WINPEC Working Paper Series No. E2306
September 2023

Heterogeneous Treatment Effect of Retirement on
Cognitive Function

SATO Koryu, NOGUCHI Haruko, and INOUE Kosuke

Waseda INstitute of Political EConomy
Waseda University
Tokyo, Japan

Heterogeneous Treatment Effect of Retirement on Cognitive
Function
By KORYU SATO, HARUKO NOGUCHI, AND KOSUKE INOUE*
This study used instrumental variable causal forests to explore theheterogeneous treatment effect of retirement on cognitive function
using data from 19 countries. We found that, on average, retirees
have better cognitive function than workers and that the conditional
averagetreatment

effectsvary

dependingonindividuals’

characteristics. Policymakers should provide early retirement
options in the pension system to allow individuals to decide when to
retire. The balance between the social benefits of raising the statepension age and the individual costs of increasing the risk ofdementia by delaying retirement should be considered. (JEL I10, J26,
C26)

* Sato: Department of Social Epidemiology, Graduate School of Medicine and School of Public Health, Kyoto University,
Room 204, Science Frontier Laboratory, Yoshida-Konoecho, Sakyo-ku, Kyoto-shi, Kyoto 606-8315, Japan; Graduate
School of Economics, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, Japan (email:sato.koryu.8i@kyoto-u.ac.jp). Noguchi: Graduate School of Economics, Waseda University, 1-6-1 Nishiwaseda, Shinjukuku, Tokyo 169-8050, Japan (email: h.noguchi@waseda.jp). Inoue: the Hakubi Project, Department of Social
Epidemiology, Graduate School of Medicine and School of Public Health, Kyoto University, Room 204, Science Frontier
Laboratory, Yoshida-Konoecho, Sakyo-ku, Kyoto-shi, Kyoto 606-8315, Japan (email: inoue.kosuke.2j@kyoto-u.ac.jp).
This study was supported by the Japan Society for the Promotion of Sciences (grant number: 20K18931, 23H03164) andthe Health Care Science Institute Research Grant. The funders had no role in the study design; in the collection, analysis,
and interpretation of the data; in the writing of the report; or in the decision to submit the article for publication. There areno conflicts of interest to declare. This analysis used data or information from: the Harmonized SHARE dataset andCodebook, Version F as of June 2022; the Harmonized ELSA dataset and Codebook, Version G.2 as of July 2021; RANDHRS Longitudinal File 2018 (V2); and the Harmonized HRS dataset and Codebook, Version C as of January 2022. The
survey harmonization was funded by the National Institute on Aging (grant number: R01 AG030153, RC2 AG036619, R03
AG043052) and conducted by the Gateway to Global Aging Data in collaboration with the research team of the surveys.
The HRS was sponsored by the National Institute on Aging (grant number: NIA U01AG009740) and was conducted by the
University of Michigan. The harmonized datasets and more information are available through the Gateway to Global
Aging Data website (https://g2aging.org/). This study used publicly available data that obtained informed consent from allparticipants and ethical approval from relevant local ethics committees. Thus, the Ethics Committee of Kyoto University
exempted this study from review.

1

I. Introduction
The cognitive health of older people is a global concern. In 2015, there were 47
million people with dementia, and this number is projected to increase 1.6-fold to
75 million by 2030 (World Health Organization 2017). Given the rapid escalationin the demographic prevalence of people with dementia, the resulting economic
burden borne by society is poised to be significant. This burden includes not only
the direct costs attributable to medical interventions and long-term care but also theindirect costs experienced by informal caregivers, such as opportunity costs,
alternative labor expenses, foregone earnings, and the psychosocial encumbrances
experienced (Hurd et al. 2013; Wimo et al. 2017; Cimler et al. 2019; Wittenberg etal. 2019). The key approach to mitigating the increasing prevalence of dementia
lies in the comprehensive elucidation of the causal relationship between dementia
and the biological, epidemiological, and socioeconomic determinants that could
potentially exert an impact on its pathogenesis.
Within the realm of economics, a subset of investigations has particularly
centered on the potential ramifications of retirement behavior on dementia,
although a consensus in findings has not yet been unequivocally established. An
underpinning challenge in empirical studies resides in the endogenous nature ofcharacterizing the retirement decision, a phenomenon encapsulated as the “healthy
worker survivor effect” (Arrighi and Hertz-Picciotto 1994). The phenomenon inwhich healthier people tend to sustain their employment results in a fundamental
disparity in cognitive function between those in the workforce and retirees. This
inconsistency stems from inherent dissimilarities in principles between the twogroups. In the absence of a thorough resolution of endogeneity within an empiricalmodel, retirement becomes erroneously linked to a decline in cognitive function.
To address these endogeneity issues, empirical researchers often use the statepension age (SPA) to identify the causal effects of retirement on cognitive function,2

