS Mean 0.9151 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 2.3251 D.W.( 2) 2.1801 

 
115 

PM4549MA_P = 0.89473 - 0.00002 * RM4549 - 0.00016 * RM4549.1 - 0.00034 * RM4549.2 - 0.00049 * RM4549.3 - 0.00054 * RM4549.4 - 

0.00040 * RM4549.5 - B2_2064DI * B1_M4554D * RM4549DI 

PLM4549MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm4549ma+b2_2064di*b1_m4554d*rm4549di+(0.00195*(rm4549+rm4549.1)/2) 

 = 0.89473 

 (655.751) 

 Sum Sq 0.0004 Std Err 0.0053 LHS Mean 0.8947 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.5173 D.W.( 2) 1.7125 

 

 

PM5054MA_P = 0.84912 + 0.00112 * RM5054 + 0.00103 * RM5054.1 + 0.00023 * RM5054.2 - 0.00078 * RM5054.3 - 0.00149 * RM5054.4 - 

0.00139 * RM5054.5 - B2_2064DI * B1_M4554D * RM5054DI 

PLM5054MA 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 plm5054ma+b2_2064di*b1_m4554d*rm5054di+(0.00128*(rm5054+rm5054.1)/2) 

 = 0.84912 

 (202.943) 

 Sum Sq 0.0037 Std Err 0.0162 LHS Mean 0.8491 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 0.8062 D.W.( 2) 1.4293 

AGE 20 TO 54 

LABOR FORCE PARTICIPATION RATES (PRELIMINARY) 

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 

LABOR FORCE PARTICIPATION RATES 

PM2024 = PM2024_P 

PM2529 = PM2529_P 

PM3034 = PM3034_P 

PM3539 = PM3539_P 

PM4044 = PM4044_P 

PM4549 = PM4549_P 

PM5054 = PM5054_P 

LABOR FORCE PARTICIPATION RATES BY MARITAL STATUS 

PM2024NM = PM2024NM_P * PM2024 / PM2024_P 

PM2529NM = PM2529NM_P * PM2529 / PM2529_P 
116 

PM3034NM = PM3034NM_P * PM3034 / PM3034_P 

PM3539NM = PM3539NM_P * PM3539 / PM3539_P 

PM4044NM = PM4044NM_P * PM4044 / PM4044_P 

PM4549NM = PM4549NM_P * PM4549 / PM4549_P 

PM5054NM = PM5054NM_P * PM5054 / PM5054_P 

PM2024MS = PM2024MS_P * PM2024 / PM2024_P 

PM2529MS = PM2529MS_P * PM2529 / PM2529_P 

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 = - 0.76902 - B2_2064DI * B1_M5559D * 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 

PM55 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm55_adj-(-b1_m5559d*b2_2064di*rm55di+pm55e_de+d09a:pm55_dm-0.00297* 

 (rm5559+rm5559.1)/2) 

 = - 0.76902 

 (290.186) 

 Sum Sq 0.0015 Std Err 0.0103 LHS Mean -0.7690 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.5153 D.W.( 2) 1.9558 

 

PM56 = - 0.76098 - B2_2064DI * B1_M5559D * 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 

PM56 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm56_adj-(-b1_m5559d*b2_2064di*rm56di+pm56e_de+d09a:pm56_dm-0.00297* 

 (rm5559+rm5559.1)/2) 

 = - 0.76098 

 (354.432) 

 Sum Sq 0.0010 Std Err 0.0083 LHS Mean -0.7610 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 0.9629 D.W.( 2) 1.0276 

 
117 

PM57 = - 0.71065 - B2_2064DI * B1_M5559D * 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 

PM57 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm57_adj-(-b1_m5559d*b2_2064di*rm57di+pm57e_de+d09a:pm57_dm-0.00297* 

(rm5559+rm5559.1)/2) 

 = - 0.71065 

 (310.143) 

 Sum Sq 0.0011 Std Err 0.0089 LHS Mean -0.7107 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.6000 D.W.( 2) 1.5177 

 

PM58 = - 0.69412 - B2_2064DI * B1_M5559D * 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 

PM58 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm58_adj-(-b1_m5559d*b2_2064di*rm58di+pm58e_de+d09a:pm58_dm-0.00297* 

 (rm5559+rm5559.1)/2) 

 = - 0.69412 

 (253.081) 

 Sum Sq 0.0016 Std Err 0.0106 LHS Mean -0.6941 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 2.4020 D.W.( 2) 1.1615 

PM59 = - 0.60153 - B2_2064DI * B1_M5559D * 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 

PM59 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm59_adj-(-b1_m5559d*b2_2064di*rm59di+pm59e_de+d09a:pm59_dm-0.00297* 

 (rm5559+rm5559.1)/2) 

 = - 0.60153 

 (198.600) 

 Sum Sq 0.0019 Std Err 0.0117 LHS Mean -0.6015 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.3589 D.W.( 2) 1.9976 

PM60 = - 0.58858 - B2_2064DI * B1_M6064D * 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 

PM60 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 
118 

 Date: 18 NOV 2009 

 pm60_adj-(-b1_m6064d*b2_2064di*rm60di+pm60e_de+d09a:pm60_dm-0.00598* 

 (rm6064+rm6064.1)/2) 

 = 0.01566 * pf58_adj - 0.58858 

 (0.20056) (12.4405) 

 Sum Sq 0.0012 Std Err 0.0097 LHS Mean -0.5791 

 R Sq 0.0031 R Bar Sq -0.0736 F 1, 13 0.0402 

 D.W.( 1) 2.4571 D.W.( 2) 1.6803 

PM61 = - 0.55646 - B2_2064DI * B1_M6064D * 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 

PM61 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm61_adj-(-b1_m6064d*b2_2064di*rm61di+pm61e_de+d09a:pm61_dm-0.00598* 

 (rm6064+rm6064.1)/2) 

 = 0.08544 * pf59_adj - 0.55646 

 (0.91866) (10.4384) 

 Sum Sq 0.0017 Std Err 0.0116 LHS Mean -0.5076 

 R Sq 0.0610 R Bar Sq -0.0113 F 1, 13 0.8439 

 D.W.( 1) 1.5689 D.W.( 2) 1.9879 

AGE 62 TO 74 

 PM62 = 0.26329 * PF60 - 0.29161 - B2_2064DI * B1_M6064D * RM62DI + PM62E_DE + PM62_DM + 0.00203 * RM6064 + 0.00160 * 

RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * RM6064.5 - 0.60 * RRADJ_M62 - 0.02 * 

POT_ET_TXRT_62 

PM62 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm62_adj-(-b1_m6064d*b2_2064di*rm62di+pm62e_de+d09a:pm62_dm-0.00598* 

 (rm6064+rm6064.1)/2-0.60*rradj_m62-0.02*pot_et_txrt_62) 

 = 0.26329 * pf60_adj - 0.29161 

 (3.03035) (6.36388) 

 Sum Sq 0.0021 Std Err 0.0127 LHS Mean -0.1531 

 R Sq 0.4140 R Bar Sq 0.3689 F 1, 13 9.1830 

 D.W.( 1) 1.6709 D.W.( 2) 2.6665 

 PM63 = 0.40940 * PF61 - 0.29495 - B2_2064DI * B1_M6064D * RM63DI + PM63E_DE + PM63_DM + 0.00203 * RM6064 + 0.00160 * 

RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * RM6064.5 - 0.55 * RRADJ_M63 - 0.02 * 

POT_ET_TXRT_63 

PM63 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm63_adj-(-b1_m6064d*b2_2064di*rm63di+pm63e_de+d09a:pm63_dm-0.00598* 

 (rm6064+rm6064.1)/2-0.55*rradj_m63-0.02*pot_et_txrt_63) 
119 

 = 0.40940 * pf61_adj - 0.29495 

 (4.33250) (6.38037) 

 Sum Sq 0.0027 Std Err 0.0143 LHS Mean -0.0953 

 R Sq 0.5908 R Bar Sq 0.5593 F 1, 13 18.7706 

 D.W.( 1) 2.3641 D.W.( 2) 1.4502 

 PM64 = 0.47933 * PF62 - 0.22665 - B2_2064DI * B1_M6064D * RM64DI + PM64E_DE + PM64_DM + 0.00203 * RM6064 + 0.00160 * 

RM6064.1 - 0.00021 * RM6064.2 - 0.00235 * RM6064.3 - 0.00374 * RM6064.4 - 0.00331 * RM6064.5 - 0.50 * RRADJ_M64 - 0.02 * 

POT_ET_TXRT_64 

PM64 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm64_adj-(-b1_m6064d*b2_2064di*rm64di+pm64e_de+d09a:pm64_dm-0.00598* 

 (rm6064+rm6064.1)/2-0.50*rradj_m64-0.02*pot_et_txrt_64) 

 = 0.47933 * pf62_adj - 0.22665 

 (3.85359) (4.39193) 

 Sum Sq 0.0041 Std Err 0.0177 LHS Mean -0.0286 

 R Sq 0.5332 R Bar Sq 0.4973 F 1, 13 14.8502 

 D.W.( 1) 1.3486 D.W.( 2) 1.7240 

 PM65 = 0.72722 * PF63 - 0.35819 - B2_2064DI * B1_M6569D * RM65DI_EFF + PM65E_DE + PM65_DM + 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 

PM65 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm65_adj-(pm65e_de+d09a:pm65_dm-0.00389*(rm6569+rm6569.1)/2-0.45* 

 rradj_m65-0.02*pot_et_txrt_65) 

 = 0.72722 * pf63_adj - 0.35819 

 (6.79574) (9.27279) 

 Sum Sq 0.0024 Std Err 0.0136 LHS Mean -0.0968 

 R Sq 0.7803 R Bar Sq 0.7634 F 1, 13 46.1821 

 D.W.( 1) 1.9507 D.W.( 2) 2.4425 

 

 PM66 = 0.38684 * PF64 - 0.20883 - B2_2064DI * B1_M6569D * RM66DI_EFF + PM66E_DE + PM66_DM + 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 

PM66 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm66_adj-(pm66e_de+d09a:pm66_dm-0.00389*(rm6569+rm6569.1)/2-0.40* 

 rradj_m66-0.02*pot_et_txrt_66) 

 = 0.38684 * pf64_adj - 0.20883 

 (3.84518) (6.36042) 

 Sum Sq 0.0029 Std Err 0.0151 LHS Mean -0.0835 

 R Sq 0.5321 R Bar Sq 0.4961 F 1, 13 14.7854 

 D.W.( 1) 1.4843 D.W.( 2) 2.6786 
120 

 PM67 = 0.35012 * PF65 - 0.15975 + PM67E_DE + PM67_DM + 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 

PM67 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm67_adj-(pm67e_de+d09a:pm67_dm-0.00389*(rm6569+rm6569.1)/2-0.35* 

 rradj_m67-0.02*pot_et_txrt_67) 

 = 0.35012 * pf65_adj - 0.15975 

 (2.57310) (4.49414) 

 Sum Sq 0.0039 Std Err 0.0173 LHS Mean -0.0690 

 R Sq 0.3374 R Bar Sq 0.2865 F 1, 13 6.6209 

 D.W.( 1) 2.5130 D.W.( 2) 2.3224 

 PM68 = 0.95984 * PF66 - 0.26305 + PM68E_DE + PM68_DM + 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 

PM68 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm68_adj-(pm68e_de+d09a:pm68_dm-0.00389*(rm6569+rm6569.1)/2-0.30* 

 rradj_m68-0.02*pot_et_txrt_68) 

 = 0.95984 * pf66_adj - 0.26305 

 (6.75736) (8.03455) 

 Sum Sq 0.0040 Std Err 0.0176 LHS Mean -0.0440 

 R Sq 0.7784 R Bar Sq 0.7613 F 1, 13 45.6618 

 D.W.( 1) 1.5450 D.W.( 2) 2.2137 

PM69 = 0.74113 * PF67 - 0.22589 + PM69E_DE + PM69_DM + 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 

PM69 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm69_adj-(pm69e_de+d09a:pm69_dm-0.00389*(rm6569+rm6569.1)/2-0.30* 

 rradj_m69-0.02*pot_et_txrt_69) 

 = 0.74113 * pf67_adj - 0.22589 

 (6.16586) (8.98258) 

 Sum Sq 0.0033 Std Err 0.0159 LHS Mean -0.0729 

 R Sq 0.7452 R Bar Sq 0.7256 F 1, 13 38.0179 

 D.W.( 1) 1.8167 D.W.( 2) 1.8770 

PM70 = 0.46445 * PF68 - 0.23451 + PM70E_DE + PM70_DM - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * 

RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * RM7074.5 

PM70 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm70_adj-(pm70e_de+d09a:pm70_dm-0.00045*(rm7074+rm7074.1)/2) 

 = 0.46445 * pf68_adj - 0.23451 

 (3.13923) (8.70423) 
121 

 Sum Sq 0.0030 Std Err 0.0153 LHS Mean -0.1508 

 R Sq 0.4312 R Bar Sq 0.3874 F 1, 13 9.8548 

 D.W.( 1) 1.6266 D.W.( 2) 1.7115 

PM71 = 0.27684 * PF69 - 0.20679 + PM71E_DE + PM71_DM - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * 

RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * RM7074.5 

PM71 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm71_adj-(pm71e_de+d09a:pm71_dm-0.00045*(rm7074+rm7074.1)/2) 

 = 0.27684 * pf69_adj - 0.20679 

 (2.45836) (11.2222) 

 Sum Sq 0.0017 Std Err 0.0114 LHS Mean -0.1621 

 R Sq 0.3174 R Bar Sq 0.2648 F 1, 13 6.0435 

 D.W.( 1) 2.0356 D.W.( 2) 2.6476 

PM72 = 0.77240 * PF70 - 0.25289 + PM72E_DE + PM72_DM - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * 

RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * RM7074.5 

PM72 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm72_adj-(pm72e_de+d09a:pm72_dm-0.00045*(rm7074+rm7074.1)/2) 

 = 0.77240 * pf70_adj - 0.25289 

 (4.46799) (10.6268) 

 Sum Sq 0.0030 Std Err 0.0152 LHS Mean -0.1480 

 R Sq 0.6056 R Bar Sq 0.5753 F 1, 13 19.9629 

 D.W.( 1) 2.5174 D.W.( 2) 2.4964 

 PM73 = 0.65971 * PF71 - 0.19394 + PM73E_DE + PM73_DM - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * 

RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * RM7074.5 

PM73 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm73_adj-(pm73e_de+d09a:pm73_dm-0.00045*(rm7074+rm7074.1)/2) 

 = 0.65971 * pf71_adj - 0.19394 

 (4.09270) ( 9.6357) 

 Sum Sq 0.0022 Std Err 0.0131 LHS Mean -0.1127 

 R Sq 0.5630 R Bar Sq 0.5294 F 1, 13 16.7502 

 D.W.( 1) 1.6480 D.W.( 2) 2.6493 

 PM74 = 0.78464 * PF72 - 0.17649 + PM74E_DE + PM74_DM - 0.00013 * RM7074 - 0.00016 * RM7074.1 - 0.00013 * RM7074.2 - 0.00006 * 

RM7074.3 + 0.00000 * RM7074.4 + 0.00003 * RM7074.5 

PM74 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pm74_adj-(pm74e_de+d09a:pm74_dm-0.00045*(rm7074+rm7074.1)/2) 

 = 0.78464 * pf72_adj - 0.17649 

 (3.48183) (7.13863) 
122 

 Sum Sq 0.0030 Std Err 0.0151 LHS Mean -0.0915 

 R Sq 0.4825 R Bar Sq 0.4427 F 1, 13 12.1231 

 D.W.( 1) 1.8314 D.W.( 2) 1.4740 

AGE 75 TO 79 

PM75 = PM74.4 * 0.920 + DPM75O_FE 

PM76 = PM75.4 * 0.920 + DPM75O_FE 

PM77 = PM76.4 * 0.920 + DPM75O_FE 

PM78 = PM77.4 * 0.920 + DPM75O_FE 

PM79 = PM78.4 * 0.920 + DPM75O_FE 

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 

PM87 = PM87_P * PM80O / PM80O_P 

PM88 = PM88_P * PM80O / PM80O_P 
123 

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 

 RNLF1617_H = (- 0.00741 + 0.23393 * RF1617CU6 + 0.00051 * (RF1617 + RF1617.1)/2) 

RNLF1617_H 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlf1617_h 

 = 0.23393 * rf1617cu6 + 0.00051 * (rf1617+rf1617.1)/2 - 0.00741 

 (8.23195) (2.03397) (1.69048) 

 Sum Sq 0.0000 Std Err 0.0013 LHS Mean 0.0255 

 R Sq 0.8827 R Bar Sq 0.8631 F 2, 12 45.1464 

 D.W.( 1) 1.9427 D.W.( 2) 1.9760 

 

RNLF1617_S+RNLF1617_O2 = (0.01166 * YEAR + 0.00616 * (RF1617 + RF1617)/2 - 0.69608) 

RNLF1617_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlf1617_s+rnlf1617_o2 

 = 0.00616 * (rf1617+rf1617.1)/2 + 0.01166 * year - 0.69608 

 (3.77102) (22.1659) (10.2653) 

 Sum Sq 0.0008 Std Err 0.0083 LHS Mean 0.5854 

 R Sq 0.9770 R Bar Sq 0.9731 F 2, 12 254.625 

 D.W.( 1) 1.7133 D.W.( 2) 2.6877 

 

 

PF1617 = 0.98681 - (B2_2064DI * B1_F1617D * RF1617DI) - (- 0.00741 + 0.23393 * RF1617CU6 + 0.00051 * MOVAVG(5,RF1617)) 

 - (- 0.69608 + 0.01166 * TR_PF1617 + 0.00616 * MOVAVG(5,RF1617)) 

PF1617_AADJ 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 8 NOV 2009 
124 

 pf1617_aadj+b2_2064di*b1_f1617d*rf1617di+rnlf1617_s+rnlf1617_h+ 

 rnlf1617_o2 

 = 0.98681 

 (2200.07) 

 Sum Sq 0.0000 Std Err 0.0017 LHS Mean 0.9868 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 1.3375 D.W.( 2) 1.7772 

 

 RNLF1819_H = (-0.00080 + 0.22814 * RF1819CU6 + 0.00318 * (RF1819 + RF1819.1)/2) 

RNLF1819_H 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlf1819_h 

 = 0.22814 * rf1819cu6 + 0.00318 * (rf1819+rf1819.1)/2 - 0.00080 

 (4.59623) (3.03414) (0.05838) 

 Sum Sq 0.0002 Std Err 0.0042 LHS Mean 0.0728 

 R Sq 0.7711 R Bar Sq 0.7330 F 2, 12 20.2141 

 D.W.( 1) 1.9216 D.W.( 2) 2.0402 

 

RNLF1819_S+RNLF1819_O2 = (0.00764 * YEAR + 0.00667 * (RF1819 + RF1819.1)/2 - 0.53433) 

RNLF1819_S 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 7 NOV 2009 

 rnlf1819_s+rnlf1819_o2 

 = 0.00667 * (rf1819+rf1819.1)/2 + 0.00764 * year - 0.53433 

 (4.02033) (18.4794) (10.2363) 

 Sum Sq 0.0005 Std Err 0.0067 LHS Mean 0.3252 

 R Sq 0.9662 R Bar Sq 0.9605 F 2, 12 171.394 

 D.W.( 1) 2.6533 D.W.( 2) 2.6698 

 

PF1819 = 0.98200 

 - (B2_2064DI * B1_F1819D * RF1819DI) 

 - (-0.00080 + 0.22814 * RF1819CU6 + 0.00318 * MOVAVG(5,RF1819)) 

 - (- 0.53433+ 0.00764 * TR_PF1819 + 0.00667 * MOVAVG(5,RF1819)) 

PF1819_AADJ 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 8 NOV 2009 

 pf1819_aadj+b2_2064di*b1_f1819d*rf1819di+rnlf1819_s+rnlf1819_h+ 

 rnlf1819_o2 

 = 0.98200 

 (1428.98) 
125 

 Sum Sq 0.0001 Std Err 0.0027 LHS Mean 0.9820 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.9389 D.W.( 2) 2.5627 

AGE 20 TO 44 

(NOTE: THE REGRESSIONS IN THIS SECTION OF WERE BASED ON LFPR NOT SEASONALLY ADJUSTED MARCH DATA. SINCE 

WE WANT TO PROJECT SEASONAL ADJUSTED VALUES, WE APPLIED A SEASONAL ADJUSTMENT (SA) FACTOR TO THE 

ESTIMATES. THE SA FACTOR REPRESENTS THE RATIO OF THE SA TO THE NOT SA MARCH 2009 VALUES FOR FEMALES 2024, 

2529, 3034, 3539, AND 4044.) 

FEMALES - NEVER MARRIED WITH AT LEAST 1 OWN CHILD UNDER AGE 6 

 

PF2024NMC6U_P = ( 0.70868 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 

0.00052 * RF2024.5 - B2_2064DI * B1_F2024D * RF2024DI) * 1.0160 

PF2024NMC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024nmc6u_maj+b2_2064di*b1_f2024d*rf2024di+(0.00163*movavgf2024) 

 = 0.70868 

 (90.3041) 

 Sum Sq 0.0081 Std Err 0.0272 LHS Mean 0.7087 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.3094 D.W.( 2) 1.3334 

 

PF2529NMC6U_P = ( 0.74861 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 

0.00013 * RF2529.5 - B2_2064DI * B1_F2534D * RF2529DI) * 0.9981 

PF2529NMC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529nmc6u_maj+b2_2064di*b1_f2534d*rf2529di+(0.00223*movavgf2529) 

 = 0.74861 

 (84.7812) 

 Sum Sq 0.0103 Std Err 0.0306 LHS Mean 0.7486 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.9411 D.W.( 2) 2.6489 

 

PF3034NMC6U_P = ( 0.73944 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI) * 0.9980 

PF3034NMC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 11 periods from 1998 to 2008 

 Date: 7 NOV 2009 

 pf3034nmc6u_maj+b2_2064di*b1_f2534d*rf3034di-(0.00219*movavgf3034) 
126 

 = 0.73944 

 (82.4756) 

 Sum Sq 0.0088 Std Err 0.0297 LHS Mean 0.7394 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 10 NC 

 D.W.( 1) 0.5524 D.W.( 2) 1.4988 

 

PF3539NMC6U_P = ( 0.75363 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 

+ 0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI) * 0.9989 

PF3539NMC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3539nmc6u_maj+b2_2064di*b1_f3544d*rf3539di+(0.00294*movavgf3539) 

 = 0.75363 

 (43.4406) 

 Sum Sq 0.0397 Std Err 0.0601 LHS Mean 0.7536 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.1836 D.W.( 2) 1.2835 

 

PF4044NMC6U_P = ( 0.73920 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI) * 0.9989 

PF4044NMC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044nmc6u_maj+b2_2064di*b1_f3544d*rf4044di+(0.00336*movavgf4044) 

 = 0.73920 

 (27.1826) 

 Sum Sq 0.0976 Std Err 0.0942 LHS Mean 0.7392 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 0.8825 D.W.( 2) 1.5609 

 

 

FEMALES - NEVER MARRIED NO OWN CHILDREN UNDER AGE 6 

PF2024NMNC6_P = ( 1.13654 - 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 - B2_2064DI * B1_F2024D * RF2024DI) * 1.0160 

PF2024NMNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024nmnc6_maj+b2_2064di*b1_f2024d*rf2024di+(0.00163*movavgf2024) 

 = - 0.00366 * year + 1.13654 

 (4.05623) (12.2888) 

 Sum Sq 0.0012 Std Err 0.0108 LHS Mean 0.7616 

 R Sq 0.6220 R Bar Sq 0.5842 F 1, 10 16.4530 

 D.W.( 1) 2.0236 D.W.( 2) 1.9870 

 
127 

PF2529NMNC6_P = ( 0.98148 - 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 - B2_2064DI * B1_F2534D * RF2529DI) * 0.9981 

PF2529NMNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529nmnc6_maj+b2_2064di*b1_f2534d*rf2529di+(0.00223*movavgf2529) 

 = - 0.00111 * year + 0.98148 

 (1.16711) (10.0848) 

 Sum Sq 0.0013 Std Err 0.0113 LHS Mean 0.8680 

 R Sq 0.1199 R Bar Sq 0.0319 F 1, 10 1.3621 

 D.W.( 1) 1.6528 D.W.( 2) 2.2981 

 

PF3034NMNC6_P = ( 0.84901 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI) * 0.9980 

PF3034NMNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 11 periods from 1998 to 2008 

 Date: 7 NOV 2009 

 pf3034nmnc6_maj+b2_2064di*b1_f2534d*rf3034di-(0.00219*movavgf3034) 

 = 0.84901 

 (165.157) 

 Sum Sq 0.0029 Std Err 0.0170 LHS Mean 0.8490 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 10 NC 

 D.W.( 1) 0.5820 D.W.( 2) 1.1688 

 

PF3539NMNC6_P = ( 0.84953 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 

0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI) * 0.9989 

PF3539NMNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3539nmnc6_maj+b2_2064di*b1_f3544d*rf3539di+(0.00294*movavgf3539) 

 = 0.84953 

 (152.920) 

 Sum Sq 0.0041 Std Err 0.0192 LHS Mean 0.8495 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.1860 D.W.( 2) 1.2464 

 

PF4044NMNC6_P = ( 0.83790 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI) * 0.9989 

PF4044NMNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044nmnc6_maj+b2_2064di*b1_f3544d*rf4044di+(0.00336*movavgf4044) 
128 

 = 0.83790 

 (145.443) 

 Sum Sq 0.0044 Std Err 0.0200 LHS Mean 0.8379 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.2197 D.W.( 2) 1.8270 

 

 

FEMALES - MARRIED SPOUSE PRESENT WITH AT LEAST 1 OWN CHILD UNDER AGE 6 

PF2024MSC6U_P = ( 0.69043 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 

0.00052 * RF2024.5 - B2_2064DI * B1_F2024D * RF2024DI - 0.1*IF2024MSC6U) * 1.0160 

PF2024MSC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024msc6u_maj+b2_2064di*b1_f2024d*rf2024di+0.1*if2024msc6u+ 

 (0.00163*movavgf2024) 

 = 0.69043 

 (74.8521) 

 Sum Sq 0.0112 Std Err 0.0320 LHS Mean 0.6904 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.1094 D.W.( 2) 0.7434 

 

PF2529MSC6U_P = ( 0.76218 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 

0.00013 * RF2529.5 - B2_2064DI * B1_F2534D * RF2529DI - 0.1*IF2529MSC6U) * 0.9981 

PF2529MSC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529msc6u_maj+b2_2064di*b1_f2534d*rf2529di+0.1*if2529msc6u+ 

 (0.00223*movavgf2529) 

 = 0.76218 

 (110.394) 

 Sum Sq 0.0063 Std Err 0.0239 LHS Mean 0.7622 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 0.6195 D.W.( 2) 0.9444 

 

PF3034MSC6U_P = ( 0.78186 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI - 0.1*IF3034MSC6U) * 0.9980 

PF3034MSC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3034msc6u_maj+b2_2064di*b1_f2534d*rf3034di+0.1*if3034msc6u- 

 (0.00219*movavgf3034) 

 = 0.78186 

 (211.713) 

 Sum Sq 0.0018 Std Err 0.0128 LHS Mean 0.7819 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 
129 

 D.W.( 1) 0.7088 D.W.( 2) 0.9441 

 

PF3539MSC6U_P = ( 0.79072 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 

0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI - 0.1*IF3539MSC6U) * 0.9989 

PF3539MSC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3539msc6u_maj+b2_2064di*b1_f3544d*rf3539di+0.1*if3539msc6u+ 

 (0.00294*movavgf3539) 

 = 0.79072 

 (252.139) 

 Sum Sq 0.0013 Std Err 0.0109 LHS Mean 0.7907 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.0179 D.W.( 2) 1.6902 

 

PF4044MSC6U_P = ( 0.79356 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI - 0.1*IF4044MSC6U) * 0.9989 

PF4044MSC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044msc6u_maj+b2_2064di*b1_f3544d*rf4044di+0.1*if4044msc6u+ 

 (0.00336*movavgf4044) 

 = 0.79356 

 (105.974) 

 Sum Sq 0.0074 Std Err 0.0259 LHS Mean 0.7936 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 2.5927 D.W.( 2) 2.0366 

 

 

FEMALES - MARRIED SPOUSE PRESENT NO OWN CHILDREN UNDER AGE 6 

PF2024MSNC6_P = ( 0.79421 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 

0.00052 * RF2024.5 - B2_2064DI * B1_F2024D * RF2024DI) * 1.0160 

PF2024MSNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024msnc6_maj+b2_2064di*b1_f2024d*rf2024di+(0.00163*movavgf2024) 

 = 0.79421 

 (102.852) 

 Sum Sq 0.0079 Std Err 0.0267 LHS Mean 0.7942 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.1263 D.W.( 2) 0.9691 

PF2529MSNC6_P = ( 0.83502 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 

0.00013 * RF2529.5 - B2_2064DI * B1_F2534D * RF2529DI) * 0.9981 

PF2529MSNC6_MAJ 
130 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529msnc6_maj+b2_2064di*b1_f2534d*rf2529di+(0.00223*movavgf2529) 

 = 0.83502 

 (193.893) 

 Sum Sq 0.0024 Std Err 0.0149 LHS Mean 0.8350 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.4523 D.W.( 2) 0.6163 

 

PF3034MSNC6_P = ( 0.80379 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI) * 0.9980 

PF3034MSNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3034msnc6_maj+b2_2064di*b1_f2534d*rf3034di-(0.00219*movavgf3034) 

 = 0.80379 

 (157.883) 

 Sum Sq 0.0034 Std Err 0.0176 LHS Mean 0.8038 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 0.8444 D.W.( 2) 1.2470 

 

PF3539MSNC6_P = ( 0.80906 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 + 

0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI) * 0.9989 

PF3539MSNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3539msnc6_maj+b2_2064di*b1_f3544d*rf3539di+(0.00294*movavgf3539) 

 = 0.80906 

 (272.016) 

 Sum Sq 0.0012 Std Err 0.0103 LHS Mean 0.8091 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 0.9588 D.W.( 2) 1.7718 

PF4044MSNC6_P = ( 0.82602 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI) * 0.9989 

PF4044MSNC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044msnc6_maj+b2_2064di*b1_f3544d*rf4044di+(0.00336*movavgf4044) 

 = 0.82602 

 (410.094) 

 Sum Sq 0.0005 Std Err 0.0070 LHS Mean 0.8260 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.4267 D.W.( 2) 2.0136 
131 

FEMALES - MARRIED SPOUSE ABSENT WITH AT LEAST 1 OWN CHILD UNDER AGE 6 

PF2024MAC6U_P = ( 0.95787 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 

0.00052 * RF2024.5 - B2_2064DI * B1_F2024D * RF2024DI - 0.16722 * IF2024MAC6U) * 1.0160 

PF2024MAC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024mac6u_maj+b2_2064di*b1_f2024d*rf2024di+(0.00163*movavgf2024) 

 = - 0.16722 * if2024mac6u + 0.95787 

 (0.98479) (3.96975) 

 Sum Sq 0.0237 Std Err 0.0487 LHS Mean 0.7206 

 R Sq 0.0884 R Bar Sq -0.0028 F 1, 10 0.9698 

 D.W.( 1) 1.8725 D.W.( 2) 2.5264 

 

PF2529MAC6U_P = ( 0.90653 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 

0.00013 * RF2529.5 - B2_2064DI * B1_F2534D * RF2529DI - 0.10000 * IF2529MAC6U) * 0.9981 

PF2529MAC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529mac6u_maj+b2_2064di*b1_f2534d*rf2529di+0.1*if2529mac6u+ 

 (0.00223*movavgf2529) 

 = 0.90653 

 (91.9140) 

 Sum Sq 0.0128 Std Err 0.0342 LHS Mean 0.9065 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.2658 D.W.( 2) 1.9769 

 

PF3034MAC6U_P = ( 0.88071 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI - 0.10000 * IF3034MAC6U) * 0.9980 

PF3034MAC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3034mac6u_maj+b2_2064di*b1_f2534d*rf3034di+0.1*if3034mac6u- 

 (0.00219*movavgf3034) 

 = 0.88071 

 (85.6422) 

 Sum Sq 0.0140 Std Err 0.0356 LHS Mean 0.8807 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.1334 D.W.( 2) 1.0452 

 

PF3539MAC6U_P = ( 0.90258 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 

+ 0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI - 0.10000 * IF3539MAC6U) * 0.9989 

PF3539MAC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 
132 

 pf3539mac6u_maj+b2_2064di*b1_f3544d*rf3539di+0.1*if3539mac6u+ 

 (0.00294*movavgf3539) 

 = 0.90258 

 (90.1282) 

 Sum Sq 0.0132 Std Err 0.0347 LHS Mean 0.9026 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.7297 D.W.( 2) 1.8179 

 

 

PF4044MAC6U_P = ( 0.89876 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI - 0.10000 * IF4044MAC6U) * 0.9989 

PF4044MAC6U_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044mac6u_maj+b2_2064di*b1_f3544d*rf4044di+0.1*if4044mac6u+ 

 (0.00336*movavgf4044) 

 = 0.89876 

 (51.9091) 

 Sum Sq 0.0396 Std Err 0.0600 LHS Mean 0.8988 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.3740 D.W.( 2) 1.4527 

 

FEMALES - MARRIED SPOUSE ABSENT NO OWN CHILDREN UNDER AGE 6 

PF2024MANC6_P = ( 0.75174 - 0.00087 * RF2024 - 0.00099 * RF2024.1 - 0.00063 * RF2024.2 - 0.00007 * RF2024.3 + 0.00041 * RF2024.4 + 

