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Federal Reserve Bank of Chicago

The Effects of Health Insurance and
Self-Insurance on Retirement Behavior
Eric French and John Bailey Jones

REVISED
November 2, 2010
WP 2001-19

The Effects of Health Insurance and
Self-Insurance on Retirement Behavior
Eric French

John Bailey Jones∗

Federal Reserve Bank of Chicago

University at Albany, SUNY

November 2, 2010

Abstract
This paper provides an empirical analysis of the effects of employer-provided health
insurance, Medicare, and Social Security on retirement behavior. Using data from the
Health and Retirement Study, we estimate a dynamic programming model of retirement
that accounts for both saving and uncertain medical expenses. Our results suggest that
Medicare is important for understanding retirement behavior, and that uncertainty and
saving are both important for understanding the labor supply responses to Medicare.
Half the value placed by a typical worker on his employer-provided health insurance is
the value of reduced medical expense risk. Raising the Medicare eligibility age from 65
to 67 leads individuals to work an additional 0.074 years over ages 60-69. In comparison,
eliminating two years worth of Social Security benefits increases years of work by 0.076
years.

∗
Comments welcome at efrench@frbchi.org and jbjones@albany.edu. We thank Joe Altonji, Peter
Arcidiacono, Gadi Barlevy, David Blau, John Bound, Chris Carroll, Mariacristina De Nardi, Tim Erikson,
Hanming Fang, Donna Gilleskie, Lars Hansen, John Kennan, Spencer Krane, Hamp Lankford, Guy Laroque,
John Rust, Dan Sullivan, Chris Taber, the editors and referees, students of Econ 751 at Wisconsin, and
participants at numerous seminars for helpful comments. We received advice on the HRS pension data from
Gary Englehardt and Tom Steinmeier, and excellent research assistance from Kate Anderson, Olesya Baker,
Diwakar Choubey, Phil Doctor, Ken Housinger, Kirti Kamboj, Tina Lam, Kenley Peltzer, and Santadarshan
Sadhu. The research reported herein was supported by the Center for Retirement Research at Boston College
(CRR) and the Michigan Retirement Research Center (MRRC) pursuant to grants from the U.S. Social
Security Administration (SSA) funded as part of the Retirement Research Consortium. The opinions and
conclusions are solely those of the authors, and should not be construed as representing the opinions or policy
of the SSA or any agency of the Federal Government, the CRR, the MRRC, or the Federal Reserve System.
Recent versions of the paper can be obtained at http://www.albany.edu/~jbjones/papers.htm.

Introduction
One of the largest social programs for the rapidly growing elderly population is Medicare.

In 2008, Medicare had 44.1 million beneficiaries and $481 billion of expenditures, making it
only slightly smaller than Social Security.1
Prior to receiving Medicare at age 65, many individuals receive health insurance only if
they continue to work. This work incentive disappears at age 65, when Medicare provides
health insurance to almost everyone. An important question, therefore, is whether Medicare
significantly affects the labor supply of the elderly. This question is crucial when considering
Medicare reforms; the fiscal effects of such reforms depend on how labor supply responds.
However, there is relatively little research on the labor supply responses to Medicare.
This paper provides an empirical analysis of the effect of employer-provided health insurance and Medicare in determining retirement behavior. Using data from the Health and
Retirement Study, we estimate a dynamic programming model of retirement that accounts
for both saving and uncertain medical expenses. Our results suggest that Medicare is important for understanding retirement behavior, because it insures against medical expense
shocks that can exhaust a household’s savings.
Our work builds upon, and in part reconciles, several earlier studies. Assuming that individuals value health insurance at the cost paid by employers, Lumsdaine et al. (1994) and
Gustman and Steinmeier (1994) find that health insurance has a small effect on retirement
behavior. One possible reason for their results is that they find that the average employer contribution to health insurance is modest, and declines by only a small amount after age 65. If
workers are risk-averse, however, and if health insurance allows them to smooth consumption
when facing volatile medical expenses, they could value employer-provided health insurance
well beyond the cost paid by employers. Medicare’s age-65 work disincentive thus comes not
only from the reduction in average medical costs paid by those without employer-provided
health insurance, but also from the reduction in the volatility of those costs.
1

Figures taken from 2009 Medicare Annual Report (The Boards of Trustees of the Hospital Insurance and
Supplementary Medical Insurance Trust Funds, 2009).

Addressing this point, Rust and Phelan (1997) and Blau and Gilleskie (2006, 2008) estimate dynamic programming models that account explicitly for risk aversion and uncertainty
about out-of-pocket medical expenses. Their estimated labor supply responses to health insurance are larger than those found in studies that omit medical expense risk. Rust and
Phelan and Blau and Gilleskie, however, assume that an individual’s consumption equals his
income net of out-of-pocket medical expenses. In other words, they ignore an individual’s
ability to smooth consumption through saving. If individuals can self-insure against medical
expense shocks by saving, prohibiting saving will overstate the consumption volatility caused
by medical cost volatility. It is therefore likely that Rust and Phelan and Blau and Gilleskie
overstate the value of health insurance, and thus the effect of health insurance on retirement.
In this paper we construct a life-cycle model of labor supply that not only accounts for
medical expense uncertainty and health insurance, but also has a saving decision. Moreover,
we include the coverage provided by means-tested social insurance to account for the fact
that Medicaid provides a substitute for other forms of health insurance. To our knowledge,
ours is the first study of its kind. While van der Klaauw and Wolpin (2008) and Casanova
(2010) also estimate retirement models that account for both savings and uncertain medical
expenses, they do not focus on the role of health insurance, and thus use much simpler models
of medical expenses.
Almost everyone becomes eligible for Medicare at age 65. However, the Social Security
system and pensions also provide retirement incentives at age 65. This makes it difficult to
determine whether the high job exit rates observed at age 65 are due to Medicare, Social
Security, or pensions. One way we address this problem is to exploit variation in employerprovided health insurance. Some individuals receive employer-provided health insurance only
while they work, so that their coverage is tied to their job. Other individuals have retiree
coverage, and receive employer-provided health insurance even if they retire. If workers value
access to health insurance, those with retiree coverage should be more willing to retire before
age 65. Our data show that individuals with retiree coverage tend to retire about a half year
earlier than individuals with tied coverage. This suggests that employer-provided health
3

insurance is a determinant of retirement.
One problem with using employer-provided health insurance to identify Medicare’s effect
on retirement is that individuals may choose to work for a firm because of its post-retirement
benefits. The fact that early retirement is common for individuals with retiree coverage may
not reflect the effect of health insurance on retirement. Instead, individuals with preferences
for early retirement may be self-selecting into jobs that provide retiree coverage. To address
this issue, we measure self-selection into jobs with different health insurance plans. We
allow the value of leisure and the time discount factor to vary across individuals. Modelling
preference heterogeneity with the approach used by Keane and Wolpin (1997), we find that
individuals with strong preferences for leisure are more likely to work for firms that provide
retiree health insurance. However, self-selection does not affect our main results.
Estimating the model by the Method of Simulated Moments, we find that the model fits
the data well with reasonable parameter values. Next, we simulate the labor supply response
to changing some of the Medicare and Social Security retirement program rules. Raising the
Medicare eligibility age from 65 to 67 would increase years worked by 0.074 years. Eliminating
two years worth of Social Security benefits would increase years worked by 0.076 years. Thus,
even after allowing for both saving and self-selection into health insurance plans, the effect
of Medicare on labor supply is as large as the effect of Social Security. One reason why we
find that Medicare is important is that we find that medical expense risk is important. Even
when we allow individuals to save, they value the consumption smoothing benefits of health
insurance. We find that about half the value a typical worker places on his employer-provided
health insurance comes from these benefits.
The rest of paper proceeds as follows. Section 2 develops our dynamic programming model
of retirement behavior. Section 3 describes how we estimate the model using the Method of
Simulated Moments. Section 4 describes the HRS data that we use in our analysis. Section 5
presents life cycle profiles drawn from these data. Section 6 contains preference parameter
estimates for the structural model, and an assessment of the model’s performance, both within
and outside of the estimation sample. In Section 7, we conduct several policy experiments.
4

In Section 8 we consider a few robustness checks. Section 9 concludes.

The Model
In order to capture the richness of retirement incentives, our model is very complex and

has many parameters. Appendix A provides definitions for all the variables used in the main
text.

2.1

Preferences and Demographics

Consider a household head seeking to maximize his expected discounted (where the subjective discount factor is β) lifetime utility at age t, t = 59, 60, ..., 95. Each period that
he lives, the individual derives utility from consumption, Ct , and hours of leisure, Lt . The
within-period utility function is of the form

U (Ct , Lt ) =

1−ν
1
Ctγ L1−γ
.
t
1−ν

(1)

We allow both β and γ to vary across individuals. Individuals with higher values of β are
more patient, while individuals with higher values of γ place less weight on leisure.
The quantity of leisure is

Lt = L − Nt − φP t Pt − φRE REt − φH Ht ,

(2)

where L is the individual’s total annual time endowment. Participation in the labor force
is denoted by Pt , a 0-1 indicator equal to one when hours worked, Nt , are positive. The
fixed cost of work, φP t , is treated as a loss of leisure. Including fixed costs helps us capture
the empirical regularity that annual hours of work are clustered around 2000 hours and 0
hours (Cogan, 1981). Following a number of studies,2 we allow preferences for leisure, in
our case the value of φP t , to increase linearly with age. Workers that leave the labor force
2
Examples include Rust and Phelan (1997), Blau and Gilleskie (2006, 2008), Gustman and Steinmeier
(2005), Rust et al. (2003), and van der Klaauw and Wolpin (2008).

can re-enter; re-entry is denoted by the 0-1 indicator REt = 1{Pt = 1 and Pt−1 = 0}, and
individuals re-entering the labor market incur the cost φRE . The quantity of leisure also
depends on an individual’s health status through the 0-1 indicator Ht = 1{healtht = bad},
which equals one when his health is bad.
Workers alive at age t survive to age t + 1 with probability st+1 . Following De Nardi
(2004), workers that die value bequests of assets, At , according to the function b(At ):

b(At ) = θB

(1−ν)γ
At + κ
.
1−ν

(3)

The survival probability st , along with the transition probabilities for the health variable
Ht , depend on age and previous health status.

2.2

Budget Constraints

The individual holds three forms of wealth: assets (including housing); pensions; and
Social Security. He has several sources of income: asset income, rAt , where r denotes the
constant pre-tax interest rate; labor income, Wt Nt , where Wt denotes wages; spousal income,
yst ; pension benefits, pbt ; Social Security benefits, sst ; and government transfers, trt . The
asset accumulation equation is

At+1 = At + Yt + sst + trt − Mt − Ct .

(4)

Mt denotes medical expenses. Post-tax income, Yt = Y (rAt + Wt Nt + yst + pbt , τ ), is a
function of taxable income and the vector τ , described in Appendix B, that captures the tax
structure.
Individuals face the borrowing constraint

At + Yt + sst + trt − Ct ≥ 0.

(5)

Because it is illegal to borrow against future Social Security benefits and difficult to borrow

against many forms of future pension benefits, individuals with low non-pension, non-Social
Security wealth may not be able to finance their retirement before their Social Security
benefits become available at age 62 (Kahn, 1988; Rust and Phelan, 1997; Gustman and
Steinmeier, 2005).3
Following Hubbard et al. (1994, 1995), government transfers provide a consumption floor:

trt = max{0, Cmin − (At + Yt + sst )}.

(6)

Equation (6) implies that government transfers bridge the gap between an individual’s “liquid
resources” (the quantity in the inner parentheses) and the consumption floor. Treating Cmin
as a sustenance level, we further require that Ct ≥ Cmin . Our treatment of government
transfers implies that individuals will always consume at least Cmin , even if their out-ofpocket medical expenses exceed their financial resources.

2.3

Medical Expenses, Health Insurance, and Medicare

We define Mt as the sum of all out-of-pocket medical expenses, including insurance premia and expenses covered by the consumption floor. We assume that an individual’s medical
expenses depend upon five components. First, medical expenses depend on the individual’s
employer-provided health insurance, It . Second, they depend on whether the person is working, Pt , because workers who leave their job often pay a larger fraction of their insurance
premiums. Third, they depend on the individual’s self-reported health status, Ht . Fourth,
medical expenses depend on age. At age 65, individuals become eligible for Medicare, which
is a close substitute for employer-provided coverage.4 Offsetting this, as people age their
health declines (in a way not captured by Ht ), raising medical expenses. Finally, medical
3
We assume time-t medical expenses are realized after time-t labor decisions have been made. We view
this as preferable to the alternative assumption that the time-t medical expense shocks are fully known
when workers decide whether to hold on to their employer-provided health insurance. Given the borrowing
constraint and timing of medical expenses, an individual with extremely high medical expenses this year could
have negative net worth next year. Because many people in our data have unresolved medical expenses,
medical expense debt seems reasonable.
4
Individuals who have paid into the Medicare system for at least 10 years become eligible at age 65. A
more detailed description of the Medicare eligibility rules is available at http://www.medicare.gov/.

expenses depend on the person-specific component ψt , yielding:

ln Mt = m(Ht , It , t, Pt ) + σ(Ht , It , t, Pt ) × ψt .

(7)

Note that health insurance affects both the expectation of medical expenses, through m(.)
and the variance, through σ(.)
Even after controlling for health status, French and Jones (2004a) find that medical
expenses are very volatile and persistent. Thus we model the person-specific component of
medical expenses, ψt , as

ψt = ζt + ξt ,

ξt ∼ N (0, σξ2 ),

ζt = ρm ζt−1 + ǫt ,

ǫt ∼ N (0, σǫ2 ),

(8)
(9)

where ξt and ǫt are serially and mutually independent. ξt is the transitory component, while
ζt is the persistent component, with autocorrelation ρm .
We assume that medical expenditures are exogenous. It is not clear ex ante whether this
causes us to understate or overstate the importance of health insurance. On the one hand,
individuals with health insurance receive better care. Our model does not capture this benefit,
and in this respect understates the value of health insurance. Conversely, treating medical
expenses as exogenous ignores the ability of workers to offset medical shocks by adjusting
their expenditures on medical care. This leads us to overstate the consumption risk facing
uninsured workers, and thus the value of health insurance. Evidence from other structural
analyses suggests that our assumption of exogeneity leads us to overstate the effect of health
insurance on retirement.5
5
To our knowledge, Blau and Gilleskie (2008) is the only estimated, structural retirement study to have
endogenous medical expenditures. Although Blau and Gilleskie (2008) do not discuss how their results would
change if medical expenses were treated as exogenous, they find that even with several mechanisms (such as
prescription drug benefits) omitted, health insurance has “a modest impact on employment behavior among
older males”. De Nardi, French and Jones (2010) study the saving behavior of retirees. They find that the
effects of reducing means-tested social insurance are smaller when medical care is endogenous, rather than
exogenous. They also find, however, that even when medical expenditures are a choice variable, they are a
major reason why the elderly save.

Differences in labor supply behavior across health insurance categories are an integral
part of identifying our model. We assume that there are three mutually exclusive categories
of health insurance coverage. The first is retiree coverage, where workers keep their health
insurance even after leaving their jobs. The second category is tied health insurance, where
workers receive employer-provided coverage as long as they continue to work. If a worker
with tied health insurance leaves his job, he can keep his health insurance coverage for that
year. This is meant to proxy for the fact that most firms must provide “COBRA” health
insurance to workers after they leave their job. After one year of tied coverage and not
working, the individual’s insurance ceases.6 The third category consists of individuals whose
potential employers provide no health insurance at all, or none. Workers move between these
insurance categories according to

2.4




retiree if



It =
tied
if




 none
if

It−1 = retiree
It−1 = tied

and Nt−1 > 0

It−1 = none or

(It−1 = tied

(10)

and Nt−1 = 0)

Wages and Spousal Income

We assume that the logarithm of wages at time t, ln Wt , is a function of health status
(Ht ), age (t), hours worked (Nt ) and an autoregressive component, ωt :

ln Wt = W (Ht , t) + α ln Nt + ωt .

(11)

The inclusion of hours, Nt , in the wage determination equation captures the empirical regularity that, all else equal, part-time workers earn relatively lower wages than full
time workers. The autoregressive component ωt has the correlation coefficient ρW and the
6

Although there is some variability across states as to how long individuals are eligible for employer-provided
health insurance coverage, by Federal law most individuals are covered for 18 months (Gruber and Madrian,
1995). Given a model period of one year, we approximate the 18-month period as one year. We do not model
the option to take up COBRA, assuming that the take-up rate is 100%. Although the actual take-up rate
is around 32 (Gruber and Madrian, 1996), we simulated the model assuming that the rate was 0%, so that
individuals transitioned from tied to none as soon as they stopped working, and found very similar labor
supply patterns. Thus assuming a 100% take-up rate does not seem to drive our results.

normally-distributed innovation ηt :

ωt = ρW ωt−1 + ηt ,

ηt ∼ N (0, ση2 ).

(12)

Because spousal income can serve as insurance against medical shocks, we include it in
the model. In the interest of computational simplicity, we assume that spousal income is a
deterministic function of an individual’s age and health status:

yst = ys(Ht , t).

