Measuring Defined Benefit Plan Replacement Rates Using 

PenSync 

James H. Moore, Jr. 

Office of Research, Evaluation, and Statistics, Division of Policy Evaluation, Social Security Administration 

500 E. Street SW, Suite 910, Washington, DC 20254 

james.h.moore@ssa.gov 

Abstract 

This paper creates a synthetic pension data set through the use of regression and statistical matching 

procedures, and as a by-product, updates income replacement rates from defined benefit plans. This new 

data set contains detailed socioeconomic variables along with in-depth, employer-provided pension data. 

Through the use of data from the Internal Revenue Service (IRS) Form W-2, two earnings-based measures 

of replacement rates are calculated to evaluate the effectiveness of a defined benefit pension plan in 

meeting the income needs of retirees. The findings suggest that variation in pension replacement rates stem 

from differences in the types of benefit formulas, individual earnings, years of participation in the pension 

plan, and employment characteristics. 

I. Introduction 

Will future generations of retirees have adequate retirement income to maintain their pre-retirement 

standard of living? The Social Security Administration (SSA), in an effort to better understand retirement 

income security, developed a micro-simulation model-Modeling Income in the Near Term (MINT) 1 to 

project retirement income of persons born between 1926 and 1965. There are three main sources of 

retirement income-social security, employer pension benefits (both from defined benefit and defined 

contribution pension plans), and personal savings. This study will focus on a method for projecting income 

from defined benefit (DB) pension plans. 

Version 1 of the MINT used replacement rates calculated by the Bureau of Labor Statistics (BLS) to 

estimate retirement benefits from the private sector, as well as state and local government DB plans. Since 

BLS no longer publishes replacement rates 2

 and there are no other sources to obtain replacement rates, 

SSA has developed an experimental replacement rate calculation requiring BLS data on pension plans, and 

data from the Survey of Income and Program Participation (SIPP) linked to earnings histories. Work was 

done under a Memorandum of Understanding between BLS and SSA under which BLS data would be 

analyzed at BLS and only results of statistical equations could be taken off -site. 

Two key components-pension plan characteristics and pre-retirement earnings- are used to calculate 

replacement rates. The statistical equations developed at BLS are used to estimate pension plan 

characteristics as a function of job characteristics. These are statistically matched to SIPP individuals. SSA 

administrative data on earnings are used to develop two measures of earnings and to calculate DB benefit 

1

 The MINT model is a micro-simulation model developed to estimate the distributional effects of proposed 

social security policy alternatives on current and future beneficiaries’ retirement income. The MINT model 

projects retirement income from social security, pensions, personal investments or savings, and partial 

retirement earnings. For a complete description of the MINT project, see the final reports prepared by 

RAND (Panis and Lillard, 1999), the Urban Institute (Toder et al., 1999), and Social Security 

Administration, Office of Research, Evaluation and Statistics (Butrica et al., 2001). 

2

 1993 was the last year BLS published replacement rates for full-time employees in medium and large 

private establishments and 1994 for State and local government employees. 

3

 The Pension Insurance Modeling System model is a simulation model constructed by the Pension 

Guaranty Benefit Corporation of its pension insurance program. 

Page 112 
 

 

 

 

 

 

 

 

amounts. DB benefit amounts and pre-retirement earnings are then used to calculate replacement rates. The 

resulting dataset is called PenSync. 

Estimating future pension income is especially problematic in light of the major changes that have occurred 

in the world of pensions. For example, over the last two decades the demographics of individuals covered 

by a pension have changed drastically as well as the type of pension plan providing the coverage. As 

recently as the mid-1990s the majority of individuals covered by a pension were covered by a DB plan. 

Currently, the majority are covered by a defined contribution (DC) plan. Not only has the type of pension 

changed but also the design of pension plans has changed (Mitchell 1998 and Papke 1999). Anew type of 

pension plan has evolved as well. Cash balance plans have gained popularity over the past few years 

(Elliott and Moore 2000). According to data recently released by BLS, cash balance plan participation has 

increased nearly fourfold between 1997 and 2000, from 6 percent to 23 percent. 

Currently no dataset collects enough information to analyze these changes in pension plan coverage and 

design. The methodology in this paper, through a statistical match, brings together detailed information on 

pension plans and plan providers with survey data on plan participants and administrative data on earnings 

histories in order to improve the estimation of pension income for future retirees. 

The arrangement of this paper is as follows: Section II presents the methodology, wherein a brief 

description of the key components of a DB plan is given and a description of the models used to replicate 

the EBS data are discussed. The subsequent section describes the data. Section IV discusses the statistical 

matching procedure and the assumptions. Section V presents results and section VI provides the 

conclusion. 

II. Data 

One of the major sources of data used in this study comes from the 1995 EBS - an employer-based survey. 

The EBS provides representative data on the incidence and detailed provisions of the nation’s DB pension 

plans in all nonagricultural private-sector establishments employing 100 or more full- and part-time 

employees in all 50 states and the District of Columbia. The EBS sample used in the study contains 4,925 

observations. For the average person, DB plan provisions are very difficult to interpret. 3 In light of this 

fact, Appendix A briefly describes some of the key provisions found in a DB plan, including the benefit 

formulas and some of their key components as well as eligibility requirements. 

The SIPP provides data on representative samples of the nation’s households. The SIPP collects data on 

sources and amounts of income, labor force information, program participation, eligibility data, and general 

demographic characteristics. This study focused on the data collected in the Retirement Expectations 

Pension Plan Coverage Topical Module and the Work History Topical Module. To make the SIPP 

analogous to the EBS, the SIPP sample is restricted to nonagricultural private-sector wage and salary 

workers who worked at an establishment with 100 or more employees and were covered by a DB plan. The 

self-employed are not included in this sample and individuals must have at least 5 years of employment on 

their current job. The sample also consists of individuals who were born between 1930 and 1955 who 

ranged in age from 40 to 65 in 1995. In accordance with the above restrictions, this sample has 2,508 

observations for analysis. 