0.00052 * RF2024.5 - B2_2064DI * B1_F2024D * RF2024DI) * 1.0160 

PF2024MANC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2024manc6_maj+b2_2064di*b1_f2024d*rf2024di+(0.00163*movavgf2024) 

 = 0.75174 

 (36.5819) 

 Sum Sq 0.0557 Std Err 0.0712 LHS Mean 0.7517 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.2773 D.W.( 2) 1.2901 

 

PF2529MANC6_P = ( 0.82060 - 0.00056 * RF2529 - 0.00070 * RF2529.1 - 0.00057 * RF2529.2 - 0.00029 * RF2529.3 - 0.00002 * RF2529.4 + 

0.00013 * RF2529.5 - B2_2064DI * B1_F2534D * RF2529DI) * 0.9981 

PF2529MANC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf2529manc6_maj+b2_2064di*b1_f2534d*rf2529di+(0.00223*movavgf2529) 

 = 0.82060 

 (106.580) 
133 

 Sum Sq 0.0078 Std Err 0.0267 LHS Mean 0.8206 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.0693 D.W.( 2) 1.4430 

 

PF3034MANC6_P = ( 0.83806 - 0.00081 * RF3034 - 0.00065 * RF3034.1 + 0.00005 * RF3034.2 + 0.00089 * RF3034.3 + 0.00143 * RF3034.4 

+ 0.00128 * RF3034.5 - B2_2064DI * B1_F2534D * RF3034DI) * 0.9980 

PF3034MANC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3034manc6_maj+b2_2064di*b1_f2534d*rf3034di-(0.00219*movavgf3034) 

 = 0.83806 

 (139.142) 

 Sum Sq 0.0048 Std Err 0.0209 LHS Mean 0.8381 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.1221 D.W.( 2) 1.3141 

 

PF3539MANC6_P = ( 0.86613 - 0.00195 * RF3539 - 0.00216 * RF3539.1 - 0.00128 * RF3539.2 + 0.00002 * RF3539.3 + 0.00111 * RF3539.4 

+ 0.00132 * RF3539.5 - B2_2064DI * B1_F3544D * RF3539DI) * 0.9989 

PF3539MANC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf3539manc6_maj+b2_2064di*b1_f3544d*rf3539di+(0.00294*movavgf3539) 

 = 0.86613 

 (351.138) 

 Sum Sq 0.0008 Std Err 0.0085 LHS Mean 0.8661 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.5170 D.W.( 2) 2.4012 

 

PF4044MANC6_P = ( 0.85937 - 0.00026 * RF4044 - 0.00050 * RF4044.1 - 0.00068 * RF4044.2 - 0.00076 * RF4044.3 - 0.00070 * RF4044.4 - 

0.00046 * RF4044.5 - B2_2064DI * B1_F3544D * RF4044DI) * 0.9989 

PF4044MANC6_MAJ 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 pf4044manc6_maj+b2_2064di*b1_f3544d*rf4044di+(0.00336*movavgf4044) 

 = 0.85937 

 (318.503) 

 Sum Sq 0.0010 Std Err 0.0093 LHS Mean 0.8594 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.2467 D.W.( 2) 1.8874 

 

LABOR FORCE PARTICIPATION RATES BYMARITAL STATUS (PRELIMINARY) 

PF2024NM_P = (PF2024NMC6U_P * NF2024NMC6U + PF2024NMNC6_P * NF2024NMNC6) / NF2024NM 

PF2024MS_P = (PF2024MSC6U_P * NF2024MSC6U + PF2024MSNC6_P * NF2024MSNC6) / NF2024MS 
134 

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 + 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 - B2_2064DI * B1_F4554D * RF4549DI 

PLF4549NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 plf4549nm+b2_2064di*b1_f4554d*rf4549di-(0.00072*(rf4549+rf4549.1)/2) 

 -pf4549e_de 

 = 0.03650 

 (13.0077) 

 Sum Sq 0.0010 Std Err 0.0097 LHS Mean 0.0365 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 1.0546 D.W.( 2) 1.4590 

 

PF5054NM_P = 0.05788 + 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 - B2_2064DI * B1_F4554D * RF5054DI 

PLF5054NM 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 2002 to 2008 

 Date: 7 NOV 2009 

 plf5054nm+b2_2064di*b1_f4554d*rf5054di+(0.00195*(rf5054+rf5054.1)/2) 

 -pf5054e_de 

 = 0.05788 

 (38.3113) 

 Sum Sq 0.0001 Std Err 0.0040 LHS Mean 0.0579 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 6 NC 

 D.W.( 1) 3.1637 D.W.( 2) 0.7955 

 
135 

FEMALES - MARRIED SPOUSE PRESENT 45 TO 54 

PF4549MS_P = 0.03842 + 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 - B2_2064DI * B1_F4554D * RF4549DI - 0.15 * RF4549MSCU6 

PLF4549MS 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 plf4549ms+b2_2064di*b1_f4554d*rf4549di-(0.00072*(rf4549+rf4549.1)/2) 

 +0.15*rf4549mscu6-pf4549e_de 

 = 0.03842 

 (31.6040) 

 Sum Sq 0.0002 Std Err 0.0042 LHS Mean 0.0384 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 11 NC 

 D.W.( 1) 1.2060 D.W.( 2) 2.1805 

 

PF5054MS_P = - 0.40180 + 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 - B2_2064DI * B1_F4554D * RF5054DI - 0.12 * RF5054MSCU6 

PLF5054MS 

 ANNUAL data for 8 periods from 2002 to 2008 

 plf5054ms+b2_2064di*b1_f4554d*rf5054di+(0.00195*(rf5054+rf5054.1)/2) 

 +0.12*rf5054mscu6-pf5054e_de 

 = 0.00454 * year - 0.40180 

 (5.45138) (4.59712) 

 Sum Sq 0.0001 Std Err 0.0044 LHS Mean 0.0746 

 R Sq 0.8560 R Bar Sq 0.8272 F 1, 5 29.7175 

 D.W.( 1) 2.8597 D.W.( 2) 1.3228 

 

FEMALES - MARRIED SPOUSE ABSENT 45 TO 54 

PF4549MA_P = 0.06830 + 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 - B2_2064DI * B1_F4554D * RF4549DI - 0.1 * RF4549MACU6 

PLF4549MA 

 Ordinary Least Squares 

 ANNUAL data for 12 periods from 1997 to 2008 

 Date: 7 NOV 2009 

 plf4549ma+b2_2064di*b1_f4554d*rf4549di+0.1*rf4549macu6-(0.00072* 

 (rf4549+rf4549.1)/2)-pf4549e_de 

 = 0.06830 

 (22.7782) 

 Sum Sq 0.0012 Std Err 0.0104 LHS Mean 0.0683 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 11 NC 

 D.W.( 1) 0.4904 D.W.( 2) 0.6582 

 

PF5054MA_P = 0.08983 + 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 - B2_2064DI * B1_F4554D * RF5054DI - 0.2 * RF5054MACU6 

PLF5054MA 

 Ordinary Least Squares 
136 

 ANNUAL data for 12 periods from 2002 to 2008 

 Date: 7 NOV 2009 

 plf5054ma+b2_2064di*b1_f4554d*rf5054di+0.2*rf5054macu6+(0.00195* 

 (rf5054+rf5054.1)/2)-pf5054e_de 

 = 0.08983 

 (31.6098) 

 Sum Sq 0.0003 Std Err 0.0075 LHS Mean 0.0898 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 6 NC 

 D.W.( 1) 0.7619 D.W.( 2) 1.1327 

 

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 

FINAL EQUATIONS 

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 
137 

PF2529NMC6U = PF2529NMC6U_P * PF2529 / PF2529_P 

PF3034NMC6U = PF3034NMC6U_P * PF3034 / PF3034_P 

PF3539NMC6U = PF3539NMC6U_P * PF3539 / PF3539_P 

PF4044NMC6U = PF4044NMC6U_P * PF4044 / PF4044_P 

PF2024NMNC6 = PF2024NMNC6_P * PF2024 / PF2024_P 

PF2529NMNC6 = PF2529NMNC6_P * PF2529 / PF2529_P 

PF3034NMNC6 = PF3034NMNC6_P * PF3034 / PF3034_P 

PF3539NMNC6 = PF3539NMNC6_P * PF3539 / PF3539_P 

PF4044NMNC6 = PF4044NMNC6_P * PF4044 / PF4044_P 

PF2024MSC6U = PF2024MSC6U_P * PF2024 / PF2024_P 

PF2529MSC6U = PF2529MSC6U_P * PF2529 / PF2529_P 

PF3034MSC6U = PF3034MSC6U_P * PF3034 / PF3034_P 

PF3539MSC6U = PF3539MSC6U_P * PF3539 / PF3539_P 

PF4044MSC6U = PF4044MSC6U_P * PF4044 / PF4044_P 

PF2024MSNC6 = PF2024MSNC6_P * PF2024 / PF2024_P 

PF2529MSNC6 = PF2529MSNC6_P * PF2529 / PF2529_P 

PF3034MSNC6 = PF3034MSNC6_P * PF3034 / PF3034_P 

PF3539MSNC6 = PF3539MSNC6_P * PF3539 / PF3539_P 

PF4044MSNC6 = PF4044MSNC6_P * PF4044 / PF4044_P 

PF2024MAC6U = PF2024MAC6U_P * PF2024 / PF2024_P 

PF2529MAC6U = PF2529MAC6U_P * PF2529 / PF2529_P 

PF3034MAC6U = PF3034MAC6U_P * PF3034 / PF3034_P 

PF3539MAC6U = PF3539MAC6U_P * PF3539 / PF3539_P 

PF4044MAC6U = PF4044MAC6U_P * PF4044 / PF4044_P 

PF2024MANC6 = PF2024MANC6_P * PF2024 / PF2024_P 

PF2529MANC6 = PF2529MANC6_P * PF2529 / PF2529_P 

PF3034MANC6 = PF3034MANC6_P * PF3034 / PF3034_P 

PF3539MANC6 = PF3539MANC6_P * PF3539 / PF3539_P 

PF4044MANC6 = PF4044MANC6_P * PF4044 / PF4044_P 

AGE 55 TO 61 

PF55 = - B1_F5559D * B2_2064DI * RF55DI + 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 

PF55 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf55_adj+b1_f5559d*b2_2064di*rf55di+0.00318*(rf5559+rf5559.1)/2- 

 pf55e_de-d09a:pf55_dm 

 = 0.00368 * pf55coh48 - 0.90941 

 (3.77468) (9.31588) 

 Sum Sq 0.0019 Std Err 0.0119 LHS Mean -0.5411 

 R Sq 0.5229 R Bar Sq 0.4862 F 1, 13 14.2482 

 D.W.( 1) 1.0397 D.W.( 2) 1.6408 

PF56 = - B1_F5559D * B2_2064DI * RF56DI + 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 

PF56 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 
138 

 pf56_adj+b1_f5559d*b2_2064di*rf56di+0.00318*(rf5559+rf5559.1)/2- 

 pf56e_de-d09a:pf56_dm 

 = 0.00486 * pf56coh48 - 0.96865 

 (4.70516) (9.34013) 

 Sum Sq 0.0025 Std Err 0.0140 LHS Mean -0.4810 

 R Sq 0.6300 R Bar Sq 0.6016 F 1, 13 22.1385 

 D.W.( 1) 0.9310 D.W.( 2) 1.2475 

PF57 = - B1_F5559D * B2_2064DI * RF57DI + 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 

PF57 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf57_adj+b1_f5559d*b2_2064di*rf57di+0.00318*(rf5559+rf5559.1)/2- 

 pf57e_de-d09a:pf57_dm 

 = 0.00344 * pf57coh48 - 0.85033 

 (4.24608) (10.4308) 

 Sum Sq 0.0018 Std Err 0.0119 LHS Mean -0.5044 

 R Sq 0.5810 R Bar Sq 0.5488 F 1, 13 18.0292 

 D.W.( 1) 2.0633 D.W.( 2) 1.8663 

PF58 = - B1_F5559D * B2_2064DI * RF58DI + 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 

PF58 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf58_adj+b1_f5559d*b2_2064di*rf58di+0.00318*(rf5559+rf5559.1)/2- 

 pf58e_de-d09a:pf58_dm 

 = 0.00362 * pf58coh48 - 0.83081 

 (6.73964) (15.3264) 

 Sum Sq 0.0009 Std Err 0.0084 LHS Mean -0.4658 

 R Sq 0.7775 R Bar Sq 0.7604 F 1, 13 45.4228 

 D.W.( 1) 2.5327 D.W.( 2) 2.8198 

PF59 = - B1_F5559D * B2_2064DI * RF59DI + 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 

PF59 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf59_adj+b1_f5559d*b2_2064di*rf59di+0.00318*(rf5559+rf5559.1)/2- 

 pf59e_de-d09a:pf59_dm 

 = 0.00470 * pf59coh48 - 0.85665 

 (6.04743) (10.8998) 

 Sum Sq 0.0021 Std Err 0.0127 LHS Mean -0.3818 

 R Sq 0.7378 R Bar Sq 0.7176 F 1, 13 36.5714 

 D.W.( 1) 1.4831 D.W.( 2) 1.9926 

 
139 

PF60 = - B1_F6064D * B2_2064DI * RF60DI + 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 

PF60 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf60_adj+b1_f6064d*b2_2064di*rf60di-0.00349*(rf6064+rf6064.1)/2- 

 pf60e_de-d09a:pf60_dm 

 = 0.00819 * pf60coh48 - 1.18744 

 (13.9257) (19.9841) 

 Sum Sq 0.0013 Std Err 0.0098 LHS Mean -0.3607 

 R Sq 0.9372 R Bar Sq 0.9323 F 1, 13 193.925 

 D.W.( 1) 2.1311 D.W.( 2) 1.7547 

PF61 = - B1_F6064D * B2_2064DI * RF61DI + 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 

PF61 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf61_adj+b1_f6064d*b2_2064di*rf61di-0.00349*(rf6064+rf6064.1)/2- 

 pf61e_de-d09a:pf61_dm 

 = 0.00520 * pf61coh48 - 0.87850 

 (5.74368) ( 9.6049) 

 Sum Sq 0.0030 Std Err 0.0151 LHS Mean -0.3536 

 R Sq 0.7173 R Bar Sq 0.6956 F 1, 13 32.9899 

 D.W.( 1) 2.0958 D.W.( 2) 2.0774 

AGE 62 TO 74 

PF62 = - B1_F6064D * B2_2064DI * RF62DI + 0.00141 * RF6064 + 0.00166 * RF6064.1 + 0.00116 * RF6064.2 + 0.00033 * RF6064.3 - 

0.00041 * RF6064.4 - 0.00066 * RF6064.5 + PF62E_DE + PF62_DM + 0.00523 * PF62COH48 - 0.56287 - 0.5100 * RRADJ_F62 - 0.02 * 

POT_ET_TXRT_62 

PF62 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf62_adj+b1_f6064d*b2_2064di*rf62di-0.00349*(rf6064+rf6064.1)/2+0.51 

 *rradj_f62+0.02*pot_et_txrt_62-pf62e_de-d09a:pf62_dm 

 = 0.00523 * pf62coh48 - 0.56287 

 (6.34821) (6.75410) 

 Sum Sq 0.0025 Std Err 0.0138 LHS Mean -0.0343 

 R Sq 0.7561 R Bar Sq 0.7373 F 1, 13 40.2998 

 D.W.( 1) 1.7531 D.W.( 2) 2.4286 

PF63 = - B1_F6064D * B2_2064DI * RF63DI + 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 

PF63 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 
140 

 Date: 18 NOV 2009 

 pf63_adj+b1_f6064d*b2_2064di*rf63di-0.00349*(rf6064+rf6064.1)/2+ 

 0.4675*rradj_f63+0.02*pot_et_txrt_63-pf63e_de-d09a:pf63_dm 

 = 0.00659 * pf63coh48 - 0.68289 

 (9.22934) (9.46029) 

 Sum Sq 0.0019 Std Err 0.0119 LHS Mean -0.0173 

 R Sq 0.8676 R Bar Sq 0.8574 F 1, 13 85.1806 

 D.W.( 1) 1.6169 D.W.( 2) 2.3628 

PF64 = - B1_F6064D * B2_2064DI * RF64DI + 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 

PF64 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf64_adj+b1_f6064d*b2_2064di*rf64di-0.00349*(rf6064+rf6064.1)/2+ 

 0.425*rradj_f64+0.02*pot_et_txrt_64-pf64e_de-d09a:pf64_dm 

 = 0.00745 * pf64coh48 - 0.72813 

 (8.28211) (8.00872) 

 Sum Sq 0.0029 Std Err 0.0150 LHS Mean 0.0242 

 R Sq 0.8407 R Bar Sq 0.8284 F 1, 13 68.5934 

 D.W.( 1) 1.0198 D.W.( 2) 1.3213 

PF65 = - B1_F6569D * B2_2064DI * RF65DI_EFF + 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 

PF65 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf65_adj+0.00201*(rf6569+rf6569.1)/2+0.3825*rradj_f65+0.02* 

 pot_et_txrt_65-pf65e_de-d09a:pf65_dm 

 = 0.00348 * pf65coh48 - 0.37490 

 (3.59639) (3.82708) 

 Sum Sq 0.0034 Std Err 0.0162 LHS Mean -0.0229 

 R Sq 0.4987 R Bar Sq 0.4602 F 1, 13 12.9340 

 D.W.( 1) 0.8931 D.W.( 2) 1.5475 

 

PF66 = - B1_F6569D * B2_2064DI * RF66DI_EFF + 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 

PF66 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf66_adj+0.00201*(rf6569+rf6569.1)/2+0.34*rradj_f66+0.02* 

 pot_et_txrt_66-pf66e_de-d09a:pf66_dm 

 = 0.00512 * pf66coh48 - 0.52851 

 (6.49443) (6.63217) 

 Sum Sq 0.0023 Std Err 0.0132 LHS Mean -0.0114 
141 

 R Sq 0.7644 R Bar Sq 0.7463 F 1, 13 42.1776 

 D.W.( 1) 0.9621 D.W.( 2) 2.0946 

PF67 = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5 + 

PF67E_DE + PF67_DM + 0.00518 * PF67COH48 - 0.53735 - 0.2975 * RRADJ_F67 - 0.02 * POT_ET_TXRT_67 

PF67 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf67_adj+0.00201*(rf6569+rf6569.1)/2+0.2975*rradj_f67+0.02* 

 pot_et_txrt_67-pf67e_de-d09a:pf67_dm 

 = 0.00518 * pf67coh48 - 0.53735 

 (5.22734) (5.36828) 

 Sum Sq 0.0036 Std Err 0.0166 LHS Mean -0.0146 

 R Sq 0.6776 R Bar Sq 0.6528 F 1, 13 27.3250 

 D.W.( 1) 0.7870 D.W.( 2) 1.5420 

PF68 = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5 + 

PF68E_DE + PF68_DM + 0.00400 * PF68COH48 - 0.41046 - 0.2550 * RRADJ_F68 - 0.02 * POT_ET_TXRT_68 

PF68 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf68_adj+0.00201*(rf6569+rf6569.1)/2+0.255*rradj_f68+0.02* 

 pot_et_txrt_68-pf68e_de-d09a:pf68_dm-0.004*pf68coh48 

 = - 0.41046 

 (108.710) 

 Sum Sq 0.0030 Std Err 0.0146 LHS Mean -0.4105 

 R Sq -0.0000 R Bar Sq -0.0000 F 0, 14 NC 

 D.W.( 1) 0.7062 D.W.( 2) 1.1088 

PF69 = 0.00029 * RF6569 + 0.00014 * RF6569.1 - 0.00023 * RF6569.2 - 0.00063 * RF6569.3 - 0.00086 * RF6569.4 - 0.00072 * RF6569.5 + 

PF69E_DE + PF69_DM + 0.00400 * PF69COH48 - 0.36706 - 0.2550 * RRADJ_F69 - 0.02 * POT_ET_TXRT_69 

PF69 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf69_adj+0.00201*(rf6569+rf6569.1)/2+0.255*rradj_f69+0.02* 

 pot_et_txrt_69-pf69e_de-d09a:pf69_dm-0.004*pf69coh48 

 = - 0.36706 

 (98.8825) 

 Sum Sq 0.0029 Std Err 0.0144 LHS Mean -0.3671 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 0.9091 D.W.( 2) 1.1132 

PF70 = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5 + 

PF70E_DE + PF70_DM + 0.00424 * PF70COH48 - 0.49282 

PF70 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf70_adj+0.00258*(rf7074+rf7074.1)/2-pf70e_de-d09a:pf70_dm 
142 

 = 0.00424 * pf70coh48 - 0.49282 

 (7.83319) (9.00853) 

 Sum Sq 0.0011 Std Err 0.0091 LHS Mean -0.0647 

 R Sq 0.8252 R Bar Sq 0.8117 F 1, 13 61.3589 

 D.W.( 1) 1.6075 D.W.( 2) 1.6542 

PF71 = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5 + 

PF71E_DE + PF71_DM + 0.00300 * PF71COH48 - 0.37390 

PF71 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf71_adj+0.00258*(rf7074+rf7074.1)/2-pf71e_de-d09a:pf71_dm-0.003* 

 pf71coh48 

 = - 0.37390 

 (129.175) 

 Sum Sq 0.0018 Std Err 0.0112 LHS Mean -0.3739 

 R Sq 0.0000 R Bar Sq 0.0000 F 0, 14 NC 

 D.W.( 1) 1.0361 D.W.( 2) 1.3180 

PF72 = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5 + 

PF72E_DE + PF72_DM + 0.00286 * PF72COH48 - 0.34670 

PF72 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf72_adj+0.00258*(rf7074+rf7074.1)/2-pf72e_de-d09a:pf72_dm 

 = 0.00286 * pf72coh48 - 0.34670 

 (4.76520) (5.71954) 

 Sum Sq 0.0013 Std Err 0.0100 LHS Mean -0.0581 

 R Sq 0.6359 R Bar Sq 0.6079 F 1, 13 22.7071 

 D.W.( 1) 2.3870 D.W.( 2) 1.8950 

PF73 = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5 + 

PF73E_DE + PF73_DM + 0.00370 * PF73COH48 - 0.41058 

PF73 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 

 pf73_adj+0.00258*(rf7074+rf7074.1)/2-pf73e_de-d09a:pf73_dm 

 = 0.00370 * pf73coh48 - 0.41058 

 (7.43111) (8.16624) 

 Sum Sq 0.0009 Std Err 0.0083 LHS Mean -0.0373 

 R Sq 0.8094 R Bar Sq 0.7948 F 1, 13 55.2214 

 D.W.( 1) 1.7723 D.W.( 2) 1.9443 

PF74 = - 0.00009 * RF7074 - 0.00028 * RF7074.1 - 0.00048 * RF7074.2 - 0.00063 * RF7074.3 - 0.00064 * RF7074.4 - 0.00046 * RF7074.5 + 

PF74E_DE + PF74_DM + 0.00304 * PF74COH48 - 0.35113 

PF74 

 Ordinary Least Squares 

 ANNUAL data for 15 periods from 1994 to 2008 

 Date: 18 NOV 2009 
143 

 pf74_adj+0.00258*(rf7074+rf7074.1)/2-pf74e_de-d09a:pf74_dm 

 = 0.00304 * pf74coh48 - 0.35113 

 (6.28948) (7.18186) 

 Sum Sq 0.0009 Std Err 0.0081 LHS Mean -0.0439 

 R Sq 0.7527 R Bar Sq 0.7336 F 1, 13 39.5576 

 D.W.( 1) 1.7882 D.W.( 2) 1.6804 

AGE 75 TO 79 

PF75 = PF74.4 * 0.900 + DPF75O_FE 

PF76 = PF75.4 * 0.900 + DPF75O_FE 

PF77 = PF76.4 * 0.900 + DPF75O_FE 

PF78 = PF77.4 * 0.900 + DPF75O_FE 

PF79 = PF78.4 * 0.900 + DPF75O_FE 

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 
144 

PF87 = PF87_P * PF80O / PF80O_P 

PF88 = PF88_P * PF80O / PF80O_P 

PF89 = PF89_P * PF80O / PF80O_P 

PF90 = PF90_P * PF80O / PF80O_P 

PF91 = PF91_P * PF80O / PF80O_P 

PF92 = PF92_P * PF80O / PF80O_P 

PF93 = PF93_P * PF80O / PF80O_P 

PF94 = PF94_P * PF80O / PF80O_P 

PF95 = PF95_P * PF80O / PF80O_P 

PF96 = PF96_P * PF80O / PF80O_P 

PF97 = PF97_P * PF80O / PF80O_P 

PF98 = PF98_P * PF80O / PF80O_P 

PF99 = PF99_P * PF80O / PF80O_P 

PF100 = PF100_P * PF80O / PF80O_P 

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 

 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 
145 

 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 

 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) 
146 

 - 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] 

 (0.72412) (0.51868) 

 Polynomial lags: 

 rm3539_dpk 

 from 0 to 5 degree 3 near far 
147 

 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 

 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 
148 

 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 

 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] 
149 

 (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) 

 Polynomial lags: 

 rm7074_dpk 

 from 0 to 5 degree 3 near far 
150 

 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) 

 Polynomial lags: 

 rf1617_dpk 

 from 0 to 5 degree 3 near far 
151 

 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 
152 

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 
153 

 = - 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) 
154 

 Polynomial lags: 

 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 
155 

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 
156 

 pf7074_dpk 

 = - 0.00009 * rf7074_dpk - 0.00028 * rf7074_dpk[-1] 

 (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 
157 

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 
158 

 D.W. (1) 3.2586 

 D.W. (2) 0.9766 

EF2024NAS = (0.08908 * RTP.1 - 0.07176) * EF2024 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef2024nas/ef2024 = 0.08908 * rtp.1 - 0.07176 

 (2.54605) (2.05763) 

 Sum Sq 0.0000 

 Std Error 0.0017 

 LHS Mean 0.0170 

 R-Squared 0.6836 

 R Bar Squared 0.5782 

 F-STAT 1, 3 6.4824 

 D.W. (1) 2.6600 

 D.W. (2) 1.5247 

EF2534NAS = (0.00906 * RTP.1 + 0.03539) * EF2534 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef2534nas/ef2534 = 0.00906 * rtp.1 + 0.03539 

 (0.34277) (1.34366) 

 Sum Sq 0.0000 

 Std Error 0.0013 

 LHS Mean 0.0444 

 R-Squared 0.0377 

 R Bar Squared 0.2831 

 F-STAT 1, 3 0.1175 

 D.W. (1) 3.0818 

 D.W. (2) 1.1094 

EF3544NAS = (-0.01869 * RTP.1 + 0.08087) * EF3544 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef3544nas/ef3544 = -0.01869 * rtp.1 + 0.08087 

 (0.70565) (3.06320) 

 Sum Sq 0.0000 

 Std Error 0.0013 

 LHS Mean 0.0622 

 R-Squared 0.1424 

 R Bar Squared 0.1435 

 F-STAT 1, 3 0.4979 

 D.W. (1) 2.2440 

 D.W. (2) 2.1852 

EF4554NAS = (0.07232 * RTP.1 - 0.00701) * EF4554 

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 
159 

 R Bar Squared 0.6436 

 F-STAT 1, 3 8.2229 

 D.W. (1) 1.7821 

 D.W. (2) 2.7029 

EF5564NAS = (0.07872 * RTP.1 + 0.00466) * EF5564 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef5564nas/ef5564 = 0.07872 * rtp.1 + 0.00466 

 (1.38159) (0.08196) 

 Sum Sq 0.0000 

 Std Error 0.0028 

 LHS Mean 0.0831 

 R-Squared 0.3889 

 R Bar Squared 0.1851 

 F-STAT 1, 3 1.9088 

 D.W. (1) 2.6092 

 D.W. (2) 2.2686 

EF65ONAS = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef6569nas/ef6569 = 0.10940 

 (37.7493) 

 Sum Sq 0.0002 

 Std Error 0.0065 

 LHS Mean 0.1094 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 3.0431 

 D.W. (2) 1.2204 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 ef7074nas/ef7074 = 0.12265 

 (16.4939) 

 Sum Sq 0.0011 

 Std Error 0.0166 

 LHS Mean 0.1226 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 1.0289 

 D.W. (2) 1.7188 

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 
160 

 R Bar Squared 0.0000 

 F 0, 4 NC 

 D.W. (1) 1.6889 

 D.W. (2) 1.2345 

EM1617NAS = (-0.23035 * RTP.1 + 0.24985) * EM1617 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em1617nas/em1617 = -0.23035 * rtp.1 + 0.24985 

 (5.08538) (5.53372) 

 Sum Sq 0.0000 

 Std Error 0.0022 

 LHS Mean 0.0203 

 R-Squared 0.8961 

 R Bar Squared 0.8614 

 F-STAT 1, 3 25.8611 

 D.W. (1) 2.4658 

 D.W. (2) 1.6839 

EM1819NAS = (-0.05782 * RTP.1 + 0.07265) * EM1819 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em1819nas/em1819 = -0.05782 * rtp.1 + 0.07265 

 (3.43044) (4.32458) 

 Sum Sq 0.0000 

 Std Error 0.0008 

 LHS Mean 0.0150 

 R-Squared 0.7969 

 R Bar Squared 0.7291 

 F-STAT 1, 3 11.7679 

 D.W. (1) 3.3262 

 D.W. (2) 1.0399 

EM2024NAS = (-0.09206 * RTP.1 + 0.11567) * EM2024 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em2024nas/em2024 = -0.09206 * rtp.1 + 0.11567 

 (2.44839) (3.08618) 

 Sum Sq 0.0000 

 Std Error 0.0018 

 LHS Mean 0.0239 

 R-Squared 0.6665 

 R Bar Squared 0.5553 

 F-STAT 1, 3 5.9946 

 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 
161 

 LHS Mean 0.0522 

 R-Squared 0.7254 

 R Bar Squared 0.6338 

 F-STAT 1, 3 7.9230 

 D.W. (1) 1.8300 

 D.W. (2) 2.9632 

EM3544NAS = (0.02739 * RTP.1 + 0.05236) * EM3544 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em3544nas/em3544 = 0.02739 * rtp.1 + 0.05236 

 (0.61129) (1.17241) 

 Sum Sq 0.0000 

 Std Error 0.0022 

 LHS Mean 0.0797 

 R-Squared 0.1108 

 R Bar Squared 0.1857 

 F-STAT 1, 3 0.3737 

 D.W. (1) 2.5508 

 D.W. (2) 2.2676 

EM4554NAS = (0.06217 * RTP.1 + 0.03411) * EM4554 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em4554nas/em4554 = 0.06217 * rtp.1 + 0.03411 

 (1.91738) (1.05544) 

 Sum Sq 0.0000 

 Std Error 0.0016 

 LHS Mean 0.0961 

 R-Squared 0.5507 

 R Bar Squared 0.4009 

 F-STAT 1, 3 3.6764 

 D.W. (1) 2.5497 

D.W. (2) 1.5554 

EM5564NAS = (-0.04776 * RTP.1 + 0.16626) * EM5564 

Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em5564nas/em5564 = -0.04776 * rtp.1 + 0.16626 

 (0.60480) (2.11226) 

 Sum Sq 0.0000 

 Std Error 0.0039 

 LHS Mean 0.1187 

 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 
162 

 Std Error 0.0069 

 LHS Mean 0.1653 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 1.7716 

 D.W. (2) 2.9645 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em7074nas/em7074 = 0.17798 

 (22.9265) 

 Sum Sq 0.0012 

 Std Error 0.0174 

 LHS Mean 0.1780 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 1.7116 

 D.W. (2) 2.1991 

 

 Ordinary Least Squares 

 ANNUAL data for 5 periods from 2000 to 2004 

 Date: 9 NOV 2005 

 em75onas/em75o = 0.19058 

 (20.1892) 

 Sum Sq 0.0018 

 Std Error 0.0211 

 LHS Mean 0.1906 

 R-Squared 0.0000 

 R Bar Squared 0.0000 

 F-stat 0, 4 NC 

 D.W. (1) 2.7330 

 D.W. (2) 0.9992 

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) 
163 

EM2024AW = EAW * (-0.00664 + 0.10493 * RTP + 2.00153 * EM2024/E - 0.08191) 

EM2534AW = EAW * (-0.02065 + 0.38358 * RTP - 0.98380 * EM2534/E + 0.00751) 

EM3544AW = EAW * (0.00402 - 0.15663 * RTP + 1.72119 * EM3544/E + 0.05679) 

EM4554AW = EAW * (0.00834 + 0.03746 * RTP + 0.46522 * EM4554/E + 0.00144) 

EM5564AW = EAW * (-0.00655 + 0.03521 * RTP + 0.46852 * EM5564/E - 0.00037) 

EM65OAW = EAW * (-0.00114 + 0.07640 * RTP + 3.25911 * EM65O/E - 0.10058) 

EF1617AW = EAW * (-0.00055 - 0.05470 * RTP + 1.41760 * EF1617/E + 0.04979) 

EF1819AW = EAW * (0.00102 - 0.07375 * RTP + 0.78394 * EF1819/E + 0.07226) 

EF2024AW = EAW * (0.00112 - 0.05971 * RTP + 0.57256 * EF2024/E + 0.05907) 

EF2534AW = EAW * (0.00623 + 0.08868 * RTP + 1.00897 * EF2534/E - 0.15142) 

EF3544AW = EAW * (0.00687 - 0.00259 * RTP + 0.51319 * EF3544/E - 0.00937) 

