Working Paper Series

Congressional Budget Office

Washington, DC

HOW DOES DIFFERENTIAL MORTALITY 

AFFECT SOCIAL SECURITY

FINANCES AND PROGRESSIVITY?

Amy Rehder Harris(e-mail: amy.harris@cbo.gov)

John Sabelhaus(e-mail: john.sabelhaus@cbo.gov)

Congressional Budget Office

Washington, DC

May 2005

2005-5

Working papers in this series are preliminary and are circulated to stimulate discussion

and critical comment. These papers are not subject to CBO’s formal review and editing

processes. The analysis and conclusions expressed in them are those of the authors and

should not be interpreted as those of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series can be obtained at

www.cbo.gov/tech.cfm. 
Abstract

The Congressional Budget Office Long-Term (CBOLT) model uses dynamic micro-simulation

for a representative sample of the population to analyze the aggregate and distributional effects

of Social Security policy. In the model, overall mortality rates by age and sex are calibrated to

match Social Security Trustees projections, and differential mortality (the difference in death

rates across socioeconomic groups) is introduced using a combination of disability-specific

mortality and a technique for the non-disabled developed by Lillard and Panis (1999). In this

paper, the question of how differential mortality affects Social Security finances and

progressivity is approached through sensitivity analysis using CBOLT. The model is solved

using a range of assumptions about differential mortality, and the impact on various outcomes is

assessed. In contrast to inferences in several recent studies, the results here suggest that

differential mortality does not play a significant role in determining progressivity or system

finances. It is true that socioeconomic differentials in death rates work counter to Social

Security’s statutory redistribution and make the system costs higher, but the effects are probably

only of second-order significance. 
1

The authors would like to thank Josh O’Harra and Kevin Perese of CBO, who worked on the micro

modules used in this paper, and Ryan Edwards, who provided useful comments on an earlier version of the paper. 

1

1. Introduction1

It is widely acknowledged that the U.S. Social Security system is expected to become

insolvent within a few decades (Social Security Administration (2004), Congressional Budget

Office (2004-A)), and also clear that any steps taken to address the expected financial imbalance

will involve a decrease in net benefits (a reduction in benefits or increase in taxes) for some

group at some point in time. The tradeoff between restoring overall financial solvency and

avoiding negative distributional consequences is crucial to the debate over how and when to

reform Social Security. One of the modeling assumptions that affects estimates of both system

finances and progressivity is differential mortality–the negative correlation between

socioeconomic status and mortality rates. This paper uses the Congressional Budget Office

Long-Term (CBOLT) micro-simulation model to investigate the role that differential mortality

plays in determining overall system finances and progressivity.

Differential mortality has been raised as a point by various observers to support very

different visions for reforming Social Security. The current Social Security system is

progressive in a statutory sense because beneficiaries with low lifetime earnings get a higher

replacement rate (ratio of benefits to average lifetime earnings) than their higher-earning

counterparts. However, most analysts agree that the statutory redistribution is offset at least in

part because beneficiaries with low lifetime earnings die younger and get benefits for a shorter

period. Some proponents of moving the system towards individual accounts have argued

that–because the current system is not effectively progressive anyway–having net benefits tied

more closely to individuals’ earnings would not affect (or could even increase) overall
2

See, for example, Feldstein (2005).

3

See, for example, Diamond and Orszag (2004).

4

See Preston and Elo (1995), Pappas, Hadden, and Fisher (1993), Lauderdale (2001), and Elo and Smith

(2003). 

5

The Lillard and Panis (1999) differential mortality formulation was originally developed for the Social

Security Administration’s Modeling Income in the Near Term (MINT) micro-simulation. The MINT model has

been used extensively is previous studies of Social Security redistribution–see, for example, Cohen, Steuerle, and

Carasso (2001) and Smith, Toder, and Iams (2003/2004). 

2

progressivity.2 At the other end of the political spectrum, some proponents of raising net taxes

on higher lifetime earners argue that the goal of reform should be to establish (or re-establish)

progressivity in a system where it is currently lacking because differential mortality eliminates

the desired redistribution embodied in the law.3

 As a corollary, some argue that if the long-run

financial imbalance in Social Security is attributable to higher lifetime earners collecting benefits

longer, higher earners should be the ones to fund those benefits.

The idea that socioeconomic status and mortality are negatively correlated is well

established in a number of studies, and there is some evidence that the relationship is changing,

at least by education, over time.4

 This paper uses sensitivity analysis as an approach to

understanding the role played by differential mortality in Social Security. The CBOLT microsimulation model introduces differential mortality through two distinct channels, and those

channels are altered to test for the significance of differences in death rates. First, the model

incorporates a direct relationship between earnings and Disability Insurance (DI) claiming and

then between DI status and mortality, generating an indirect (but very powerful) link between

earnings and mortality. Second, for the non-disabled, CBOLT adopts the Lillard and Panis

(1999) model of differential mortality which has explicit socioeconomic covariates including

earnings, marital status, and education.5

 This second channel in particular allows some
6

Fullerton and Mast (2005) organize their discussion of Social Security progressivity around this classifier

principle. 

7

Coronado, Fullerton, and Glass (2002), Liebman (2002), Gustman and Steinmeier (2001), Armour and

Pitts (2004).

3

flexibility (by varying estimated coefficients) for specifying the effect that differential mortality

has on progressivity and system finances, and thus it is possible to run counter-factual

experiments to understand the role played by differential mortality. 

The effect of differential mortality on Social Security system progressivity has been

analyzed in several previous papers, but the results here go beyond those efforts in several ways. 

