How Do Pre-Retirement Job Characteristics Shape One’s Post-Retirement Cognitive
Performance?
Dawn C. Carr, PhD1
Stanford University
Melissa Castora-Binkley, PhD
University of South Florida
Ben Lennox Kail, PhD
Georgia State University
Robert Willis, PhD
University of Michigan
Laura Carstensen, PhD
Stanford University
November 9, 2015
1
Carr, corresponding author, can be reached at 579 Serra Mall, Stanford, CA, 94305; email:
carrdc@stanford.edu; (650) 736-8643 (phone); (650) 723-1217 (fax). We are grateful to Michael
Hurd for his comments on an earlier version of this paper at the conference on “Working Longer” at
the Stanford Institute of Economic Policy Research, October 8-9, 2015.
1
ABSTRACT
Objectives: This study seeks to examine whether pre-retirement occupational
characteristics impact cognitive changes associated with retirement.
Method: Using data from the Health and Retirement Study, we examined a sample of adults
age 50 years or older with normal cognitive function over four waves who, at baseline, were
working full-time and subsequently either retire (n=721) or remain full time (n=1,296). We
adjusted for potential selection bias using propensity scores. Exploratory factor analysis
was used to identify two key job factors – intellectual and mechanical – which were coded
as low, moderate, or high.
Results: Among retirees, the lowest cognitively complex jobs were related to a significantly
greater level of cognitive decline relative to both those who retired from moderate or the
highest cognitively complex jobs. Among retirees, low compared to high mechanically
complex jobs were associated with significantly less decline. Remaining in full-time work
was related to consistent levels of cognitive decline regardless of cognitive or mechanical
complexity of one’s job. Among those in the highest cognitively complex and those in
moderately mechanical jobs, there were no differences in cognitive decline between
continuous full-time workers and retirees.
Discussion: These findings contribute to the growing base of research helping explain how
occupational factors influence cognitive changes that occur with aging and retirement. We
suggest that scaffolding theory, a recent theory from cognitive psychology and
neuroscience, in combination with human capital theory may explain the mechanism
underlying our findings.
Key Terms: cognitive performance, retirement, propensity score weighting, Health and
Retirement Study
2
Running Head: Pre-Retirement Job Characteristics and Cognitive Decline
3
INTRODUCTION
At a population level, there is growing evidence that retirement has a significant,
negative impact on one’s cognitive performance in later life. This finding is not merely
because those with declining cognition retire while those with more robust cognitive
performance continue to work. Rather, several papers find that the negative impact of early
retirement on cognition, measured by a test of episodic memory, is causal (Rohwedder &
Willis, 2010; Bonsang, Adam, & Perelman, 2012; Celidoni, Bianco, & Weber, 2013). These
findings have been interpreted in the context of the long standing “use it or lose it”
hypothesis that holds that cognitive declines associated with aging can be reduced by
engaging in mental exercise. The negative impact of retirement on cognition then follows
from the further hypotheses that the work environment provides more mental stimulation
than the home environment and, possibly, that the expectation of early retirement reduces
the incentive older workers to exert the mental effort needed to maintain their skills.
While evidence is accumulating that leaving work has a negative impact on the
cognitive performance of older people, the mechanisms that underlie this effect have not
been fully clarified. In this paper, we build on findings of several recent studies of older
adults which suggest that pre-retirement job characteristics shape the degree to which
retirement influences changes in cognitive performance. This paper adds to this line of
research by estimating how retirement impacts change in cognitive performance over a sixyear time span among workers whose jobs vary in complexity in both cognitive and
mechancial dimensions.
To help develop hypotheses about the impact of occupational complexity, we draw
on recent advances in cognitive psychology and neuroscience that are embodied in the
“scaffolding theory of aging and cognition” (STAC) proposed by Park and Reuter-Lorenz
2009). The STAC is motivated by noting that while many components of cognition such as
4
working memory, ability to learn and recall new information and fluid intelligence (i.e.,
reasoning ability) decline with age, most older adults continue to be able to function quite
well despite these declines. Park and Reuter-Lorenz argue that the aging brain develops
compensatory scaffolding (i.e. recruitment of additional neural circuitry) to shore up the
deteriorating components whose function has become noisy, inefficient or both.
Experimental evidence shows that sustained cognitive effort in learning a new complex task
has a postive effect on episodic memory (Park et al. 2014)
We argue that the scaffolding theory is consistent with human capital theory. In that
theory, an individual’s productivity in a given task depends on reasoning ability (Gf: fluid
inteligence) and on the extent of knowledge relevant for that task (Gc: crystallized
inteligence) where Gf and Gc tend to be complementary. Early in life, Gf increases the
productivity of people in acquiring useful knowledge through schooling, job experience and
and other activities (e.g., managing finances, rearing children). Later in life, accumulated
knowledge increases the productivity of persons whose reasoning ability has declined.
When asked to solve a novel problem, brain imaging studies show that the left pre-frontal
cortex of young people lights up, suggesting that Gf is primarly involved in finding a
solution. For older people confronted with the same problem, both the left and right lobes
light up, suggesting that retreival of knowledge through memory processes as well as
reasoning are involved. In addition, the studies find that higher performing older adults
show a greater degree of bi-lateral activity than lower performing adults. Cognitively
complex jobs plausibly require more mental exercise in order to maintain skills and
perform more challenging tasks. This, in turn, stimulates compensatory scaffolding which
serves to reduce the decline of episodic memory (Li, Baldassi, Johnson, & Weber, 2012) .
Moreover, greater scaffolding may enhance performance in non-work environments, thus
lessening the effect of retirement on cognition.
5
Estimating the effect on cognition of stopping work versus the alternative of
continuing to work inherently involves dealing with missing data on the unobserved
alternative. Since any given individual can follow only one alternative, it is impossible to
know what that person’s cognitive score would have been had he or she followed the other
alternative. If it were possible to randomly assign people to a “treatment” consisting of a
given pattern of work and retirement, we could estimate the average treatment effect (ATE)
by calculating the difference in the mean cognitive change experienced by people who
follow each alternative. However, individuals (or their employers) choose which path will
be followed; hence, the assignment to a given treatment is non-random.
In this paper, we employ a counterfactual framework involving a comparison of
potential outcomes—i.e., mean change in cognition over a six year period—for persons who
are are fully employed during their first two waves in the Health and Retirement Study and
are fully retired during the next two waves compared to a second group who who work full
time during all four waves. Under the assumption that selection into these two groups is
random, conditional on observable characteristics measured at baseline, the difference in
potential outcomes provides an unbiased measure of the causal average treatment effect of
retirement on cognition. We discuss the plausibility of this assumption in the context of
describing our econometric model.
Previous Literature
Three recent papers have begun to examine how the complexity of the work
environment is related to cognitive change. The first, using data from the Swedish
Adoption/Twin Study of Aging (Finkel, Andel, Gatz, & Pedersen, 2009) examined complexity
of occupation on cognitive trajectory at retirement. This study found that individuals with
occupations involving “high engagement with people” experienced greater improvement in
6
verbal skills up until retirement, but experienced a faster rate of decline following
retirement. The authors proposed that taking away work from one’s lifestyle as a key source
of mental exercise, i.e., engaging with people, had a detrimental effect on cognitive aging.
A second study of US adults showed that those who engaged in more mentally
demanding jobs had higher cognitive function prior to retirement, and experienced less
decline in cognitive performance following retirement (Fisher et al., 2014). The authors
proposed that these results might stem from individuals with more cognitively complex
jobs accumulating greater cognitive resilience through their pre-retirement job from which
to off-set the effects of cognitive aging following retirement.
Finally, a study using National Survey of Japanese Elderly longitudinal data (Kajitani,
Sakata, & McKenzie, 2013) similarly found that men who have careers that require high
mathematical development, reasoning development, and language development experience
less decline in memory following retirement. They also observed that jobs high in physical
engagement related to greater deterioration in memory loss after retirement.
In combination, these three studies offer compelling evidence that the
characteristics of one’s work environment and associated lifestyle play critical roles in one’s
cognitive functioning prior to and following the retirement transition. However, these
studies did not take into consideration the alternative to retirement – the expected
cognitive trajectory had those individuals continued working. Notably, some individuals
may experience a hastening of age-related cognitive decline despite continued employment,
which may be unrelated to a retirement transition per se and perhaps related instead to
pre-retirement occupational factors. Other individuals alternatively may experience little or
no decline with or without a retirement transition. In fact, our recent research shows that
the effects of work-retirement patterns on cognitive performance are not universal. For
some social groups, the retirement transition offers no better or worse effect on cognitive
7
performance than does continuous full-time work (Carr et al., under review). As a result, the
effect attributed to retirement in previous research may be related to other factors. The
current study seeks to address this by examining the effect of retirement relative to not
retiring on cognitive change for those with similar occupational characteristics.
Theoretical Framework
One reason working may offer a better cognitive trajectory relative to retirement is
that working provides a more cognitively beneficial lifestyle (Rohwedder & Willis, 2010). In
other words, when people retire and stop working, they stop “using it,” and subsequently
“lose it,” or rather, they experience more rapid cognitive decline (Foster & Taylor, 1920). It
is not necessarily just the capacity to learn that impacts cognitive performance, but the
motivation to seek out cognitively engaging opportunities. Being removed from a complex
environment, as occurs with retirement, may modify one’s cognitive trajectory because an
individual is no longer required to engage in cognitively complex tasks. Some people do not
seek out opportunities to maintain their cognitive function after they retire (Schooler, 1984,
1990; Schooler, Mulatu, & Oates, 2004).