assuming that reaching the SPA exogenously increases the probability ofretirement. 1 Retirement dramatically changes individuals’ budget constraints and0Ftime allocation between labor and leisure, which affects the level of health attained(Grossman 1972). Thus, policymakers need to pay attention to the potential
ramifications of delayed retirement due to increasing SPA based on individuals’
characteristics.
This study aims to explore the heterogeneous treatment effect of retirement on
cognitive function using the instrumental variable (IV) forests algorithm developed
by Athey, Tibshirani, and Wager (2019). The basic idea of the IV forests estimationis that it is a combination of the generalized method of moments (GMM) andrandom forests. We used SPA as an IV for retirement, and the GMM produced IV
estimates. Random forests can detect observations that have similar treatment
effects. Hence, the IV forests calibrate the conditional average treatment effects
based on the GMM localized by “similarity” weights derived from a random
forests-based algorithm. This novel method has several advantages for theinvestigation of heterogeneous treatment effects. First, it is a data-driven, machinelearning-based approach capable of unveiling concealed effect modifiers.
Conventional research has often focused on a limited set of modifiers, assessing
their effect heterogeneity through interaction terms and the stratification ofanalytical samples. IV forests diverge from conventional approaches byaccommodating a wide array of potential covariates, Second, it substantiallymitigates the risk of model misspecification primarily because of its nonparametricnature. This is a notable feature in studying the effects of retirement on health, giventhat a previous review highlighted the inconsistency in the existing literature, partly

1
Many developed countries are increasing SPA to accommodate the rapidly aging population (Organisation for
Economic Co-operation and Development 2021). For example, the United States has increased the SPA from 65 to 66 by2009 and restarted increasing it to 67 by 2027 (Li 2022). The United Kingdom continues to increase the SPA from 65 to 67
by 2028 and has a further plan to increase it to 68 (United Kingdom Government 2014).

3

attributing it to issues with model specifications (Nishimura, Oikawa, and Motegi2018). Third, the algorithm is superior to classical random-forest-based algorithms
by providing asymptotic normal estimates using a sample splitting techniquereferred to as “honesty.” This is an essential property for testing hypotheses andcalculating confidence intervals.
Indeed, through its pioneering and initial application of the IV forest
methodology, distinguished by its distinctive attributes described in the previous
paragraph, this study on the impact of retirement on cognitive function makes
noteworthy contributions to the extant research landscape, as follows. First, througha data-driven, machine-learning-based approach, this study has unveiled hitherto
unacknowledged factors that modify the effect of retirement, including variables
such as income, assets, and pre-retirement health conditions and behaviors. Retirees
find themselves endowed with more leisure time but are constrained by financial
resources for health-related investments. However, individuals with higher
socioeconomic status during their pre-retirement phase possess the financial means
to allocate resources toward enhancing their cognitive function. This can beunderstood within the framework of the Grossman model (Grossman 1972), in
which individuals with greater financial capacity experience fewer constraints on
their lifetime budgets than those with lower socioeconomic status. Similarly, ourfindings indicate that individuals with better health prior to retirement tend to
exhibit superior cognitive function post-retirement, aligning with the theory thatstates that individuals with less time spent sick have the luxury of dedicating moretime to health-related investments than their less-healthy counterparts.
Consequently, we found that individuals with robust health, along with higher
educational attainment, financial assets, and income, tend to accrue more
substantial cognitive benefits from retirement.
Second, our study differs from prior studies as it refrains from imposing
parametricassumptions