Two sources of administrative earnings data are considered for the construction of the earnings measures – 

the detailed earnings record (DER) and the Summary Earnings Records (SER) maintained by the Social 

Security Administration. The DER contains wages, tips, other compensation, and deferred wage data from 

1981 through 2001. These data are provided to the IRS on the Form W-2 from employers on all persons 

with wages including non-filers and other non-covered employees. The SER contains Social Securitycovered earnings derived from payroll tax records for the years 1951 through 1999 (up to the taxable wage 

ceiling). After reviewing both datasets it was determined that the DER had significant advantages over the 

SER. One major advantage of using the DER is that there are earnings data for each job in each year, 

3

 To learn more about DB plans and their features see work by Gerald Cole. 

Page 113 
whereas the SER’s earnings data is a sum of all earnings from all jobs in each year. By using the DER, it is 

possible to separate earnings out by job, which makes it possible to isolate one DB plan with the earnings 

from one job instead of having a sum of earnings from multiple jobs. 

III. Methodology 

Overview 

Diagram 1 shows the flow of the systematic procedures applied to create PenSync and replacement rates. 

The first step is to determine the structure of the data and to select the proper econometric technique that 

best fits the data. Ordinary least-squares (OLS) regression is used to fit continuous explanatory and 

dependent variables. But, since the dependent variable that represents formula type is categorical, the 

traditional OLS multiple regression analysis is not appropriate. A discrete dependent variable model fits 

the data substantially better than least square methodology (Agresti, 1990). Therefore this study will use a 

multinomial logit (MNL) model to fit the categorical dependent variable. 

The next step involves estimating the MNL and the OLS models to obtain coefficient estimates. The 

resulting coefficient estimates are used to produce predicted values by a process of multiplying the 

estimated coefficients by the observed EBS data. The end product is a database called PenPred. 

The next step in the process is to statistically match the predicted pension plan characteristics 

(PenPred) to the SIPP by job characteristics. This assigns a DB plan with detailed plan characteristics 

to the analytical sample of workers in the SIPP who reported being covered by a DB pension plan. 

The resulting dataset is called PenSync. The final two steps involve constructing an algorithm to 

calculate benefit amounts and calculating the replacement rate for each individual in the sample. 

Diagram 1. The creation of PenSync and replacement rates 

Estimate the 

MNL & OLS 

Equations 

Create 

PenSync 

 

Statistically 

Match

PenPred to SIPP 

Create 

PenPred 

Calculate

Replacement 

Rate 

Calculate 

Benefit Amount 

 

 

 

 

 

 

 

The following paragraphs provide more detailed explanations of the methodology applied in this study. 

Model Specification 

MNL Model Specification. The employer's choice of pension formula is modeled using MacFadden's 

random utility framework. Nine alternatives are identified: two flat dollar amount; four types of terminal 

earnings; two types of percent of career average; or a cash balance plan.4

 In choosing which type of 

formula to provide, employers may consider a variety of job characteristics of their employees, such as 

occupation and work schedule. The decision may also be affected by the characteristics of the employers, 

themselves, such as type of industry, number of employees, and presence of a union (see Table A.1 in 

Appendix A for the descriptive statistics of job characteristics variables used to model the choice of benefit 

formula). For any employer, the utility of choice j to employer i is expressed as: 

Page 114 

 

4 See Appendix A for a brief description of these alternatives. 
Uij=Vij(Ei

, Wi) + εij (1)

where; 

Uij is the overall utility of choice j for employer i, 

V(E,W) represents utility determined by the observed data, 

E is a vector of employer characteristics, 

W is a vector of employee characteristics within the firm, 

ε is a vector of unobserved components, and 

j denotes pension formula alternatives. 

Utility-maximizing behavior implies that employer i will only choose a particular alternative j if Uij > Uik 

for all k not equal to j. The error term ε is assumed to be a random variable and includes idiosyncrasies and 

measurement errors. Employer i chooses the alternative which derives the greatest utility. This decision is 

random and can be expressed as: Uij > Uik. 

The probability of any given alternative j being chosen by an employer can be 

expressed as: 

P = P(U ij > Uik) for all k<>j (2) 

By substitution of equation 1, 

P = P(Vij + εij > Vik + εik, for all k<>j) 

Rearranging, 

P = P[(ε ij- εik) > (Vij -Vik), for all k<>j] (3) 

By knowing the distribution of the random ε‘s, we can derive the distribution of each difference εij-εik for 

all j, j<>k, and by using equation 3 we can calculate the probability that the employer will choose 

alternative j. 

Letting Xij=(Ei

, Wi) and assuming V is a linear function of components of X, we operationalize Equation 2 

as: 

Uij = βjXij+ εij (4) 

where βj

 is a vector of coefficient values indicating the effect of the various Xij's on employer i's utility for 

option j. Note that βj

 is subscript by the choice index j. This means that in the analysis a given Xij is 

allowed to "interact" with each choice option. For example, union status may have one effect on the utility 

of choosing a dollar formula and another effect on the utility of choosing a cash balance plan. 

As mentioned earlier, a MNL approach is used to determine the probability that an employer will choose 

one of nine mutually exclusive benefit formulas: 

(1) Flat Dollar Amount times years of service with a fixed dollar amount times years of service; 

(2) Flat Dollar Amount times years of service with a varying dollar amount times years of service; 

(3) Percent of terminal earnings with a fixed percent of earnings averaged over the last few year of 

employment; 

(4) Percent of terminal earnings with varying percent of earnings averaged over a specified period of 

consecutive years of employment; 

(5) Percent of terminal earnings with varying percent of earnings averaged over the last few year of 

employment; 

(6) Percent of terminal earnings with a fixed percent of earnings averaged over a specified period of 

consecutive years of employment; 

(7) Percent of terminal earnings with a fixed percent of earnings averaged over the employee career; 

(8) Percent of terminal earnings with varying percents of earnings averaged over the employee career; 

(9) Cash balance plan. 

Page 115 
The MNL model is frequently used to analyze situations in which there are multiple choice alternatives. 