First, most previous studies focus only on the non-disabled population, and generally only

hypothetical “example” earners or one cohort of individuals who reach (or are projected to

reach) retirement benefit eligibility age. CBOLT operates on a representative sample of the

population for the period between 1984 and, in a typical simulation, 2110, and thus allows much

broader cross-sectional and longitudinal analysis. The second confounding factor in previous

studies of progressivity is that differential mortality is often analyzed along with other variables

that affect estimates of redistribution–most notably, the characteristics that are used to classify

individuals into the groups across which redistribution is being measured.6

 Indeed, some

researchers have concluded that Social Security in its current form is not progressive at all, once

individuals are properly classified.7

 That conclusion is often interpreted to mean “differential

mortality eliminates the statutory redistribution in Social Security.” Indeed, it is shown here that

differential mortality probably plays a fairly modest role in that conclusion once the differences

in classifier variables are accounted for. 

In addition to studying progressivity, the sensitivity analysis approach used in this paper
4

is also useful for investigating the role that differential mortality plays in Social Security system

finances. The experiments presented here are designed to address how much of the long-run

financial imbalance in Social Security is attributable to the relative differences in life expectancy

suggested by various models of differential mortality. Analogous to the conclusions about

progressivity, differential mortality (holding overall mortality by age and sex fixed) has only a

modest impact on system finances. 

These conclusions about the effect of differential mortality on Social Security finances

and progressivity are both model and measure dependent, but there is good reason to believe

they would generalize to other models and alternative measures for outcomes or classifiers when

subjected to the same sort of test. The reason to expect that the conclusions about differential

mortality will hold is quite simple: differences in death rates across age groups dominate the

effect of differential death rates within age groups. That is, even when the extent of differentials

is increased arbitrarily to generate very skewed death rates by income at every age there is only a

modest effect on conclusions about overall progressivity or finances, because differences in

death rates across age groups are so much larger. The simulations here hold overall mortality by

age and sex fixed, and that effect is shown to dominate the results. 
8

The macro growth model framework is not discussed here, but is closely related to the approach in

Bosworth and Burtless (2002, 2004) with two important differences: aggregate labor input is summed from the micro

model in CBOLT, and aggregate private saving adjusts to target a stable long-run capital output ratio. That saving

assumption effectively neutralizes the impact of assumptions about other components of the Federal budget and

creates a stable baseline similar to the one used by the Social Security Trustees when they analyze system finances. 

5

2. Differential Mortality in the CBOLT Micro Model

The Congressional Budget Office Long-Term (CBOLT) model integrates a microsimulation approach with a macro-economic/unified budget framework for studying questions

that involve both aggregate and distributional analysis. This section provides an overview of

CBOLT and describes the methods by which differential mortality is introduced into the

analysis. 

Overview of the CBOLT Model

The basic design principle behind the CBOLT micro-simulation is to first generate

realistic demographic, economic, and policy outcomes for a large representative sample, then to

apply the complex Social Security program rules and solve for micro-distributional and

aggregate budgetary outcomes. The modeling process begins with a large-scale Social Security

Administration (SSA) longitudinal data file from which a sample is drawn to become the basic

input to the micro simulation. The sampled data file is then used as a starting point for applying

CBOLT’s micro-processes (methods for projecting individual demographic and economic

outcomes over time) which are estimated using various data sources and calibrated over history. 

The micro simulation is also integrated with a comprehensive macro/budgetary model, so the

projections provide insights about both Social Security system finances and estimates of

progressivity.8

 
9

The micro transition processes are described in detail in a series of technical papers available on the CBO

web site. For a more detailed overview of the micro-modules, see O’Harra, Sabelhaus, and Simpson (2004); for a

discussion of the marital transition processes see O’Harra and Sabelhaus (2002); for a discussion of the labor force

participation and earnings projections see Harris and Sabelhaus (2003); and for a discussion of the mate-matching

algorithms see Perese (2002).

6

The starting point in any micro-simulation model is the base data file. CBOLT uses the

Social Security Administration (SSA) Continuous Work History Sample (CWHS), which is a

one-in-one-hundred sample covering every Social Security number ever issued. For each

observation in the data file, the CWHS reports a comprehensive earnings and worker benefit

history along with basic demographics. The primary advantages of the CWHS are that the

sample is very large (indeed, CBOLT uses only one-tenth of the CWHS, so the model itself is a

one-in-one-thousand sample) the data is from high-quality administrative records (as opposed to

limited and sometimes biased self-reported data) and the data set is updated annually (so CBOLT

can be re-based every year). The primary disadvantage of the CWHS is the lack of

comprehensive demographics and other information that is available from public surveys, but

that shortcoming is resolved in the calibration process discussed below. 

Given a micro base file, the second step in any micro-simulation is specifying transition

equations–the processes by which demographic and economic outcomes for individuals in the

micro sample evolve over time. CBOLT operates on the basic processes (birth, education, labor

supply, earnings, first marriage, divorce, remarriage, mate matching, benefit claiming, benefit

awards, and ultimately death) needed to calculate Social Security taxes and benefits and to

integrate the micro outcomes with the macro growth model and unified budget framework.9

Those processes are estimated using a number of different data sources that each provide unique

information on a particular demographic or economic process. The micro-transition processes
10Even the limited-behavior version of the micro-simulation based-approach leads to important insights

about Social Security that do not come through in other analyses. First, all else equal, the micro-simulation

generates projected benefit awards for male OAI workers below those based on standard actuarial techniques,

because CBOLT properly captures observed shifts in the historical relative earnings profiles (CBO, 2004-A). 

Second, direct analysis of the micro-level outcomes suggests there are serious problems with using hypothetical

“example” workers to analyze the impact of proposed reforms (CBO, 2004-B, C, D).

11Social Security coverage rates were much lower for working age cohorts before then, and also the

availability of earnings data above the taxable maximum did not occur until the 1980s. 