andexhibits

4

reducedsusceptibility

to

model

misspecification. This is a hallmark of the IV forests approach. As an illustration,
Nishimura, Oikawa, and Motegi (2018) have previously elucidated that variancesin outcomes within earlier research endeavors might stem from variations in model
specifications, as observed in their replication of prior studies. The existing
literature has shown inconsistent results even though researchers have used thesame datasets and employed SPA as an IV for retirement. Using data from the
Health and Retirement Study (HRS), Bonsang, Adam, and Perelman (2012)
demonstrated the detrimental effect of retirement on cognitive function, whereas
Coe et al. (2012) found no evidence of the effect. Among studies using data fromthe Survey of Health, Ageing and Retirement in Europe (SHARE), Celidoni, Dal
Bianco, and Weber (2017) showed a detrimental effect, Coe and Zamarro (2011)indicated a non-significant association, and Bianchini and Borella (2016) found that
retirement improved cognitive function. In other countries, studies using data fromthe English Longitudinal Study on Ageing (ELSA) and the Japanese Study ofAging and Retirement (JSTAR) did not find clear associations between retirement
and cognitive function (Nishimura, Oikawa, and Motegi 2018; Rose 2020),
whereas analysis using data from the Korean Longitudinal Study of Aging indicateda beneficial effect (Nishimura, Oikawa, and Motegi 2018).
Finally, it is worth noting that our findings have significant and valuable policy
implications, transcending the application of a new analytical framework forassessing the impact of retirement on cognitive function. Building upon the findingsthat postponing retirement could accelerate the decline in cognitive function insome individuals, we estimated the fiscal costs of dementia care resulting from anincrease in SPA. Our projections indicate that the United Kingdom is poised toincur greater financial burdens than the United States due to the absence of early
retirement options, thereby affecting a substantial portion of the workforce. The
introduction of early retirement into the present system could, to some extent,
alleviate escalating costs. Thus, we recommend that policymakers consider

5incorporating provisions for early retirement into the pension system to enable
individuals to make retirement decisions according to their unique circumstances.
Additionally, we underscore the favorable impact of physical activity on the postretirement period. The promotion of physical activity initiatives can potentiallyalleviate the adverse effects of delayed retirement on cognitive health.
The remainder of this paper is organized as follows. Section II describes the data
used in this study, Section III presents the empirical model, Section IV reports theresults, and Section V discusses the results and concludes the paper.
II. Data
A. Harmonized Panel Data
This study uses harmonized panel datasets from the HRS, ELSA, and SHARE
provided by the Gateway to Global Aging Data project (Lee, Phillips, and Wilkens
2021). 2 Our data comprised three waves: we obtained covariates (except for age)
1F

from the HRS and ELSA in 2014 and SHARE in 2015; age and labor force status
were ascertained via the HRS and ELSA in 2016 and SHARE in 2017; and theoutcome of cognitive function was assessed in the HRS and ELSA in 2018 and
SHARE in 2019. 3
2F

Appendix A presents a sample flowchart. Of the 94,824 individuals who
participated in the first wave, 49,555 were followed-up with in all three waves. We

2
The harmonized datasets are available from https://g2aging.org/ (Accessed: January 21, 2023). This project provides “afree public resource designed to facilitate cross-national and longitudinal studies on aging.” Although the harmonizeddatasets of the Irish Longitudinal Study on Ageing, the Longitudinal Aging Study in India, and the Malaysia Ageing andRetirement Study were also available, they were harmonized only for one wave and thus excluded. Data from the Mexican
Health and Aging Study and the China Health and Retirement Longitudinal Study were also excluded because they conductedinterviews triennially and their harmonized variables were limited. We neither used data from the Costa Rican Longevity
and Healthy Aging Study, the Japanese Study of Aging and Retirement, and the Korean Longitudinal Study of Aging because
we previously found that IVs in these countries were weak (Sato and Noguchi 2023).
3
A total of 17 countries participated in all the three waves of the SHARE, namely, Austria, Belgium, Croatia, Czech
Republic, Denmark, Estonia, France, Germany, Greece, Israel, Italy, Luxembourg, Poland, Slovenia, Spain, Sweden, andSwitzerland.