One potential mechanism related to the beneficial effects of cognitively complex
environments like work could be the building of cognitive capacity throughout one’s life
span (even into later life). That is, spending many years in intellectually stimulating or
mechanically complex environments – likely related to both educational attainment and
occupation factors (Potter, Plassman, Helms, Foster, & Edwards, 2006) – leads to greater
neuronal development, and that accumulation of excess neuronal resources, or cognitive
reserve, may help people stave off the cognitive losses that come with aging (Fratiglioni &
Wang, 2007).
8
Regardless of the specific mechanisms at play, an individual’s cognitive aging
process appears to be influenced by a combination of mental stimulation across the life
span (i.e., the tendency of those with greater cognitive function to pursue more complex
jobs and activities leading to more significant accumulation of cognitive resources), and the
individual and environmental factors that impact one’s cognitive engagement in later life
(i.e., the extent to which an individual is capable and motivated to maintain cognitive
function in spite of changes to the environment) (Salthouse, 2012; Salthouse, 2006;
Salthouse, Atkinson, & Berish, 2003; Salthouse, Berish, & Miles, 2002). Thus, the potential
relation between retirement and cognitive decline might be thought of as a response to the
way pre-retirement cognitive engagement “habits” adapt to a non-work lifestyle and
environment.
To understand this process, we rely on the Scaffolding Theory of Cognitive
Engagement (STAC). According to STAC, brains respond to changes associated with aging
through utilization of “scaffolding,” or the development of effective adaptive responses
(Park & Reuter-Lorenz, 2009). They write:
Scaffolding is a normal process present across the lifespan that involves use
and development of complementary, alternative neural circuits to achieve a
particular cognitive goal. Scaffolding is protective of cognitive function in the
aging brain, and available evidence suggests that the ability to use this
mechanism is strengthened by cognitive engagement, exercise, and low
levels of default network engagement.
It is plausible that certain job characteristics, particularly intellectual and
mechanical tasks, shape one’s ability to cognitively adapt to age- and environment-related
changes. The skills, abilities, and behaviors utilized while engaging in work-related tasks, or
during certain job-related training, skills, and education, can be thought of as a form of
“scaffolding” that can be honed during one’s career and tapped into during the post-work
period. So-called cognitive maintenance following retirement (despite disengagement from
9
work) could also be thought of as cognitive “resilience” because the effects of retirement on
cognition are less than expected (Mukherjee et al., 2014). Alternatively, in some cases, a job
may be cognitively stimulating enough to maintain cognitive function while working, but
not offer sufficient cognitive scaffolding to adapt to the deficit of work-related stimulation in
retirement, yielding significant cognitive loss. To that end, it is important to account for
level of complexity and the effect on retirement by occupational characteristics between
those who retire and those who continue to work when studying cognition as it relates to
the retirement process.
Research Question and Hypotheses
Specifically, this research is designed to address the following research question:
How do pre-retirement occupational characteristics (i.e., intellectual and mechanical) impact
cognitive changes associated with retiring relative to staying engaged in full-time work?
Based on empirical evidence and the STAC, we propose three hypotheses. First, we
hypothesize that the relationship between retirement and cognitive decline is dependent on
the cognitive stimulation of the pre-retirement job. Specifically, those with jobs that require
more intellectual engagement will be more resilient and thus, experience less cognitive
decline relative to those with jobs that require less intellectual engagement. However, those
with jobs that require more mechanical engagement will be less resilient and thus,
experience more cognitive decline relative to those with jobs that require less mechanical
engagement. Second, we hypothesize that the effect of intellectual and mechanical complexity
of work will be less significant for those who continue to engage in full-time work than for
those who go on to retire. In other words, we expect that the work “lifestyle” will facilitate
maintenance of cognitive performance when people retire, but the absence of a work
10
lifestyle will increase the importance of non-work lifestyles in determining the impact of
retirement on cognitive performance.
DESIGN AND METHOD
Our study uses the Health and Retirement Study (HRS), a nationally representative
longitudinal survey of individuals over age 50 (and their spouses, regardless of the spousal
age). We use data from biennial waves of the HRS from 1992 to 2010. These data are ideal
for this study because they offer the most comprehensive nationally representative panel
data on US older adults available, including information about cognitive performance and
work behaviors (Lachman & Weaver, 1997; RAND Center for the Study of Aging, 2008;
Smith et al., 2012). For the current study, we include only individuals older than 50.
Selection of Full-Time Workers and Retirees
To test our hypotheses, we selected two samples: full-time workers and retirees.
First, to evaluate the effect of pre-retirement job complexity on change in cognitive
performance, we began by identifying full-time workers – i.e., those who worked 35 hours
or more and self-identified as not retired. From this group, we identified two samples –
those who transition from full-time work in wave t to retirement in wave t+1and those who
stay working full-time in both waves. We exclude retirees who engage in paid work for two
reasons. First, given the focus of this study on the lasting cognitive impact on departing
from paid work, those engaging in paid work in retirement are still participating in a “work
lifestyle.” While it may be helpful to assess the effect of variations in pathways to retirement
on the cognitive decline trajectory, individuals whose labor force status was recorded as
“retired” (even if they did engage in part-time paid work) were not consistently asked about
their occupation, preventing us from taking into consideration how work tasks changed
11
post-retirement. Additionally, recent research suggests that regardless of how retirement is
defined, the relative effect of characteristics of pre-retirement work on post-retirement
cognitive performance does not change (Kajitani et al., 2013). Thus, for this study, we
choose a conservative definition for retirement, limiting our retiree sample to those
individuals who transition from full-time work to complete retirement (i.e., for the first time
while participating in the HRS, self-identifying as being retired and working 0 hours per
week).
Second, in order to accurately measure cognitive changes in association with a
potential retirement transition, we selected specific pre- and post-retirement cognitive
performance measures. First, there is evidence that people may begin cognitively
disengaging from work in preparation for retirement, and this may result in cognitive
decline while working in the period leading up to retirement (Bonsang et al., 2012; Willis,
2013). Thus, to avoid this complication, our baseline cognitive performance occurs two
waves prior to retirement, limiting our sample only to those working full-time for two
consecutive waves prior to retirement. Second, the long-term adjustment to retirement,
with regard to a shift in the cognitive performance trajectory, does not occur until at least
one full year following retirement (Bonsang et al., 2012). Thus, to ensure that our postretirement cognitive performance is observed with an appropriate lag, our post-retirement
measure derives from cognitive status at the wave following reported retirement, limiting
our sample to only those retirees who continuously remain fully retired in the wave
following reported retirement.
Because persistent full time workers are not, by definition, observed making a
retirement transition, we use the most recent four-wave period of consistent full-time work
for the full-time working sample. For this group, baseline cognition is measured at Time 1,
compared with cognitive performance in Time 4 of continuous full-time work.
12
Third, in order to minimize the potential endogenous effect of declining cognitive
status accelerating the decision to retire and therefore, increasing the effect of retirement
on change in cognitive performance, we only considered individuals with normal preretirement cognitive performance. Specifically, we excluded all individuals who had a
cognitive score indicating cognitive impairment during either of the two waves of full-time
work preceding potential retirement. Our final pooled sample of retirees included 721
individuals observed over four consecutive waves with complete data, two prior and two
following potential retirement. Our total sample of full-time workers included 1,296
individuals. Figure 1 provides the breakdown of our identification of the final samples
based on work-retirement patterns.
Measure of Cognitive Status
Cognitive performance is based on a 27-point test. This test derives from the
Telephone Interview for Cognitive Status (TICS) (Brandt, Spencer, & Folstein, 1988), which
has been validated for use as a screening instrument for cognitive performance (Plassman,
Newman, Welsh, & Breitner, 1994; Welsh, Breitner, & Mgruder-Habib, 1993). The TICS is
composed of measures of episodic memory (a 10-word immediate and delayed recall test (0
to 20 points)), working memory (a timed serial 7s test (0 to 5 points)), and processing
speed (backwards-counting test (0 to 2 points)). The total score ranges from 0 to 27, with
higher scores indicating better performance. These tests were administered every two
years.
Cognitive scores were standardized using the average score for HRS respondents
ages 51-55: a mean of 17.05, standard deviation corrected for measurement error, equal to
13
2.46.2 Our outcome variable is the difference in the standardized cognitive score from Time
1 to Time 4. A one-unit change in cognitive score is the equivalent of 4.57 points. A positive
score indicates improvement in cognitive performance from Time 1 to Time 4. Negative
scores indicate decline. The TICS has validated cut-points differentiating normal cognitive
functioning (≥12) from impairment (i.e., those with lower than 12 points) (Crimmins, Kim,
Langa, & Weir, 2011; Fisher, Rodgers, & Weir, 2009; Langa et al., 2005).
Job Complexity
HRS respondents’ occupations at each wave of HRS (based on U.S. Census codes)
were linked to the O*NET database (via a crosswalk that links U.S. Census codes with the
Standard Occupation Classification (SOC) codes in the O*NET) to obtain external
occupational-level ratings of job characteristics pertaining to occupation at each wave.3 The
O*NET program is the primary source of occupational data in the United States. The O*NET
database contains information on standardized occupation-specific characteristics and is
publicly available. The O*NET-SOC taxonomy is a set of characteristics for a set of
standardized occupations that correspond to the U.S. Census. Each occupation characteristic
score is calculated based on a rating scale related to abilities (i.e., the expected abilities
required in order to engage in a given job), activities (i.e., the expectation of participation in
activities associated with a given job), and contexts (i.e., the situational aspects of day-to-
2
The corrected standard deviation of the change score is calculated using the formula
   s (  / (2   )) where  s  4.57 is the standard deviation of the raw scores in the 51-55 age
group and   0.45 is the test-retest correlation of the 27-point scale across four waves in the
analysis sample. Note that the test-retest correlation for the full sample is about 0.6; the smaller
value in the analysis sample reflects attenuation due to dropping those with scores below 12.