2.5

(13)

Social Security and Pensions

Because pensions and Social Security generate potentially important retirement incentives, we model the two programs in detail.
Individuals receive no Social Security benefits until they apply. Individuals can first
apply for benefits at age 62. Upon applying the individual receives benefits until death.
The individual’s Social Security benefits depend on his Average Indexed Monthly Earnings
(AIM E), which is roughly his average income during his 35 highest earnings years in the
labor market.
The Social Security System provides three major retirement incentives.7 First, while
income earned by workers with less than 35 years of earnings automatically increases their
AIM E, income earned by workers with more than 35 years of earnings increases their AIM E
only if it exceeds earnings in some previous year of work. Because Social Security benefits
increase in AIM E, this causes work incentives to drop after 35 years in the labor market.
We describe the computation of AIM E in more detail in Appendix D.
Second, the age at which the individual applies for Social Security affects the level of
benefits. For every year before age 65 the individual applies for benefits, benefits are reduced
7

A description of the Social Security rules can be found in recent editions of the Green Book (Committee
on Ways and Means). Some of the rules, such as the benefit adjustment formula, depend on an individual’s
year of birth. Because we fit our model to a group of individuals that on average were born in 1933, we use
the benefit formula for that birth year.

by 6.67% of the age-65 level. This is roughly actuarially fair. But for every year after age 65
that benefit application is delayed, benefits rise by 5.5% up until age 70. This is less than
actuarially fair, and encourages people to apply for benefits by age 65.
Third, the Social Security Earnings Test taxes labor income of beneficiaries at a high rate.
For individuals aged 62-64, each dollar of labor income above the “test” threshold of $9,120
leads to a 1/2 dollar decrease in Social Security benefits, until all benefits have been taxed
away. For individuals aged 65-69 before 2000, each dollar of labor income above a threshold
of $14,500 leads to a 1/3 dollar decrease in Social Security benefits, until all benefits have
been taxed away. Although benefits taxed away by the earnings test are credited to future
benefits, after age 64 the crediting rate is less than actuarially fair, so that the Social Security
Earnings Test effectively taxes the labor income of beneficiaries aged 65-69.8 When combined
with the aforementioned incentives to draw Social Security benefits by age 65, the Earnings
Test discourages work after age 65. In 2000, the Social Security Earnings Test was abolished
for those 65 and older. Because those born in 1933 (the average birth year in our sample)
turned 67 in 2000, we assume that the earnings test was repealed at age 67. These incentives
are incorporated in the calculation of sst , which is defined to be net of the earnings test.
Pension benefits, pbt , are a function of the worker’s age and pension wealth. Pension
wealth (the present value of pension benefits) in turn depends on pension accruals. We
assume that pension accruals are a function of a worker’s age, labor income, and health
insurance type, using a formula estimated from confidential HRS pension data. The data
show that pension accrual rates differ greatly across health insurance categories; accounting
for these differences is essential in isolating the effects of employer-provided health insurance.
When finding an individual’s decision rules, we assume further that the individual’s existing
pension wealth is a function of his Social Security wealth, age, and health insurance type.
Details of our pension model are described in Section 4.3 and Appendix C.
8
The credit rates are based on the benefit adjustment formula. If a year’s worth of benefits are taxed away
between ages 62 and 64, benefits in the future are increased by 6.67%. If a year’s worth of benefits are taxed
away between ages 65 and 66, benefits in the future are increased by 5.5%.

2.6

Recursive Formulation

In addition to choosing hours and consumption, eligible individuals decide whether to
apply for Social Security benefits; let the indicator variable Bt ∈ {0, 1} equal one if an
individual has applied. In recursive form, the individual’s problem can be written as

Vt (Xt ) = max

Ct ,Nt ,Bt

(

1−ν
1
γ
1−γ
Ct (L − Nt − φP t Pt − φRE REt − φH Ht )
+ β(1 − st+1 )b(At+1 )
1−ν
)
Z
+ βst+1 Vt+1 (Xt+1 )dF (Xt+1 |Xt , t, Ct , Nt , Bt ) ,
(14)

subject to equations (5) and (6). The vector Xt = (At , Bt−1 , Ht , AIM Et , It , Pt−1 , ωt , ζt−1 )
contains the individual’s state variables, while the function F (·|·) gives the conditional distribution of these state variables, using equations (4) and (7) - (13).9 The solution to the
individual’s problem consists of the consumption rules, work rules, and benefit application
rules that solve equation (14). These decision rules are found numerically using value function
iteration. Appendix E describes our numerical methodology.

Estimation
To estimate the model, we adopt a two-step strategy, similar to the one used by Gourinchas

and Parker (2002) and French (2005). In the first step we estimate or calibrate parameters
that can be cleanly identified identified without explicitly using our model. For example,
we estimate mortality rates and health transitions straight from demographic data. In the
second step, we estimate the preference parameters of the model, as well as the consumption
floor, using the method of simulated moments (MSM).
9

Spousal income and pension benefits (see Appendix C) depend only on the other state variables and are
thus not state variables themselves.

3.1

Moment Conditions

The objective of MSM estimation is to find the preference vector that yields simulated
life-cycle decision profiles that “best match” (as measured by a GMM criterion function) the
profiles from the data. The moment conditions that comprise our estimator are:
1. Because an individual’s ability to self-insure against medical expense shocks depends
upon his asset level, we match 1/3rd and 2/3rd asset quantiles by age. We match these
quantiles in each of T periods (ages), for a total of 2T moment conditions.
2. We match job exit rates by age for each health insurance category. With three health
insurance categories (none, retiree and tied), this generates 3T moment conditions.
3. Because the value a worker places on employer-provided health insurance may depend
on his wealth, we match labor force participation conditional on the combination of
asset quantile and health insurance status. With 2 quantiles (generating 3 quantileconditional means) and 3 health insurance types, this generates 9T moment conditions.
4. To help identify preference heterogeneity, we utilize a series of questions in the HRS
that ask workers about their preferences for work. We combine the answers to these
questions into a time-invariant index, pref ∈ {high, low, out}, which is described in
greater detail in Section 4.4. Matching participation conditional on each value of this
index generates another 3T moment conditions.
5. Finally, we match hours of work and participation conditional on our binary health
indicator. This generates 4T moment conditions.
Combined, the five preceding items result in 21T moment conditions. Appendix F provides a detailed description of the moment conditions, the mechanics of our MSM estimator,
the asymptotic distribution of our parameter estimates, and our choice of weighting matrix.

3.2

Initial Conditions and Preference Heterogeneity

A key part of our estimation strategy is to compare the behavior of individuals with
different forms of employer-provided health insurance. If access to health insurance is an
important factor in the retirement decision, we should find that individuals with tied coverage
retire later than those with retiree coverage. In making such a comparison, however, we
must account for the possibility that individuals with different health insurance options differ
systematically along other dimensions as well. For example, individuals with retiree coverage
tend to have higher wages and more generous pensions.
We control for this “initial conditions” problem in three ways. First, the initial distribution of simulated individuals is drawn directly from the data. Because households with
retiree coverage are more likely to be wealthy in the data, households with retiree coverage
are more likely to be wealthy in our initial distribution. Similarly, in our initial distribution
households with high levels of education are more likely to have high values of the persistent
wage shock ωt .
Second, we model carefully the way in which pension and Social Security accrual varies
across individuals and groups.
Finally, we control for unobservable differences across health insurance groups by introducing permanent preference heterogeneity, using the approach introduced by Heckman and
Singer (1984) and adapted by (among others) Keane and Wolpin (1997) and van der Klaauw
and Wolpin (2008). Each individual is assumed to belong to one of a finite number of preference “types”, with the probability of belonging to a particular type a logistic function of
the individual’s initial state vector: his age, wealth, initial wages, health status, health insurance type, medical expenditures, and preference index.10 We estimate the type probability
parameters jointly with the preference parameters and the consumption floor.
10

These discrete type-based differences are the only preference heterogeneity in our model. For this reason
many individuals in the data make decisions different from what the model would predict. Our MSM procedure
circumvents this problem by using moment conditions that average across many individuals. One way to
reconcile model predictions with individual observations is to introduce measurement error. In earlier drafts
of this paper (French and Jones, 2004b) we considered this possibility by estimating a specification where we
allowed for measurement error in assets. Adding measurement error, however, had little effect on either the
preference parameter estimates or policy experiments, and we dropped this case.

In our framework, correlations between preferences and health insurance emerge because
people with different preferences systematically select jobs with different types of health
insurance coverage. Workers in our data set are first observed in their fifties; by this age,
all else equal, jobs that provide generous post-retirement health insurance are more likely
to be held by workers that wish to retire early. One way to measure this self-selection is to
structurally model the choice of health insurance at younger ages, and use the predictions of
that model to infer the correlation between preferences and health insurance in the first wave
of the HRS. Because such an approach is computationally expensive, we instead model the
correlation between preferences and health insurance in the initial conditions.

3.3

Wage Selection

We estimate a selection-adjusted wage profile using the procedure developed in French
(2005). First, we estimate a fixed effects wage profile from HRS data, using the wages observed
for individuals who are working. The fixed-effects estimator is identified using wage growth
for workers. If wage growth rates for workers and non-workers are the same, composition
bias problems—the question of whether high wage individuals drop out of the labor market
later than low wage individuals—are not a problem. However, if individuals leave the market
because of a wage drop, such as from job loss, then wage growth rates for workers will be
greater than wage growth for non-workers. This selection problem will bias estimated wage
growth upward.
We control for selection bias by finding the wage profile that, when fed into our model,
generates the same fixed effects profile as the HRS data. Because the simulated fixed effect
profiles are computed using only the wages of those simulated agents that work, the profiles
should be biased upwards for the same reasons they are in the data. We find this bias-adjusted
wage profile using the iterative procedure described in French (2005).

Data and Calibrations

4.1

HRS Data

We estimate the model using data from the Health and Retirement Survey (HRS). The
HRS is a sample of non-institutionalized individuals, aged 51-61 in 1992, and their spouses.
With the exception of assets and medical expenses, which are measured at the household level,
our data are for male household heads. The HRS surveys individuals every two years, so that
we have 8 waves of data covering the period 1992-2006. The HRS also asks respondents
retrospective questions about their work history that allow us to infer whether the individual
worked in non-survey years. Details of this, as well as variable definitions, selection criteria,
and a description of the initial joint distribution, are in Appendix G.
As noted above, the Social Security rules depend on an individual’s year of birth. To
ensure that workers in our sample face a similar set of Social Security retirement rules, we
fit our model to the data for the cohort of individuals aged 57-61 in 1992. However, when
estimating the stochastic processes that individuals face we use the full sample, plus Assets
and Health Dynamics of the Oldest Old (AHEAD) data, which provides information on these
processes at older ages. With the exception of wages, we do not adjust the data for cohort
effects. Because our subsample of the HRS covers a fairly narrow age range, this omission
should not generate much bias.

4.2

Health Insurance and Medical Expenses

We assign individuals to one of three mutually exclusive health insurance groups: retiree,
tied, and none, as described in Section 2. Because of small sample problems, the none group
includes those with private health insurance as well as those with no insurance at all. Both
face high medical expenses because they lack employer-provided coverage. Private health
insurance is a poor substitute for employer-provided coverage, as high administrative costs
and adverse selection problems can result in prohibitively expensive premiums. Moreover,
private insurance is much less likely to cover pre-existing medical conditions. Because the

model includes a consumption floor to capture the insurance provided by Medicaid, the none
group also includes those who receive health care through Medicaid. We assign those who
have health insurance provided by their spouse to the retiree group, along with those who
report that they could keep their health insurance if they left their jobs. Both of these groups
have health insurance that is not tied to their job. We assign individuals who would lose
their employer-provided health insurance after leaving their job to the tied group. Appendix
H shows our estimated (health insurance-conditional) job exit rate profiles are robust to
alternative coding decisions.
The HRS has data on self-reported medical expenses. Medical expenses are the sum of
insurance premia paid by households, drug costs, and out-of-pocket costs for hospital, nursing
home care, doctor visits, dental visits, and outpatient care. Because our model explicitly
accounts for government transfers, the appropriate measure of medical expenses includes
expenses paid for by government transfers. Unfortunately, we observe only the medical
expenses paid by households, not those paid by Medicaid. Therefore, we impute Medicaid
payments for households that received Medicaid benefits, as described in Appendix G.
We fit these data to the medical expense model described in Section 2. Because of
small sample problems, we allow the mean, m(.), and standard deviation, σ(.), to depend
only on the individual’s Medicare eligibility, health insurance type, health status, labor force
participation and age. Following the procedure described in French and Jones (2004a), m(.)
and σ(.) are set so that the model replicates the mean and 95th percentile of the cross-sectional
distribution of medical expenses in each of these categories. Details are in Appendix I.
Table 1 presents summary statistics, conditional on health status. Table 1 shows that for
healthy individuals who are 64 years old, and thus not receiving Medicare, average annual
medical expenses are $3,360 for workers with tied coverage and $6,010 for those with none, a
difference of $2,650. With the onset of Medicare at age 65, the difference shrinks to $1,030.11
11
The pre-Medicare cost differences are roughly comparable to EBRI’s (1999) estimate that employers on
average contribute $3,288 per year to their employees’ health insurance. They are larger than Gustman and
Steinmeier’s (1994) estimate that employers contribute about $2,500 per year before age 65 (1977 NMES data,
adjusted to 1998 dollars with the medical component of the CPI).

Thus, the value of having employer provided health insurance coverage largely vanishes at
age 65.
Retiree Retiree Working Not Working
Age = 64, without Medicare, Good Health
Mean
$3,160
$3,880
Standard Deviation
$5,460
$7,510
99.5th Percentile
$32,700
$44,300
Age = 65, with Medicare, Good Health
Mean
$3,320
$3,680
Standard Deviation
$4,740
$5,590
99.5th Percentile
$28,800
$33,900
Age = 64, without Medicare, Bad Health
Mean
$3,930
$4,830
Standard Deviation
$6,940
$9,530
99.5th Percentile
$41,500
$56,100
Age = 65, with Medicare, Bad Health
Mean
$4,130
$4,580
Standard Deviation
$6,030
$7,120
99.5th Percentile
$36,600
$43,000

Tied Working

Tied Not Working

None

$3,360
$5,040
$30,600

$5,410
$10,820
$63,500

$6,010
$15,830
$86,900

$3,830
$5,920
$35,800

$4,230
$9,140
$52,800

$4,860
$7,080
$43,000

$4,170
$6,420
$38,900

$6,730
$13,740
$80,400

$7,470
$20,060
$109,500

$4,760
$7,530
$45,500

$5,260
$11,590
$66,700

$6,040
$9,020
$54,700

Table 1: Medical Expenses, by Medicare and Health Insurance Status

later version
Retiree
working
not working
Age < 65
Mean
99.5th Percentile
Age ≥ 65
Mean
99.5th Percentile

Tied

COBRA

None

3994.3891
45342.4987

5015.6304
52943.7293

4235.6760
42309.1367

7012.0350
82514.0614

7722.7168
105800.1045

4142.3761
35402.0366

4520.2544
42865.8863

4821.5927
40985.5849

5184.0517
68727.5124

5984.7325
53558.5724

Table 2: Summary Statistics for Medical Expenses: Unhealthy Individuals

As Rust and Phelan (1997) emphasize, it is not just differences in mean medical expenses
that determine the value of health insurance, but also differences in variance and skewness. If
health insurance reduces medical expense volatility, risk-averse individuals may value health
insurance at well beyond the cost paid by employers. To give a sense of the volatility,
Table 1 also presents the standard deviation and 99.5th percentile of the medical expense
distributions. Table 1 shows that for healthy individuals who are 64 years old, annual medical
18

expenses have a standard deviation of $5,040 for workers with tied coverage and $15,830 for
those with none, a difference of $10,790. With the onset of Medicare at age 65, the difference
shrinks to $1,160. Therefore, Medicare not only reduces average medical expenses for those
without employer-provided health insurance. It reduces medical expense volatility as well.
Parameter
ρm
σǫ2
σξ2

Variable
autocorrelation of persistent component
innovation variance of persistent component
innovation variance of transitory component

Estimate
(Standard Errors)
0.925 (0.003)
0.04811 (0.008)
0.6668 (0.014)

Table 3: Variance and Persistence of Innovations to Medical Expenses

The parameters for the idiosyncratic process ψt , (σξ2 , σǫ2 , ρm ), are taken from French and
Jones (2004a, “fitted” specification). Table 3 presents the parameters, which have been
normalized so that the overall variance, σψ2 , is one. Table 3 reveals that at any point in time,
the transitory component generates almost 67% of the cross-sectional variance in medical
expenses. The results in French and Jones reveal, however, that most of the variance in
cumulative lifetime medical expenses is generated by innovations to the persistent component.
For this reason, the cross sectional distribution of medical expenses reported in Table 1
understates the lifetime risk of medical expenses. Given the autocorrelation coefficient ρm of
0.925, this is not surprising.

4.3

Pension Accrual

Appendix C describes how we use confidential HRS pension data to construct the accrual
rate formula. Figure 1 shows the average pension accrual rates generated by this formula
when we simulate the model.
Figure 1 reveals that workers with retiree coverage face the sharpest drops in pension
accrual after age 60.12 While retiree coverage in and of itself provides an incentive for early
retirement, the pension plans associated with retiree coverage also provide the strongest
12
Because Figure 1 is based on our estimation sample, it does not show accrual rates for earlier ages.
Estimates that include the validation sample show, however, that those with retiree coverage have the highest
pension accrual rates in their early and middle 50s.

Figure 1: Average Pension Accrual Rates, by Age and Health Insurance Coverage

incentives for early retirement. Failing to capture this link will lead the econometrician to
overstate the effect of retiree coverage on retirement.

4.4

Preference Index

In order to better measure preference heterogeneity in the population (and how it is
correlated with health insurance), we estimate a person’s “willingness” to work using three
questions from the first (1992) wave of the HRS. The first question asks the respondent the
extent to which he agrees with the statement, “Even if I didn’t need the money, I would
probably keep on working.” The second question asks the respondent, “When you think
about the time when you will retire, are you looking forward to it, are you uneasy about it,
or what?” The third question asks, “How much do you enjoy your job?”
To combine these three questions into a single index, we regress wave 5-7 (survey year
2000-2004) participation on the response to the three questions along with polynomials and
interactions of all the state variables in the model: age, health status, wages, wealth, and
AIME, medical expenses, and health insurance type. Multiplying the numerical responses to
the three questions by their respective estimated coefficients and summing yields an index.
We then discretize the index into three values: high, for the top 50% of the index for those
20

working in wave 1; low, for the bottom 50% of the index for those working in wave 1; and out
for those not working in wave 1. Appendix J provides additional details on the construction
of the index. Figure 6 below shows that the index has great predictive power: at age 65,
participation rates are 56% for those with an index of high, 39% for those with an index of
low, and 12% for those with an index of out.