7

are primarily designed to capture correlations between individual characteristics (as opposed to

reflecting optimizing economic decisions) and thus the results are useful for distilling the firstorder impact of choosing micro-simulation for studying Social Security.10

The micro transition processes developed for projecting future individual outcomes are

also used to assign information that is not available in the base (CWHS) data file. CBOLT uses

a “historical simulation” approach to assign the demographic characteristics that are not present

on the micro base file. Although this type of imputation-based assignment is used in all major

micro-simulation projects, it is quite extensive in CBOLT and deserves special mention. The

basic idea is to assign missing characteristics in history using the same methods for projecting

forward, then test and calibrate the processes using external data sources available in history.

The initial CBOLT micro sample is actually drawn to be representative of the U.S. 

population for the period 1984 through 2002.11 The historical simulation process begins in 1984,

when each individual gets initial unobserved characteristics assigned based on their observed

characteristics (a standard imputation). Then, each micro process is applied and then calibrated

so it generates the actual observed distributions (say population by marital status) that are known

from some external data sources. The model is also carefully tested for its ability to reproduce

empirical covariances (say, between husband and wife ages). Perhaps the most important test of

the model is that it matches Social Security system outcomes (numbers of beneficiaries and
8

average benefits by type of benefit award) in the historical period. 

How Differential Mortality Enters in CBOLT

Differential mortality is introduced into CBOLT through two channels. The first channel

is for the disabled (actually, the Disability Insurance (DI) beneficiary) population, for whom

differential mortality is implicit because the probability of becoming a DI beneficiary is a

function of earnings, and the probability of a transition off DI through death is much higher than

death rates for the non-disabled population. The second channel for differential mortality applies

to the non-disabled, and uses estimates of the correlation between death rates and various

socioeconomic characteristics from Lillard and Panis (1999).

Before discussing the two distinct mortality processes in detail, it is useful to step back

and understand how differential mortality fits into the general flow of a CBOLT simulation (see

Figure 1). The simple schematic in Figure 1 for differential mortality over the course of one

simulation year suggests some important connections that should be kept in mind. Working

backwards, the actual period t mortality covariates for the disabled population are age, sex, and

length of time on DI. For the non-disabled, the covariates again include age and sex, but also the

common variables between CBOLT and the Lillard and Panis (1999) equation, which are

education, marital status, and earnings. The schematic makes it clear that the various paths for

differential mortality causation are actually more complicated than the final covariates would

suggest. For example, in CBOLT, earnings affect the probability of marital transitions (O’Harra

and Sabelhaus, 2002) which in turn affects labor supply (Harris and Sabelhaus, 2002) which in

turn affects earnings in the next period. Thus, even if marital status was the only covariate (other
12For an alternative approach to assigning differential mortality using external data sources, see Brown,

Liebman, and Pollett (2002) 

9

than age and sex) in the mortality equation, there would still be differential mortality in the

model (with respect to earnings) through the other linkages. 

The link between earnings and mortality for the DI population in CBOLT is very

straight-forward. The probability of entering DI in any given year is a function of age, sex, and

earnings. The effect of earnings is estimated using the CBOLT input data file (the CWHS,

described above) for the period 1984 to 2002 (see Figure 2). The bar chart shows the fraction of

new DI entrants coming from each earnings decile–workers in the bottom decile have something

like four times the probability of going on DI relative to workers in the top decile. As with other

aspects of the model, these probabilities are evaluated in the “historical simulation” process with

an eye towards whether or not the distribution of benefit awards is consistent with actual data. 

Given that an individual in CBOLT is assigned DI beneficiary status, they face a much

higher death rate than if they had remained non-disabled (see Figure 3). The probability of death

for DI beneficiaries in CBOLT is based directly on data provided by the Office of the Chief

Actuary (OCACT) at the Social Security Administration. The death rates for new DI

beneficiaries are quite high for the first two years a person is receiving benefits, but even the

rates for people who have been on DI for ten years are very high–orders of magnitude larger than

the average death rates in these age/sex groups. The combination of earnings-based entry onto

DI and much higher than average death rates together generate an indirect but very powerful

differential mortality in the outcomes. 

The differential mortality process for the non-disabled population is based directly on the

work of Lillard and Panis (1999).12 In order to estimate a differential mortality equation for the
13While developing the CBOLT micro-simulation capability over the last few years CBO has explicitly

avoided generating projections based on demographic assumptions that differ from OCACT, focusing rather on the

economic differences between the models. 

14The actual process in a micro-simulation is actually a little more complicated because the model operates

on a micro sample. In a simulated population sampled at less than 100%, applying expected death rates directly will

always generate too little population over long periods, because there is an asymmetry that arises when death is

assigned randomly. Basically, you can always generate more deaths when people (randomly) did not die in an

earlier year–when they should have–but you cannot bring people back to life who (randomly) died too early. Thus,

the actual CBOLT micro algorithm adjusts death rates for cumulative deaths on a cohort basis. 

10

SSA Modeling Income in the Near Term (MINT) project, Lillard and Panis (1999) used the

Panel Survey of Income Dynamics (PSID) data set that provided them with both cross-sectional

and longitudinal variation. The authors used a number of covariates that are also included in the

CBOLT model (education, marital status dummies, and earnings) but also a few that are not

(race, in particular). In addition, they went to great lengths to adjust the estimated coefficients

on the basic variables (age, sex, and calendar time) so that the PSID-based estimates generated

overall death rates that matched Vital Statistics outcomes. 