3
We are grateful to Peter Hudomiet for sharing his cross-walk of HRS occupational codes and
O*NET’s SOC codes.
14
day working associated with a given job). For example, the degree to which a job involves
getting information is assessed, with a total score calculated on a range from 0 to 1 based on
how often that particular job typically requires getting information.
A total of 36 job-related abilities, activities, and contexts were available for the
standard occupations coded in the Health and Retirement Study. To identify meaningful job
factors, we used exploratory factor analysis (see Appendix A for the full list). Excluding all
items with an alpha score below 0.60, two factors emerged from the remaining 18 items.
Using an iterative selection process, we excluded all variables that loaded on both factors,
and then systematically removed items until we identified the fewest number of items with
the highest alpha score. As shown in Table 1A, the first factor, which we describe as the
“intellectual” factor, includes five items: (1) making decisions and solving problems; (2)
thinking creatively; (3) coaching and developing others; (4) frequency of decision-making;
and (5) freedom to make decisions. The second factor, which we describe as the
“mechanical” factor, includes four items: (1) inspecting equipment, structures or material;
(2) handling and moving objects; (3) controlling machines and processes; and (4) operating
vehicles, mechanized devices or equipment (see Table 1B). The Chronbach’s alpha scores
for these factors are 0.952 and 0.958 respectively. The scores for the intellectual measure
ranged from 2.417 to 3.724, and the mechanical measure ranged from 0.916 to 2.773.
To get a general sense of how the intellectual and mechanical tertials relate to
broader occupational categories, we identified all major occupation categories (an HRS
variable that reflects the broad Census categorization for major occupation types) that fell
into each tertial. Table 2 shows the breakdown of occupational types, demonstrating that
the highest level of the intellectual variable includes primarily individuals in managerial
positions (e.g., legislators, CEOs, marketing managers, administrators and officials in the
public administration sector, and accountants and auditors). The middle group is composed
15
primarily of individuals with professional specialty positions (e.g., social workers,
statisticians, dentists, dieticians and teachers), and secondarily in personal services jobs
(e.g., supervisors of welfare service aides, hairdressers, or child care workers),
mechanics/repair work, construction, and precision production jobs (e.g., machinists). The
lowest cognitive grouping is composed primarily of individuals in sales (e.g., insurance sales
occupations and apparel sales clerks) and clerical jobs (e.g., secretaries and typists), and
secondarily personal services and operator jobs (e.g., printing machine operators, textile
sewing machine operators).
Regarding the mechanical variable, the highest mechanical group is composed
primarily of individuals who work in mechanical, construction, precision production, and
operator jobs. The moderate mechanical group is composed of individuals primarily in sales
positions and health and personal services jobs. The lowest mechanical group is composed
of individuals who are in managerial, professional specialty, and clerical positions.
Covariates
Demographic covariates included gender, race (an indicator of whether an
individual is non-Hispanic white (reference group), non-Hispanic black, Hispanic, or
another race), and age (a continuous measure at Time 3 because our selection required
individuals to be at least 50 at potential retirement), education (in years). Because changes
in health status could initiate a retirement transition or a change in cognitive status, we
include measures that adjust for potential pre-retirement health decline: (a) raw cognitive
score at Time 2, a continuous measure of frailty at Time 2; and (b) to adjust for the potential
causal effect of declining health as an impetus for the retirement transition, we also include
a measure for change in self-rated health observed at Time 3 (relative to Time 2). Frailty (at
Time 2) is measured following Yang and Lee (2010), as an index based on 30-items : 8
16
chronic illnesses, 5 activities of daily living limitations, 7 instrumental activities of daily
living limitations, 8 depressive symptoms (Radloff, 1977), obesity (i.e., body mass index of
30 or greater), and self-rated health (a five point likert item with higher values indicating
better health.
Given the significant relationship between physical engagement behaviors and
cognitive performance (Ahlskog, Geda, Graff-Radford, & Petersen, 2011; Hindin & Zelinski,
2012; Langlois et al., 2013), we include a dichotomous measure of frequency of moderate
physical engagement (1 = every day, 2 = > once per week, 3 = once per week, 4 = one to
three times per week, 5 = never). Unfortunately, this measure was only available
consistently at Time 4 for the entire pooled sample (i.e., HRS included a consistent measure
of moderate engagement beginning in 2002).
Econometric Model
Our goal is to estimate the effect on the trajectory of cognitive performance of a worker’s
decision to choose full retirement versus continuing full-time work among workers whose
longest jobs varied in intellectual complexity or, alternatively, in mechanical complexity.
Following Rohwedder and Willis (2010), we call this the “mental retirement effect” or the
MRE. Ideally, our estimate of the MRE could be interpreted as causal, representing the
potential loss (or gain) in cognitive performance that a given worker could expect if he or
she were to fully retire rather than continue working full time. Taken literally, it is
impossible to achieve this ideal even in a hypothetical randomized controlled trial in which
young adults are randomly assigned to occupations and subsequently assigned to full
retirement when they reach a randomly chosen age sometime after, say, their mid-50s. The
reason, of course, is that people only live their life once and, consequently, one cannot
estimate the counterfactual MRE at the individual level.
17
Using the language of the “Rubin causal model” (Holland 1986),the best we could
achieve in this hypothetical experiment is to estimate the mean “potential outcomes” or
POMs of people assigned to retirement or continued work for a given level of complexity, j,
of the occupation to which they been assigned. The mental retirement effect is then just the
difference between these POMs:
(1)
MRE j  POM (retirement | complexity  j )  POM (work | complexity  j ) ,
where j  low, medium, high corresponds to the intellectual complexity or, alternatively,
the mechanical complexity of the occupation based on O*Net Data.
Obviously, this hypothetical experiment is impossible to conduct for practical and
ethical reasons. In addition, it would be economically inefficient since many people would
be assigned to occupations for which they lack the requisite abilities, education or interests
and be assigned to retirement when they prefer to continue working or conversely. (Think
of a physics department in which the janitor is assigned to give course lectures and Einstein
is assigned to empty the waste baskets.) Self-selection in competitive labor markets tends
to create the most productive matches between the skills, capabilities and preferences of
individuals and the employers’ demands for workers to conduct particular tasks (Roy,
1951; Willis and Rosen, 1979). From this point of view, the most relevant MREs to estimate
are for people in the occupations they have actually chosen. Indeed, the results from the
hypothetical experiment would likely be highly misleading because many people would be
assigned to tasks they dislike or cannot perform—a mismatch that the designers of the
randomization may observe imperfectly, if at all—possibly causing changes in cognitive
performance that do not occur among well-matched workers.
While self-selection helps us choose the most relevant comparisons to make in
judging how the effect of retirement on the trajectory of cognition is influenced by
occupational complexity, it creates important challenges to our ability to obtain unbiased
18
measures of MRE j . Self-selection throughout life in the level and type of education,
occupational choice, labor supply and in other areas of life such as marriage, fertility,
residential location, etc. create heterogeneity among individuals that is likely to be
correlated with both the level of cognitive performance when they enter the HRS and with
their subsequent retirement decision. Some of this heterogeneity can be controlled using
observed covariates in the data, but we also need to worry about unobserved heterogeneity.
Our econometric model attempts to address these issues. As shown in Figure 1, the
sample we study consists of N persons who are working full-time at Time 1 and Time 2. Of
these, R individuals are completely retired at Time 3 and Time 4 and W people continue
working full time in Time 3 and Time 4. Individuals with other patterns of work and
retirement are excluded.
Denoting the parameters that pertain to members of the two groups by the
superscripts R and W, a person’s cognitive score at Time 1, is assumed to be a linear
function of a set of observed variables, xi1 ; a person-specific fixed effect,  i , that captures
unobserved heterogeneity and an iid measurement error term, ui1 , with mean zero and
variance  u2 , that captures the difference between cognitive scores on the HRS and the
latent variable, “true ability.”
Thus, the observed test scores at Time 1 of people in groups R and W, conditional on
the complexity of their longest occupation, vary according to both observable variables,
xi1 ; unobserved factors embodied in  i and measurement error:
(2)
cogijR1  xi1 jR1  i  ui1; j  low, medium, high, i  R , and
(3)
cogijW1  xi1 Wj1  i  ui1 ; j  low, medium, high,, i  W .
The coefficients  jR1 and  Wj1 in (2) and (3) capture the potentially different effects
of observable variables that characterize a person’s life history depending on whether the
19
person belongs to the group of people who are fully retired by Time 3 or to the group who
continue working through Time 3 and Time 4. Also note that the average cognitive score at
Time 1 of persons in groups R and W may differ because “selection on observables” causes
the distribution of x1i to differ between those who retire and those who do not. Likewise, it
is possible that “selection on unobservables” causes the mean value of  i to differ between
persons in the two groups. In analogy with equations (2) and (3), the levels of cognition at
Time 4 in the R and W groups are given by:
(4)
(5)
cogijR4  xi 2  jR4  i  u41; j  low, medium, high, i  R
cogijW4  xi 2  Wj 4  i  ui 4 ; j  low, medium, high, i  W .