4.5

Wages

Recall from equation (11) that ln Wt = α ln(Nt ) + W (Ht , t) + ωt . Following Aaronson and
French (2004), we set α = 0.415, which implies that a 50% drop in work hours leads to a 25%
drop in the offered hourly wage. This is in the middle of the range of estimates of the effect
of hours worked on the offered hourly wage.
We estimate W (Ht , t) using the methodology described in section 3.3.
The parameters for the idiosyncratic process ωt , (ση2 , ρW ) are estimated by French (2005).
The results indicate that the autocorrelation coefficient ρW is 0.977; wages are almost a
random walk. The estimate of the innovation variance ση2 is 0.0141; one standard deviation
of an innovation in the wage is 12% of wages.

4.6

Remaining Calibrations

We set the interest rate r equal to 0.03. Spousal income depends upon an age polynomial and health status. Health status and mortality both depend on previous health status
interacted with an age polynomial.

Data Profiles and Initial Conditions

5.1

Data Profiles

Figure 2 presents some of the labor market behavior we want our model to explain. The
top panel of Figure 2 shows empirical job exit rates by health insurance type. Recall that
Medicare should provide the largest labor market incentives for workers that have tied health

insurance. If these people place a high value on employer-provided health insurance, they
should either work until age 65, when they are eligible for Medicare, or they should work until
age 63.5 and use COBRA coverage as a bridge to Medicare. The job exit profiles provide
some evidence that those with tied coverage do tend to work until age 65. While the age-65
job exit rate is similar for those whose health insurance type is tied (20%), retiree (17%), or
none (18%), those with retiree coverage have higher exit rates at 62 (22%) than those with
tied (14%) or none (18%).13 At almost every age other than 65, those with retiree coverage
have higher job exit rates than those with tied or no coverage. These differences across health
insurance groups, while large, are smaller than the differences in the empirical exit profiles
reported in Rust and Phelan (1997).
The low job exit rates before age 65 and the relatively high job exit rates at age 65 for
those with tied coverage suggests that some people with tied coverage are working until age
65, when they become eligible for Medicare. On the other hand, job exit rates for those with
tied coverage are lower than those with retiree coverage for every age other than 65, and are
not much higher at age 65. This suggests that differences in health insurance coverage may
not be the only reason for the differences in job exit rates.
The bottom panel of Figure 2 presents observed labor force participation rates. In comparing participation rates across health insurance categories, it is useful to keep in mind the
transitions implied by equation (10): retiring workers in the tied insurance category transition into the none category. Because of this, the labor force participation rates for those with
tied insurance are calculated for a group of individuals that were all working in the previous
period. It is therefore not surprising that the tied category has the highest participation
rates. Conversely, it is not surprising that the none category has the lowest participation
rates, given that category includes tied workers who retire.

13
The differences across groups are statistically different at 62, but not at 65. Furthermore, F -tests reject
the hypothesis that the three groups have identical exit rates at all ages at the 5% level.

Job Exit Rates by Health Insuran ce Type, Data
0

n
0

"'a
N

Data, no H.l.
Data, retiree H.l.

..":"'

L{)

·;;: ci
w
.D

"'ci
0

"' 59
0

Age

Participation Rates by Health Insurance Type, Data

c:
Ol

+---+---·

"'ci
..":"'

-----+---+--........... ..

:+" ... , ........ - ............

,"'
"

r:
0

a:
c
0

0
D..

a
L{)

:~ ""
ci
"t
0

"!
0

"' 58
0

+--·
59

Data, no H.l.
Data, retiree H.l.
Data, tied H.l.

Age

Figure 2: Job Exit and Participation Rates, Data

5.2

Initial Conditions

Each artificial individual in our model begins its simulated life with the year-1992 state
vector of an individual, aged 57-61 in 1992, observed in the data. Table 4 summarizes this
initial distribution, the construction of which is described in Appendix G. Table 4 shows
that individuals with retiree coverage tend to have the most asset and pension wealth, while
individuals in the none category have the least. The median individual in the none category
has no pension wealth at all. Individuals in the none category are also more likely to be in
bad health, and not surprisingly, less likely to be working. In contrast, individuals with tied
coverage have high values of the preference index, suggesting that their delayed retirement
reflects differences in preferences as well as in incentives.
Retiree

T ied

N one

Age
Mean
58.7
58.6
58.7
Standard deviation
1.5
1.5
1.5
AIM E (in thousands of 1998 dollars)
Mean
24.9
24.9
16.0
Median
27.2
26.9
16.2
Standard deviation
9.1
8.6
9.2
Assets (in thousands of 1998 dollars)
Mean
231
205
203
Median
147
118
52
Standard deviation
248
251
307
Pension Wealth (in thousands of 1998 dollars)
Mean
129
80
17
Median
62
17
0
Standard deviation
180
212
102
Wage (in 1998 dollars)
Mean
17.4
17.6
12.0
Median
14.7
14.6
8.6
Standard deviation
13.4
12.4
11.2
Preference index
Fraction out
0.27
0.04
0.48
Fraction low
0.42
0.44
0.19
Fraction high
0.32
0.52
0.33
Fraction in bad health
0.20
0.13
0.41
Fraction working
0.73
0.96
0.52
Number of observations
1,022
225
455
Table 4: Summary Statistics for the Initial Distribution

Baseline Results

6.1

Preference Parameter Estimates

The goal of our MSM estimation procedure is to match the life cycle profiles for assets,
hours and participation found in the HRS data. In order to use these profiles to identify preferences, we make several identifying assumptions, the most important being that preferences
vary with age in two specific ways; (1) through changes in health status; and (2) through
the linear time trend in the fixed cost φP t . Therefore, age can be thought of as an “exclusion restriction”, which changes the incentives for work and savings in ways that can not be
captured with changes in preferences.
Table 5 presents preference parameter estimates. The first 3 rows of Table 5 show the
parameters that vary across the preference types. We assume that there are three types
of individuals, and that the types differ in the utility weight on consumption, γ, and their
time discount factor, β. Individuals with high values of γ have stronger preferences for work.
Individuals with high values of β are more patient and thus more willing to defer consumption
and leisure. Table 5 reveals significant differences in γ and β across preference types, which
are discussed in some detail in Section 6.2.
Table 5 also shows the fraction of workers belonging to each preference type. Averaging
over the three types reveals that the average value of β, the discount factor, implied by our
model is 0.913, which is slightly lower than most estimates. The discount factor is identified
by the intertemporal substitution of consumption and leisure, as embodied in the asset and
labor supply profiles.
Another key parameter is ν, the coefficient of relative risk aversion for the consumptionleisure composite. A more familiar measure of risk aversion is the coefficient of relative risk
aversion for consumption. Assuming that labor supply is fixed, it can be approximated as
2

U/∂C )C
− (∂ ∂U/∂C
= −(γ(1 − ν) − 1). The weighted average value of the coefficient is 5.0. This

value falls within the range of estimates found in recent studies by Cagetti (2003) and French
(2005), but it is larger than the values of 1.1, 1.8, and 1.0 reported by Rust and Phelan

(1997), Blau and Gilleskie (2006), and Blau and Gilleskie (2008) respectively, in their studies
of retirement.
Parameters that vary across
Type 0
γ: consumption weight
0.412
(0.045)
β: time discount factor
0.945
(0.074)
Fraction of individuals
0.267
Parameters that
ν: coefficient of relative
risk aversion, utility
κ: bequest shifter,
in thousands
L: leisure endowment,
in hours
φP 0 : fixed cost of work at age 60,
in hours
φRE : hours of leisure lost when
re-entering labor market

individuals
Type 1 Type 2
0.649
0.967
(0.007) (0.203)
0.859
1.124
(0.013) (0.328)
0.615
0.118

are common to all individuals
7.49
θB : bequest weight†
(0.311)
444
cmin : consumption floor
(28.4)
4,060
φH : hours of leisure lost,
(44)
bad health
826
φP 1 : fixed cost of work:
(20.0)
age trend, in hours
94.0
(8.63)

0.0223
(0.0012)
4,380
(167)
506
(20.9)
54.7
(2.58)

χ2 statistic = 775; Degrees of freedom = 171
Method of simulated moments estimates.
Diagonal weighting matrix used in calculations. See Appendix F for details.
Standard errors in parentheses.
† Parameter expressed as marginal propensity to consume out of
final-period wealth.
Parameters estimated jointly with type probability prediction equation. See
Appendix K for estimated coefficients of the type probability prediction equation.
Table 5: Estimated Structural Parameters

The risk coefficient ν and the consumption floor Cmin are identified in large part by
the asset quantiles, which reflect precautionary motives. The bottom quantile in particular
depends on the interaction of precautionary motives and the consumption floor. If the consumption floor is sufficiently low, the risk of a catastrophic medical expense shock, which
over a lifetime could equal over $100,000 (see French and Jones (2004a)), will generate strong
precautionary incentives. Conversely, as emphasized by Hubbard, Skinner and Zeldes (1995),
a high consumption floor discourages saving among the poor, since the consumption floor

effectively imposes a 100% tax on the saving of those with high medical expenses and low
income and assets.
Our estimated consumption floor of $4,380 is similar to other estimates of social insurance
transfers for the indigent. For example, when we use Hubbard, Skinner and Zeldes’s (1994,
Appendix A) procedures and more recent data, we find that the average benefit available
to a childless household with no members aged 65 or older was $3,500. A value of $3,500
understates the benefits available to individuals over age 65; in 1998 the Federal SSI benefit
for elderly (65+) couples was nearly $9,000 (Committee on Ways and Means, 2000, p. 229).
On the other hand, about half of eligible households do not collect SSI benefits (Elder and
Powers, 2006, Table 2), possibly because transactions or “stigma” costs outweigh the value
of public assistance. Low take-up rates, along with the costs that probably underly them,
suggest that the effective consumption floor need not equal statutory benefits.
The bequest parameters θB and κ are identified largely from the top asset quantile. It
follows from equation (3) that when the shift parameter κ is large, the marginal utility of
bequests will be lower than the marginal utility of consumption unless the individual is rich.
In other words, the bequest motive mainly affects the saving of the rich; for more on this
point, see De Nardi (2004). Our estimate of θB implies that the marginal propensity to
consume out of wealth in the final period of life (which is a nonlinear function of θB , β, γ, ν
and κ) is 1 for low income individuals and 0.022 for high-income individuals.
Turning to labor supply, we find that individuals in our sample are willing to intertemporally substitute their work hours. In particular, simulating the effects of a 2% wage change
reveals that the wage elasticity of average hours is 0.486 at age 60. This relatively high labor
supply elasticity arises because the fixed cost of work generates volatility on the participation margin. The participation elasticity is 0.353 at age 60, implying that wage changes
cause relatively small hours changes for workers. For example, the Frisch labor supply elasticity of a type-1 individual working 2,000 hours per year at age 60 is approximated as
P0
− L−NNt −φ
×
t

1
(1−γ)(1−ν)−1

= 0.19.

The fixed cost of work at age 60, φP 0 , is 826 hours per year, and increases by φP 1 = 55
27

hours per year. The fixed cost of work is identified by the life cycle profile of hours worked by
workers. Average hours of work (available upon request) do not drop below 1,000 hours per
year (or 20 hours per week, 50 weeks per year) even though labor force participation rates
decline to near zero. In the absence of a fixed cost of work, one would expect hours worked
to parallel the decline in labor force participation. (See Rogerson and Wallenius, 2009.) The
time endowment L is identified by the combination of the participation and hours profiles.
The time cost of bad health, φH , is identified by noting that unhealthy individuals work fewer
hours than healthy individuals, even after conditioning on wages. The re-entry cost, φRE ,
of 94 hours, is identified by exit rates. In the absence of a re-entry cost, workers are more
willing to “churn” in and out of the labor force, raising exit rates.

6.2

Preference Heterogeneity and Health Insurance

Table 5 shows considerable heterogeneity in preferences. To understand these differences,
Table 6 shows simulated summary statistics for each of the preference types. Table 6 reveals
that Type-0 individuals have the lowest value of γ, i.e., they place the highest value on
leisure. 92% of Type-0 individuals were out of the labor force in wave 1. Type-2 individuals,
in contrast, have the highest value of γ. 84% of Type-2 individuals have a preference index
of high, meaning that they were working in wave 1 and self-reported having a low preference
for leisure. Type-1 individuals fall in the middle, valuing leisure less than Type-0 individuals,
but more than Type-2 individuals. 54% of Type-1 individuals have a preference index value
of low.
Including preference heterogeneity allows us to control for the possibility that workers with
different preferences select jobs with different health insurance packages. Table 6 suggests
that some self-selection is occurring, as it reveals while 14% of workers with tied coverage are
Type-2 agents, who have the lowest disutility of work, only 5% are Type-0 agents, who have
the highest disutility. In contrast, 11% of workers with retiree coverage are Type-2 agents,
and 27% are Type-0 agents. This suggests that workers with tied coverage might be more
willing to retire later than those with retiree coverage because they have a lower disutility
28

of work. However, Section 6.4 shows that accounting for this correlation has little impact on
the estimated effect of health insurance on retirement.
Type 0

Type 1

Type 2

Key preference parameters
γ∗
0.412
0.649
0.967
β∗
0.945
0.859
1.124
Means by preference type
Assets ($1, 000s)
150
215
405
Pension Wealth ($1, 000s)
92
97
74
Wages ($/hour)
11.3
19.0
11.1
Probability of health insurance type, given preference type
Health insurance = none
0.371
0.222
0.261
Health insurance = retiree
0.607
0.603
0.581
Health insurance = tied
0.023
0.175
0.158
Probability of preference index value, given preference type
Preference Index = out
0.922
0.068
0.034
Preference Index = low
0.039
0.539
0.131
Preference Index = high
0.039
0.392
0.835
Fraction of individuals
0.267
0.615
0.118
∗ Values of β and γ are from Table 5.
Table 6: Mean Values by Preference Type, Simulations

6.3

Simulated Profiles

The bottom of Table 5 displays the overidentification test statistic. Even though the
model is formally rejected, the life cycle profiles generated by the model match up well with
the life cycle profiles found in the data.
Figure 3 shows the 1/3rd and 2/3rd asset quantiles at each age for the HRS sample and
for the model simulations. For example, at age 64 about one third of the men in our sample
live in households with less than $80,000 in assets, and about one third live in households
with over $270,000 of assets. Figure 3 shows that the model fits both asset quantiles well.
The model is able to fit the lower quantile in large part because of the consumption floor of
$4,350; the predicted 1/3rd quantile rises when the consumption floor is lowered.
The three panels in the left hand column of Figure 4 show that the model is able to
replicate the two key features of how labor force participation varies with age and health
29

Figure 3: Asset Quantiles, Data and Simulations

insurance. The first key feature is that participation declines with age, and the declines are
especially sharp between ages 62 and 65. The model underpredicts the decline in participation
at age 65 (a 4.9 percentage point decline in the data versus a 3.5 percentage point decline
predicted by the model), but comes closer at age 62 (a 10.6 percentage point decline in the
data versus a 10.9 percentage point decline predicted by the model).
The second key feature is that there are large differences in participation and job exit rates
across health insurance types. The model does a good job of replicating observed differences
in participation rates. For example, the model matches the low participation levels of the
uninsured. Turning to the lower left panel of Figure 5, the data show that the group with the
lowest participation rates are the uninsured with low assets. The model is able to replicate
this fact because of the consumption floor. Without a high consumption floor, the risk of
catastrophic medical expenses, in combination with risk aversion, would cause the uninsured
to remain in the labor force and accumulate a buffer stock of assets.

Partici pation Rates, Tie d Health lnsu ranee

Job Ex it Rates, Tied Health Insurance

- - Data. tied H.l.
----- S"1mu lati on:s, t ic:d H.l.

c
0

·;:
w

·o

"'
0

..a

·-e

..<;

a..
"

0 59

64-

Age

Participation Rates, Retiree Health Insuran ce

Job Exit Rates, Retiree Health Insurance

m
ci

- - Data, reti ree H.l.
------ Simulations, r etiree H.l.

n::
"

cr:

·x
w
..a

.e-

g
59

64-

Age

Participation Rates , No Health Insurance

Job Exit Rates, No Health Insuran ce

"
m

- - Data, no H.l.
------ Simulation8, no H_l

-a
""

·.-0

:§

..a

t::

a..

0
0

0 59

Age

Figure 4: Participation and Job Exit Rates, Data and Simulations

Participation Rates, Data, Tied Health Insurance

Participation, Simulations, Tied Health Insurance

Low assets, tied H .1. , simulations
------ Medium assets, tied H.l., simulations
High assets, tie d H.l., simulations

+-64

Age

Participation Rates, Data, Retiree Health Insura nce

Participation, Simulations, Retiree Health Insurance

.e-

"
Low assets. retiree H.l.. simulations
Medium assets , retiree H.l., simulations

M~dium

a:sst":ts, retiree: H.l., data
High assets. retiree H.l.. data

HiQh assets. retiree H.l.. simulations

Age

Participation Rates, Data, No Health Insurance

Participation, Simulations, No Health Insurance

~r----r---,----~--~----r----r---,----~--~----~--0

~r----r---,r---~--~----~---r----r---,----,----~--,

Age

... _
--+---to.

' ' .... _

+---

.......~ .......

-... --

-+-- -....

''
...........
··'""+---+---""+..

