The Impact of Health on Labor Supply Near Retirement

Abstract

Estimates of how health affects employment vary considerably. We assess how different methods and health measures impact estimates of the impact of health on employment using a unified framework for the US and England. We find that subjective and objective health measures, and subjective measures instrumented by objective measures produce similar estimates when using sufficiently rich objective measures. Moreover, a single health index can capture the relevant health variation for employment. Health deterioration explains up to 15% of the decline in employment between ages 50 and 70. Effects are larger for the US than England, and for the low educated.

Full text

The impact of health on labor supply near retirement
Richard Blundell
University College London
Jack Britton
Institute for Fiscal Studies
Monica Costa Dias
Institute for Fiscal Studies
Eric French
University College London∗
October 2020
Abstract
Estimates of how health affects employment vary considerably. We assess how different methods
and health measures impact estimates of the impact of health on employment using a unified
framework for the US and England. We find that subjective and objective health measures, and
subjective measures instrumented by objective measures produce similar estimates when using
sufficiently rich objective measures. Moreover, a single health index can capture the relevant
health variation for employment. Health deterioration explains up to 15% of the decline in
employment between ages 50 and 70. Effects are larger for the US than England, and for the
low educated.
I10, J24, J26, E24
Keywords: Health, Cognition, Labor Supply, Retirement
∗Acknowledgements: We thank the editor Donna Gilleskie and two referees, Naoki Aizawa, Robert Moffitt, Robert
Willis, and seminar participants at the Conference on Working Longer at IFS, the ELSA Wave 7 Launch Conference,
Annual Health Econometrics Workshop, and the Netspar Annual Pension Workshop for helpful comments. Financial
support from the Michigan Retirement Research Center (Grant G-2014-13567), the Alfred P. Sloan Foundation, the
Economic and Social Research Council (ESRC Centre for the Microeconomic Analysis of Public Policy at the IFS,
Grant ES/M010147/1, and Grant ES/P001831/1) is gratefully acknowledged. Jack Britton also thanks the British
Academy for financial support, Grant CH00096.0000. The views expressed in this paper are those of the authors and
not necessarily those of the Social Security Administration, the MRRC or the British Academy.
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1 Introduction
Despite the growing literature and the increasing availability of rich data, there is still no consensus
about the importance of health for employment. The existing literature has developed many empir-
ical approaches and applied them to different datasets collected in different contexts. This naturally
led to estimates of the effects of health on employment that differ significantly from study to study.
Currie and Madrian (1999), O’Donnell et al. (2015) and French and Jones (2016) review the em-
pirical evidence and advance some potential explanations for the discrepancies between estimates.
Most of these relate to the measurement and modeling of health.1
Ideally one would like to have a composite index of health representing ‘working capacity’ or
‘health stock’ – a comprehensive description of health status that could be used in a variety of
contexts and facilitate comparisons across studies. The difficulty, of course, resides on the fact
that such an index is not readily observable. This has led to a proliferation of different methods
to proxy it. For instance, some applications adopt a multi-dimensional description of health, with
many variables affecting employment in a flexible way; other applications rely on a constructed
health index that is then related to employment. The type of information used to describe health
also varies across studies. Some use ‘objective’ indicators, which unambiguously describe specific
health conditions (such as arthritis), while others use ‘subjective’ accounts of self-reported health
to obtain a comprehensive measure of health status. Furthermore, there is no agreement about
which specific objective and subjective health variables should be used. Moreover, various modeling
strategies have also been adopted, often resulting in different estimates of the effect of health. For
instance, studies using cross-sectional data tend to focus on the overall impact of health, while
longitudinal data can be used to estimate the impact of changes in health.
Despite the important differences, there is still little systematic research assessing the relative
1Currie and Madrian (1999) state that ‘although the question of how health affects participation has been inten-
sively studied little consensus on the magnitude of the effects has been reached.’ They argue that one key reason
for this is the range of different approaches for measuring health. Table 4 of their paper highlights the range of
estimates. Tables 18.3 and 18.4 of O’Donnell et al. (2015) highlight the same qualitative findings hold from the more
recent literature addressing this question. For example, they show that French (2005) estimates that a work limiting
physical impairment or nervous condition results in a 45ppt reduction in the probability of employment at age 62,
while Smith (2004) estimates that a new major diagnosis is associated with a 15ppt reduction for 50-62 year olds.
Smith (2004) also estimates much small effects for minor diagnoses, aligning with McClellan (1998).
2

merits of the various methods. In this study, we aim to fill this gap by addressing the following
questions. Is the choice of health measure important for measuring its impact on employment?
How should the health measures becoming available in survey data be combined into a health
index? Is a single health measure sufficient to capture the impact of health on employment, or
is it important to allow for multiple measures? Are cross sectional methods appropriate, or is it
necessary to consider individual heterogeneity by accounting for initial conditions?
To answer these questions, we revisit many of the approaches proposed in the literature within
a unified framework. We produce a set of estimates that can be compared across specifications,
and contrast the resulting estimates using formal statistical tests, relating their differences to the
underlying measurement and modeling choices. Specifically, we compare estimates of health effects
obtained by using either subjective measures or objective measures. We deal with various sources
of measurement error, including justification bias, by combining the two sets of health variables
and using the objective measures as instruments for the subjective measures. We recognise that
some of the objective health measures may suffer from the same sources of justification bias as
the subjective health measures, and test for this by restricting the set of instruments to the most
serious conditions that require urgent medical attention. We use principal components and factor
analysis to construct a parsimonious single health index that summarises information from multiple
health measures. An index of the common variation across these variables is likely to be a better
summary of health status than any of the original measures taken individually, and is likely to
be less sensitive to measurement error. We enlarge our empirical model to include cognition, a
dimension that is not typically considered in other studies but that is closely intertwined with
health and may capture a finer detail of how poor health impairs work.
Our empirical analysis is based on two large longitudinal surveys of older people, the US Health
and Retirement Study (HRS) and the English Longitudinal Study of Ageing (ELSA). These are
high-quality longitudinal datasets that include many different measures of health, all key requisites
to support the replication of the alternative measures and models of health and employment used in
past studies. Moreover, their very similar structures and information supports the use of harmonized
3

measures and estimation procedures in producing comparable estimates for the two countries.
Our key findings are as follows. First, we find that objective and subjective health measures
deliver similar estimates if a sufficiently large set of objective measures is used; controlling for
only a limited number of health conditions, however, may reduce the estimated impact of health on
employment by two thirds. Second, we find that a single health index, while sometimes rejected from
a statistical standpoint, produces estimates of the effect of health on employment that are similar
to those obtained using multiple health indexes. Third, using objective measures to instrument
for subjective measures also produces similar, although slightly larger estimates. Fourth, we find
that properly accounting for heterogeneity in background characteristics by controlling for initial
conditions is a more important modeling issue than the choice of the health measure. Fifth, although
cognition is significantly related to employment, we find that it has little added explanatory power
once we also control for health, suggesting that cognition is not a key driver of employment at these
ages.
For direct comparison across groups, countries and methods, we calculate the share of the
decline in employment between ages 50 and 70 that can be explained by declines in health. Overall
we find that, depending on country, gender and education, declines in health explain between 3%
and 15% of the decline in employment. These effects are larger for high school dropouts and tend
to decline with education. They are also larger in US than in England, generally by a factor of 2 to
3. We estimate that the majority of the differences across countries is driven by the stronger effect
of health on employment in the US, rather than by differential declines in health or employment.
However, the key findings we outline above are consistent across the two countries.
The rest of the paper is outlined as follows. Section 2 provides an overview of the literature
investigating the impact of health on labor supply. Section 3 outlines the methods we use to
measure health and cognition, and develops a unifying framework under which the most commonly
used models of health and employment can be compared. Section 4 describes the ELSA and
HRS datasets and our constructed measures of health and cognition. Section 5 presents our main
estimates and examines the sources of differences between the US and England. Section 6 presents
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a simple dynamic structural model of employment and retirement with health, and uses the model
to discuss the various mechanisms through which health affects employment and our empirical
strategy. Section 7 concludes.
2 Literature
This paper brings together several strands in the literature on health and employment. First, it
relates to the large literature aiming to quantify the impact of health on employment and to establish
the relative merits of subjective health measures, objective health measures and subjective measures
instrumented by objective measures in estimating this effect. Concerns about various sources of
bias afflicting estimates using each of these measures have impeded comparisons across studies and
precluded the emergence of a clear picture on the importance of health effects. On their own,
objective indicators describe diagnosed health conditions but relate only to a subset of the relevant
conditions and miss severity information, hence providing an incomplete view of health. In turn,
subjective indicators offer a comprehensive view of health status, but are often crude categorical
measures of health and are particularly vulnerable to reporting error. However, subjective measures
instrumented by objective ones are immune to the measurement issues afflicting each set of measures
taken independently if these are unrelated, and can therefore be used to benchmark estimates
using only one type of health measure. We use the three approaches to assess and quantify how
measurement error, justification bias and limited health information bias estimates of the impact
of health on employment.
Early research suggests that subjective measures produce significantly larger estimates of the
impact of health on employment than objective measures. For example, Bound (1991) found
differences of nearly one order of magnitude when using future mortality as an objective health
measure. However, estimates relying exclusively on objective variables tend to use more detailed
health information than Bound (1991) did. For instance, Bartel and Taubman (1979) uses variables
describing heart disease, psychiatric conditions, arthritis and asthma; more recent work using the
Health and Retirement Survey (HRS) enlarges this list (e.g. Smith, 2004). We add to this literature
5

by including more objective variables and by showing how adding information on health conditions
changes the estimated effect. Consistent with past results, we find that limiting the number of
objective measures produces estimates that are significantly smaller than those obtained using
subjective measures. However, these differences vanish once a sufficiently large number of objective
measures is used.
In turn, there are widespread concerns that estimates using subjective measures are biased up
due to justification bias, whereby non-working individuals tend to report lower levels of health
partly to justify their work status (e.g. Butler et al., 1987). The extent of justification bias has
been heavily studied, with mixed results. Benitez-Silva et al. (2004) cannot reject the hypothesis
that self reported disability is an unbiased measure of true disability, while Kreider and Pepper
(2007) find that non-workers tend to over-report disability rates. However, subjective measures
are also subject to other forms of reporting error, particularly as they are often relatively crude
measures. Such measurement error may lead to attenuation bias in the estimates of health effects,
which will at least partly counteract the effect of justification bias. Studies of measurement error
in subjective measures show that it is not negligible. For instance, Crossley and Kennedy (2002)
find that 28% of all respondents change their reported health status when being asked the same
self assessed health question twice in the same interview (French, 2005, shows similar evidence of
misreporting).
Stern (1989) suggests using objective measures to instrument for subjective measures. Bound
(1991) shows that this procedure produces estimates that are close to those using subjective mea-
sures, suggesting that measurement error and justification bias in subjective measures roughly
offset. Dwyer and Mitchell (1999), McGarry (2004), and Giustinelli and Shapiro (2018) circumvent
concerns of justification bias by examining the relationship between health and expected retirement.
Similarly, Pamela and Shapiro (2018) use responses to hypothetical questions about people’s retire-
ment decisions given different hypothetical health levels. Their approach is to focus on those who
have not yet retired and who, therefore, do not need to justify retirement on bad health. They find
strong links between subjective health measures and expected retirement. We contrast estimates
6

using subjective measures, objective measures, and objective measures instrumenting for subjective
measures, and find that all three approaches produce surprisingly similar estimates when using the
full set of objective measures available in the HRS and ELSA.
Second, this paper also connects to the literature contrasting cross-sectional and panel data
methods in estimating the impact of health. It has been noticed that cross-sectional estimates are
vulnerable to reverse causality and simultaneity, both leading to upward bias. For instance, it is
conceivable that higher incomes cause better health. The Grossman (1972) model implies that
those with higher income may be able to purchase better nutrition and health care, improving later
health outcomes. On the other hand, the simultaneous determination of health and employment
could result from common (unobserved) drivers of both outcomes. For instance, it may be the
case that high-income parents invest more in both the health and the education of their children,
leading to better health and income outcomes later in life. In line with this view, Case et al. (2002)
show that child health is positively related to household income and, most importantly, that this
relationship becomes stronger over time, as the child ages.
Panel data methods offer the tools to deal with the confounding effects of reverse causality
and simultaneity bias. Smith (2004), Blau and Gilleskie (2001) and Gilleskie and Hoffman (2014)
emphasize the difference between panel and cross sectional methods for the purpose of estimating
health effects, and we revisit this issue. We find that including a full set of initial conditions and
focusing on estimating the impact of changes in health on employment reduces the magnitude of
the health coefficients by half. These findings are consistent with non-negligible bias induced by
reverse causality and simultaneity.
The final strand of the literature to which this paper relates is that assessing the ability of parsi-
monious representations of health to capture the relevant finer detail present in multiple measures.
A parsimonious representation of health is especially valuable in contexts where high-dimensional
problems are impractical, such as when estimating complex models. But whether the single index
is a sufficiently detailed representation of health remains an open question. We show that a single
health index captures well the variation in health that matters for employment. To the best of our
7