EF4554AW = EAW * (0.00185 + 0.08747 * RTP + 0.28022 * EF4554/E - 0.08053) 

EF5564AW = EAW * (-0.00140 - 0.03001 * RTP - 0.59383 * EF5564/E + 0.07088) 

EF65OAW = EAW * (0.00096 + 0.06768 * RTP + 1.04213 * EF65O/E - 0.07359) 

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 
164 

EF2024NAWPH_R = MAX (0.001, -0.18707 * MOVAVG (20, RTP.1) - 0.00223 + 2.12060 * 1/YEAR + 0.00820 * NU10/NF2024 + 

0.14537) * EF2024 + EF2024NAWPH.ADJ 

EF2534NAWPH_R = MAX (0.001, 0.01874 * MOVAVG (4, RTP.1) - 0.04167 * MOVAVG (20, RTP.5) - 0.00090 + 1.55167 * 1/YEAR + 

0.01021 * NU10/NF2534 - 0.00170) * EF2534 + EF2534NAWPH.ADJ 

EF3544NAWPH_R = (0.00622 * MOVAVG (4, RTP.1) - 0.06062 * MOVAVG (20, RTP.5) + 0.00008 + 0.29372 * MOVAVG (12, 

EF2534NAWPH.36/EF2534.36) + 0.06187) * EF3544 + EF3544NAWPH.ADJ 

EF4554NAWPH_R = (0.02788 * MOVAVG (4, RTP.1) - 0.10996 * MOVAVG (20, RTP.5) - 0.00349 + 0.53068 * MOVAVG (12, 

EF3544NAWPH.36/EF3544.36) + 0.08883) * EF4554 + EF4554NAWPH.ADJ 

EF5564NAWPH_R = (0.05939 * MOVAVG (4, RTP.1) - 0.10618 * MOVAVG (8, RTP.5) - 0.00579 + 0.66195 * MOVAVG (12, 

EF4554NAWPH.36/EF4554.36) + 0.05966) * EF5564 + EF5564NAWPH.ADJ 

EF65ONAWPH_R = (0.22642 * MOVAVG (4, RTP.1) - 0.02069 + 0.33505 * MOVAVG (12, EF5564NAWPH.36) - 0.19707) + 

EF65ONAWPH.ADJ 

EM1617NAWPH_R = MAX (0.001, -0.05284 * MOVAVG (4, RTP.1) - 0.17833 * MOVAVG (4, RTP.5) - 0.00768 + 9.19738 * 1/YEAR - 

0.00588 * MINW/CPIW_U + 0.16862) * EM1617+ EM1617NAWPH.ADJ 

EM1819NAWPH_R = MAX (0.001, -0.07122 * MOVAVG (4, RTP.1) - 0.03737 * MOVAVG (4, RTP.5) - 0.00282 + 3.76796 * 1/YEAR - 

0.00499 * MINW/CPIW_U + 0.08727) * EM1819+ EM1819NAWPH.ADJ 

EM2024NAWPH_R = MAX (0.001, -0.00450 * MOVAVG (4, RTP.1) - 0.02345 * MOVAVG (4, RTP.5) - 0.00113 - 0.00057 * 

MINW/CPIW_U + 0.03265) * EM2024 + EM2024NAWPH.ADJ 

EM2534NAWPH_R = MAX (0.001, - 0.00490 * MOVAVG (4, RTP.5) - 0.00054 - 0.00051 * MINW/CPIW_U + 0.00789) * EM2534 + 

EM2534NAWPH.ADJ 

EM3544NAWPH_R = (-0.00446 * MOVAVG (4, RTP.5) - 0.00041 - 0.00053 * MINW/CPIW_U + 0.00726) * EM3544 + 

EM3544NAWPH.ADJ 

EM4554NAWPH_R = (-0.00039 + 0.00129) * EM4554 + EM4554NAWPH.ADJ 

EM5564NAWPH_R = (-0.00015 + 0.00200) * EM5564 + EM5564NAWPH.ADJ 

EM65ONAWPH_R = (-0.00679 + 0.64405 * MOVAVG (12, EM5564NAWPH.36) + 0.00231) + EM65ONAWPH.ADJ 

ENAWPH_R = EF1617NAWPH_R + EF1819NAWPH_R + EF2024NAWPH_R + EF2534NAWPH_R + EF3544NAWPH_R + 

EF4554NAWPH_R + EF5564NAWPH_R + EF65ONAWPH_R + EM1617NAWPH_R + EM1819NAWPH_R + 

EM2024NAWPH_R + EM2534NAWPH_R + EM3544NAWPH_R + EM4554NAWPH_R 

 + EM5564NAWPH_R + EM65ONAWPH_R 

ENAWPH = IF LONGRANGE = 0 

 THEN ENAWPH_R 

 ELSE ENAWPH.1 * (E_FE/E_FE.1) 

EM1617NAWPH = EM1617NAWPH_R * (ENAWPH/ENAWPH_R) 

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 
165 

EF5564NAS_R = (0.07872 * RTP.1 + 0.00466) * EF5564 + EF5564NAS.ADJ 

EF65ONAS_R = (0.10940 * EF6569 + 0.12265 * EF7074 + 0.14137 * EF75O) + EF65ONAS.ADJ 

EM1617NAS_R = (-0.23035 * RTP.1 + 0.24985) * EM1617 + EM1617NAS.ADJ 

EM1819NAS_R = (-0.05782 * RTP.1 + 0.07265) * EM1819 + EM1819NAS.ADJ 

EM2024NAS_R = (-0.09206 * RTP.1 + 0.11567) * EM2024 + EM2024NAS.ADJ 

EM2534NAS_R = (-0.09661 * RTP.1 + 0.14843) * EM2534 + EM2534NAS.ADJ 

EM3544NAS_R = (0.02739 * RTP.1 + 0.05236) * EM3544 + EM3544NAS.ADJ 

EM4554NAS_R = (0.06217 * RTP.1 + 0.03411) * EM4554 + EM4554NAS.ADJ 

EM5564NAS_R = (-0.04776 * RTP.1 + 0.16626) * EM5564 + EM5564NAS.ADJ 

EM65ONAS_R = (0.16527 * EM6569 + 0.17798 * EM7074 + 0.19058 * EM75O) + EM65ONAS.ADJ 

ENAS_R = EF1617NAS_R + EF1819NAS_R + EF2024NAS_R + EF2534NAS_R + EF3544NAS_R + EF4554NAS_R + EF5564NAS_R + 

EF65ONAS_R + EM1617NAS_R + EM1819NAS_R + EM2024NAS_R + EM2534NAS_R + EM3544NAS_R + 

EM4554NAS_R + EM5564NAS_R + EM65ONAS_R 

ENAS = IF LONGRANGE = 0 

 THEN ENAS_R 

 ELSE ENA * (ENAS.1/ENA.1) 

EM1617NAS = EM1617NAS_R * (ENAS/ENAS_R) 

EM1819NAS = EM1819NAS_R * (ENAS/ENAS_R) 

EM2024NAS = EM2024NAS_R * (ENAS/ENAS_R) 

EM2534NAS = EM2534NAS_R * (ENAS/ENAS_R) 

EM3544NAS = EM3544NAS_R * (ENAS/ENAS_R) 

EM4554NAS = EM4554NAS_R * (ENAS/ENAS_R) 

EM5564NAS = EM5564NAS_R * (ENAS/ENAS_R) 

EM65ONAS = EM65ONAS_R * (ENAS/ENAS_R) 

EF1617NAS = EF1617NAS_R * (ENAS/ENAS_R) 

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 
166 

ENAU = ENAU_R 

EM1617NAU = EM1617NAU_R * (ENAU/ENAU_R) 

EM1819NAU = EM1819NAU_R * (ENAU/ENAU_R) 

EM2024NAU = EM2024NAU_R * (ENAU/ENAU_R) 

EM2534NAU = EM2534NAU_R * (ENAU/ENAU_R) 

EM3544NAU = EM3544NAU_R * (ENAU/ENAU_R) 

EM4554NAU = EM4554NAU_R * (ENAU/ENAU_R) 

EM5564NAU = EM5564NAU_R * (ENAU/ENAU_R) 

EM65ONAU = EM65ONAU_R * (ENAU/ENAU_R) 

EF1617NAU = EF1617NAU_R * (ENAU/ENAU_R) 

EF1819NAU = EF1819NAU_R * (ENAU/ENAU_R) 

EF2024NAU = EF2024NAU_R * (ENAU/ENAU_R) 

EF2534NAU = EF2534NAU_R * (ENAU/ENAU_R) 

EF3544NAU = EF3544NAU_R * (ENAU/ENAU_R) 

EF4554NAU = EF4554NAU_R * (ENAU/ENAU_R) 

EF5564NAU = EF5564NAU_R * (ENAU/ENAU_R) 

EF65ONAU = EF65ONAU_R * (ENAU/ENAU_R) 

EFNAU = EF1617NAU + EF1819NAU + EF2024NAU + EF2534NAU + EF3544NAU + EF4554NAU + EF5564NAU + EF65ONAU 

EMNAU = EM1617NAU + EM1819NAU + EM2024NAU + EM2534NAU + EM3544NAU + EM4554NAU + EM5564NAU + 

EM65ONAU 

Agricultural 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) 
167 

EM4554AW = EM4554AW_R * (EAW/EAW_R) 

EM5564AW = EM5564AW_R * (EAW/EAW_R) 

EM65OAW = EM65OAW_R * (EAW/EAW_R) 

EF1617AW = EF1617AW_R * (EAW/EAW_R) 

EF1819AW = EF1819AW_R * (EAW/EAW_R) 

EF2024AW = EF2024AW_R * (EAW/EAW_R) 

EF2534AW = EF2534AW_R * (EAW/EAW_R) 

EF3544AW = EF3544AW_R * (EAW/EAW_R) 

EF4554AW = EF4554AW_R * (EAW/EAW_R) 

EF5564AW = EF5564AW_R * (EAW/EAW_R) 

EF65OAW = EF65OAW_R * (EAW/EAW_R) 

EFAW = EF1617AW+ EF1819AW+ EF2024AW+ EF2534AW+ EF3544AW+ EF4554AW+ EF5564AW+ EF65OAW 

EMAW = EM1617AW+ EM1819AW+ EM2024AW+ EM2534AW+ EM3544AW+ EM4554AW+ EM5564AW+ EM65OAW 

Self-employed 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) 
168 

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) 

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 
169 

AHWM2534NAW = 17.0559 * RTP - 0.29076 * 1 + 0.04542 *YEAR + 22.5121 

AHWM3544NAW = 18.3314 * RTP - 0.30475 * 1 + 0.04409 *YEAR + 22.3275 

AHWM4554NAW = 16.0678 * RTP - 0.12289 * 1 + 0.07446 *YEAR + 21.4366 

AHWM5564NAW = 10.8277 * RTP + 0.23715 * 1 + 30.8975 

AHWM65ONAW = -0.28038 * 1 + 5.40682 * RTP + 25.4797 

Females 

AHWF1617NAW = 17.2598 * RTP + 7.31262 * RTP.1 - 24.9241 * RNF1617S + 16.9218 

AHWF1819NAW = 18.7922 * RTP + 13.1066 * RTP.1 - 18.9417 * RNF1819S- 16.2182 * PF1819 + 0.81920 * 1 + 16.7826 

AHWF2024NAW = -219.154 * PF2024 + 12.4226 * RTP - 0.98470 * 1 + 158.354 * (PF2024)2

 + 98.6034 

AHWF2534NAW = -39.2904 * PF2534 + 39.6515 * (PF2534)2

 + 9.10839 * RTP- 0.33503 * 1 + 35.8525 

AHWF3544NAW = -39.2904 * PF3544 + 39.6515 * (PF3544)2

 + 7.40115 * RTP- 0.38214 * 1 + 36.9133 

AHWF4554NAW = 8.64511 * RTP - 63.8042 * PF4554 + 59.9107 * (PF4554)2

 - 0.58355 * 1 + 44.0723 

AHWF5564NAW = 6.61506 * RTP - 0.28969 * 1 + 8.36882 * PF5564 + 24.8288 

AHWF65ONAW = -0.43916 * 1 + 26.5228 + (8.36882/2) * (PF65O- 0.086) 

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 
170 

AHWM2024NAW = 20.1161 * MOVAVG (2, RTP.1) - 10.2292 * RNM2024S - 2.28628 * (PM2024NM * NM2024NM/ (PM2024NM * 

NM2024NM + PM2024MS * NM2024MS + PM2024MA * NM2024MA)) + 23.2252 + AHWM2024NAW.ADJ 

AHWM2534NAW = MIN (45, 17.0559 * MOVAVG (2, RTP.1) - 0.29076 * 1 + 0.04542 *YEAR + 22.5121) + AHWM2534NAW.ADJ 

AHWM3544NAW = MIN (45, 18.3314 * MOVAVG (2, RTP.1) - 0.30475 * 1 + 0.04409 *YEAR + 22.3275) + AHWM3544NAW.ADJ 

AHWM4554NAW = MIN (45, 16.0678 * MOVAVG (2, RTP.1) - 0.12289 * 1 + 0.07446 *YEAR + 21.4366) + AHWM4554NAW.ADJ 

AHWM5564NAW = 10.8277 * MOVAVG (2, RTP.1) + 0.23715 * 1 + 30.8975 + AHWM5564NAW.ADJ 

AHWM65ONAW = -0.28038 * 1 + 5.40682 * MOVAVG (2, RTP.1) + 25.4797 + AHWM65ONAW.ADJ 

Females 

AHWFNAW1 = AHWF1617NAW* (EF1617 -EF1617NAS-EF1617NAU-EF1617AW-EF1617AS-EF1617AU) 

AHWFNAW2 = AHWF1819NAW* (EF1819 -EF1819NAS-EF1819NAU-EF1819AW-EF1819AS-EF1819AU) 

AHWFNAW3 = AHWF2024NAW* (EF2024 -EF2024NAS-EF2024NAU-EF2024AW-EF2024AS-EF2024AU) 

AHWFNAW4 = AHWF2534NAW* (EF2534 -EF2534NAS-EF2534NAU-EF2534AW-EF2534AS-EF2534AU) 

AHWFNAW5 = AHWF3544NAW* (EF3544 -EF3544NAS-EF3544NAU-EF3544AW-EF3544AS-EF3544AU) 

AHWFNAW6 = AHWF4554NAW* (EF4554 -EF4554NAS-EF4554NAU-EF4554AW-EF4554AS-EF4554AU) 

AHWFNAW7 = AHWF5564NAW* (EF5564 -EF5564NAS-EF5564NAU-EF5564AW-EF5564AS-EF5564AU) 

AHWFNAW8 = AHWF65ONAW * (EF65O -EF65ONAS-EF65ONAU-EF65OAW-EF65OAS-EF65OAU) 

AHWFNAW = (AHWFNAW1 + AHWFNAW2 + AHWFNAW3 + AHWFNAW4 + AHWFNAW5 + AHWFNAW6 + AHWFNAW7 

 + AHWFNAW8) / (EF – 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 
171 

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) 

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 
172 

 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 

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 
173 

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 

 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)) 
174 

 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 

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 
175 

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 

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 
176 

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 

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 
177 

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 
178 

2.3 OASDI Covered Employment and Earnings (COV) 

Total At-Any-Time Employment 

Males 

Aged 1 through 9 

CEM1 = 0.00026 * NM1 

CEM2 = 0.00031 * NM2 

CEM3 = 0.00025 * NM3 

CEM4 = 0.00019 * NM4 

CEM5 = 0.00036 * NM5 

CEM6 = 0.00042 * NM6 

CEM7 = 0.00165 * NM7 

CEM8 = 0.00239 * NM8 

CEM9 = 0.00279 * NM9 

Aged 10 through 15 

TEM1013 = 0.01969 * (NM10 + NM11 + NM12 + NM13 + NM10[+1] + NM11[+1] + NM12[+1] + NM13[+1])/2 

TEM1415 = (0.42767 * RTP - 1.02624 * NM1415 / (NM1415 + NM1617) + 0.23102) * ((NM14 + NM15 + NM14[+1] + NM15[+1])/2) 

Females 

Aged 1 through 9 

CEF1 = 0.00028 * NF1 

CEF2 = 0.00023 * NF2 

CEF3 = 0.00020 * NF3 

CEF4 = 0.00031 * NF4 

CEF5 = 0.00041 * NF5 

CEF6 = 0.00055 * NF6 

CEF7 = 0.00129 * NF7 

CEF8 = 0.00156 * NF8 

CEF9 = 0.00212 * NF9 

Aged 10 through 15 

TEF1013 = IF YEAR < = 110 

THEN (0.04615 * RTP - 0.00014 * YEAR - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] + 

NF13[+1])/2 

ELSE (0.04615 * RTP - 0.00014 * 110 - 0.02268) * (NF10 + NF11 + NF12 + NF13 + NF10[+1] + NF11[+1] + NF12[+1] 

+ NF13[+1])/2 

TEF1415 = (0.48500 * RTP - 0.79002 * NF1415 / (NF1415 + NF1617) + 0.02205) * ((NF14 + NF15 + NF14[+1] + NF15[+1])/2) 

Total Males, Total Females and Combined Total 

TEM = CEM1 + CEM2 + CEM3 + CEM4 + CEM5 + CEM6 + CEM7 + CEM8 + CEM9 + TEM1013 + TEM1415 + TEM16O 

TEF = CEF1 + CEF2 + CEF3 + CEF4 + CEF5 + CEF6 + CEF7 + CEF8 + CEF9 + TEF1013 + TEF1415 + TEF16O 

TE = TEM + TEF 

Male Disaggregates Aged 16 and Over 

TEM1617 = (-0.0337 - 1.32778 * REM1617_A + 1.11118 + RNM1617MAX-0.5 * 0.0637 - 0.161 * RILEM1519) * (EM1617 

 * REM1617_M * REM2_1617 - EM1617AU - EM1617NAU + NM1617M) 

TEM1819 = (-0.0267 - 0.60094 * REM1819_A + 0.89703 + RNM1819MAX-0.5 * 0.0637 - 0.265 * RILEM1519) * (EM1819 

 * REM1819_M * REM2_1819 - EM1819AU- EM1819NAU + NM1819M) 

TEM2024 = (-0.0196 + 0.02072 + 0.82020 + RNM2024MAX-0.50 * 0.0176 - 0.357 * RILEM2024 -0.80 * (REM2024_A + 

RM2024D)) 

 * (EM2024 * REM2024_M * REM2_2024 - EM2024AU - EM2024NAU + NM2024M) 

TEM2529 = (-0.0113 + 0.02898 + 0.81312 + RNM2529MAX-0.50 * 0.0214 - 0.416 * RILEM2529 - 0.80 * (REM2529_A + 

RM2529D)) 

 * (EM2529 * REM2529_M * REM2_2529 - EM2529AU - EM2529NAU + NM2529M) 

TEM3034 = (0.0062 - 0.00445 + 0.55577 + RNM3034MAX-0.50 * 0.0416 - 0.424 * RILEM3034 - 0.50 * (REM3034_A + RM3034D)) 

 * (EM3034 * REM3034_M * REM2_3034 - EM3034AU - EM3034NAU + NM3034M) 

TEM3539 = (-0.0092 + 0.00162 + 0.50480 + RNM3539MAX-0.50 * 0.0279 - 0.423 * RILEM3539 -0.45 * (REM3539_A + 

RM3539D))* (EM3539 * REM3539_M * REM2_3539 - EM3539AU - EM3539NAU + NM3539M) 
179 

TEM4044 = (-0.0083 + 0.01717 + 0.41973 + RNM4044MAX-0.50 * 0.0062 - 0.418 * RILEM4044 - 0.40 * (REM4044_A + 

RM4044D)) * (EM4044 * REM4044_M * REM2_4044 - EM4044AU - EM4044NAU + NM4044M) 

TEM4549 = (-0.0026 - 0.00292 + 0.52707 + RNM4549MAX-0.50 * 0.0010 - 0.410 * RILEM4549 -0.50 * (REM4549_A + 

RM4549D))* (EM4549 * REM4549_M * REM2_4549 - EM4549AU-EM4549NAU + NM4549M) 

TEM5054 = (-0.0008 + 0.02301 + 0.53226 + RNM5054MAX - 0.50 * 0.0025 - 0.395 * RILEM5054 -0.50 * (REM5054_A + 

RM5054D)) 

 * (EM5054 * REM5054_M * REM2_5054 -EM5054AU-EM5054NAU + NM5054M) 

TEM5559 = (-0.0010 - 0.00842 + 0.46888 + RNM5559MAX - 0.50 * 0.0042 - 0.356 * RILEM5559 -0.40 * (REM5559_A + 

RM5559D))* (EM5559 * REM5559_M * REM2_5559 -EM5559AU-EM5559NAU + NM5559M) 

TEM6064 = (-0.0030 + 0.04966 + 0.59056 + RNM6064MAX - 0.50 * 0.0051 - 0.248 * RILEM6064 - 0.50 * (REM6064_A + 

RM6064D))* (EM6064 * REM6064_M * REM2_6064 -EM6064AU-EM6064NAU) 

TEM6569 = (-0.82949 * REM6569_A + 0.10116 + 1.55172) * (EM6569 * REM6569_M * REM2_6569 - EM6569AU - EM6569NAU) 

TEM70O = (0.01973 * 96 - 0.34903) * (EM70O* REM70O_M * REM2_70O-EM70OAU-EM70ONAU) 

TEM16O = TEM1617 + TEM1819 + TEM2024 + TEM2529 + TEM3034 + TEM3539 + TEM4044 + TEM4549 + TEM5054 + 

TEM5559 + TEM6064 + TEM6569 + TEM70O 

 

Female Disaggregates Aged 16 and Over 

TEF1617 = (0.0106 - 1.52661 * REF1617_A - 0.02280 + 1.17229 + RNF1617MAX + 0.5 * 0.0631 - 0.161 * RILEF1519) * (EF1617 

 * REF1617_M * REF2_1617 - EF1617AU - EF1617NAU + NF1617M) 

TEF1819 = (0.0166 - 0.56521 * REF1819_A + 0.04837 + 0.85527 + RNF1819MAX-0.5 * 0.0631 - 0.252 * RILEF1519) * (EF1819 

 * REF1819_M * REF2_1819 - EF1819AU - EF1819NAU + NF1819M) 

TEF2024 = (0.0202 + 0.02418 + 0.89686 + RNF2024MAX - 0.50 * 0.0349 - 0.318 * RILEF2024 - 0.90 * (REF2024_A + RF2024D)) 

 * (EF2024 * REF2024_M * REF2_2024 - EF2024AU - EF2024NAU + NF2024M) 

TEF2529 = (0.0185 + 0.03554 + 0.68431 + RNF2529MAX - 0.50 * 0.0378 - 0.342 * RILEF2529 - 0.70 * (REF2529_A + RF2529D)) 

 * (EF2529 * REF2529_M * REF2_2529 - EF2529AU - EF2529NAU + NF2529M) 

TEF3034 = (0.0156 + 0.00488 + 0.47083 + RNF3034MAX - 0.50 * 0.0465 - 0.340 * RILEF3034 - 0.45 * (REF3034_A + RF3034D)) 

 * (EF3034 * REF3034_M * REF2_3034 - EF3034AU - EF3034NAU + NF3034M) 

TEF3539 = (0.0156 + 0.000796 + 0.41423 + RNF3539MAX - 0.50 * 0.0318 - 0.343 * RILEF3539 - 0.40 * (REF3539_A + RF3539D)) 

 * (EF3539 * REF3539_M * REF2_3539 - EF3539AU - EF3539NAU + NF3539M) 

TEF4044 = (0.0127 + 0.00312 + 0.35298 + RNF4044MAX - 0.50 * 0.0135 - 0.353 * RILEF4044 - 0.35 * (REF4044_A + RF4044D)) 

 * (EF4044 * REF4044_M * REF2_4044 - EF4044AU - EF4044NAU + NF4044M) 

TEF4549 = (0.0064 + 0.00138 + 0.40080 + RNF4549MAX - 0.50 * 0.0086 - 0.358 * RILEF4549 - 0.40 * (REF4549_A + RF4549D)) 

 * (EF4549 * REF4549_M * REF2_4549 - EF4549AU - EF4549NAU + NF4549M) 

TEF5054 = (0.0037 + 0.01202 + 0.39021 + RNF5054MAX - 0.50 * 0.0089 - 0.336 * RILEF5054 - 0.40 * (REF5054_A + RF5054D)) 

 * (EF5054 * REF5054_M * REF2_5054 - EF5054AU - EF5054NAU + NF5054M) 

TEF5559 = (0.0034 + 0.03036 + 0.32074 + RNF5559MAX - 0.50 * 0.0094 - 0.280 * RILEF5559 - 0.30 * (REF5559_A + RF5559D)) 

 * (EF5559 * REF5559_M * REF2_5559 - EF5559AU - EF5559NAU + NF5559M) 

TEF6064 = (0.0030 + 0.02068 + 0.49318 + RNF6064MAX - 0.50 * 0.0115 - 0.176 * RILEF6064 - 0.45 * (REF6064_A + RF6064D)) 

 * (EF6064 * REF6064_M * REF2_6064 - EF6064AU - EF6064NAU) 

TEF6569 = 1.42 * (EF6569 * REF6569_M * REF2_6569 - EF6569AU - EF6569NAU) 

TEF70O = (0.92002 * TEM70O / (EM70O* REM70O_M * REM2_70O - EM70OAU - EM70ONAU) + 0.12035) * (EF70O * REF70O_M 

* REF2_70O-EF70OAU-EF70ONAU) 

TEF16O = TEF1617 + TEF1819 + TEF2024 + TEF2529 + TEF3034 + TEF3539 + TEF4044 + TEF4549 + TEF5054 + TEF5559 + 

TEF6064 + TEF6569 + TEF70O 

Self-Employed Only 

SEOCMB = 0.039 * (TEFC_N_N + TESL_N_N + EPRRB) 

SEOCMBL1 = 0.039 * (TEFC_N_N.1 + TESL_N_N.1 + EPRRB.1) 

SEO = (SEO.1 * (EAS + ENAS) / (EAS.1 + ENAS.1) + (SEOCMB - SEOCMBL1)) * MULTSEO 

Combination Workers 

CMB_TOT = ((-0.01468 + 0.06227 * RTP.1 -0.0008) * WSWA - SEOCMB) * MULTCMB 

CSW_TOT = SEO + CMB_TOT 

AW_CMBTOT = 1.4953 * ACWA 

W_CMBTOT = AW_CMBTOT * CMB_TOT 

CMB_WRELMAX = TAXMAX/AW_CMBTOT 

CMB Wage Andover Curve 

CMB_WAO1 = IF (CMB_WRELMAX < 0.0543009) 

 THEN 1 - 0.722659 * CMB_WRELMAX0.65 - 0.461913 * CMB_WRELMAX0.8

 ELSE IF (CMB_WRELMAX<0.1086018) 

 THEN -1.02884 * CMB_WRELMAX0.6 + 0.324761 * CMB_WRELMAX1.6 + 1.02015 

 ELSE IF (CMB_WRELMAX < 0.1629027) 
180 

 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 

 

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 
181 

OASDI Wages 

Covered Employment and Wages – Federal Civilian Government 

TEFC = (TEFC.1 / EGGEFC.1) * EGGEFC 

TEFC_N = IF (CSRS.1 > 0) THEN TEFC_N.1/CSRS.1 * CSRS - TEFC_N_SW ELSE 0 

TEFC_N_N = TEFC_N * 0.86 

TEFC_N_O = (TEFC_N - TEFC_N_N) 

TEFC_O = (TEFC - TEFC_N) 

WEFC = (WEFC.1 / WSGGEFC.1) * WSGGEFC 

WEFC_O = (WEFC -WEFC_N) * ADJ_FSA_FC 

Covered Employment and Wages - State and Local Govt. 

TESL = (TESL.1/EGGESLMAX.1) * EGGESLMAX 

TESL_O = (TESL_O.1/TESL.1) * TESL 

TESL_N = (TESL-TESL_O) 

TESL_N_O = (TESL_N_O_HI + TESL_N_O_NHI) 

TESL_N_O_HI = (TESL_N - TESL_N_O_NHI - TESL_N_N_NHI) * CER_MQGE_O 

TESL_N_O_NHI = (TESL_N_O_NHI_S + TESL_N_O_NHI_E + TESL_N_O_NHI_NS) 

TESL_N_S = TESL_N_S.1 * (NF1819 + NF2024 + NM1819 + NM2024) / (NF1819.1 + NF2024.1 + NM1819.1 + 

NM2024.1) 

TESL_N_E = TESL_N_E.1 * (TESL / TESL.1) 

TESL_N_O_NHI_S = TESL_N_S * (TESL_N_O_NHI_S.1/TESL_N_S.1) 

TESL_N_O_NHI_E = TESL_N_E * 0.6 

TESL_N_O_NHI_NS = TESL_N_O_NHI_NS.1 * ESR_NS 

TESL_N_N = (TESL_N - TESL_N_O) 

TESL_N_N_HI = (TESL_N_N - TESL_N_N_NHI) 

TESL_N_N_NHI = (TESL_N_N_NHI_S + TESL_N_N_NHI_E + TESL_N_N_NHI_NS) 

TESL_N_N_NHI_S = (TESL_N_S - TESL_N_O_NHI_S) 

TESL_N_N_NHI_E = (TESL_N_E - TESL_N_O_NHI_E) 

TESL_N_N_NHI_NS = TESL_N_N_NHI_NS.1 * ESR_NS 

WESL = (WESL.1/WSGGESL.1) * WSGGESL 

WESL_O = (WESL_O.1/WSGGESL.1) * WSGGESL 

WESL_N = (WESL - WESL_O) 

WESL_N_HI = (WESL_N - WESL_N_NHI) 

WESL_N_NHI = (WESL_N_NHI_S + WESL_N_NHI_E + WESL_N_NHI_NS) 

WESL_N_NHI_S = WESL_N_NHI_S.1 * (TESL_N_S/TESL_N_S.1) * (AWSGGESL/AWSGGESL.1) 

WESL_N_NHI_E = WESL_N_NHI_E.1 * (TESL_N_E/TESL_N_E.1) * (AWSGGESL/AWSGGESL.1) 

RAWR_NS = IF (AWR_NS = 0) THEN 0 ELSE AWR_NS/AWR_NS.1 

WESL_N_NHI_NS = IF (ESR_NS = 0) THEN 0 ELSE WESL_N_NHI_NS.1 * (TESL_N_O_NHI_NS + TESL_N_N_NHI_NS) / 

 (TESL_N_O_NHI_NS.1 + TESL_N_N_NHI_NS.1) * (AWSGGESL/AWSGGESL.1) * RAWR_NS 

Self-Employed Earnings Sector 

Covered SENE 

CSE_TOT = (YF +YNF) / (YF.1 + YNF.1) * CSE_TOT.1 

CSE_CMB_N = (CSE_TOT / (CMB_TOT + SEO)) / (CSE_TOT.1 / (CMB_TOT.1 + SEO.1)) * (CSE_CMB_N.1 / (CMB_TOT.1 - 

CMB.1)) * (CMB_TOT - CMB) 

CSE = CSE_TOT - CSE_CMB_N 

ACSE_SEO = (CSE_TOT / (SEO + 0.416488 * CMB_TOT)) 

ACSE_CMB_TOT = 0.416488 * ACSE_SEO 

CSE_SEO = ACSE_SEO * SEO 

CSE_CMB_TOT = ACSE_CMB_TOT * CMB_TOT 

CSE_CMB = CSE_CMB_TOT - CSE_CMB_N 

ACSE_CMB = CSE_CMB/CMB 

Present Law OASDI and HI Covered Wages and Earnings 

WSGMLC = CML * WSGFM 

WSGFCA = WEFC_O 

CFCA = WSGFCA/WSGGEFC 

CSLHI = (WESL_O+WESL_N_HI)/WSGGESL 

WSGSLCA = WESL_O 

WSPH_O = CPH * WSPH 
182 

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 

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 
183 

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 
184 

2-4 Effective Taxable Payroll (TAXPAY)

2-4.1 Ratio of taxable employee to total covered OASDI wages (RWTEE) 

IF(RM.LT.0.439103091)THEN 

 RWTEE=RM-(0.26651/1.5)*RM**1.5-(0.388274/1.9)*RM**1.9 

ELSE IF(RM.LT.1.313896269)THEN 

 RWTEE=(1.17877/1.5)*RM**1.5-(2.9291/0.68)*DEXP(-0.68*RM)-2.31401*RM+4.327630386 

ELSE IF(RM.LT.2.570433485)THEN 

 RWTEE=-(0.0202216/0.25)*DEXP(-0.25*RM)-(1.329/1.4)*DEXP(-1.4*RM)+0.00944271*RM+0.904661863 

ELSE IF(RM.LT.4.418783378)THEN 

 RWTEE=-(0.0654817/0.35)*DEXP(-0.35*RM)-(1.415/1.51)*DEXP(-1.51*RM)+0.000676576*RM+0.954098019 

ELSE IF(RM.LT.14.73231225)THEN 

 RWTEE=-(0.0110626/0.15)*DEXP(-0.15*RM)-(0.0472319/0.45)*DEXP(-0.45*RM)-(0.257195/0.95)*DEXP(- 

0.95*RM)+0.000367645*RM+0.970880621 

ELSE 

 RWTEE=-(0.179935/0.75)*RM**(-0.75)+0.999970738 

END IF 

Where 

 RM = OASDI taxable maximum / average covered OASDI wage 

 RWTEE = Ratio if OASDI taxable employee to covered wages 

2-4.2 Taxable employee OASDI wages (WTEE) 