We are interested in estimating the effect of retirement on cognition for each
complexity category by comparing the change in cognition between Time 1 and Time 4 for
those who retire with the change in cognition for those who continue working by
occupational complexity. Within the potential outcomes framework, the potential outcome
for individuals in Group R is obtained by subtracting equation (2) from equation (4) and
taking the expected value to obtain:
(6)
POM iR  E( xi 2 Wj 4  ui 4  ui1 )  xi 2 Rj 4 ; j  low, medium, high, i  R ..
Similarly, the POM for Group W is obtained by subtracting equation (3) from equation (5)
and taking expected values to obtain:
(7)
POM iW  E( xi 2 Wj 4  ui 4  ui1 )  xi 2 Wj 4i; j  low, medium, high, i  W
where  Rj 4   jR4   jR4 and  Wj 4   Wj 4   Wj 4 . Note that unobserved heterogeneity,  i , is
eliminated by these subtractions so that person-specific POMs are only subject to selection
on observables, xi 2 , and that measurement error has no effect; i.e., E (ui 4  ui1 )  0 .
If the selection of individuals into the R and W groups and into occupations with
low, medium and high levels of complexity were random, we could simply apply the formula
20
in equation (1) to obtain an unbiased estimate of the mental retirement effect for persons in
occupations of each degree of complexity by calculating POM Rj  POM Wj . There are two
major threats that we need to address before we can claim to have estimated the causal
effect of retirement: reverse causation and self-selection on observables.
Reverse causation would occur if cognitive change is a significant cause of
retirement. Worry about reverse causation has motivated the use of IV methods in papers
such as Rohwedder and Willis (2010), Bonsang, et al. (2012) and others. As described
earlier, we have tried to guard against reverse cognition by eliminating people with low
cognitive scores from our analytic sample and by including the cognitive score just before
retirement at Time 2 as a control variable. In addition, we note that there is little evidence
in the literature to suggest that cognitive decline is an important cause of retirement. For
example, Rohwedder and Willis (2010, Figure 5) display the OLS regression line between
cognition and retirement in their cross-national sample. It has nearly the same slope as the
IV relationship that they estimate. We believe that it is reasonable to assume that reverse
causation is not present in our analysis.
The existence of self-selection on observables is much more plausible for
occupational choice and retirement decisions. For example, occupational choice is strongly
related to education and retirement both directly and indirectly through economic and
R
R
health status. Suppose we estimate the mean cognitive change, POM high
 xi 2 hight
4 , from
data on people in group R whose longest job was in a highly complex occupation and
imagine that education is the only covariate in xi 2 . In order to calculate the causal effect of
retirement on cognitive change, we would like to compare the mean cognition of people in
group R with people in group W with the same level of education in order to isolate the
R
W
causal effect of retirement on cognitive change equal to MREhigh  ( high
  high
)ed where ed
21
R
W
is the common mean education and the sign and magnitude of ( high
  high
) determines the
sign and magnitude of MREhigh . Since it is likely that continuing workers, on average, have
more education than those who retire, failure to correct for selection on education will lead
to an overstatement of the mental retirement effect.
Fortunately, there are a number of approaches in the statistical and econometric
literature on treatment effects and the related literature on missing data that allow us to
correct for selection on observables. If, for the moment, we ignore self-selection into
occupations, we need only deal with the binary decision to fully retire or continue working
full time. The method we use combines two popular approaches: regression adjustment and
inverse probability weighting (Curtis, Hammill, Eisenstein, Kramer & Anstrom, 2007).
Regression adjustment of sample means uses covariates that predict selection into the R
and W groups to make the distribution of covariates in the two groups comparable, in
analogy to our univariate example of education. Inverse probability weighting is motivated
by the recognition that data on potential outcomes of Group R, had they continued working
full time, is missing and, conversely, potential outcomes if they had retired are missing for
members of Group W. Both approaches make use of a propensity model that estimates the
probability that an individual is a member of Group R or Group W (Abadie & Imbens, 2012).
It been shown that this approach has a “doubly robust” property such that unbiased
estimates of treatment effects can be obtained even if either the POM model or the
propensity model (but not both) is misspecified (Wooldridge, 2007).
Recently, (Cattaneo 2010) has extended this approach to allow estimation of multivalued treatment effects using semi-parametric methods and this approach is implemented
in parametric form in the ipwra option of the teffects command in Stata 14 (StataCorp,
22
2013).4 Using this command, we estimate six POM equations described in equations (6) and
(7) in order to estimate the three Mental Retirement Effects for persons in low, medium and
high complexity jobs described in Equation (1). The probabilities that individuals self-select
into one of these six states are estimated using a multivariate logit propensity model. This
model is estimated for two alternative definitions of occupational complexity: intellectual
complexity and mechanical complexity.
RESULTS
We now turn to our estimates of the potential outcome means, POM Wj and
POM Wj , and the mental retirement effects, MRE j , measured by the average treatment
effect on the change in cognition effect over a six year period beginning two waves before
full retirement and ending one wave after retirement. These effects are estimated for three
levels of intellectual complexity of the individual’s job at baseline, reported in Table 4, and
by three levels of mechanical complexity of the baseline job reported in Table 5. We also
report the results of the auxiliary potential outcome and propensity equations in Appendix
Tables A1 and A2.
We hypothesized that those with the most intellectually complex jobs will
experience less cognitive decline with retirement relative to those with the least
intellectually complex jobs. The results presented in Table 4a strongly support this
hypothesis. The first row of Table 4a shows that the average cognitive decline (POM) for a
person who retires is much greater for persons in low complexity jobs than in high
complexity jobs (-0.742 compared to -0.256) with the decline for moderate complexity in
between (-0.449). The second row shows that cognitive decline shows little variation with
4
For additional details and references to the literature, see the documentation of the teffects
command in the Stata manual.
23
intellectual complexity for those who continue working (-0.282, -0.216, -0.300 respectively
for low, moderate, and high complexity). The difference between the POMs for the retired
and full time workers in the third row provides causal estimates of the effect of retirement
on cognition. Workers who retire from the least complex jobs suffer a highly significant
decrease of -0.460 standard deviations compared to what they would expect had they
continued full time work. Retirement from a job with moderate intellectual complexity
causes a smaller marginally significant decline of -0.233 standard deviations while there is
no effect on cognition of retirement from a highly intellectually complex job. Figure 2
presents these results in graphical form with effect sizes corrected for test-retest
measurement error as described in footnote 2.
Corresponding results for jobs classified by mechanical complexity are presented in
Table 5 and in graphical form in Figure 3. The causal effects of retirement are negative, but
smaller and less significant for job complexity on this dimension than for intellectual
complexity of the job. However, as is clear the Figure 3, in contrast to the case of intellectual
complexity, the negative effect of retirement on cognition is greatest for retirement from
jobs with high mechanical complexity, and least for those with moderate mechanical
complexity.
To further clarify the observed cognitive changes with respect to level of intellectual
and mechanical complexity, Figure 4 depicts the percentile change at Time 4 relative to
Time 1. Relative to the normally distributed cognitive performance of healthy 50-54 year
olds in the population (for which our data are normed), cognitive performance declines
associated with aging occur over the 6-year time frame, but in differing amounts. Assuming
that cognition is normally distributed, a worker who has a low intellectually complex job
at Time 1 and 2 was at the 50th percentile of the baseline distribution at Time 1, would be
expected to fall to the 23rd percentile six years later if they retired, but only the 39th
24
percentile if they continued working, whereas a worker with a high intellectually
complex job would only decline to the 40th percentile if they retired and would decline at
a slightly higher rate (down to about the 30th percentile) if they continued working fulltime. For those with high mechanically complex jobs, retirement would predict a decline
to the 22nd percentile versus a decline only to the 38th percentile with continuous full-time
work. For those with low mechanically complex jobs, retirement would predict a decline
to the 35th percentile, and continuous full-time work the 43rd percentile.
DISCUSSION AND CONCLUSION
Fluid intelligence—the capacity to think and reason—as well as the cognitive
mechanics that underpin this capacity including working and episodic memory, processing
speed and other components of intelligence or executive function all follow a declining path
from early adulthood until death in a process called “normal cognitive aging.” At advanced
ages, dementing diseases such as Alzheimer’s disease begin to disable a significant fraction
of the elderly, but most people will die with normal cognition and, conversely, very few
older workers under the age of 75 have experienced the onset of dementia. Recently,
cognitive psychologists and neuroscientists have begun to ask why it is that many older
people can function so effectively at work, in the family and in society despite the dramatic
declines in measures of fluid intelligence they have suffered since they were young. Indeed,
they note, the puzzle is deepened when one recognizes that most of the leaders in
government, business, education and the military tend to be drawn from the older part of
the working population in almost every society.
Cognitive scientists believe that a clue to the resolution of this puzzle is to be found
in the observation that, unlike fluid intelligence, crystallized intelligence—the accumulation
of knowledge and wisdom—tends to continue to increase over the life cycle. To an
economist, crystallized intelligence is essentially the same thing that economists call human
25
capital (McArdle and Willis, 2011). Human capital is durable knowledge that is acquired
through investment in education, on-the-job training and learning-by-doing by combining
effort, knowledge and cognitive ability. Because it is durable, the stock of human capital
tends to grow over the life course, although toward the end of working life it may decline as
the rate of investment falls below the rate of depreciation (forgetting) and the rate of
obsolescence (failure to replace obsolete knowledge with current best practice).
Economists emphasize both pecuniary and non-pecuniary incentives to invest in the
accumulation of human capital. They also note that the productivity of human capital tends
to become more specialized as the person matures because of the incentive to acquire skills
necessary to conduct the tasks required by one’s occupation. It also seems likely, especially
in the knowledge economy, that an individual’s current productivity depends on his or her
ability to carry out a complex novel task by accessing relevant pieces of knowledge—
resident in their brain, books, the web or another person’s brain—and use their fluid
intelligence to assemble those pieces in ways that are relevant to the execution of the task.