knowledge, we are the first to test the single index assumption in this way. The closest example
in the literature is Blau and Gilleskie (2001), who argue that ‘no single measure of health is ade-
quate to explain labor force transitions of older men’. They draw this conclusion from a series of
estimates that add, sequentially, more subjective and objective measures in the HRS. We obtain
similar results to Blau and Gilleskie (2001) when gradually adding more objective and subjective
health variables in our employment estimates. But we find that a single measure combining several
subjective health variables through principal components analysis is sufficient to capture the overall
impact of health on employment.
3 Methods for estimating the effect of health and cognition on
employment
Despite the growing literature on the effect of health on employment, there is still no agreement on
its magnitude. The lack of consensus may be partly due to the variety of empirical approaches and
datasets that have been used to measure these effects. A key source of differences relates to how
health is measured. Ideally one would like a summary measure of health linked to work capacity,
but such a measure is not readily observed in the data. Current datasets do not include all the
health variables that affect work capacity, and those that are included may suffer from measurement
error and justification bias to different degrees. Alternative estimation approaches deal differently
with these problems as we discuss below.
Here we bring together these approaches under a common unifying framework to contrast their
predictions and assess the validity of their underlying assumptions. Specifically, we address the
following issues: (1) how should we expect estimates of the effect of health on employment to differ
when using objective versus subjective measures? (2) how should using objective health measures
to instrument for subjective measures affect the estimates? (3) is a single health index sufficient,
or should multiple health indexes be used to capture the effect of health on employment? We show
how to use multiple objective and subjective measures to answer these questions.
Our analysis is based on a simple empirical model of employment, for which we consider two
8

alternative but similar specifications. The first uses a linear probability framework. For individual
iat time t:
Yit =θ0+θHH∗
it +θXXit +eit (1)
where Yis a binary indicator of employment, H∗is health status, with the superscript highlighting
that health is not directly observed in data, and Xare other drivers of employment, which we discuss
in detail below. The second specification assumes that Yis determined by the, latent index Y∗as
follows:
Y∗
it =θ0+θHH∗
it +θXXit +eit
Yit =1{Y∗
it >0}.(2)
In this case, we will assume that eit is normally distributed and thus estimate the model using a
probit.
These employment equations are derived from a structural model of life-cycle labour supply and
health, which we present and discuss in section 6. The structural model provides an interpretation
for the parameter of interest in this study, which is θH. Expressions (24) and (25) in section 6,
which are derived directly from the economic model of behaviour, demonstrate the many ways in
which health affects employment that are subsumed into θH. These include the impact of health
on the utility cost of work, pay from work, entitlement to benefits such as those for disability,
and expectations about future work, pay and lifespan given the persistent nature of health. Our
empirical analysis will not allow us to disentangle these various mechanisms. Instead, the focus
of this study is on how to estimate the overall effect of health on employment through all of the
above channels (θH) in ways that are robust to measurement error in health and to biases from self
justification or other sources.
The structural model also guides our choice of the other covariates in the regression equations,
which we denote by X. In this paper we are not interested on the value of their related parameters,
but it is nevertheless important that we control for the right set of covariates in order to understand
how to interpret estimates of θH. For instance, the structural analysis in section 6 demonstrates
that it is important to control for age and time in order to capture how preferences for work and
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the monetary incentives to so (including pay for work and benefits) change around the age of
retirement and differentially for different generations. Therefore, Xincludes time dummies and
a second order polynomial in age. Our structural analysis also reveals the need to control for
initial conditions in health and employment, which are meant to capture permanent heterogeneity
in preferences, productivity, and health. If these initial conditions are not included, estimates of θH
would be confounded by unobserved factors driving both employment and health. One issue that
the structural model shows is that it is the initial employment index (Y∗) capturing the propensity
to work that ought to be accounted for in the initial condition. That index, however, is not observed;
what is observed instead is employment status (Y). Using the structural model, we characterise
what governs the latent index Y∗, and complete the initial condition for employment with those for
its other determinants in the initial period. These include work experience, wealth, marital status
and the fixed health traits that we capture by health status during childhood. Conditionally on this
rich set of covariates, we then assume that the health status H∗is independent of the unexplained
driver of employment, e.
In what follows, we discuss the measurement of health and the identification and estimation of
the parameter of interest, θH. In discussing the potential bias in alternative estimation procedures
we will, for simplicity, focus on the linear employment equation specified in equation 1. All results
also hold for the probit specification in equation 2.
3.1 Measuring health using objective measures
The health stock can be formalized by a combination of all health conditions (and combinations
of conditions) that limit work, ho
kfor k= 1, . . . , K. These are typically labeled ‘objective’ health
measures because they represent medical health conditions that can be unambiguously identified;
indeed some surveys report only conditions that have been medically diagnosed and for which the
respondent receives treatment.
Assuming a linear functional form, we write
H∗
it =
K
X
k=1
αkho
kit (3)
10

and this expression can be replaced in equation (1) to yield
Yit =θ0+
K
X
k=1
˜
θHk ho
kit +θXXit +eit (4)
where ˜
θHk =θHαk
In practice, the simple specification in equation (4) is sensitive to potentially serious measure-
ment problems for four reasons. First, the number of observed conditions Kois smaller than the
total number of health conditions Ksince one can only ever observe a limited subset of the relevant
medical conditions. This is true even if one has full access to medical records, as only diagnos-
able conditions under current technology can be observed. Health status can be decomposed into
observed and unobserved objective conditions:
H∗
it =
Ko
X
k=1
αkho
kit +qit (5)
where qsummarises the contribution to health status of the K−Kounobserved conditions. Con-
sequently, the effect of health can only partly be determined. Second, not all health conditions are
equally important for overall health and thus employment, a fact that is expressed by the multiple
parameters ˜
θHk . While some conditions may be so debilitating as to completely impair work (like
strokes) others may have more limited consequences for work capacity (like diabetes). Hence, the
magnitude of the estimated impact will depend critically on exactly which conditions are accounted
for. Third, estimates of the impact of specific observed conditions may be biased if unobserved
conditions are related to observed ones. And fourth, most health measures only describe whether
respondents suffer from certain conditions, not the severity of those conditions. This is a key source
of measurement error biasing the estimated effects, potentially towards zero.
To put it more formally, consider the linear regression model of employment in equation 1
and assume that the true health stock H∗is a combination of two conditions, (ho
1, ho
2). For this
discussion we also ignore the correlation between health and the Xvariables. We normalize the
variance of the objective measures to equal that of H∗,2and ensure that all variables are ordered
2This is an innocuous standardization to ensure that all health variables are measured on a similar scale, that of
11

in the same direction (say, higher values for better health) so that (α1, α2)∈[0,1]2. Suppose that
ho
1is observed and measured without error, but ho
2is unobserved. In such case, the OLS estimator
of θHyields
plim ˆ
θo
H=Cov(Y, ho
1)
Var(ho
1)
=Cov(θ0+˜
θH1h0
1+˜
θH2h0
2+θXX+e, ho
1)
Var(ho
1)
=θHα1+θHα2
Cov(ho
1, ho
2)
Var(H∗).
If Cov(ho
1, ho
2) = 0 then plim ˆ
θo
H=θHα1and will thus identify the effect of the first health condition
ho
1, which is smaller than the impact of the global health measure (θH) under the assumptions
stated above. Moreover, had one observed ho
2instead of ho
1, a different impact would be identified
(specifically, θHα2).
In the likely case where the two health condition measures are positively correlated (with a
second health condition being more prevalent among those who already suffer from the first health
condition), then the estimated effect of health will be closer to the true overall effect (hence less
biased) than under the case where they are uncorrelated. A prediction based on model estimates of
how much changes in health status drives employment (as described below in Section 3.7) will still
be biased towards zero for two reasons: first, the likely attenuation bias in the estimated coefficient,
and second, the failure to account for all the relevant variation in health in the presence of missing
variables.
Applications that use objective health measures often combine information from numerous
health conditions. This may attenuate the estimation bias but will generally not eliminate it.
With many health measures, the formula for the asymptotic limits described above becomes more
complex, although the key insight is the same: the index will understate the true causal effect of
health on employment because it does not capture all relevant variation in health, and the extent
of the bias depends on how strongly correlated the omitted variables are with the observed ones.
In fact, using any linear combination of the observed health measures (such as the first principal
H∗.
12

component of the objective measures) will understate the true causal effect. The lack of detailed
medical data on the severity of a condition can be viewed as a specific case of missing variables and
will, as in the general omitted variable case, lead to attenuation bias.
In the empirical application, we use the complete set of medically diagnosed conditions (for
which the respondent is getting treatment) common to the two datasets. These amount to 10
objective measures in total. We have produced a parallel set of results by augmenting the set of
objective measures with observed variables measuring Activities of Daily Living (ADL), which are
meant to capture general levels of health that may limit work. Our results are not sensitive to this
choice.3
3.2 Measuring health using subjective measures
Although we cannot observe H∗directly, we do observe ‘subjective’ measures hs
kfor k= 1, . . . , Ks.
These are self-reported health measures that describe overall health status and provide an alter-
native to using objective measures to describe heath. The literature has interpreted the subjective
measures as noisy measures of a single latent health stock H∗. Thus, while the different objective
measures describe different subcomponents of the health stock (as shown in equation (3)), the sub-
jective measures are overall (noisy) measures of the single latent health stock. This idea can be
formalized by the following set of measurement equations, which relate the observable subjective
health indicators hs
kto the unobservable latent health index H∗:
hs
kit =βkH∗
it +ukit for k= 1, . . . , Ks(6)
where ukrepresents the measurement error in observed health variable k.
In practice, studies that model health as a latent variable typically use a single indicator of
health (Bound et al. (1999); Bound et al. (2010); Disney et al. (2006)). Instead, we use all the
subjective measures of health that are contained in both the HRS and ELSA surveys, which total
three, and extract a health index using Principal Component Analysis.4This is a natural approach
3See Online Appendix Section 4.1. There is some ambiguity as to whether it is appropriate to include these ADL
measures as objective health measures, but we decided to follow the common practice and exclude them.
4We also used Factor Analysis, and obtained results that were very similar to those we report here. The measures
13

if one wants to summarise the common information in many subjective measures, each being a
noisy measure of the same latent health variable.5It turns out that the results are not sensitive
to the procedure used to extract the variation from the subjective measures; we show only results
using Principal Components Analysis in the main text (see Online Appendix Section 4.2 for some
results using Factor Analysis).
Let Hsbe the subjective health index constructed using the subjective health measures. The
single index is a parsimonious approach that can be used in a variety of contexts; it is particularly
useful when keeping the number of health variables low is paramount, such as for estimation of
structural models of health. Moreover, the use of common variation across many subjective health
measures (using approaches such as factor analysis or principal components analysis) helps mitigate
the importance of measurement error if the noise across different variables is independent.
However, measurement error is unlikely to be completely eliminated by the use of many measures
in constructing the health index. In particular, justification bias affecting all underlying subjective
measures implies that measurement error is not classical. So we write
Hs
it =H∗
it +vit.(7)
If the unobserved component of employment (e) and the measurement error (v) are uncorrelated,
estimates of the health effect θHwill be biased towards zero. In the more likely event that (e, v) are
positively related – those not working tend to report lower levels of health partly to justify their
working status – the direction of the overall bias is ambiguous. Indeed, the OLS estimator of θH
in equation 1 using Hsto proxy H∗has asymptotic limit:
plim ˆ
θs
H=θHVar(H∗) + Cov(e, v)
Var(H∗) + Var(v)(8)
which may be greater or smaller than the parameter of interest θHdepending on the sign and
relative size of Cov(e, v). O’Donnell et al. (2015) suggest that justification bias dominates and
of subjective health and, more broadly, the datasets we use in the empirical exercise are described in Section 4 below.
5While it would also be possible to construct an index of health based on the objective variables, it would not be
as compelling to do so as objective measures reflect different aspects of health, rather than the same latent index.
14

Cov(e, v)>0, resulting in an upward biased estimate of θH. However, Stern (1989) and Dwyer
and Mitchell (1999) do not find that justification bias dominates.
3.3 Using instrumental variables to deal with measurement error and justifica-
tion bias
Thus far we have seen that approaches using exclusively objective measures suffer from omitted
variable bias and are likely to produce estimates of the impact of health that are downward biased.
Approaches using only subjective measures suffer both from measurement error and justification
bias, leading to estimates that could be either upward or downward biased. One way of dealing with
the biases afflicting estimates based on subjective health measures is to use instrumental variables.
We have many potential instruments to choose from if measurement error and justification bias in
the subjective measures are independent from objective health conditions, namely the entire set of
objective health measures.
It is straightforward to see that any subset of the objective health measures can be used to
instrument the subjective index. For simplicity, consider the case where we only have one objective
measure (indexed k) and use it to instrument the subjective health index. The first stage regresses
Hson ho
kand the estimated coefficient (call it ˆη) converges in probability to
plim ˆη=η=Cov(Hs, ho
k)
Var(ho
k)
=Cov(H∗, ho
k)
Var(H∗)
=αkVar(H∗) + Pl6=kαlCov(ho
l, ho
k)
Var(H∗)
Recall that H∗is a combination of all objective health conditions (as described in equation (3)),
each of which has been standardized to have a variance equal to that of H∗.
The predicted value of Hsis, therefore, ˆηho
k. The second stage instrumental variables estimate
15

using the linear employment equation 1 is
plim ˆ
θIV
H=Cov(Y, ηho
k)
η2Var(ho
k)
=θH
Cov(H∗, ho
k)
ηVar(H∗)=θH.
Under the IV exclusion restrictions, we can assess the importance of biases confounding estimates
of θHbased on objective measures (due to omitted variables) and based on subjective measures
(due to measurement error and justification bias). We do this by comparing IV estimates to those
obtained using only objective or subjective health measures.
It is straightforward to show that the IV approach is valid even if there is measurement error
in the objective measures, so long as that measurement error is orthogonal to that affecting the
subjective measures. In particular, this assumption requires that the justification bias generally
associated with subjective measures does not permeate into responses to the survey questions on
objective health measures. We discuss the plausibility of this assumption in the Online Appendix.
3.4 Tests of the single index assumption
We now turn to discuss the plausibility of the single index assumption. The ’single index as-
sumption’ states that there exists an index of multiple measures of self-reported health status Hs,
constructed as a composite measure of the subjective health variables, that contains all relevant
health information for employment. Under this assumption, the objective measures impact em-
ployment only through their impact on Hs. This is a restriction on model (1) in which the latent
measure of health (H∗) can be a function of multiple health conditions with varying implications
for work capacity as described in equations (3) and (4). We use this restriction to derive a spec-
ification test below. Notice that measurement error and justification bias are not ruled out by
this assumption. Indeed, we do allow for both sources of noise in Hs, as described in equation
(7). The single index assumption imposes that any measurement error in Hs(vin equation (7)) is
independent of H∗:
vit ⊥H∗
it.
16