'•-

Hig h assets, no H.l., data

High assets, no H.l., simulations

Age

Figure 5: Labor Force Participation Rates by Asset Grouping, Data and Simulations

The panels in the right hand column of Figure 4 compare observed and simulated job exit
rates for each health insurance type. The model does a good job of fitting the exit rates of
workers with retiree or tied coverage. For example, the model captures the high age-62 job
exit rates for those with retiree coverage and the high age-65 job exit rates for those with
tied coverage. However, it fails to capture the high exit rates at age 65 for workers with no
health insurance.
Figure 6 shows how participation differs across the three values of the discretized preference index constructed from HRS attitudinal questions. Recall that an index value of out
implies that the individual was not working in 1992. Not surprisingly, participation for this
group is always low. Individuals with positive values of the preference index differ primarily
in the rate at which they leave the labor force. Although low-index individuals initially work
as much as high-index individuals, they leave the labor force more quickly. As noted in our
discussion of the preference parameters, the model replicates these differences by allowing the
taste for leisure (γ) and the discount rate (β) to vary across preference types. When we do
not allow for preference heterogeneity, the model is unable to replicate the patterns observed
in Figure 6. This highlights the importance of the preference index in identifying preference
heterogeneity.

Figure 6: Labor Force Participation Rates by Preference Index, Data and Simulations

6.4

The Effects of Employer-Provided Health Insurance

The labor supply patterns in Figures 2 and 4 show that those with retiree coverage retire
earlier than those with tied coverage. However, the profiles do not identify the effects of
health insurance on retirement, for three reasons. First, as shown in Table 4, those with
retiree coverage have greater pension wealth than other groups. Second, as shown in Figure 1, pension plans for workers with retiree coverage provide stronger incentives for early
retirement than the pension plans held by other groups. Third, as shown in Table 6, preferences for leisure vary by health insurance type. In short, retirement incentives differ across
health insurance categories for reasons unrelated to health insurance incentives.
To isolate the effects of employer-provided health insurance on labor supply, we conduct
some additional simulations. We give everyone the pension accrual rates of tied workers
so that pension incentives are identical across health insurance types. We then simulate
the model twice, assuming first that all workers have retiree health insurance coverage at
age 59, then tied coverage at age 59. Across the two simulations, households face different
medical expense distributions, but in all other dimensions the distribution of incentives and
preferences is identical.
This exercise reveals that if all workers had retiree coverage rather than tied coverage the
job exit rate at age 62 would be 8.4 percentage points higher. In contrast, the raw difference
in model-predicted exit rates at age 62 is 10.5 percentage points. (The raw difference in the
data is 8.2 percentage points.) The high age-62 exit rates of those with retiree coverage are
thus partly due to more generous pensions and stronger preferences for leisure. Even after
controlling for these factors, however, health insurance is still an important determinant of
retirement.
The effects of health insurance can also be measured by comparing participation rates.
We find that the labor force participation rate for ages 60-69 would be 5.1 percentage points
lower if everyone had retiree, rather than tied, coverage at age 59. Furthermore, moving
everyone from retiree to tied coverage increases the average retirement age (defined as the
oldest age at which the individual works plus one) by 0.34 years.
34

In comparison, Blau and Gilleskie’s (2001) reduced-form estimates imply that having
retiree coverage, rather than tied coverage, increases the job exit rate 7.5 percentage points
at age 61. Blau and Gilleskie also find that accounting for selection into health insurance plans
modestly increases the estimated effect of health insurance on exit rates. Other reduced form
findings in the literature are qualitatively similar to Blau and Gilleskie. For example, Madrian
(1994) finds that retiree coverage reduces the retirement age by 0.4-1.2 years, depending on
the specification and the data employed. Karoly and Rogowski (1994), who attempt to
account for selection into health insurance plans, find that retiree coverage increases the job
exit rate 8 percentage points over a 2 12 year period. Our estimates, therefore, lie within the
lower bound of the range established by previous reduced form studies, giving us confidence
that the model can be used for policy analysis.
Structural studies that omit medical expense risk find smaller health insurance effects than
we do. For example, Gustman and Steinmeier (1994) find that retiree coverage reduces years
in the labor force by 0.1 years. Lumsdaine et al. (1994) find even smaller effects. Structural
studies that include medical expense risk but omit self-insurance find bigger effects. Our
estimated effects are larger than Blau and Gilleskie’s (2006, 2008), who find that retiree
coverage reduces average labor force participation 1.7 and 1.6 percentage points, respectively,
but are smaller than the effects found by Rust and Phelan (1997).14

6.5

Model Validation

Following several recent studies (e.g., Keane and Wolpin, 2007), we perform an out-ofsample validation exercise. Recall that we estimate the model on a cohort of individuals
aged 57-61 in 1992. We test our model by considering the HRS cohort aged 51-55 in 1992;
we refer to this group as our validation cohort. These individuals faced different Social
Security incentives than did the estimation cohort. The validation cohort did not face the
14
Blau and Gilleskie (2006) consider the retirement decision of couples, and allow husbands and wives to
retire at different dates. Blau and Gilleskie (2008) allow workers to choose their medical expenses. Because
these modifications provide additional mechanisms for smoothing consumption over medical expense shocks,
they could reduce the effect of employer-provided health insurance.

Social Security earnings test after age 65, had a later full retirement age, and faced a benefit
adjustment formula that more strongly encouraged delayed retirement. In addition to facing
different Social Security rules, the validation cohort possessed different endowments of wages,
wealth, and employer benefits. A useful test of our model, therefore, is to see if it can predict
the behavior of the validation cohort.

Age
60
61
62
63
64
65
66
67
Total, 60-67

Data
1933 1939
Difference†
(1)
(2)
(3)
0.657 0.692
0.035
0.636 0.642
0.006
0.530 0.545
0.014
0.467 0.508
0.041
0.408 0.471
0.063
0.358 0.424
0.066
0.326 0.382
0.057
0.314 0.374
0.060
3.696 4.037
0.341
† Column (2) − Column (1)

Model
1933 1939 Difference∗
(4)
(5)
(6)
0.650 0.706
0.056
0.622 0.677
0.055
0.513 0.570
0.057
0.456 0.490
0.035
0.413 0.449
0.037
0.378 0.459
0.082
0.350 0.430
0.080
0.339 0.386
0.047
3.721 4.168
0.447
∗ Column (5) − Column (4)

Table 7: Participation Rates by Birth Year Cohort

Columns (1)-(3) of Table 7 show the participation rates observed in the data for each
cohort, and the difference. The data suggest that the change in the Social Security rules
coincides with increased labor force participation, especially at later ages. By way of comparison, Song and Manchester (2007), examining Social Security administrative data, find
that between 1996 and 2003, participation rates increased by 3, 4 and 6 percentage points
for workers turning 62-64, 65, and 66-69, respectively. These differences are similar to the
differences between the 1933 and 1939 cohorts in our data, as shown in column 3.
Columns (4)-(6) of Table 7 show the participation rates predicted by the model. The
simulations for the validation cohort use the initial distribution and Social Security rules
for the validation cohort, but use the parameter values estimated on the older estimation
cohort.15 Comparing Columns (3) and (6) shows that the model-predicted increase in labor
15

We do not adjust for business cycle conditions. Because the validation cohort starts at age 53, 6 years
before the estimation cohort, the validation exercise requires its own wage selection adjustment and pension
prediction equation. Using the baseline preference estimates, we construct these inputs in the same way

supply (0.45 years), resembles the increase observed in the data (0.35 years).

Policy Experiments
The preceding sections showed that the model fits the data well, given plausible preference

parameters. In this section, we use the model to predict how changing the Social Security
and Medicare rules would affect retirement behavior. The results of these experiments are
summarized in Table 8.
SS = 65 SS = 67† SS = 65 SS = 67†
MC = 65 MC = 65 MC = 67 MC = 67
Age
(1)
(2)
(3)
(4)
60
0.650
0.651
0.651
0.652
61
0.622
0.625
0.623
0.626
62
0.513
0.526
0.516
0.530
63
0.456
0.469
0.460
0.472
64
0.413
0.426
0.422
0.433
65
0.378
0.386
0.407
0.415
66
0.350
0.358
0.374
0.381
67
0.339
0.346
0.341
0.347
68
0.307
0.311
0.307
0.312
69
0.264
0.270
0.264
0.270
Total 60-69
4.292
4.368
4.366
4.438
SS = Social Security normal retirement age
MC = Medicare eligibility age
† Benefits reduced by two years, as described in text

Data
(5)
0.657
0.636
0.530
0.467
0.407
0.358
0.326
0.314
0.304
0.283
4.283

Table 8: Effects of Changing the Social Security Retirement and Medicare Eligibility Ages

The first column of Table 8 shows model-predicted labor market participation at ages 60
through 69 under the 1998 Social Security rules. Under the 1998 rules, the average person
works a total of 4.29 years over this 10-year period. The fifth column of Table 8 shows that
this is close to the total of 4.28 years observed in the data.
The Social Security rules are slowly evolving over time. If current plans continue, by
2030 the normal Social Security retirement age, the date at which workers can receive “full
we construct their baseline counterparts. In addition, we adjust the intercept terms in the type prediction
equations so that the validation cohort generates the same distribution of preference types as the estimation
sample.

benefits”, will have risen from 65 to 67. Raising the normal retirement age to 67 effectively
eliminates two years of Social Security benefits. Column (2) shows the effect of this change.16
The wealth effect of lower benefits leads years of work to increase by 0.076 years, to 4.37
years.17
The third column of Table 8 shows participation when the Medicare eligibility age is
increased to 67.18 Over a 10-year period, total years of work increase by 0.074 years, so that
the average probability of employment increases by 0.74 percentage points per year. This
amount is larger than the changes found by Blau and Gilleskie (2006), whose simulations
show that increasing the Medicare age increases the average probability of employment by
0.1 percentage points, but is smaller than the effects suggested by Rust and Phelan’s (1997)
analysis.
The fourth column shows the combined effect of cutting Social Security benefits and
raising the Medicare eligibility age. The joint effect is an increase of 0.146 years, 0.072
years more than that generated by cutting Social Security benefits in isolation. In summary,
the model predicts that raising the Medicare eligibility age will have almost the same effect
on retirement behavior as the benefit reductions associated with a higher Social Security
retirement age. Medicare has an even bigger effect on those with tied coverage at age 59.19
Simulations reveal that for those with tied coverage, eliminating two years of Social Security
benefits increases years in the labor force by 0.12 years, whereas shifting forward the Medicare
16
Under the 2030 rules, an individual claiming benefits at age 65 would receive an annual benefit 13.3%
smaller than the benefit he would have received under the 1998 rules (holding AIM E constant). We thus
implement the two-year reduction in benefits by reducing annual benefits by 13.3% at every age.
17
In addition to reducing annual benefits, the intended 2030 rules would impose two other changes. First,
the rate at which benefits increase for delaying retirement past the normal age would increase from 5.5% to
8.0%. This change, like the reduction in annual benefits, should encourage work. However, raising the normal
retirement age implies that the relevant earnings test for ages 65-66 would become the stricter, early-retirement
test. This change should discourage work. We find that when we switch from the 1998 to the 2030 rules, the
effects of the three changes cancel out, so that total hours over ages 60-69 are essentially unchanged.
18
By shifting forward the Medicare eligibility age to 67, we increase from 65 to 67 the age at which medical
expenses can follow the “with Medicare” distribution shown in Table 1.
19
Only 13% of the workers in our sample had tied coverage at age 59. In contrast, Kaiser/HRET (2006)
estimated that about 50% of large firms offered tied coverage in the mid-1990s. We might understate the share
with tied coverage because, as shown in the Kaiser/HRET study, the fraction of workers with tied (instead
of retiree) coverage grew rapidly in the 1990s, and our health insurance measure is based on wave-1 data
collected in 1992. In fact, the HRS data indicate that later waves had a higher proportion of individuals with
tied coverage than wave 1. We may also be understating the share with tied coverage because of changes in
the wording of the HRS questionnaire; see Appendix H for details.

eligibility age to 67 would increase years in the labor force by 0.28 years.
To understand better the incentives generated by Medicare, we compute the value Type-1
individuals place on employer-provided health insurance, by finding the increase in assets that
would make an uninsured Type-1 individual as well off as a person with retiree coverage. In
particular, we find the compensating variation λt = λ(At , Bt , Ht , AIM Et , ωt , ζt−1 , t), where

Vt (At , Bt , Ht , AIM Et , ωt , ζt−1 , retiree) = Vt (At + λt , Bt , Ht , AIM Et , ωt , ζt−1 , none).

Table 9 shows the compensating variation λ(At , 0, good, $32000, 0, 0, 60) at several different
asset (At ) levels.20 The first column of Table 9 shows the valuations found under the baseline
specification. One of the most striking features is that the value of employer-provided health
insurance is fairly constant through much of the wealth distribution. Even though richer
individuals can better self-insure, they also receive less protection from the governmentprovided consumption floor. These effects more or less cancel each other out over the asset
range of -$5,700 to $147,000. However, individuals with asset levels of $600,000 place less
value on retiree coverage, because they can better self-insure against medical expense shocks.
Part of the value of retiree coverage comes from a reduction in average medical expenses—
because retiree coverage is subsidized—and part comes from a reduction in the volatility of
medical expenses—because it is insurance. In order to separate the former from the latter,
we eliminate medical expense uncertainty, by setting the variance shifter σ(Ht , It , t, Bt , Pt )
to zero, and recompute λt , using the same state variables and mean medical expenses as
before. Without medical expense uncertainty, λt is approximately $11,000. Comparing the
two values of λt shows that for the typical worker (with $147,000 of assets) about half of
the value of health insurance comes from the reduction of average medical expenses, and half
comes from the reduction of medical expense volatility.
The first two columns of Table 9 measure the lifetime value of health insurance as an asset
20
In making these calculations, we remove health-insurance-specific differences in pensions, as described
in section 6.4. It is also worth noting that for the values of Ht and ζt−1 considered here, the conditional
differences in expected medical expenses are smaller than the unconditional differences shown in Table 1.

Asset Levels

Compensating Assets
With
Without
Uncertainty Uncertainty
(1)
(2)

Compensating Annuity
With
Without
Uncertainty Uncertainty
(3)
(4)

Baseline Case
-$5,700
$20,400
$10,700
$4,630
$2,530
$51,600
$19,200
$10,900
$4,110
$2,700
$147,200
$21,400
$10,600
$4,180
$2,540
$600,000
$16,700
$11,900
$2,970
$2,360
No-Saving Cases
(a) -$6,000
$112,000
$8,960
$11,220
$2,160
(b) -$6,000
$21,860
$6,862
$3,884
$2,170
Compensating variation between retiree and none coverages for agents
with type-1 preferences.
Calculations described in text.
No-Saving case (a) uses benchmark preference parameter values;
case (b) uses parameter values estimated for no-saving specification.
Table 9: Value of Employer-Provided Health Insurance

increment that can be consumed immediately. An alternative approach is to express the value
of health insurance as an illiquid annuity comparable to Social Security benefits. Columns (3)
and (4) show this “compensating annuity”.21 When the value of health insurance is expressed
as an annuity, the fraction of its value attributable to reduced medical expense volatility falls
from one-half to about 40 percent. In most other respects, however, the asset and annuity
valuations of health insurance have similar implications.
To sum, allowing for medical expense uncertainty greatly increases the value of health
insurance. It is therefore unsurprising that we find larger effects of health insurance on
retirement than do Gustman and Steinmeier (1994) and Lumsdaine et al. (1994), who assume
that workers value health insurance at its actuarial cost.
21

b t , where
To do this, we first find compensating AIM E, λ

b t , ωt , ζt−1 , none).
Vt (At , Bt , Ht , AIM Et , ωt , ζt−1 , retiree) = Vt (At , Bt , Ht , AIM Et + λ

This change in AIM E in turn allows us to calculate the change in expected pension and Social Security
benefits that the individual would receive at age 65, the sum of which can be viewed as a compensating
annuity. Because these benefits depend on decisions made after age 60, the calculation is only approximate.

Alternative Specifications
To consider whether our findings are sensitive to our modelling assumptions, we re-

estimate the model under three alternate specifications.22 Table 10 shows model-predicted
participation rates under the different specifications, along with the data. The parameter estimates behind these simulations are shown in Appendix K. Column (1) of Table 10 presents
our baseline case. Column (2) presents the case where individuals are not allowed to save.
Column (3) presents the case with no preference heterogeneity. Column (4) presents the
case where we remove the subjective preference index from the type prediction equations
and the GMM criterion function. Column (5) presents the data. In general, the different
specifications match the data profile equally well.

Age
60
61
62
63
64
65
66
67
68
69
Total 60-69

Baseline
(1)
0.650
0.622
0.513
0.456
0.413
0.378
0.350
0.339
0.307
0.264
4.292

No
Saving
(2)
0.648
0.632
0.513
0.457
0.429
0.380
0.334
0.327
0.308
0.282
4.309

Homogeneous
Preferences
(3)
0.621
0.595
0.517
0.453
0.409
0.365
0.351
0.345
0.319
0.286
4.260

No
Preference
Index
(4)
0.653
0.625
0.516
0.459
0.417
0.381
0.357
0.346
0.314
0.273
4.340

Data
(5)
0.657
0.636
0.530
0.467
0.407
0.358
0.326
0.314
0.304
0.283
4.283

Table 10: Model Predicted Participation, by Age: Alternative Specifications

Table 11 shows how total years of work over ages 60-69 are affected by changes in Social
Security and Medicare under each of the alternative specifications. In all specifications,
decreasing the Social Security benefits and raising the Medicare eligibility age increase years
of work by similar amounts.
22
In earlier drafts of this paper (French and Jones, 2004b, 2007), we also estimated a specification where
housing wealth is illiquid. Although parameter estimates and model fit for this case were somewhat different
than our baseline results, the policy simulations were similar.