6included 43,052 individuals aged 50–80 years in the second wave but excluded
29,519 individuals who did not work in the first wave and 722 individuals whoneither worked nor retired in the second wave (e.g., unemployed, disabled, or
homemaker). Finally, 12, 811 participants were included for the development of IV
forests.
B. Cognitive Function
We examined episodic memory as a measure of cognitive function. It involves
the ability to recall past experiences, which declines with age (Tulving 2002). It
was assessed in accordance with the Consortium to Establish a Registry for
Alzheimer’s Disease (CERAD) Battery (Morris et al. 1989). Participants listened
to 10 common words and were immediately asked by an interviewer to recall as
many words as possible. They were then asked to recall the words again after
approximately five minutes. Hence, the total number of words that the participants
could recall ranged between 0 and 20 and represented their cognitive function, as
in previous studies (Bonsang, Adam, and Perelman 2012; Coe and Zamarro 2011;
Coe et al. 2012; Bianchini and Borella 2016; Celidoni, Dal Bianco, and Weber
2017; Nishimura, Oikawa, and Motegi 2018; Rose 2020).
C. Retirement and State Pension Age
Labor force status was self-reported in the surveys, as described in Appendix B
and by Zamarro and Lee (2012). We restricted the sample to those who worked
during the first wave. In the second wave, we defined retirees as those who selfidentified as “retired,” regardless of their working status (i.e., including those who
were “partly retired”), following previous literature (Bianchini and Borella 2016;
Atalay, Barrett, and Staneva 2019). Other studies have defined retirement as notworking (Coe and Zamarro 2011; Bonsang, Adam, and Perelman 2012; Bingley

7and Martinello 2013), and we checked the robustness of our findings using anarrower definition of retirement.
To eliminate bias stemming from endogenous selection for retirement, SPA wasused as an IV for retirement. We employed the joint instruments of early retirementage (ERA) and official retirement age (ORA) to predict retirement following themethod of a previous study (Coe and Zamarro 2011). A binary ERA variable
discerned whether participants reached the earliest eligibility age for receiving
either reduced or full pension, subject to specific conditions. Likewise, a binary
ORA variable denoted whether participants reached the age of entitlement to theminimum guaranteed pension or full pension without any requirements. The ERA
variable was set to zero for all participants in countries where early retirement
schemes were not implemented. Appendix C shows the SPA of each country
collected from “Social Security Programs Throughout the World” (United States
Social Security Administration, 2020), “Pensions at a Glance” (Organisation for
Economic Co-operation and Development 2021), and websites of the national
authorities. Figures 1 (men) and 2 (women) describe the changes in retirement rates
according to age using data from the second wave. We observed some jumps inretirement rates around the SPA.

8

FIGURE 1. RETIREMENT RATE OF MEN
Notes: Each dot represents the average retirement rate for each 4-month interval (monthly age data was unavailable inEngland). The retirement rate is calculated by dividing the number of retirees by the sum of retirees and workers. The dashed
red line denotes the early retirement age, while the solid red line represents the official retirement age in the year of thesecond wave survey.

9

FIGURE 2. RETIREMENT RATE OF WOMEN
Notes: Each dot represents the average retirement rate for each 4-month interval (monthly age data was unavailable inEngland). The retirement rate is calculated by dividing the number of retirees by the sum of retirees and workers. The dashed
red line denotes the early retirement age, while the solid red line represents the official retirement age in the year of thesecond wave survey.

D. Covariates
We considered 60 harmonized covariates obtained from the first wave to develop
IV forests. Table 1 presents definitions of these covariates.