The single index assumption underpins much of the empirical work on the impact of health on
labor supply. In particular, it is critical in contexts where dealing with multiple health dimensions
is impractical, such as in large structural models. We now use our methods to assess the validity of
this assumption using data that is now becoming widely available in developed countries. To the
best of our knowledge, this has not been done before.
First, we use our subjective measures. Under the single index assumption, all subjective mea-
sures of health are noisy measures of the same concept. Thus, each individual measure should
have little predictive value for employment above and beyond a summary measure of all subjective
variables. We test this assumption by including the Second and Third Principal Components of
health in the employment model, in addition to the First Principal Component. Formally, we test
the explanatory power of the added principal components.6
Second, we use the objective measures to assess the single index assumption. One simple point
is that the single index assumption implies that the effect of health estimated using the index
should not be smaller than that estimated using objective measures. This is because a correctly
specified health index should capture all relevant health information for employment, while objective
measures can only capture part of the relevant variation (as explained above). We therefore compare
the magnitude of the health effects based on the single subjective health index and the full set of
objective measures.
A slightly more subtle point is that the IV approach with multiple instruments provides the
means to test the validity of the single index assumption using a Sargan overidentification test
(Hansen (1982)). The intuition is simple: if the single index assumption is valid, all the objective
measures (the instruments) should affect labor supply only through the subjective health index. For
this reason, the IV residuals eIV should not be correlated with the instruments. With 10 objective
measures, we have 9 overidentification conditions.
In practice, we implement the test following the suggestion in Davidson and MacKinnon (2003).
6Not excluding the Second and Third Principal Components means rejecting the joint hypotheses of a single index,
model specification (such as linearity, homogeneity, etc.) and no measurement error. However, not rejecting the joint
hypotheses shows that the single index assumption is difficult to reject.
17

For the linear probability regression model in equation 1, we construct the IV residuals:
ˆeIV
it =Yit −ˆ
θIV
0−ˆ
θIV
HHs
it −ˆ
θIV
XXit.(9)
Under the single index assumption, we know that:
E[ˆeI V
it ho
kit |Xit] = 0 for k= 1, . . . , Ko.(10)
So we regress the residual on all health objective measures and the exogenous variables X, and
calculate the F-statistic associated with the hypothesis that all health coefficients are jointly equal
to zero. For the latent index model of employment in equation 2 we use the over-identification test
developed in Lee (1992), based on the minimum distance estimator proposed in Newey (1987) (see
also Rivers and Vuong (1988)).7
3.5 Health measures and the estimation of the effects of other determinants of
employment
The focus of this paper is on obtaining consistent estimates of the impact of health on employment
θH. Here we discuss how our various approaches to measuring health affect estimates of the effects of
other drivers of employment θX. We point out that instrumenting subjective health using objective
measures of health can deliver consistent estimates of θHbut will not in general deliver consistent
estimates of θX, a result highlighted in Bound (1991).
In the context of a structural model such as that discussed in section 6 of this paper, health
affects both employment and, throughout life, other choices and outcomes including savings towards
retirement, offered wages, and other financial incentives to retire (see also Gilleskie et al. (2017a)).
In the statistical model of employment in equation (1), which can be derived from that structural
7Although failure to reject the null supports the single index assumption, the results from this test should be
considered cautiously. As noticed by Deaton (2010) the exclusion restrictions are an IV identification assumption
that cannot be tested, even in the presence of multiple instruments. In our case, the residuals ˆeIV can be orthogonal
to the instruments even if the single index assumption does not hold, because in such case orthogonality is being
tested at a biased estimate of θH(Newey (1985)). In turn, in cases where the single index assumption is valid but the
impact of health is heterogeneous, each instrument may be valid in isolation (identifying effects at different margins,
for different sub-populations). But by taking all instruments together it may be impossible to find a value of ˆ
θIV
1for
which the orthogonality conditions are satisfied (Imbens and Angrist (1994), Angrist et al. (2000)).
18

model, these other economic variables are contained in X. However, since health status is not
observed, the statistical model of employment needs to be completed with a description of how
health is measured. In this paper we consider two alternative proxy measures, based on objective
and subjective health measures as expressed in equations (5) and (7), respectively. The error in
these measures may be correlated with the other drivers of employment (X) in ways that bias the
estimates of their effects. Moreover, since the nature of that error differs across health measures,
so will its consequences for the estimation of the effects of Xon employment.
To be more specific, consider first the use of an incomplete set of objective health measures as
described in section 3.1. If the omitted health conditions (ho
2in the notation of that section) are
correlated with the covariates Xin the employment equation 1, the resulting estimates of θXwill be
biased. To focus ideas, consider estimates of the effect of age on employment. In our specification,
the age coefficient is particularly interesting as it summarises the joint roles of changing preferences
and monetary incentives to retire in driving employment of older workers. We expect it to be
negative, as older people are increasingly less likely to work. If health deteriorates faster later in
life and in ways that are not fully captured by observed objective health ho
1, then the age coefficient
would partly encapsulate the effects of the deterioration of health along the unobserved dimensions
ho
2. In this case, estimates of the age effects would be downward biased, away from zero, which
means that one would overplay the effect of age on retirement.
The consequence of using a subjective health index for the direction and magnitude of the bias
of the age effects on employment near retirement is more ambiguous. To be concrete, suppose that
justification bias dominates other sources of measurement error, so that Cov(e, v)>0 in equation
(8); this will result in upward biased estimates of the impact of health on employment (θH). The
mismeasurement of H∗can affect estimates of the age effects in two ways that may partly cancel
out. First, the bias in θHleads to an over-prediction of the role of health deterioration with age
in driving employment. In our regression model, this would be partly compensated by an age
effect biased towards zero. That would be the only source of bias if age is independent of the
justification error, but not otherwise. The second source of bias arises precisely if the measurement
19

error in health status is correlated with age. For instance, one could think that the importance
of justification bias fades with age if old age is widely accepted as a valid reason for not working,
in which case younger workers under-report their health more strongly than older workers. This
would bias the estimate of the age coefficient downwards or away from zero partly to compensate
for the fact that subjective health under-predicts the true pace of health deterioration with age.
The ultimate direction of the bias in θtwould, in this case, be undetermined a priori. If, on the
contrary, justification error becomes more important with age as more workers stop working, then
instead subjective health would over-predict the true pace of health deterioration with age and the
two sources of bias would push the age coefficient in the same direction, towards zero.
Finally we note that instrumenting subjective health using objective health would remedy bias
from the first source by producing consistent estimates of θH. However, it will have no impact
on the second source of bias given that subjective health rather than actual health is used in the
statistical model.
3.6 Cognition
Cognition is not only a determinant of productivity in work, it may also affect work capacity in a
way that is not otherwise observed in objective and subjective health variables. It may, therefore,
be a critical driver of labor supply and we are interested in determining its effect. We therefore
enlarge our model to control for cognition. We observe several measures of cognition, described in
Section 4.4 below. These are test scores, measured by the interviewer, and thus not subject to the
sources of bias that may afflict health measures. Yet, our cognition measures will provide only an
incomplete representation of cognitive ability, implying our estimates of the cognition effects may
be biased towards zero. Denoting the latent cognition index by C∗, the extended model is
Yit =θ0+θHH∗
it +θCC∗
it +θXXit +eit.(11)
As in the case of health, we construct a parsimonious representation of cognitive ability under
the single index assumption by summarising the cognition variables in a single index using Principal
20

Component Analysis. 8When using this extended model, we supplement the initial conditions in
Xwith cognition measured when each individual is first observed.
3.7 Comparable measure of the impact of health and cognition
To facilitate the comparability of results across the various specifications, we construct a global
measure of the impact of health or cognition by predicting their cumulative impact on employment
over the 20 years period that span from 50 to 70 years of age. The parameter we calculate is
ˆ
δM=ΘM¯
M70 −¯
M50
¯
Y70 −¯
Y50
(12)
where the upper bar represents represents average predictions from a fixed effects regressions of
measures M(for health and cognition) and Y(for employment) on age. Hence, ¯
X70 −¯
X50 (for
X=M, Y ) is simply the average change in measure Xthat individuals experience between the
ages of 50 and 70. The fixed effects net out differences across cohorts and attrition in the panel
that could confound our estimates of individual-level decline in health, cognition or employment.
In measuring changes in health and cognition as workers get older, we rely on the exact same
measures that were used to estimate each model. So the change in health or cognition that we
consider to calculate ˆ
δwill depend on which specific measure was used in estimating Θ. For
instance, we use changes in subjective health and in instrumented subjective health to quantify the
impacts implied by estimates based on the respective measure. If the subjective health is afflicted
by justification error that varies with age then that age dependence will be reflected on our measure
of health deterioration in the 20 years from age 50 based on the subjective index but not on its
instrumented counterpart.
When using various measures of health and cognition together in the same regression model –
such as, for instance, when estimating a model of employment on objective health measures – we
8As for health, we investigate the use of Factor Analysis as an alternative but find almost no difference in the
results.
21

use changes in each measure to calculate the single impact parameter
ˆ
δ=X
j
Θj¯
Mj,70 −¯
Mj,50
¯
Y70 −¯
Y50
(13)
where jindexes the various health and cognition measures included in the employment regression
model. Here again Θjis the marginal effect of health or cognition measure jevaluated at the mean
of all covariates in the case of the probit model, or simply the estimate ˆ
θjfor the linear model.
A similar metric has been used by French (2005). Cutler et al. (2013) calculate the decline in
employment not explained by declining health.
ΘMis a function of the estimated parameters. In the probit specification, it is the estimated
marginal effect of health or cognition evaluated at the mean of all explanatory variables. In the
linear model, ΘMequals the estimate of θM,ˆ
θMwhere Mdenotes the corresponding measure of
health or cognition.9
4 Data and descriptive statistics
This paper uses waves 1 to 6 of the English Longitudinal Study of Ageing (ELSA), covering years
2002-2012, and waves 3 to 11 of the US Health and Retirement Study (HRS), covering years 1996-
2012. We excluded the first two waves of HRS because of non-negligible changes in the questionnaire
that happened in wave 3. Moreover, it is the later version of the HRS that informed the design
of ELSA, so it is for these waves where the two surveys are most comparable. In both cases,
the sampling is designed to become representative of the population aged 50 or older of their
respective countries as the survey matures. Both HRS and ELSA collect biannual longitudinal
data on respondents and their spouses, for the latter irrespective of their age, on a vast range of
socio-economic, demographic, health and cognition variables.
ELSA respondents are a subsample of the Health Survey for England (HSE) in 1998, 1999 or
2001, representing the population of non-institutionalized individuals living in England and aged
9As noted before and in Bound (1991), estimates of the coefficients associated with other drivers of employment
Xmay be biased even when ˆ
θMis not. Note that the only parameter we use to calculate δMin the linear framework
(equation 1) is ˆ
θM, so predictions from a linear model will not be affected by bias in other coefficients. However, the
marginal effects in the non-linear model depend on all parameters and, hence, may be affected.
22