No
Homogeneous
Baseline Saving
Preferences
Rule Specification
(1)
(2)
(3)
Baseline: SS = 65, MC = 65
4.292
4.309
4.260
SS = 67: Lower benefits†
4.368
4.399
4.335
SS = 65, MC = 67
4.366
4.384
4.322
SS = 67† and MC = 67
4.438
4.456
4.395
SS = Social Security normal retirement age
MC = Medicare eligibility age
† Benefits reduced by two years, as described in text

No
Preference
Index
(4)
4.340
4.411
4.417
4.482

Table 11: Effects of Changing the Social Security Retirement and Medicare Eligibility Ages, Ages 60-69, Alternative Specifications

8.1

No Saving

We have argued that the ability to self-insure through saving significantly affects the value
of employer-provided health insurance. One test of this hypothesis is to modify the model so
that individuals cannot save, and examine how labor market decisions change. In particular,
we require workers to consume their income net of medical expenses, as in Rust and Phelan
(1997) and Blau and Gilleskie (2006, 2008).
The second column of Table 10 contains the labor supply profile generated by the nosaving specification. Comparing this profile to the baseline case in column (1) shows that, in
addition to its obvious failings with respect to asset holdings, the no-saving case matches the
labor supply data no better than the baseline case.23
Table 9 displays two sets of compensating values for the no-saving case. Case (a), which
uses the parameter values from the benchmark case, shows that eliminating the ability to
save greatly increases the value of retiree coverage: when assets are -$6,000, the compensating
annuity increases from $4,600 in the baseline case (with savings) to $11,200 in no-savings
case (a). When there is no medical expense uncertainty, the comparable figures are $2,530 in
the baseline case and $2,160 in the no-savings case. Thus, the ability to self-insure through
23

Because the baseline and no-savings cases are estimated with different moments, their overidentification
statistics are not comparable. However, inserting the decision profiles generated by the baseline model into
the moment conditions used to estimate the no-savings case produces an overidentification statistic of 349,
while the no-saving specification produces an overidentification statistic of 398.

saving significantly reduces the value of employer-provided health insurance. Case (b) shows
that using the parameter values estimated for the no-saving specification, which include a
lower value of the risk parameter ν, also lowers the value of insurance.
Simulating the responses to policy changes, we find that raising the Medicare eligibility
age to 67 leads to an additional 0.075 years of work, an amount almost identical to that of
the baseline specification.

8.2

No Preference Heterogeneity

To assess the importance of preference heterogeneity, we estimate and simulate a model
where individuals have identical preferences (conditional on age and health status). Comparing columns (1), (3) and (5) of Table 10 shows that the model without preference heterogeneity matches aggregate participation rates as well as the baseline model. However, the
no-heterogeneity specification does much less well in replicating the way in which participation varies across the asset distribution, and, not surprisingly, does not replicate the way in
which participation varies across our discretized preference index.
When preferences are homogeneous the simulated response to delaying the Medicare eligibility age, 0.062 years, is similar to the response in the baseline specification. This is
consistent with our analysis in Section 6.4, where not accounting for preference heterogeneity
and insurance self-selection appeared to only modestly change the estimated effects of health
insurance on retirement.

8.3

No Preference Index

In the baseline specification, we use the preference index (described in Section 4.4) to
predict preference type, and the GMM criterion function includes participation rates for
each value of the index. Because labor force participation differs sharply across the index in
ways not predicted by the model’s other state variables, we interpret the index as a measure
of otherwise unobserved preferences toward work. It is possible, however, that using the
preference index causes us to overstate the correlation between health insurance and tastes for
43

leisure. For example, Table 4 shows that employed individuals with retiree coverage are more
likely to have a preference index that is low than employed individuals with tied coverage.
This means that workers with retiree coverage are more likely to report looking forward to
retirement, and thus more likely to be assigned a higher desire for leisure. But workers with
retiree coverage may be more likely to report looking forward to retirement simply because
they would have health insurance and other financial resources during retirement. As a
robustness test, we remove the preference index, and the preference index-related moment
conditions, and re-estimate the model.
Type 0

Type 1

Type 2

Key preference parameters
γ∗
0.405
0.647
0.986
∗
β
0.962
0.858
1.143
Means by preference type
Assets ($1, 000s)
115
231
376
Pension Wealth ($1, 000s)
60
108
85
Wages ($/hour)
11.0
18.4
13.5
Probability of health insurance type, given preference type
Health insurance = none
0.392
0.193
0.394
Health insurance = retiree
0.560
0.633
0.518
Health insurance = tied
0.047
0.174
0.089
Probability of preference index value, given preference type
Preference Index = out
0.523
0.216
0.224
Preference Index = low
0.247
0.399
0.363
Preference Index = high
0.230
0.385
0.413
Fraction with preference type 0.246
0.635
0.119
Table 12: Mean Values by Preference Type, Alternative Specification

Table 12 contains summary statistics for the preference groups generated by this alternative specification. Comparing Table 12 to the baseline results contained in Table 6 reveals that
eliminating the preference index from the type prediction equations changes only modestly
the parameter estimates and the distribution of insurance coverage across the three preference
types. The model without the preference index provides less evidence of self-selection: when
the preference index is removed the fraction of high preference for work, type-2 individuals
with tied coverage falls from 15.8% to 8.9%.
Table 11 shows that excluding the preference index only slightly changes the estimated
44

effect of Medicare and Social Security on labor supply. Given that self-selection has only a
small effect on our results when we include the preference index, it should come as no surprise
that self-selection has only a small effect when we exclude the index.

Conclusion
Prior to age 65, many individuals receive health insurance only if they continue to work.

At age 65, however, Medicare provides health insurance to almost everyone. Therefore, a
potentially important work incentive disappears at age 65. To see if Medicare benefits have
a large effect on retirement behavior, we construct a retirement model that includes health
insurance, uncertain medical costs, a savings decision, a non-negativity constraint on assets
and a government-provided consumption floor.
Using data from the Health and Retirement Study, we estimate the structural parameters
of our model. The model fits the data well, with reasonable preference parameters. In
addition, the model does a satisfactory job of predicting the behavior of individuals who, by
belonging to a younger cohort, faced different Social Security rules than the individuals upon
which the model was estimated.
We find that health care uncertainty significantly affects the value of employer-provided
health insurance. Our calculations suggest that about half of the value workers place on
employer-provided health insurance comes from its ability to reduce medical expense risk.
Furthermore, we find evidence that individuals with higher tastes for leisure are more likely
to choose employers that provide health insurance to early retirees. Nevertheless, we find
that Medicare is important for understanding retirement, especially for workers whose health
insurance is tied to their job. For example, the effects of raising the Medicare eligibility age
to 67 are just as large as the effects of reducing Social Security benefits.

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Appendix A: Cast of Characters
Preference Parameters
γ
consumption weight
β
time discount factor
ν
coefficient of RRA, utility
θB
bequest weight
κ
bequest shifter
Cmin
consumption floor
L
leisure endowment
φH
leisure cost of bad health
φP t
fixed cost of work
φP 0
fixed cost, intercept
φP 1
fixed cost, time trend
φRE
re-entry cost
Decision Variables
Ct
consumption
Nt
hours of work
Lt
leisure
Pt
participation
At
assets
Bt
Social Security application
Financial Variables
Y (·)
after-tax income
τ
tax parameter vector
r
real interest rate
yst
spousal income
ys(·)
mean shifter, spousal income
sst
Social Security income
AIM Et Social Security wealth
pbt
pension benefits

Health-related Parameters
Ht
health status
Mt
out-of-pocket medical expenses
It
health insurance type
m(·) mean shifter, logged medical expenses
σ(·)
volatility shifter, logged medical expenses
ψt
idiosyncratic medical expense shock
ζt
persistent medical expense shock
ǫt
innovation, persistent shockk
ρm
autocorrelation, persistent shock
σǫ2
innovation variance, persistent shock
ξt
transitory medical expense shock
σξ2
variance, transitory shock
Wage-related Parameters
Wt
hourly wage
W (·) mean shifter, logged wages
α
coefficient on hours, logged wages
ωt
idiosyncratic wage shock
ρW
autocorrelation, wage shock
ηt
innovation, wage shock
ση2
innovation variance, wage shock
Miscellaneous
st
survival probability
pref discrete preference index
Xt
state vector, worker’s problem
λ(·)
compensating variation
T
number of years in GMM criterion

Table 13: Variable Definitions, Main Text

Appendix B: Taxes
Individuals pay federal, state, and payroll taxes on income. We compute federal taxes on
income net of state income taxes using the Federal Income Tax tables for “Head of Household”
in 1998. We use the standard deduction, and thus do not allow individuals to defer medical
expenses as an itemized deduction. We also use income taxes for the fairly representative
state of Rhode Island (27.5% of the Federal Income Tax level). Payroll taxes are 7.65% up to
a maximum of $68,400, and are 1.45% thereafter. Adding up the three taxes generates the
following level of post-tax income as a function of labor and asset income:
50

Pre-tax Income (Y)
0-6250
6250-40200
40200-68400
68400-93950
93950-148250
148250-284700
284700+

Post-Tax Income
0.9235Y
5771.88 + 0.7384(Y-6250)
30840.56 + 0.5881(Y-40200)
47424.98 + 0.6501(Y-68400)
64035.03 + 0.6166(Y-93950)
97515.41 + 0.5640(Y-148250)
174474.21 + 0.5239(Y-284700)

Marginal Tax Rate
0.0765
0.2616
0.4119
0.3499
0.3834
0.4360
0.4761

Table 14: After Tax Income

Appendix C: Pensions
Although the HRS pension data allow us to estimate pension wealth with a high degree
of precision, Bellman’s curse of dimensionality prevents us from including in our dynamic
programming model the full range of pension heterogeneity found in the data. Thus we thus
use the pension data to construct a simpler model of pensions. The fundamental equation
behind our model of pensions is the accumulation equation for pension wealth, pwt :

pwt+1 =



 (1/st+1 )[(1 + r)pwt + pacct − pbt ] if living at t + 1

 0

(15)

otherwise

where pacct is pension accrual and pbt is pension benefits. Two features of this equation
bear noting. First, a pension is worthless once an individual dies. Dividing through by the
survival probability st+1 ensures that the expected value of pensions E(pwt+1 |pwt , pacct , pbt )
equals (1 + r)pwt + pacct − pbt , the actuarially fair amount. Second, since pension accrual
and pension interest are not directly taxed, the appropriate rate of return on pension wealth
is the pre-tax one. Pension benefits, on the other hand, are included in the income used to
calculate an individual’s income tax liability.
Simulating equation (15) requires us to know pension benefits and pension accrual. We
calculate pension benefits by assuming that at age t, the pension benefit is

pbt = pft × pbmax
,
t

(16)

where pbmax
is the benefit received by individuals actually receiving pensions (given the
t
earnings history observed at time t) and pft the probability that a person with a pension
is currently drawing pension benefits. We estimate pft as the fraction of respondents who
are covered by a pension that receive pension benefits at each age; the fraction increases
fairly smoothly, except for a 23-percentage-point jump at age 62. To find the annuity pbmax
t
given pension wealth at time t (and assuming no further pension accruals so that pacck = 0
for k = t, t + 1, ..., T ), note first that recursively substituting equation (15) and imposing
pwT +1 = 0 reveals that pension wealth is equal to the present discounted value of future
pension benefits:

pwt =

T
1 X S(k, t)
pfk pbmax
k ,
1+r
(1 + r)k−t

(17)

k=t

where S(k, t) = (1/st )

j=t sj

gives the probability of surviving to age k, conditional on

having survived to time t. If we assume further that the maximum pension benefit is constant
from time t forward, so that pbmax
= pbmax
, k = t, t + 1, ..., T , this equation reduces to
t
k
pwt = Γt pbmax
,
t
T
1 X S(k, t)
pfk .
Γt ≡
1+r
(1 + r)k−t

(18)
(19)

k=t

Using equations (16) and (18), pension benefits are thus given by

pbt = pft Γ−1
t pwt .

(20)

Next, we assume pension accrual is given by

pacct = α0 (It , Wt Nt , t) × Wt Nt ,

(21)

where α0 (.) is the pension accrual rate as a function of health insurance type, labor income,

and age. We estimate α0 (.) in two steps, estimating separately each component of:

α0 = E(pacct |Wt Nt , It , t, pent = 1) Pr(pent = 1|It , Wt Nt )

(22)

where pacct is the accrual rate for those with a pension, and pent is a 0-1 indicator equal to 1
if the individual has a pension.
We estimate the first component, E(pacct |Wt Nt , It , t, pent = 1), from restricted HRS
pension data. To generate a pension accrual rate for each individual, we combine the pension
data with the HRS pension calculator to estimate the pension wealth that each individual
would have if he left his job at different ages. The increase in pension wealth gained by
working one more year is the accrual. Assuming that pension benefits are 0 as long as the
worker continues working, it follows from equation (15) that

pacct = st+1 pwt+1 − (1 + r)pwt .

(23)

The HRS pension data have a high degree of employer- and worker-level detail, allowing us to estimate pension accrual accurately. With accruals in hand, we then estimate
E(pacct |Wt Nt , It , t, pent = 1) by regressing accrual rates on a fourth-order age polynomial,
indicators for age greater than 62 or 65, log income, log income interacted with the age variables, health insurance indicators, and health insurance indicators interacted with the age
variables, using the subset of workers that have a pension on their current job.
Figure 7 shows estimated pension accrual, by health insurance type and earnings. It
shows that those with retiree coverage have the sharpest declines in pension accrual after age
60. It also shows that once health insurance and the probability of having a pension plan are
accounted for, the effect of income on pension accrual is relatively small. Our estimated age
(but not health insurance) pension accrual rates line up closely with Gustman et al. (1998),
who also use the restricted firm-based HRS pension data.
In the second step, we estimate the probability of having a pension, Pr(pent = 1|It , Wt Nt , t),
using unrestricted self-reported data from individuals who are working and are ages 51-55.
53

−.05

Accrual Rate
.05
.1

.15

Pension Accrual Rates, by Age and Health Insurance Type

60
age

retiree
none

tied
one s.d. increase in earnings

Figure 7: Pension Accrual Rates for Individuals with Pensions, by Age, Health Insurance Coverage and Earnings

The function Pr(pent = 1|It , Wt Nt , t) is estimated as a logistic function of log income, health
insurance indicators, and interactions between log income and health insurance.
Table 15 shows the probability of having different types of pensions, conditional on health
insurance. The table shows that only 8% of men with no health insurance have a pension,
but 64% of men with tied coverage and 74% of men with retiree insurance have a pension.
Furthermore, it shows that those with retiree coverage are also the most likely to have defined
benefit (DB) pension plans, which provide the strongest retirement incentives after age 62.
Variable
Defined Benefit
Defined Contribution
Both DB and DC
Total
Number of
Observations

Probability of Pension Type
No Insurance Retiree Insurance Tied Insurance
.026
.412
.260
.050
.172
.270
.006
.160
.106
.082
.744
.636
343

955

369

Table 15: Probability of having a pension on the current job, by health insurance
type, working men, age 51-55

Combining the restricted data with the HRS pension calculator also yields initial pension
balances as of 1992. Mean pension wealth in our estimation sample is $93,300. Disaggregating
54

by health insurance type, those with retiree coverage have $129,200, those with tied coverage
have $80,000, and those with none have $17,300. With these starting values, we simulate
pension wealth in our dynamic programming model with equation (15), using equation (21)
to estimate pension accrual, and using equation (20) to estimate pension benefits. Using these
equations, it is straightforward to track and record the pension balances of each simulated
individual.
But even though it is straightforward to use equation (15) when computing pension wealth
in the simulations, it is too computationally burdensome to include pension wealth as a
separate state variable when computing the decision rules. Our approach is to impute pension
wealth as a function of age and AIME. In particular, we impute a worker’s annual pension
benefits as a function of his Social Security benefits:

b (P IAt , It−1 , t) =
pb
t

[γ0,k,0 + γ0,k,1 t + γ0,k,2 t2 ] · 1{It−1 = k}

k∈{retiree,tied,none}

+ γ3 P IAt + [γ4,0 + γ4,1 t + γ4,2 t2 ] · max{0, P IAt − 9, 999.6}
+ [γ5,0 + γ5,1 t + γ5,2 t2 ] · max{0, P IAt − 14, 359.9},

(24)

where P IAt is the Social Security benefit the worker would get if he were drawing benefits at
time t; as shown in Appendix D below, PIA is a monotonic function of AIME. Using equations
b . Equation (24) is estimated with
(18) and (24) yields imputed pension wealth, pw
c t = Γt pb
t

regressions on simulated data generated by the model. Since these simulated data depend
on the γ’s—pw
c t affects the decision rules used in the simulations—the γ’s solve a fixed-point
problem. Fortunately, estimates of the γ’s converge after a few iterations.

This imputation process raises two complications. The first is that we use a different
pension wealth imputation formula when calculating decision rules than we do in the simulations. If an individual’s time-t pension wealth is pw
c t , his time-t + 1 pension wealth (if living)

should be

c
c t + pacct − pbt ].
pw
c t+1 = (1/st+1 )[(1 + r)pw
55

This quantity, however, might differ from the pension wealth that would be imputed using
b t+1 where pb
b t+1 is defined in equation (24). To correct for this, we
P IAt+1 , pw
c t+1 = Γt+1 pb

c
increase non-pension wealth, At+1 , by st+1 (1 − τt )(pw
c t+1 − pw
c t+1 ). The first term in this

expression reflects the fact that while non-pension assets can be bequeathed, pension wealth

cannot. The second term, 1 − τt , reflects the fact that pension wealth is a pre-tax quantity—
pension benefits are more or less wholly taxable—while non-pension wealth is post-tax—taxes
are levied only on interest income.
A second problem is that while an individual’s Social Security application decision affects
his annual Social Security benefits, it should not affect his pension benefits. (Recall that we
reduce PIA if an individual draws benefits before age 65.) The pension imputation procedure
we use, however, would imply that it does. We counter this problem by recalculating PIA
when the individual begins drawing Social Security benefits. In particular, suppose that a
decision to accelerate or defer application changes P IAt to remt P IAt . Our approach is to
use equation (24) find a value P IA∗t such that
b (P IA∗ ) + P IA∗ = (1 − τt )pb
b (P IAt ) + remt P IAt ,
(1 − τt )pb
t
t
t
t
so that the change in the sum of PIA and imputed after-tax pension income equals just the
change in PIA, i.e., (1 − remt )P IAt .