10

TABLE 1—DEFINITION OF COVARIATESTypeDefinition

Age

Continuous

Men
Foreign-born

BinaryBinaryEducation

OrderedMarriedLiving alone

BinaryBinaryNumber of children

BinaryAsset

Continuous

IncomeContinuous

Occupation

BinaryPhysical demand

OrderedPart-time job

BinarySelf-employed

BinaryBaseline cognition

Continuous

Self-rated healthOrderedDepression

ContinuousLife satisfaction

Continuous

Diagnosed diseases

BinaryThis variable is the participant’s age in months at the time of the second wave
interview.
This variable is coded as 1 for men and 0 for women.
This variable is coded as 1 if the interview did not take place in the country ofbirth and 0 otherwise.
This variable is coded as 1 for less than upper secondary education, 2 for upper
secondary and vocational training, and 3 for tertiary education according to the1997 International Standard Classification of Education.
This variable is coded as 1 for married or partnered and 0 for otherwise.
This variable is coded as 1 for those whose household size is 1 and 0 forotherwise.
Based on a variable indicating the number of participant’s living children(including natural, foster, adopted, or stepchildren), we created two binary
variables; “no children” indicates 1 if the number of children is zero and 0 forotherwise; “≥3 children” indicates 1 if the number of children is three or more
and 0 for otherwise.
This variable is the net value of assets at the couple-level unit calculated as thevalue of all wealth components (including housing, financial, and non-financial
assets) minus that of all debts. To make the variables in different surveys
comparable, we standardized them to z-scores for each survey. See Angrisaniand Lee (2012b) for details about the harmonization of wealth measures.
This variable is the total income at the couple-level including earnings, capitalincome, pensions, and public transfers. To make the variables in different
surveys comparable, we standardized them to z-scores for each survey. See
Angrisani and Lee (2012a) for details about the harmonization of income
measures.
We created four binary variables indicating the participant’s occupation:
professional, clerk, service and sales, and manual labor. We categorizedoccupations based on the 2010 Census occupations in the HRS, the Standard
Occupational Classification (2000) in the ELSA, and the 1988 International
Standard Classification of Occupations in the SHARE. See Appendix D for
details about the occupational codes.
This variable is a 4-point Likert scale indicating the degree to which theparticipant agrees that their job is physically demanding: 1 = strongly disagree; 2= disagree; 3 = agree; 4 = strongly agree.
This variable is coded as 1 if the participant works less than 35 hours per week
and 0 otherwise.
This variable is coded as 1 if the participant reports being self-employed and 0
otherwise.
This variable indicates baseline cognitive function measured in the same way as
the outcome.
This variable is a 5-point Likert scale indicating self-rated health: 1 = poor; 2 =fair; 3 = good; 4 = very good; 5 = excellent.
Higher scores of this variable indicate more severe depression. The HRS and the
ELSA use a short version of the Center for Epidemiologic Studies Depression(CES-D) to measure depression, while the SHARE uses the EURO-D scale. To
make the variables using different measures comparable, we standardized themto z-scores for each survey.
Higher scores of this variable indicate higher levels of participants’ life
satisfaction. The HRS uses a 5-point Likert scale, the ELSA uses a 7-point
Likert scale, and the SHARE uses a 10-point Likert scale to measure life
satisfaction. The harmonized datasets provide a variable standardized to z-scoresfor each survey to make them comparable.
We have nine variables of chronic medical conditions: namely, hypertension,
diabetes, cancer, lung disease, heart disease, stroke, arthritis, psychiatricproblems, and hyperlipemia. These variables indicate 1 if a doctor has ever told
the participant that he or she has the conditions and 0 for otherwise. See Hu andLee (2012) for details about the harmonization of chronic medical conditions.