50 or older in 2002/03. Later interviews were conducted in 2004/05, 2006/07, 2008/09, 2010/11
and 2012/13, with booster samples every 6 years.
The HRS began in 1992, with a representative sample of non-institutionalized individuals living
in the United States aged 51 to 61 and their spouses. These individuals were interviewed biannually,
even when later admitted to nursing homes (although, for consistency with ELSA, we exclude those
in nursing homes), and refreshment samples were added every 6 years. We augment the HRS dataset
with the RAND HRS Data File which contains cleaned versions (including some minor imputations)
of the core HRS variables.
Throughout the paper, we focus on the retirement period using data for respondents and their
spouses aged 50-70. Sample sizes for our population of interest are outlined in Table 1. Increases
in waves 3 and 6 in ELSA and 4, 7 and 10 in HRS are due to refreshment samples. The overall
sample size in the HRS is more than twice that for ELSA, due to both the larger number of waves
and the larger number of individuals in each wave. The total number of observations reported at
the bottom row of Table 1 represents individual×time observations.
Table 1: ELSA and HRS years and sample sizes
ELSA HRS
Year Wave Sample Size Wave Sample Size
1996 3 10,215
1998 4 13,369
2000 5 11,996
2002 1 8,008 6 10,724
2004 2 6,104 7 12,126
2006 3 6,403 8 10,618
2008 4 7,426 9 9,264
2010 5 6,620 10 13,156
2012 6 6,834 11 11,805
Total 41,395 103,273
Notes: Sample sizes for 50-70 year olds only. Total row gives total number of observations, meaning some individuals appear
multiple times.
Our analysis separates three educational groups: College degree or equivalent, High School
degree or equivalent (GCSE or A level in England), and High School Dropout (no GCSE qualifica-
23

tions in England).10 We use the American labels in all future references. Figure 1 plots education
levels against date of birth year for men aged 50 to 70 in ELSA and the HRS (Figure 2 shows
the equivalent figures for women). The education composition of the English labor force changed
considerably over these cohorts, with the proportion of men who at least graduated from High
School increasing from about 35% among those born in the early 30s to about 80% among those
born in the early 60s. English women departed from a lower basis of about 20% but reached similar
education levels to those of men in the later cohorts.
0 .2 .4 .6 .8 1
Share of population
1930 1940 1950 1960
Year of Birth
ELSA, Men
0 .2 .4 .6 .8 1
Share of population
1930 1940 1950 1960
Year of Birth
College
High School
High School Dropout
HRS, Men
Figure 1: ELSA and HRS Education groups on D.O.B. year for men
Although the younger cohorts born in the 1960s look very similar across the two countries,
there are important differences in the education achievement of older cohorts; education levels are
much higher in the US than England for the older cohorts. In contrast, men and women from
the younger cohorts are more likely to graduate from college in England than the US and are
equally likely to leave school without qualifications. It is therefore important to bear in mind that
individuals lacking any qualification in HRS are likely to be from lower in their country’s skill
distribution than their counterparts in ELSA.
10These groupings closely resemble those used in Banks et al. (2015).
24

0 .2 .4 .6 .8 1
Share of population
1930 1940 1950 1960
Year of Birth
ELSA, Women
0 .2 .4 .6 .8 1
Share of population
1930 1940 1950 1960
Year of Birth
College
High School
High School Dropout
HRS, Women
Figure 2: ELSA and HRS Education groups on D.O.B. year for women.
The two surveys contain life history information that we use to describe permanent individual
characteristics that drive both health, cognition and employment outcomes. Specifically, we use
historical data on health during childhood and accumulated years of working experience in first
observation to capture long-term health status and labor market attachment. These variables
complete the set of initial conditions we control for, which also include health, employment, marital
status and non-housing wealth observed when each individual first joins the sample.
4.1 Employment Profiles
We now turn to our key outcome variable, employment. Figure 3 shows significant declines in
employment for all three education groups for both genders, particularly after age 60. In ELSA,
employment among men starts from a higher base than that of women, and declines later; a sharp
decline coincides with the State Pension Age (at 65 for men, 60 for women) in both groups. In
contrast, both men and women experience similar declines in employment rates with age in the
US, where the Early (62) and Normal (66 for most of the sample period) Retirement Age is the
same for the two genders. These profiles for the two countries are suggestive of the importance of
25

retirement incentives in driving the decline in employment. Employment rates are flatter in the
HRS than in ELSA, implying that a higher proportion of Americans than English are still working
in their late 60s. Finally, the education gradient is much stronger in the US than it is in England.
Fewer High School Dropouts are in work during their 50s in the US than England. This feature is
likely to be linked to the differences in education attainment of Americans and English, with High
School Dropouts being a much larger, and hence probably less disadvantaged, group in England.11
0 .2 .4 .6 .8 1
Employment
50 55 60 65 70
Age
ELSA, Men
0 .2 .4 .6 .8 1
Employment
50 55 60 65 70
Age
HRS, Men
0 .2 .4 .6 .8 1
Employment
50 55 60 65 70
Age
ELSA, Women
0 .2 .4 .6 .8 1
Employment
50 55 60 65 70
Age
HRS, Women
High School Dropout High School College
Figure 3: ELSA Employment on age, by gender and education
4.2 Objective measures of health
As described in the methods Section 3, we consider health variables in two broad categories, ob-
jective and subjective. Here we focus on the former. Table 2 summarizes the objective health
11Both datasets also provide information on working hours and hourly wages. Considering working hours instead
of the dichotomous employment outcome does not change our findings, so we omit it here. Results for hourly wage
rates, however, were much nosier than those for employment. This was not unexpected as selection into work is likely
to play a key role in determining estimates of the impact of health on hourly wages if those who remain in work
are healthier than those who drop out (and increasingly so with age). The age profiles of hourly wages and working
hours can be found in the Online Appendix, but we do not further investigate these impacts here.
26

measures we consider, which include reports of the health conditions for which respondents receive
medical treatment (such as cancer or diabetes). For comparability, we only use variables that are
present both surveys.
The differences between the US and England are stark; prevalence in the US is larger for 8
out the the 10 conditions for which the respondent is treated (top 10 rows in the Table)), and
is often twice or even three times larger in magnitude. For example, cancer prevalence is 3% in
ELSA for both men and women, but the figures in the HRS are, respectively, 8% and 11%; diabetes
prevalence is 9% and 6% for men and women in ELSA and is 19% and 17% in HRS; the numbers
for arthritis are 23% and 34% in ELSA and up to 44% and 57% in HRS.
These reported health differences have been well documented before in Banks et al. (2006) and
Banks et al. (2016). They may reflect a combination of differences across the two countries, in health
status, diagnosing rates and respondents’ information about their health conditions. Meanwhile,
gender differences are similar across the two countries; typically women are more likely to have
arthritis and psychiatric problems, but are less likely to have suffered from a stroke, heart attack
or diabetes.
Table 2: Objective health variables, averages by gender
ELSA HRS
Variable Men Women Men Women
Cancer 0.03 0.03 0.08 0.11
Diabetes 0.09 0.06 0.19 0.17
Sight 0.02 0.02 0.04 0.05
Hearing 0.05 0.02 0.06 0.02
Blood pressure 0.30 0.26 0.50 0.50
Arthritis 0.23 0.34 0.44 0.57
Psychiatric 0.05 0.08 0.12 0.21
Lung Disease 0.04 0.04 0.08 0.10
Stroke 0.02 0.01 0.06 0.04
Heart Attack 0.03 0.01 0.02 0.01
N 18,913 22,482 44,499 58,764
Notes: Includes individuals aged 50-70. All variables are binary measures.
Panels A and C of Figure 4 show how the prevalence of arthritis changes between the ages of
50 and 70, by gender and education in England and the US. The plotted lines show smoothed age
trends using a moving averages of 3 years. The clear positive gradient with age for all groups is
indicative of how health deteriorates around the retirement age. This unsurprising finding justifies
27

the focus on this age group of much of the economic literature on health and employment in
developed countries. The graphs also show that the prevalence of arthritis is higher among women
and those with less education in both countries. The latter is also typical of many health conditions:
less educated and poorer individuals tend to report lower levels of health. However, the sharpest
difference is that between England and the US, with arthritis being much more prevalent for all
groups in the US.
Panel A Panel B Panel C Panel D
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
ELSA MA(3), Men
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
ELSA FE, Men
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
HRS MA(3), Men
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
HRS FE, Men
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
ELSA MA(3), Women
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
ELSA FE, Women
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
HRS MA(3), Women
0 .2 .4 .6 .8
Arthritis
50 55 60 65 70
Age
HRS FE, Women
High School Dropout High School College
Figure 4: Prevalence of arthritis by age, gender and education.
Notes: MA(3) indicates a 3-year moving average and FE indicates fixed effects estimates.
These figures may mask cohort differences in the prevalence of the disease. To deal with this,
we net out fixed effects by estimating
hit =αi+βt+uit
where hit is a health outcome of interest for individual iaged t,αare the individual fixed effects
(normalized to have mean zero in the population), and βtare a full set of age dummy variables that
28

capture health-age profiles net of fixed effects. We then plot the estimated age profile βt. Note that
this fixed effects specification captures all time invariant factors. For example, a cohort effect is just
the average fixed effect of everyone within that cohort. In our application it is important to net out
fixed effects particularly when looking at health profiles conditional on education because of the
rapid increase in education attainment over the sample period, especially in England. Specifically,
the shift towards more education implies that highly educated individuals in the older cohorts of
our sample may be drawn from a more selected sample, with different health outcomes, than equally
educated individuals from the younger cohort. The fixed effects estimator, which is identified by
individual changes in health with age, eliminates the effects of such compositional changes on the
level of health. In addition, because fixed effects tracks the same people over time, it addresses the
issue of non-random attrition from the sample due to death or other reasons. Profiles for arthritis
are shown in Panels B and D of Figure 4, respectively for England and the US. The patterns are
similar to those in the raw data, but the age gradient is noticeably steeper for most groups. The
full set of figures describing the prevalence of health outcomes by age is available in Section 2.2 of
the Online Appendix.
4.3 Subjective measures of health
The indicators of subjective health are summarized in Table 3. These are variables of self-reported
health, describing general health and whether it hinders work or the ability to perform normal
daily activities. The means reported in the table show some interesting patterns. Responses to all
questions are well aligned across the two countries, with English people reporting slightly better
health than Americans but with much more modest differences than those observed for objective
health measures. This is remarkable given the considerably higher prevalence of disease in the US
as described by the objective measures. It must be driven, at least to an extent, by large differences
between the two countries in the way individuals report their own health. This is consistent with
results in Banks et al. (2016) showing that Americans set lower thresholds for good and excellent
self reported health than do the English, and in Kapteyn et al. (2007) showing that Americans set
lower thresholds for being non-disabled than the Dutch.
29

Finally, the English tend to report lower levels of health as children than Americans do, with
around 12% of ELSA respondents reporting bad health as child compared to 7% of HRS respon-
dents.
Table 3: Subjective health variables, averages by gender
ELSA HRS
Variable Men Women Men Women
Health limits activities 0.41 0.54 0.54 0.67
Self reported health 2.61 2.57 2.75 2.78
Health limits work 0.24 0.25 0.25 0.27
N 18,851 22,446 44,500 58,773
Notes: Includes individuals aged 50-70. “Health limits activities” and “Health limits work” are binary measures; “Self-reported
health” is a 5-point categorical variable, where “5” is excellent.
We summarize the subjective measures of health in a single index that we think captures well
the global measure of health status, the first component from a Principal Component Analysis
of the three subjective health measures.12 The age profiles of the index are shown in Figure 5.
The patterns are much more similar across the two countries than those found for the objective
measures. There is again a clear ordering by education group and a negative gradient with age.
Removing fixed effects changes the patterns for the US more than it does for England, by making
the age profiles steeper.
4.4 Cognition
High quality survey information on cognitive functioning only recently started to become available.
It exists in both ELSA and HRS, with respondents being given a battery of cognitive tests. The
literature on cognitive skills in adults (e.g. Choi et al. (2014)) has distinguished between measures
of crystallized intelligence (which relies on accessing information from long-term memory) and fluid
intelligence (the capacity to think logically and solve problems in novel situations, independent of
acquired knowledge).13 Our focus is on fluid measures, primarily because they are available in both
12Plots for the each of the subjective measures can be found in Section 2.3 of the Online Appendix, while more
detail on the distribution of the measures and the weights assigned to each variable and the estimates from the first
stage IV regression can all be found in Section 3.1 of the Online Appendix.
13See Banks et al. (2010) for a good description of the cognitive function measures in ELSA and Choi et al. (2014)
for more on measures of cognition and how they vary with age, gender and education.
30

Panel A Panel B Panel C Panel D
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
ELSA MA(3), Men
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
ELSA FE, Men
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
HRS MA(3), Men
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
HRS FE, Men
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
ELSA MA(3), Women
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
ELSA FE, Women
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
HRS MA(3), Women
-1 -.5 0 .5 1 1.5
Subjective Health
50 55 60 65 70
Age
HRS FE, Women
High School Dropout High School College
Figure 5: Single subjective health index by age, gender and education.
Notes: MA(3) indicates a 3-year moving average and FE indicates fixed effects estimates.
surveys across several waves,14 though also because previous studies have found that it is fluid and
not crystallized intelligence that is positively correlated to labor outcomes (for example, Anger and
Heineck (2010) and Heineck and Anger (2010)).
Both datasets include several cognitive measures of fluid intelligence. We focus on two of the
tests in the survey alongside two of the Instrumental Activities of Daily Living (IADL) measures
which also reflect cognition. The measures are summarized in Table 4. The table shows that Amer-
icans do slightly worse in cognition tests than the English, with 10% (respectively 3%) reporting
difficulty using a map, 4% (2%) reporting difficulty managing money, and average scores of 5.8
(6.1) and 4.8 (4.9) out of 10 in the recall and delayed recall tests.
Similar to the construction of our health index, we construct a cognition index that summarizes
the information content of the four cognition variables using Principal Component Analysis. The
14ELSA does include a numeracy test in some waves (specifically, waves 1, 4 and 6), which might be considered a
crystalized measure (and is used in Banks et al. (2010)).
31