In short, although fluid intelligence and crystallized intelligence are distinct components of
intelligence, they complement each other in helping individuals accomplish valued goals
during their hours of work and also in their hours outside of work in dealing with their
family and friends, enjoying hobbies, leisure activities and so on.
The scaffolding theory of Park & Reuter-Lorenz (2009) provides intriguing links
between the theory of fluid and crystallized intelligence in psychology, the analysis of brain
structure and function in neuroscience and the theory of human capital in economics. It
suggests that when a person solves a novel task, new neural circuits are created in the
brain. If a circuit continues to be accessed, it will become a long-lasting part of the person’s
mental capacity, but if it is not used it will be destroyed by the ongoing pruning process by
which the brain maintains an efficient allocation of its scarce resources. Thus, scaffolding
26
theory provides an underlying mechanism for the “use it or lose it” hypothesis that, in turn,
inspired the mental retirement hypothesis of Rohwedder and Willis (2010) that we
investigate in this paper.
In addition, scaffolding theory provides clues about the neurological and
psychological mechanisms that underlie the formation of forms of crystallized intelligence
embodied in the specialized skills and knowledge that a worker brings to the labor market
and that constitute his or her stock of human capital. The theory implies that people who
perform complex and novel tasks lay down more circuitry than people who do simpler,
repetitive tasks. Importantly, we conjecture that the combinatorics of bringing together
different relevant pieces of knowledge involved the tasks that a worker performs during a
career in a complex occupation may spill over into increased capacity to engage in and
enjoy a wide variety of activities in non-work activities that can be pursued during
retirement. Conversely, engagement in less complex, repetitive activities in low skilled jobs
is likely to have been learned early in the career and have little transferability to non-work
activities. The structure of working life may help with the maintenance of cognitive
capabilities, but workers in low skilled jobs are likely to have developed relatively little
scaffolding to buffer the effects of leaving work unless they have developed independent
interests in cognitively challenging activities that they pursue during retirement.
Our empirical analysis of the differential effects of full time retirement on the
trajectory of cognition is quite consistent with previous empirical studies that suggest that
pre-retirement job characteristics shape the cognitive performance trajectory following
retirement and with the theoretical predictions of scaffolding theory, especially, as it is
augmented by insights from theory and evidence from the human capital literature in
economics. We find clear evidence of differential “mental retirement effects” (MREs) when
intellectual complexity is used as the criterion for occupational complexity and the change
27
in cognition is measured over a six year time span beginning two HRS waves before
retirement and ending one wave after retirement. We find that full time workers in low
complexity jobs have a predicted decline of cognition for those who fully retire that is three
times larger than it is for those who continue working full-time. We also estimate a smaller,
marginally significant MRE effect for workers in moderately complex jobs, with a cognitive
decline that is twice as great if they retire than if they continue working. However, among
workers in highly skilled jobs, retirement has no effect on cognition. (Indeed, retirees in this
group have a very small and insignificant cognitive advantage relative to full-time workers.)
Interestingly, the differentials in MRSs by intellectual complexity occur entirely
because of differential negative impacts of retirement on cognition. Among those who
continued working full-time, decline is essentially invariant across the different categories
of complexity. This pattern suggests that the productivity of human capital accumulated
during the working career is more transferable to non-work settings, the greater the
intellectual complexity of the job. It also suggests that reduced mental effort in maintaining
one’s skills as the date of retirement approaches (what Rohwedder and Willis (2010) called
the “on-the-job retirement effect”) is not responsible for the MRE effect. If it were, we would
expect that those with the most skills in the most complex occupations would have the
greatest scope to decrease their human capital investment in anticipation of retirement.
We used an alternative classification of occupational complexity based on
mechanical complexity rather than intellectual complexity. By construction, the two
classifications are essentially orthogonal in the sense that they involve non-overlapping
O*NET characteristics. On this criterion, we find the opposite pattern of differential by
complexity than we found for the intellectual complexity classification. The largest cognitive
declines occur among workers in the most complex occupations and the smallest occur for
those in the least complex occupations. In addition, we see greater declines with increased
28
complexity for both those who continue working and for those who retire, although the
retirement effects are much larger.
We conjecture that these differences in the patterns of cognitive decline for
mechanical complexity compared to intellectual complexity might also be explained by
scaffolding theory. It seems plausible that workers in jobs involving complex machinery or
equipment develop knowledge that is not very transferable to the non-work environment
they encounter when they retire. In addition, it seems likely that workers in such jobs face
greater dangers that their skills will become obsolete due to changing technology than
workers in intellectually complex jobs and, therefore, have an incentive to reduce their
investment effort in maintaining their skills as the date of retirement draws near.
The validity of our empirical findings and their interpretation as causal effects, as
we explain at length in the paper, depend on the assumption that differences between
people who self-select into different occupations and make different decisions about work
and retirement can be adequately controlled with observable variables. Our focus on change
in cognition rather than level of cognition strengthens the plausibility of the assumption of
selection observables—also known as conditional ignorability or unconfoundedness—by
eliminating person-specific fixed effects. But ultimately, the plausibility of our findings
depends on whether similar effects are found using different data and different methods. In
this respect, we see much scope for using data generated by psychologists and
neuroscientists as well as additional analysis of survey data such as HRS. There is even
potential for combining the different types of data as discussed in “What is a representative
brain?” (Falk, et al., 2013). While this paper addresses the complexity and characteristics of
the work environment, we also believe that further study of the non-work environment and
its impact on cognition should be a high priority for future research.
29
Funding:
This work was supported by funding from the Alfred P. Sloan Foundation.
30
Table 1A: Intellectual Complexity Items
Item-Test
Correlation
Alpha
Making Decisions and Solving Problems
0.977
0.925
Thinking Creatively
0.957
0.937
Coaching and Developing Others
0.957
0.931
Frequency of Decision-Making
0.880
0.957
Freedom To Make Decisions
0.914
0.947
Test scale
0.952
Table 1B: Mechanical Complexity Items
Item-Test
Correlation
Alpha
Inspecting Equipment, Structures, or Material
0.962
0.943
Handling and Moving Objects
0.956
0.939
Controlling Machines and Processes
0.960
0.936
0.920
0.961
Operating Vehicles, Mechanized Devices or
Equipment
Test scale
0.958
31
Table 2: Occupational Distribution By Job Complexity Level
Total
Lowest
Moderate
Sample
Intellectual
Intellectual
N
N
N
%
Managerial Specialty
410
20.33
Professional Specialty
432
21.42
Sales
178
8.82
145
Clerical/Administrative Support
407
20.18
Services: Household, cleaning, and building
5
0.25
Services: Protection
26
1.29
Services: Food preparation
27
1.34
26
Health services
42
2.08
Personal services
72
Farming/Forestry/Fishing
%
%
Highest
Intellectual
Lowest
Moderate
Highest
Mechanical
Mechanical
Mechanical
N
%
N
%
N
%
N
%
410
84.54
375
31.62
17
4.57
18
3.92
419
35.33
7
1.88
6
1.31
170
45.7
8
1.74
13
3.49
2
0.44
5
1.34
24
6.45
2
0.44
26
6.99
1
0.22
4
0.87
417
54.94
15
3.09
18.76
12
1.58
21
4.33
386
49.94
7
0.92
14
2.89
3
0.39
2
0.26
24
3.16
3.36
1
0.13
38
4.92
3
0.4
1
0.21
42
11.29
3.57
95
12.29
71
9.35
1
0.21
68
18.28
21
1.04
46
5.95
20
2.64
1
0.21
21
4.58
Mechanics/Repair
68
3.37
34
4.4
65
8.56
3
0.62
68
14.81
Construction Trade/Extractors
61
3.02
54
7.11
7
1.44
61
13.29
Precision Production
71
3.52
68
8.96
3
0.62
71
15.47
Operators: Machine
104
5.16
95
12.29
6
0.79
3
0.62
104
22.66
Operators: Transportation, etc.
55
2.73
46
5.95
7
0.92
2
0.41
55
11.98
Operators: Handlers, etc.
38
1.88
34
4.4
2
0.26
2
0.41
38
8.28
Total
Score Range
2,017
2
392
33.05
0.41
773
759
485
1,186
372
459
2.42 – 3.07
3.09 – 3.59
3.62 – 3.72
0.92 – 1.27
1.33 – 1.94
2.31 – 2.77
32
Table 3: Unadjusted Characteristics of Samples
All
Full Retiree
Full-Time
Min
Max
Characteristics
Raw Intellectual Complexity Score
3.246
0.389
3.195***
0.399
3.274
0.380
2.417
3.724
Raw Mechanical Complexity Score
1.475
0.591
1.520*
0.626
1.450
0.569
0.916
2.773
Cognitive Score (Time 1)
18.114
2.992
18.191
2.999
18.070
2.988
12
27
Cognitive Score (Time 2)
18.014
3.119
17.745**
3.231
18.164
3.046
12
27
Cognitive Score (Time 3)
17.663
3.412
17.327***
3.503
17.849
3.347
3
27
Cognitive Score (Time 4)
17.291
3.450
16.928***
3.501
17.492
3.405
4
27
-0.335
1.426
-0.514***
1.454
-0.235
1.401
-7.724
4.472
0
1
1
17
0
1
Standardized Change in Cognition
(Time 1 to Time 4)
Propensity Score Covariates
Black
0.113
Education (years)
13.909
Female
0.496
Wealth (in deciles)
5.760
2.835
5.682
2.612
5.802
2.952
1
10
Income (in deciles)
6.100
2.835
6.166
2.624
6.063
2.946
1
10
Age (Time 1)
57.934
4.731
59.624***
4.557
56.994
4.563
47
80
Age 62 or Older (Time 2)
0.329
0
1
Time Span (Months Time 1 to Time 4)
72.722
4.118
72.165***
3.389
73.032
4.443
62
86
Frailty Index (Time 2)
-0.112
0.094
-0.130***
0.105
-0.102
0.086
-0.741
0
-122
0.804
-0.141
0.880
-0.112
0.758
-4
3
2.759
1.183
2.761
1.216
2.757
1.165
1
5
Change in Self-Rated Health
(Time 3 relative to Time 2)
Freq. of Moderate Activity (Time 4)
N
0.115
2.413
0.112
13.513***
2.325
0.509
2.434
0.489
0.501***
2,017
14.130
721
0.234
1,296
Note: * p<0.05; **p<0.01; ***p<0.001; significant differences tested using chi-square tests for dichotomous
variables and t-test difference tests for continuous variables.