Appendix D: Computation of AIME
We model several key aspects of Social Security benefits. First, Social Security benefits
are based on the individual’s 35 highest earnings years, relative to average wages in the
economy during those years. The average earnings over these 35 highest earnings years are
called Average Indexed Monthly Earnings, or AIME. It immediately follows that working
an additional year increases the AIME of an individual with less than 35 years of work.
If an individual has already worked 35 years, he can still increase his AIME by working an
additional year, but only if his current earnings are higher than the lowest earnings embedded
in his current AIME. To account for real wage growth, earnings in earlier years are inflated
56

by the growth rate of average earnings in the overall economy. For the period 1992-1999,
average real wage growth, g, was 0.016 (Committee on Ways and Means, 2000, p. 923). This
indexing stops at the year the worker turns 60, however, and earnings accrued after age 60
are not rescaled.24 Furthermore, AIME is capped. In 1998, the base year for the analysis,
the maximum AIME level was $68,400.
Precisely modelling these mechanics would require us to keep track of a worker’s entire
earnings history, which is computationally infeasible. As an approximation, we assume that
(for workers beneath the maximum) annualized AIME is given by

AIM Et+1 = (1 + g × 1{t ≤ 60})AIM Et
+

1
max 0, Wt Nt − αt (1 + g × 1{t ≤ 60})AIM Et ,
35

(25)

where the parameter αt approximates the ratio of the lowest earnings year to AIM E. We
assume that 20% of the workers enter the labor force each year between ages 21 and 25, so
that αt = 0 for workers aged 55 and younger. For workers aged 60 and older, earnings update AIM Et only if current earnings replace the lowest year of earnings, so we estimate αt by
simulating wage (not earnings) histories with the model developed in French (2005), calculat
ing the sequence 1{time-t earnings do not increase AIM Et } t≥60 for each simulated wage

history, and estimating αt as the average of this indicator at each age. Linear interpolation
yields α56 through α59 .
AIME is converted into a Primary Insurance Amount (PIA) using the formula



0.9 × AIM Et
if AIM Et < $5, 724



P IAt =
$5, 151.6 + 0.32 × (AIM Et − 5, 724)
if $5, 724 ≤ AIM Et < $34, 500




 $14, 359.9 + 0.15 × (AIM E − 34, 500) if AIM E ≥ $34, 500
t
t

(26)

Social Security benefits sst depend both upon the age at which the individual first receives
24

After age 62, nominal benefits increase at the rate of inflation.

Social Security benefits and the Primary Insurance Amount. For example, pre-Earnings Test
benefits for a Social Security beneficiary will be equal to PIA if the individual first receives
benefits at age 65. For every year before age 65 the individual first draws benefits, benefits
are reduced by 6.67% and for every year (up until age 70) that benefit receipt is delayed,
benefits increase by 5.0%. The effects of early or late application can be modelled as changes
in AIME rather than changes in PIA, eliminating the need to include age at application as a
state variable. For example, if an individual begins drawing benefits at age 62, his adjusted
AIME must result in a PIA that is only 80% of the PIA he would have received had he first
drawn benefits at age 65. Using equation (26), this is easy to find.

Appendix E: Numerical Methods
Because the model has no closed form solution, the decision rules it generates must be
found numerically. We find the decision rules using value function iteration, starting at time
T and working backwards to time 1. We find the time-T decisions by maximizing equation
(14) at each value of XT , with VT +1 = b(AT +1 ). This yields decision rules for time T and the
value function VT . We next find the decision rules at time T − 1 by solving equation (14),
having solved for VT already. Continuing this backwards induction yields decision rules for
times T − 2, T − 3, ..., 1.
The value function is directly computed at a finite number of points within a grid,
{Xi }Ii=1 ;25 We use linear interpolation within the grid (i.e., we take a weighted average of the
value functions of the surrounding gridpoints) and linear extrapolation outside of the grid to
evaluate the value function at points that we do not directly compute. Because changes in
assets and AIME are likely to cause larger behavioral responses at low levels of assets and
AIME, the grid is more finely discretized in this region.
25

In practice, the grid consists of: 32 asset states, Ah ∈ [−$55,000, $1, 200,000]; 5 wage residual states,
ωi ∈ [−0.99, 0.99]; 16 AIME states, AIM Ej ∈ [$4,000, $68,400]; 3 states for the persistent component of
medical expenses, ζk , over a normalized (unit variance) interval of [−1.5, 1.5]. There are also two application
states, two health states, and two states for participation in the previous period. This requires solving the
value function at 61, 440 different points for ages 62-69, when the individual is eligible to apply for benefits, at
31, 260 points before age 62 (when application is not an option) or at ages 70-71 (when we impose application),
and at 15, 360 points after age 71 (when we impose retirement as well).

At time t, wages, medical expenses and assets at time t + 1 will be random variables.
To capture uncertainty over the persistent components of medical expenses and wages, we
convert ζt and ωt+1 into discrete Markov chains, following the approach of Tauchen (1986);
using discretization rather than quadrature greatly reduces the number of times one has to
interpolate when calculating Et (V (Xt+1 )). We integrate the value function with respect to
the transitory component of medical expenses, ξt , using 5-node Gauss-Hermite quadrature
(see Judd, 1999).
Because of the fixed time cost of work and the discrete benefit application decision, the
value function need not be globally concave. This means that we cannot find a worker’s optimal consumption and hours with fast hill climbing algorithms. Our approach is to discretize
the consumption and labor supply decision space and to search over this grid. Experimenting
with the fineness of the grids suggested that the grids we used produced reasonable approximations.26 In particular, increasing the number of grid points seemed to have a small effect
on the computed decision rules.
We then use the decision rules to generate simulated time series. Given the realized state
vector Xi0 , individual i’s realized decisions at time 0 are found by evaluating the time-0 decision functions at Xi0 . Using the transition functions given by equations (4) through (13),
we combine Xi0 , the time-0 decisions, and the individual i’s time-1 shocks to get the time-1
state vector, Xi1 . Continuing this forward induction yields a life cycle history for individual i. When Xit does not lie exactly on the state grid, we use interpolation or extrapolation
to calculate the decision rules. This is true for ζt and ωt as well. While these processes
are approximated as finite Markov chains when the decision rules are found, the simulated
sequences of ζt and ωt are generated from continuous processes. This makes the simulated life
26

The consumption grid has 100 points, and the hours grid is broken into 500-hour intervals. When this grid
is used, the consumption search at a value of the state vector X for time t is centered around the consumption
gridpoint that was optimal for the same value of X at time t + 1. (Recall that we solve the model backwards in
time.) If the search yields a maximizing value near the edge of the search grid, the grid is reoriented and the
search continued. We begin our search for optimal hours at the level of hours that sets the marginal rate of
substitution between consumption and leisure equal to the wage. We then try 6 different hours choices in the
neighborhood of the initial hours guess. Because of the fixed cost of work, we also evaluate the value function
at Nt = 0, searching around the consumption choice that was optimal when Ht+1 = 0. Once these values are
found, we perform a quick, “second-pass” search in a neighborhood around them.

cycle profiles less sensitive to the discretization of ζt and ωt than when ζt and ωt are drawn
from Markov chains.
Finally, to reduce the computational burden, we assume that all workers apply for Social
Security benefits by age 70, and retire by age 72: for t ≥ 70, Bt = 1; and for t ≥ 72, Nt = 0.

Appendix F: Moment Conditions, Estimation Mechanics, and the Asymptotic Distribution of Parameter Estimates
Following Gourinchas and Parker (2002) and French (2005), we estimate the parameters
of the model in two steps. In the first step we estimate or calibrate parameters that can be
cleanly identified without explicitly using our model. For example, we estimate mortality
rates and health transitions from demographic data. As a matter of notation, we call this set
of parameters χ. In the second step, we estimate the vector of “preference” parameters, θ =

γ0 , γ1 , γ2 , β0 , β1 , β2 , ν, L, φP 0 , φP 1 , φRE , θB , κ, Cmin , preference type prediction coefficients , using the method of simulated moments (MSM).

We assume that the “true” preference vector θ0 lies in the interior of the compact set
Θ ⊂ R39 . Our estimate, θ̂, is the value of θ that minimizes the (weighted) distance between
the estimated life cycle profiles for assets, hours, and participation found in the data and the
simulated profiles generated by the model. We match 21T moment conditions. They are,
for each age t ∈ {1, ..., T }: two asset quantiles (forming 2T moment conditions), labor force
participation rates conditional on asset quantile and health insurance type (9T ), labor market
exit rates for each health insurance type (3T ), labor force participation rates conditional on
the preference indicator described in the main text (3T ), and labor force participation rates
and mean hours worked conditional upon health status (4T ).
Consider first the asset quantiles. As stated in the main text, let j ∈ {1, 2, ..., J} index asset quantiles, where J is the total number of asset quantiles. Assuming that the
age-conditional distribution of assets is continuous, the πj -th age-conditional asset quantile,
Qπj (Ait , t), is defined as

Pr Ait ≤ Qπj (Ait , t)|t = πj .
In other words, the fraction of age-t individuals with less than Qπj in assets is πj . As is
well known (see, e.g., Manski, 1988, Powell, 1994 or Buchinsky, 1998; or the review in Chernozhukov and Hansen, 2002), the preceding equation can be rewritten as a moment condition

by using the indicator function:

E 1{Ait ≤ Qπj (Ait , t)}|t = πj .

(27)

The model analog to Qπj (Ait , t) is gπj (t; θ0 , χ0 ), the jth quantile of the simulated asset
distribution. If the model is true then the data quantile in equation (27) can be replaced by
the model quantile, and equation (27) can be rewritten as:

E 1{Ait ≤ gπj (t; θ0 , χ0 )} − πj |t = 0,

j ∈ {1, 2, ..., J}, t ∈ {1, ..., T }.

(28)

Since J = 2, equation (28) generates 2T moment conditions.
Equation (28) is a departure from the usual practice of minimizing a sum of weighted
absolute errors in quantile estimation. The quantile restrictions just described, however, are
part of a larger set of moment conditions, which means that we can no longer estimate θ by
minimizing weighted absolute errors. Our approach to handling multiple quantiles is similar
to the minimum distance framework used by Epple and Seig (1999).27
The next set of moment conditions uses the quantile-conditional means of labor force
participation. Let P j (I, t; θ0 , χ0 ) denote the model’s prediction of labor force participation
given asset quantile interval j, health insurance type I, and age t. If the model is true,
P j (I, t; θ0 , χ0 ) should equal the conditional participation rates found in the data:

P j (I, t; θ0 , χ0 ) = E[Pit | I, t, gπj−1 (t; θ0 , χ0 ) ≤ Ait ≤ gπj (t; θ0 , χ0 )],

(29)

with π0 = 0 and πJ+1 = 1. Using indicator function notation, we can convert this conditional
27

Buchinsky (1998) shows that one could include the first-order conditions from multiple absolute value
minimization problems in the moment set. However, his approach involves finding the gradient of gπj (t; θ, χ)
at each step of the minimization search.

moment equation into an unconditional one (e.g., Chamberlain, 1992):

E([Pit − P j (I, t; θ0 , χ0 )] × 1{Iit = I}
× 1{gπj−1 (t; θ0 , χ0 ) ≤ Ait ≤ gπj (t; θ0 , χ0 )} | t) = 0,

(30)

for j ∈ {1, 2, ..., J + 1} , I ∈ {none, retiree, tied}, t ∈ {1, ..., T }. Note that gπ0 (t) ≡ −∞
and gπJ +1 (t) ≡ ∞. With 2 quantiles (generating 3 quantile-conditional means) and 3 health
insurance types, equation (29) generates 9T moment conditions.
As described in Appendix J, we use HRS attitudinal questions to construct the preference
index pref ∈ {high, low, out}. Considering how participation varies across this index leads
to the following moment condition:

E Pit − P (pref, t; θ0 , χ0 ) | prefi = pref, t = 0,

(31)

for t ∈ {1, ..., T }, pref ∈ {0, 1, 2}. Equation (31) yields 3T moment conditions, which are
converted into unconditional moment equations with indicator functions.
We also match exit rates for each health insurance category. Let EX(I, t; θ0 , χ0 ) denote
the fraction of time-t−1 workers predicted to leave the labor market at time t. The associated
moment condition is

E [1 − Pit ] − EX(I, t; θ0 , χ0 | Ii,60 = I, Pi,t−1 = 1, t = 0,

(32)

for I ∈ {none, retiree, tied}, t ∈ {1, ..., T }. Equation (32) generates 3T moment conditions,
which are converted into unconditional moments as well.28
Finally, consider health-conditional hours and participation. Let ln N(H, t; θ0 , χ0 ) and
P (H, t; θ0 , χ0 ) denote the conditional expectation functions for hours (when working) and
28
Because exit rates apply only to those working in the previous period, they normally do not contain the
same information as participation rates. However, this is not the case for workers with tied coverage, as
a worker stays in the tied category only as long as he continues to work. To remove this redundancy, the
exit rates in equation (32) are conditioned on the individual’s age-60 health insurance coverage, while the
participation rates in equation (29) are conditioned on the individual’s current coverage.

participation generated by the model for workers with health status H; let ln Nit and Pit
denote measured hours and participation. The moment conditions are

E ln Nit − ln N (H, t; θ0 , χ0 ) | Pit > 0, Hit = H, t = 0,

E Pit − P (H, t; θ0 , χ0 ) | Hit = H, t = 0,

(33)
(34)

for t ∈ {1, ..., T }, H ∈ {0, 1}. Equations (33) and (34), once again converted into unconditional form, yield 4T moment conditions, for a grand total of 21T moment conditions.
Combining all the moment conditions described here is straightforward: we simply stack
the moment conditions and estimate jointly.
Suppose we have a data set of I independent individuals that are each observed for T periods. Let ϕ(θ; χ0 ) denote the 21T -element vector of moment conditions that was described
in the main text and immediately above, and let ϕ̂I (.) denote its sample analog. Note that
we can extend our results to an unbalanced panel, as we must do in the empirical work, by
simply allowing some of the individual’s contributions to ϕ(.) to be “missing”, as in French
c I denote a 21T × 21T weighting matrix, the MSM estimator θ̂
and Jones (2004a). Letting W
is given by

arg min
θ

I
c I ϕ̂I (θ, χ0 ),
ϕ̂I (θ, χ0 )′ W
1+τ

(35)

where τ is the ratio of the number of observations to the number of simulated observations.
To find the solution to equation (35), we proceed as follows:
1. We aggregate the sample data into life cycle profiles for hours, participation, exit rates
and assets.
2. Using the same data used to estimate the profiles, we generate an initial distribution
for health, health insurance status, wages, medical expenses, AIME, and assets. See
Appendix G for details. We also use these data to estimate many of the parameters
contained in the belief vector χ, although we calibrate other parameters. The initial
64

distribution also includes preference type, assigned using our type prediction equation.
3. Using χ, we generate matrices of random health, wage, mortality and medical expense
shocks. The matrices hold shocks for 90,000 simulated individuals.
4. We compute the decision rules for an initial guess of the parameter vector θ, using χ
and the numerical methods described in Appendix E.
5. We simulate profiles for the decision variables. Each simulated individual receives a
draw of preference type, assets, health, wages and medical expenses from the initial
distribution, and is assigned one of the simulated sequences of health, wage and medical
expense shocks. With the initial distributions and the sequence of shocks, we then use
the decision rules to generate that person’s decisions over the life cycle. Each period’s
decisions determine the conditional distribution of the next period’s states, and the
simulated shocks pin the states down exactly.
6. We aggregate the simulated data into life cycle profiles.
7. We compute moment conditions, i.e., we find the distance between the simulated and
true profiles, as described in equation (35).
8. We pick a new value of θ, update the simulated distribution of preference types, and
repeat steps 4-7 until we find the value of θ that minimize that minimizes the distance
between the true data and the simulated data. This vector of parameter values, θ̂, is
our estimated value of θ0 .29
Under the regularity conditions stated in Pakes and Pollard (1989) and Duffie and Singleton (1993), the MSM estimator θ̂ is both consistent and asymptotically normally distributed:
√

I(θ̂ − θ0 )

N (0, V),

Because the GMM criterion function is discontinuous, we search over the parameter space using a Simplex
algorithm written by Honore and Kyriazidou. It usually takes 2-4 weeks to estimate the model on a 48-node
cluster, with each iteration (of steps 4-7) taking around 15 minutes.

with the variance-covariance matrix V given by

V = (1 + τ )(D′ WD)−1 D′ WSWD(D′ WD)−1 ,

where: S is the 21T × 21T variance-covariance matrix of the data;
D=

∂ϕ(θ, χ0 )
∂θ ′

(36)
θ=θ0

c I }.
is the 21T × 39 Jacobian matrix of the population moment vector; and W = plim→∞ {W

Moreover, Newey (1985) shows that if the model is properly specified,
I
ϕ̂I (θ̂, χ0 )′ R−1 ϕ̂I (θ̂, χ0 )
1+τ

χ221T −39 ,

where R−1 is the generalized inverse of

R = PSP,
P = I − D(D′ WD)−1 D′ W.
c I converges to S−1 , the
The asymptotically efficient weighting matrix arises when W

inverse of the variance-covariance matrix of the data. When W = S−1 , V simplifies to
(1 + τ )(D′ S−1 D)−1 , and R is replaced with S. But even though the optimal weighting
matrix is asymptotically efficient, it can be severely biased in small samples. (See, for example,
Altonji and Segal, 1996.) We thus use a “diagonal” weighting matrix, as suggested by Pischke