WTEE = RWTEE * WSC 

Where 

 RWTEE = Ratio of OASDI taxable employee to covered wages 

 WSC = OASDI total covered wages 

 WTEE = OASDI taxable employee wages 

2-4.3 Ratio of multi-employer refund wages to total OASDI covered wages (RMER) 

RMER = ( MER(-1) / WSC(-1) ) - 0.03217 * ( RWTEE – RWTEE(-1) ) - 0.00024*( RU - RU(-1) ) 

Where 

 MER(-1) = Multi-employer refund wages in prior year 

 RMER = Ratio of multi-employer refund wages to total OASDI covered wages 

 RU = Annual average civilian unemployment rate 

 RWTEE = Ratio of OASDI taxable employee to covered wages 

 WSC(-1) = OASDI total covered wages in prior year 

2-4.4 Multi-employer refund wages (MER) 

MER = RMER * WSC 

Where 

 MER = OASDI multi-employer refund wages 

 RMER = Ratio of multi-employer refund wages to total OASDI covered wages 

 WSC = OASDI total covered wages 

2-4.5 Taxable employer OASDI wages (WTER) 

WTER = WTEE + MER 

Where 

 MER = OASDI multi-employer refund wages 

 WTEE = OASDI taxable employee wages 

 WTER = OASDI taxable employer wages 

2-4.6 Ratio of taxable to covered self-employment earnings (RSET) 
185 

Preliminary 

BASECT = 47831.98 

BASECW = 36831.79 

BASEO = 23448.56 

Self-employed only 

SECSEO = CSE - SECCMB 

ASESEO = SECSEO / SEO 

ASEO96 = ASESEO(1996) 

ASESEO = ASESEO * BASEO / ASEO96 

O = TAXMAX / ASESEO 

IF(O.LT.0.021323273)THEN 

 OTR=O-(401.8/3.8)*O**3.8 

ELSE IF(O.LT.0.170586184)THEN 

 OTR=(12.6861/1.1)*O**1.1-(10.7855/1.15)*O**1.15-(.208585/1.9)*O**1.9-1.58102*O-.0000212479 

ELSE IF(O.LT.0.938224014)THEN 

 OTR=-(2.03924/2.5)*DEXP(-2.5*O)+(2.52113/1.6)*O**1.6-(1.11979/2.2)*O**2.2-1.33547*O+.825500132 

ELSE IF(O.LT.1.705861843)THEN 

 OTR=-(.375957/.3)*DEXP(-.3*O)-(.642976/2.3)*DEXP(-2.3*O)-.108863*O+1.555087525 

ELSE IF(O.LT.2.302913488)THEN 

 OTR=-(.248596/.25)*DEXP(-.25*O)-(1.003/2.2)*DEXP(-2.2*O)-.0565126*O+1.368881905 

ELSE IF(O.LT.3.624956417)THEN 

 OTR=-(.207896/.15)*DEXP(-.15*O)-(3.99112/2.5)*DEXP(-2.5*O)-.0699402*O+1.823982598 

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 
186 

ELSE IF(CW.LT.2.3077888)THEN 

 CWTR=-(.12964/.5)*DEXP(-.5*CW)-(.644861/1.5)*DEXP(-1.5*CW)+.0183343*CW+.731280763 

ELSE IF(CW.LT.2.9865502)THEN 

 CWTR=-(.361318/.8)*DEXP(-.8*CW)+.0219491*CW+.698954858 

ELSE IF(CW.LT.4.3440731)THEN 

 CWTR=-(.193202/.45)*DEXP(-.45*CW)+.00425171*CW+.82237055 

ELSE IF(CW.LT.5.4300913)THEN 

 CWTR=-(.0560412/.25)*DEXP(-.25*CW)-(.311286/.8)*DEXP(-.8*CW)+.00297316*CW+.854848493 

ELSE IF(CW.LT.13.5752283)THEN 

 CWTR=-(.0995677/.32)*DEXP(-.32*CW)+.00355234*CW+.843717127 

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 
187 

 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 

 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 
188 

 SET = OASDI taxable self-employment earnings 

 TRSE = OASDI self-employment tax rate 

2-4.11 OASDI quarterly taxable wage liability (WTLQ) 

Federal Civilian 

 Annual total wages (OASDI + MQGE) 

BAFCW = 34198.84 

AWCFC = WCFC / ECFC * BAFCW / AWCFCTOT97 

T=MAX/AWCFC 

IF(T.LT.0.014620379)THEN 

 FCTR=T-(1.04262/1.73)*T**1.73 

ELSE IF(T.LT.0.292407578)THEN 

 FCTR=-(1.22471/1.6)*T**1.6+(.826746/1.8)*DEXP(-1.8*T)+1.8535*T-.459368449 

ELSE IF(T.LT.0.760259704)THEN 

 FCTR=-(.635082/2D0)*T**2+(.604884/2.9)*T**2.9-(.403213/4.6)*T**4.6+.910343*T+.002291358 

ELSE IF(T.LT.1.228111829)THEN 

 FCTR=-(.162181/1.7)*T**1.7+(.143632/2.7)*T**2.7-(.312012/3.4)*T**3.4+.841165*T+.011332647 

ELSE IF(T.LT.1.520519407)THEN 

 FCTR=-(1.34084/3.5)*T**3.5+(1.09868/5D0)*T**5-(.404253/5.8)*T**5.8+1.17397*T-.222555715 

ELSE IF(T.LT.2.339260627)THEN 

 FCTR=(.671304/.5)*DEXP(-.5*T)-(3.27076/1.4)*DEXP(-1.4*T)+.126626*T+.353367869 

ELSE IF(T.LT.3.50889094)THEN 

 FCTR=(.0571643/.95)*DEXP(-.95*T)-(3.17633/1.8)*DEXP(-1.8*T)+.000623031*T+.996284293 

ELSE IF(T.LT.4.970928832)THEN 

 FCTR=-(12.3148/2.25)*DEXP(-2.25*T)+.0000698013*T+.999222265 

ELSE 

 FCTR=-(.0285502/2D0)*T**(-2D0)+1.00007094 

END IF 

WTFCTOT=FCTR*WCFC 

Where 

 AWCFC = Average covered Federal Civilian wages (OASDI plus MQGE) 

 AWCFCTOT97 = Average covered Federal Civilian wages (OASDI plus MQGE) for 1997 

 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 
189 

ELSE IF(T.LT.2.592341034)THEN 

 FCTR=(.557032/1.2)*DEXP(-1.2*T)-(5.40739/2.2)*DEXP(-2.2*T)+.0102014*T+.960037325 

ELSE 

 FCTR=-(32.3187/3.5)*DEXP(-3.5*T)+1.000030482 

END IF 

WTFCHO=FCTR*WCFC 

Where 

 AWCFC = Average covered Federal Civilian MQGE wages 

 AWCFCHO97 = Average covered Federal Civilian MQGE wages for 1997 

 BAFCW = Average Federal Civilian MQGE wages in 1% sample data for 1997 used to produce equations 

 ECFC = Covered Federal Civilian MQGE employment 

 FCTR = Ratio of taxable to covered Federal Civilian MQGE wages 

 MAX = OASDI taxable maximum 

 T = Ratio of the OASDI taxable maximum to average covered Federal Civilian MQGE wages 

 WCFC = Covered Federal Civilian MQGE wages 

 WTFCHO = Taxable Federal Civilian MQGE wages 

Annual OASDI taxable wages 

WTFC = WTFCTOT – WTFCHO 

Where 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTFCHO = Taxable Federal Civilian MQGE wages 

 WTFCTOT = Taxable Federal Civilian wages (OASDI plus MQGE) 

Quarterly OASDI covered wages 

CFCQD(1) = .98357 * TCFCD(I,1) + FCPD(I,1) 

CFCQD(2) = .98909 * TCFCD(I,2) + FCPD(I,2) 

CFCQD(3) = 1.01833 * TCFCD(I,3) + FCPD(I,3) 

CFCQD(4) = 1.00814 * TCFCD(I,4) + FCPD(I,4) 

QWCFCOD(J) = CFCQD(J) * WTFC 

Where 

 CFCQD = Proportion of annual OASDI covered Federal Civilian wages paid in each quarter 

 FCPD = Payday variable for Federal Civilian wages based on calendar 

 I = Calendar year 

 J = Quarter 

 TCFCD = Proportion of annual NIPA Federal Civilian wages paid in each quarter 

 QWCFCOD = Quarterly OASDI covered Federal Civilian wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

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 
190 

 QWTFC(I,4)=WTFC-QWTFC(I,1)-QWTFC(I,2)-QWTFC(I,3) 

ELSE 

 Second and third quarter covered is completely taxable. 

 QWTFC(I,2)=QWCFC(I,2) 

 QWTFC(I,3)=QWCFC(I,3) 

 QWTFC(I,4)=WTFC-QWTFC(I,1)-QWTFC(I,2)-QWTFC(I,3) 

END IF 

Where 

 CFCQD = Proportion of annual OASDI covered Federal Civilian wages paid in each quarter 

 FCQ = Sum of proportions of annual OASDI covered Federal Civilian wages paid in each quarter for quarters two to four 

 FCQD = Proportion of annual OASDI taxable Federal Civilian wages paid in each quarter 

 FCTR = Ratio annual OASDI taxable to covered Federal Civilian wages 

 I = Calendar year 

 TCFCD = Proportion of annual NIPA Federal Civilian wages paid in each quarter 

 QWCFC = Quarterly OASDI covered Federal Civilian wages 

 QWTFC = Quarterly OASDI taxable Federal Civilian wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTFC2 = Total OASDI taxable Federal Civilian wages paid in quarters two to four 

 Quarterly OASDI taxable wage liabilities 

WTLQFCEE(I, J) = QWTFC(I, J) * TRWEE(I) 

WTLQFCER(I, J) = QWTFC(I, J) * TRWER(I) 

WTLQFC(I, J) = WTLQFCEE(I, J) + WTLQFCER(I, J) 

Where 

 I = Calendar year 

 J = Quarter 

 TRWEE = OASDI employee tax rate 

 TRWER = OASDI employer tax rate 

 WTLQFC = Quarterly OASDI taxable Federal Civilian combined employee-employer wage liabilities 

 WTLQFCEE = Quarterly OASDI taxable Federal Civilian employee wage liabilities 

 WTLQFCER = Quarterly OASDI taxable Federal Civilian employer wage liabilities 

Military wages 

 Annual OASDI taxable wages 

BACMW = 16439.95 

ACMW = AWCML * BACMW / AWCML97 

T = MAX / ACMW 

IF(T.LT.0.060827432)THEN 

 MTR=T-(.712875/2)*T**2 

ELSE IF(T.LT.0.182482295)THEN 

 MTR=(.71197/1.8)*T**1.8-(1.59752/2D0)*T**2+.97587*T+0.000542413 

ELSE IF(T.LT.0.608274315)THEN 

 MTR=-(1.75026/2D0)*T**2+(2.86837/3D0)*T**3-(1.90346/4D0)*T**4+1.10056*T-.006441373 

ELSE IF(T.LT.1.094893767)THEN 

 MTR=-(.700864/1.4)*T**1.4-(.40042/3.3)*T**3.3+(.197091/4.1)*T**4.1+1.33615*T-.056637087 

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 
191 

 AWCML = Average OASDI covered military wages 

 AWCML97 = Average OASDI covered military wages in 1997 

 BACMW = Average OASDI covered military wages in 1% sample data for 1997 used to produce equations 

 MAX = OASDI taxable maximum 

 MTR = Ratio of OASDI taxable to covered military wages 

 T = Ratio of the OASDI taxable maximum to average covered military wages 

 WCML = Annual OASDI covered military wages 

 WTML = Annual OASDI taxable military wages 

Quarterly OASDI covered wages 

CMLQD(1) = .97978*TCMLD(I,1)*MLPD(I,1) 

CMLQD(2) = 1.002*TCMLD(I,2)*MLPD(I,2) 

CMLQD(3) = 1.02145*TCMLD(I,3)*MLPD(I,3) 

CMLQD(4) = .99689*TCMLD(I,4)*MLPD(I,4) 

QWCML = CMLQD(J)*WCML 

Where 

 CMLQD = Proportion of annual OASDI covered military wages paid in each quarter 

 I = Calendar year 

 J = Quarter 

 MLPD = Payday variable for military wages based on calendar 

 QWCML = Quarterly OASDI covered military wages 

 TCMLD = Proportion of annual NIPA military wages paid in each quarter 

 WCML = Annual OASDI covered military wages 

Quarterly OASDI taxable wages 

T=MAX/AWCML 

IF(MLTR.LT.0.776)QML(1)=CMLQD(1)+.393565-.018307*T-3.44641/T+15.6381/T**2-40.0168/T**3+62.0449/T**4-

57.525/T**5+30.2498/T**6-7.8664/T**7+.674629/T**8 

IF(MLTR.LT.0.952)QML(2)=CMLQD(2)+.844748-.0401062*T-7.24247/T+32.4957/T**2-83.3328/T**3+129.374/T**4-

122.526/T**5+68.2737/T**6-20.1479/T**7+2.34289/T**8 

IF(MLTR.LT.0.985)QML(3)=CMLQD(3)-2.62266+.125592*T+22.5832/T-105.727/T**2+300.027/T**3-540.915/T**4+622.304/T**5-

441.658/T**6+175.722/T**7-29.8987/T**8 

IF(MLTR.LT.1.)QML(4)=CMLQD(4)+2.37295-.111565*T-21.1954/T+106.049/T**2-330.637/T**3+658.869/T**4-

835.626/T**5+648.641/T**6-279.392/T**7+50.9246/T**8 

IF(MLTR.LT.0.776)THEN 

 QWTML(I,1:4)=QML(1:4)*WTML 

ELSE IF(MLTR.LT.0.952)THEN 

 QWTML(I,1)=QWCML(I,1) 

 TOTWG1=WTML-QWTML(I,1) 

 Q1=QML(2)+QML(3)+QML(4) 

 QML(2:4)=QML(2:4)/Q1 

 QWTML(I,2:4)=QML(2:4)*TOTWG1 

ELSE IF(MLTR.LT.0.985)THEN 

 QWTML(I,1)=QWCML(I,1) 

 QWTML(I,2)=QWCML(I,2) 

 TOTWG1=WTML-QWTML(I,1)-QWTML(I,2) 

 Q1=QML(3)+QML(4) 

 QML(2:4)=QML(2:4)/Q1 

 QWTML(I,2:4)=QML(2:4)*TOTWG1 

ELSE IF(MLTR.LT.1.)THEN 

 QWTML(I,1)=QWCML(I,1) 

 QWTML(I,2)=QWCML(I,2) 

 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 
192 

 QML = Proportion of annual OASDI taxable military wages paid in each quarter 

 QWCML = Quarterly OASDI covered military wages 

 QWTML = Quarterly OASDI taxable military wages 

 T = Ratio of the OASDI taxable maximum to average covered military wages 

 TOTWG1 = Annual OASDI taxable military wages for all quarters except first or first and second 

 WTML = Annual OASDI taxable military wages 

 Quarterly OASDI taxable wage liabilities 

WTLQMLEE(I, J) = QWTML(I, J) * TRWEE(I) 

WTLQMLER(I, J) = QWTML(I, J) * TRWER(I) 

WTLQML(I, J) = WTLQMLEE(I, J) + WTLQMLER(I, J) 

Where 

 I = Calendar year 

 J = Quarter 

 TRWEE = OASDI employee tax rate 

 TRWER = OASDI employer tax rate 

 WTLQML = Quarterly OASDI taxable military combined employee-employer wage liabilities 

 WTLQMLEE = Quarterly OASDI taxable military employee wage liabilities 

 WTLQMLER = Quarterly OASDI taxable military employer wage liabilities 

Federal 

WCF = WCFC + WCML 

QWCF = QWCFC + QWCML 

WTF = WTFC + WTML 

QWTF = QWTFC + QWTML 

WTLQFEE(I,J) = QWTF(I,J) * TRWEE(I) 

WTLQFER(I,J) = QWTF(I,J) * TRWER(I) 

WTLQF(I,J) = WTLQFEE(I,J) + WTLQFER(I,J) 

Where 

 I = Calendar year 

 J = Quarter 

 QWCF = Quarterly OASDI covered Federal wages 

 QWCF C = Quarterly OASDI covered Federal Civilian wages 

 QWCML = Quarterly OASDI covered military wages 

 QWTF = Quarterly OASDI taxable Federal wages 

 QWTFC = Quarterly OASDI taxable Federal Civilian wages 

 QWTML = Quarterly OASDI taxable military wages 

 WCF = Annual OASDI covered Federal wages 

 WCFC = Annual OASDI covered Federal Civilian wages 

 WCML = Annual OASDI covered military wages 

 WTF = Annual OASDI taxable Federal wages 

 WTFC = Annual OASDI taxable Federal Civilian wages 

 WTLQF = Quarterly OASDI taxable Federal combined employee-employer wage liabilities 

 WTLQFEE = Quarterly OASDI taxable Federal employee wage liabilities 

 WTLQFER = Quarterly OASDI taxable Federal employer wage liabilities 

 WTML = Annual OASDI taxable military wages 

State and Local wages 

 Annual OASDI taxable wages 

BACW = 21583.61 

AWCSL = WCSL / ESLC * BACW / AWCSLOD97 

S = MAX / ASLC 

IF(S.LT.0.02316573)THEN 

 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 
193 

ELSE IF(S.LT.3.243202261)THEN 

 SLTR=-(2.40293/.2)*DEXP(-.2*S)+(6.44952/.4)*DEXP(-.4*S)-(5.64852/.6)*DEXP(-.6*S)-.278204*S+5.099074279 

ELSE IF(S.LT.5.559775305)THEN 

 SLTR=-(.0434955/.6)*DEXP(-.6*S)-(4.00403/1.7)*DEXP(-1.7*S)+.00006219*S+.997065459 

ELSE IF(S.LT.18.53258435)THEN 

 SLTR=-(.0272758/.5)*DEXP(-.5*S)+.0000671826*S+.997657785 

 ELSE 

 SLTR=-(.00861948/.7)*S**(-.7)+1.000492941 

END IF 

WTSL=SLTR*WCSL 

Where 

 AWCSL = Average OASDI covered State and Local wages adjusted for average wage used to produce equations 

 AWCSLOD97 = Average OASDI covered State and Local wages for 1997 

 BACW = Average OASDI covered State and Local wages in 1% sample data for 1997 used to produce equations 

 ESLC = OASDI covered State and Local employment 

 MAX = OASDI taxable maximum 

 S = Ratio of the OASDI taxable maximum to average covered State and Local wages 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WCSL = OASDI covered State and Local wages 

 WTSL = OASDI taxable State and Local wages 

Quarterly OASDI covered wages 

CSLQD(1)=1.0131455*TCSLD(I,1)+SLPD(I,1) 

CSLQD(2)=1.0431906*TCSLD(I,2)+SLPD(I,2) 

CSLQD(3)=.9060524*TCSLD(I,3)+SLPD(I,3) 

CSLQD(4)=1.0365866*TCSLD(I,4)+SLPD(I,4) 

QWCSL=CSLQD(1:4)*WCSL 

Where 

 CSLQD = Proportion of annual OASDI covered State and Local wages paid in each quarter 

 I = Calendar year 

 QWCSL = Quarterly OASDI covered State and Local wages 

 SLPD = Payday variable for State and Local wages based on calendar 

 TCSLD = Proportion of annual NIPA State and Local wages paid in each quarter 

 WCSL = Annual OASDI covered State and Local wages 

Quarterly OASDI taxable wages 

QSL(1)=(CSLQD(1)-.24087*(1.-1./SLTR)) 

QSL(2)=(CSLQD(2)-1.0492*(1.-1./SLTR)+.51259*(1.-1./SLTR**2)-.07643*(1.-1./SLTR**3)) 

QSL(3)=(CSLQD(3)-5.99032*(1.-SLTR**2)+13.238*(1.-SLTR**3)-11.3291*(1.-SLTR**4)+3.52237*(1.-SLTR**5)) 

QSL(4)=(CSLQD(4)+8.99897*(1.-SLTR**.25)-5.48866*(1.-SLTR**.5)) 

TQSL=QSL(2)+QSL(3)+QSL(4) 

QSL(2:4)= QSL(2:4)/TQSL 

QWTSL(I,1)=QSL(1)*WTSL 

QWTSL(I,2:4)=QSL(2:4)*(WTSL- QWTSL(I,1)) 

Where 

 CSLQD = Proportion of annual OASDI covered State and Local wages paid in each quarter 

 I = Calendar year 

 QSL = Proportion of annual OASDI taxable State and Local wages paid in each quarter 

 QWTSL = Quarterly OASDI taxable State and Local wages 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WTSL = OASDI taxable State and Local wages 

Quarterly OASDI taxable wage liabilities 

WTLQSL(I,J) = QWTSL(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 TRW = OASDI combined employee-employer tax rate 

 WTLQSL = Quarterly OASDI taxable State and Local combined employee-employer wage liabilities 
194 

Private household quarterly OASDI taxable wages and liabilities 

QWTPHH(I,J) = WCPHH(I) * QDPHH(J) 

WTLQPHH(I,J) = QWTPHH(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QDPHH = Proportion of annual OASDI taxable private household wages paid in each quarter 

 QWTPHH = Quarterly OASDI taxable private household wages 

 TRW = OASDI combined employee-employer tax rate 

 WCPHH = Annual OASDI covered private household wages 

 WTLQPHH = Quarterly OASDI taxable private household combined employee-employer wage liabilities 

Farm taxable wages 

 Annual OASDI 

BAFMW = 7467.91 

AWCFM97 = ACFMW(1997) 

F = MAX / (ACFMW * BAFMW / AWCFM97) 

IF(F.LT.0.066953142)THEN 

 FMTR=F- (1.30211/1.75)*F**1.75 

ELSE IF(F.LT.0.401718855)THEN 

 FMTR=-(1.18244/1.35)*F**1.35+(.25412/1.75)*F**1.75+1.24681*F-.001598087 

ELSE IF(F.LT.0.669531425)THEN 

 FMTR=-(.508764/.6)*DEXP(-.6*F)-(.300083/2.8)*DEXP(-2.8*F)+.0188542*F+.966550312 

ELSE IF(F.LT.1.87468799)THEN 

 FMTR=-(.638146/.6)*DEXP(-.6*F)-(.0322774/1.5)*DEXP(-1.5*F)-.033706*F+1.133974442 

ELSE IF(F.LT.2.41031313)THEN 

 FMTR=-(2.64644/1.1)*DEXP(-1.1*F)+(17.4638/2)*DEXP(-2*F)-(26.4191/2.5)*DEXP(-2.5*F)+.00686748*F+.909154345 

ELSE IF(F.LT.4.82062626)THEN 

 FMTR=-(1.06567/1.3)*F**1.3+(.073837/2.1)*F**2.1+1.31021*F-.007628879 

ELSE IF(F.LT.6.427501679)THEN 

 FMTR=-(.178355/.5)*DEXP(-.5*F)-(1.70356/1.3)*DEXP(-1.3*F)+.00115171*F+.959096096 

ELSE IF(F.LT.10.7125028)THEN 

 FMTR=-(.0474377/0.35)*DEXP(-.35*F)-(1.32456/1)*DEXP(-1*F)+.0016146*F+.957903052 

ELSE IF(F.LT.11.38203422)THEN 

 FMTR=-(.0581938/.35)*DEXP(-.35*F)+.00130453*F+.961918378 

ELSE IF(F.LT.24.1031313)THEN 

 FMTR=-(.0492564/.3)*DEXP(-.3*F)+.000761577*F+.97040299 

ELSE 

 FMTR=-(.00304904/.06)*DEXP(-.06*F)+1.000606299 

END IF 

TFMW=FMTR*WCFM 

Where 

 ACFMW = Annual average OASDI covered farm wages 

 AWCFM97 = Annual average OASDI covered farm wages for 1997 

 BAFMW = Average farm wage in 1% sample data for 1997 used to produce equations 

F = Ratio of taxable maximum to annual average OASDI covered farm wages adjusted for average wage used in 

equations 

 FMTR = Ratio of OASDI taxable to covered farm wages 

 MAX = OASDI taxable maximum 

 TFMW = Annual OASDI taxable farm wages 

Quarterly OASDI wages and liabilities 

QWTFM(I,J) = TTFMD(I,J) * TFMW 

WTLQFM(I,J) = QWTFM(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 
195 

 QWTFM = Quarterly OASDI taxable farm wages 

 TFMW = Annual OASDI taxable farm wages 

 TRW = OASDI com 

 TTFMD = Proportion of annual OASDI taxable farm wages paid in each quarter 

 WTLQFM = Quarterly OASDI taxable farm combined employee-employer wage liabilities 

Quarterly OASDI taxable employee tips 

QWTTIPSEE(I,J) = QDTIP(J) * WTTIPSEE(I) 

QWTTIPSEE(I,2) = QWTTIPSEE(I,2) + WTTIPSSR(I) 

WTLQTIPSEE(I,J) = QWTTIPSEE(I,J) * TRW(I) 

Where 

 I = Calendar year 

 J = Quarter 

 QDTIP = Proportion of annual OASDI taxable tips received in each quarter 

 QWTTIPSEE = Quarterly OASDI taxable tips received by employees 

 WTLQTIPSEE = Quarterly OASDI combined employee-employer wage liabilities on taxable tips received by employees 

 TRW = OASDI combined employee-employer tax rate 

 WTTIPSEE = Annual OASDI taxable tips received by employees reported by employers 

 WTTIPSSR = Annual OASDI taxable tips received by employees self-reported on income tax returns 

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) 
196 

 QP(3)=-0.850885+1.824094*TWTR-0.981557*TWTR**2+PD(3)+TCPD(I,3) 

 QP(4)=0.350767-1.093966*TWTR+0.766972*TWTR**2+PD(4)+TCPD(I,4) 

END IF 

IF(PTR.LT.0.86)THEN 

 QP(J)=QP(J)+ADJTP(J) 

ELSE 

 IF((ADJCP(J)-ADJTP(J)).NE.0D0)QP(J)=QP(J)+ADJTP(J)+((PTR-BPTR)/(1.-BPTR))**4*(ADJCP(J)-ADJTP(J)) 

END IF 

QWTPNF(I, J) = QP(J) * WTPNF(I) + QWTTIPSEE(I, J) + QWTPHH(I, J) 

QWTPNF(I, 2) = QWTPNF(I, 2) + WTTIPSSR(I) 

Where 

 ACW93 = Annual average OASDI covered wage for 1993 

 AWC = Annual average OASDI covered wage for current year 

 BACW93 = Annual average OASDI covered wage for 1993 from actual data used to determine taxable to covered wage equations 

 I = Calendar year 

 J = Quarter 

 MAX = Annual OASDI taxable maximum 

NACW = Annual average OASDI covered wage for current year adjusted for average from actual data used to determine 

equations 

 PD = Payday variable for private non-farm based on calendar 

 QP = Proportion of annual OASDI taxable private non-farm wages excluding taxable tips paid in each quarter 

 QWTPNF = Quarterly OASDI taxable private non-farm wages including tips 

 TCPD = Proportion of annual NIPA private wages paid in each quarter 

 TWTR = Ratio of OASDI taxable to covered wages computed using equations based on data for 1993 

 X = Ratio of annual OASDI taxable maximum to adjusted annual average OASDI covered wage (NACW) 

Quarterly OASDI wage liabilities 

WTLQPNF(I,J) = (QWTPNF(I,J) – QWTPHH(I,J)) * TRW(I) 

Where 

 QWTPHH = Quarterly OASDI taxable private household wages 

 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 
197 

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 

 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 
198 

PWCS = OASDI taxable private non-farm wages paid in the first two months of each quarter on which taxes are 

collected in that quarter 

 QWSCPNF = Quarterly OASDI covered private non-farm wages 

 QRMREQ = Monthly deposit requirement 

 QRWREQ = Quarterly deposit requirement 

 QWSTXPHH = Quarterly OASDI taxable private non-farm wages (excluding household) 

QWTPC = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in the quarter the wages 

were paid 

QWTPF = Quarterly OASDI taxable private non-farm wages on which employers deposit taxes in the quarter after the 

wages were paid 

 RATEE(I,5) = OASDHI employee tax rate 

 RCSM = Proportion of OASDI taxable private non-farm wages wages paid in same quarter in which taxes are collected 

 RMF = Current year average wage size of firm 

SEP = Proportion of third quarter OASDI covered private non-farm wages (excluding tips and household) paid in 

September 

 TRAT = OASDHI employee tax rate 

 WSP = Economy-wide (NIPA) private wages 

SUBROUTINE ITERNU(A11,QPAR,QTOT,T,RMF,AMTOUT) 

 R=QPAR/QTOT 

 X=A11/(T*2.+.10) 

 DO 

 IWH=X*(.16011+.01998*LOG(X/RMF)-.01) 

 FWH=T*2.*X*((-1.4402*LOG(1.+X/RMF)+1.)*(1.-R)+R) 

 A1=IWH+FWH 

 D=A11/A1 

 N1=D*1000. 

 IF(N1.EQ.999.OR.N1.EQ.1000)THEN 

 RTAX=R+(1.-R)*(-1.07115*X/RMF+.38633*(X/RMF)**2+1) 

 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) 
199 

LMPW(4)=DECSL(I)-2.03892*(1.-SLTR)+1.90430*(1.-SLTR**2)-.6633*(1.-SLTR**3) 

DO J=1,4 

 SLCR(J)=(1.-LMPW(J))+LMPW(J)*LMCRPR(I-16,J) 

 QWTSLC(I,J)=SLCR(J)*QWTSL(I,J) 

 QWTSLF(I,J)=QWTSL(I,J)-QWTSLC(I,J) 

END DO 

Where 

 DECSL = Proportion of OASDI taxable State and Local wages paid in fourth quarter which are paid in December 

 I = Calendar year 

 J = Quarter 

 JUNSL = Proportion of OASDI taxable State and Local wages paid in second quarter which are paid in June 

LMCRPR = Proportion of OASDI taxable State and Local wages paid in final month of quarter on which employers are to deposit 

taxes in the same quarter 

 LMPW = Proportion of quarterly OASDI taxable State and Local wages paid in final month of quarter 

 MARSL = Proportion of OASDI taxable State and Local wages paid in first quarter which are paid in March 

 QWTSL = Quarterly OASDI taxable State and Local wages paid in quarter 

QWTSLC = Quarterly OASDI taxable State and Local wages paid in quarter on which taxes are deposited by the employer in the 

same quarter 

QWTSLF = Quarterly OASDI taxable State and Local wages paid in quarter on which taxes are deposited by the employer in the 

following quarter 

 SEPSL = Proportion of OASDI taxable State and Local wages paid in third quarter which are paid in September 

SLCR = Proportion of OASDI taxable State and Local wages paid in quarter on which taxes are deposited by the employer in 

the same quarter 

 SLTR = Ratio of OASDI taxable to covered State and Local wages 

 WCSL = Annual OASDI covered State and Local wages 

 WTSL = Annual OASDI taxable State and Local wages 

OASDI taxable wages collected on in same quarter wages paid and in following quarter 

WTQCQ(I,J)= QWTPCQ(I,J)+ QWTSLC(I,J)+QWTF(I,J) 

WTQFQ(I,J)= QWTPFQ(I,J)+ QWTSLF(I,J) 

Where 

 I = Calendar year 

 J = Quarter 

 QWTF = Quarterly OASDI taxable Federal wages 

 QWTPCQ = Quarterly OASDI taxable private wages collected on in same quarter wages paid 

 QWTPFQ = Quarterly OASDI taxable private wages collected on quarter following that in which wages paid 

 QWTSLCQ = Quarterly OASDI taxable State and Local wages collected on in same quarter wages paid 

 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 
200 

 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 
201 

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 
202 

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 
203 

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 
204 

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 
205 

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 
206 

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 
207 

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, 
208 

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 
209 

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 
210 

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 
211 

Process 3: 

Beneficiaries
212 

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 worker and their 

dependent beneficiaries. OLD-AGE AND SURVIVORS projects the number of retired workers, 

their dependent beneficiaries, and the dependent beneficiaries of deceased workers. 

All programs output data on an annual basis. 
213 

3.1. INSURED 

3.1.a. Overview 

Insured status is a critical requirement for a worker, who has participated in the covered 

economy, to receive Social Security benefits upon retirement or disability. The requirement for 

insured status depends on the age of a worker and his (or her) accumulation of quarters of 

coverage (QC). 

INSURED is a simulation model that estimates the percentage of the population that is fully 

insured (FPRO) and disability insured (DPRO) throughout the projection period. These 

estimates are used in conjunction with estimates of the Social Security area population to 

estimate the number of people that are fully insured (FINPOP) and disability insured (DINPOP). 

FINPOP is then used by the OLD-AGE AND SURVIVORS INSURANCE subprocess, and both 

FINPOP and DINPOP are used by the DISABILITY subprocess. FINPOP and DINPOP are 

projected by age, sex, and cohort. 

For each sex and birth cohort, INSURED simulates 30,000 work histories which represent the 

Social Security area population (SSAPOP). These histories are constructed from past and 

projected cover worker rates, median earnings, and amounts required for crediting QC. 

The equations for this subprocess are given below: 

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 

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 (2009 – 2090) by age (0 -100, age 100 

including age 100 and older), marital status (single, married, widowed, divorced) and 
214 

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)

Economics 

 Historical annual estimates of covered workers by sex (M, F) and age (15 – 74) for 

years (1937 – 2009). (Workflow 3.b)

 Annual projections (2010 – 2090) of covered workers that are based on the assumption 

that the portion of “other immigrants” in the Social Security Area stays constant at the 

level of the latest historical estimates by cohort and sex. The data format is the same as 

those in historical period. (Workflow 3.b)

 Annual projection (2007 – 2090) of average wage index and median covered earnings. 