Table 4: Cognitive variables, averages by gender
ELSA HRS
Variable Men Women Men Women
Immediate recall (out of 10) 5.96 6.28 5.55 6.02
Delayed recall (out of 10) 4.67 5.14 4.48 5.08
Difficulty navigating using map 0.02 0.04 0.06 0.13
Difficulty managing money 0.02 0.01 0.04 0.04
N 18,851 22,448 44,401 58,641
Notes: Includes individuals aged 50-70.
first principal component is plotted in Figure 6.15 In general, there is a clear worsening in cognition
with age as assessed by this test. What is remarkable, however, is that the age profiles in ELSA are
essentially flat once fixed effects have been removed (Panel B). This suggests that the deterioration
in cognitive skills with age seems to be explained by compositional changes across cohorts in
England: older individuals have lower cognition not because of their age, but because they were
born into older cohorts with lower cognition over their life.16 The figure also shows evidence of
a clear ordering by education group in the scoring of the recall tests, with the highest educated
scoring best and the lowest educated scoring worst. Moreover, the gap between the high educated
and the low educated is considerably larger in the US.
5 Empirical results
In this section we compare the estimates of the impact of health on employment using various
specifications commonly adopted in the literature. We use subjective health measures, either on
their own or combined in an index, and we extend the model to include cognition. We show the
importance of allowing for initial conditions when estimating the impact of health. We address the
issue of measurement error in health using instrumental variables, and demonstrate that the linear
regression model predicts accurately the impact of health on employment. And finally, we explore
the differences in results between England and the US. For conciseness, we focus on estimates based
on the latent index probit model in equation (2) and show the very similar findings we obtained
15Plots for each of the component variables are given in Section 2.6 of the Online Appendix, while the weights
assigned to each variable can be found in Section 3.1 of the Online Appendix.
16We found little evidence that these results are being driven by learning of the tests, which we investigated by
removing the first wave individuals were surveyed, with the idea that the ma jority of learning should occur between
the first and second waves individuals are observed. These figures are available from the authors on request.
32

Panel A Panel B Panel C Panel D
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
ELSA MA(3), Men
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
ELSA FE, Men
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
HRS MA(3), Men
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
HRS FE, Men
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
ELSA MA(3), Women
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
ELSA FE, Women
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
HRS MA(3), Women
-1 -.5 0 .5 1 1.5
Cognition
50 55 60 65 70
Age
HRS FE, Women
High School Dropout High School College
Figure 6: Cognition index by age, gender and education.
Notes: MA(3) indicates a 3-year moving average and FE indicates fixed effects estimates.
for the linear probability model in Section 4.4 of the Online Appendix. The effects of health and
cognition on employment are calculated using the marginal effects at the average of all regressors
included in each model.
5.1 The Effect of Subjective Measures of Health and Cognition on Labor Supply
Table 5 displays estimates of the effects of a one standard deviation improvement in the health
or cognition indexes on employment. As described in the previous section, the subjective health
index is the first principal component of the three subjective health measures and the cognition
index is the first principal component of the four cognition measures. Each cell in Panels A and B
reports estimates from a separate regression; cells in the top and bottom halves of Panel C report,
respectively, the cognition and health coefficients in regressions that control for both. Sample sizes
are shown in the bottom panel.
33

Table 5: Coefficient Estimates – Employment Regression on Cognition and Subjective Health
Men Women
ELSA HRS ELSA HRS
No IC’s IC’s No IC’s IC’s No IC’s IC’s No IC’s IC’s
[1] [2] [3] [4] [5] [6] [7] [8]
Panel A: Employment on Subjective Health
High School Dropout .177*** .085*** .194*** .138*** .128*** .057*** .161*** .127***
(.004) (.006) (.004) (.005) (.005) (.005) (.004) (.004)
High School .110*** .049*** .158*** .106*** .115*** .063*** .140*** .109***
(.005) (.005) (.003) (.003) (.004) (.005) (.002) (.003)
College .071*** .047*** .096*** .070*** .068*** .044*** .087*** .077***
(.007) (.007) (.004) (.004) (.008) (.008) (.004) (.005)
Panel B: Employment on Cognition
High School Dropout .087*** .013* .085*** .043*** .058*** .013** .073*** .037***
(.006) (.007) (.006) (.007) (.005) (.005) (.005) (.005)
High School .033*** .011** .067*** .030*** .031*** .007 .061*** .030***
(.006) (.005) (.003) (.004) (.005) (.005) (.003) (.003)
College .013* .004 .049*** .031*** .019** -.001 .029*** .018***
(.007) (.008) (.004) (.005) (.008) (.008) (.005) (.005)
Panel C: Employment on Cognition and Subjective Health
Cognition
High School Dropout .035*** .001 .044*** .029*** .026*** .006 .034*** .016***
(.006) (.007) (.006) (.006) (.005) (.005) (.005) (.005)
High School .009* .005 .035*** .017*** .008* .001 .030*** .016***
(.005) (.005) (.003) (.003) (.005) (.005) (.003) (.003)
College -.001 -.002 .030*** .021*** .006 -.006 .014*** .009*
(.007) (.008) (.004) (.004) (.008) (.008) (.005) (.005)
Subjective Health
High School Dropout .168*** .085*** .185*** .135*** .122*** .056*** .153*** .125***
(.005) (.006) (.005) (.005) (.005) (.005) (.004) (.004)
High School .108*** .048*** .151*** .104*** .114*** .063*** .134*** .106***
(.005) (.005) (.003) (.003) (.004) (.005) (.002) (.003)
College .071*** .047*** .090*** .067*** .066*** .045*** .084*** .076***
(.007) (.007) (.004) (.004) (.008) (.008) (.004) (.005)
Sample sizes 4,692 4,692 5,777 5,777 6,957 6,957 9,199 9,199
6,327 6,326 18,756 18,756 7,911 7,911 29,905 29,905
3,362 3,362 9,238 9,238 2,759 2,759 9,682 9,682
Notes: All estimates include age, age squared, and wave dummies. ICs stands for initial conditions. These include the initial
value of the health and cognition variables included in the regression as well as initial employment, working experience,
wealth and marital status, and health in childhood. * indicates significant at 10%,** 5%, *** 1%.
The relationship between subjective health and employment is shown in Panel A. Estimates in
Column 1 are for men in England; they are obtained from a set of education-specific regressions
of employment on the subjective health index and a basic set of controls that only includes a
quadratic polynomial in age and year dummies. In ELSA, a one standard deviation improvement
in the subjective health index is associated with 17.7% higher employment amongst high school
dropout men; comparable estimates for high school graduates and college graduates are 11.0% and
7.1%, respectively.
34

However, estimates of the effects of subjective health on employment may be biased by un-
observed factors that relate to both. For instance, individuals from poor backgrounds may have
missed on the critical investments that foster good health as well as other skills required in work
environments. If poor health and unobserved skill deficits lower employment rates later in life,
then failure to control for skill will confound estimates of the employment effects of health. To deal
with this sort of problem, we add a full set of initial conditions to the regression model, including
health status during childhood, accumulated years of working experience, as well as health, cogni-
tion, employment, marital status and non-housing wealth when first observed in the sample. These
variables capture existing heterogeneity at the start of the observation period that relates to both
employment and health.
For men in ELSA, the new set of estimates controlling for initial conditions can be found in
Column 2. The reported coefficients in Panel A measure the impact of changes in health on changes
in employment during later working years. The effects of health roughly halve with the inclusion
of initial conditions in the regression model, showing that indeed much of the relationship between
health and employment among English men is spurious. We find very similar patterns for English
women (see Panel A, Columns 5 and 6), although with estimates that are generally slightly smaller.
HRS estimates, meanwhile, are modestly larger than ELSA estimates but are less affected by the
inclusion of initial conditions (Columns 3-4 and 7-8 for men and women, respectively).
Panel B shows equivalent estimates for the effects of cognition. These are always smaller than
the effects of subjective health. In ELSA, a one standard deviation improvement in the cognition
index of men is associated with 8.7%, 3.3% and 1.3% higher employment rates among high school
dropouts, high school graduates and college graduates, respectively (Column 1, Panel B). Adding
initial conditions to the regression model, which now include the cognition index but not the health
index in the first observation period, considerably reduces the estimated effects. HRS estimates are
larger, and are again less affected by the inclusion of initial conditions. Estimates for women are
very similar to those for men.
Panel C in Table 5 shows results for employment regressions on both the cognition and subjective
35

health indexes. It shows that health remains a strong determinant of employment among older
workers even when accounting for cognition, but that cognition plays a much more modest role (if
any) after accounting for health. In line with findings in Panels A and B, Panel C also highlights the
importance of controlling for permanent heterogeneity when estimating the impacts of cognition
and subjective health on employment. We therefore focus exclusively on estimates from regression
models that include initial conditions in what follows.
Table 6: Share of Employment Decline Explained by Cognition and Subjective Health
Men Women
ELSA HRS ELSA HRS
Panel A: Subjective Health
High School Dropout .072*** .123*** .045*** .101***
(.013) (.017) (.007) (.014)
High School .041*** .111*** .047*** .112***
(.008) (.006) (.009) (.006)
College .040*** .084*** .023*** .077***
(.011) (.010) (.008) (.009)
Panel B: Cognition
High School Dropout .002 .037*** -.003 .057***
(.003) (.010) (.003) (.011)
High School .001 .028*** -.001 .033***
(.002) (.004) (.001) (.005)
College -.001 .034*** 0.000 .018***
(.002) (.007) (.001) (.006)
Panel C: Cognition and Subjective Health
High School Dropout .072*** .145*** .043*** .124***
(.013) (.019) (.008) (.016)
High School .041*** .125*** .047*** .127***
(.008) (.007) (.009) (.007)
College .040*** .104*** .023*** .085***
(.012) (.011) (.008) (.011)
Sample sizes 4,692 5,777 6,957 9,199
6,326 18,756 7,911 29,905
3,362 9,238 2,759 9,682
Notes: All estimates include age, age squared, wave dummies and the full set
of initial conditions. Standard errors are bootstrapped with 500 repetitions.
* indicates significant at 10%,** 5%, *** 1%.
Table 6 displays estimates of the share in employment decline between ages 50 and 70 that can
be explained by a decline in health and/or cognition over the same period. It uses the coefficients in
Table 5 to calculate the percentage change in employment explained (δin Equation 13). Estimates
in Column 1 of Panel A show that the deterioration in health explains between 4.0% and 7.2%
of the decline in men’s employment in ELSA. The impact is largest for the high school dropouts
and falls with education. Column 1 in Panel C shows that these estimates are barely affected by
36

Table 7: Percent Differences in the Explained Share of Employment Decline and p-values for Testing
Null of No Differences – Explanatory Value of Adding Cognition
Percent differences p-values
Men Women Men Women
ELSA HRS ELSA HRS ELSA HRS ELSA HRS
[1] [2] [3] [4] [5] [6] [7] [8]
Panels C versus A of Table 6
High School Dropout 0.1 18.1 -4.3 22.1 0.499 0.189 0.439 0.146
High School -0.3 12.7 -0.4 13.4 0.496 0.078 0.495 0.055
College 1.6 22.6 3.2 10.2 0.484 0.111 0.473 0.298
Notes: Estimates of relative differences in Columns 1-4 compare figures in Panels A and C of Table 6, with
Panel A as the baseline. p−values in Columns 5-8 for testing the equality of the same δestimates.
the inclusion of cognition, in line with cognition having a negligible impact on the employment of
older workers in England (see also Panel B). Contrasting Columns 1 and 3 in the Table shows that
changes in health and cognition explain generally less of the changes in employment of women than
men, particularly among those who leave education without qualifications.
Results for the HRS display similar patterns to those found in ELSA, only stronger (Columns
2 and 4 in the Table). In particular, they suggest that both health and cognition play a role in
explaining the decline in employment of American workers near retirement age, though the impact
of health decline is about 2 to 4 times larger than that of cognition decline (Panels A and B).
Moreover, cognition explains about 2 additional percentage points of the decline in employment
when added to health in the same regression model (Panel C versus A).
The incremental value of cognition is tested in Table 7. Figures in Columns 1 to 4 show
the change in explained share of employment decline induced by adding cognition in addition to
health, in percentage terms relative to the effect of health alone; these numbers are obtained from
comparing estimates in Panel C and A of Table 6. Columns 5 to 8 show the p-values for testing the
equality between the same two sets of estimates, with and without cognition. The results suggest
that cognition increases modestly the explained employment decline in the HRS but the differences
are never statistically significant at a 5% level. In line with our earlier findings for ELSA, cognition
plays no discernible role in driving employment in England.
By summarising the information on subjective health in a single index, we may be discard-
ing important information. Our subjective health index is constructed using three variables. In
37

principle, each of the three variables could have independent explanatory power for employment
beyond their contribution to the index. To test whether this is the case, we estimated alternative
empirical specifications of the employment regression model and used them to predict the share
of employment decline driven by health over the same 50-70 age period (δin Equation 13). Esti-
mates are displayed in Table 8. Panel A reproduces Panel A in Table 6 and is the reference set of
estimates, obtained using the single subjective health index. Panel B adds all three measures of
subjective health separately to the employment regression; this has little effect on the estimates.17
Panel C includes only one of the subjective health variables directly measured in the questionnaire,
the dichotomous variable for whether health limits work; estimates of the δ’s are modestly lower
in this case, suggesting that this single measure misses some of the drivers of employment, or that
there is significant measurement error in the variable. Section 4.3 of the Online Appendix shows
estimates using the other subjective measures individually. The individual subjective measures
always produce smaller and more variable estimates of the impact of health than the health index
using all three measures. This suggests that a single health index, if properly constructed, is suffi-
cient for capturing the effect of health on employment; however, a single subjective measure is not
sufficient.18
Table 9 further quantifies the importance of accounting for more detailed subjective health
information by comparing Panels B and C with Panel A of Table 8. Columns 1-4 detail the
percentage differences between the estimates in these panels, using estimates in Panel A as baseline,
while Columns 5-8 detail the p-values for testing their equality. The figures in the top panel reveal
that the relative differences induced by fully accounting for the subjective health information are
generally small and mostly negative. In most cases we fail to reject equality; in some cases we do
reject, but the only rejection of a positive difference (which would indicate that the three measures
separately contain more information for employment than the composite index) is for women with
17An intermediate specification including the two first principal components was also tried. It showed very similar
results to those in Panel B. These are available from the authors upon request.
18Attenuation bias from measurement error is a more serious problem when using the subjective measures separately
(as in Panel B of Table 8) than for estimates based on the single composite subjective health index (as in Panel A).
This is because measurement error that is not common across the underlying subjective health measures is cleared
from the index but will contaminate estimates based directly on the observed subjective variables. This can help
explaining why some of the estimates in Panel B are lower than their counterparts in Panel A of the Table.
38