(1995). The diagonal weighting scheme uses the inverse of the matrix that is the same as S
along the diagonal and has zeros off the diagonal of the matrix.
We estimate D, S and W with their sample analogs. For example, our estimate of S is the
21T × 21T estimated variance-covariance matrix of the sample data. That is, one diagonal
b I will be the variance estimate 1 PI [1{Ait ≤ Qπ (Ait , t)}− πj ]2 , while a typical
element of S
j
i=1
I

off-diagonal element is a covariance. When estimating parameters, we use sample statistics,

b π (Ait , t). When computing the
so that Qπj (Ait , t) is replaced with the sample quantile Q
j

chi-square statistic and the standard errors, we use model predictions, so that Qπj is replaced

with its simulated counterpart, gπj (t; θ̂, χ̂). Covariances between asset quantiles and hours
and labor force participation are also simple to compute.
The gradient in equation (36) is straightforward to estimate for most moment conditions;
we merely take numerical derivatives of ϕ̂I (.). However, in the case of the asset quantiles and
quantile-conditional labor force participation, discontinuities make the function ϕ̂I (.) nondifferentiable at certain data points. Therefore, our results do not follow from the standard
GMM approach, but rather the approach for non-smooth functions described in Pakes and
Pollard (1989), Newey and McFadden (1994, section 7) and Powell (1994). We find the asset
quantile component of D by rewriting equation (28) as

F (gπj (t; θ0 , χ0 )|t) − πj = 0,
where F (gπj (t; θ0 , χ0 )|t) is the empirical c.d.f. of time-t assets evaluated at the modelpredicted πj -th quantile. Differentiating this equation yields

Djt = f (gπj (t; θ0 , χ0 )|t)

∂gπj (t; θ0 , χ0 )
,
∂θ ′

(37)

where Djt is the row of D corresponding to the πj -th quantile at year t. In practice we find
f (gπj (t; θ0 , χ0 )|t), the p.d.f. of time-t assets evaluated at the πj -th quantile, with a kernel
density estimator. We use a kernel estimator for GAUSS written by Ruud Koning.
To find the component of the matrix D for the asset-conditional labor force participation
rates, it is helpful to write equation (30) as

Pr(It−1 = I) ×

gπj (t;θ0 ,χ0 )
gπj−1 (t;θ0 ,χ0 )

E(Pit |Ait , I, t) − P j (I, t; θ0 , χ0 ) f (Ait |I, t)dAit = 0,

which implies that

Djt = − Pr(gπj−1 (t; θ0 , χ0 ) ≤ Ait ≤ gπj (t; θ0 , χ0 )|I, t)

∂P j (I, t; θ0 , χ0 )
∂θ ′

+ [E(Pit |gπj (t; θ0 , χ0 ), I, t) − P j (I, t; θ0 , χ0 )]f (gπj (t; θ0 , χ0 )|I, t)

∂gπj (t; θ0 , χ0 )

∂θ ′

∂gπj−1 (t; θ0 , χ0 )
− [E(Pit |gπj−1 (t; θ0 , χ0 ), I, t) − P j (I, t; θ0 , χ0 )]f (gπj −1 (t; θ0 , χ0 )|I, t)
∂θ ′
× Pr(It−1 = I),
with f (gπ0 (t; θ0 , χ0 )|I, t)

(38)
∂gπ0 (t;θ0 ,χ0 )
∂θ ′

= f (gπJ +1 (t; θ0 , χ0 )|I, t)

∂gπJ +1 (t;θ0 ,χ0 )
∂θ ′

≡ 0.

Appendix G: Data and Initial Joint Distribution of the State Variables
Our data are drawn from the HRS, a sample of non-institutionalized individuals aged
51-61 in 1992. The HRS surveys individuals every two years; we have 8 waves of data
covering the period 1992-2006. We use men in the analysis.
We dropped respondents for the following reasons. First, we drop all individuals who
spent over 5 years working for an employer who did not contribute to Social Security. These
individuals usually work for state governments. We drop these people because they often
have very little in the way of Social Security wealth, but a great deal of pension wealth, a
type of heterogeneity our model is not well suited to handle. Second, we drop respondents
with missing information on health insurance, labor force participation, hours, and assets.
When estimating labor force participation by asset quantile and health insurance for those
born 1931-35 for the estimation sample [and 1936-41 for the validation sample], we begin
with 21,376 [36,702] person year observations. We lose 3,872 [6,919] observations because
of missing labor force participation, 2,109 [2,480] observations who worked over 5 years for
firms that did not contribute to Social Security, 602 [1,074] observations due to missing
wave 1 labor force participation (needed to construct the preference index), and 2,103 [3,023]
observations due to missing health insurance data. In the end, from a potential sample of
21,376 [36,702] person-year observations for those between ages 51 and 69, we keep 12,870
[23,206] observations.
68

The labor market measures used in our analysis are constructed as follows. Hours of work
are the product of usual hours per week and usual weeks per year. To compute hourly wages,
we use information on how respondents are paid, how often they are paid, and how much
they are paid. For salaried workers, annual earnings are the product of pay per period and
the number of pay periods per year. The wage is then annual earnings divided by annual
hours. If the worker is hourly, we use his reported hourly wage. We treat a worker’s hours
for the non-survey (e.g. 1993) years as missing.
For survey years the individual is considered in the labor force if he reports working over
300 hours per year. The HRS also asks respondents retrospective questions about their work
history. Because we are particularly interested in labor force participation, we use the work
history to construct a measure of whether the individual worked in non-survey years. For
example, if an individual withdraws from the labor force between 1992 and 1994, we use the
1994 interview to infer whether the individual was working in 1993.
The HRS has a comprehensive asset measure. It includes the value of housing, other real
estate, autos, liquid assets (which includes money market accounts, savings accounts, T-bills,
etc.), IRAs, stocks, business wealth, bonds, and “other” assets, less the value of debts. For
non-survey years, we assume that assets take on the value reported in the preceding year.
This implies, for example, that we use the 1992 asset level as a proxy for the 1993 asset level.
Given that wealth changes rather slowly over time, these imputations should not severely
bias our results.
Medical expenses are the sum of insurance premia paid by households, drug costs, and
out-of-pocket costs for hospital, nursing home care, doctor visits, dental visits, and outpatient
care. As noted in the text, the proper measure of medical expenses for our model includes
payments made by Medicaid. Although individuals in the HRS report whether they received
Medicaid, they do not report the payments. The 2000 Green Book (Committee on Ways and
Means, 2000, p. 923) reports that in 1998 the average Medicaid payment was $10,242 per
beneficiary aged 65 and older, and $9,097 per blind or disabled beneficiary. Starting with
this average, we then assume that Medicaid payments have the same volatility as the medical
69

care payments made by uninsured households. This allows us to generate a distribution of
Medicaid payments.
To measure health status we use responses to the question: “would you say that your
health is excellent, very good, good, fair, or poor?” We consider the individual in bad health
if he responds “fair” or “poor”, and consider him in good health otherwise.30 We treat the
health status for non-survey years as missing. Appendix H describes how we construct the
health insurance indicator.
We use Social Security Administration earnings histories to construct AIME. Approximately 74% of our sample released their Social Security Number to the HRS, which allowed
them to be linked to their Social Security earnings histories. For those who did not release
their histories, we use the procedure described below to impute AIME as a function of assets,
health status, health insurance type, labor force participation, and pension type.
The HRS collects pension data from both workers and employers. The HRS asks individuals about their earnings, tenure, contributions to defined contribution (DC) plans, and
their employers. HRS researchers then ask employers about the pension plans they offer
their employees. If the employer offers different plans to different employees, the employee is
matched to the plan based on other factors, such as union status. Given tenure, earnings, DC
contributions, and pension plan descriptions, it is then possible to calculate pension wealth
for each individual who reports the firm he works for. Following Scholz et al. (2006), we use
firm reports of defined benefit (DB) pension wealth and individual reports of DC pension
wealth if they exist. If not, we use firm-reported DC wealth and impute DB wealth as a
function of wages, hours, tenure, health insurance type, whether the respondent also has a
DC plan, health status, age, assets, industry and occupation. We discuss the imputation
procedure below.
Workers are asked about two different jobs: (1) their current job if working or last job if
not working; (2) the job preceding the one listed in part 1, if the individual worked at that job
for over 5 years. Pension wealth from both of these jobs are included in our measure of pension
30

Bound et al. (2003) consider a more detailed measure of health status.

wealth. Below we give descriptives for our estimation sample (born 1931-1935) and validation
sample (born 1936-1941). 41% of our estimation sample [and 52% of our validation sample]
are currently working and have a pension (of which 56% [57% for the validation sample] have
firm-based pension details), 6% [5%] are not working, and had a pension on their last job (of
which 62% [62%] have firm-based pension details), and 32% [32%] of all individuals had a
pension on another job (of which 35% [29%] have firm-based pension details).
To generate the initial joint distribution of assets, wages, AIME, pensions, participation,
health insurance, health status and medical expenses, we draw random vectors (i.e., random
draws of individuals) from the empirical joint distribution of these variables for individuals aged 57-61 in 1992, or 1,701 observations. We drop observations with missing data on
labor force participation, health status, insurance, assets, and age. We impute values for
observations with missing wages, medical expenses, pension wealth, and AIME.
To impute these missing variables, we follow David et al. (1986) and Little (1988) and use
the following predictive mean matching regression approach. First, we regress the variable of
interest y (e.g., pension wealth) on the vector of observable variables x, yielding y = xβ + ǫ.
Second, for each sample member i we calculate the predicted value ŷi = xi β̂, and for each
member with an observed value of yi we calculate the residual ε̂i = yi − ŷi . Third, we sort
the predicted value ŷi into deciles. Fourth, for missing observations, we impute εi by finding
a random individual j with a value of ŷj in the same decile as ŷi , and setting εi = ε̂j . The
imputed value of yi is ŷi + ε̂j .
As David et al. (1986) point out, our imputation approach is equivalent to hot-decking
when the “x” variables are discretized and include a full set of interactions. The advantages of
our approach over hot-decking are two-fold. First, many of the “x” variables are continuous,
and it seems unwise to discretize them. Second, we have very few observations for some
variables (such as pension wealth on past jobs), and hot-decking is very data-intensive. A
small number of “x” variables generate a large number of hot-decking cells, as hot-decking
uses a full set of interactions. We found that the interaction terms are relatively unimportant,
but adding extra variables were very important for improving goodness of fit when imputing
71

pension wealth.
If someone is not working (and thus does not report a wage), we use the wage on their
last job as a proxy for their current wage if it exists, and otherwise impute the log wage
as a function of assets, health, health insurance type, labor force participation, AIME, and
quarters of covered work. We predict medical expenses using assets, health, health insurance
type, labor force participation, AIME, and quarters of covered earnings.
Lastly, we must infer the persistent component of the medical expense residual from
medical expenses. Given an initial distribution of medical expenses, we construct ζt , the
persistent medical expense component, by first finding the normalized log deviation ψt , as
described in equations (7) and (10), and then applying standard projection formulae to impute
ζt from ψt .

Appendix H: Measurement of Health Insurance Type and Labor Force Participation
Much of the identification in this paper comes from differences in medical expenses and job
exit rates between those with tied health insurance coverage and those with retiree coverage.
Unfortunately, identifying these health insurance types is not straightforward. The HRS has
rather detailed questions about health insurance, but the questions asked vary from wave to
wave. Moreover, in no wave are the questions asked consistent with our definitions of tied or
retiree coverage. Fortunately, our estimated health insurance specific job exit rates are not
very sensitive to our definition of health insurance, as we show below.
In all of the HRS waves (but not AHEAD waves 1 and 2), the respondent is asked whether
he has insurance provided by a current or past employer or union, or a spouse’s current or
past employer or union. If he responds no to this question, we code his coverage as none.
We assume that this question is answered accurately, so that there is no measurement error
when individual reports that his insurance category is none. All of the measurement error
problems arise when we allocate individuals with employer-provided coverage between the
retiree and tied categories.
If an individual has employer-provided coverage in waves 1 and 2 he is asked “Is this
72

health insurance available to people who retire?” In waves 3-8 the analogous question is “If
you left your current employer now, could you continue this health insurance coverage up
to the age of 65?”. For individuals younger than 65, the question asked in waves 3-8 is a
more accurate measure of whether the individual has retiree coverage. In particular, a “yes”
response in waves 1 and 2 might mean only that the individual had tied coverage, but could
acquire COBRA coverage if he left his job. Thus the fraction of individuals younger than
65 who report that they have employer-provided health insurance but who answer “no” to
the follow-up question roughly doubles between waves 2 and 3. On the other hand, for those
older than 65, the question used in waves 3-8 is meaningless.
Our preferred approach is to use the wave 1 response to determine who has retiree
coverage. It is possible, however, to estimate the probability of response error to this variable.
Consider first the problem of distinguishing the retiree and tied types for those younger than
65. As a matter of notation, let I denote an individual’s actual health insurance coverage,
and let I ∗ denote the measure of coverage generated by the HRS questions. To simplify the
notation, assume that the individual is known to have employer-provided coverage—I = tied
or I = retiree—so that we can drop the conditioning statement in the analysis below. Recall
that many individuals who report retiree coverage in waves 1 and 2 likely have tied coverage.
We are therefore interested in the misreporting probability Pr(I = tied|I ∗ = retiree, wv <
3, t < 65), where wv denotes HRS wave and t denotes age. To find this quantity, note first
that by the law of total probability:

Pr(I = tied|wv < 3, t < 65) =
Pr(I = tied|I ∗ = tied, wv < 3, t < 65) × Pr(I ∗ = tied|wv < 3, t < 65) +
Pr(I = tied|I ∗ = retiree, wv < 3, t < 65) × Pr(I ∗ = retiree|wv < 3, t < 65).
Now assume that all reports of tied coverage in waves 1 and 2 are true:

Pr(I = tied|I ∗ = tied, wv < 3, t < 65) = 1.

(39)

Assume further that for individuals younger than 65 there is no measurement error in waves
3-8, and that the share of younger individuals with tied coverage is constant across waves:

Pr(I = tied|wv < 3, t < 65) = Pr(I = tied|wv ≥ 3, t < 65)
= Pr(I ∗ = tied|wv ≥ 3, t < 65).
Inserting these assumptions into equation (39) and rearranging yields the mismeasurement
probability:

Pr(I = tied|I ∗ = retiree, wv < 3, t < 65)
=

Pr(I ∗ = tied|wv ≥ 3, t < 65) − Pr(I ∗ = tied|wv < 3, t < 65)
.
Pr(I ∗ = retiree|wv < 3, t < 65)

(40)

To account for mismeasurement in waves 1 and 2 for those 65 and older, we again assume
that all reports of tied health insurance are true. We assume further that Pr(I = tied|I ∗ =
retiree, wv < 3, t ≥ 65) = Pr(I = tied|I ∗ = retiree, wv < 3, t < 65): the fraction of retiree
reports in waves 1 and 2 that are inaccurate is the same across all ages. We can then apply the
mismeasurement probability for people younger than 65, given by equation (40), to retiree
reports by people 65 and older.
The second misreporting problem is that the “follow-up” question in waves 3 through 8
is completely uninformative for those older than 65. Our strategy for handling this problem
is to treat the first observed health insurance status for these individuals as their health
insurance status throughout their lives. Since we assume that reports of tied coverage are
accurate, older individuals reporting tied coverage in waves 1 and 2 are assumed to receive
tied coverage in waves 3 through 8. (Recall, however, that if an individual with tied coverage
drops out of the labor market, his health insurance is none for the rest of his life.) For older
individuals reporting retiree coverage in waves 1 and 2, we assume that the misreporting
probability—when we choose to account for it—is the same throughout all waves. (Recall
that our preferred assumption is to assume that a “yes” response to the follow-up question

in waves 1 and 2 indicates retiree coverage.)
A related problem is that individuals’ health insurance reports often change across waves,
in large part because of the misreporting problems just described. Our preferred approach
for handling this problem is classify individuals on the basis of their first observed health
insurance report. We also consider the approach of classifying individuals on the basis of
their report from the previous wave.
Figure 8 shows how our treatment of these measurement problems affects measured job
exit rates. The top two graphs in Figure 8 do not adjust for measurement error. The bottom
two graphs account for the measurement error problems, using the approached described by
equation (40). The two graphs in the left column use the first observed health insurance
report whereas the graphs in the right column use the previous period’s health insurance
report. Figure 8 shows that the profiles are not very sensitive to these changes. Those with
retiree coverage tend to exit the labor market at age 62, whereas those with tied and no
coverage tend to exit the labor market at age 65.
Another, more conceptual, problem is that the HRS has information on health insurance
outcomes, not choices. This is an important problem for individuals out of the labor force with
no health insurance; it is unclear whether these individuals could have purchased COBRA
coverage but elected not to do so.31 To circumvent this problem we use health insurance in
the previous wave and the transitions implied by equation (10) to predict health insurance
options. For example, if in the previous wave an individual reports working and having
health insurance that is tied to his job, that individual’s choice set is tied health insurance
and working or COBRA insurance and not working.32

For example, the model predicts that all HRS respondents younger than 65 who report having tied health
insurance two years before the survey date, work one year before the survey date, and are not currently
working should report having COBRA coverage on the survey date. However, 19% of them report having no
health insurance.
32
We are assuming that everyone eligible for COBRA takes up coverage. In practice, only about 32 of those
eligible take up coverage (Gruber and Madrian, 1996). In order to determine whether our failure to model the
COBRA decision is important, we shut down the COBRA option (imposed a 0% take-up rate) and re-ran the
model. Eliminating COBRA had virtually no effect on labor supply.