(Workflow 3.f)

 “Other immigrant” workers with earnings posted to the Master Earnings File (MEF) by 

sex (M, F), age (16 – 95), and for years (2009 – 2090). (Workflow 3.g)

 Total “other immigrant” workers by sex (M, F), age (16 – 95), and for years (2009 – 

2090). (Workflow 3.h)

Beneficiaries 

 Disabled-worker beneficiaries at year end (2009 – 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.e)

Short-Range OCACT data 

 FINPOP by age (14 – 95, age 95 including age 95 and older) and sex (M, F) from the 

end of year1969 to the end of Short-Range projection period (2020). (Workflow 2.f)

(MKS-2011.2) 

DINPOP by age (15 – 66) and sex (M, F) from the end of year 1969 to the end of 

Short-Range projection period (2020). (Workflow 2.g) (MKS-2011.2) 

 

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 1937-2007. Data are updated using the data in the most recent Social 

Security Annual Statistical Supplement Table 4.B6. (Workflow 2.b) (MKS-2011.2) 
215 

 Number of disabled workers by age (20-69) and sex (M, F) for years 1958-2009. 

Ages 66-69 are zeros. Data are updated using the data from the historical disability 

file “wkrben”. (Workflow 2.e) (MKS-2011.2) 

 The amount required for crediting one quarter of coverage for years 1937-2007 from 

a OCACT web site. (Workflow 2.d) (MKS-2011.2) 

 Historical series of annual median earnings of all covered workers for years 1937-

2007. Data are updated using the data in the most recent Social Security Annual 

Statistical Supplement Table 4.B6. (Workflow 2.c) (MKS-2011.2) 

 The number of all covered workers (wage/salary workers, self-employed workers) by 

sex and amount of earnings for 2007 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-2011.2) 

 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-2011.1)

 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-2011.1)

 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-2011.1)

 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-2011.1)

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, 

the amounts required for crediting QC, and a cumulative worker distribution by earnings level. 

Covered worker rates by age and sex are defined as the ratio of covered workers to the Social 

Security area population. Historical and projected numbers of covered workers and the Social 

Security area population, which are provided by the Economics and Demography sections 

respectively, are used to calculate the rates for ages 15 through 69. For ages, 13 and 14, 

INSURED estimates covered worker rates based on the covered worker rates at age 15. 
216 

The amount of earnings needed to earn one QC is specified by law for each year of the historical 

period. Its projection assumes the same growth rate as the Social Security average wage index. 

 

The cumulative worker distribution by earnings level is called ‘FRAC’. It is a function of 

covered earnings relative to median earnings. For a given ratio of covered earnings relative to 

median earnings, FRAC returns the percentage of covered workers whose earnings relative to 

median earnings are less than the given ratio. It is constructed based on the latest historical data. 

It is used for each age and sex and is assumed to remain constant throughout the projection 

period. The program uses FRAC to estimate the percentage of covered workers that earn 0, 1, 2, 

3 or 4 QC in a given year. Thus, for a particular age and sex, the 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 

rates, the female SRCH and SLCT values are graded toward the male values29. 

 

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 
217 

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 fully insured 

percentage (FSIM) is calculated as the percentage of the 30,000 simulated records meeting the 

QC requirements for insured status. The same calculation is applied to the disability-insured 

percentage (DSIM). 

For each sex and cohort, FSIM and DSIM are determined at ages 13 to 69. FSIM is assumed to 

remain the same beyond age 69. 

A multiplicative adjustment is applied to both FSIM and DSIM to reflect future changes in the 

proportion of ‘other immigrants’ in the Social Security area population (OIMPOP) and the 

proportion of ‘other immigrants’ whose earnings are posted to the MEF (ADJLPR) from that in 

the base year for each cohort. Thus the adjustment factor is 

 1 [ ( ) * (1 ( ))]

1 [ ( ) * (1 ( ))]

OIMPOP base year ADJLPR base year

OIMPOP projection year ADJLPR projection year

 

  by cohort and sex. 

 

 percent of the male rate. 
218 

A second additive adjustment, DINADD, is made to DSIM. It accounts for workers who fail to 

meet the requirement for disability-insured status solely because of having no earnings while 

receiving disability benefits. INSURED assumes that workers who have been on the disability 

rolls for more than 3 years would be in this situation30. Thus, DINADD is 

# of workers on the disability rolls morethan3 years

Social Security Area population by age, sex, and cohort. 

If the adjusted results for DSIM are not consistent with historical data, an additional age-sexspecific additive adjustment (DIADJ) is used to bring the simulated results in line with the 

historical estimates. 

Finally, incorporation of Short-Range projections produces FPRO and DPRO. For the first 10 

years, FPRO and DPRO are set equal to Short-Range estimates. The difference in terms of the 

percentage between the Long-Range and Short-Range projections at the end of 10th year is 

linearly phased out during the next ten years by cohort and sex. 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. 

 

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. 
219 

 DISABILITY 

3.2.a. Overview

The Social Security Administration pays monthly disability benefits to workers who are insured 

for disability benefits and meet the definition of “disabled”. Provided that they meet certain 

requirements, spouses and children of disabled-worker beneficiaries may also receive monthly 

benefits. 

DISABILITY projects the number of disabled-worker beneficiaries in current-payment status 

(DIB) at the end of each year by age at entitlement, sex, and duration from entitlement. The 

number of DIB at the end of each year is based on the number of disabled-worker beneficiaries 

who are currently entitled to benefits (CE). The number of CE at the end of year is obtained by 

adding the number of newly entitled CE (New Entitlements) during the year and subtracting the 

number of CE who leave the disability rolls (Exits) during the year to the number of CE at the 

end of the prior year. Disabled-worker beneficiaries who leave the disability rolls (Exits) do so 

by recovering from disabilities (Recoveries), by dying (Deaths), or by converting to retired 

worker status (Conversions). A disabled-worker beneficiary converts to retired worker status 

upon reaching Normal Retirement Age (NRA), the age at which a person first becomes entitled 

to unreduced retirement benefit. 

DISABILITY also projects the number of future dependent beneficiaries of DIB by category, 

age, and sex. The six categories are minor child, student child, disabled adult child, young 

spouse, married aged spouse and divorced aged spouse. The numbers of dependent beneficiaries 

of DIB are obtained by multiplying the relevant subset of the SSA area population (Exposures) 

by a series of probabilities that relate to the regulations and requirements for obtaining benefits 

(Linkages). 

 New Entitlements(year) = ExposureBOY  Incidence Rate(year) (3.2.1) 

 where BOY is beginning of year. 

 Exits(year) = Recoveries(year) + Deaths(year) + Conversions(year) (3.2.2) 

 where Recoveries(year) = CEBOY  Recovery Rate(year) 

 where Deaths(year) = CEBOY  Death Rate(year). 

CEEOY = CEEOY-1 + New Entitlements (year) – Exits(year), (3.2.3) 

 where EOY is end of year, EOY-1 is end of prior year. 

Dependent Beneficiaries of DIB EOY = Exposures EOY  Linkages EOY (3.2.4) 

 
220 

3.2.b. Input Data

Trustees Assumptions 

Each year, the Trustees set the assumption for the ultimate age-sex-adjusted incidence rate and 

the ultimate age-sex-adjusted recovery rate. This is achieved by setting the age-adjusted 

incidence rate and the age-adjusted recovery rate for each sex. The ultimate level for the age-sexadjusted incidence rate 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, the ultimate incidence rate is adjusted to 

match a “target” incidence rate. The following chart shows these “target” incidence rates by age 

group and sex. 

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 2.15 2.43 1.71 2.36 3.26 4.38 5.79 9.14 15.70 20.29 9.00 

Female 1.50 1.65 1.72 2.46 3.39 4.56 6.03 9.41 14.09 14.84 8.34 

Age Group

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 2011 Trustees Report was 5.6 per 1,000. Using 

a standard population of DIBs as of December 1999, the age-sex-adjusted recovery rate for the 

2011 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. Data as of December 31 of year z-1 are assumed equal to data as of January 1 of year z. 

 Demography 

 January Social Security area population by age, sex, and marital status31 (dimensioned 

(0:100,1:2,1:4)) for beginning of years 1971-2091. 

 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. 

 Total married lives by age of husband crossed with age of wife (dimensioned 

(14:100,14:100)) for beginning of years 1971-2091. 

 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. 

 Probabilities of death by sex, age and year (1:2,15:100,2009:2090). 

Economics 

 Unemployment rates by age group (16-19, 20-24,...,60-64), sex and year (1990:2022). 

 

31 Single, married, widowed, divorced. 
221 

Beneficiaries (from INSURED subprocess #3.1) 

 Disability-insured population by age, sex and year (15:69,1:2,1969:2090) from the 2011 

Trustees Report. 

 Disability-insured population by age, sex and year (15:69,1:2,1969:2090) from the 2010 

Trustees Report. 

 Fully insured population by age, sex and marital status (14:95,1:2,1:4) for years 1970-

2090. 

Other input data 

Only the most recent year data is updated annually for this category except as noted otherwise 

below: 

 The December 2010 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). 

 December 2010 and December 2009 data from the MBR containing the number of DIB 

by age, sex and year [(15:66,1:2,1969:2010) and (15:66,1:2,1969:2009), respectively. 

 December data from the MBR containing the number of dependent beneficiaries by age, 

sex of the account holder, and year for the following beneficiary categories. 

1) Minor child (0:17,1:2,1970:2010) 

2) Student child (18:21,1:2,1970:2010) 

3) Disabled adult child (age group1:932,1:2,1970:2010) 

4) Young spouse (19:64,1:2,1970:2010) 

5) Married aged spouse (62:100,1:2,1970:2010) 

6) Divorced aged spouse (62:100,1:2,1970:2010) 

 Totals for each category are also read. 

 December data from the MBR containing the number of DIB awards by age, sex and year 

(15:67,1:2,1970:2010). 

 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 

year (1:2,1970:2010). 

 December data from the MBR containing the number of DIB deaths by age, sex and year 

(15:67,1:2,1975:2010). 

 December data from the MBR containing the number of estimated DIB recoveries by 

age, sex and year (15:67,1:2,1975:2010). 

 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+,1:2,1970:2010) 

 

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. 
222 

 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 

(2:11,1:2,1973:2010). 

 December data from the MBR containing the number of DIB awards by duration, age, 

sex and year (0:5,0:65,1:2,1993:2009). 2009 Awards were retrieved for this year’s TR, 

1993-2008 Awards have not been updated. 

 Average incidence rates by age and sex (15:66,1:2) for the base period 1995-2004 based 

on awards data from 1995-2009 (also known as the base incidence rates). These values 

are updated when time and data are available. 

 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 know as 

the base probabilities of death) are from a forthcoming update to Actuarial Study No. 

118. These values are updated when time and data are available. 

 Probability of recovery for DIB’s – in a multiple-decrement environment by duration, age 

and sex (0:10,15:65,1:2) for the base period 2001-2005. These numbers (also know as 

the base probabilities of recovery) are from a forthcoming update to Actuarial Study No. 

118. These values are updated when time and data are available. 

 Death rate projection factors from the 2010 Trustees Report by age group (15-19,20-

24,...,60-64), sex and year (1:2,1:10,2010:2090). 

 Recovery rate projection factors and recovery rates from the 2010 Trustees Report by age 

group (15-19,20-24,...,60-64), sex and year (1:2,1:10,2010:2090). 

 Initial Incurred but not reported (IBNR)34 factors by duration, age and sex (0:10, 15: 69, 

1:2) based on 2002 entitlements (awards data from 2002-2007). 

 Ultimate IBNR factors by duration, age and sex (0:10, 15: 69, 1:2) based on 1995-2004 

entitlements (awards data from 1995-2009). These values are updated 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. 

 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. These values are updated only when there 

is a change in the NRA or in the present law. 

 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. These values are updated only when there is a change in the NRA or in the present 

law. 

 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. 

 

34 IBNR factors reflect the proportion of DIBs entitled to benefits who have been awarded since the year of their 

entitlement. 
223 

 Retroactive factors35 by year (1969:2009). These values are estimated using OCACT 

beneficiary data. 

 APROJ factors by auxiliary beneficiary category (1:7) for years 2011-2030. These seven 

categories are; minor child, student child, disabled adult child, young wife, young 

husband, age wife and aged husband. These values are calculated by comparing ShortRange and Long- Range numbers for auxiliary beneficiaries. 

 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. 

 Ultimate RPROJG values by sex and age group calculated to reach a target value and 

updated this year based on the new base probabilities of death and recovery. 

3.2.c. Development of Output

Equation 3.2.1 – New Entitlements 

New entitlements are calculated by multiplying age-sex-specific incidence rates to the exposed 

population at the beginning of the year. The exposed population is the disability-insured 

population less the currently entitled population. Future age-sex-specific incidence rates are 

calculated by multiplying the base incidence rates by the incidence rate projection factors 

(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. The regression equations are described 

in detail in Appendix 3.2-1. Then the IPROJGs are run through the main model and the resulting 

incidence rates by age group and sex are analyzed. If necessary, an adjustment for each year is 

made to the female IPROJG for any age group in order to limit the ratio of (1) female incidence 

rate to (2) male incidence rate to 1.10. Again, the IPROJGs are run through the main model with 

the IPROJGs at the end of the short-range period (2020) held constant throughout the rest of the 

long-range period and the resulting ultimate age-adjusted incidence rates (years 2030 and later) 

for men and women are analyzed. If the ultimate age-adjusted incidence rates for men (5.76) and 

women (5.55) are not achieved then adjustments are made to the IPROJGs in the twentieth year 

of the projection period (2030). The IPROJGs are further adjusted by age and sex to reach 

“target” incidence rates. These “target” incidence rates were determined based on a recent 

review of historical and projected award rates by age group and sex. Ultimate age-sex-specific 

incidence rates are reached in the twentieth year of the projection period. For projection periods 

between the tenth and twentieth years, the IPROJGs are linearly interpolated between the 

ultimate IPROJGs values and the IPROJGs values at the end of short-range period. Additional 

adjustments to the IPROJGs during the short-range period may be made for reconciliation 

between the long-range model and the short-range model. For the 2011 Trustees Report, 

 

35 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. 
224 

IPROJG adjustments were made in the short-range period to project the spike in disability claims 

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, the recovery projection factors (RPROJGs) by age group and sex are 

based on linear interpolation between an estimated starting level for the RPROJGs and an 

estimated tenth year projection target level for the RPROJGs. For each age group and sex, the 

starting RPROJGs are calculated the following way: 

 RPROJGTR11(2010) = RPROJGTR10 (2010)  actual recovery rate(2010) / estimated 

 recovery rate TR10(2010) 

Because there is no apparent upward or downward trend, the average recovery rates for the last 

ten historical years are used as the target values for the 10th year (2020). Then, for each age 

group and sex, the tenth year level of the RPROJGs is calculated the following way: 

 RPROJGTR11(2020) = RPROJGTR11 (2010) target value recovery rate (2020) / 

 actual recovery rate (2010) 

For the second 10 years of the projection period, the RPROJGs are linearly interpolated between 

the ultimate RPROJG value and the RPROJG value at the end of short-range period (2020). 

Ultimate recovery rates by sex are assumed to be reached in the twentieth year of the projection 

period. Ultimate recovery rates by age group and sex are determined by analyzing historical 

recovery rates. Additional adjustments may be made to the RPROJGs to reconcile with the shortrange model. 

For the first year of the projection period, the death projection factors (DPROJGs) by age group 

and sex are determined so that they achieve a targeted death rate. The targeted death rate is 

determined by fitting an exponential curve to historical death rates for DIBs by age group and 

sex (see Appendix 3.2-1). For the rest of the projection period, the DPROJGs are assumed to 

improve at the same rate as the general population for that age group and sex. The DPROJGs for 

each year by 5-year age group and sex are calculated the following way: 
225 

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 (DIBs who have been awarded benefits). This data is 

based on a 100 percent sample of the Master Beneficiary Record (MBR) at the end of the year. 

Disabled-worker beneficiaries are disaggregated by age at entitlement, sex and duration of 

entitlement. This population is converted to a currently entitled population by dividing each age, 

sex and duration cell by the appropriate duration-age-sex-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. This currently entitled population is then 

reduced by multiplying by the appropriate duration-age-sex-year-specific IBNR factor. The 

result is the following year’s disabled-worker beneficiaries in current-payment status. The 

process is performed over each sex, age of entitlement and duration of entitlement throughout the 

projection period. 

Equation 3.2.4 – Dependent Beneficiary of Disabled Workers 

There are six dependent-beneficiary categories; minor child, student child, disabled adult child, 

young spouse, married aged spouse and divorced aged spouse. Projections are disaggregated by 

age of the beneficiary and sex of the account holder. Presented below are the linkages and the 

exposure used in each of the projections of dependent beneficiaries. 

Minor Child 

Exposure: Single SSA population by single ages 0-17 

Linkages: pMCAGA = Probability that parent is under NRA 

pMCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pMCDPA = Probability that disability insured parent under 

NRA is disabled 

MCRES = Residual Factor 

Student Child 

Exposure: Single SSA population by single ages 18-19 

Linkages: pSCAGA = Probability that parent is under NRA 

pSCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pSCDPA = Probability that disability insured parent under 

NRA is disabled 
226 

pSCDPC = Probability that student is in an eligible school 

SCRES = Residual Factor 

Disabled Adult Child 

Exposure: Single SSA population by age groups 18-19, 20-24, 25-29, 

 30-34, 35-39, 40-44, 45-49, 50-54, 55-59 

Linkages: pDCAGA = Probability that parent is under NRA 

pDCDIA = Probability that parent is disability insured given 

that the parent is under NRA 

pDCDPA = Probability that disability insured parent under 

NRA is disabled 

pDCDPC = Probability that adult child is disabled 

DCRES = Residual Factor 

Young Spouse 

Exposure: Married SSA population by sex and by single ages 20-64 

Linkages: pYSAGA = Probability that account holder is under NRA 

pYSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 

pYSDPA = Probability that disability insured account holder 

under NRA is disabled 

pYSETB = Probability that young spouse is not subject to 

 earnings test 

pYSMCB = Probability that young spouse has a minor child 

 beneficiary in his/her care 

pYSDCB = Probability that young spouse has a disabled child 

 beneficiary in his/her care 

YSRES = Residual Factor 

Married Aged Spouse 

Exposure: Married SSA population by sex and by single ages 62-100 

Linkages: pMSAGA = Probability that account holder is under NRA 

pMSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 

pMSDPA = Probability that disability insured account holder 

under NRA is disabled 

pMSFIB = Probability that beneficiary is not insured 

MSRES = Residual Factor 

Divorced Aged Spouse 

Exposure: Divorced SSA population by sex and by single ages 62-100 

Linkages: pDSDEA = Probability that account holder is living 

pDSAGA = Probability that account holder is under NRA 

pDSDIA = Probability that account holder is disability 

 insured given that the account holder is under 

 NRA 
227 

pDSDPA = Probability that disability insured account holder 

under NRA is disabled 

pDSFIB = Probability that beneficiary is not insured 

pDSDMB = Probability that beneficiary was married 10 or 

 more years 

The residual factors for each of the dependent categories are estimated using a 10-year Least 

Squares regression formula. These residual factor values are then held constant for the duration 

of the long range period. If the 10-year Least Squares method results in a negative residual 

factor, the last historical residual factor is held instead.

APROJ factors may be developed for a dependent beneficiary category to match short range 

results during the first 10 years of the projection period. These factors are phased out linearly 

over the second ten years of the projection period. 
228 

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: 1994-2007 

Adjusted R square: 0.69909982 

Standard Deviation: 0.29670100 

Coefficient Intercept: 0.47542853 

Coefficient Slope1: -0.10261889 

Coefficient Slope2: 0.84410156 

Independent Variable: 20-24 unemployment rates 

Independent Variable: 20-24 incidence rates 

Dependent Variable: 20-24 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.81911954 

Standard Deviation: 0.18603036 

Coefficient Intercept: 0.12284935 

Coefficient Slope1: -0.19505861 

Coefficient Slope2: 0.99262442 

Independent Variable: 25-29 unemployment rates 

Independent Variable: 25-29 incidence rates 

Dependent Variable: 25-29 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.59382127 

Standard Deviation: 0.14912750 

Coefficient Intercept: 0.53495337 

Coefficient Slope1: 0.02274484 

Coefficient Slope2: 0.74420159 

Independent Variable: 30-34 unemployment rates 

Independent Variable: 30-34 incidence rates 

Dependent Variable: 30-34 incidence rates 

Observation Period: 1994-2007 
229 

Adjusted R square: 0.59119928 

Standard Deviation: 0.10453329 

Coefficient Intercept: 1.31424348 

Coefficient Slope1: 0.11150404 

Coefficient Slope2: 0.44593197 

Independent Variable: 35-39 unemployment rates 

Independent Variable: 35-39 incidence rates 

Dependent Variable: 35-39 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.60193615 

Standard Deviation: 0.17066421 

Coefficient Intercept: 1.59271766 

Coefficient Slope1: 0.17609813 

Coefficient Slope2: 0.49772509 

Independent Variable: 40-44 unemployment rates 

Independent Variable: 40-44 incidence rates 

Dependent Variable: 40-44 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.67062745 

Standard Deviation: 0.19374658 

Coefficient Intercept: 1.76645537 

Coefficient Slope1: 0.21828541 

Coefficient Slope2: 0.59110663 

Independent Variable: 45-49 unemployment rates 

Independent Variable: 45-49 incidence rates 

Dependent Variable: 45-49 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.77159762 

Standard Deviation: 0.19289450 

Coefficient Intercept: 2.77371308 

Coefficient Slope1: 0.39258820 

Coefficient Slope2: 0.52644899 

Independent Variable: 50-54 unemployment rates 

Independent Variable: 50-54 incidence rates 

Dependent Variable: 50-54 incidence rates 

Observation Period: 1994-2007 
230 

Adjusted R square: 0.79834920 

Standard Deviation: 0.33456357 

Coefficient Intercept: 4.94280366 

Coefficient Slope1: 0.84564139 

Coefficient Slope2: 0.48594682 

Independent Variable: 55-59 unemployment rates 

Independent Variable: 55-59 incidence rates 

Dependent Variable: 55-59 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.62686419 

Standard Deviation: 0.53302884 

Coefficient Intercept: 8.64358032 

Coefficient Slope1: 1.02567991 

Coefficient Slope2: 0.44600678 

Independent Variable: 60-64 unemployment rates 

Independent Variable: 60-64 incidence rates 

Dependent Variable: 60-64 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.69449555 

Standard Deviation: 0.39349032 

Coefficient Intercept: 7.93709654 

Coefficient Slope1: 0.76257597 

Coefficient Slope2: 0.51071066 

Female 

Independent Variable: 16-19 unemployment rates 

Independent Variable: 15-19 incidence rates 

Dependent Variable: 15-19 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.83187846 

Standard Deviation: 0.14916787 

Coefficient Intercept: 0.30435768 

Coefficient Slope1: -0.07221972 

Coefficient Slope2: 0.85252070 

Independent Variable: 20-24 unemployment rates 

Independent Variable: 20-24 incidence rates 

Dependent Variable: 20-24 incidence rates 

Observation Period: 1994-2007 
231 

Adjusted R square: 0.74789581 

Standard Deviation: 0.15931155 

Coefficient Intercept: 0.39826138 

Coefficient Slope1: -0.08486466 

Coefficient Slope2: 0.81397184 

Independent Variable: 25-29 unemployment rates 

Independent Variable: 25-29 incidence rates 

Dependent Variable: 25-29 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.77034496 

Standard Deviation: 0.13008274 

Coefficient Intercept: 0.32652901 

Coefficient Slope1: -0.01864806 

Coefficient Slope2: 0.84711309 

Independent Variable: 30-34 unemployment rates 

Independent Variable: 30-34 incidence rates 

Dependent Variable: 30-34 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.79134722 

Standard Deviation: 0.12889235 

Coefficient Intercept: 0.83659037 

Coefficient Slope1: 0.17359566 

Coefficient Slope2: 0.68817488 

Independent Variable: 35-39 unemployment rates 

Independent Variable: 35-39 incidence rates 

Dependent Variable: 35-39 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.72468850 

Standard Deviation: 0.19012840 

Coefficient Intercept: 1.20842668 

Coefficient Slope1: 0.17945974 

Coefficient Slope2: 0.68131621 

Independent Variable: 40-44 unemployment rates 

Independent Variable: 40-44 incidence rates 

Dependent Variable: 40-44 incidence rates 

Observation Period: 1994-2007 
232 

Adjusted R square: 0.80424280 

Standard Deviation: 0.19565838 

Coefficient Intercept: 1.30122209 

Coefficient Slope1: 0.23677606 

Coefficient Slope2: 0.74744637 

Independent Variable: 45-49 unemployment rates 

Independent Variable: 45-49 incidence rates 

Dependent Variable: 45-49 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.86081034 

Standard Deviation: 0.17229631 

Coefficient Intercept: 2.81548715 

Coefficient Slope1: 0.59904133 

Coefficient Slope2: 0.57074200 

Independent Variable: 50-54 unemployment rates 

Independent Variable: 50-54 incidence rates 

Dependent Variable: 50-54 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.64444355 

Standard Deviation: 0.30652993 

Coefficient Intercept: 3.25915616 

Coefficient Slope1: 0.36787847 

Coefficient Slope2: 0.67573649 

Independent Variable: 55-59 unemployment rates 

Independent Variable: 55-59 incidence rates 

Dependent Variable: 55-59 incidence rates 

Observation Period: 1994-2007 

Adjusted R square: 0.58128215 

Standard Deviation: 0.44396571 

Coefficient Intercept: 6.75800873 

Coefficient Slope1: 0.75859980 

Coefficient Slope2: 0.52489251 

Independent Variable: 60-64 unemployment rates 

Independent Variable: 60-64 incidence rates 

Dependent Variable: 60-64 incidence rates 

Observation Period: 1994-2007 
233 

Adjusted R square: 0.70537698 

Standard Deviation: 0.33059858 

Coefficient Intercept: 6.51704485 

Coefficient Slope1: 0.72935473 

Coefficient Slope2: 0.50225130 

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: 2001-2010 

Adjusted R square: 0.28684 

Standard Deviation: 0.26083 

Coefficient Intercept: 126.70251 

Coefficient Slope1: -0.06172 

Independent Variable: Year 

Independent Variable: 20-24 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.43572 

Standard Deviation: 0.06431 

Coefficient Intercept: 42.68138 

Coefficient Slope1: -0.01996 

Independent Variable: Year 

Independent Variable: 25-29 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.81940 

Standard Deviation: 0.04156 

Coefficient Intercept: 61.89173 

Coefficient Slope1: -0.02959 

Independent Variable: Year 

Independent Variable: 30-34 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.94345 

Standard Deviation: 0.03151 
234 

Coefficient Intercept: 88.24108 

Coefficient Slope1: -0.04265 

Independent Variable: Year 

Independent Variable: 35-39 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.93805 

Standard Deviation: 0.02542 

Coefficient Intercept: 68.68417 

Coefficient Slope1: -0.03280 

Independent Variable: Year 

Independent Variable: 40-44 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.81701 

Standard Deviation: 0.03763 

Coefficient Intercept: 56.43891 

Coefficient Slope1: -0.02659 

Independent Variable: Year 

Independent Variable: 45-49 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.85067 

Standard Deviation: 0.02659 

Coefficient Intercept: 45.79197 

Coefficient Slope1: -0.02116 

Independent Variable: Year 

Independent Variable: 50-54 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.55918 

Standard Deviation: 0.03125 

Coefficient Intercept: 27.85551 

Coefficient Slope1: -0.01212 

Independent Variable: Year 

Independent Variable: 55-59 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.82252 

Standard Deviation: 0.01375 
235 

Coefficient Intercept: 23.51514 

Coefficient Slope1: -0.00990 

Independent Variable: Year 

Independent Variable: 60-64 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.92615 

Standard Deviation: 0.01676 

Coefficient Intercept: 43.29823 

Coefficient Slope1: -0.01969 

Female 

Independent Variable: Year 

Independent Variable: 15-19 death rates 

Observation Period: 2001-2010 

Adjusted R square: -0.02035 

Standard Deviation: 0.38394 

Coefficient Intercept: 79.43485 

Coefficient Slope1: -0.03829 

Independent Variable: Year 

Independent Variable: 20-24 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.53006 

Standard Deviation: 0.08084 

Coefficient Intercept: 62.15592 

Coefficient Slope1: -0.02972 

Independent Variable: Year 

Independent Variable: 25-29 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.73468 

Standard Deviation: 0.05741 

Coefficient Intercept: 66.96330 

Coefficient Slope1: -0.03218 

Independent Variable: Year 

Independent Variable: 30-34 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.77016 
236 

Standard Deviation: 0.04344 

Coefficient Intercept: 56.06109 

Coefficient Slope1: -0.02670 

Independent Variable: Year 

Independent Variable: 35-39 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.82899 

Standard Deviation: 0.02951 

Coefficient Intercept: 46.21329 

Coefficient Slope1: -0.02171 

Independent Variable: Year 

Independent Variable: 40-44 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.85436 

Standard Deviation: 0.02869 

Coefficient Intercept: 49.34798 

Coefficient Slope1: -0.02317 

Independent Variable: Year 

Independent Variable: 45-49 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.87080 

Standard Deviation: 0.02180 

Coefficient Intercept: 40.86371 

Coefficient Slope1: -0.01885 

Independent Variable: Year 

Independent Variable: 50-54 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.89290 

Standard Deviation: 0.01854 

Coefficient Intercept: 38.92772 

Coefficient Slope1: -0.01780 

Independent Variable: Year 

Independent Variable: 55-59 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.96736 
237 

Standard Deviation: 0.01193 

Coefficient Intercept: 46.44700 

Coefficient Slope1: -0.02150 

Independent Variable: Year 

Independent Variable: 60-64 death rates 

Observation Period: 2001-2010 

Adjusted R square: 0.94034 

Standard Deviation: 0.01545 

Coefficient Intercept: 44.25418 

Coefficient Slope1: -0.02033 
238 

3.3. Old-Age and Survivors Insurance

3.3.a. Overview

Every month, the Social Security program pays benefits to retired workers and their dependents. 

It also provides benefits to eligible dependents of deceased workers. The OLD-AGE AND 

SURVIVORS subprocess projects the number of people expected to receive benefits over the 

next 75 years. The projection method is very similar to the method used for dependent 

beneficiaries of disabled workers in the DISABILITY subprocess. The projection of 

beneficiaries is computed by multiplying a subset of the Social Security area population by a 

series of probabilities of the conditions that a person must meet to receive benefits. The main 

program receives all necessary input data and performs all preliminary calculations. It then calls 

each individual beneficiary type subroutine where all beneficiary calculations are made. 

Retired workers and their dependent beneficiaries are categorized as follows: 

 retired workers (RWN) by age (62-95+), sex, and marital status (single, married, 

widowed, divorced) 

 aged spouses of retired workers (ASRWN), by age (62-95+), sex of the account holder, 

and marital status of the beneficiary (married, divorced) 

 young spouses of retired workers (YSRWN) by age-group (under 25, 25-29,..., 65-69) and 

sex of the account holder 

 minor, student, and disabled adult children of retired workers (MCRWN, SCRWN, and 

DCRWN, respectively) by age of the child (0-17 for minor, 18-19 for student, age groups 

18-19, 20-24, ..., 55-59, 60+ for disabled adult) and sex of the account holder 

Dependent beneficiaries of deceased workers include: 

 aged spouses of deceased workers, ASDWN, by age (60-95+), sex of the account holder, 

marital status (widowed, divorced) and insured status (insured, uninsured) 

 disabled spouses of deceased workers (DSDWN) by age (50-69), sex of the account 

holder and marital status (widowed, divorced) 

 young spouses of deceased workers (YSDWN) by age-group (under 25, 25-29,..., 65-69), 

sex of the account holder and marital status of the beneficiary (widowed, divorced) 

 minor, student, and disabled adult children of deceased workers (MCDWN, SCDWN, and 

DCDWN, respectively) by age of the child (0-17 for minor, 18-19 for student, age groups 

18-19, 20-24,..., 55-59, 60+ for disabled adult) and sex of the account holder 

Lastly, the number of deaths of insured workers (LUMSUM) is estimated by 5-year age group 

(20-24, 25-29,..., 80-84, 85+) and sex. 
239 

Equations 3.3.1-13 indicate the flow of calculations of beneficiaries. 

ASDWN  ASDWN() (3.3.1) 

RWN  RWN() (3.3.2) 

ASRWN  ASRWN() (3.3.3) 

DSDWN  DSDWN() (3.3.4) 

MCRWN  MCRWN() (3.3.5) 

MCDWN  MCDWN() (3.3.6) 

SCRWN  SCRWN() (3.3.7) 

SCDWN  SCDWN() (3.3.8) 

DCRWN  DCRWN() (3.3.9) 

DCDWN  DCDWN() (3.3.10) 

 ) YSRWN  YSRWN( (3.3.11) 

 ) YSDWN  YSDWN( (3.3.12) 

LUMSUM  LUMSUM () (3.3.13) 

The appendix 3.3-1 at the end of this section provides a listing with explanation of the acronyms 

used in this documentation. 

 

3.3.b. Input Data

All data are updated annually unless otherwise noted. Timing of data received is denoted ‘BOY’ 

(beginning of year) or ‘EOY’ (end of year). 