Table 8: Share of Employment Decline Explained by Subjective Health - Various Specifications
Men Women
ELSA HRS ELSA HRS
Panel A: First principal component
High School Dropout .072*** .123*** .045*** .101***
(.013) (.017) (.007) (.014)
High School .041*** .111*** .047*** .112***
(.008) (.006) (.009) (.006)
College .040*** .084*** .023*** .077***
(.011) (.010) (.008) (.009)
Panel B: Three subjective measures separately
High School Dropout .060*** .106*** .033*** .107***
(.015) (.017) (.009) (.017)
High School .032*** .110*** .039*** .123***
(.011) (.007) (.008) (.007)
College .011 .080*** .028*** .078***
(.013) (.012) (.011) (.010)
Panel C: Health limits work
High School Dropout .029*** .084*** .014* .104***
(.011) (.016) (.007) (.016)
High School .020*** .101*** .020*** .119***
(.006) (.007) (.006) (.006)
College -.003 .068*** .003 .071***
(.007) (.009) (.006) (.009)
Sample sizes 4,692 5,777 6,957 9,199
6,326 18,756 7,911 29,905
3,362 9,238 2,759 9,682
Notes: All estimates include age, age squared, wave dummies and the full set
of initial conditions. Standard errors are bootstrapped with 500 repetitions.
* indicates significant at 10%,** 5%, *** 1%.
Table 9: Percent Differences in the Explained Share of Employment Decline and p-values for Testing
Null of No Differences – Explanatory Value of Added Subjective Health Information
Percent differences p-values
Men Women Men Women
ELSA HRS ELSA HRS ELSA HRS ELSA HRS
[1] [2] [3] [4] [5] [6] [7] [8]
Panels B vs A (three separate subjective measures)
High School Dropout -16.0 -13.7 -27.5 5.4 0.076 0.039 0.075 0.274
High School -21.1 -1.0 -16.9 9.8 0.148 0.404 0.171 0.001
College -72.8 -5.4 26.4 1.5 0.001 0.183 0.231 0.411
Panels C vs A (health limits work)
High School Dropout -58.9 -32.1 -68.6 3.0 0.000 0.002 0.000 0.388
High School -51.6 -8.9 -58.4 6.1 0.000 0.048 0.001 0.084
College -106.3 -19.6 -84.6 -8.1 0.000 0.012 0.005 0.193
Notes: Estimates of relative differences in Columns 1-4 compare figures in Panels A to C of Table 8, with
Panel A as the baseline. p−values in Columns 5-8 for testing the equality of the same δestimates.
high school diploma in the HRS, for whom the relative difference is very modest.
However, the inspection of the bottom panel in Table 9 reveals that the information in a
39

single observed measure significantly under-represents the variation in subjective health relevant
for employment, particularly in ELSA. For all groups in ELSA, the share of employment decline
explained by changes in this measure is at least 50% lower than the same measure for the subjective
health index. For the HRS, the use of the single measure ‘health limits work’ also produces smaller
effects of changes in health on employment than those produced by our health index, but the
differences are smaller and only statistically significant at conventional levels for men.
Overall we find that the single subjective health index captures the variation in health that
is responsible for the decline in the employment rates of older workers as well as more detailed
measures of subjective health do. Our parsimonious yet complete representation of health is par-
ticularly useful in contexts that are only practical with low-dimensional specifications, such as in
structural models of health, employment and earnings. We therefore focus on results based on the
single subjective health index in what follows.
5.2 Using Instrumental Variables to Address Justification Bias and Measure-
ment Error in Subjective Health Measures
Subjective health measures can be afflicted by justification bias and measurement error that con-
found estimates of the effects of health on employment if subjective health is used as a proxy for
health status. We address this problem by instrumenting it with the full set of objective measures.
Objective measures focus on specific conditions and thus may provide an incomplete picture of
health status, but they are likely to be strongly related to the subjective measures. Moreover,
measurement error and justification bias in subjective health is likely to be unrelated to objec-
tive health. These features make the objective measures an ideal candidate for instrumenting the
subjective health index. Since the direction of the bias resulting from using subjective health to
proxy health status is indeterminate a priori, so is the direction of the correction from instrument-
ing it (see discussion in sections 3.2 and 3.3): IV estimates should be smaller than their linear
counterparts if justification bias dominates, while the opposite holds if attenuation bias dominates.
We start by testing the strength of the instruments when using the entire set of objective
measures, and will then discuss how estimates of the effects of health on employment change with
40

instrumenting. To test for weak instruments, we compare the F-statistics to Stock-Yogo critical
values: we reject the null of no statistically significant relationship between the subjective health
index and the objective health measures at the 5% significance level for all gender ×education ×
country cells, whether or not cognition is included in the regression model of employment. This
demonstrates that the objective measures are strong predictors of the subjective health index.
IV estimates of the fraction of employment decline explained by health and cognition are shown
in the two panels of Table 10, Panel A for the impact of health only and Panel B for the joint impact
of health and cognition. The estimates in both panels are very close; they are also overall similar
to the OLS estimates of the impact of subjective health and cognition on employment in Table 8.
They reveal that declining health can explain at most 15% of the decline in employment around
retirement age, and that cognition adds little to this and only for the HRS. What is also apparent
from these estimates is that both health and cognition are stronger drivers of the employment
choices for Americans than for the English. We further discuss this point in Section 5.4.
Table 10: Share of Employment Decline Explained by Subjective Health and Cognition - Subjective
Health Instrumented using Objective Health
Men Women
ELSA HRS ELSA HRS
Panel A: Subjective health
High School Dropout .086*** .142*** .055*** .136***
(.022) (.024) (.015) (.023)
High School .053*** .112*** .058*** .134***
(.015) (.011) (.016) (.011)
College .052*** .132*** .028** .100***
(.019) (.021) (.013) (.018)
Panel B: Subjective health and cognition
High School Dropout .085*** .158*** .054*** .147***
(.022) (.024) (.016) (.022)
High School .053*** .122*** .058*** .144***
(.014) (.011) (.016) (.011)
College .054*** .142*** .029** .103***
(.020) (.020) (.014) (.018)
Sample sizes 4,692 5,777 6,957 9,199
6,326 18,756 7,911 29,905
3,362 9,238 2,759 9,682
Notes: All estimates include age, age squared, wave dummies and the full set
of initial conditions. Standard errors are bootstrapped with 500 repetitions.
* indicates significant at 10%,** 5%, *** 1%.
The two panels of Table 11 compare the IV estimates in Panels A and B of Table 10 with their
OLS counterparts, respectively in Panels A and C of Table 6; the first four columns show the relative
41

differences between the IV and OLS estimates, using OLS estimates as the baseline, and Columns
5-8 show the p-values for testing their equality. The results suggest that measurement error and
justification bias do not seriously affect estimates, or at least that they offset. The OLS estimates
are of similar order of magnitude, albeit systematically smaller (hence the positive differences in
columns 1 to 4), than similar IV estimates. The null hypothesis that the OLS and IV estimates are
equal is not rejected at conventional levels in most cases. In the couple of cases where it is rejected,
which are both in the HRS, IV estimates are larger than their OLS counterparts.
Table 11: Percent Differences in the Explained Share of Employment Decline and p-values for
Testing Null of No Differences – Comparing OLS and IV estimates
Percent differences p-values
Men Women Men Women
ELSA HRS ELSA HRS ELSA HRS ELSA HRS
[1] [2] [3] [4] [5] [6] [7] [8]
Panel A of Table 10 vs Panel A of Table 6 (subjective health only)
High School Dropout 19.6 15.4 22.5 34.5 0.294 0.272 0.280 0.100
High School 29.8 1.1 22.5 20.1 0.247 0.462 0.284 0.048
College 31.2 55.7 23.0 29.4 0.295 0.021 0.377 0.136
Panel B of Table 10 vs Panel C of Table 6 (subjective health and cognition)
High School Dropout 18.8 9.0 27.0 18.8 0.300 0.342 0.263 0.198
High School 29.6 -2.2 23.8 13.1 0.247 0.415 0.275 0.117
College 32.9 37.3 22.7 21.1 0.290 0.049 0.378 0.201
Notes: Estimates of relative differences in Columns 1-4 compare figures in Panels A and C of Table 6 with
those in Panels A and B of Table 10, with Table 6 as the baseline. p−values in Columns 5-8 for testing the
equality of the same δestimates.
For the IV approach to be valid, any measurement error affecting the objective measures must be
orthogonal to that affecting the subjective measures. In particular, this rules out justification bias
affecting both objective and subjective measures. It also rules out the possibility that detection
of objective health conditions may be related to economic conditions, which might be the case
if seeking medical attention is a choice affected by access to health insurance, or if those with
higher socioeconomic status are more likely to be aware of their health problems (e.g., Johnston
et al. (2009)), for example. We test the validity of the IV approach by restricting the number of
objective instruments to represent only major conditions. These major conditions usually require
medical attention, making it unlikely that people would wrongly report whether they suffer from
one of them. The results from these estimates are shown in Section 4.3 of the Online Appendix
42

and are not statistically different from the estimates using the full set of instruments. We therefore
conclude that the measurement errors in our objective health measures and subjective health index
are unlikely to be correlated. Our findings suggest that justification bias, which has been a major
concern in the literature and is expected to bias estimates of the impact of health upwards, is either
not very important or is more than compensated by attenuation bias from measurement error in
the subjective measures.
Table 12 provides additional evidence on the validity of the single index assumption using the
overidentification restrictions supplied by the many instruments we are using. If the objective
measures affect employment only through their effect on subjective health, then the IV residuals
should not be systematically related to any of the objective health measures.
Table 12: Overidentification Test
Men Women
ELSA HRS ELSA HRS
[1] [2] [3] [4]
Panel A: Subjective Health
High School Dropout 0.221 0.217 0.134 0.001
High School 0.106 0.000 0.284 0.000
College 0.280 0.000 0.093 0.000
Panel B: Subjective Health, with Cognition
High School Dropout 0.203 0.238 0.136 0.001
High School 0.110 0.000 0.290 0.000
College 0.283 0.000 0.079 0.000
Notes: Table compares F-Statistic to χ2Critical Values, giving
p−values for the null of no statistical relationship between our
objective measures and the IV residuals.
We implemented the test by regressing the IV residuals on all the objective health measures and
all other explanatory variables in the employment regression, and then calculating the F-Statistic for
the full set of objective measures (as suggested by Davidson and MacKinnon (2003); see equations
9 and 10).19 The residuals were clustered at the individual level to account for serial correlation. In
Table 12 we show the p-values for testing the null hypothesis that objective measures affect labor
supply only through the subjective health (the IV exclusion restriction). The test results show
that the exclusion restriction is rejected in the majority of the cases in the HRS, whether or not
cognition is included in the regression model, but it is never rejected with the ELSA data.
19In practice we do the non-linear version of this test.
43

One possibility is that the impact of health on employment varies with health conditions, in
line with the argument that it is the serious and persistent conditions that most affect employment.
We test whether this may be the case by restricting the objective instruments to a subset of major
health conditions. These are heart problems, lung disease and whether the individual has suffered
a stroke or heart attack. When re-running the test on these more homogeneous set of conditions
we find much stronger support for the single index assumption. Table A17 in the Online Appendix
shows that, whether or not cognition is included in the regression, the null is only rejected for three
out of twelve cases (in all cases, better educated individuals from the HRS). This result suggests
that the impact of changes in health may be more important if these are driven by the onset of
more serious (and potentially long-lasting) health conditions.
5.3 Assessing bias due to omitted objective health measures
Objective health information is only collected for a subset of the relevant conditions, which is likely
to result in downward biased estimates of the impact of health on employment as discussed in
section 3.1. Here we assess the bias when using only a limited set of objective measures to proxy
for health. We estimated the alternative model of health as a function of the entire set of objective
measures in equation (4) to assess the severity of bias due to omitted objective measures; estimates
using all objective measures can be found in Panel D of Table 13. Even when they are added in a
fully flexible format, all objective measures together predict an employment decline that is generally
smaller than the estimated effects based on the subjective heath index – see Table 14 for percent
differences and p-values for testing the equality of predicted share in employment decline explained
by objective and subjective measures. The differences are modest, although statistically significant
for many groups, particularly in the HRS. For high school dropout women in both ELSA and the
HRS, the share of the employment fall predicted by health is actually larger when using the full
set of objective measures than when using the subjective health index; however, the differences are
small and only statistically significant for the HRS data.
These results are consistent with the hypothesis that using only a limited set of objective
measures provides an incomplete view of the health status affecting work capacity, and under-
44