However, it is widely known that a potentially important drawback of the MNL model is the Independence 

from Irrelevant Alternatives (IIA) property; that is, the model can only be applied to 

situations where alternatives from which you can choose are totally independent. 

To test for the existence of IIA, a model is constructed where the alternatives include choosing one type of 

benefit formula over a different type of benefit formula. If the employer views the alternatives as differing 

only along irrelevant dimensions, when the model is re-estimated it will not show a significant difference in 

explanatory power from the original model. The model used in this paper passed the IIA assumption. 

This finding is not entirely surprising, given that there are many incentives embedded in the different types 

of pension formulas offered by employers. Some pension formula types are geared towards retaining 

employees, while others encourage retirement. Therefore, depending upon the incentive sought by the 

employer, his decision to offer a particular type of pension formula is independent. Again, the purpose of 

the IIA test is to ensure that the alternatives presented to employers are indeed viewed as independent. 

Interested readers should refer to Greene (1990), Train (1986), and Ben-Akiva and Lerman (1985). 

Therefore, in this context for a given employer i, with characteristic xi, the probability of choosing a given 

benefit formula can be estimated with the following MNL model. 

 

ij 

BF ij = K

e 

ijk ∑ e

v 

k =1

 

 

 

 

 , where (5) 

 

 

 

v

BFij = the probability that the employer i choose formula j, 

vij = ∑βmXijm = the deterministic component of utility of formula j to employer i, 

Xijm = the m-th explanatory variable for formula j and employer i, m= 1....M, and 

βm = coefficient to be estimated. 

The MNL model includes information on characteristics of the employer, his employees and pension plan 

characteristics. For a description of the values of the dependent variable see Table A.2. In addition to 

predicting the formula type, the quantitative values common to each formula type is estimated using OLS. 

OLS Model Specification. The quantitative variables for employer i and formula j can be written as: 

QVij = β0ij + β1ij X + εij; (6) 

where: 

QVij is a set of quantitative pension provision variables used in the pension benefit calculation and i 

denotes the ith employer. The coefficients are estimated by linear least squares-multiple regression. β0i is a 

constant, X is a vector of job characteristics of the employer and his employees, pension plan 

characteristics, and εi

 is an error term. See Table A.3 for a listing and definition of the quantitative pension 

variables. 

IV. Creating the Synthetic Pension File 

As shown in diagram 1, the first two steps in creating PenSync involve fitting the MNL and OLS models to 

the EBS data set to score5

 a new data set of predicted observations (SAS, 2001). Table A.4 gives an 

overview of the accuracy of the MNL model. The model predicted the correct formula on average 71 

percent of the time. Many of the incorrect predictions were among similar type of formulas. For example, 

5

 For a description of SAS Proc Score procedure visit the following web address: 

http://ftp.sas.com/techsup/download/stat/scorenew.html 

Page 116 
 

 

 

 

 

 

 

 

 

 

the model predicted flat dollar formula with a fixed dollar amount (FDF) with a 95.77 percent accuracy 

rate, while only predicting flat dollar formula with a varying dollar amount (FVD) correctly 20.45 percent 

of the time. However, when the model incorrectly predicted FVD it predicted that it would be a FDF 50 

percent of the time. FVD and FDF are very similar in their design and any attempts that were made to 

increase the prediction accuracy flawed the model with multicollinearity and over specification. The results 

from the OLS models are found in Table A.5. 

To summarize the procedure, the step involved estimating equations 5 and 6 to generate a set of coefficient 

estimates, which are used to replicate the EBS data. The resulting coefficients estimates are used to 

produce predicted values by a process of multiplying the estimated coefficient by the observed EBS data. 

This multiplication process is repeated for each variable in the equations specified above. The end product 

is a database containing the predicted values for each observation required to compute a pension benefit 

amount along with the related explanatory variables. The database is called PenPred. To assess the 

quality of PenPred the resulting means and standard deviations are compared to those of the EBS (See 

Appendix A.6). 

Statistical Matching 

Statistical matching is a process of linking data from multiple data sets on the basis of similar 

characteristics rather than unique identifying information. In a statistical match, each observation in 

one microdata set (a base database) is assigned one or more observations from another microdata set 

(secondary database). The assignment is made based upon similar characteristics because the files 

lacked the same unique identifier. 

There exists a substantial amount of research concerning the validity of using statistically matched data for 

analysis. Earlier work by Okner (1972 and 1974), Alter (1974), Radner, et al (1980), and Barry (1988) 

carefully documented some of the shortcomings of statistical matching. In particular, Benjamin Okner 

points out some of the common problems with statistical matching, which are data comparability, handling 

of missing data, specific techniques for matching, and the definition and evaluation of goodness of a match. 

The next few paragraphs briefly discuss the steps taken to address Okner’s concerns. 

Data Comparability 

In an effort to make the PenPred data and the SIPP data compatible, the following harmonization criterions 

are verified. These criterions are well discussed in literature6

: 

(1) Unit harmonization: it is necessary that records of the different sources refer to the same unit. The 

unit of analysis for this study is workers. 

(2) Target population harmonization: if the data set refers to different target populations, it is important 

to select just those records that refer to the population of interests. Both datasets are a sample of 

workers employed in private nonagricultural industries and occupations and participate in a DB plan. 

(3) Variable harmonization: the common variables should be defined in the same way. Both datasets 

use Standard Industry Codes and Census Occupation Codes to categorize the industry and occupation, 

respectively. 

Missing Data 

There are three common approaches to handling missing data: impute the missing data, model the 

probability of missingness, or ignore the missing data. After testing to make sure that there were no 

significant differences on the key variables between cases with missing data and records without missing 

data, the more conservative approach to handling missing data is used. Hence, missing values are replaced 

with means for each variable (Little and Rubin, 1987, Kim and Curry, 1977, Roth, 1994). 

6

 Statistical Matching: a tool for integrating data in National Statistical Institutes by 

Marcello D’Orazio, Marco Dizio and Mauro Scanu can be found on the following webpage: 

http://webfarm.jrc.cec.eu.int/ETK-NTTS/Papers/final_papers/43.pdf. 