The CBOLT differential mortality module uses a subset of the coefficients from the

Lillard and Panis (1999) model because (1) only that subset of the socioeconomic independent

variables overlap, and (2) CBOLT is calibrated to match OCACT projected populations, and

thus the basic variables in the equation (age, sex, time) are not needed.13 Calibration to OCACT

implies that the overall mortality rates by age, sex, and year in any simulation are taken as given

in a CBOLT simulation–the only question is how those deaths should be distributed within the

micro sample in the group. Thus, the approach used for introducing the differential effects is to

start with the coefficients from Lillard and Panis (1999), then, during the simulation, adjust the

(implied) constant of the log-hazard equation in each age/sex/year cell for the effects of the other

independent variables such that the overall predicted death rate for that cell matches OCACT.14
15For example, although education and marital status are simple categorical variables, the CBOLT

education classes do not match Lillard and Panis (1999) exactly. Also, earnings is a continuous variable that

requires some construction. The CBOLT measure is the difference between the individual’s and the age/sex mean of

“average lifetime earnings” through the year prior to when death is being assigned, which is very similar to the

variable Lillard and Panis (1999) constructed with the PSID.

16For example, one can look at how the average lifetime earnings of a cohort changes as they age to gauge

whether or not the differentials in death rates make sense, because attrition of below average individuals will

increase the average of those remaining. In CBOLT, when differential mortality is assigned using the Lillard and

Panis (1999) coefficients, the projected within-cohort average Primary Insurance Amount (PIA)–which is based

directly on average earnings–rises systematically between the ages of 62 and 80 at roughly the same pace evident in

both history and in OCACT projections.

11

The approach taken to introducing differential mortality for the non-disabled captures the

effects of education, marital status, and earnings, but there are reasons to be cautious about

exactly how to apply the Lillard and Panis (1999) coefficients in CBOLT.15 There is some

indirect evidence that CBOLT generates the right amount of differential mortality, at least by

earnings, which is the focus of this paper.16 In any case, the approach here of using sensitivity

analysis (which involves arbitrarily raising or lowering the Lillard and Panis (1999) coefficient

on earnings) is the best way to approach this situation in which there is a good deal of

uncertainty about the size of the differential mortality effect. The principal conclusions of this

paper is that differential mortality does not seem to affect outcomes as much as other authors

have argued–a conclusion based on varying differences in death rates from negligible to highly

skewed.
17The statutory progressivity stems from the fact that, although the Social Security tax rate is equal across

earnings groups up to the taxable maximum, the formula for determining the actual benefit at retirement (through the

Primary Insurance Amount (PIA)) replaces a significantly higher fraction of earnings for low lifetime earners than it

does for high lifetime earners. CBO 2004-A shows those replacement rates differ by a factor of two between the

lowest and highest lifetime earnings quintiles. 

12

3. Differential Mortality and Social Security System Progressivity

If socioeconomic characteristics and mortality are negatively correlated Social Security

will be less progressive in practice than it is in a statutory sense.17 Several previous studies of

Social Security progressivity have been undertaken with differential mortality as one of the

considerations in the analysis, rather than the focus, as in this paper. However, those previous

studies also suggest that the other important inputs into any estimate of progressivity–the

measure of redistribution itself, the population subgroup being studied, and the characteristics

used to classify people for measuring net returns–all potentially interact with the effects of

differential mortality. Thus, in addition to focusing on the effects of differential mortality, the

analysis here presents measures of progressivity using CBOLT which vary all of these inputs. 

CBOLT Base-Case Estimates of Social Security Progressivity

The starting point for analyzing the impact of differential mortality on progressivity is the

published analysis based on the CBOLT model (see Figure 4; from CBO 2004-A). Given the

nature of official publications (showing extensive variation for a set of results is less feasible

than in an academic publications) the CBO had to make choices from the myriad of possible

measures of redistribution, possible population subgroups, and possible classifiers for organizing

the sample into the groups across which progressivity is measured. Given those choices, the

estimates published by the CBO are somewhat striking in that they seem contrary to the common
18The interesting pattern across cohorts–falling then rising net returns–is due to two competing trends. 

First, the changes in Normal Retirement Age (NRA) for the baby boom and beyond permanently lowers net returns

relative to earlier cohorts, but increasing life expectancy eventually overwhelms that effect, and net returns begin to

rise for cohorts born after the 1970s in particular. 

13

belief based on recent empirical studies that Social Security is not very progressive in practice. 

CBO reported (and it is evident in Figure 4) that Social Security generates a wide disparity in net

returns across earnings groups, and that holds for cohorts for whom significant amounts of actual

data already exist (the 1940s birth cohort in particular) as well as for cohorts for whom all of

their outcomes are projected (1990s and beyond). 

The estimates shown in Figure 4 are particularly striking because there is no immediate

reason based on the literature to suspect that the choices made to generate the estimates are

particularly biased towards finding progressivity. The measure of net returns presented is the

ratio of the present value of lifetime Social Security benefits to lifetime Social Security taxes,

discounted at a fixed real interest rate. If that present value ratio equals 100 percent, then at the

chosen discount rate the people in that group get out in present value exactly what they put in. 

Thus the estimates in Figure 1 suggest individuals in the lowest earnings quintile get back about

twice what they pay in to the system, while people in the top quintile get back only half.18 Note,

however, that the CBO choice of discount rate (3.3 percent real; chosen to match CBO’s

projected rate on Social Security Trust Fund assets) implies that the cohort average for the

present value ratio is somewhat below 100 percent (a point which is discussed further in the

sensitivity analysis below). 

One of the primary reasons for the disparity between the CBO results and conclusions

from the academic literature is that the CBOLT approach allows for a more comprehensive

concept of population subgroup. Figure 1 includes everyone in a birth cohort who survives
19The age of death cutoff chosen for inclusion in the distributional analysis is somewhat arbitrary. The

determining factor in CBOLT is the goal of comprehensively sampling the 1940s cohort. Since the CBOLT micro

sample is representative of living individuals as of 1984, the age 45 cutoff guarantees that people born in 1940 who

survive through age 45 will be statistically represented. 