Long-Range OCACT Data 

Demography 

 Social Security area population by year (EOY 1970-2090), single year of age (0-100+), 

sex, and marital status (single, married, widowed, divorced) 

 Deaths by year (during years 2010-2090), 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 (0-17), sex of primary account 

holder (parent), status of primary (retired or deceased), and age of the other parent (15-

24,25-29,...,65-69) 

 Married couples by year (EOY 1970-2090), age of husband (62-95+) and age of wife 

(62-95+) 
240 

 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 1970-2085), single year of age (70,100), and sex 

Economics 

 Covered wages and employment in the Federal Civilian and State and Local Sectors 

(during years 1998-2090) 

 Labor force participation rates for age 62 by year (during years 1970-2090) and sex 

Beneficiaries 

 Fully insured persons by year (EOY 1970-2090), 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 1998-2010), age (60-95+) and 

sex 

 The following is received for EOY 2009 and 2010: 

a. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced) 

b. Retired workers by age (62-95+) and sex 

c. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced) 

d. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced) 

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased) 

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased) 

g. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased) 

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex 

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced) 

j. Total parent beneficiaries 

Note: Each year, data for the most recent historical year is appended. 

 The following is received for EOY 2020: 

a. Retired workers by age group (62-64, 65-69) and sex 
241 

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 

 Total amount of lump-sum death payments during 2009 

Other Input Data 

 For EOY 1970-2004, obtained from the MBR10PER dataset on the mainframe: 

a. Aged spouses of deceased workers by age (60-95+), sex and marital status (widowed, 

divorced) 

b. Retired workers by age (62-95+) and sex 

c. Aged spouses of retired workers by age (62-95+), sex and marital status (married, 

divorced) 

d. Disabled widow(er)s by age (50-64), sex and marital status (widowed, divorced) 

e. Minor children by age (0-17), sex of parent and status of parent (retired, deceased) 

f. Student children by age (18-19), sex of parent and status of parent (retired, deceased) 

g. Disabled adult children by age (20-95+), sex of parent and status of parent (retired, 

deceased) 

h. Young spouses of retired workers by age group (under 25, 25-29,...,60-64) and sex 

i. Young spouses of deceased workers by age group (under 25, 25-29,...,65-69), sex and 

marital status (widowed, divorced) 

j. Total parent beneficiaries 

Note: this data will not be updated 

 Number of beneficiaries with benefits withheld due to receipt of a significant government 

pension by sex and marital status (married, widowed) for EOY 2009 from the 2010 

Annual Statistical Supplement 

 Age distribution of beneficiaries with benefits withheld due to receipt of a significant 

government pension by age (60-95+) and sex, computed as an average from the 2001 

through 2005 WEP 100-percent sample (Note: these values are only updated about every 

five years and will be based on averages from five years of data.)

 Proportions of disabled adult children of retired and deceased workers (proportioned by 

age and sex of the child) from the 2003 MBR ten-percent sample. (Note: The RSB 
242 

program calculates disabled adult children by sex of the primary account holder, not by 

sex of the child. The RSB program outputs a file which is used for Annual Update #9, 

which calculates beneficiaries by sex. Therefore the 2003 proportions are applied to 

estimate the breakdown of disabled adult children by sex of the child. This input file will 

not be updated.). 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 

updated when there is a Social Security law change regarding the NRA) 

 Elasticity factors by age (65-69) and sex for the elimination of the earnings test after 

NRA 

 Prevalence rate regression coefficients (slope and y-intercept value by sex) 

 Regressed prevalence rate by sex for the most recent historical year 

 Adjustment factors which account for the difference between estimated and actual 

historical retired worker prevalence rates by year (EOY 1970-2090), 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 Short-Range 

offices. Factors are computed for: 

a. Retired workers by age group (62-64, 65-69) and sex 

b. Insured widows by age group (60-64,...,80-84,85+) 

c. Uninsured widows by age group (60-64, 65+) 

d. Total disabled widows 

e. Female young spouses of deceased workers 

f. Female aged spouses of retired workers by age group (62-64, 65+) 

g. Female young spouses of retired workers 

h. Minor children by status of parent 

i. Student children by status of parent 

j. Disabled adult children by status of parent 

3.3.c. Development of Output

Several acronyms are used to describe the equations presented below. Acronyms that are not 

preceded with a subscript generally refer to the number of beneficiaries. For example, RWN 

refers to the number of retired workers. Acronyms that are preceded with a ‘p’ refer to 

probabilities. For example, FIA pRW refers to the probability that a person is fully insured. 

Equation 3.3.1 – Aged Spouses of Deceased Workers (ASDWN) 
243 

The number of aged spouses of deceased workers (widow(er)s), along with all linkage 

factors, are projected by age, sex of the account holder (sa=1 for male, sa=2 for female), 

marital status and insured status. Age ranges from 60 to 95+, marital status includes 

widowed (mb=1) and divorced (mb=2), and insured status includes insured (in=1) and 

uninsured (in=2). Note that all variables preceded by the letter p are calculated probabilities. 

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+ is calculated as follows: 

POP DEA FIA MBB

FIB GPB RES

ASDWN ASDW pASDW pASDW pASDW

pASDW pASDW pASDW

  

  (3.3.1) 

The projected number of insured aged spouses of deceased workers over age 70 are 

calculated by applying termination rates to the population already receinving such benefits: 

ASDWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOPmb) for each possible marital 

status. 

ASDWPOP  SSAPOPmb

pASDWDEA represents the probability that the primary account holder (PAH) is deceased. 

For the widowed population, this factor is set equal to one. For the divorced population, this 

factor is set equal to the portion of the total widowed (SSAPOPwid) and married (SSAPOPmar) 

population who are widowed. 

 1, mb = 1 (widowed) 

 , 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, it is assumed that the age of her deceased husband, AH, ranges from AW6 to AW+12 with a lower and upper bound of 60 and 95+. Further, it is assumed that the 

more likely age of the husband is AW+3. For each age, pASDWFIA is calculated as a 

weighted average of the portion of the Social Security area population who are fully insured 

at each possible age of the husband (FINSAH). For example, for a widow age 70, it is 

assumed that the age of her husband is between 64 and 82, therefore the weighted average of 

the portion of the population who are fully insured males is calculated, applying the highest 

weight of 10 to age 73, and a linearly reduced weight to zero for each age above and below 

73. The same concept is used for widow(er)s with the assumption that the age of his 

deceased wife ranges from AH-12 to AH+6, with a greater likelihood of her age being AH-3. 

Let WEIGHT represent the specific weight applied to each potential age of the spouse. 

 

pASDWDEA = 
244 

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 young-spouse benefit can be received up to age 69 if all 

other eligibility requirements are met. Since the minimum age requirement to receive a 

widow(er) benefit is 60, it is necessary to remove those receiving a young-spouse benefit 

( ab YSDWN ), where ab represents the 5-year age bracket36. A uniform breakdown is assumed 

to divide the age groups into single-age estimates. 

 1, 65 ≤ age < NRA and in = 2 

 0, elsewhere 

 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. 

 

36 There are no young spouses at NRA or above. 

pASDWMBB = 65≤ age <NRA 

 and in = 2 

FACTORage =

age = 60-64 

 and in = 2 

age = 60-69 

and in = 1 
245 

 ,

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 no 

factor is applied. 

 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, 

year pASDWRES is calculated as the ratio of ASDWN, the actual number of widow(er)s, to the 

number of persons meeting all previously mentioned requirements by age, sex, insured 

status, and marital status. 

, 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, a least squares regression is used over 

the last ten years of historical data to determine a starting value in TRYR-1 for 

year pASDWRES from which future values are projected. In addition, for each sex, insured status, 

and marital status, the regressed values of TRYR1 pASDWRES are graduated over age using a 

weighted minimized third-difference formula to produce ASDW ESTRES . ASDW ESTRES are the 

preliminary estimates of TRYR9 pASDWRES , the values in the tenth year of the projection period. 

In addition, adjustments by age group (60-64, 65-69, 70-74, 75-79, 80-84, 85+ for insured; 

60-64, 65+ for uninsured), ASDW SRADJ , are applied to the tenth year of the projection period 

pASDWGPB = 

year < TRYR, 

in = 1 OR 

year ≤ 1978 
246 

in order to match the projections made by the Short-Range office. The values 

of year pASDWRES for intermediate years are linearly interpolated between TRYR1 pASDWRES and 

N,TRYR9 pRWRES (equal to ) ASDW ASDW ESTRES SRADJ  . After the 10th year, these adjustment 

factors are linearly graded to one over the 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) 

The numbers of retired-worker beneficiaries, along with all linkage factors, are projected by 

age, sex, and marital status. Age ranges from 62 to 95+, and marital status includes single, 

married, widowed, and divorced (ms = 1 to 4). The projected number of retired-worker 

beneficiaries is calculated as follows: 

RWN RW pRW pRW pRW pRW     POP FIA DBB WBB RES (3.3.2) 

RWPOP represents the subset of the population from which these beneficiaries are drawn and 

is set equal to the Social Security area population (SSAPOPms) for ms = 1 to 4. 

RWPOP  SSAPOPms

pRWFIA represents the probability that the primary account holder (PAH) is insured, and is 

set equal to the portion of the Social Security area population that is fully insured (FINS) for 

ms=1 to 4. 

POP

FIA RW

FINS pRW 

pRWDBB represents the probability that the PAH is not receiving a disabled-worker or 

disability-conversion benefit. This factor is set equal to the portion of fully insured workers 

who are neither disabled-worker beneficiaries nor converted from disabled-worker 

beneficiaries (DIBCON). ASDWN represents the number of aged spouses of deceased 

workers. 

 

 1 ,

POP FIA

DIBCON

RW pRW   ms = 1-2 

 1 ,

DIBCON

DIBCON ASDWN

POP FIA

DIBCON ASDWN

RW pRW

            

   ms = 3-4 

pRWDBB = 
247 

pRWWBB represents the probability that the PAH is not receiving a widow(er) benefit, and is 

set equal to the portion of fully insured workers that is not aged spouses of deceased workers. 

 1, ms = 1-2 

 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 pRWRES

, . 

For each historical year and sex, N year pRWRES

, is calculated as the ratio of RWN, the actual 

number of retired workers, to the number of persons meeting all previously mentioned 

requirements by age, sex, and marital status. 

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 and labor force participation rates (LFPRyear) at age 62, 

by sex, follow an inverse linear relationship over the historical period. This relationship is 

assumed to hold in the projection period, and therefore used to calculate REGPRyear, the 

regressed prevalence rate based on the projected LFPRyear at age 62 for each year and sex. 

Note that prevalence rates are calculated on a cohort basis37. The regression equation used to 

estimate the prevalence rates is: 

REGPR year = -0.97559 × LFPR year + 0.91387 for male with an R2

 value of 0.90230, and 

REGPR year = -0.83643 × LFPR year + 0.78290 for female with an R2

 value of 0.84972 

The future prevalence rate at age 62, year pRWRES

62, , is then set equal to the sum of the regressed 

prevalence rate (REGPRyear) and ERROR, the difference between the actual prevalence rate 

and the regressed prevalence rate in the most recent historical year, which is phased out 

linearly. 

 

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. 

pRWWBB
248 

62, 9 ( ) max 0, 10year year

RES

TRYR year pRW REGPR ERROR    

     

To compute N year pRWRES

, for ages 63 to 69 in the projection period, several preliminary 

variables must be calculated. These include: 

 MBAPIAN, for N = 62,70 (same for both sexes), 

 year ESTPRN , for N = 63,69 and by sex, 

 DIFFADJN, for N = 63,69 and by sex, 

 year ESTPR N 2 for N = 63,69 and by sex, and 

 EARNN, for N = 65,69 and by sex. 

MBAPIAN is the ratio of the monthly benefit amount (MBA) to the primary insurance amount 

(PIA) at age N and is calculated on a cohort basis for N = 62,70. The calculation of 

MBAPIAN is based on the normal retirement age (NRA), delayed retirement credits (DRC), 

and actuarial reduction factors; ARFLE3 when the difference between NRA and age at 

retirement is less than 3, and ARFGT3 when the difference is greater than 3 within each 

cohort. If a person retires after NRA, his/her benefits are increased by DRC for each year the 

age exceeds NRA. If a person retires before NRA, his/her benefits are decreased by ARFLE3

for each of the first three years that NRA exceeds the age, and further decreased by ARFGT3

for any remaining years. 

 1 ( ) ,   N 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. This estimate is based on MBAPIAN, assuming that the retirement decision by a 

worker is totally and completely influenced by the expected change in the portion of PIA that 

is payable at each age relative to the potential change after the initial eligibility. 

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 and 64, the value used beginning in TRYR is the average 

of the last 5 years’ differences between the actual and estimated PR. This value is held 

constant throughout the projection period. For ages 65 to 69 the difference between the 

 MBAPIAN = 

 , N = 62 and year ≥ TRYR-1 

N = 63-69
249 

actual and estimated prevalence rate is computed for 1999, the last year prior to the 

elimination of the earnings test at NRA. The ultimate value of DIFFADJN, reached in 2010, 

is calculated as the average difference of the five years; 1995 through 1999. The values for 

DIFFADJN for years 1999 through 2009 are linearly interpolated. 

ESTPR2 N  ESTPRN  DIFFADJ N

Another adjustment (EARNN) is needed for ages 65 to 69 which take into account the 

scheduled increases in NRA and the elimination of the earnings test at NRA. This 

adjustment measures what portion of the remaining workers, who would not have applied for 

benefits if the earnings test legislation in 2000 had not have been enacted, decide to receive 

benefits and continue to work. 

, 2 (1 2 ) , N year

RES N N N pRW ESTPR ESTPR EARN    N = 65-69 and year ≥ TRYR 

For age 70, it is assumed that the values of the latest actual N year pRWRES

, by sex would change 

linearly to the ultimate level of 0.995 for male and 0.99 for female over the first 20 years of 

the projection period. 

 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, N year pRWRES

, is assumed to stay constant at the level when the age was 

70 because there is no incentive to delay applying for benefits beyond age 70. 

, 70, ( 70)  year N

RES

N year pRWRES pRW , for N = 71-95+ and year ≥ TRYR 

In addition, adjustments by age group (62-64, 65-69) and sex, RW SRADJ , are applied to the 

tenth year of the projection period in order to match the projections made by the Short-Range 

office. These adjustments are also applied to N year pRWRES

, for all years after TRYR+9. The 

values of N year pRWRES

, for intermediate years are linearly interpolated between N,TRYR1 pRWRES

and N,TRYR9 pRWRES . 

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. 

 sa = 1 and 

 year ≥ TRYR 

sa = 2 and 

year ≥ TRYR 
250 

( )

,

year N AE

N year N year AE

AE N year

RES

INCRATE RWN RWN

pRW

 

  , AE ≤ N

where the incidence rate for a given AE = N and year is calculated as the change in the 

prevalence rate at age N to the prevalence rate at age N-1 in the previous year. 

 , , N year

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) 

The number of aged spouses of retired workers, along with all linkage factors, are projected 

by age, sex of the account holder (sa = 1,2), and marital status of the beneficiary. Age ranges 

from 62 to 95+, and marital status includes married (mb = 1) and divorced (mb = 2). The 

projected number of aged spouses of retired workers is calculated as follows: 

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 is set equal to the Social Security area population (SSAPOPmb) for mb = 1,2. 

ASRWPOP  SSAPOPmb

pASRWDEA represents the probability that the PAH is not deceased. For the married 

population, no factor is applied. For the divorced population, the factor is set equal to the 

portion of the total married and widowed population who are married. 
251 

 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 is set equal to 

the portion of the married population with a spouse (PAH) at least age 62 (MAR62PLUS). 

pASRWAGA = 

SSAPOPmar

MAR62PLUS

 

pASRWFIA represents the probability that the PAH is fully insured, and is set equal to the 

portion of married couples of the required age where the PAH is fully insured (FI_PAH). 

For example, when the program is estimating the number of female aged spouse of retired 

workers, this factor will find the portion where their spouse, the male PAH, is fully insured. 

 62 _ 

62 FIA

MAR PLUS FI PAH

pASRW MAR PLUS

  



pASRWCPA represents the probability that the PAH is receiving benefits. This factor is set 

equal to the portion of eligible married couples where the PAH is receiving benefits 

(RETIRED). If the beneficiary is divorced, no factor is applied, since it is not required for the 

retired worker to be receiving benefits for the divorced aged spouse to receive benefits. 

 

 1, year ≥ 1985 and mb = 2 

  

 

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, no factor is 

applied. Otherwise, this factor is set equal to the portion of potentially eligible widow(er)s 

where the spouse of the PAH is not receiving a young-spouse benefit ( ab YSRWN ), where ab 

represents the 5-year age group.38

 

38 There are no young spouses at NRA or above. 

pASRWDEA = 

pASRWCPA = 
252 

 1, 65 ≤ age < NRA 

 0, elsewhere 

 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. This factor is 

set equal to the portion of the married and divorced population that is not fully insured. For 

example, when the program is estimating the number of female aged spouse of retired 

workers, this factor will find the portion of female beneficiaries that is fully insured. 

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, year pASRWRES is calculated as the 

pASRWMBB = 

 age = 62-64 

 and mb = 1

 65 ≤ age < NRA 

 and mb = 1 

FACTORage =

pASRWGPB = 
253 

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     

For each age, sex , and marital status, a least squares regression is used over the last ten 

years of historical data to determine a starting value in TR-1 for year pASRWRES from which 

future values are projected. In addition, for each sex and marital status, the regressed values 

of TRYR1 pASRWRES are graduated over age using a weighted minimized third-difference 

formula to compute ASRW ESTRES . ASRW ESTRES are the preliminary estimates of 

TRYR9 pASRWRES , the values in the tenth year of the projection period. For female spouses, 

additional adjustments by age group (62-64, 65+), ASRW SRADJ , are applied to the tenth year 

of the projection period in order to match the projections made by the Short-Range office. 

The values of year pASRWRES for intermediate years are linearly interpolated between 

TRYR1 pASRWRES and TRYR9 pASRWRES (equal to ASRW ASRW ESTRES SRADJ  ). After the 10th year of 

the projection period, these adjustment factors are linearly graded to one over the 10 years 

beyond the end of the short-range period, thus gradually eliminating the effect of the shortrange adjustment factors, so that we ultimately return to the long-range projections. 

Equation 3.3.4 – Disabled Spouses of Deceased Workers (DSDWN) 

The number of disabled spouses of deceased workers, along with all linkage factors, are 

projected by age, sex of the account holder (sa = 1 for male, sa = 2 for female) and marital 

status. Age ranges from 50 to 69, and marital status includes widowed (mb = 1) and divorced 

(mb = 2). The projected number of disabled spouses of deceased workers is calculated as 

follows: 

 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 these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOPmb) for mb = 1,2. 

DSDWPOP  SSAPOPmb

pDSDWDEA represents the probability that the primary account holder is deceased. For the 

widowed population, no factor is applied. For the divorced population, this factor is set equal 

to the portion of the total widowed and married population that is widowed. 

year < TRYR
254 

 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, it is assumed that the age of her deceased husband, AH, ranges from AW-6

to AW+12 with a lower and upper bound of 50 and 95+. Further, it is assumed that the more 

likely age of the husband is AW+3. For each age, pDSDWFIA is calculated as a weighted 

average of the portion of the Social Security area population that is fully insured (FINS), at 

each possible age of the husband. For example, if the widow is age 65, it is assumed that the 

age of the husband is between 59 and 77, therefore the weighted average of the portion of the 

population who are fully insured males is calculated, applying the highest weight of ten to 

age 68 and a linearly reduced weight to zero for each age above and below 68. The same 

concept is used for widow(er)s with the assumption that the age of his deceased wife ranges 

from AH-12 to AH+6, with a greater likelihood of her age being AH-3. Let WEIGHT

represent the specific weight applied to each age. 

WEIGHTAH 10  AW  3  AH

WEIGHTAW 10  AH  3 AW

 

12

6

12

6

,

AW

AH 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 and is set equal to the 

disability prevalence rates (DISPREV) by age and sex received from the DISABILITY 

subprocess. 

 

pDSDWSSB  DISPREV

pDSDWDEB represents the probability that the disabled spouse is not dually eligible for 

another type of benefit. This factor is assumed to remain at a constant level by sex. 

 0.85, sa = 1 

pDSDWDEA = 
255 

 pDSDWDEB = 

 0.06, sa = 2 

pDSDWRES represents the probability that a person who is eligible to receive disabled-spouse 

benefits actually receive the benefits. For all historical years, year pDSDWRES is calculated as 

the ratio of DSDWN, the actual number of disabled spouses of deceased workers receiving 

benefits, to the number of persons meeting all previously mentioned requirements by age, 

sex, and marital status. 

, 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, a least squares regression is used over the 

last ten years of historical data to determine a starting value in TR-1 for year pDSDWRES from 

which future values are projected. In addition, for each sex and marital status, the regressed 

values of TRYR1 pDSDWRES are graduated over age using a weighted minimized third-difference 

formula to compute DSDW ESTRES . DSDW ESTRES are the preliminary estimates of 

TRYR9 pDSDWRES , the values in the tenth year of the projection period. For female disabled 

spouses, an adjustment, DSDW SRADJ , is applied to the tenth year of the projection period in 

order to match the projections made by the Short-Range office. The values of 

year pDSDWRES for intermediate years are exponentially interpolated between TRYR1 pDSDWRES and 

TRYR9 pDSDWRES (equal to DSDW DSDW ESTRES SRADJ  ). After the 10th year of the projection 

period, the adjustment factors are linearly graded to one over the 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 pDSDWRES is equal 

to year pDSDWRES at age 64 times an adjustment which accounts for the additional ages as NRA 

changes. 

 1, NRA ≥ age + 1 

 NRA – age, age < NRA < age + 1 

 

( 64) ,64

,64

,63 ,

age year

year year RES

RES RES age year

RES

pDSDW pDSDW pDSDW FACTOR pDSDW



 

     

Equation 3.3.5-6 – Minor Children of Retired and Deceased Workers (MCRWN and MCDWN ) 

FACTORage =

 age = 65-69 and 

 age < NRA 
256 

The number of minor children of retired workers, MCRWN, is projected by age of the minor 

(am = 0 to 17) and sex of the account holder (sa = 1 for male, sa = 2 for female), and is 

calculated by multiplying the number of minor children in the most recent historical year, 

BASE_MCRWN, by two factors which reflect changes in (1) the number of children in the 

population, and (2) the proportion of retired workers to the population, at ages where a 

worker is most likely to have a minor child. 

1 ,62 71

, ,,

,20 71

_ _ _

year

year TRYR year sa

sa am sa am sa am year

sa

RW RATIO

MCRWN BASE MCRWN POPRATIO

POP RATIO

 



  (3.3.5) 

An adjustment, MCRW SRADJ , is applied to the tenth year of the projection period in order to 

match the projections made by the Short-Range office. These adjustments are also applied to 

year MCRWNsa, am for all years after TRYR+9. The values of year MCRWNsa, am for intermediate years 

are linearly interpolated between 1

,

TRYR MCRWNsa am and 9

,

TRYR MCRW MCRWN SRADJ sa am  . 

The number of minor children of deceased workers, along with all linkage factors, is 

projected by age of the minor (am = 0 to 17) and sex of the account holder (sa = 1 for male, 

sa = 2 for female), and is calculated as follows: 

MCDWN MCDW pMCDW pMCDW pMCDW    POP DEA FIA RES (3.3.6) 

MCDWPOP represents the subset of the population from which these beneficiaries are drawn 

and is set equal to the Social Security area population (SSAPOP). 

MCDWPOP  SSAPOP

pMCDWDEA represents the status of the parent (PAH). This is set equal to the portion of the 

minor population where at least one parent is deceased. CHI_DEA represents the number of 

children having at least one deceased parent. 

POP

DEA MCDW

CHI DEA pMCDW _ 

pMCDWFIA represents the probability that the parent (PAH) is fully insured. This is set 

equal to the portion of the population aged 25 + am to 35 + am where the PAH is fully 

insured (FI_PAH). 

 

35

25

35

25

_

am

am

FIA am

am

SSAPOP FI PAH

pMCDW

SSAPOP
















257 

pMCDWRES represents the probability that a child who is eligible to receive minor-child 

benefits actually receive the benefits. For all historical years, year pMCDWRES is calculated as 

the ratio of MCDWN, the actual number of minor children of deceased workers receiving 

benefits, to the number of number of persons meeting all previously mentioned requirements 

by age and sex of the parent. 

, year

RES

POP DEA FIA

MCDWN pMCDW MCDW pMCDW pMCDW    year < TRYR 

For each age and sex of parent, a least squares regression is used over the last ten years of 

historical data to determine a starting value in TR-1 for year pMCDWRES from which future 

values are projected. An adjustment, MCDW SRADJ , is applied to the tenth year of the 

projection period in order to match the projections made by the Short-Range office. The 

values of year pMCDWRES for intermediate years are linearly interpolated between the regressed 

values for TRYR1 pMCDWRES and TRYR MCDW 9

RES pMCDW SRADJ   . After the 10th year of the 

projection period, the adjustment factors are linearly graded 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) 

The number of student children of retired and deceased workers, along with all linkage 

factors, are projected by age of the student (as = 18 to 19) and sex of the account holder (sa = 

1 for male, sa = 2 for female). The projected number of student children of retired and 

deceased workers is calculated as follows: 

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 are set equal to the Social Security area population (SSAPOP). 

SCRWPOP  SCDWPOP  SSAPOP

pSCRWDEA and pSCDWDEA represent the status of the parent (PAH). For student children of 

retired workers, this is set equal to the proportion of the subset of the population where 
258 

neither parents are deceased. For student children of deceased workers, this is set equal to 

the proportion of the subset of the population where at least one parent is deceased. 

CHI_DEA represents the number of student children having at least one deceased parent. 

POP

DEA SCRW

CHI DEA pSCRW _  1

POP

DEA SCRW

CHI DEA pSCDW _ 

pSCRWAGA and pSCDWAGA represent the probability that the PAH is age 62 or older. For 

student children of retired workers, this is set equal to the proportion of the student 

population that has one parent age 62 or older, CHI_62+. For student children of deceased 

workers, the factor is set equal to one. 

POP

AGA SCRW

CHI pSCRW   _ 62

 

pSCDWAGA  1

pSCRWFIA and pSCDWFIA represent the probability that the PAH is fully insured. For 

student children of retired workers, this is set equal to the portion of the population aged 62 

to 64+as where the PAH is fully insured (FI_PAH). For student children of deceased 

workers, the factor is calculated similarly with the population being aged 25+as to 35+as. 

 

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, this factor is set equal to the portion of the population 

aged 62 to 64+as where the PAH is receiving benefits (RETIRED). For student children of 

deceased workers, this factor is set equal to one. 
259 

 

 

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 is calculated 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, year pSCRWRES and 

year pSCDWRES are calculated as the ratio of SCRWN and SCDWN, the actual number of student 

children receiving benefits, to the number of number of persons meeting all previously 

mentioned requirements by age and sex of the parent. 

, 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, a least squares regression is used over the last ten years of 

historical data to determine a starting value in TR-1 for year pSCRWRES from which future 

values are projected. An adjustment, SCRW SRADJ , is applied to the tenth year of the 

projection period in order to match the projections made by the Short-Range office. The 

values of year pSCRWRES for intermediate years are linearly interpolated between the regressed 

values for TRYR1 pSCRWRES and TRYR SCRW 9

RES pSCRW SRADJ   . After the 10th year of the 

projection period, the adjustment factors are linearly graded 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. Values of 

year pSCDWRES are calculated similarly. 

pSCRWSSB =pSCDWSSB = 

year < TRYR 

year < TRYR
260 

Equation 3.3.9-10 – Disabled Adult Children of Retired and Deceased Workers (DCRWN and 

DCDWN) 

The number of disabled adult children of retired and deceased workers, along with all linkage 

factors, are projected by age-group of the disabled adult child (ad = 1-10) and sex of the 

account holder (sa = 1 for male, sa = 2 for female). The age groups are 18-19, 20-24, ..., 55-

59, 60+. The projected number of disabled adult children of retired and deceased workers is 

calculated as follows: 

 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) 

All factors are calculated similar to those for student children with the exception of the 

following. 

pDCRWDEA is set equal to the proportion of the married and widowed population who are 

married (for ages of the parent that are reasonable based on the given age range of the 

disabled child). pDCDWDEA is calculated similarly for disabled children of deceased 

workers. 

mar wid

mar

SSAPOP SSAPOP

SSAPOP

 , ad = 1-9 

 pDCRWDEA 

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 is assumed to remain constant. For 
261 

the projection period, for ad=6-10, pDCRWSSB and pDCDWSSB are set equal to the 

preliminary factor, plus an adjustment which accounts for the year. 

 0.012, ad = 1-2 

 0.009, ad = 3 

 0.007, ad = 4 

 0.006, ad = 5 

 0.005, ad = 6 

 0.004, ad = 7-10 

 min 0.005, 0.0001 ,   DCPREM year TRYR      

 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, year pDCRWRES

and year pDCDWRES are calculated 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     

An adjustment, DCRW SRADJ , is applied to the tenth year of the projection period in order to 

match the projections made by the Short-Range office. The values of year pDCRWRES for 

intermediate years are linearly interpolated between TRYR1 pDCRWRES and 

TRYR DCRW 9

RES pDCRW SRADJ   . After the 10th year of the projection period, the adjustment 

factors are linearly graded 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. Values of year pDCDWRES are calculated 

similarly. 

Equation 3.3.11-12 – Young Spouses of Retired and Deceased Workers (YSRWN and YSDWN) 

The number of young spouses of retired and deceased-workers, along with all linkage 

factors, are projected by age-group (ab = 1-10) of the young spouse and sex of the account 

DCPREM = 

pDCRWSSB 

=pDCDWSBB= 

 ad = 7-10 and 

 year > TRYR+1 

,year < TRYR

year < TRYR
262 

holder (sa = 1 for male, sa = 2 for female). Young spouses of deceased workers are also 

projected by marital status of the young spouse (mb = 1 for widowed and mb = 2 for 

divorced). The age groups are under 25, 25-29 ..., 65-69. The projected number of young 

spouses of retired and deceased-workers is calculated as follows: 

YSRWN 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 these 

beneficiaries are drawn. YSRWPOP is set equal to the married Social Security area population 

(SSAPOPmar) and YSDWPOP is set equal to SSAPOPmb for mb = 1-2. 

YSRWPOP  SSAPOPmar

YSDWPOP  SSAPOPmb

pYSDWDEA represent the probability that the PAH is deceased. For mb=1, no factor is 

applied. For mb=2, this factor is set equal to the portion of young spouses that is widowed. 

 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. pYSRWAGA is 

set equal to the portion of the married population who has an aged spouse (AGSP). 

POP

AGA YSRW

AGSP pYSRW 

pYSRWECB and pYSDWECB represent the probability that the young spouse has an entitled 

child in their care. pYSRWECB is set equal to the portion of persons meeting the previously 

mentioned requirements who have a minor or disabled adult child in their care. pYSDWECB

,by marital status, is set equal to the portion of persons meeting the previously mentioned 

requirements who have a minor or disabled adult child in their care. ab MCRWN and 

ab DCRWN represent the total number of minor and disabled adult children of retired workers 

where the other parent (young spouse) is in the age bracket ab. 

pYSDWDEA = 
263 

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. This factor is set equal to one divided 

by the number of children in the average family (ASOFab) for the given age bracket of the 

spouse. For young spouses of retired workers, no factor is applied for sa=2. 

 1 , ASOFab

 sa = 1 

 1, sa = 2 

ab

FSB ASOF pYSDW 1 

pYSDWRMB represents the probability that the spouse is not remarried. This factor is 

assumed to remain constant at 0.600. 

 0.600 RMB pYSDW

pYSRWRES and pYSDWRES represent the probability that a person who is eligible to receive 

young-spouse benefits actually receive the benefits. For all historical years, year pYSRWRES is 

calculated as the ratio of YSRWN, the actual number of young spouses of retired workers 

receiving benefits, to the number of persons meeting all previously mentioned requirements 

by age, sex, and marital status. year pYSDWRES is calculated similarly, using the number of 

young spouses of deceased workers. 

, 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 

pYSRWFSB =
264 

For each age, sex , and marital status, a least squares regression is used over the last ten years 

of historical data to determine a starting value in TR-1 for year pYSRWRES . In addition, for each 

sex and marital status the regressed values of TRYR1 pYSRWRES are graduated over age using a 

weighted minimized third-difference formula to compute YSRW ESTRES . YSRW ESTRES are 

the preliminary estimates of TRYR9 pYSRWRES , the values in the tenth year of the projection 

period. For female young spouses, an adjustment, YSRW SRADJ , is applied to the tenth year of 

the projection period in order to match the projections made by the Short-Range office. The 

values of year pYSRWRES for intermediate years are exponentially interpolated between 

TRYR1 pYSRWRES and TRYR9 pYSRWRES (equal to YSRW YSRW ESTRES SRADJ  ). After the 10th year of 

the projection period, the adjustment factors are linearly graded to one over the 10 years 

beyond the end of the short-range period, thus gradually eliminating the effect of the shortrange adjustment factors, so that we ultimately return to the long-range projections. Values 

of year pYSDWRES are calculated similarly. 

Equation 3.3.13 – Number of Deaths of Insured Workers (LUMSUMab) 

The number of deaths of insured workers is projected by sex and 5-year age group (ab = 1-

14). Age groups include 20-24, 25-29,...,80-84, 85+. EXPOSUREab, the estimated number 

of lump-sum payments paid during the year for age group ab, is calculated as the number of 

total deaths during the year times the probability that the deceased was fully insured and has 

a surviving spouse or child. BASE is calculated as the ratio of the actual total amount of 

lump-sum death payments paid in TRYR-1 to the estimated total amount of lump-sum 

payments paid in TRYR-1. LUMSUM ab is then calculated for each year in the projection 

period. 