Page 117 
 

 

 

 

 

 

 

Selection of the Matching Variables 

Let’s begin with PenPred, henceforward called the universe "U". U consists of a set of N records. For 

each record there are values for R variables. U is represented by an N x R matrix, in which each of the 

N rows contains the values of the R variables for one record. The R variables represent the industry 

code, the occupation code, and the union status, all of which are considered key variables for matching 

based on analysis performed on the EBS data. The SIPP consists of a set of M records. For each 

record there are values for the S variables that are represented by an M x S matrix, in which each of the 

M rows contains the values of the S variables for one record. The S variables represent the industry 

code, the occupational code, and the union status. 

As mentioned earlier, to enable two or more data sources to be statistically matched, a set of variables 

common to all data sets must be found. These common characteristics are referred to as X variables, X 

= (x1,...,xp). The ith record in U, are denoted as Ui

, which contains j observed variables, as shown 

below: 

Ui

 = (uil ui2...uij) (7) 

Similarly the ith, record in the SIPP contains h observed variables: 

SIPPi

 = (SIPPil SIPPi2... SIPPih) (8) 

Where: x1 = the worker 2 digit standard industry classification;7 

 

x2 = the worker 3 digit standard occupational classification;8

 and 

x3 = the worker union status. 

The remaining variables in each of the files are referred to as Y on the PenPred file and Z on the SIPP file . 

Where Y = (Y1...Yq) and y1 is a vector of predicted values of all pension provisions and Z= (Z1...Zr) and z1 

is a vector of socioeconomic and work history variables. 

Specification of the Distance Function 

The statistical matching procedure is carried out by minimizing a distance function. The distance function 

is defined as the absolute difference in the numerical value of the occupations and the union status of two 

cases: The distance between the ith worker in the U and the jth worker in the SIPP is defined by 

Dij =∑ I − I + O −O + U −U in jn in jn in jn (9) 

k ( ) ( ) ( )

n=1 

Where: (n = 1,...,k) and 

Dij 

(Iin - Ijn) = the distance between the values of the nth pair of industry variables in the ith record. 

 (Since it is the cohort variable if must always equal 0) 

(Oin – Ojn) = the distance between the values of the nth pair of occupation code variables in the ith

 record. 

(Uin - Ujn) = the distance between the values of the nth pair of union status variables in the ith 

 record. 

= the distance between the ith U record and the jth SIPP record. 

Certain X variables may be treated as cohort variables. A cohort variable establishes subclasses of the 

records in each of the two files with matching permitted only between a pair of cases in the same subclass. 

In this study, x1 “industry” is the cohort variable. For example, a worker in the mining industry on the 

SIPP file can only be matched to another worker in the mining industry in the U file. 

Assumptions 

This section presents assumptions relevant for the statistical match procedures. 

7

 All workers are classified into one of over 82 industries according to their industrial classification. 

8

 All workers are classified into one of over 820 occupations according to their occupational definition. 

Page 118 
 

 

 

 

 

 

 

 

Assumption 1. No unobserved heterogeneity exists between the predicted data and the observed data. 

Stated differently, the probability associated with being covered by a given pension formula and having a 

particular set of job characteristics are analogous across the three datasets. This is an identifying 

assumption. 

π(x,y| X, DataBLS ) - π (x,y,| X, DataSIPP) - π (x,y,| X, DataPenSync ) = 0 (10) 

where x= type of pension plan, y = formula type, and X is a vector of individual job characteristics (e.g., 

Industry, occupation, and union status). 

Sensitivity analysis was conducted to check the validity of this assumption. Basic descriptive analysis 

revealed that the mean values of the observed data are very similar to the predicted data. Cross tabulations 

also revealed similarities between the three datasets. 

Assumption 2. Workers will remain on their current job until they reach the normal retirement age. 

π(x,y|Xt

 , DataSIPP ) - π(x,y|Xt+i, DataSIPP ) = 0, (11) 

where i = start year of current job,..., retirement year 

Many DB plans allow workers to retire prior to the normal retirement date, but the worker's benefit is 

reduced by an actuarial reduction factor. The current version of PenSync does not have the capability to 

model early retirement; therefore, it is assumed that workers will remain on their current job until they 

satisfy the normal retirement provision specified in their DB plan. By asserting that workers will remain on 

their current job, an obvious assumption is that workers will continue to work in the same industry and 

occupation. To test the feasibility of remaining on the current job, the SIPP and the DER data were used to 

measure tenure on the current job and the frequency of job change. The SIPP data reveals that the average 

tenure on the current DB pension job was 18 years and the DER data reveals that between the start year of 

the current job and 2003, 63 percent of the workers in the sample remained with their same employer. To 

further test these assumptions, the SIPP data is used to check how often a worker reports changing industry 

and/or occupations. When analyzing the full panel of the SIPP, 92 percent and 90 percent of the workers 

report remaining in the same industry and occupation, respectively. 

Assumption 3. The SIPP reported pension job for employer 1 is the highest earnings job in the W-2 file in 

each year. 

π(x,y| Xt DER t SIPP , Data ) - π(x,y| X , Data ) = 0 (12) 

where X = earnings in a given year and t= 1951...2002. 

This assumption assumes that the pension module job 1

9

 on the SIPP is the same as the DER job reporting 

the highest wage. SIPP respondents are asked the question about calendar-year wage and salaries twice per 

panel. Respondents are encouraged to refer to their respective W-2 form or other documents to ensure 

accuracy. To test the validity of this assumption, the earnings total reported in the SIPP for the pension job 

is compared to the highest wage job in the DER for the same year. The SIPP reported earnings are very 

similar to the DER highest earnings, varying by plus or minus $2,000 annually. Respondents in the SIPP 

can also report earnings and pension coverage from two employers; therefore, to further ensure that the 

probability that the pension job reported for employer 1 is indeed the DER highest wage job, analysis is 

conducted on the second job reported in the SIPP. The analysis reveals that less than 3 percent of the 

unweighted individuals who reported having a DB type pension reported having a DB pension on their 

second job. 