14

through the age of 45.19 The most significant difference with respect to most published papers

on progressivity is the inclusion of people who receive benefits from the disability insurance

(DI) program. Those individuals generally have low lifetime and annual earnings (as described

in the last section, based on empirical patterns) but obviously get benefits at younger ages and

potentially for longer periods. There are, of course, other possible subgroups one could study,

and one would expect that differences in present value ratios would get smaller as those groups

get more homogeneous (this possibility is also explored in the sensitivity analysis below). 

The final set of decisions needed to generate Figure 1 (or any estimates of redistribution)

involve the way in which individuals in the micro sample are classified into groups. The

groupings here are by quintiles of total lifetime earnings measured on a household basis. 

Specifically, the sum of real earnings over a given person’s lifetime is the basic classifier if they

remain single in all years. If they happen to be married in a given year (CBOLT is an annual

model) then the earnings measure for that year is a function of their earnings plus their spouse’s

earnings (adjusted for economies of scale in household consumption). Thus, one of the standard

criticisms of some progressivity measures–low earning spouses who are entitled to auxiliary

benefits should be classified along with their high earning spouses, rather than as low earners–is

already addressed in the baseline CBO estimates (however, as with the other two input decisions

for the baseline, the issue of classifier is explored further below). 

Sensitivity of Progressivity Estimates Part 1: Discount Rates, Subgroups, and Classifiers
15

The choices underlying the estimates in Figure 1–discount rate used to measure net

return, population subgroup studied, and earnings classifier selected–all have possible

implications for the estimated redistribution in Social Security. More importantly, from the

perspective of this paper, there is also a potential interaction between the estimated effect of

differential mortality and each of the choices. That is, varying the rate of differential mortality

may not have much impact given a particular set of choices for the discount rate, population

subgroup, and classifier, but it might for some other choices for those three inputs. Thus, the

first step in evaluating the effect of differential mortality on progressivity is to consider the

overall sensitivity with respect to the three input choices and the possible interactions of each

with differential mortality.

The first decision analyzed is the choice of discount rate used in the net return

calculations (see Figure 5). One would expect that lowering the discount rate from the 3.3

percent real to some arbitrarily lower number (in this case, 2.0 percent real) would increase the

present value of benefits relative to the present value of taxes because taxes are paid before

benefits are received. Figure 5 shows that indeed is the case. The overall cohort present value

ratios using a 2.0 percent discount rate are slightly above 100 percent, which suggests that 2.0

percent real is a close approximation to the cohort-level internal rates of return in the model. 

Although this choice does have a big impact on the level of present-value ratios (the lowest

quintile gets back 2.5 to 3 times what they put in; the highest quintile something like 90 percent)

the effect is similar across the quintiles, so the impact on progressivity estimates is much more

modest. 

There is reason to believe that the choice of discount rate could bias the inferences about
20Liebman (2002) provides a useful discussion of the role of the discount rate in progressivity studies. 

21The smallest group–OAI worker beneficiaries–is generally the one considered in studies that use example

or representative earners, such as Garrett (1995), Steuerle and Bakija (1994), and Armour and Pitts (2004).

16

the effects of differential mortality, however, so the alternative 2.0 percent real discount rate is

used for the remaining calculations in this paper. The explanation goes like this: if one uses a

discount rate that is too high, then increasing the extent of differential mortality (the gap between

low and high earner lifespans) will not have a big impact on estimates of progressivity because

the extra years of benefits that are shifted from low to high earners are discounted by an

arbitrarily high factor.20

The second important input to consider is the choice of population subgroup (see Figure

6). One would expect that as the population subgroup becomes more homogeneous, the

estimated progressivity would fall, and that is indeed the case. The progression of groups

considered in Figure 6 is from the base case–the entire population surviving through age 45–to

that group less the DI beneficiary population, to just the subgroup who qualifies for and lives

long enough to receive Old Age Insurance (OAI) worker benefits.21 Unlike the effect of

changing the discount rate, the impact on progressivity of moving to increasingly more

homogeneous populations is very significant. The present value ratios in the bottom quintile of

lifetime earners fall by a factor of nearly two, while the ratios for the top quintile are affected

much less. This result is intuitive: more of the people in the top quintile are OAI worker

beneficiaries than in the bottom quintile, so the restriction has different effects. There is no

obvious choice of the “correct” subgroup for the analysis of differential mortality below, so the

remaining tables are all constructed to reflect outcomes across the possible choices.

The third choice made in order to develop estimates of progressivity is the classifier itself
17

(see Table 1). The base case classifier underlying the results in Figures 4 through 6 is total

lifetime earnings on a household basis, as described above. There are a number of other viable

approaches to classifying individuals, and Table 1 considers three alternatives for the four

population subgroups in the 1960s birth cohort. The first alternative, which causes the system to

look more progressive than in the base case, is individual lifetime earnings. The second and

third, which cause the system to look slightly less progressive than in the base case, are lifetime

earnings (on a household basis) through age 45 only, and potential earnings (again on a

household basis) for individuals at age 45. 

Classifying people in the sample by individual rather than household lifetime earnings

has a strong effect on progressivity long recognized in the literature. Many of the people

classified as low lifetime earners are spouses of high lifetime earners; indeed, they are able to

remain out of the labor force because they have sufficient household-level resources to do so. 

What that implies, however, is that their estimated net present value ratios will be quite high,

because they pay in very little and receive extensive auxiliary (spouse and survivor) benefits. 

The effect on progressivity of switching to the individual lifetime earnings classifier holds across

all four population subgroups considered: the entire population, the DI beneficiary population,

the non-DI beneficiary population, and the OAI worker beneficiary population. The effect is

weakest for the OAI worker beneficiaries, which makes sense because there are by definition no

spouse beneficiaries in that group (though there are OAI dual beneficiaries, who still benefit

from a spouse’s higher earnings). 