LUMSUM EXPOSURE BASE ab ab   (3.3.13) 
265 

Appendix 3.3-1: Glossary 

AB: age group of the beneficiary 

AD: age of the disabled child 

AGSP: married population where at least one spouse is age 62 or older 

AM: age of the minor child 

ARFGT3: actuarial reduction factor for ages more than 3 years below normal retirement age 

ARFLE3: actuarial reduction factor for ages less than 3 years below normal retirement age 

AS: age of the student child 

ASDW: aged spouse of deceased worker by linkage factor, age (60-95+), sex of the account 

holder, marital status (widowed, divorced) and insured status (insured, uninsured). Linkage 

factors are: 

ASDWPOP : population of potential aged spouse of retired workers 

DEA pASDW : probability that the primary account holder (PAH) is deceased 

FIA pASDW : probability that the PAH was fully insured at death 

MBB pASDW : probability that the widow(er) is not receiving a young-spouse benefit for 

 the care of a child 

FIB pASDW : probability that the aged widow(er) is fully insured 

pASDWGPB : probability that the aged-widow(er)'s benefits are not withheld or offset 

 totally because of receipt of a significant government pension based on 

 earnings in noncovered employment 

pASDWRES : probability that a widow(er) eligible to receive his/her own retired-worker 

 benefits would instead apply for and receive widow(er) benefits 

ASDWN: final number of aged spouse of deceased workers (product of all linkage factors) 

ASOF: average number of children in a family, by age group (under 25, 25-29 ..., 65-69) 

ASRW: aged spouse of retired worker by linkage factor, age (62-95+), sex of the account 

holder, and marital status of the beneficiary (married, divorced). Linkage factors are: 

ASRW : POP population of potential aged spouse of retired worker beneficiaries 

DEA pASRW : probability that the primary account holder (PAH) is not deceased 

pASRW : AGA probability that the PAH is of the required age 

FIA pASRW : probability that the PAH is fully insured 

pASRW : CPA probability that the PAH is receiving benefits 

MBB pASRW : probability that the beneficiary is not receiving a young-spouse benefit 

FIB pASRW : probability that the aged spouse is not fully insured 

pASRW : GPB probability that the aged-spouse's benefits are not withheld because of 

 receipt of a significant government pension based on earnings in 

noncovered employment 

pASRW : RES probability that a person who is eligible to receive aged-spouse benefits 

 actually receive the benefits 

ASRWN: final number of aged spouse of retired workers (product of all linkage factors) 
266 

AH: age of husband 

AW: age of wife 

BASE: ratio of actual to estimated total amount of lump-sum death payments paid in TRYR-1 

CHI_62+: number of children having at least one parent aged 62 or older 

CHI_DEA: number of children having at least one deceased parent 

CON: number of persons converted from disabled-worker beneficiaries 

DCDW: disabled child of deceased workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as SCDW. 

DCDW : POP population of potential disabled children 

pDCDW : AGA probability that the PAH is age 62 or older 

DEA pDCDW : probability that the parent is either retired or deceased 

FIA pDCDW : probability that the PAH is fully insured 

pDCDW : CPA probability that the PAH is receiving benefits 

pDCDW : SSB probability that the child is indeed disabled 

pDCDW : RES probability that a child who is eligible to receive disabled-child benefits 

 actually receive the benefits 

DCDWN: final number of disabled children of deceased workers (product of all linkage factors)

DCPREM: preliminary calculation of the probability that a child is disabled, by age 

DCRW: disabled child of retired workers by linkage factor, age group of the child (18-19, 20-

24,..., 55-59, 60+) and sex of the account holder. Linkage factors are same as those for DCDW. 

DCRWN: final number of disabled children of retired workers (product of all linkage factors) 

DIB: number of disabled-worker beneficiaries 

DIFFADJ: adjustment which accounts for the difference between the actual and estimated 

prevalence rate at each age in the most recent historical years 

DISPREV: disability prevalence rate by age and sex 

DRC: delayed retirement credit 

DSDW: disabled spouse of deceased worker by linkage factor, age (50-69), sex of the account 

holder, and marital status (widowed, divorced). Linkage factors are: 

DSDW : POP population of potential beneficiaries 

DEA pDSDW : probability that the primary account holder (PAH) is deceased 

FIA pDSDW : probability that the PAH was fully insured at death 

pDSDW : SSB probability that the spouse is indeed disabled 

DEB pDSDW : probability that the disabled spouse is not receiving another type of benefit 

pDSDW : RES probability that a person who is eligible to receive disabled-spouse 

benefits actually receive the benefits 

DSDWN: final number of disabled spouse of deceased workers (product of all linkage factors) 

ERROR: actual prevalence rate minus the regressed prevalence rate in the most recent historical 

year 

ESTPR: preliminary estimate of the prevalence rate for retired workers 

ESTPR2: secondary estimate of the prevalence rate for retired workers 
267 

ESTRES: preliminary estimate of the RES factor for the tenth year of the projection period 

EXPOSURE: estimated number of lump-sum payments by age group (20-24, 25-29,...,80-84, 

85+) 

FACTOR: adjustment for calculation of MBB factor of aged spouse of deceased worker 

FINS: portion of the SSA population that is fully insured 

FI_PAH: portion of married population where one spouse is fully insured 

FP: status of the parent (retired, deceased) 

GPOAGE: portion, by age, of the total beneficiaries expected to receive a significant 

government pension 

GPWHLD: total number of beneficiaries (for all ages) expected to receive a significant 

government pension 

IN: insured status of the beneficiary 

LFPR: labor force participation rates for age 62, by sex 

LUMSUM: number of deaths of insured workers by sex and age group (20-24,...,80-84,85+) 

MAR62PLUS: number of couples where both husband and wife are age 62 and over 

MS: marital status of the primary account holder 

MB: marital status of the beneficiary 

MBAPIA: ratio of the monthly benefit amount (MBA) to the primary insurance amount (PIA) 

by age (62-70) and sex 

MCDW: minor children of deceased workers by linkage factor, age of the child (0-17) and sex 

of the account holder. Linkage factors are: 

MCDW : POP population of potential minor children 

DEA pMCDW : probability that the parent is either retired or deceased 

FIA pMCDW : probability that the PAH is fully insured 

pMCDW : RES probability that a child who is eligible to receive minor-child benefits 

 actually receive the benefits 

MCDWN: final number of minor children of deceased workers (product of all linkage factors) 

MCRW: minor children of retired workers by linkage factor, age of the child (0-17) and sex of 

the account holder. 

MCRWN: final number of minor children of retired workers (product of all linkage factors) 

NRA: normal retirement age 

PAH: primary account holder 

REGPR: regressed prevalence rate for retired workers 

RETIRED: number of retired workers receiving benefits 

RW: retired workers by linkage factor, age (62-95+), sex, and marital status (single, married, 

widowed, divorced). Linkage factors are: 

RW : POP population of potential retired-worker beneficiaries 

FIA pRW : probability that the primary account holder (PAH) is insured 

DBB pRW : probability that the PAH is not receiving a disabled-worker benefit 

pRW : WBB probability that the PAH is not receiving a widow(er) benefit 
268 

pRW : RES retirement prevalence rate; probability that a fully insured worker (not receiving 

 disability or widow(er)’s benefits) would receive a retired-worker benefit 

RWN: final number of retired workers (product of all linkage factors) 

SA: sex of the account holder 

SCDW: student children of deceased workers by linkage factor, age of the student (18-21) and 

sex of the account holder. Linkage factors are: 

SCDW : POP population of potential student children 

DEA pSCDW : probability that the parent is either retired or deceased 

pSCDW : AGA probability that the PAH is age 62 or older 

FIA pSCDW : probability that the PAH is fully insured 

pSCDW : CPA probability that the PAH is receiving benefits 

pSCDW : SSB probability that the child is indeed attending school 

pSCDW : RES probability that a child who is eligible to receive student-child benefits 

 actually receive the benefits 

SCDWN: final number of student children of deceased workers (product of all linkage factors) 

SCRW: student children of retired workers by linkage factor, age of the student (18-21) and sex 

of the account holder. Linkage factors are same as SCDW. 

SCRWN: final number of student children of retired workers (product of all linkage factors) 

SRADJ: adjustment to match short-range projections in 10th year of projection period 

SSAPOP: Social Security area population by age (0:100), sex, and marital status (single, 

married, widowed, divorced) 

SX: sex of the beneficiary 

TRYR: first year of the projection period 

WEIGHT: estimated probability applied to each possible age of the spouse, given the age of the 

primary account holder 

YSDW: young spouse of deceased worker by linkage factor, age group (under 25, 25-29,...,65-

69), sex of the account holder and marital status (widowed, divorced). Linkage factors are: 

YSDW : POP population of potential young spouse of deceased workers 

DEA pYSDW : probability that the primary account holder (PAH) is of the required age 

pYSDW : ECB probability that the young spouse has an entitled child in their care 

pYSDW : FSB probability that the young spouse is not already receiving benefits based 

on another child in their care 

pYSDWRMB : probability that the young spouse is not remarried 

pYSDW : RES probability that a person who is eligible to receive young-spouse benefits 

 actually receive the benefits 

YSDWN: final number of young spouse of deceased workers (product of all linkage factors) 

YSRW: young spouse of retired worker by linkage factor, age group (under 25, 25-29,...,65-69) 

and sex of the account holder. Linkage factors are: 

YSRW : POP population of potential young spouse of retired workers 

pYSRW : AGA probability that the primary account holder (PAH) is of the required age 
269 

pYSRW : ECB probability that the young spouse has an entitled child in their care 

pYSRW : FSB probability that the young spouse is not already receiving benefits based 

on another child in their care 

pYSRW : RES probability that a person who is eligible to receive young-spouse benefits 

actually receive the benefits 

YSRWN: final number of young spouse of retired workers (product of all linkage factors) 
270 

Process 4: 

Trust Fund 

Operations & 

Actuarial Status 
271 

4. Trust Fund Operations and Actuarial Status 

OCACT uses the Trust Fund Operations and Actuarial Status Process to project (1) the annual 

flow of income from payroll taxes, taxation of benefits, and interest on assets in the trust fund 

and (2) the annual flow of cost from benefit payments, administration of the program, and 

railroad interchange. The annual flows are projected for each year of the 75-year projection 

period. In addition, this subprocess produces annual and summarized values to help access the 

financial status of the Social Security program. 

The Trust Fund Operations and Actuarial Status Process is composed of three subprocesses: 

TAXATION OF BENEFITS, AWARDS, and COST. As a rough overview, TAXATION OF 

BENEFITS projects, for each year during the 75-year projection period, the amount of income 

from taxation of benefits as a percent of benefits paid. AWARDS projects information needed to 

determine the benefit levels of newly awarded retired workers and disabled workers by age and 

sex. COST uses information from the AWARDS and TAXATION OF BENEFITS 

subprocesses, as well as information from other processes, to project the annual flow of income 

and cost to the trust funds. In addition, COST produces annual and summarized measures of the 

financial status of the Social Security program. 
272 

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 the 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. 
273 

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 

- Projected SSA wage index series by year, updated yearly 

Other input Data 

- OTA’s projected percent of benefits taxable and average marginal tax rates by 

type of benefit (OASI 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. 

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 1.00 and 0.99 to project smooth 

transitional RTB ratios for OASI and DI benefits, respectively. 
274 

The ultimate RTB ratios used in the projection are based on OTA’s ultimate ratios, reduced by 

about 5 percent.39 The 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 2020 OASDI beneficiary population distribution, due to improved mortality. 

For the 2011 Trustees Report, the ultimate RTB ratios for up to 50 percent of OASI and DI 

benefits taxable were set at 0.058 and 0.029, respectively. 

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. 

 

39 The 5 percent is observed in the output table “tables.0000” of the FORTRAN side simulation program 

TB1116.f90. 
275 

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).40 The 

selected sample, referred to as “sample”, contains 234,018 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 subintervals41 (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 

 

40 A record is selected if the year of initial entitlement equals 2007 and the beneficiary is in current pay status as of 

Dec. 2007, 2008 or 2009. Retired beneficiaries over age 70 and disability beneficiaries under age 20 or over age 64 

were excluded. 

41 The current law PIA formula has two bend points. For the purposes of PAP, the Awards subprocess instead uses 

30 subintervals. 
276 

 AIMEn (r) is the AIME amount contained within the nth interval for record r. 

4.2.b. Input Data

Long-Range OCACT Projection Data 

Demography– 

 Social Security area population by sex and age. 

o From 1951 to 2090 

o Updated annually 

Economics – 

 Covered workers by sex and age--all. 

o From 1951 to 2090 

o Updated annually 

 Covered workers by sex and age—with earnings posted to the Master Earnings File 

(MEF) only. - used with CWHS data to project future earnings levels 

o From 1951 to 2090 

o Updated annually 

 Average Wage Index (AWI), projected values. 

o From 2010 to 2090 

o Updated annually 

 Average Taxable Earnings (ATE) —with earnings posted to the Master Earnings File 

(MEF) only. – used with CWHS data to project future earnings levels 

o From 1951 to 2008 

o Updated annually 

 Projected Covered Worker Rate (for validation) 

o From 2010 to 2090 

o Updated annually 

 COLA (Cost Of Living Adjustment) – not used in SOSI 

o From 2010 to 2090 

o Updated annually 

 Projected Wage Base (to reflect relative changes in relative taxable maximum levels 

over time) 

o From 1951 to 2015 

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 

2007, and are in current pay status as of Dec. 2007, 2008 or 2009. 

 SSN
277 

 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 2006 

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 2008 Continuous Work History Sample (CWHS).

o From 1951 to 2008

o Updated annually

 AWI, Average Wage Index, historical values 

o From 1951 to 2009 

o Data obtained from OCACT internet site. 

o Updated annually 

 Wage base 

o From 1951 to 2011 

o Data obtained from OCACT internet site. 

o Updated annually 

 COLA, cost of living adjustment – not used in SOSI 

o From 1975 to 2010 

o Data obtained from OCACT internet site. 

o Updated annually 

 Amount of earnings needed to earn one quarter of coverage 

o From 1951 to 2011 

o 1978-2011 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 2010 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 2011 
278 

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 CWHS42. 

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 

 

42 This file is a 1% sample of individuals who had covered earnings at some point in their work histories. 
279 

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 workers in the economy in this 

group that have some earnings in this period, to (2) the total midyear population in this group in 

this period. Economy-wide covered worker rates are calculated separately for each age-sex group 

and each historical and projected calendar year based on input data from the Economics and 

Demography subprocesses. 

In projecting sample covered worker rates, examination is done of the change in economy-wide 

covered worker rates, by age group, between the “base period” (representing individuals retiring 

in the sample year) and the “projection period” (representing individuals retiring in a year later 

than the sample year). Details of how this change is used to estimate the change in a covered 

worker rate for retired workers from a current period in the sample to a future period are given 

below for male and female, respectively. For additional explanation of this calculation, refer to 

examples 1.1 and 1.2 in appendix 4.2-2 of this subprocess. 

 

 MALE 

 The ratio of (1) the absolute difference in the economy-wide male covered worker 

rate between the two periods to (2) the potential difference in the economy-wide 

male worker rate in the sample year (i.e., 1 – economy-wide covered worker rate), 

multiplied by 

 The corresponding potential difference in the sample’s male covered worker rates 

(i.e. 1 – sample male covered worker rate)). 

FEMALE 
280 

 The ratio of (1) the absolute difference in the economy-wide female covered 

worker rate between the two periods to (2) the difference between the projected 

sample male covered worker rate and the economy-wide female worker rate in the 

sample year, is multiplied by 

 The corresponding difference between the projected sample male covered worker 

rate and the sample female covered worker rate. 

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 2011 TR data. The calculation 

of the change in covered worker rate changes slightly if there is a reduction in relevant economywide covered worker rates. Example 1.3 gives an example of the calculations done for males if 

economy-wide covered worker rates decline. 

A similar procedure exists for projecting sample covered worker rates for disabled workers. See 

Example 1.4 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 

distribution of the number of years of earnings for retired female beneficiaries. Female records 

with 10 or fewer years of earnings are not modified. A distribution limit is set for those female 

workers with 11 to 25 total years of career earnings within the projection year. This 

distributional limit changes each projected year. In the first year, the distribution limit for 

females is equal to the male distribution plus 97% of the difference between the initial male and 

female distributions within the sample. In each subsequent year, the percentage decreases by 

three percent until it reaches 0%. Thus, the females’ years of earnings distribution for those with 

11 to 25 years of earnings is adjusted to approach that of the males. 

If a record is selected for adding earnings in a particular year, the amount of earnings added is 

based on the career earnings pattern of the selected record. When earnings are added to a record, 

AWARDS calculates the ratio of (1) the record’s Average Indexed Earnings, 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 

 

43 Individuals in the sample affected by the Windfall Elimination Provision are less likely to have earnings removed 

or added by this process. 

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 2007 sample. 
281 

 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 and calculated using earnings adjusted to reflect 

wage base changes for those retiring in year f. 

For additional explanation of this calculation, refer to example 2 in appendix 4.2-2 of this 

subprocess. 

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 

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 

 

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. 

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. 
282 

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, 



   

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 2011 

Trustees Report, α was set equal to -0.07 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 

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 2011 Trustees Report, α = 0.02 for females and α = 0.03 for males. 

However, when earnings for the year are increased for OABs, the ratio takes into account that 

among OABs, there are many more workers with earnings near or above the future wage base. 

In order to account for this, AWARDS first computes z, such that 
283 



 



  















  

















 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

  

, 

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)  . 

(3) h(t) is the dollar amount from interval j(t) to the wage base, 

h(t)  IntervaLenght(t)  (21- j(t)) . 

Now the covered earnings of OAB records are multiplied by the ratio 

  

ATE ( )

z(t) ratio(t) 1

f t , 

where α =0.03 for males and α = 0.02 for females. 

As AWARDS applies ratio(t) to Earnings(r, t) by each record, it makes sure 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. 

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, 
284 













  

i

i

t

i

r t

Earnings(r,t), if t

, if t

AverageWage ( )

AverageWage ( ) Earnings( , ) IndexedEar nings(r,t)

Step 2: Determine Computation Years 

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. 

ElapsedYearsmin  Year of disabilityonset,Year attainedage62 max1951,Year attainedage22

Divide the elapsed years by five and truncate. Subtract this number (cannot exceed five) 

from the number of elapsed years. 

Y must be at least 2. 

Step 3: Determine AIME 

Finally, an individual’s AIME is computed by summing the highest Y indexed earnings and 

dividing by the number of months in those years. Hence, for each record, 

Y 12

Highest Y Indexed Earnings (r) AIME(r)

   . 

Equation 4.2.3 – AIMEn(r)

The Possible AIME value is divided into 30 intervals (bend point subintervals). The length of 

each interval in 1979 dollars is given below: 

 $45, if 0 < n ≤ 13 

 bpn = $100, if 14 ≤ n ≤ 18 

 $200, if 19 ≤ n ≤ 28 

















 



   ,5

5

ElapsedYears Y Elapsed Y ears min
285 

 $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 

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 2010 to 2090 by sex, age (20-64 for disabled workers, and 62-70 for retired workers), and 

trust fund. The ratio of these values gives the average potential AIME percentages (PAPS) 
286 

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. 
287 

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, 
288 

  













   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   0  1

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 . 
289 

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)

Task: In projecting the 2007 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 2007 sample 

are age 40-44 in the base period, 1977-1989, and the counterpart group of 

males retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

 Based on the 2007 sample, the covered worker rate for males age 40-44 in 

the base period = 88.0%. 

 Economy-wide covered worker rate for males age 40-44 = 85.0% in the 

base period. 

 Economy-wide covered worker rate for males age 40-44 = 91.0% in the 

projection period. 

Calculations: 

1. The difference between the economy-wide covered worker rate for males 

age 40-44 in the projection period and in the base period is 91.0% - 85.0% 

or 6.0%. 

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 6/15 or 40.0 %. 

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%. 
290 

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 4.8% (40.0 % * 12.0% = 4.8% ). 

6. The amount in step 5 (4.8%) would be added to the sample’s covered 

worker rate in the base period 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 - Female ) 

Task: In projecting the 2007 sample of newly entitled female beneficiaries to represent 

newly entitled female beneficiaries in 2050, an adjustment to the earnings histories for 

those females age 40-44 is needed to reflect higher covered worker rates expected for 

females in this age group. 

This example illustrates the calculation of the projected covered worker rate for females 

who are age 40-44 in the projection period. We will be comparing the group of females 

age 40-44 in the base period with its counterpart group of females age 40-44 in the 

projection period. 

Information given: 

 Newly entitled retired female beneficiaries represented in the 2007 sample 

are age 40-44 in the base period, 1977-1989, and the counterpart group of 

females retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

 Based on the 2007 sample, the covered worker rate for females age 40-44 

in the base period = 75.0%. 

 Economy-wide covered worker rate for females age 40-44 = 68.0% in the 

base period. 

 Economy-wide covered worker rate for females age 40-44 = 72.0% in the 

projection period. 

 Sample covered worker rate for males age 40-44 = 80.0% in the projection 

period. 

Calculations: 

1. The absolute difference in the economy-wide covered worker rate for 

females age 40-44 from the base period to the projection period is 72.0% - 

68.0% or 4.0%. 

2. The difference between the projected sample covered worker rate for 

males age 40-44 and the economy-wide covered worker rate for females 

age 40-44 in the base period is 80.0% - 68.0% or 12.0%. 

3. The ratio from steps 1 and 2 is 4.0/12.0 or 33 1/3 %. 
291 

4. The difference between the projected sample covered worker rate for 

males age 40-44 and sample’s covered worker rate for the females age 40-

44 in the base period is 80.0%-75.0% or 5.0%. 

5. The ratio from step 3 is multiplied by the potential difference in the 

sample’s covered worker rate for females age 40-44 in the base period to 

yield 1.667% (33 1/3 % * 5.0% = 1.667% ). 

6. The amount in step 5 (1.667%) would be added to the sample covered 

worker rate for females age 40-44 in the base period (75.0%) to yield the 

sample covered worker rate for females who are age 40-44 in the 

projection period (76.667%). 

Example 1.3: (OASI-Male with decreasing economy-wide covered 

worker rates)

Task: In projecting the 2007 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 2007 sample 

are age 40-44 in the base period, 1977-1989, and the counterpart group of 

males retiring in 2050 is age 40-44 in the projection period, 2020-2032. 

 Based on the 2007 sample, the covered worker rate for males age 40-44 in 

the base period = 88.0%. 

 Economy-wide covered worker rate for males age 40-44 = 85.0% in the 

base period. 

 Economy-wide covered worker rate for males age 40-44 = 75.0% in the 

projection period. 

Calculations: 

1. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the projection period is 100.0% - 75.0% or 25.0%. 

2. The potential difference in the economy-wide covered worker rate for 

males age 40-44 in the base period is 100.0% - 85.0% or 15.0%. 

3. The ratio from steps 1 and 2 is 25/15 or 166 2/3 %. 
292 

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% ). 

The amount in step 5 (20.0%) would be subtracted from 100% to yield the sample 

covered worker rate for males who are age 40-44 in the projection period (80.0%).

Example 1.4: (DI-Male with decreasing economy-wide covered worker 

rates)

Task: In projecting the 2007 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 2007 sample 

are age 40-44 in the base period, 1977-1989, and the counterpart group of 

males retiring in 2040 is age 40-44 in the projection period, 2010-2022. 

 Based on the 2007 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 
293 

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 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 0.825 or (2040-2007)/40. 

 Weighting factor 2 is 0.175 or (1-0.825). 

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 (0.825) by the economy-wide covered worker 

rate for males age 40-44 in the projection period (0.85) to yield 70.1% 

(0.825*0.85) 

8. Multiply weighting factor 2 (0.175) by the amount in step 6 (0.8) to yield 

14% (0.175*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 (84.1%). 

Example 2: 

Task: In projecting the 2007 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 
294 

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 2007 sample 

are age 40-44 in the base period, 1977-1989, and the counterpart group of 

males retiring in 2020 will be age 40-44 in the projection period, 1990-

2002. 

 Based on the 2007 sample, a male record, r = 60,000, has been randomly 

selected to replace his zero taxable earnings reported in the base year 1984 

with an amount based on his career earnings pattern. This record is age 63 

in 2007, and his year of birth is 1944. 

 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 1984 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 2006, (2) converting 

them to 2006 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 1944 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 2007 sample. 

 The projected Average Taxable Earnings50 of males retiring in 2020 for the 

projection year 1997 (converted to 1984 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 

 

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. 
295 

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 2008 CWHS file supplied by the 

Economic subprocess as the base year on which to build our projections. 

This example illustrates the calculation of the projected Average Taxable Earnings of the 

CWHS in 2009 for 42 year old females, CWHSATE42,female(2009). 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 2008 CWHS data. 

 

Information given: 

 The total number of female covered workers age 42 in 2008 reported in the 

CWHS, CWHSCW42,female(2008) is 16,108. 

 The total taxable earnings for females age 42 in 2008 reported in the 

CWHS is $547,926,646. 

 The economy-wide number of covered workers for females age 42 in 2008 

is 1,630,779. 

 The economy-wide number of covered workers for females age 42 in 2009 

is 1,542,195. 

 The economy-wide Average Taxable Earnings (ATE) in 2008 is $33,219. 

 The economy-wide ATE in 2009 is $33,228. 

Calculations: 

1. The growth in the economy-wide covered workers for females age 42 

from 2008 to 2009 is 1,542,195/1,630,779 or 0.9457. 

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 

2008, CWHSCW42,female(2008) to yield the projected covered workers for 

females who are age 42 in 2009, CWHSCW42,female(2009), 0.9457*16,108 or 

15,233 

3. The CWHS Average Taxable Earnings for females age 42 in 2008, 

CWHSATE42,female(2008) is computed using the given CWHS total taxable 

 

52 Because not all earnings are posted for the most recent years for a given CWHS file, adjustment factors, based on 

historical trends, are applied by the Economic subprocess to complete these earnings. For the 2008 CWHS, 

adjustment factors were applied to data in years 2005 through 2008. 
296 

earnings and total covered workers for females age 42 in 2008 

($547,926,646 / 16,108 = $34,016). 

4. The economy-wide growth rate in the average taxable earnings from 2008 

to 2009 is $33,228 / $34,016 or 0.9768 

5. The growth rate in step 4 (0.9768) is applied to the amount in step3

($33,228) to estimate the preliminaryCWHS Average Taxable Earnings 

for females age 42 in 2008, CWHSATE’42,female(2009) = $32,457 

(0.9768*$33,228) 

6. The value from step 5 ($32,457) is multiplied by the value in step 2 

(15,233) to yield the preliminary CWHS projected total taxable earnings 

for females age 42 in 2009 ($509,650,481). 

7. Note a final multiplicative adjustment is made to CWHSATE’42,female(2009) 

to obtain CWHSATE42,female(2009). This adjustment is made once the 

preliminary taxable earnings have been computed for each age and sex in 

2009 in order to ensure the growth rate in the aggregate average taxable 

earnings between 2008 and 2009 matches the growth rate in the ATE from 

the Economic process. 

Example 4: 

Task: In projecting the 2007 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 1977. 

 

Information given: 

 A cohort of newly entitled retired female beneficiaries retiring at ages 62 to 

70 represented in the 2007 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 2007 sample, the average taxable earnings for females in the 

base year 1977 is $4,536. 

 

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. 
297 

 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 2008 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 1977 dollar amounts) is $4,640. 

Calculations: 

1. The increase in the average taxable earnings for females ages 32-40 in the 

CWHS from the base year 1977 ($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 2007 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 2007 sample. 

 For newly entitled females retiring in 2033, the average taxable earnings 

(ATE2023) for the projection year 2023 is $19,97055. 

 

54 Amount is in 1977 dollars, ‘sample year dollars’. 

55 Amount is in 1997 dollars, ‘sample year dollars’. 
298 

 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 1997 dollar amounts) is 

$57,600 

 The number of females in the projected 2033 sample with earnings below 

the wage base in 2023 is 52,800. 

 The dollar amounts below the wage base in 2023 are divided into 20 equal 

intervals, IntervalLength(2023), of $2,880 each. 

 The number of females in the 2033 sample who in 2023 have earnings 

falling in the 20th interval (their earnings are between $54,720 and 

$57,600) is 465 

 For female OABs the constant α when δ(t) is positive is 0.02. 

Calculations: 

 The interval in which $56,010 (the wage base in 2023 minus δ(2023) or 

$57,600-$1,590) falls within is interval j(2023) and is found by rounding 

δ(2023)/ IntervalLength(2023) or ($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 2007 
299 

 This OAB beneficiary is record # 150000 in the sample ( r = 150000) 

 The AIME for this individual is $3,000 

 The initial eligibility year is 2005, 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 2005 dollars is given by the equation 

bpn (r) = bpn * AWI (2003) / AWI (1977) 

where bpn is the length of interval n in 1979 dollars 

 The average wage index (AWI) for year 2003 is $34,064.95 

 The AWI for year 1977 is $9,779.44 

 When converting the intervals from 1979 dollars to 2005 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 ($2,734.41). The AIME for this individual 

in 16th interval is $265.59 

 AIMEn (150000) for interval 1 through15 equals bpn (150000) for the 

corresponding intervals, such that PAPn = AIMEn / bpn = 1 for these 

intervals 

 AIME16(15000) = $265.59, such that PAP16 = $265.59 / $348.33 = 0.7625 

 AIMEn (150000) for interval 17 through 30 equals 0, such that PAPn = 0 

for these intervals. 
300 

 The following table details these results. 

n 

bpn in 

1979 

dollars 

bpn (r) in 

2005 

dollars

 bp ( )

1

n r

n

k

 in 

2005 dollars

AIMEn (r) 

in 2005 

dollars

PAPn 

in 2005 

dollars 

 1 $45 $156.75 $156.75 $156.75 1 

2 45 156.75 313.50 156.75 1 

3 45 156.75 470.25 156.75 1 

4 45 156.75 627.00 156.75 1 

5 45 156.75 783.75 156.75 1 

6 45 156.75 940.50 156.75 1 

7 45 156.75 1,097.25 156.75 1 

8 45 156.75 1,254.00 156.75 1 

9 45 156.75 1,410.75 156.75 1 

10 45 156.75 1,567.50 156.75 1 

11 45 156.75 1,724.25 156.75 1 

12 45 156.75 1,881.00 156.75 1 

13 45 156.75 2,037.75 156.75 1 

14 100 348.33 2,386.08 348.33 1 

15 100 348.33 2,734.41 348.33 1 

16 100 348.33 3,082.74 265.59 0.7625 

17 100 348.33 3,431.07 0 0 

18 100 348.33 3,779.40 0 0 

19 200 696.66 4,476.06 0 0 

20 200 696.66 5,172.72 0 0 

21 200 696.66 5,869.38 0 0 

22 200 696.66 6,566.04 0 0 

23 200 696.66 7,262.70 0 0 

24 200 696.66 7,959.36 0 0 

25 200 696.66 8,656.02 0 0 

26 200 696.66 9,352.68 0 0 

27 200 696.66 10,049.34 0 0 

28 200 696.66 10,746.00 0 0 

29 1000 3,483.32 14,229.32 0 0 

30 1000 3,483.32 17,712.64 0 0 
301 

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 contributions and taxation of benefits. 

The other component of income is interest earned on the trust fund assets. The three components 

of cost are scheduled benefits, administrative expenses, and the railroad interchange. Each of 

these components is projected for each trust fund (OASI and DI). The end-of-year assets is 

computed by taking the beginning-of-year assets (ASSETS), adding payroll contributions 

(CONTRIB), taxation of benefits (TAXBEN), and interest income (INT), and subtracting 

scheduled benefits (BEN), administrative expenses (ADM), and the railroad interchange (RR). 

Equations 4.3.1 through 4.3.6 outline this overall structure and sequence. 

CONTRIB = CONTRIB(·) (4.3.1) 

BEN = BEN(·) (4.3.2)

 TAXBEN = TAXBEN(·) (4.3.3)

ADM = ADM(·) (4.3.4) 

 RR = RR(·) (4.3.5) 

 

INT = INT(·) (4.3.6) 

 ASSETS ASSETS CONTRIB TAXBEN INT BEN ADM RR EOY BOY     

The COST subprocess produces annual values that help assess the financial status of the OASI, 

DI, and combined funds. These include the annual income rate (ANN_INC_RT), annual cost 

rate (ANN_COST_RT), and trust fund ratio (TFR) as outlined below. 

ANN_INC_RT = ANN_INC_RT (·) (4.3.7) 

ANN_COST_RT = ANN_COST_RT (·) (4.3.8) 

TFR = TFR(·) (4.3.9) 

The COST subprocess also produces summarized values. These values are computed for the 

entire 75-year projection periods, as well as 25- and 50-year periods. These include 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). 
302 

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-2011 for the 2011 TR 

 ni+74 represents the final year of the projection period-2085 for the 2011 TR 

 nf represents the last year the cost program will project-2090 for the 2011 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 2007 

 

4.3.b. Input Data 

Data received as input from the short-range office are presented first. Then data from long range 

and all other sources are identified separately for each equation. 

Short-range OCACT Data 

 Estimates for the first ten years of the projection period for the first six equations 

mentioned above. 

 Assets at the beginning of year ni. 

 All of this information is updated annually. 