Significance indicates statistically significant difference relative to individuals who stay full-time prior to
adjustment.
a Self-rated
health is scored on a five point scale such that 1= excellent and 5=poor health.
33
Table 4A: Adjusted POM Estimates for Changes in Cognitive Performance, Time 1 to Time 4
by Level of Intellectual Complexity
Level of Intellectual Complexity of Job
Low
Moderate
High
Robust St. Error Robust St. Error Robust St. Error
-0.742
-0.449
-0.256
0.096
0.109
0.135
-0.282
-0.216
-0.300
0.077
0.073
0.092
ATE
-0.460
-0.233
0.045
(sig)
**
+
Retire
Stay Full-Time
Table 4B: Significant Within-Group Differences in Cognitive Decline: Level of Intellectual
Complexity of One’s Job By Work Transition Group
Level of Intellectual Complexity of Job
Retire
Low
Low
Moderate
vs.
vs.
vs.
Moderate
High
High
*
***
Stay Full-Time
34
Table 5A: Adjusted POM Estimates for Changes in Cognitive Performance, Time 1 to Time 4
by Level of Mechanical Complexity
Level of Mechanical Complexity of Job
Low
Moderate
High
Robust St. Error Robust St. Error Robust St. Error
-0.397
-0.398
-0.765
0.086
0.133
0.154
-0.178
-0.274
-0.296
0.061
0.127
0.114
ATE
-0.219
-0.124
-0.469
(sig)
*
Retire
Stay Full-Time
*
Table 5B: Significant Within-Group Differences in Cognitive Decline: Level of Mechanical
Complexity of One’s Job By Work Transition Group
Level of Mechanical Complexity of Job
Retire
Low
Low
Moderate
vs.
vs.
vs.
Moderate
High
High
*
+
Stay Full-Time
35
Figure 1: Sample Selection
Time 1
Time 2
Time 3
Time 4
Fully Retire
Work 35+,
Work 35+,
Work 0,
Work 0,
(n = 721)
Not Retired
Not Retired
Retired
Retired
Work 35+,
Work 35+,
Work 35+,
Work 35+,
Not Retired
Not Retired
Not Retired
Not Retired
Stay Full Time
(n = 1,296)
36
Figure 2: Estimates For Intellectual Complexity
Low
Moderate
High
Decline (Standard Deviations)
0.00
-0.20
-0.22
-0.26
-0.28
-0.30
-0.40
Retire
Stay Full-Time
-0.45
+
-0.60
-0.80
-0.74
***
37
Figure 3: Estimates For Mechanical Complexity
Low
Moderate
High
Decline (Standard Deviations)
0.00
-0.20
-0.18
-0.27
-0.30
-0.40
-0.40
-0.60
-0.80
Retire
-0.40
Stay Full-Time
*
-0.77
*
-1.00
38
Figure 4: Depiction of Percentile Change, Time 4 Relative To Time 1, and Retiring Relative To Staying Full-Time
INTELLECTUAL COMPLEXITY
a. Fully Retire
50%
50.0%
50%
40%
39.9%
40%
32.7%
30%
22.9%
20%
50.0%
10%
40.9%
5%
37.9%
0%
30%
9.9%
-5%
-8.8%
-10%
20%
-15%
10%
Time 1
Time 4
10%
50%
50%
40%
40%
34.5%
34.6%
30%
Time 4
Time 1
50.0%
5%
43.0%
0%
22.2%
10%
Time 1
Time 4
-5%
30%
20%
-15%
10%
50-54 year olds
Time 4
38.3%
-10%
20%
***
e. Causal Effect of Retirement
d. Stay Full-Time
50.0%
+
-16.0%
-20%
Time 1
c. Fully Retire
MECHANICAL COMPLEXITY
15% c. Causal Effect of Retirement
b. Stay Full-Time
Time 1
Low
Time 4
Moderate
-4.7%
-8.4% *
-16.1% *
-20%
High
39
Appendix A: O*NET Job Characteristics Variables
Characteristics indicate the degree to which a particular job involves each.
A. Abilities:
1. Deductive reasoning
2. Inductive reasoning
3. Mathematical reasoning
4. Arm-hand steadiness
5. Finger dexterity
6. Multi-limb coordination
B. Activities:
1. Getting information
2. Inspecting equipment, structures, or material
3. Processing information
4. Analyzing data or information
5. Making decisions and solving problems
6. Thinking creatively
7. Developing objectives and strategies
8. Handling and moving objects
9. Controlling machines and processes
10. Operating vehicles, mechanized devices or equipment
11. Interacting with computers
12. Repairing and maintaining mechanical equipment
13. Repairing and maintaining electronic equipment
14. Documenting/recording information
15. Establishing and maintaining interpersonal relationships
16. Assisting and caring for others
17. Performing for or working directly with the public
18. Coaching and developing others
40
C. Contexts:
1. Face-to-face discussions
2. Coordinate or lead others
3. Responsibility for outcomes and results
4. Spend time making repetitive motions
5. Impact of decisions on co-workers or company results
6. Frequency of decision-making
7. Freedom to make decisions
8. Degree of automation
9. Importance of being exact or accurate
10. Importance of repeating same tasks
11. Structured versus unstructured work
12. Pace determined by speed of equipment
41
Table A1. Potential Outcome Mean Estimate Models by Retirement Status and Intellectual Complexity of Longest Occupation
Non-Hispanic Black
Cognitive performance (time 2)
Education (years)
Age (time 1)
Low
Complexity
Moderate
Complexity
Age 62 or Higher (time 2)
Time Span (Months between
time 1 and time 4)
Female
Wealth (in quintiles, time 2)
Income (in quintiles, time 2)
Frailty Score (time 2)
Change in Self-Rated Health
(time 3 relative to time 2)
Regular moderate exercise
Constant
Non-Hispanic Black
Cognitive performance (time 2)
Education (years)
Age (time 1)
Age 62 or Higher (time 2)
Time Span (Months between
time 1 and time 4)
Female
Wealth (in quintiles, time 2)
Income (in quintiles, time 2)
Frailty Score (time 2)
Change in Self-Rated Health
(time 3 relative to time 2)
Regular moderate exercise
Constant
Intellectual Complexity
Fully Retired
Stayed Working Full-Time
at Time 3/4
at Time 3/4
Robust
Robust
Coef.
Coef.
SE
SE
-0.3830+
0.2161
0.0653
0.2118
0.0192
0.0279
0.0561*
0.0273
-0.0395
0.0451
-0.0301
0.0349
0.0259
0.0326
-0.0061
0.0347
Mechanical Complexity
Fully Retired
Stayed Working Full-Time
at Time 3/4
at Time 3/4
Robust
Robust
Coef.
Coef.
SE
SE
0.0470
0.2963
-0.0444
0.2054
-0.0243
0.0269
0.0249
0.0277
0.0364
0.0412
-0.1749***
0.0098
-0.0086
0.0312
-0.0485+
0.0286
-0.3352
0.2997
-0.1254
0.3368
-0.3691
0.2378
0.0536
0.2779
-0.0005
0.0208
-0.0166
0.0171
0.0233
0.0232
-0.0040
0.0126
0.1076
-0.0445
-0.0001
-2.1180*
0.1712
0.0335
0.0326
0.8634
0.2259
0.0207
0.0128
0.1709
0.1451
0.0270
0.0305
0.7830
-0.0017
0.0487
-0.0058
-0.5853
0.1762
0.0347
0.0431
0.7623
0.0406
0.0185
0.0969***
0.6897
0.1286
0.0225
0.0244
0.6719
-0.2901**
0.0999
0.1054
0.0950
-0.0449
0.0932
-0.0966
0.0863
-0.1462*
0.0640
0.1143
0.0715
-0.1785*
0.0744
0.0320
0.0591
-1.5140
-1.2356***
0.0067
0.0450
-0.0197
0.1479
2.4745
0.3349
0.0375
0.0469
0.0397
0.3605
0.1255
-0.3570
-0.0261
0.0256
-0.0320
0.3265
2.3278
0.2823
0.0240
0.0328
0.0273
0.3158
-1.3650
-0.7699+
0.0594
-0.0525
0.0323
-1.2851**
2.1572
0.4106
0.0445
0.0611
0.0538
0.4490
4.1570*
0.3180
-0.0442
0.0288
0.0129
-0.0267
2.0347
0.2948
0.0376
0.0416
0.0457
0.4764
0.0191
0.0317
-0.0045
0.0177
-0.0856*
0.0379
-0.0524
0.0422
-0.0773
0.0246
0.0418
-0.3222
0.2225
0.0433
0.0581
1.0318
0.5057***
-0.0382
0.0780**
1.3605
0.1504
0.0264
0.0290
1.1433
0.0518
0.0897
0.0167
0.9789
0.2541
0.0632
0.0666
0.9111
0.0039
-0.0227
0.0216
-0.7907
0.2788
0.0393
0.0409
1.3557
0.0285
0.1218
-0.0124
0.1099
-0.2749+
0.1501
0.0212
0.1337
-0.2034**
-1.1811
0.0791
3.4569
0.1184
1.3319
0.0738
1.8136
-0.2266+
4.1824
0.1351
4.8482
0.0910
2.8195
0.1019
4.8336
42
Table A1. Potential Outcome Mean Estimate Models by Retirement Status and Intellectual Complexity of Longest Occupation (cont).