The other alternatives to the base case classifier are intended to capture two other

features of real world populations. The first uses the same lifetime earnings measure as in the
18

base case, but the summation is truncated at age 45. That is, any earnings after age 45 have no

impact on the individual’s quintile position. This specification is meant to eliminate the possible

reverse causation in the tabulations–people who die shortly after age 45 will have low earnings

based on the total lifetime measure, but there is no reason (other than differential mortality) to

suspect they will have low earnings based on the measure of earnings through age 45. The last

classifier is intended to capture the effect of labor market choices and shocks. This measure is

the “potential” household earnings for each person in the sample, defined as the earnings which

would have occurred at age 45 if the individual (and spouse if one is present) had worked fulltime and experienced no labor market shocks. 

Truncating the summation of lifetime earnings at age 45 (the third classifier in Table 1)

has relatively little impact relative to using total lifetime earnings (the second and base case

classifier) but the explanation for that varies depending on the population subgroup. The

primary reason is that lifetime earnings through age 45 are a good predictor of total lifetime

earnings for most people, and for those people who experience a shock that breaks the

connection between pre-45 and post-45 earnings, there are offsetting effects. In the total

population, a person who earns enough while young to win a spot in the highest quintile but who

then experiences a negative shock is more likely to get DI benefits but also more likely to die

younger, which are offsetting events for net returns. In the OAI worker sample, the effect of

using the lifetime earnings through age 45 classifier is even more modest, but that is because

receipt of OAI benefits is itself an additional qualifier–one has to survive through age 62 at least

to get OAI benefits, so all that is being tested is whether pre-45 lifetime earnings are a good

predictor of total lifetime earnings (which they are).
22In order to simulate micro samples of earnings in which the correlation between annual and lifetime

earnings are realistic the individual permanent differentials actually evolve slowly over the lifetime as well. See

Harris and Sabelhaus (2002).

19

Using potential household earnings at age 45 to classify people makes the estimates of

progressivity lower than under the other three groupings. This classifier is best understood after

a little background on the micro earnings process in CBOLT. Every person in the CBOLT micro

model gets a randomly assigned “earnings differential” the year they first enter the labor market. 

The earnings differential term captures the well-known observation that overall age-sex-cohorteducation earnings profiles have low explanatory power for any given individual, but adding a

highly correlated idiosyncratic error term greatly improves the fit. The differential is effectively

a percent deviation between the individual earnings and the average for the age-sex-cohorteducation group of which the individual is a member.22

Adding the earnings differential to the predicted profile average is the first step towards

solving for actual earnings in CBOLT. The earnings differential interacted with the age-sexcohort-education group average represents what the individual would earn if they worked full

time, experienced no unemployment, and experienced no other random “transitory” shocks to

earnings. That concept is exactly what the potential earnings classifier means–what the

individual would earn working full-time with no shocks. It is measured on a household basis

because the same calculation is carried out for the individual’s spouse (but when the individual is

45, not when the spouse is 45) and the sum is (as with the second and third classifiers) adjusted

for economies of scale in consumption. 

Using potential household earnings at age 45 lowers estimated progressivity relative to

the base case classifier, but by no means eliminates Social Security redistribution. For the entire
20

population, the present value ratio in the bottom quintile falls significantly relative to the other

classifiers, which makes sense because the potential earnings of some low earners (non-working

spouses in particular) are much higher than actual earnings. However, the effect is much more

modest for the other population subgroups. In particular, under the potential earnings classifier,

the present value ratios for the bottom quintile remain about one and a half times the ratio in the

top quintile. Thus, using the base assumptions about differential mortality, CBOLT shows

significant progressivity even for the most narrow subgroup (OAI worker beneficiaries) using

the broadest classifier considered (potential household income at age 45). 

Sensitivity of Progressivity Estimates Part 2: Differential Mortality

The analysis of Social Security redistribution in the last section shows that a wide range

of progressivity estimates can be derived depending on how one specifies the measure of

redistribution, the population subgroup being studied, and the classifier used to divide the

population into quintiles. But the key question of this paper is how differential mortality affects

those estimates. In this section, the rate of (non-DI) differential mortality is systematically

varied in order to answer that question. The key insight from these experiments is that

introducing arbitrarily large disparities in death rates by earnings does not fundamentally change

the estimates of progressivity, and thus differential mortality itself has only a modest impact on

the gap between statutory and actual redistribution. 

The method by which differentials in death rates are systematically altered for these

experiments is to operate directly on the coefficients in the Lillard and Panis (1999) mortality

equation. The range considered here is from no differential mortality (all coefficients set to zero)
21

to a tripling of the coefficient on earnings in the mortality equation. The result of varying the

coefficients is to generate varying degrees of differentials in death rates (see Figure 7). If there

is no differential mortality, the relative mortality rates by earnings quintile are all one. The base

case differentials (the darkest bars in Figure 7) indicate that individuals in the lowest quintile

have 1.4 times the average death rate within an age-sex group, while people in the highest

quintile have a death rate of 0.8 times the average. Figure 7 shows that the extreme case

considered–a tripling of the coefficient on earnings in the differential mortality

equation–generates a range for relative mortality of 2.7 for the lowest quintile to 0.4 for the

highest quintile. In short, controlling for age and sex, people in the lowest earnings quintile are

something like seven times more likely to die than people in the highest earnings quintile.