Covariate11

Health limitation

BinaryDifficulty in ADL

BinaryDifficulty in IADL

BinaryEyesight and hearing

OrderedPain problems

BinaryObesity

BinaryPhysical activity

BinaryHeavy drinking

BinarySmoking

BinaryCountries

BinaryThis variable indicates 1 if the participant reports that an impairment or healthproblem limits the kind or amount of paid work and 0 for otherwise.
This variable indicates 1 if the participant has difficulties with any of the five
ADL including bathing or showering, dressing, eating, getting in and out of bed,
and walking across a room, and 0 for otherwise.
This variable indicates 1 if the participant has difficulties with any of the five
IADL including using the telephone, managing money, taking medications,
shopping for groceries, and preparing a hot meal, and 0 for otherwise.
We have three 5-point Likert scales for self-reported distance eyesight, neareyesight, and hearing: 1 = poor; 2 = fair; 3 = good; 4 = very good; 5 = excellent.
This variable indicates 1 if the participant reports being troubled with pain and 0
otherwise.
This variable indicates 1 if the participant’s body mass index is 30 kg/m2 or
higher and 0 otherwise (World Health Organization 2021).
This variable indicates 1 if the participant engages in vigorous or moderate
physical activity once or more per week and 0 for otherwise.
This variable indicates 1 if the participant reports having 15 or more drinks per
week for men and 8 or more drinks for women and 0 for otherwise (National
Institute on Alcohol Abuse and Alcoholism 2023).
This variable indicates 1 if the participant reports smoking now and 0 otherwise.
We have 19 binary variables indicating the place of the interview: namely,
Austria, Belgium, Croatia, Czech Republic, Denmark, England, Estonia, France,
Germany, Greece, Israel, Italy, Luxembourg, Poland, Slovenia, Spain, Sweden,
Switzerland, and United States.

Notes: HRS stands for the Health and Retirement Study, ELSA stands for the English Longitudinal Study on
Ageing, and SHARE stands for the Survey of Health, Ageing and Retirement in Europe. ADL and IADL standfor activities of daily living and instrumental activities of daily living, respectively.

III. Empirical Model
A. IV forests
To assess the heterogeneous treatment effect of retirement, we used an IV forests
algorithm developed by Athey, Tibshirani, and Wager (2019). Suppose that 𝑛𝑛

samples indexed by 𝑖𝑖 = 1, … , 𝑛𝑛 are independent and identically distributed.

Observations 𝑂𝑂𝑖𝑖 = {𝑌𝑌𝑖𝑖 , 𝑊𝑊𝑖𝑖 , 𝑍𝑍𝑖𝑖 } include an outcome 𝑌𝑌𝑖𝑖 ∈ ℝ (cognitive function), a
treatment assignment 𝑊𝑊𝑖𝑖 ∈ {0,1} (retirement), and an IV 𝑍𝑍𝑖𝑖 ∈ {0,1} (SPA), alongwith a set of auxiliary covariates 𝑋𝑋𝑖𝑖 ∈ 𝒳𝒳. The conditional effects of interest 𝜃𝜃(𝑥𝑥)are solutions to the local moment conditions(1)

𝔼𝔼�𝜓𝜓𝜃𝜃(𝑥𝑥),𝜐𝜐(𝑥𝑥) (𝑂𝑂𝑖𝑖 ) � 𝑋𝑋𝑖𝑖 = 𝑥𝑥] = 0 ∀ 𝑥𝑥 ∈ 𝒳𝒳,

12where 𝜓𝜓(∙) is a scoring function and 𝜈𝜈(𝑥𝑥) is an optional nuisance parameter. The
IV forests estimates 𝜃𝜃�(𝑥𝑥), 𝜈𝜈̂ (𝑥𝑥) are obtained by solving(𝜃𝜃�(𝑥𝑥), 𝜈𝜈̂ (𝑥𝑥)) ∈ arg min ��∑𝑛𝑛𝑖𝑖=1 𝛼𝛼𝑖𝑖 (𝑥𝑥)𝜓𝜓𝜃𝜃,𝜈𝜈 (𝑂𝑂𝑖𝑖 )�2 �.