Long-range OCACT and other Data

i. Equation 4.3.1 – Tax Contributions (CONTRIB)

Economics-Process 2 

 Projected effective taxable payroll for years nim1 through nf, updated yearly 

Other 

 Projected employee/employer payroll tax rate, by trust fund and year, for years 

1981 through nf, updated as needed (e.g., as required due to legislative changes) 

ii. Equation 4.3.2 – Scheduled Benefits (BEN)
303 

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 1-A Table Supplement 

 Total (aggregate) PIA and MBA, actuarially reduced, of DI male and female workers 

in current payment status, updated yearly from the 1-A Table Supplement 

 Cumulative distribution of AIME dollars for newly entitled retired-worker 
304 

beneficiaries by age (62 through 70) and sex, for years nim1 through nf, updated 

yearly from subprocess 4.2 

 Cumulative distribution of AIME dollars for newly entitled disabled-worker 

beneficiaries by age (20 through 64) and sex, for years nim1 through nf, updated 

yearly from subprocess 4.2. Ages 15 through 19 are assumed to have the same 

distribution of dollars as does age 20. Ages 65 and 66 are assumed to have the same 

distribution of dollars as does age 64 

 Age distribution of newly entitled retired-worker beneficiaries in the AIME awards 

sample by sex, updated in years that the sample changes, from subprocess 4.2 

 Starting average PIA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly 

 Starting average PIA matrix for disabled-worker benefits, for the year nim1, by age in 

current-pay, duration and sex, updated yearly 

 Starting average PIA matrix for beneficiaries who convert from disabled worker to 

retirement worker status for the year nim1, by age in current-pay and sex, updated 

yearly 

 Starting average MBA matrix for retired-worker benefits for the year nim1, by age at 

entitlement, age in current-pay and sex, updated yearly 

 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 qlink11.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 

 Year in which ultimate WEP factor is reached by age at initial entitlement (62-70), 

updated every 2 years 
305 

 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 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, 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 

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 
306 

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 average benefit to OASI average benefit for the 

year nim1, 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, reviewed annually 

 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 
307 

Demographics-Process 1 

 Single year population and mortality rate data for years 1941 through 2100, updated 

yearly 

 Population projections by single year of age, 75-99, from nim2 to 2100, updated 

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 2085, updated yearly 

 Aggregate number of covered workers aged less than 15, and aged 75 and over, from 

years ni through 2085, updated yearly 

Beneficiaries-Process 3 

 Total projected disabled workers by age for years 2010 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 

2010 to 2090. 

 Awards-Process 4 

 Projected number of workers and total taxable earnings by single year of age (15-74) 

and sex from 2010 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 

December 2010 Master Beneficiary Record (MBR)56—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 

2010 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 1991-2007 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 

 

56 For disabled adult children of deceased workers and lump-sum beneficiaries, data were extracted from a 1- 

percent sample of the December 2010 MBR, mainframe dataset ACT.TAPEL.CAN1210. For the other 18 auxiliary 

beneficiary categories, data was extracted from the 100 percent December 2010 MBR, mainframe dataset 

ACT.TAPEH.MBR100.D1012.CANSORT. 
308 

for years 1991-2007 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. 

4.3.c. Development of Output 

i. Equation 4.3.1 – Payroll Tax Contributions (CONTRIB)

It would be natural to estimate the payroll tax contributions by trust fund by multiplying the 

applicable employer/employee tax rate by effective taxable payroll. However, tax contributions 

are reported on a cash basis. That is, tax contribution amounts are attributed to the year in which 

they are actually received by the trust funds, while taxable payroll is attributed to the year in 

which earnings are paid. In other words, the lag between the time the tax liability is incurred and 

when the taxes are actually collected must be reflected. If lag represents the proportion of 

incurred payroll taxes estimated to be received by the trust fund (tf) in year yr, then tax 

contributions (CONTRIB) are given by the formula 

(, ) (, ) ( )

(1 ) ( , 1) ( 1)

CONTRIB tf yr lag tax rate tf yr payroll yr

lag tax rate tf yr payroll yr

 

    

for yr ns  .

The value of lag is estimated from the combined OASI and DI tax contributions estimated to be 

collected in the final year of the short-range period, ns, and is given by 

 

 

2 2

1 1

2

1

( , ) ( , 1) ( 1)

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

tf tf

tf

CONTRIB tf ns taxrate tf ns payroll ns

lag

taxrate tf ns payroll ns taxrate tf ns payroll ns

 



  



   

 



. 

For the first ten years of the long-range period, tax contributions are set equal to those provided 

by the short-range office. The same value of lag is used for all years, and both trust funds, 

thereafter. 

ii. Equation 4.3.2 – Scheduled Benefits (BEN)
309 

(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 

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 benefits, one for males and one 

for females, for December nim1 (2010 for the 2011 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 
310 

given a workers’ compensation adjustment and a post-entitlement adjustment. For each 

duration 0,1,...,7, j  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). 

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. 
311 

 1

61

(1 ( 1)) (1 ( )) 64

_ (,) (1 ( ( 62)) 64 66.

ag

k

COLA yr COLA yr ag

Cum COLA ag yr COLA yr k ag



    

       

 

2

62

1 ( ) 63

_ (,) (1 ( ( 62)) 63 66.

ag

k

COLA yr ag

Cum COLA ag yr COLA yr k ag



  

       





 6 1 , 12 2

wj   j=1,2. 

 PIA_factori represent the PIA factor for interval i (equal to 0.90 for intervals i=1..,,4, 

0.32 for intervals i=5,...,18, and 0.15 for intervals i=19,...,30). 

 AIME_dollarsi represent the length of interval i, expressed in 1979 dollars.

 dpapi (yr,sx,ag) represent the DPAP value for newly entitled disabled workers in 

year yr whose sex is sx and age is ag. 

To take into account the workers’ compensation offset to disability benefits, administrative 

data is reviewed, from which a factor is developed and applied to the average award benefit. 

We now describe how this factor, facm p yr sx 2( , ) is computed. The 1-A table supplement as 

of the end of December 2010, 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 MBA and PIA respectively 

for DIBs that are not actuarially reduced as found in the 1-A table. In the historical period 

1988-nim1 we define facm p yr sx 2( , ) to be the ratio of the total MBA to the total PIA for 

those not actuarially reduced. In other words, 

_ _ (,) 2( , ) . _ _ (,)totmba DIB nar yr sx facm p yr sx totpia DIB nar yr sx 

In the period ni through ns+9, facm p yr sx 2( , ) is defined as follows. Let 

1/10

2 ( 1, ) min(0.985, 2 ( 1, ) ). 2 ( 11, )facm p yr sx x facm p yr sx facm p yr sx

        

The 0.985 ceiling was added due to concerns that the projection method would lead to a 

significant understatement on the effect of workers’ compensation offsets. 

This value is further adjusted by the variable facm2p_param to reflect the offset amounts that 

end within the first entitlement year. For the 2011 TR the data suggests this factor should be 

.30. As a result, for yr = ni, ... , ns+9, 

2 ( , ) (1 ) 0.30

0.30 0.70 .

facm p yr sx x x

x

  



The factor reaches its ultimate value in years ns+10 and later. 
312 

The preliminary average PIA for newly entitled disabled worker beneficiaries may now be 

defined. It is equal to 

30

1

2

1

_ (, , ) _ _ (,, )

_ (, , ) _ ( , )

2 ( , ).

i ii

i

jj j

j

LR awdpia sx ag yr PIA factor AIME dollars dpap yr sx ag

w Wage Idx sx ag yr Cum COLA ag yr

facm p yr sx







 

     







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 

year of DI entitlement that are not captured by the current method. 

Workers’ Compensation Offset Factors

For each duration 1,...,7, j  and 8+ and sex we define a workers’ compensation factor. This 

factor is applied to the average worker PIA matrix as mentioned above. It is 

denoted ( , , ). wkcomp yr sx dur Let 2 _ ( ) facm p pct dur be defined as in the following table. 

Duration Cumulative product above set at x% of 

way between original facm2p and 1 

1 0.439532 

2 0.623144 

3 0.706830 

4 0.760547 
313 

5 0.815270 

6 0.841684 

7 0.862697 

8+ 0.885714 

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 ( , ,1) wkcomp yr sx 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 1-A table supplement as of the 

end of December, 2010, contains total award PIA and MBA data for disabled workers, by 

sex, for beneficiaries both non-actuarially reduced and actuarially reduced. Let 

totmba nar yr sx _ (,) and totpia nar yr sx _ (,) be the total MBA and PIA respectively for DIBs 

that are not actuarially reduced as found in the 1-A table. Similarly, let totmba ar yr sx _ (,) and 

totpia ar yr sx _ (,) be the total MBA and PIA respectively for cases that are actuarially 

reduced. In the historical period 1988-nim1 we define fam p yr sx 2( , ) to be the ratio of the 

total MBA to the total PIA for those not actuarially reduced. In other words, 

_ (, ) _ (, ) 2( , ) . _ (, ) _ (, )totmba ar yr sex totpia nar yr sex Fam p yr sex totpia ar yr sex totpia nar yr sex  

In the period ni through ns+9, facm p yr sx 2( , ) is defined by 

1/10

2 ( 1, ) 2 ( , ) 2 ( 1, ) . 2 ( 11, )Fam p yr sx Fam p yr sx Fam p yr sx Fam p yr sx

        

The factor reaches its ultimate value in years ns+10 and later. 

More Workers’ Compensation Offsets 

As mentioned above, we also we provide a relatively small reduction to 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 0.2767% 

1 0.1872% 

2 0.0715% 

3 0.0486% 

4 0.0134% 
314 

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 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 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. 

Computation of Average MBA for DI Workers 

The disabled worker PIA as presented in the average benefit matrix was already incremented 

by age and duration using a COLA and a workers’ compensation adjustment. The average 

PIA by year, age and duration, is denoted ( , , , ). avgpia yr ag sx dur The overall average MBA 

by year and sex is the weighted average of ( , , , ) 2 ( , , ), avgpia yr ag sx dur Fam p yr sx dur  the 

weights being the number of DI workers in current payment status by age, sex, and duration. 

DI Conversions

Disabled-worker beneficiaries convert to retired-worker beneficiary status (called DI 

conversions) at normal retirement age (NRA). The average DI conversion benefit for a given 

sex and single age 65 through NRA is the weighted average of the average DI conversion 

benefits for that sex and age, weighted by the number of people in current pay in each 

duration. Both the average conversion benefit for each sex and age 65 though NRA and the 

number of people in current pay for these ages are used in the computation of average retired 

worker benefits (see subsection (2) below). 

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. 
315 

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 

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 
316 

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 

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 for 

single year ages 62 through 69, and ages 70+. The two bendpoints of the PIA formula, BP1 

and BP2, are indexed by the increase in the average wage index. In 1979 dollars, the values 

of BP1 and BP2 are $180 and $1,085 respectively. The AIME dollars between 0 and BP1 

are divided into four intervals (each of length $45 in 1979 dollars). The AIME dollars 

between BP1 and BP2 are divided into fourteen intervals (nine of length $45 and five of 

length $100, in 1979 dollars). Twelve additional intervals are added beyond BP2 (ten of 

length $200 and two of length $1,000, in 1979 dollars). 
317 

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.57

 ( ( 62)) _ (,) ( 2)

avgwg yr ag Wage Idx ag yr avgwg nbase

   

Then the average PIA for these newly entitled retired worker beneficiaries is equal to 

 

30

1

_ (, , ) _ ( , ) (,, )

_ _ 1 ( , , ). i ii

i

LR awdpia sx ag yr Wage 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 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 

 

57 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. 
318 

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. 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 
319 

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) 

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 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 
320 

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 : 

 

() () ()

1

PIA(yr,M) PIA(yr,F) PctExp ( ) ( ) PIA(yr,M)

kk k

yra 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 newly entitled retired worker beneficiaries 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)

kk k ni ni 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( 2009, ) .

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 0.91440 0.0 0.23 40 

2 Widow 1.68044 0.0 0.55 35 

3 Widower -0.01773 0.05153 0.06 75 
321 

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 

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)

kk k

yr b c yr   

( 1,2 k  ) project the average excess benefit amounts of wife (1) and widow (2) beneficiaries as 

a percentage of the male retired worker benefit. 

The 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( 2009, ) .

k k

k targ ult c yr yr phaseyrs

phaseyrs

  

The table below shows the regression coefficients and other relevant adjustments in the 2011 

Trustees Report. 

k Type ( )

1

k b Targeted Value (2085) in 

Nominal Dollars 

( ) k targ

Add-factoring 

Phase-in Years 

phaseyrs 

1 Wife 0.43368 3,527 38 
322 

2 Widow 1.19728 9,169 35 

The average excess amount of widower beneficiaries is estimated to be a fixed percentage (46%) 

of the average excess amount of widow beneficiaries. That is, 

(3) (2) AvgExcPct ( ) 0.46 AvgExcPct ( ). yr yr  

Annualizing Excess Amounts 

The process to annualize excess amounts is very similar to the process for annualizing auxiliary 

benefits. 

For each dual entitlement category, the number of beneficiaries is simply 

() () ( , ) PctExp ( ) ExposedPop ( ). cat cat cp yr cat yr yr   With this method, however, no linkage 

factor is used. Instead, the projected average excess amount, as explained above, is used. 

Therefore, 

11 () ()

i=0

AggExcess( , ) 

(12 ) = ( , 1) ( 1) ( , ) ( ) . 12 12

cat cat

yr cat

i i cp cat yr AvgExcAmt yr cp cat yr AvgExcAmt yr             

(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 dur sex age dur dur ( , , , ) ( , , , ) / ( , ,max(15, ), ).   
323 

 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 ibnr yr dur sex age dur _ ( , , , ) ( , , , ) ( , , , 1)    for 

higher durations, 1 9   dur and 10+. 

Let dur be a duration, 0 through 9 or 10+. Define 

 0

_ ( ) (1 ( )).

dur

j

Cum COLA dur COLA yr j   

 For 0,...,10, i 

2 0

5 0 and 0 

_ () 12 0 and 0

6 0 and 

dur

dur i

Num Months i

dur i dur

dur i dur

 



       



  

Then the aggregate retroactive payments for disabled workers, in millions, are defined to be 

Retro_DIB(sex,yr) 

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

 

   

This 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. 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 
324 

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 over the 10-

year period. From the 20th year forward, the projection is the pure long-range value. 

iii. Equation 4.3.3 – Taxation of Benefits (TAXBEN)

The short-range office provides taxation of benefits levels by trust fund in the short-range period 

. These implicitly give, for each year, an estimated taxation of benefits factor, by trust fund, 

equal to the estimated taxation of benefits as a percentage of benefits scheduled to be paid. The 

long-range office projects these factors independently for every year of the projection period, 

also by trust fund. (See subprocess 4.1.) The difference in the factors between the two offices at 

the end of the short-range period is phased out linearly over the next ten years. The long-range 

projection of taxation of benefits is estimated by multiplying the projected taxation of benefits 

factors by the benefits scheduled to be paid, by trust fund. If taxben_factor(tf,yr) is the 

percentage of scheduled benefits for the year, by trust funds, estimated to be collected as taxation 

on benefits, then 

TAXBEN tf yr taxben factor tf yr BEN tf yr (, ) _ (, ) (, )  

for yr ns  10.

iv. Equation 4.3.4 – Administrative Expenses (ADM)

Administrative expenses are estimated separately by trust fund. In the short-range period, the 

short-range office provides the estimates of administrative expenses by trust fund. Thereafter, 

administrative expenses are computed by multiplying the previous year’s administrative 

expenses by three factors: annual changes in total beneficiaries, annual changes in AWI, and one 

minus annual productivity growth. As a formula, if ticp(tf,yr) is the total estimated number of 

beneficiaries in current-pay status by trust fund and year, AWI(yr) is the average wage index in 

year yr, and prod is the ultimate assumed annual growth in productivity, then 

( , ) ( , 1) [ ( , ) / ( , 1)] [ ( ) / ( 1)]

(1 )

ADM tf yr ADM tf yr ticp tf yr ticp tf yr AWI yr AWI yr

prod

    

 
325 

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 rr tf yr yield yr ( , ) [0.25 _ cost( , 2) 0.75 _ cost( , 1)] [1 1.25 ( )].       

Note that the railroad cost is increased by the yield rate on the combined OASDI trust funds for 

year yr. This formula takes into account the fact that that there is a delay from the end of the 

fiscal year to the time of valuation. 

The total cost in year yr is broken down in to four components: railroad benefits in year yr, 

railroad administrative expenses in year yr, railroad contributions in year yr, and railroad 

taxation of benefits in year yr. 

Projections of numbers of newly entitled retired workers are determined by analyzing the ratio of 

new entitlements to previous levels of railroad employment using 1997-2008 new entitlement 

data in the analysis. After initial entitlement, a mortality rate of 5.9% for 2009 is assumed based 

on analysis of recent Railroad Retirement Board financial interchange data, with mortality 

assumed to improve thereafter. For projections of newly entitled disabled workers a similar 

trend analysis based on prior employment is used. A “mortality” rate (deaths plus recoveries 

plus conversions to retired worker benefits) is determined using Railroad Retirement Board 

(RRB) data, with the rate assumed constant thereafter. 

Assuming a 90/10 male/female split, the average benefit level for an OASI railroad worker is 

calculated as a ratio to the average OASI retired worker benefit. This ratio is constant 

throughout the projection period and is derived by comparing MBR and Railroad Board data. 

Additionally a constant loading factor based on the same data is applied to aggregate worker 

benefits to determine the aggregate benefit amounts for auxiliary OASI beneficiaries. This same 

approach is used to determine similar constants for DI railroad benefits. The aggregate disabled 

worker railroad benefits (and beneficiaries) are estimated in the same way. 
326 

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 inflation rate    (1 ) (1 ) 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: 

 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 
327 

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 3rdof 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 cycling58) 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 

(, ) _ _ (, ) . ( )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: 

 

58 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. 
328 

(, ) (, ) . (, )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 yield yr payroll yr v yr _ ( ) (1 0.5 ( )) ( ) ( ).    

We also define 

PV INC tf yr PV TAX tf yr PV TAXBEN tf yr _ (, ) _ (, ) _ (, )  

and 

PV COST tf yr PV BEN tf yr PV RR tf yr PV ADM tf yr _ ( , ) _ ( , ) _ ( , ) _ ( , ).  

Summarized rates are calculated using beginning of period assets and a target fund. Let yr1 = the 

first year of the valuation period and yr2 = the ending year of the valuation. Then the 

summarized income rate is: 
329 

2

1

2

1

1

1 2

( , ) _ ( ,)

_ _ (, , ) .

_ ()

yr

BOY

j yr

yr

j yr

ASSETS tf yr PV INC tf j

SUMM INC RT tf yr yr

PV PAYROLL j





 

     





The summarized cost rate is similarly computed: 

2

1

2

1

2

1 2

_ ( ,) _ ( , )

_ _ (, , ) .

_ ()

yr

j yr

yr

j yr

PV COST tf j PV TARG tf yr

SUMM COST RT tf yr yr

PV PAYROLL j





    

  





The 75-year actuarial balance is computed for a period beginning January 1 of the Trustees 

Report year, ni. It includes both beginning of period assets and a target fund. Therefore, 

75 ( ) _ _ ( , , 74) _ _ ( , , 74). ACTBAL tf SUMM INC RT tf ni ni SUMM COST RT tf ni ni yr

  

In general, an actuarial balance may be computed for any given subperiod of the projection 

period. In general, actuarial balances for a subperiod beginning on January 1 of year ni and 

continuing through the end of year yr are computed using 

, ( ) _ _ ( , , ) _ _ ( , , ). ACTBAL tf SUMM INC RT tf ni yr SUMM COST RT tf ni yr ni yr  

The unfunded obligation of a trust fund for a given period is the excess of the present value of 

the net cash deficits for each year of that period over the trust fund balance at the beginning of 

the period. The unfunded obligation for the period beginning on January 1 of year ni and 

continuing through the end of year yr is computed using 

_ ( , ) [ _ ( , ) _ ( , )] ( , ).

yr

BOY

j ni

UNF OBL tf yr PV COST tf j PV INC tf j ASSETS tf ni   

ix. Equation 4.3.14—Closed Group Unfunded Obligation 

The closed group is defined as individuals who attain specified ages in the first year of the 

projection period (ni). The Statement of Social Insurance displays unfunded obligations for 

closed groups (1) attaining 15 or later in 2011, (2) attaining 62 or older in 2011, and (3) attaining 

15 to 61 in 2011. 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. 
330 

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 2011, a 3-

year-old minor child receiving benefits in 2011 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 2011. 

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 2011 through 2110, is used by the cost program to compute payroll tax 

contributions attributable to the closed group. For each year, the closed group payroll factors are 

determined as follows: 

 The number of projected workers by single year of age (ages 1-99) and sex are 

multiplied by the associated average earnings by age/sex. 

 Then, the portion of total taxable earnings attributable to the closed group is 

calculated. 

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: 
331 

 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 17 years of earnings data 

(1991-2007) in the averaging calculations. Average taxable earnings for ages 1-14 are 

obtained by analyzing historical 1991-2007 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 2007 to the projected 

population of that group in 2007 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 2007. 

These ratios by age are then averaged for all 17 years, from which earnings ratios to 

overall average earnings are developed judgmentally. This process is done separately by 

sex. 

Benefits 

Methodologies for computing benefits attributable to the closed groups differs among benefit 

categories, as described below: 

Retired Workers 

For each age in current pay, the number of beneficiaries is multiplied by the corresponding 

average benefit amount across all ages of entitlement. The same applies for DI conversion 

cases. Retroactive benefits for the current year, by age, are then calculated. The closed-group 

factors for old-age benefits for each year are found by summing the benefit amounts 

attributable to the specified closed group, as a proportion of total retired worker benefits for 

all ages. This process is done separately by sex. 

Disabled Workers 

For each age from 20 to the year before normal retirement age, the program adds the 

products of the number of beneficiaries for each duration and the PIA for that duration. 

Retroactive benefits for the current year, by age, are then calculated. The closed-group 

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. 
332 

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 to the number of years younger than age 119. 

(119 ker ) (1.040 /1.028) deceased wor age Benefitadj  

This exponent is intended to reflect differences in average levels of benefits, with younger 

deceased spouses having higher benefits based on real wage growth. The closed group 

factors, then, are obtained by determining the proportion of total benefit amounts attributable 

to the closed group. 

For aged widow(er)s in dual entitlement status (i.e. aged widow(er)s with a smaller worker 

benefit) we do similar calculations with the assumption that the age distributions are equal to 

the combined distribution of non-dually entitled aged widow(er)s and aged divorced 

widow(er)s. 

Other Beneficiary Categories 
333 

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). 
334 

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 (2007 for the 2011 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 
335 

oadsrs and oadscp are indexed by age, ages = 62, ..., 70. For a given sex, the matrix oads is 

constructed with the following properties: 

70

62

() (, )

ageentAWD

oadscp ageentRSB oads ageentRSB ageentAWD  

and 

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 ageentAWDoads ageentRSB ageentAWD w

oadscp ageentRSB  

As matrices, opap w opap 1  (and is another 9 10  matrix). 

Consider the following example. In this example, the projection year is 2040, and the sex is 

males. 
336 

The oadsrs vector (from subprocess 4.2) is as follows. 

62 63 64 65 66 67 68 69 70

Male 0.3843 0.1416 0.0791 0.1588 0.2128 0.0106 0.0048 0.0041 0.0040

The unaligned age-sex distribution (from subprocess 3.3) is as follows. 

62 63 64 65 66 67 68 69 70

Male 0.2917 0.1428 0.0563 0.1170 0.1252 0.2283 0.0097 0.0204 0.0086

The age-sex distribution (from subprocess 3.3) in 2007, 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 0.3843 0.1416 0.0791 0.1588 0.2128 0.0106 0.0048 0.0041 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 0.2917 0.1428 0.0563 0.1170 0.1252 0.2283 0.0097 0.0204 0.0086

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 0.2917 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2917

63 0.0926 0.0502 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1428

64 0.0000 0.0563 0.0000 0.0000 0.0000 0.

ageentRSB ageentAWD

0000 0.0000 0.0000 0.0000 0.0563

65 0.0000 0.0351 0.0791 0.0028 0.0000 0.0000 0.0000 0.0000 0.0000 0.1170

66 0.0000 0.0000 0.0000 0.1252 0.0000 0.0000 0.0000 0.0000 0.0000 0.1252

67 0.0000 0.0000 0.0000 0.0308 0.1975 0.0000 0.0000 0.0000 0.0000 0.2283

68 0.0000 0.0000 0.0000 0.0000 0.0097 0.0000 0.0000 0.0000 0.0000 0.0097

69 0.0000 0.0000 0.0000 0.0000 0.0056 0.0106 0.0042 0.0000 0.0000 0.0204

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0041 0.0040 0.0086

Total 0.3843 0.1416 0.0791 0.1588 0.2128 0.0106 0.0048 0.0041 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) 0.2917.  

In this case (as is usually the case), oadscp is less. The difference 

oadsrs oadscp (62) (62) 0.3843 0.2917 0.0926   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) 0.1428 0.0926 0.0502,   is oads(63,63). 
337 

Now we have that the row sum is oadscp(63). We want the column sum to be oadsrs(63). 

We move down to oads(64,63). Since 

oadsrs oads oadscp (63) (63,63) 0.1416 0.0502 0.0914 0.0563 (64),   by the row sum 

constraint we are forced to have oads(64,63) 0.0563.  

Now move one lower. Since 0.1416 0.0563 0.0502 0.0351 (65) 0.1170,    oadscp the entry 

oads(65,63) 0.0351.  

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 oadsrs (65) (65,63) 0.1170 0.0351 0.0819 0.0791 (64),    by the column 

sum constraint we are forced to have oads(65,64) 0.0791. 

The column constraint is now met, and we move right to (65,65). oads For the row sum to 

be oadscp(65) we have oads(65,65) 0.1170 0.0791 0.0351 0.0028.   

Since the row constraint is now met, we move down to (66,65). oads 

oadscp oadsrs oads (66) 0.1252 (65) (65,65) .1588 .0028 .1560,     so by the row constraint 

oads(66,65) 0.1252.  

Now we can get the column total to match oadsrs(65) by setting 

oads(67,65) 0.1588 0.1252 0.0028 0.0308. 

Now that this column constraint is met, we move one column over to (67,66). oads In order 

to meet the row constraint, 

oads oadscp oads (67,66) (67) (67,65) 0.2283 0.0308 0.1975.    

Since the row constraint is met, we move one row down to (68,66). oads Since 

oads oadscp oadsrs (67,66) (68) (66),   we have (68,66) (68) 0.0097. oads oadscp   

Since the row constraint is met, we now move one row down to (69,66). oads We cannot put 

oadscp(69) 0.0204  there or else the column constraint would be violated. Hence 

oads oadsrs oads oads (69,66) (66) (67,66) (68,66) 0.2128 0.1975 0.0097 0.0056     and 

the column constraint is met. 

Now move one column over to (69,67). oads We put (69,67) (67) 0.0106 oads oadsrs  

there since that meets the column constraint and the row constraint remains unsatisfied. 
338 

So move over to the next column, (69,68). oads We cannot put (68) oadsrs there since that 

would violate the row constraint. It follows that 

oads oadscp oads oads (69,68) (69) (69,66) (69,67) 0.0204 0.0056 0.0106 0.0042.    

 Now the row constraint is satisfied and we move down to the last row and (70,68). oads By 

the column constraint, this entry is forced to be 0.0006. 

Moving to column 69, again, by the column constraint, the entry (70,69) oads is forced to be 

0.0041. 

Finally, by the row and column constraints, the last entry, (70,70), oads 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 0.6485 0.3515 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 0.3000 0.6761 0.0239 0.0000 0.0000 0.0000 0.0000 0.0000

66 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000

67 0.0000 0.0000 0.0000 0.1349 0.8651 0.0000 0.0000 0.0000 0.0000

68 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000

69 0.0000 0.0000 0.0000 0.0000 0.2745 0.5196 0.2059 0.0000 0.0000

70 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0698 0.4767 0.4535

Then, as matrices, 1 , opap w opap   as one may verify. For display purposes the transposes 

of opap and opap1 are shown. 

 

 opap 62 63 64 65 66 67 68 69 70 

1 0.9992 0.9992 0.9982 0.9988 0.9988 0.9962 0.9883 0.9942 0.9938 

2 0.9865 0.9864 0.9832 0.9818 0.9910 0.9514 0.8932 0.9125 0.9235 

3 0.9557 0.9567 0.9559 0.9509 0.9776 0.8702 0.7677 0.7735 0.8109 

4 0.9220 0.9261 0.9265 0.9205 0.9614 0.7910 0.6873 0.6579 0.6898 

5 0.8891 0.8972 0.8996 0.8938 0.9444 0.7422 0.6423 0.5869 0.6434 

6 0.8588 0.8691 0.8759 0.8706 0.9284 0.7058 0.5954 0.5501 0.6151 

7 0.8288 0.8395 0.8501 0.8491 0.9123 0.6794 0.5507 0.5221 0.5822 

8 0.7991 0.8117 0.8265 0.8267 0.8968 0.6417 0.5186 0.5042 0.5505 

9 0.7705 0.7845 0.8040 0.8042 0.8813 0.6163 0.4957 0.4848 0.5209 

10 0.7420 0.7580 0.7785 0.7820 0.8646 0.5897 0.4794 0.4659 0.4935 

11 0.7128 0.7303 0.7543 0.7589 0.8446 0.5620 0.4587 0.4409 0.4744 

12 0.6835 0.7007 0.7264 0.7342 0.8252 0.5467 0.4442 0.4286 0.4603 
339 

13 0.6532 0.6692 0.6971 0.7076 0.8041 0.5289 0.4284 0.4127 0.4498 

14 0.6026 0.6172 0.6468 0.6611 0.7636 0.5025 0.4058 0.4008 0.4282 

15 0.5294 0.5399 0.5745 0.5935 0.7028 0.4671 0.3703 0.3652 0.3950 

16 0.4551 0.4612 0.5007 0.5234 0.6385 0.4380 0.3369 0.3392 0.3730 

17 0.3816 0.3865 0.4243 0.4535 0.5705 0.4127 0.3021 0.3197 0.3478 

18 0.3118 0.3202 0.3579 0.3923 0.5028 0.3761 0.2704 0.3063 0.3243 

19 0.2202 0.2348 0.2740 0.3116 0.4076 0.3211 0.2344 0.2768 0.2884 

20 0.1264 0.1441 0.1782 0.2181 0.3020 0.2623 0.1880 0.2451 0.2398 

21 0.0599 0.0762 0.1045 0.1361 0.2031 0.1958 0.1499 0.1958 0.1868 

22 0.0195 0.0275 0.0426 0.0589 0.0954 0.1076 0.0906 0.1325 0.1212 

23 0.0030 0.0048 0.0084 0.0163 0.0256 0.0377 0.0322 0.0497 0.0421 

24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0014 0.0040 0.0053 

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 
340 

 opap1 62 63 64 65 66 67 68 69 70 

1 0.9992 0.9992 0.9992 0.9985 0.9988 0.9988 0.9988 0.9953 0.9936 

2 0.9865 0.9865 0.9864 0.9841 0.9818 0.9898 0.9910 0.9505 0.9160 

3 0.9557 0.9561 0.9567 0.9560 0.9509 0.9740 0.9776 0.8791 0.7899 

4 0.9220 0.9234 0.9261 0.9262 0.9205 0.9559 0.9614 0.8171 0.6745 

5 0.8891 0.8919 0.8972 0.8987 0.8938 0.9376 0.9444 0.7779 0.6165 

6 0.8588 0.8624 0.8691 0.8737 0.8706 0.9206 0.9284 0.7450 0.5828 

7 0.8288 0.8326 0.8395 0.8469 0.8491 0.9038 0.9123 0.7177 0.5513 

8 0.7991 0.8035 0.8117 0.8221 0.8267 0.8873 0.8968 0.6873 0.5262 

9 0.7705 0.7754 0.7845 0.7982 0.8042 0.8709 0.8813 0.6652 0.5019 

10 0.7420 0.7476 0.7580 0.7724 0.7820 0.8534 0.8646 0.6434 0.4794 

11 0.7128 0.7190 0.7303 0.7472 0.7589 0.8330 0.8446 0.6192 0.4573 

12 0.6835 0.6895 0.7007 0.7189 0.7342 0.8129 0.8252 0.6030 0.4441 

13 0.6532 0.6588 0.6692 0.6890 0.7076 0.7911 0.8041 0.5847 0.4306 

14 0.6026 0.6077 0.6172 0.6383 0.6611 0.7498 0.7636 0.5551 0.4135 

15 0.5294 0.5331 0.5399 0.5646 0.5935 0.6880 0.7028 0.5127 0.3790 

16 0.4551 0.4572 0.4612 0.4894 0.5234 0.6230 0.6385 0.4730 0.3543 

17 0.3816 0.3833 0.3865 0.4136 0.4535 0.5547 0.5705 0.4339 0.3311 

18 0.3118 0.3148 0.3202 0.3474 0.3923 0.4879 0.5028 0.3897 0.3117 

19 0.2202 0.2253 0.2348 0.2631 0.3116 0.3946 0.4076 0.3274 0.2789 

20 0.1264 0.1326 0.1441 0.1689 0.2181 0.2907 0.3020 0.2582 0.2384 

21 0.0599 0.0656 0.0762 0.0968 0.1361 0.1941 0.2031 0.1885 0.1883 

22 0.0195 0.0223 0.0275 0.0385 0.0589 0.0905 0.0954 0.1008 0.1243 

23 0.0030 0.0036 0.0048 0.0075 0.0163 0.0243 0.0256 0.0332 0.0450 

24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0044 

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