Table 13: Share of Employment Decline Explained by Objective Health
Men Women
ELSA HRS ELSA HRS
Panel A: Blood pressure only
High School Dropout .030** .050*** .013 .053***
(.013) (.013) (.009) (.012)
High School .008 .023*** .004 .024***
(.009) (.006) (.007) (.006)
College .007 .034*** .005 .035***
(.009) (.010) (.010) (.009)
Panel B: Add Arthritis, Psychiatric, Lung
High School Dropout .061*** .102*** .045*** .126***
(.017) (.015) (.015) (.017)
High School .022* .061*** .039*** .075***
(.012) (.009) (.013) (.009)
College .024* .062*** .004 .056***
(.013) (.014) (.016) (.015)
Panel C: Add Cancer, Diabetes, Stroke, Heart Attack
High School Dropout .080*** .156*** .068*** .181***
(.018) (.019) (.017) (.022)
High School .033** .081*** .039*** .098***
(.013) (.011) (.013) (.010)
College .038** .096*** .012 .075***
(.015) (.017) (.016) (.016)
Panel D: Add Sight, Hearing – full specification
High School Dropout .081*** .152*** .067*** .197***
(.019) (.019) (.018) (.023)
High School .034** .084*** .038*** .101***
(.013) (.011) (.013) (.010)
College .038** .100*** .017 .073***
(.015) (.017) (.016) (.017)
Sample sizes 4,692 5,777 6,957 9,199
6,326 18,756 7,911 29,905
3,362 9,238 2,759 9,682
Notes: All estimates include age, age squared, wave dummies and the full set
of initial conditions. Standard errors are bootstrapped with 500 repetitions.
* indicates significant at 10%,** 5%, *** 1%.
Table 14: Percent Differences in the Explained Share of Employment Decline and p-values for
Testing Null of No Differences – Comparing Subjective and Objective Health Measures
Percent differences p-values
Men Women Men Women
ELSA HRS ELSA HRS ELSA HRS ELSA HRS
[1] [2] [3] [4] [5] [6] [7] [8]
Panel D of Table 13 vs Panel A of Table 10
High School Dropout -5.7 6.8 21.6 44.6 0.405 0.331 0.163 0.006
High School -36.6 -24.9 -33.9 -25.0 0.022 0.001 0.066 0.000
College -27.4 -23.9 -38.8 -26.4 0.159 0.028 0.159 0.004
Notes: Estimates of relative differences in Columns 1-4 compare figures in Panel D of Table 13 and those in
Panel A of Table 10, with the latter as baseline. p−values in Columns 5-8 for testing the equality of the
same δestimates.
45

estimates the impact of health on employment (recall discussion in Section 3.1). More generally,
however, our predictions of the effects of health based on objective and subjective measures are
much more similar than has been suggested in previous studies. Existing estimates based on
objective measures used only a subset of the measures we use here and found that they produced
much smaller estimates than subjective IV estimates: Bound (1991), for example, found that, a
single objective measure (future mortality) produced estimates of the effect of health that were only
about one tenth of the size of the subjective or IV estimates. Interestingly, but perhaps predictably,
we now find that a comprehensive set of objective health measures available in the HRS and ELSA
produces estimates that are much closer to the subjective IV estimates.
To further investigate the effects of using limited subsets of objective health measures, Panels
A to C of Table 13 show estimates of the explained share of employment decline from regressions
that gradually add more objective measures. The set of estimates in Panel A are based on a single
health measure, specifically whether the individual reports that they have high blood pressure;
estimates of the impact of health on employment in this specification are very small and naby
are not statistically significant at conventional levels. These results align well with the findings in
Bound (1991).20 The surprising results, however, are in Panel B. They show that the estimates of
the impact of health quickly converge to levels very close to those obtained when using the full set
of objective measures by adding just 3 more measures of objective health that arguably capture a
wide range of conditions (arthritis, psychiatric and lung diseases). Further adding more conditions
does not much change the estimates (Panels C and D). This suggests that the attenuation bias
5.4 Exploring between-country differences
Our estimates show that the share of decline in employment that is explained by declines in health
is consistently greater in the US than it is in England for all groups, often larger by a factor of
20We also estimated the effects of health on employment using each of the objective measures on their own, and
then every pair combination. Consistently with results in Panel A and those of Bound (1991) before us, the estimates
obtained in this way are always very small and mostly statistically insignificant at conventional levels. Moreover, we
reject the hypothesis of equality between these effects and those obtained using the full specification in Panel D in
the vast majority of cases. The equality between the effects based on two objective conditions and those obtained
using the full specification is not rejected only in 7 out of 435 cases. Using a single condition, we reject the null of
equality in all cases (out of 110). This clearly shows that very parsimonious models lead to systematic downward
bias in measuring the impact of health on employment.
46

approximately three. Here we decompose the differences in our main set of estimates for the US
and England – the δparameters defined in Equation (13) and presented in Table 10. Table 15 uses
an Oaxaca decomposition to describe how much of the difference δUS −δE ngland is explained by
differences in the impact of health and cognition on employment (θ), differences in deterioration
in health and cognition (∆H) and differences in the employment decline (∆Y). Breakdowns are
provided for both sets of estimates from Table 10, depending on whether only health (Panel A) or
also cognition (Panel B) are accounted for in estimating δ.21
Table 15: Oaxaca Decomposition of US-English differences
Men Women
θ∆H∆Y θ ∆H∆Y
Subjective health
High School Dropout 0.97 -0.04 0.07 0.85 -0.24 0.38
High School 0.97 -0.08 0.11 0.69 0.09 0.22
College 0.57 0.11 0.32 0.76 0.03 0.20
Subjective health and cognition
High School Dropout 1.03 -0.08 0.05 0.85 -0.19 0.33
High School 0.93 -0.02 0.10 0.74 0.06 0.20
College 0.70 0.01 0.30 0.86 -0.06 0.20
Notes: Decomposition of the US-English differences in the estimates of δby its different
components. Estimates are blanked out where they are uninformative. The columns
labelled ‘θ’, ‘∆H’ and ‘∆Y’ show the shares explained by differences in the estimated
coefficients, health declines and employment declines, respectively.
The general picture for all cases is that the majority of the between-country differences in how
much of the decline in health is explained by health or health and cognition can be attributed to
differences in the impact of these variables on employment (θ); differences in the decline of health,
cognition and employment are less relevant. The role of the impact of health on employment is
particularly dominant among men with less than college education, for whom it drives almost the
entirety of the between countries difference. For other groups, across countries differences in θ’s
explain two thirds or more of the differences in δ’s.
The larger response of employment to health in the US may result from differences in the
institutional backgrounds of the two countries shaping the employment responses to health around
21A description of the decomposition procedure can be found in Section 5 of the Online Appendix.
47

retirement age. For instance, the two countries differ in the provision of health insurance, which
is universal in England but not in the US, the generosity of disability benefits and the rigor of its
entitlement rules, and the design of financial incentives to retire and their age-dependence. For
example, the US disability system, which provides a health dependent benefit, is more generous
than the English one, and provides benefits only if beneficiaries do not work. Thus unhealthy
Americans have a strong incentive not to work. Compared to the US, England provides more
generous out of work benefits for reasons unrelated to health, such as unemployment benefits. All
these institutions are expected to play an important role in determining retirement choices and
their dependence on health. While establishing the importance of these channels certainly merits
further research, this is beyond the scope of this paper.
Less than one quarter of the difference for men, but more than one quarter of the difference
for women, can be explained by a larger employment drop in England among those in their 50s
and 60s. Here we notice that employment drops sharply in England at the state pension age (60
for women, 65 for men), but it declines much more gradually and slowly in the US (recall Figure
3). While this is likely related to differences in the retirement incentives for these age groups, it
implies that Americans are more likely to work into older ages than the English. Hence, Americans
may be more exposed to the onset of health conditions leading to retirement during their (longer)
working lives. In turn, the English are more likely to be already retired when experiencing a similar
deterioration in health.
6 A framework to understand the employment choices of older
workers
The previous section presents reduced form evidence that bad health is associated with lower
employment, conditional on past employment, health, and other variables. This section presents an
economic model of employment choices, savings and health for older workers, and use it to motivate
the empirical strategy used in the previous section, to highlight its underlying assumptions, to guide
the interpretation of our estimates and to discuss the key mechanisms that drive the impact of health
48

on employment. The structural model can be used to identify and quantify such mechanisms (e.g.
preferences, productivity, and financial incentives).
6.1 The model
We consider the problem of individuals deciding whether to work near retirement age. Our aim here
is to focus on the simplest dynamic model that can represent the many ways in which health affects
employment among older workers. In our model, individuals decide in each period whether to work,
how much to consume and how much to save for the future. They do so in a risky environment,
where they face uncertainty in future health, wages and preferences for working. Health-related
benefits, or disability benefits, partially insure against income losses associated with bad health,
but as with other social insurance instruments, they also change working incentives. Individuals
may save to further insure themselves against economic consequences of health and other shocks.
In what follows, we briefly formalise the model.
Preferences
Individuals are indexed by i. They seek to maximize the expected discounted value of their present
and future utility by choosing employment at each age t. We consider a single cohort, so age and
time are used interchangeably. In each period, workers derive utility from consumption and leisure
in a way that depends on health status:
u(Cit, Yit , Hit, ξi, ζit) = Yit ∗(θ0+θ1Hit +ξi+ζit)+C1−γ
it
1−γ(14)
where uis the per-period utility function, Cis consumption, Yis employment status and assumes
the values 0 and 1 for not-working and working respectively, and His health. Including health in
the utility function formalizes the idea that working is more costly in periods of poor health and
captures the empirical regularity that sick people work less. Finally, ξand ζrepresent unobserved
idiosyncratic permanent and transitory preferences for work, respectively.
49

Budget Sets
The potential earned income of individual iat age t,Wit, is realized if Yit = 1. It varies with
age and health status. For simplicity, we omit other exogenous characteristics that may drive
wages. We allow for two individual-level unobserved components in wages, a permanent unobserved
heterogeneity element φ, which we interpret as ability, and a time-varying wage shock ν. Earned
income is, therefore:
Wit =ω(t, Hit φi, νit).(15)
Individuals in bad health may be eligible to benefits Bt(Hit) but entitlement depends on their
other income, being taxed away at a rate τt(WitYit, Hit ), which may change over time and with
the age of the individual as s/he approaches retirement. So the asset accumulation equation is:
Ait+1 = (1 + r) [Ait +Wit Yit (1 −τt(WitYit , Hit)) + Bt(Hit)−Cit].(16)
Health and mortality
When deciding about employment and savings, individuals are faced with health uncertainty. We
pose that health follows an age-dependent Markov process
Hit =h(t, Hit−1, ψi, it) (17)
where ψand ζare the unobserved permanent and transitory elements of health. In line with our
empirical findings, we model health as a uni-dimensional variable.
Besides its impact on the utility cost of work and wages, we also formalise the impact of health
on survival: a worker alive at age twith health status Hsurvives to age t+ 1 with probability
s(t, H).
Structure of the unobserved components
We allow for unobserved heterogeneity in health, wages and preferences for work (ψi, φi, ξi), and for
arbitrary correlation between these three dimensions of heterogeneity. We also consider transitory
50

unexpected shocks to health, wages and preferences, (it, νit, ζit), which are serially uncorrelated,
mutually independent and independent from the unobserved heterogeneity components.
The individual’s problem
At age t, the state vector of the worker iis Ωit = (Hit , Wit, Ait, t, ψi, φi, ξi, ζit). In recursive form,
the worker’s problem is
Vt(Ωit) = max
Yit,Cit
{u(Cit, Yit , Hit, ξi, ζit) + β s(t, Hit) EtVt+1 (Ωit+1)}(18)
subject to equations (15)-(17). In the above equation, βis the subjective discount factor.
6.2 How health affects employment of older workers
The addition of health to an otherwise stylized structural model of employment and savings exposes
various channels through which health affects employment. In our simple model, a negative health
shock reduces preferences for work, wages and expected longevity, and it increases entitlement to
benefits.22
Formally, the structural labor supply function is
Yit =Y(Hit, Wit , Ait, t, φi, ψi, ξi, ζit |θ) (19)
where θis the set of all parameters in equations (14)-(18). In the context of this labor supply
function, we can see multiple pathways by which health deterioration with age may impact labor
supply. In particular, we identify five channels through which bad health shocks can discourage
work, all of which are expressed in our structural model:23
1. Preferences. Bad health can raise the marginal utility of leisure relative to that of consumption
(Capatina, 2015). This is embodied in equation (14), where health is allowed to interact with
22These are only some of the mechanisms driving employment changes among older workers. They may also face
increasingly unfavorable incentives to work created by the tax, benefit and pension systems. Changes in health
interact with these other mechanisms by altering the value of wealth holdings and the entitlement to pensions and
benefits.
23One mechanism that we do not consider explicitly is medical expenses. This is important in the US (see
Pashchenko and Porapakkarm 2013, Kitao 2014, Kim 2012) but less so in the UK or in most other European
countries, where full coverage of medical expenditures is independent of income and employment.
51

the utility value of working. For this reason, health Himpacts employment directly in
equation (19).
2. Productivity. Bad health can lower workers’ productivity and resulting wages. This is rep-
resented in equation (15), where function ω(.) captures the potentially negative impact of
health on wages. So health may affect employment indirectly through wages W.
3. Disability insurance benefits. People in sufficiently bad health may qualify for benefits from
disability programs. This is embodied in B, the benefit amount, and also in τ, the share of
earned income that is taxed away. Those receiving benefits have incentives to reduce labor
supply through several channels. First, the benefits provide income, allowing individuals to
purchase more leisure. Second, in many countries the benefits are means-tested and sometimes
limit work altogether. Moreover, in the US, beneficiaries can receive Medicare or Medicaid
health insurance depending on their working income, with excessively high income triggering
the loss of benefits.
4. Expectations of future employment and earnings capacity. The persistent health process
described equation (17) implies that current shocks may have long-lasting effects on future
health and thus future employment and earnings capacity. This changes the value of savings
and, hence, that of employment.
5. Life expectancy. With shorter expected lifespans, individuals in bad health may not need to
work as long to accumulate savings for retirement. This effect operates through the survival
probability s(t, H) in equation (18).
Most papers consider only a subset of these channels. For example, French (2005) and Capatina
(2015) consider four of the five channels, excluding only disability benefits. French et al. (2018)
and Kitao (2014) accounts for disability benefits but French et al. (2018) use a stylized model
of disability benefits and Kitao (2014) uses a very stylized model of demographic transitions and
health insurance.
52