.15

exit rate

.15
.05

.05

exit rate

.25

Robustness Check:
no measurement error corrections, last period’s health insurance

.25

Baseline Case:
no measurement error corrections, use first observed health insurance

age
tied health insurance
no health insurance

retiree health insurance coverage

tied health insurance
no health insurance

retiree health insurance coverage

.15

exit rate

.25

Robustness Check:
measurement error corrections, last period’s health insurance

.25

Robustness Check:
measurement error corrections and first observed health insurance

.05

exit rate

64
age

age
tied health insurance
no health insurance

age
retiree health insurance coverage

tied health insurance
no health insurance

retiree health insurance coverage

Figure 8: Job Exit Rates Using Different Measures of Health Insurance Type

Our preferred specification, which we use in the analysis, is to use the first observed health
insurance report, and to not use the measurement error corrections.
Because agents in our model are forward-looking, we need to know the health-insuranceconditional process for medical expenses facing the very old. The data we use to estimate
medical expenses for those over age 70 comes from the Assets and Health Dynamics of the
Oldest Old survey. French and Jones (2004a) discuss some of the details of the survey, as
well as some of our coding decisions. The main problem with the AHEAD is that there is no
question asked of respondents about whether they would lose their health insurance if they
left their job, so it is not straightforward to distinguish those who have retiree coverage from
those with tied coverage. In order to distinguish these two groups, we do the following. If
the individual exits the labor market during our sample, and has employer-provided health
insurance at least one full year after exiting the labor market, we assume that individual has
retiree coverage. All individuals who have employer-provided coverage when first observed,
but do not meet this criterion for having retiree coverage, are assumed to have tied coverage.
Our measure of labor force participation is based on the values reported at the time of
the interview. We also use the age at the time of the interview. For this reason, some of our
“65-year-olds” are 65 years and 0 days old, whereas others are 65 years and 364 days old.
Blau (1994) shows that most age-65 job exits occur within a few months of the 65th birthday.
Thus, we may be understating the decline in labor supply at age 65, because our participation
measure combines individuals who are exactly 65, who may not have yet left the labor force,
with those who are almost 66, who may have left the labor force market months before.
To investigate how this timing issue affects our estimated job exit rates, we use HRS
labor force histories, which provide the dates at which individuals leave the labor force, to
construct three different measures of participation by age. Figure 9 presents job exit rates
derived with the different measures.
The top left panel of Figure 9 shows job exit rates derived with the measure of participation
that we use in the paper (participation at the time of the interview). In the top right panel,
participation is measured at the time of the respondent’s birthday, so that the job exit rate
77

at age 65 measures the probability that an individual was working on his 64th birthday but
not on his 65th birthday. Relative to the baseline case, the peaks in exit rates at ages 62
and 65 are now less pronounced. The reason for this is that people who report leaving in the
months after a 65th birthday are coded as having left at age 66. For example, an individual
leaving the labor market at age 65 and 1 day would be classified as exiting the labor market
at age 66. As a result, measuring labor force participation at birthdays leads to a higher
estimated job exit rate at 66 and a lower rate at 65 than our baseline approach.
In the bottom left panel of Figure 9, participation is measured at the midpoint between
the respondents’ birthdays. For example, participation at age 65 is measured at age 65

1
2,

so that the job exit rate at age 65 measures the probability that an individual was working
at age 64

1
2

but was not at age 65 12 . This panel looks very similar to the baseline case. In

both cases job exit rates are near 20 percent at ages 62 and 65, and are lower at other ages.
Furthermore, in both cases job exit rates for those with retiree coverage are highest at age
62, whereas job exit rates for those with tied coverage are highest at age 65.
Because it seems extreme to treat an individual who leaves the labor force at age 65 and
1 day as exiting at age 66, we think measuring participation 6 months after a birthday yields
more plausible results. Because measuring participation on survey dates gives similar results
and drops fewer observations than measuring participation 6 months after a birthday, we use
participation on survey dates as our measure of participation throughout.
Another measurement issue is the treatment of the self-employed. Our preferred approach
is to include the self-employed in our analysis, and treat them as working with no health
insurance. The lower lower right panel of Figure 9 shows job exit rates when we drop the self
employed, but measure health insurance as in the baseline case. The main difference caused
by dropping the self-employed is that those with no health insurance have much higher job
exit rates, especially at age 65. Nevertheless, those with retiree coverage are still most likely
to exit at age 62 and those with tied and no health insurance are most likely to exit at age 65.

Robustness Check:
measure participation on birthday

.15

exit rate

.05

.15

exit rate

.25

Baseline Case:
no measurement error corrections, use first observed health insurance

age
tied health insurance
no health insurance

age
retiree health insurance coverage

tied health insurance
no health insurance

retiree health insurance coverage

Robustness Check:
exclude the self−employed

.15

exit rate

.05

exit rate

.15

.25

Robustness Check:
measure participation on birthday plus 6 months

age
tied health insurance
no health insurance

age
retiree health insurance coverage

tied health insurance
no health insurance

retiree health insurance coverage

Figure 9: Job Exit Rates Using Different Measures of Labor Force Participation

Appendix I: The Medical Expense Model
Recall from equation (7) that health status, health insurance type, labor force participation and age affect medical expenses through the mean shifter m(.) and the variance shifter
σ(.). Health status enters m(.) and σ(.) through 0-1 indicators for bad health, and age enters
through linear trends. On the other hand, the effects of Medicare eligibility, health insurance
and labor force participation are almost completely unrestricted, in that we allow for an almost complete set of interactions between these variables. This implies that mean medical
expenses are given by

m(Ht , It , t, Pt ) = γ0 Ht + γ1 t +

X X

γh,P,a .

h∈I P ∈{0,1} a∈{t<65,t≥65}

The one restriction we impose is that γnone,0,a = γnone,1,a for both values of a, i.e., participation does not affect health care costs if the individual does not have insurance. This implies
that there are 10 γh,P,a parameters, for a total of 12 parameters apiece in the m(.) and the
σ(.) functions.
To estimate this model, we group the data into 10-year-age (55-64, 65-74, 75-84) × health
status × health insurance × participation cells. For each of these 60 cells, we calculate both
the mean and the 95th percentile of medical expenses. We estimate the model by finding
the parameter values that best fit this 120-moment collection. One complication is that the
medical expense model we estimate is an annual model, whereas our data are for medical
expenses over two-year intervals. To overcome this problem, we first simulate a panel of
medical expense data at the one-year frequency, using the dynamic parameters from French
and Jones (2004a) shown in Table 3 of this paper and the empirical age distribution. We
then aggregate the simulated data to the two-year frequency; the means and 95th percentiles
of this aggregated data are comparable to the means and 95th percentiles in the HRS. Our
approach is similar to the one used by French and Jones (2004a), who provide a detailed
description.
Table 1 shows some of the summary statistics implied by our medical expense model.

Relative to other research on the cross sectional distribution of medical expenses, we find
higher medical expenses at the far right tail of the distribution. For example, Blau and
Gilleskie (2006) use different data and methods to find average medical expenses that are
comparable to our estimates. However, they find that medical expenses are less volatile
than our estimates suggest. For example, they find that for households in good health and
younger than 65, the maximum expense levels (which seem to be slightly less likely than
0.5% probability events) were $69,260 for those without coverage, $6,400 for those with
retiree coverage, and $6,400 for those with tied coverage. Table 1 shows that our estimates
of the 99.5th percentile (i.e., the top 0.5 percentile of the distribution) of the distributions
for healthy workers are $86,900 for those with no coverage, $32,700 for those with retiree
coverage, and $30,600 for those with tied coverage.
Berk and Monheit (2001) use data from the MEPS, which arguably has the highest quality medical expense data of all the surveys. Analyzing total billable expenses, which should
be comparable to our data for the uninsured, Berk and Monheit find that those in the top
1% of the medical expense distribution have average medical expenses of $57,900 (in 1998
dollars). Again, this is below our estimate of $86,900 for the uninsured. This discrepancy
is not surprising. Berk and Monheit’s estimates are for all individuals in the population,
whereas our estimates are for older households (many of which include two individuals). Furthermore, Berk and Monheit’s estimates exclude all nursing home expenses, while the HRS,
although initially consisting only of non-institutionalized households, captures the nursing
home expenses these households incur in later waves.

Appendix J: The Preference Index
We construct the preference index for each member of the sample using the wave 1 variables V3319, V5009, V9063. All three variables are self-reported responses to questions about
preferences for leisure and work. In V3319 respondents were asked if they agreed with the
statement (if they were working): “Even if I didn’t need the money, I would probably keep
on working.” In V5009 they were asked: “When you think about the time when you [and
your (husband/wife/partner)] will (completely) retire, are you looking forward to it, are you
81

uneasy about it, or what?” In V9063 they were asked (if they were working): “On a scale
where 0 equals dislike a great deal, 10 equals enjoy a great deal, and 5 equals neither like nor
dislike, how much do you enjoy your job?”
Because it is computationally intensive to estimate the parameters of the type probability
equations in our method of simulated moments approach, we combine these three variables
into a single index that is simpler to use. To construct this index, we regress labor force
participation on current state variables (age, wages, assets, health, etc.), squares and interactions of these terms, the wave 1 variables V3319, V5009, V9063, and indicators for whether
these variables are missing. We then partition the xβ̂ matrix from this regression into: x1 βˆ1 ,
where the x1 matrix consists V3319, V5009, V9063, and indicators for these variables being
missing; and x2 βˆ2 , where the x2 matrix contains all the other variables. Our preference index
is x1 βˆ1 .
Individuals who were not working in 1992 were not asked any of the preference questions,
and are not included in the construction of our index. Because everyone who answered the
preference questions worked in 1992, we estimate the regression models with participation
data from 1998-2006.
Finally, we discretize the index into three values: out, for those not employed in 1992; low,
for workers with an index in the bottom half of the distribution; and high for the remainder.

Appendix K: Additional Parameter Estimates
We assume that the probability of belonging to a particular type follows a multinomial
logit function. Table 16 shows the coefficients of the preference type prediction equation. One
interesting feature of this equation is that wealthy individuals who have no health insurance
coverage have a high probability of being Type-2 agents. Given that many of these individuals
are entrepreneurs, it is not surprising that they are often placed in the “motivated” group.
Table 17 shows the parameter estimates for the robustness checks. In the no-saving case,
shown in column (2), β and θB are both very weakly identified. We therefore follow Rust
and Phelan (1997) and Blau and Gilleskie (2006, 2008) by fixing β, in this case to its baseline
values of 0.95, 0.86, and 1.12 (for types 0, 1 and 2, respectively). Similarly, we fix θB to zero.
82

Preference Type 1
Parameters Std. Errors
(1)
(2)
Preference Index = out
Preference Index = low
Preference Index = high
No Insurance Coverage
Retiree Coverage
Initial Health†
Initial Wages†
Assets/Wages†
AIME/Wages†
Health Cost Shock (ψ)
Age – 60
Assets† ×(No Ins. Coverage)
† Variables

-5.33
4.79
2.35
3.35
-0.98
-1.04
2.74
-0.48
-0.25
-1.16
-0.56
-0.53

1.00
2.03
0.80
1.46
0.87
0.35
0.75
0.83
0.70
0.65
0.96
0.37

Preference Type 2
Parameters Std. Errors
(3)
(4)
-7.33
0.18
4.09
-2.45
-0.32
-0.37
-1.01
0.97
-0.21
0.22
1.72
1.41

7.77
1.32
0.73
1.76
0.47
0.27
0.44
0.61
0.44
0.47
1.67
0.54

expressed as fraction of average
Table 16: Preference type prediction coefficients

Since the asset distribution is degenerate in this no-saving case, we no longer match asset
quantiles or quantile-conditional participation rates, matching instead participation rates for
each health insurance category.
Column (4) shows the parameter estimates that result when we remove the preference
index described in Appendix J from our the type prediction equations; we also remove the
preference index-conditional moment conditions from the GMM criterion function. Although
the coefficients of the type prediction equations change dramatically, the estimated preference
parameters change very little.

Parameter and Definition
γ: consumption weight
Type 0
Type 1
Type 2
β: time discount factor
Type 0
Type 1
Type 2
ν: coefficient of relative
risk aversion, utility
θB : bequest weight†
κ: bequest shifter,
in thousands
Cmin : consumption floor
L: leisure endowment,
in hours
φH : hours of leisure lost,
bad health
φP 0 : fixed cost of work:
intercept, in hours
φP 1 : fixed cost of work:
(age – 60), in hours
φRE : hours of leisure lost,
re-entering market
χ2 statistic
Degrees of freedom

No
Preference
Index
(4)

Baseline
(1)

No
Saving
(2)

Homogeneous
Preferences
(3)

0.412
(0.045)
0.649
(0.007)
0.967
(0.203)

0.302
(0.026)
0.583
(0.007)
0.9999
NA

0.945
(0.074)
0.859
(0.013)
1.124
(0.328)
7.49
(0.311)
0.0223
(0.0012)
444
(31.7)
4,380
(167)
4,060
(44)
506
(20.9)
826
(20.0)
54.7
(2.58)
94.0
(8.63)

0.945
(NA)
0.859
(NA)
1.124
(NA)
6.35
(0.174)
0.00
(NA)
0.00
(NA)
4,440
(154)
4,130
(67)
939
(42.2)
880
(24.5)
36.5
(3.10)
77.0
(12.1)

5.78
(0.448)
0.0132
(0.0007)
786
(27.9)
5,000
(169)
4,700
(63)
303
(25.9)
1,146
(36.3)
16.9
(1.27)
155.9
(13.6)

0.962
(0.064)
0.858
(0.014)
1.143
(0.580)
7.61
(0.289)
0.0221
(0.0009)
443
(21.4)
4,430
(214)
4,090
(434)
509
(29.9)
827
(29.2)
52.7
(2.49)
95.6
(24.2)

775
171

398
86

607
169

904
145

0.550
(0.008)
NA

NA
0.970
(0.009)
NA

0.405
(0.041)
0.647
(0.008)
0.986
(0.393)

Diagonal weighting matrix used in calculations. See Appendix F for details.
Standard errors in parentheses.
† Parameter expressed as marginal propensity to consume out of
final-period wealth.
Table 17: Robustness Checks

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How Do Retail Prices React to Minimum Wage Increases?
James M. MacDonald and Daniel Aaronson

WP-00-20

Working Paper Series (continued)
Financial Signal Processing: A Self Calibrating Model
Robert J. Elliott, William C. Hunter and Barbara M. Jamieson

WP-00-21

An Empirical Examination of the Price-Dividend Relation with Dividend Management
Lucy F. Ackert and William C. Hunter

WP-00-22

Savings of Young Parents
Annamaria Lusardi, Ricardo Cossa, and Erin L. Krupka

WP-00-23

The Pitfalls in Inferring Risk from Financial Market Data
Robert R. Bliss

WP-00-24

What Can Account for Fluctuations in the Terms of Trade?
Marianne Baxter and Michael A. Kouparitsas

WP-00-25

Data Revisions and the Identification of Monetary Policy Shocks
Dean Croushore and Charles L. Evans

WP-00-26

Recent Evidence on the Relationship Between Unemployment and Wage Growth
Daniel Aaronson and Daniel Sullivan

WP-00-27

Supplier Relationships and Small Business Use of Trade Credit
Daniel Aaronson, Raphael Bostic, Paul Huck and Robert Townsend

WP-00-28

What are the Short-Run Effects of Increasing Labor Market Flexibility?
Marcelo Veracierto

WP-00-29

Equilibrium Lending Mechanism and Aggregate Activity
Cheng Wang and Ruilin Zhou

WP-00-30

Impact of Independent Directors and the Regulatory Environment on Bank Merger Prices:
Evidence from Takeover Activity in the 1990s
Elijah Brewer III, William E. Jackson III, and Julapa A. Jagtiani

WP-00-31

Does Bank Concentration Lead to Concentration in Industrial Sectors?
Nicola Cetorelli

WP-01-01

On the Fiscal Implications of Twin Crises
Craig Burnside, Martin Eichenbaum and Sergio Rebelo

WP-01-02

Sub-Debt Yield Spreads as Bank Risk Measures
Douglas D. Evanoff and Larry D. Wall

WP-01-03

Productivity Growth in the 1990s: Technology, Utilization, or Adjustment?
Susanto Basu, John G. Fernald and Matthew D. Shapiro

WP-01-04

Do Regulators Search for the Quiet Life? The Relationship Between Regulators and
The Regulated in Banking
Richard J. Rosen

WP-01-05

Working Paper Series (continued)
Learning-by-Doing, Scale Efficiencies, and Financial Performance at Internet-Only Banks
Robert DeYoung
The Role of Real Wages, Productivity, and Fiscal Policy in Germany’s
Great Depression 1928-37
Jonas D. M. Fisher and Andreas Hornstein

WP-01-06

WP-01-07

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy
Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans

WP-01-08

Outsourcing Business Service and the Scope of Local Markets
Yukako Ono

WP-01-09

The Effect of Market Size Structure on Competition: The Case of Small Business Lending
Allen N. Berger, Richard J. Rosen and Gregory F. Udell

WP-01-10

Deregulation, the Internet, and the Competitive Viability of Large Banks and Community Banks WP-01-11
Robert DeYoung and William C. Hunter
Price Ceilings as Focal Points for Tacit Collusion: Evidence from Credit Cards
Christopher R. Knittel and Victor Stango

WP-01-12

Gaps and Triangles
Bernardino Adão, Isabel Correia and Pedro Teles

WP-01-13

A Real Explanation for Heterogeneous Investment Dynamics
Jonas D.M. Fisher

WP-01-14

Recovering Risk Aversion from Options
Robert R. Bliss and Nikolaos Panigirtzoglou

WP-01-15

Economic Determinants of the Nominal Treasury Yield Curve
Charles L. Evans and David Marshall

WP-01-16

Price Level Uniformity in a Random Matching Model with Perfectly Patient Traders
Edward J. Green and Ruilin Zhou

WP-01-17

Earnings Mobility in the US: A New Look at Intergenerational Inequality
Bhashkar Mazumder

WP-01-18

The Effects of Health Insurance and Self-Insurance on Retirement Behavior
Eric French and John Bailey Jones

WP-01-19

Full text of Working Papers (Federal Reserve Bank of Chicago) : The Effects of Health Insurance and Self-Insurance on Retirement Behavior, Working Paper 2001-19

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