High
Complexity
Non-Hispanic Black
Cognitive performance time 2)
Education (years)
Age (time 1)
Age 62 or Higher (time 2)
Time Span (Months between
time 1 and time 4)
Female
Wealth (in quintiles, time 2)
Intellectual Complexity
Fully Retired
Stayed Working Full-Time
at Time 3/4
at Time 3/4
Robust
Robust
Coef.
Coef.
SE
SE
0.6043
0.4956
0.4172
0.3599
0.0213
0.0428
-0.0009
0.0289
-0.0830
0.0667
0.0111
0.0484
-0.1015*
0.0457
-0.0633*
0.0314
0.7935*
0.3976
0.5453+
0.3215
Mechanical Complexity
Fully Retired
Stayed Working Full-Time
at Time 3/4
at Time 3/4
Robust
Robust
Coef.
Coef.
SE
SE
-0.0973
0.2976
-0.4075
0.3430
0.0346
0.0351
0.0386
0.0416
-0.0854
0.0615
-0.0186
0.0440
-0.0084
0.0349
-0.0204
0.0304
0.4806
0.3332
0.5892
0.4105
0.0147
0.0339
0.0183
0.0220
0.0397
0.0327
-0.0069
0.0243
0.0299
0.0514
0.2638
0.0443
-0.3214
0.0185
0.1756
0.0296
-0.1865
-0.0796
0.2521
0.0446
-0.0253
0.0117
0.2149
0.0383
Income (in quintiles, time 2)
-0.0207
0.0465
0.0353
0.0279
-0.0248
0.0467
0.0902*
0.0420
Frailty Score (time 2)
0.2943
1.2277
1.5608
1.1358
1.1998
1.6700
3.7883**
1.3377
Change in Self-Rated Health
(time 3 relative to time 2)
-0.1738
0.1472
-0.0049
0.1121
-0.2009
0.1050
-0.0971
0.1315
Regular moderate exercise
0.0177
0.1047
0.1528+
0.0791
0.0941
0.0886
0.0985
0.0877
Constant
4.7777
3.2651
1.2647
2.8621
-2.1941
3.1228
0.3375
2.5516
43
Table A2. Propensity Model for Selection into Occupation and Retirement Treatment
(Retired, Low is omitted)
Mechanical
Intellectual Complexity
Complexity
Robust
Robust
Coef.
Coef.
SE
SE
Non-Hispanic Black
-0.0541
0.2684
0.6044+
0.3236
Cognitive performance (time 2)
-0.0166
0.0301
-0.1207**
0.0447
Education (years)
0.2443***
0.0435
-0.3827***
0.0596
Age (time 1)
0.0136
0.0285
-0.0231
0.0386
Age 62 or Higher (time 2)
-0.0531
0.3122
0.4486
0.4224
Time Span (Months between
-0.0048
0.0207
-0.0106
0.0262
time 1 and time 4)
Retired,
Female
-0.6977***
0.1827
-1.0485***
0.2558
Medium
Wealth (in quintiles, time 2)
0.0202
0.0308
-0.0683+
0.0410
Income (in quintiles, time 2)
0.1099***
0.0316
-0.2750***
0.0472
Frailty Score (time 2)
0.4628
0.9091
-1.6778
1.1175
Change in Self-Rated Health
0.0011
0.1117
-0.1238
0.1408
(time 3 relative to time 2)
Regular moderate exercise
-0.1496*
0.0744
0.0271
0.0891
Constant
-3.4824
2.3097
9.8422**
3.1447
Non-Hispanic Black
-0.8321+
0.4421
0.1059
0.3312
Cognitive performance (time 2)
0.0235
0.0358
-0.1163***
0.0347
Education (years)
0.2478***
0.0500
-0.5235***
0.0473
Age (time 1)
0.0300
0.0349
-0.0042
0.0335
Age 62 or Higher (time 2)
-0.1895
0.3718
-0.5445
0.3592
Time Span (Months between
0.0288
0.0231
-0.0176
0.0231
time 1 and time 4)
Retired,
Female
-0.4257
0.2244
-2.7988***
0.2499
High
Wealth (in quintiles, time 2)
0.0863
0.0399
-0.0448
0.0360
Income (in quintiles, time 2)
0.1620
0.0465
-0.1401***
0.0373
Frailty Score (time 2)
0.9360
1.1119
-0.6445
0.9726
Change in Self-Rated Health
-0.0868
0.1373
-0.1032
0.1242
(time 3 relative to time 2)
Regular moderate exercise
-0.1366
0.0915
-0.0034
0.0854
Constant
-9.0993***
2.7448
12.1640***
2.6609
Non-Hispanic Black
-0.1115***
0.2268
-0.2404
0.2244
Cognitive performance (time 2)
0.0032
0.0260
-0.0386+
0.0219
Working,
Low
Education (years)
Age (time 1)
Age 62 or Higher (time 2)
Time Span (Months between
time 1 and time 4)
Female
Wealth (in quintiles, time 2)
Income (in quintiles, time 2)
Frailty Score (time 2)
Change in Self-Rated Health
(time 3 relative to time 2)
Regular moderate exercise
Constant
0.0928**
-0.0932**
-0.5881*
0.0331
0.0301
0.2849
0.1727***
-0.0942***
-0.7339**
0.0360
0.0245
0.2396
0.0784***
0.0191
0.0852***
0.0149
-0.0582
-0.0334
-0.0206
3.4858***
0.1632
0.0281
0.0284
0.7976
-0.1862
-0.0132
-0.0823***
2.6317***
0.1440
0.0236
0.0257
0.7336
0.0302
0.0951
0.0728
0.0844
0.0521
0.1433
0.0642
2.1944
0.0914
-0.5280
0.0567
1.8248
44
Table A2. Propensity Model for Selection into Occupation and Retirement Treatment (cont.)
Mechanical
Intellectual Complexity
Complexity
Robust
Robust
Coef.
Coef.
SE
SE
Non-Hispanic Black
-0.0474
0.2460
0.9130***
0.2457
Cognitive performance (time 2)
0.0216
0.0270
-0.0131
0.0272
Education (years)
0.3417***
0.0419
-0.2185***
0.0449
Age (time 1)
-0.0623*
0.0312
-0.0710*
0.0319
Age 62 or Higher (time 2)
-0.8965**
0.2934
-0.8351**
0.3046
Time Span (Months between
0.0784***
0.0200
0.0630**
0.0201
time 1 and time 4)
Working, Female
-0.9128***
0.1661
-1.1840***
0.1897
Meidum
Wealth (in quintiles, time 2)
0.0010
0.0286
-0.0284
0.0324
Income (in quintiles, time 2)
-0.0330
0.0285
-0.2625***
0.0337
Frailty Score (time 2)
4.0690***
0.8356
4.0456***
0.9287
Change in Self-Rated Health
0.1073
0.1009
-0.0160
0.1061
(time 3 relative to time 2)
Working,
High
Regular moderate exercise
Constant
Non-Hispanic Black
Cognitive performance( time 2)
Education (years)
Age (time 1)
Age 62 or Higher (time 2)
Time Span (Months between
time 1 and time 4)
Female
Wealth (in quintiles, time 2)
Income (in quintiles, time 2)
Frailty Score (time 2)
Change in Self-Rated Health
(time 3 relative to time 2)
Regular moderate exercise
Constant
-0.0565
-4.7183*
-0.1397
0.0024
0.3889***
-0.0474
-0.7179*
0.0699
2.3038
0.2804
0.0299
0.0422
0.0318
0.3192
0.1451*
5.2816*
0.2069
-0.0449
-0.4795***
-0.0889*
-0.7033*
0.0737
2.3747
0.3016
0.0298
0.0481
0.0378
0.3315
0.0975***
0.0217
0.0508*
0.0213
-0.7066***
0.1364***
0.0176
3.8207***
0.1809
0.0340
0.0323
0.9297
-2.9036***
-0.0571+
-0.2698***
2.6107**
0.2179
0.0335
0.0327
1.0167
0.0917
0.1116
0.0209
0.1091
0.0027
-9.2290***
0.0749
2.3906
0.0235
12.2583***
0.0812
2.6382
45
REFERENCES
Abadie, A., & Imbens, G.W. (2012). Matching on the estimated propensity score: Harvard
University & National Bureau of Economic Research.
Ahlskog, J. E., Geda, Y. E., Graff-Radford, N. R., & Petersen, R. C. (2011). Physical exercise as a
preventive or disease-modifying treatment of dementia and brain aging. Mayo Clin
Proc, 86(9), 876-884. doi: 10.4065/mcp.2011.0252
Bonsang, E., Adam, S., & Perelman, S. (2012). Does retirement affect cognitive functioning? J
Health Econ, 31(3), 490-501. doi: 10.1016/j.jhealeco.2012.03.005
Brandt, J., Spencer, M., & Folstein, M. . (1988). The telephone interview for cognitive status.