The Matching Algorithm 

The match procedure is unconstrained. This has the advantage of permitting the closest possible match for 

a U record, but at the cost of increasing the sample variance of estimators involving the Y and Z variables. 

To avoid violating the MOU confidentially provision, particular attention is given to tabulations based on 

9

 The SIPP asks respondents about two jobs. 

Page 119 
 

small cell sizes. To avoid the possibility of unauthorized disclosure, cells with three or fewer cases were 

dropped from the sample. 

The matching algorithm also employs a decision rule: If the pair agrees on all three characteristics (i.e. 

industry, occupation, and union status), designate the pair as a Level 1 Match, else if the pair agrees on two 

of the characteristics (i.e. industry and occupation), designate the pair as a Level 2 Match, else if the pair 

agrees on two of the characteristics (i.e. industry and major occupational group (MOG)), designate the pair 

as a Level 3 Match, else if the pair agrees on one of the characteristics (i.e. industry), designate the pair as a 

Level 4 Match, else designate the pair as a non-match. As shown in Table 1, the final data file for analysis 

consists of 2508 observations, which contains detailed socioeconomic variables along with in-depth 

employer-provided pension data. This database is called PenSync. 

Table 1. Number and percent of matches by the number of levels required for the match. 

 

 

Level 1 1876 75% 

Level 2 192 8% 

Level 3 430 17% 

Level 4 10 .004% 

Total 2508 100% 

Levels Number of matches Match rate 

 

 

 

 

 

 

 

 

 

Source: Author's calculation 

Benefit Algorithm 

The final procedure in this study involves constructing an algorithm to calculate benefit amounts and the 

replacement rates for each individual in PenSync. The algorithm starts by determining the type of formula 

assigned to an individual (e.g. career average earnings, terminal earnings, cash balance, or flat dollar). For 

individuals covered by a percent of earnings times years of service formula, a subroutine is initiated to 

determine whether the earnings are based upon a career average or terminal earnings. For individuals 

covered by a career average arrangement, the benefit amount is determined by multiplying a proportion of 

the average DER earnings by the workers’ total number of credited years of service.10 For individuals 

whose benefit amounts are based upon a terminal earnings arrangement, the algorithm multiplies a 

proportion of the average DER earnings in a specified period of time, typically near the individuals’ 

retirement age. 

For individuals who are covered by a cash balance plan, their benefit amounts are represented as an account 

balance, which is equal to a percentage of the individuals' earnings during each year of participation in the 

plan credited with interest based on some index. At retirement, a cash balance plan participant typically 

receives his/her accumulated vested account as a lump sum. For purposes of this paper, once the worker 

reaches the normal retirement age specified by the plan the accumulated vested account was annuitized. 

Some benefits are not associated with earnings, but rather a dollar amount per year of service. For those 

individuals their benefit amount is determined by multiplying a fixed dollar amount by years of service in 

the plan. 

The final step in the algorithm produces a set of pension benefits and replacement rate ratios for the two 

measures of earnings, the last ten years of earnings (L10yr) and the last five years of earnings (L5yr). 

L10yr is the average of the five highest years of earnings 10 years prior to the pension plan normal 

retirement date. L5yr is the average of the three highest years of earnings 5 years prior to the pension plan 

normal retirement date. The pension plan normal retirement date is the year in which the worker satisfies 

provisions specified in their pension plan in order to receive an unreduced retirement benefit. The year 

10 For all individuals regardless of formula type, the number of credited years of service is determined by 

subtracting the pension plan normal retirement year from the year the workers reported starting his/her 

current job. For years of earnings that are outside the scope of the DER, the SER is used to supplement the 

missing data. 

Page 120 
 

 

 

 

2003 is used to verify whether an individual has satisfied the pension plan normal retirement requirement. 

All earnings and benefit amounts are measured in 2003 dollars. 

V. Results 

For workers who are eligible for normal retirement benefits prior to 2003, their DB plan is estimated to 

replace about 30 percent of last earnings. The average earnings are estimated to be about $35,000 and the 

average monthly pension benefit is $1012 (table 2). Pension replacement rates are estimated to vary by the 

type of benefit formula, employment characteristics and years of participation in the pension plan. 

Replacement rates were the lowest for those in flat dollar or career average formulas and highest for those 

in terminal earnings formulas or cash balance formulas with a 16-17 percentage point differential. 

Replacement rates were considerably lower for those in administrative/clerical or production/service jobs 

compared to those in professional/technical jobs, and lower for those in goods producing industries than 

those in nongoods producing industries. Union members are estimated to have higher replacement rates 

than nonunion members. And more years of participation in a pension plan is associated with much higher 

replacement rates. Workers who remain in the same pension plan for more than 30 years have over 60 

percent of their earnings in the five years prior to retirement replaced by their pension plans compared with 

only a 9 percent replacement rate for those with fewer than 10 years of participation. 

VI. Conclusion 

Predicting retirement income from a pension plan is a difficult task. The lack of good data is a major 

contributor. Furthermore, the lack of comprehensive pension data sources poses limitations on pension 

research and policy decisions. The methodologies applied in this paper have been in existence for decades. 

However, they still remain more of an art than a science. However, many challenges are inherent when 

employing such a procedure. They include model specifications, harmonization, and probably most 

importantly, the quality of the data involved. Nevertheless, the methodology is a reasonable approach 

given constraints from two different restricted data sets. 

Table 2. Pension Income and Replacement Rate for Workers Who Qualify for Normal Retirement 

Prior to 2003. 