Systematically varying the amount of differential mortality has only a modest impact on

estimates of progressivity (see Table 2). The estimates here are (as in Table 1) for the 1960s

cohort and use the “household lifetime earnings through age 45" classifier to divide the various

populations into quintiles. The estimates show (again, as in Table 1) that population subgroup

has a first-order impact on estimated progressivity. However, within any given population

group, the effect of varying the assumption about differential mortality is in the right direction

(more differential in death rates lowers the gap between present value ratios across quintiles) but

the effect is second-order.
22

4. Differential Mortality and Social Security System Finances

The second major research issue pursued in this study is whether socioeconomic

differentials in death rates have a significant impact on Social Security system finances. The

question of how differential mortality affects system finances is largely independent of the

analysis of redistribution in the last section, because conclusions about progressivity depend to

some extent on the other inputs to the calculations (measure of redistribution, population

subgroup, and classifier). However, the method used to investigate the connection

(systematically varying the socioeconomic differential and re-solving the model) is also useful

for investigating the relationship between differential mortality and summary measures of the

Social Security financing imbalance. The conclusion about system finances turns out to be very

similar to the inferences about progressivity. Relative to other determinants of system finances,

differential mortality has a fairly modest impact on projections of Social Security’s financial

imbalance. 

There are a number of different ways to measure the gap between Social Security

revenues and outlays. The first major decision that goes into choosing a summary measure is

whether to focus on present-value measures that summarize an entire stream of inflows and

outflows over some time period or to use a snapshot of the gap between revenues and outlays at

some point in time. Given the choice of present value or single-year gap measure, one must also

specify the time period to be considered in the calculations. The second major decision is how to

normalize the chosen measure, in particular, whether to divide by Social Security taxable payroll

(the preferred OCACT measure) or overall GDP (which CBO uses in its published tables). 

The measures of system finances using base-case differential mortality in CBOLT
23

suggest the Social Security system is probably insolvent in the long run (see Table 3). The

measures shown include the 75 year present value imbalance as a percent of taxable payroll,

the100 year present value imbalance as a percent of GDP, and the gap between revenues and

outlays as a percent of GDP in 2050 and 2100. The base-case differential mortality runs (second

row of each panel in Table 3, consistent with CBO 2004-A) imply a funding gap of 1.05 percent

of taxable payroll overall the 75 year horizon, and a present value gap of 0.57 percent of GDP

over a 100 year horizon. On an annual flow basis, the expected gap between revenues and

outlays is 1.39 percent of GDP in 2050, rising to 2.11 percent of GDP by 2100.

The direction of the effect on system finances from varying differential mortality is

exactly what one would expect. Holding overall death rates by age and sex constant in the

simulations, moving from a situation where relative death rates are constant across earnings

groups (no differential mortality) to cases where the socioeconomic differential is arbitrarily

large will make the Social Security system more expensive. If higher income beneficiaries are

more likely to survive, average benefits paid in each year will be higher. 

It is interesting to observe how insensitive those estimates actually are to varying the

mortality differential, however. The rows of Table 3 vary non-DI differential mortality from

none to triple the Lillard and Panis (1999) estimate. The dramatic differences in rates of

differential mortality (Figure 7) lead to fairly modest changes in the estimates of system financial

imbalance, on the order of the sensitivity analysis for several inputs to the projections (SSA,

2004). For example, the range for the 75 year actuarial balance (OCACT’s preferred measure of

financial imbalance) range from .83 percent of payroll if differential mortality is turned off to

1.39 percent of payroll when the model uses triple the Lillard and Panis (1999) coefficient.
24

5. Conclusion

The analysis here suggests that the oft-stated arguments about differential mortality and

Social Security are somewhat overstated. The general belief is that Social Security is not nearly

as progressive in practice–some would argue not progressive at all—as it appears if one simply

considers the statutory tax and benefit formulas. The argument is that socioeconomic differences

in mortality work counter to progressivity because lower lifetime earners are more likely to die

younger and therefore receive benefits for fewer years. A possible corollary to the argument is

that socioeconomic differentials also affect Social Security system finances, because if the

higher earners survive longer, average benefits paid out are larger than if life expectancies are

equal across the earnings distribution. 

Although the arguments about how differential mortality affects progressivity and Social

Security finances are true, the effects appear modest at best. The estimates of progressivity are

clearly affected much more by the choices made to estimate redistribution: the parameters used

to calculate net returns, the population subgroup being studied, and the classifier used to divide

the population into quintile groups. Holding those constant, the effect of differential mortality is

not very strong. Similarly, the impact on system finances seem modest, especially when one

considers how other inputs to the projections affect summary measures of the Social Security

financial shortfall. Together, these observations imply that arguments for changing Social

Security because either (1) differential mortality reverses the intended redistribution anyway or

(2) we should establish (or re-establish) real progressivity are both somewhat overblown. Social

Security as currently configured does redistribute income from lifetime high-earners to lifetime

low-earners. 
25

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Figure 1

Sources of Differential Mortality in CBOLT

Status Beginning Period t Status End P

of Period t Shocks and Decisions1 of Period t Mortalit

Marital Status Marital Transition Marital Status Non

Beginning of Period t During Period t End of Period t

E

Labor Force Participation Ma

During Period t Average L

Average Lifetime Earnings Average Lifetime Earnings

Beginning of Period t End of Period t

Earnings During Earnings DuringPeriod t-1 Period t

Earnings Shock D

During Period t

Disability Status Disability Status Disab

Beginning of Period t End of Period t

Disability Shock

During Period t

1 In addition to the effects of the indicated inputs, all shocks and decisions are a function of age, sex, and education.
Figure 2. Historical Disability Insurance Incidence by Earnings Decile and Sex in the 

(Average 1984 to 2002, Ages 20 to 64)

02468

101214161820

1 2 3 4 5 6 7 8 

Earnings Decile

Percent of New DI Claimants

Females Males
Figure 3. Social Security Administration Projected Death Rates

Disability-Insured (DI) Worker Beneficiaries by Duration 

(Ages 30 to 54)

0123456789

10

0 1 2 3 4 5 6 7 8 

Duration on Disability Insurance Program

Percent of DI Beneficiaries

Females Males
Figure 4. Projected Lifetime Benefit to Tax Ratios By Earnings and C