Neuropsychiatry, Neuropsychol. Behav. Neurol. , 1, 111-117.
Cattaneo, Matias D. 2010. “Efficient Semiparametric Estimation of Multi-Valued Treatment
Effects under Ignorability.” Journal of Econometrics 155: 138–45.
Celidoni, Martina, Chiara Dal Bianco, and Guglielmo Weber. 2013. Early Retirement and
Cognitive Decline. A Longitudinal Analysis Using SHARE Data.
Crimmins, E. M., Kim, J. K., Langa, K. M., & Weir, D. R. (2011). Assessment of cognition using
surveys and neuropsychological assessment: the Health and Retirement Study and
the Aging, Demographics, and Memory Study. J Gerontol B Psychol Sci Soc Sci, 66
Suppl 1, i162-171. doi: 10.1093/geronb/gbr048
Curtis, L. H., Hammill, B. G., Eisenstein, E. L., Kramer, J. M., & Anstrom, K. J. (2007). Using
inverse probability-weighted estimators in comparative effectiveness analyses with
observational databases. Med Care, 45(10 Supl 2), S103-107. doi:
10.1097/MLR.0b013e31806518ac
Falk, E.B. and 18 others (2013) “What is a representative brain? Neuroscience meets
population science.” Proceedings of the National Academy of Sciences, vol. 110, no.
44: 17615–17622.
Finkel, D., Andel, R., Gatz, M., & Pedersen, N. L. (2009). The role of occupational complexity
in trajectories of cognitive aging before and after retirement. Psychol Aging, 24(3),
563-573. doi: 10.1037/a0015511
Fisher, G. G., Rodgers, W. L., & Weir, D. R. (2009). HRS Imputation of Cognitive Functioning
Measures: 1992–2006 Data Description.
Fisher, G. G., Stachowski, A, Infurna, F. J., Faul, J. D., Grosch, J., & Tetrick, L. E. . (2014). Mental
work demands, retirement, and longitudinal trajectories of cognitive functioning.
Journal of Occupational Health Psychology, 19(2), 231-242. doi: 10.1037/a0035724
46
Foster, J. C., & Taylor, G. A. (1920). The applicability of mental tests to persons over fifty
years of age. Journal of Applied Psychology, 4, 39-58. doi: 10.1037/h0071260
Fratiglioni, L., & Wang, H. X. (2007). Brain reserve hypothesis in dementia. J Alzheimers Dis,
12(1), 11-22.
Hindin, S. B., & Zelinski, E. M. (2012). Extended practice and aerobic exercise interventions
benefit untrained cognitive outcomes in older adults: a meta-analysis. J Am Geriatr
Soc, 60(1), 136-141. doi: 10.1111/j.1532-5415.2011.03761.x
Holland. 1986. “Statistics and Causal Interference.” Journal of the American Statistical
Association 81 (396): 945–60.
Kajitani, Shinya, Sakata, Kei, & McKenzie, Colin. (2013). Does the definition of retirement
matter in estimating the effects of retirement on cognitive functioning? Retrieved
October 14, 2014, from http://www.mssanz.org.au/modsim2013/F4/kajitani.pdf
Lachman, ME, & Weaver, SL. (1997). Midlife Development Inventory (MIDI) personality
scales: scale construction and scoring. Brandeis University. Retrieved from
http://www.brandeis.edu/projects/lifespan/scales.html
Langa, K. M., Plassman, B. L., Wallace, R. B., Herzog, A. R., Heeringa, S. G., Ofstedal, M. B., . . .
Willis, R. J. (2005). The Aging, Demographics, and Memory Study: study design and
methods. Neuroepidemiology, 25(4), 181-191. doi: 10.1159/000087448
Langlois, F., Vu, T. T., Chasse, K., Dupuis, G., Kergoat, M. J., & Bherer, L. (2013). Benefits of
physical exercise training on cognition and quality of life in frail older adults. J
Gerontol B Psychol Sci Soc Sci, 68(3), 400-404. doi: 10.1093/geronb/gbs069
Li Y, Baldassi M, Johnson EJ & Weber EU. (2012) Compensating cognitive capabilities,
decision performance, and aging. Working Paper.
McArdle, J.J. & Willis, R.J (2012) “Cognitive Aging and Human Capital.” In Ron Sun, Ed.
Grounding Social Sciences in Cognitive Sciences. MIT Press.: 351-384.
Mukherjee, S., Kim, S., Ramanan, V. K., Gibbons, L. E., Nho, K., Glymour, M. M., . . . Crane, P. K.
(2014). Gene-based GWAS and biological pathway analysis of the resilience of
executive functioning. Brain Imaging Behav, 8(1), 110-118. doi: 10.1007/s11682013-9259-7
Park, D. C., J. Lodi-Smith, L. Drew, S. Haber, A. Hebrank, G. N. Bischof, and W. Aamodt. 2014.
“The Impact of Sustained Engagement on Cognitive Function in Older Adults: The
Synapse Project.” Psychological Science 25 (1): 103–12.
doi:10.1177/0956797613499592.
47
Park, D. C., & Reuter-Lorenz, P. (2009). The adaptive brain: Aging and neurocognitive
scaffolding. Annual Review of Psychology, 60(1), 173-196.
Plassman, BL, Newman, T., Welsh, K., & Breitner, J. (1994). Properties of the telephone
interview for cognitive status: application in epidemiological and longitudinal
studies. Neuropsychiatry, Neuropsychology, and Behavioral Neurology, 7, 235-241.
Potter, G. G., Plassman, B. L., Helms, M. J., Foster, S. M., & Edwards, N. W. (2006).
Occupational characteristics and cognitive performance among elderly male twins.
Neurology, 67(8), 1377-1382. doi: 10.1212/01.wnl.0000240061.51215.ed
Radloff, L. S. . (1977). The CES-D scale: A self-report depression scale for research in the
general population. Applied Psychological Measurement, 1(3), 385-401.
RAND Center for the Study of Aging. (2008).
Rohwedder, Susann, & Willis, R. J. (2010). Mental Retirement. Journal of Economic
Perspectives, 24(1), 119-138. doi: 10.1257/jep.24.1.119
Roy, A.D. (1951) Some thoughts on the distribution of income.” Oxford Economic Papers, Vol.
3, Issue 2, 135-146.
Salthouse, T. A. (2012). Consequences of age-related cognitive declines. Annu Rev Psychol,
63, 201-226. doi: 10.1146/annurev-psych-120710-100328
Salthouse, T. A. . (2006). Mental exercise and mental aging: Evaluating the validity of the
“use it or lose it” hypothesis. Perspectives on Psychological Science, 1(68-87). doi:
10.1111/j.1745-6916.2006.00005.x
Salthouse, T. A., Atkinson, T. M., & Berish, D. E. (2003). Executive functioning as a potential
mediator of age-related cognitive decline in normal adults. J Exp Psychol Gen,
132(4), 566-594. doi: 10.1037/0096-3445.132.4.566
Salthouse, T. A., Berish, D. E., & Miles, J. D. (2002). The role of cognitive stimulation on the
relations between age and cognitive functioning. Psychol Aging, 17(4), 548-557.
Schooler, C. (1984). Psychological effects of complex environments during the life span: A
review and theory. Intelligence, 8, 259-281. doi: 10.1016/0160-2896(84)90011-4
Schooler, C. (1990). Psychological factors and effective cognitive functioning. In J. E. Birren
& K. W. Schaie (Eds.), Handbook of the psychology of aging (3rd ed.) (Vol. xviii, pp.
347-358). San Diego, CA: Academic Press.
Schooler, C, Mulatu, MS, & Oates, G. (2004). Occupational self-direction, intellectual
functioning, and self-directed orientation in older workers: Findings and
48
implications for individuals and societies. American Journal of Sociology, 110, 161197. doi: 10.1086/385430
Smith, J, Fisher, G, King, R, Ryan, L, Clarke, P, House, J, . . . Weir, D. ( 2012). Documentation of
psychosocial measures in the HRS: 2006-2010. HRS/AHEAD Documentation Report.
In I. f. S. R. Survey Research Center, University of Michigan (Ed.). Ann Arbor, MI.
StataCorp. (2013). STATA Treatement-Effects Reference Manual: Potential outcomes /
Counterfactual Outcomes. Release 13. Retrieved October 31, 2014, from
http://www.stata.com/manuals13/te.pdf
Welsh, K.A., Breitner, J.C.S., & Mgruder-Habib, K.M. (1993). Detection of dementia in the
elderly using telephone screening of cognitive status. Neuropsychiatry
Neuropsychol. Behav. Neurol., 6, 103-110.
Willis, R. J. (2013). The cognitive demands of work and the length of working life: the case of
computerization. Paper presented at the Working Longer and Retirement
Conference, Stanford Institute for Economic Policy Research.
Willis, R.J. & Rosen, S. (1979) "Education and Self-Selection" Journal of Political Economy, 87
Supplement, October 1979, S7-S36.
Wooldridge, JM. (2007). Inverse probability weighted estimation for general missing data
problems. Jounal of Econometrics, 141, 1281-1301.
Yang, Y., & Lee, L.C. . (2010). Dynamics and heterogeneity in the process of human frailty
and aging: Evidence from the U.S. older adult population. Journal of Gerontology:
Social Sciences, 65B(2), 246-255. doi: doi:10.1093/geronb/gbp102
49