Items Percent Average Earnings Monthly Replacement Rates 

High 3 of 

last 5 

High 5 of 

last 10 

Benefit High 3 of 

last 5 

High 5 of 

last 10 

Dollars Percent

All 100 37,958 32,649 1,012 32 29 

Dollar Formula 19 35,858 30,068 818 21 24 

Terminal Earnings 54 38,921 34,381 1,144 38 30 

Career Average 10 32,233 28,192 781 21 20 

Cash Balance 17 40,600 32,614 960 32 36 

Occupation 

Professional/Technical 39 49,779 42,579 1,415 42 33 

Administrative/Clerical 18 25,148 22,607 579 24 25 

Production/Service 43 32,308 27,606 815 26 27 

Industry 

Goods Producing 40 37,828 32,999 913 26 27 

NonGoods Producing 60 38,044 32,417 1,079 36 31 

Years in the Plan 

0 – 10 16 28,015 23,711 256 9 11 

11 – 15 15 31,144 27,315 502 18 20 

16 – 20 10 33,406 29,080 845 28 31 

21 – 25 12 29,837 26,122 955 30 34 

Formula Type 

Page 121 
26 - 30 26 45,759 38,206 1,178 33 33 

Greater than 30 22 47,428 41,674 1,840 61 41 

Union Status 

Nonunion Member 66 39,594 33,930 917 25 27 

Union Member 35 34,852 30,219 1,202 46 32 

Note: High 3 of last 5 is the average of the three highest years of earnings 5 years prior to the pension plan 

normal retirement date. High 5 of last 10 is the average of the five highest years of earnings 10 years prior 

to the pension plan normal retirement date. All earnings and benefit amounts are measured in 2003 dollars. 

Eligibility for retirement depends on a workers age or the number of years of credited service, or both. The 

mean normal retirement age in PenSync is 60 with an average of 25 years of service. The normal retirement 

date is the year in which the worker satisfies provision specified in their pension plan to receive unreduced 

retirement benefit. The year 2003 is used to verify whether an individual has satisfied the normal retirement 

requirement. The mean normal retirement year in PenSync is 1998. 

Source: Author's calculation using PenSync. 

Page 122 
 

 

 

 

 

 

 

 

References: 

Alter, Horst E. 1974, “Creation of a Synthetic Data Set By Linking Records of the Canadian Survey of 

Consumer Finances With the Family Expenditure Survey 1970,” Annals of Economic and Social 

Measurement. 3(2): 373-394. 

Agresti, A. 1990. Categorical Data Analysis. New York, NY: J. Wiley & Son. 

Barry, J. T. 1988. “An Investigation of Statistical Matching.” Journal of Applied Statistics (15): 275-283. 

Ben-Akiva, Moshe, and Steven Lerman. 1985. Discrete Choice Analysis: Theory and Application to Travel 

Demand. Cambridge, MA: MIT Press 4th printing 1991. 

Bureau of Labor Statistics, U.S. Department of Labor. 1993. Employee Benefits in Medium and Large 

Private Establishments. Washington, D.C.: US GPO. 

Butrica, Barbara, A., Howard M. Iams, James Moore, and Mikki Waid. 2001. Methods in Modeling 

Incomei n the Near Term (MINT). ORES Working Study No. 91. Office of Policy, Social Security 

Administration. May. 

Cook R.D. 1979. "Influential Observations in Linear Regression." Journal of the American Statistical 

Association. 74:169-174. 

Elliot, Kenneth R., and James H. Moore. 2000. “Cash Balance Pension Plans: the New Wave.” 

Compensation and Working Conditions. 5(2): 3-12. 

Green, W.H.1990. Econometric Analysis. New York, NY: Macmillan. 

Little, R. J. A. and Rubin, D. B. 1987. Statistical Analysis with Missing Data. New York: J. Wiley and Sons 

Kim, J. O., & Curry, J. 1977. “The treatment of missing data in multivariate analysis. 

Sociological Methods and Research. 6: 215-240. 

McFadden, D. 1973. “Conditional logit analysis of qualitative choice behavior.” Frontiers in 

Econometrics, edited by P. Zarembka. New York, NY: Academic Press, Inc. 

Mitchell, Olivia S. 1998. “Developments in Pensions,” NBER Reporter, National Bureau of Economic 

Research. 

Papke, Leslie E. 1999. “Are 401(k) Plans Replacing Other Employer-Provided Pensions? Evidence from 

Panel Data.” Journal of Human Resources. 34(2): pp. 346-68. 

Okner, B. A. 1972. “Constructing a New Data Base From Existing Microdata Sets: The 1966 Merge File.” 

Annuals of Economic and Social Measurement. 1(3): 325-342. 

Radner, D.B., Allen, R., Gonzalez, M E. Jabine, T. B., and Muller, H.J. 1980. “Report on Exact and 

Statistical Matching Techniques.” Statistical Policy Working Paper, U.S. Dept. of Commerce, Washington, 

D.C.: U.S. GPO 

Rogers, Willard L. 1984. “An Evaluation of Statistical Matching.” Journal of Business & Economic 

Statistics. 2(1): 91-102. 

Roth, P. L. 1994. “Missing data: A conceptual view for applied psychologists.” Personnel Psychology. 47: 

537-560. 

Page 123 
 

 

 

Rubin, D. B. 1986. “Statistical Matching Using File Concatenation with Adjusted Weights and Multiple 

Imputations. “Journal of Business and Economic Statistics. 4:87-94. 

SAS Institute Inc. 2001. SAS Technical Support Documents 650e. Multinomial Logit, 

Discrete Choice Modeling an Introduction to Designing Choice Experiments, and Collecting, Processing, 

and Analyzing Choice Data with SAS, Cary, NC: SAS Institute Inc. 

Toder, Eric and others. 1999. “ Modeling Income in the Near Term-Projections of Retirement Income 

Through 2020 for the 1931-1960 Birth Cohorts.” Final Report, SSA Contract No. 600-96-27332. 

Washington, DC: The Urban Institute. 

Train, K. 1986. Qualitative Choice Analysis: Theory, Econometrics, and an Application to Automobile 

Demand. Cambridge, Mass.: MIT Press. 

Page 124 
 

 

 

Appendix A. 

Brief description of DB provisions 

A DB plan provides employees with guaranteed retirement benefits based on a predetermined benefit 

formula. There are three basic types of DB formulas found in the EBS data: (1) a percent of earnings per 

year of service, (2) a cash balance arrangement, and (3) a flat amount per year of service. 