(Total Population Surviving to Age 45, Classified by Household Lifetime Earnings, Discount Rate 

0

50

100150200250300

1940 1950 1960 1970 1980 1990 

Birth Cohort

Pecent Ratio

Lowest Qu

High

Overall Cohort Average
Figure 5. Effect of Discount Rate on Projected Lifetime Benefit to Tax 

(Total Population Surviving to Age 45, Classified by Household Lifetime Earnings)

0

50

100150200250300

1940 1950 1960 1970 1980 1990 

Birth Cohort

Pecent Ratio

Lowest Quin

Lowest Quintile, r = 2.0%

Highest Quintile, r = 3.5%

Highest Quintile, r = 2.0%

Overall Cohort Average, r 
Figure 6. Effect of Population Subgroup on Benefit to Tax Ratio

(Various Populations Surviving to Age 45, Classified by Household Lifetime Earnings, Discount Rat

0

50

100150200250300

1940 1950 1960 1970 1980 1990 

Birth Cohort

Pecent Ratio

Lowest Quintile, All

Lowest Quintile, N

Low

Highest Quintile, All

Highest Quintile, Non-DI

Highest Quintile, OAI
Table 1. Effect of Classifier on Projected Lifetime Benefit to Tax Ratios

(1960s Cohort, Total Population Surviving to Age 45, Discount Rate = 2.0%)

Percent Ratio of Lifetime Benefits to Lifetime Taxes Paid

Lowest Second Middle Fourth Highest Coh

Quintile Quintile Quintile Quintile Quintile Ove

Entire Population, Classified by: Total Lifetime Individual Earnings 361% 170% 118% 96% 70% 108 Total Lifetime Household Earnings 214 132 114 102 85 10 Total Household Earnings Through Age 45 182 137 113 100 87 10 Potential Household Earnings at Age 45 165 128 114 100 86 10Disability Beneficiary Population, Classified by: Total Lifetime Individual Earnings 462 227 161 129 98 17 Total Lifetime Household Earnings 317 189 161 147 136 17 Total Household Earnings Through Age 45 315 213 172 153 141 17 Potential Household Earnings at Age 45 249 200 179 158 144 17Non-Disability Population, Classified by: Total Lifetime Individual Earnings 305 148 107 89 68 9 Total Lifetime Household Earnings 154 111 102 94 80 9 Total Household Earnings Through Age 45 147 115 99 91 80 9 Potential Household Earnings at Age 45 139 110 101 89 78 9Old Age Beneficiary Population, Classified by: Total Lifetime Individual Earnings 177 132 107 92 70 9 Total Lifetime Household Earnings 134 109 99 91 77 9 Total Household Earnings Through Age 45 130 109 96 88 77 9 Potential Household Earnings at Age 45 125 105 96 86 76 9
Figure 7. CBOLT Projected Relative Mortality Rates

(Mortality by Quintile Divided by Overall Mortality for Age/Sex Group)

(Males, 30 to 64, 2005 to 2110)

0.0000.5001.0001.5002.0002.5003.000

Lowest Second Middle Fourth 

Average Lifetime Earnings Quintile

Relative Mortality Rate

Base Differential Mortality Double Differential Mortality Triple Differential Mortali

Differential 
Table 2. Effect of Differential Mortality Assumption on Projected Lifetime Benefit to Tax Rati

(1960s Cohort, Classified by Total Household Earnings Through Age 45, Discount Rate = 2.0

Percent Ratio of Lifetime Benefits to Lifetime Taxes 

Lowest Second Middle Fourth Highest 

Quintile Quintile Quintile Quintile Quintile 

Entire Population, Differential Mortality: Non-DI Differential Mortality Turned Off 184% 138% 113% 98% 83%  Base Case Differential Mortality 182 137 113 100 87  Non-DI Differential Mortality Doubled 178 136 114 102 91  Non-DI Differential Mortality Tripled 179 135 114 104 95 Disability Beneficiary Population, Differential Mortality: Non-DI Differential Mortality Turned Off 320 215 173 152 138  Base Case Differential Mortality 315 213 172 153 141  Non-DI Differential Mortality Doubled 311 211 171 154 144  Non-DI Differential Mortality Tripled 309 208 171 153 149 Non-Disability Population, Differential Mortality: Non-DI Differential Mortality Turned Off 150 116 98 88 76  Base Case Differential Mortality 147 115 99 91 80  Non-DI Differential Mortality Doubled 143 114 100 93 84  Non-DI Differential Mortality Tripled 144 114 101 95 87 Old Age Beneficiary Population, Differential Mortality: Non-DI Differential Mortality Turned Off 131 110 95 85 73  Base Case Differential Mortality 130 109 96 88 77  Non-DI Differential Mortality Doubled 128 108 96 89 80  Non-DI Differential Mortality Tripled 127 107 95 90 83 
Table 3. Effect of Differential Mortality on Social Security System Finances

Measures of OASDI Financial Status

Present Value Measures

75 Year Gap As A 100 Year Gap As A

Percent of Payroll Percent of GDP

Differential Mortality Assumption

Non-DI Differential Mortality Turned Off -0.83 -0.48

Base Case Differential Mortality -1.05 -0.57

Non-DI Differential Mortality Doubled -1.21 -0.63

Non-DI Differential Mortality Tripled -1.39 -0.70

Gap Between Revenues and Outlays

(Percent of GDP)

2050 2100

Differential Mortality Assumption

Non-DI Differential Mortality Turned Off -1.28 -2.00

Base Case Differential Mortality -1.39 -2.11

Non-DI Differential Mortality Doubled -1.48 -2.22

Non-DI Differential Mortality Tripled -1.56 -2.31