6.3 Approximation model
In this section we demonstrate how our simple reduced form model of employment, described in
detail in section 3, can be derived as an approximation to the solution of the dynamic labour supply
model. The process of doing so provides further clarity on the interpretation of the estimates in
section 5.
In the structural model, the work decision is defined as
1{Yit = 1 |Ωit }=1max
Cit
{u(Cit,1, Hit , ξi, ζit) + β s(t, Hit) EtVt+1 (Ωit+1)}(20)
−max
Cit
{u(Cit,0, Hit , ξi, ζit) + β s(t, Hit) EtVt+1 (Ωit+1)}>0
To the extent that time periods are short, separability between leisure and consumption in the
utility function implies that the marginal utility of consumption is only mildly affected by labour
supply. This simply reflects consumption smoothing, as any additional income received in a period
is consumed over time and, therefore, mostly saved in the period it is realized. But then, the
additional income from work will be valued at the marginal value of assets (which, by the envelope
condition, equals the marginal utility of consumption). We can then rewrite equation (20) as
1{Yit = 1 |Ωit }
≈1(θ0+θ1Hit +ξi+ζit) + β(1 + r)s(t, Hit )Wit(1 −τit)∂EtVt+1 (Ωit+1)
∂Ait+1
>0
=1n(θ0+θ1Hit) + C−γ
it Wit(1 −τit ) + ξi+ζit >0o
=1{Y∗
it >0}
where C−γ
it is the marginal utility of consumption, Wit(1 −τit) is the change in income induced by
a move into work, τit is an abbreviation for τt(Wit Yit, Hit) and Y∗
it is the latent employment index.
This is the discrete choice version of the marginal rate of substitution condition, a condition that
holds exactly as the time periods become arbitrarily short.
In a cross section, Hit may be correlated with Cit, Wit , τit,or ξi, leading to biased estimates of
θ1if these variables are not added to the regression model. This is for two reasons. First, while θ1
53

is a deep parameter that represents how preferences for work change with health, its estimate will
conflate other mechanisms such as the indirect impact of health on employment through its effect
on wages. Second, health is likely correlated with permanent individual characteristics that also
determine employment, such as those settled in childhood through investments and other factors.
We use initial conditions to address this second problem.
To proceed, we write the employment index for period tand an initial period 0:
Y∗
it =θ0+θ1Hit +C−γ
it Wit(1 −τit ) + ξi+ζit (21)
Y∗
i0=θ0+θ1Hi0+C−γ
i0Wi0(1 −τi0) + ξi+ζi0(22)
We then combine these two equations to obtain the following expression:
Y∗
it =θ1(Hit −Hi0) + C−γ
it Wit(1 −τit )−C−γ
i0Wi0(1 −τi0)+ (ζit −ζi0) + Y∗
i0
=θ1(Hit −Hi0) + "Cit
Ci0−γWit(1 −τit )
Wi0(1 −τi0)−1#C−γ
i0Wi0(1 −τi0)+(ζit −ζi0) + Y∗
i0(23)
≈θ1(Hit −Hi0) + −γln Cit
Ci0+ ln Wit
Wi0+ ln 1−τit
1−τi0C−γ
i0Wi0(1 −τi0)+(ζit −ζi0) + Y∗
i0
where the third approximate equality results from a simple Taylor series approximation. The key
issue to notice here is that, by using initial employment we were able to eliminate unobserved
heterogeneity in preferences for work from the employment equation.
We now project growth rates in the marginal utility of consumption, wages, and taxes, weighted
by the initial marginal of consumption and the initial after tax wage, on initial health, change in
health, initial employment index and other exogenous variables:
−γln Cit
Ci0C−γ
i0Wi0(1 −τi0) = δC0+δCH (Hit −Hi0) + δC H0Hi0+δC Y 0Y∗
i0+δCZ Zit +ωC it
ln Wit
Wi0C−γ
i0Wi0(1 −τi0) = δW0+δW H (Hit −Hi0) + δW H 0Hi0+δW Y 0Y∗
i0+δW Z Zit +ωW it
ln 1−τit
1−τi0C−γ
i0Wi0(1 −τi0) = δτ0+δτ H (Hit −Hi0) + δτ H 0Hi0+δτ Y 0Y∗
i0+δτ Z Zit +ωτ it
In the above expression, Zit summarises variables that may affect changes in consumption, wages
54

or taxes, including time dummies and a second order age polynomial. Thus the coefficients on age
in the projection of the rate of change in the tax rate (line 3) will partly capture how the work
incentives change with age around retirement.
By replacing the above expressions in equation (23) yields the key equation that motivates our
empirical specification:
Y∗
it =δ0+θH(Hit −Hi0) + δH0Hi0+δY0Y∗
i0+δZZit +ωit (24)
where
δ0=δC0+δW0+δτ0
θH=θ1+δCH +δW H +δτ H
δH0=δCH 0+δW H0+δτ H 0
δY0= 1 + δCY 0+δW Y 0+δτ Y 0
δZ=δCZ +δW Z +δτ Z
ωit = (ζit −ζi0) + ωCit +ωW it +ωτ it
(25)
The second line of equation (25) shows that θHin equation (24) measures a combined effect of
the change in health on employment, arising both from its impact on preferences to work and,
indirectly, through its impact on the marginal utility of consumption, wages and the tax rate. Here
the mechanisms discussed in the previous section are all represented: the direct impact through
preferences is captured by θ1; indirect effects through productivity and benefit entitlement are re-
flected on the parameters from the wages and tax projections, respectively; and changes in expected
future health, lifespan and consequent future value of work are reflected in the parameters from
the projection of the marginal utility of consumption.
The final line of equation (25) shows that the residual in equation (24) is a function of the
transitory shocks to preferences for work, and the orthogonal residuals from the projection of the
changes in the marginal utility of consumption, wages, and taxes on health, initial health, the initial
employment index, and Z. If ζit follows a random walk, and innovations are uncorrelated with the
initial value of health and Y∗
i0, our procedure should produce consistent estimates.
55

The expression in equation (24) can be trivially re-arranged to match our empirical specification
(2), that we repeat here for reference
Y∗
it =θ0+θHHit +θXXit +eit.
In the above equation, and as discussed in section 3, Xincludes all variables in Z(i.e. time
dummies and an age polynomial) and the initial condition in health H0. The only difference
relative to equation (24) is that the initial index Y∗
i0, which is not observed, is approximated by a
function of initial employment Yi0and a set of other variables that determine initial labour market
attachment, including working experience accumulated so far, wealth, marital status and health in
childhood.
Crucially for our purposes, the parameter of interest θHis the same in the two equations.
Therefore, the key insight from this exercise is that, by controlling for initial health and employment
while focussing on the effects of changes in health, we are able to eliminate bias in the estimation
of θHthat is induced by the potential correlation between unobserved heterogeneity in health,
preferences for work and wages, (ψi, ξi, φi). As a by-product, we are also capable of revealing the
response mechanisms encompassed in the parameter θH.
Now suppose that, instead of controlling for initial conditions, we depart from equation (21) and
project the marginal value of the additional income on current health and the exogenous variables
Z:
C−γ
it Wit (1 −τit) = ˜
δ0+˜
δHHit +˜
δZZit + ˜ωit
Replacing in equation (21) yields
Y∗
it =˜
θ0+˜
θHHit +˜
δZZit +ξi+ζit (26)
where ˜
θH=θ1+˜
δH. Equation (26) matches our empirical employment model without initial
conditions.
The two empirical models in equations (24) and (26) differ in two substantial manners. First,
56

the parameters identified in each case, θHand ˜
θH, are not the same. While θHencompasses all
the 5 response channels we describe in section 6.2, ˜
θHdoes not account for the indirect impact
on employment of the contemporaneous effects of health on productivity and benefit entitlement.
And second, by not exploiting longitudinal information, model (26) does not eliminate unobserved
heterogeneity correlated with current health. As a consequence, estimates of ˜
θHare likely to be
biased and we would expect the direction of the bias to be positive.
6.4 Using the reduced form regressions to assess structural models of health
The findings from the reduced form model inform the structural work, just as the structural model
can help us interpret the reduced form work. Our three key findings for structural modeling are as
follows.
First, and most importantly, a carefully constructed single health index captures well the in-
centives for labor supply. We found relatively little evidence against the assumption of a single
health index in our reduced form analysis, and this finding supports the use of a single index in
structural models. In fact, the vast majority of life cycle models that account for health consider
only a single health index (see French (2005), French and Jones (2011), French et al. (2018), Braun
et al. (2015), De Nardi et al. (2017), Pashchenko and Porapakkarm (2013), Aizawa and Fu (2017),
as well as the references in Footnote 24. Exceptions include Capatina et al. (2018) and Gustman
and Steinmeier (2014)). However, we found that the most commonly used measure of health in
structural studies, which assesses whether the respondent has a health condition that limits work,
understates the impact of health on labor employment modestly in the HRS and strongly in ELSA
relative to our preferred measure.
Second, dynamics are important. Accounting for initial conditions, and thus exploiting more
transitory fluctuations in health, reduces the estimated impact of health by about half in England
and a quarter in the US. Our model shows why this is important and reveals several channels
through which changes in health affects changes in employment. We should point out that it is not
obvious which of these channels are most important.
The model we described does not include all the channels by which health and employment may
57

be related. For instance, it is conceivable that higher incomes cause better health. The Grossman
(1972) model implies that those with higher income may be able to purchase better nutrition
and health care, improving later health outcomes. The structural analyses of models allowing for
both directions of causality is becoming increasingly common.24 Another potential mechanism is
embedded in the learning-by-doing model, whereby workers productivity on the job, and hence
wages, increase with accumulated working experience.25 In that case, bad health shocks that lower
current employment affect future wages because of the loss in working experience. The consequent
lower future wages negatively affect future employment, even if health recovers. We believe that
more structural work is necessary to disentangle the various mechanisms by which employment and
health are related.
Third, the US/England differences in estimates are notable. We noted an important institu-
tional difference between the two counties in that the US disability system provides a relatively
generous health benefit that is conditional on not working. Thus unhealthy Americans have a
strong incentive not to work. Compared to the US, England provides more generous out of work
benefits for reasons unrelated to health, such as unemployment benefits, but relatively less generous
disability benefits. These institutional differences suggest that modeling the labor supply incen-
tives of the disability insurance system is key to better understand how health affects employment
decisions.
7 Conclusion
This paper aims to provide a better understanding of the role of different measurements of health in
the estimation of the impact of health on employment. We find, broadly, that estimates of the share
of the decline in employment explained by declines in health are remarkably robust to the choice
of health variable used; using a single subjective measure of health, multiple subjective measures,
24 See Ozkan (2014), Fonseca et al. (2009), Blau and Gilleskie (2008), Pelgrin and St-Amour (2016), Cole et al.
(2012), Hai (2015), Halliday et al. (2017), Hugonnier et al. (2012), and Scholz and Seshadri (2016). Outside the
economics field, the predominant view is indeed that income causes health rather than vice-versa (see Brunner (2017)
for a recent review).
25Examples of papers that account for this mechanism include Capatina et al. (2018) and Gilleskie et al. (2017b).
58

multiple objective measures, or subjective measures instrumented with objective measures makes
little difference to our estimates. We conclude that this suggests measurement error and justification
bias are not important sources of bias, or at least that the two sources of bias offset one another.
We also find that while cognition is highly correlated with employment, including it as additional
health measure does not have a dramatic impact either. These findings are consistent across the
US and England.
We do find that our estimates are sensitive to four important modelling decisions, however.
First, controlling for initial conditions such as initial health and employment considerably lowers
estimates, suggesting cross sectional estimates of the relationship between health and employment
are biased. Second, consistent with Bound (1991), we find that using a very small number of
objective measures results much smaller estimates, suggesting these estimates suffer from omitted
variable bias. Third, health is a more important driver of employment among high school dropouts,
and its effects tends to drop with education. And fourth, our estimates are consistently much larger
in the US than in England. This is driven predominantly by the impact of health on employment,
rather than by differential declines in employment or health. It suggests that institutional setting
is a key component in determining the impact health has on employment.
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