According to the EBS data, the majority of workers who participate in a DB plan are covered by a percent 

of earnings per year of service formula (BLS, 2000)11. In this type of arrangement the employee benefit is 

based on a proportion of earnings per year of service for each year that an employee participates in the 

plan. The credited years of service may be based upon either a career average or final earnings. Under a 

career average arrangement the plan benefits are based on the average of the earnings paid over the entire 

period of the employee’s participation in the plan. On the other hand, under a final pay arrangement, the 

plan benefits are based on an average of the employee’s earnings during a short period of time, typically 

near the employee’s retirement age. For example, the earnings may be averaged over the last three or five 

years of employment, or over the three or five consecutive years in the 10-year period immediately prior to 

retirement during which the employee’s earnings are typically the highest. 

A cash balance plan is another type of DB plan whereby the benefit formula takes into account the 

employee’s income and number of credited years of service. Although a cash balance plan is structured to 

bear resemblance to a defined contribution plan where the benefits are represented as an account balance 

instead of as an annuity. The account balance is equal to a percentage of the employee's income during 

each year of participation in the plan, and it is also credited with interest. The interest rate is often based on 

an index, such as the rate of return on 30-year Treasury bonds. 

Some benefits are not associated with income, but rather a dollar amount per year of service. In 2000, 14 

percent of all workers in the private sector who were covered by a DB plan had this type of plan. A flat 

dollar amount per year of service formula provides a benefit amount based on a fixed dollar amount 

multiplied by years of service in the plan. To illustrate, if a plan specifies a benefit of $40 a month for each 

year of service, an employee with 30 years of participation in the plan would receive a monthly benefit of 

$1,200. 

Before an employee is entitled to benefits from the plan, he/she must become vested, which means having a 

designated number of years of service with an employer. A five-year cliff-vesting requirement is the most 

prevalent provision. Therefore, this study assumes that an individual, upon satisfying the five-year vesting 

requirement, is entitled to receive a non-forfeitable accrued benefit upon separation or retirement. 

Benefits under a DB plan are usually paid when the employee retires. All DB plans are required to specify 

an age, years of service, or some combination of the two whence an employee can receive unreduced 

benefits. The normal retirement age in most plans is 65. However, many DB plans allow early retirement 

after a stated age that is earlier than the declared normal retirement age, but the employee's benefit is 

reduced by an actuarial reduction factor. This provision is called early retirement. 

 

11 This data can be found at http://www.bls.gov/ncs/ebs/sp/ebrp0001.pdf. 

Page 125 
A.1. Descriptive Statistics for Job Characteristics Variables 

Industry 

Mining 56 1.14

Construction 49 0.99

Manufacturing 1330 27.01

Transportation 804 16.32

Wholesale 154 3.13

Retail 444 9.02

Finance 1106 22.46

Service 982 19.94

Occupational Groups 

Professional 1564 31.76

Blue Collar 1652 33.54 

Clerical 1709 34.7

Union Status 

Non Union Member 3547 72.02 

Union Member 137827.98 

Work Schedule 

Part-time 308 6.25

Fulltime 4617 93.75

Employment 

Less than 250 922 18.72 

250-499 754 15.31

500-999 886 17.99

1,000 or greater 2363 47.98 

 

Category Number Percent 

Number of Observations 4925 

Source: Author’s calculation using EBS data 

Page 126 
A.2. Description of the values for the MNL dependent variable 

 

 

 

 

 

 

1 Flat Dollar Amount times years of service with a fixed dollar amount times years of service 

2 Flat Dollar Amount times years of service with a varying dollar amount times years of service 

3 Percent of terminal earnings with a fixed percent of earnings averaged over the last few year of 

employment 

4 Percent of terminal earnings with varying percent of earnings averaged over a specified period 

of consecutive years of employment 

5 Percent of terminal earnings with varying percent of earnings averaged over the last few year of 

employment 

6 Percent of terminal earnings with a fixed percent of earnings averaged over a specified period of 

consecutive years of employment 

7 Percent of terminal earnings with a fixed percent of earnings averaged over the employee career 

8 Percent of terminal earnings with varying percents of earnings averaged over the employee 

career 

9 Cash balance plan 

Value Formula Type 

Page 127 
 

 

 

 

 

 

 

 

 

 

 

A.3 Definitions of Quantitative Variables 

DOL_DOL1 1

st dollar amount breakpoint use to calculate a flat dollar formula 

DOL_DOL2 2

nd dollar amount breakpoint use to calculate a flat dollar formula 

DOL_DOL3 3

rd dollar amount breakpoint use to calculate a flat dollar formula 

DOL_YRS1 1

st YOS breakpoint use to calculate a flat dollar formula 

DOL_YRS2 2

nd YOS breakpoint use to calculate a flat dollar formula 

NORM_AAS Sum of normal retirement age and service 

NORM_AGE Normal retirement age 

NORM_SRV Normal retirement service requirement 

NR_PAY Percent of earnings contribute to a Cash Balance plan 

NR_INT Interest rate 

EBASEYR1 1

st breakpoint for number of years to be included in the calculation of benefits 

EBASEYR2 2

nd breakpoint for number of years to be included in the calculation of benefits 

POE_DOL1 1

st breakpoint number of years to be included in the calculation of benefits 

POE_DOL2 2

nd dollar amount breakpoint use to calculate a percent of earnings formula 

POE_PCT1 1

st percent of earnings breakpoint use to calculate a percent of earnings formula 

POE_PCT2 2

nd percent of earnings breakpoint use to calculate a percent of earnings formula 

POE_PCT3 3

rd percent of earnings breakpoint use to calculate a percent of earnings formula 

POE_PCT4 4

th percent of earnings breakpoint use to calculate a percent of earnings formula 

POE_PCT5 5

th percent of earnings breakpoint use to calculate a percent of earnings formula 

POE_YRS1 1

st breakpoint number of years of service to be included in the calculation of benefits 

POE_YRS2 2

nd breakpoint number of years of service to be included in the calculation of benefits 

Page 128 
 

Table A.4 Prediction Accuracy Predicted Compared to Observed Formula Types

Observed Predicted formula Value Observed 

formula Flat Dollar Terminal Earnings Career Average Cash Balance Total 

value 1 2 3 4 5 6 7 8 9 

Frequency 1 816 6 0 14 0 1 2 1 12 852 

Percent 95.77 0.7 0 1.64 0 0.12 0.23 0.12 1.41 

2 22 9 0 13 0 0 0 0 0 44 

50 20.45 0 29.55 0 0 0 0 0 

3 0 0 112 0 43 0 0 0 0 155 

0 0 72.26 0 27.74 0 0 0 0 

4 1 1 2 1182 0 207 1 1 0 1395 

0.07 0.07 0.14 84.73 0 14.84 0.07 0.07 0 

5 0 1 29 1 315 1 0 0 0 347 

0 0.29 8.36 0.29 90.78 0.29 0 0 0 

6 0 3 4 473 0 1099 6 10 0 1595 

0 0.19 0.25 29.66 0 68.9 0.38 0.63 0 

7 0 0 0 0 0 6 11 0 0 17 

0 0 0 0 0 35.29 64.71 0 0 

8 0 0 0 0 0 132 0 83 0 215 

0 0 0 0 0 61.4 0 38.6 0 

9 34 0 0 0 0 0 1 0 270 305 

11.15 0 0 0 0 0 0.33 0 88.52 

Predicted Total 873 20 147 1683 358 1446 21 95 282 4925 

 Source: Author’s calculation using EBS and PenSync data. 

Page 129 
 Table A.5. Regression Results for Selected Quantitative Variables 

R

2 

 Constant Size Industry Work Occupation Union Dollar Career 

Schedule Status Formula Average 

dol_dol1 5.0851 -0.0005 -2.862 -2.0372 1.2767 0.3024 31.8015 0.7117 .74 

(.80890)** (.00001)** (.3666)** (.4234)** (.2336)** (.2616) (.5091)** (.4262)** 

CB 4.5894 0.0001 0.164 -0.0600 -0.0032 -0.0346 -4.8377 -4.8791 .79 

percent (.0735)** (.00001)** (.0322)** (.0372) (.0205) (.023) (.0447)** (.0375)** 

CB 5.26057 -0.0001 0.0044 0.043 0.0502 0.016 -5.2488 -5.2148 .79 

interest (.076)** (.00001) (.0333) (.0385) (.0212) (.0238) (.0462)** (.0387)** 

POE 1 -2.6099 0.0002 -0.3918 1.8657 0.6683 0.8312 -0.3176 12.9813 .67 

(.480)** (.00005)* (.2103) (.2429)** (.1340)** (.1501)** (.2921) (.2445)** 

POE 2 0.2800 0.00002 0.1202 -0.054 -0.0807 -0.2721 -0.1862 0.5662 .18 

(.0911)* (.000009) (.0399) (.0461)* (.0254) (.0285)** (.0554)* (.0464)** 

Years 1 -0.3143 0.0001 0.3194 0.0678 -0.062 0.0314 -0.3266 3.3456 .41 

(.2185) (.000002)** (.0957)* (.1106) (.0610) (.0683) (.133) (.1113)** 

Years 2 -4.3253 -0.0006 4.3718 8.346 -1.8145 3.6991 -6.4945 26.0477 .12 

(3.9373) (.0004) (1.7254) (1.993)** (1.1) (1.2312) (2.3964) (2.0059)** 

Norm_age 46.606 0.001564 5.454 -3.20707 -2 -2.98348 -2.8452 7.651 .09 

(2.01)** (.0002)** (.88)** (1.01)* (.56)* (2.98)** (1.22) (1.02)** 

Norm_srv 10.629 -0.00152 -6.373 3.71762 1.3416 2.67692 6.3605 1.856 .10 

1.94)** (.0001)** (.523)** (.604)** (.333)** (.7.)** (.723)** (.61) 

 ** Significant at 1% statistical level and * Significant at 5% statistical level. 

Page 130 
 A.6. Mean and Standard Deviation for Predicted and Observed Quantitative Variables 

Variables 

Mean Standard Deviation

Predicted Observed Difference Predicted Observed Difference 

Dol_dol1 6.40 6.33 0.06 11.81 13.83 -2.02

Dol_dol2 0.04 0.09 -0.05 0.20 1.44 -1.25

Dol_dol3 0.66 0.46 0.19 1.10 5.20 -4.10

Dol_yrs1 0.15 0.11 0.04 0.36 1.14 -0.78

Dol_yrs2 0.05 0.11 -0.06 0.22 1.81 -1.59

Norm_aas 5.32 5.30 0.02 2.03 20.10 -18.07

Norm_age 57.38 57.33 0.04 5.29 17.77 -12.49

Norm_srv 7.89 7.91 -0.02 3.23 10.59 -7.36

Nr_pay 0.31 0.30 0.01 1.21 1.34 -0.13

Nr_int 0.31 0.32 -0.01 1.21 1.41 -0.20

Ebaseyr1 2.97 2.79 0.18 1.70 2.40 -0.71

Ebaseyr2 21.24 20.76 0.48 11.67 35.52 -23.85

Poe_dol1 243.58 234.11 9.47 146.37 1877.95 -1731.58

Poe_dol2 0.00 0.00 0.00 0.00 0.00 0.00

Poe_pct1 10.19 10.24 -0.04 5.64 7.03 -1.39

Poe_pct2 0.76 0.67 0.09 0.43 0.85 -0.42

Poe_pct3 0.00 0.18 -0.18 0.00 0.43 -0.43

Poe_pct4 0.00 0.02 -0.02 0.00 0.14 -0.14

Poe_pct5 0.00 0.04 -0.04 0.00 0.21 -0.21

Poe_yrs1 5.40 5.22 0.18 2.91 11.30 -8.39

Poe_yrs2 0.50 0.43 0.06 0.50 2.28 -1.78

 Source: Author’s calculation using EBS and PenSync data. 

Page 131