(2)

If

𝜃𝜃,𝜈𝜈

the

expression

hasauniqueroot,(𝜃𝜃�(𝑥𝑥), 𝜈𝜈̂ (𝑥𝑥))solves∑𝑛𝑛𝑖𝑖=1 𝛼𝛼𝑖𝑖 (𝑥𝑥)𝜓𝜓𝜃𝜃�(𝑥𝑥),𝜈𝜈�(𝑥𝑥) (𝑂𝑂𝑖𝑖 ) = 0. The IV forests incorporate similarity weights 𝛼𝛼𝑖𝑖 (𝑥𝑥)to solve the heterogeneous estimating equation. The weights 𝛼𝛼𝑖𝑖 (𝑥𝑥) are obtainedusing random forests with a set of 𝐵𝐵 trees indexed by 𝑏𝑏 = 1, … , 𝐵𝐵
(3)

𝛼𝛼𝑏𝑏𝑏𝑏 (𝑥𝑥) =1({𝑋𝑋𝑖𝑖 ∈𝐿𝐿𝑏𝑏 (𝑥𝑥)}),|𝐿𝐿𝑏𝑏 (𝑥𝑥)|1𝛼𝛼𝑖𝑖 (𝑥𝑥) = 𝐵𝐵 ∑𝐵𝐵𝑏𝑏=1 𝛼𝛼𝑏𝑏𝑏𝑏 (𝑥𝑥).

𝐿𝐿𝑏𝑏 (𝑥𝑥) denotes the set of training samples falling in the same leaf as a target sample
𝑥𝑥 in tree 𝑏𝑏, and 𝛼𝛼𝑖𝑖 (𝑥𝑥) represents how often the 𝑖𝑖th training sample falls into thesame leaf as 𝑥𝑥. The forests-based algorithm splits training samples to maximize thesquared difference in treatment effect estimates across leaves (i.e., heterogeneity)
so that 𝛼𝛼𝑖𝑖 (𝑥𝑥) leads to a good fit of 𝜃𝜃(𝑥𝑥). The estimates 𝜃𝜃�𝑥𝑥 have the property ofasymptotic normality using a subsampling technique called “honesty” (Athey and

Imbens 2016; Wager and Athey 2018; Athey, Tibshirani, and Wager 2019). The
basic idea of “honesty” is to divide the sample into three subsets; the “splitting”
subset is used to partition samples and develop a tree; the “estimation” subset isused to estimate a treatment effect for each leaf of the fitted tree; and the “test”
subset is used to validate the estimates.
To apply the forests-based algorithm to an IV regression, Athey, Tibshirani, andWager (2019) assumed a structural model(4)

𝑌𝑌𝑖𝑖 = 𝜇𝜇(𝑋𝑋𝑖𝑖 ) + 𝜏𝜏(𝑋𝑋𝑖𝑖 )𝑊𝑊𝑖𝑖 + 𝜀𝜀𝑖𝑖

13where 𝜇𝜇(𝑋𝑋𝑖𝑖 ) denotes a nuisance intercept parameter, 𝜏𝜏(𝑋𝑋𝑖𝑖 ) is interpreted to be thecausal effect of 𝑊𝑊𝑖𝑖 on 𝑌𝑌𝑖𝑖 , and 𝜀𝜀𝑖𝑖 is an error term that can be correlated with 𝑊𝑊𝑖𝑖 . To

recover the consistency of 𝜏𝜏(𝑋𝑋𝑖𝑖 ) in the case of a correlation between 𝑊𝑊𝑖𝑖 and 𝜀𝜀𝑖𝑖 , an
IV 𝑍𝑍𝑖𝑖 is used. If 𝑍𝑍𝑖𝑖 is independent of 𝜀𝜀𝑖𝑖 conditionally on 𝑋𝑋𝑖𝑖 , and the covariance of

𝑍𝑍𝑖𝑖 and 𝑊𝑊𝑖𝑖 conditionally on 𝑋𝑋𝑖𝑖 is nonzero, 𝜏𝜏(𝑋𝑋𝑖𝑖 ) is identified as
Cov[𝑌𝑌 ,𝑍𝑍 | 𝑋𝑋 =𝑥𝑥]

(5)

𝜏𝜏(𝑋𝑋𝑖𝑖 ) = Cov[𝑌𝑌 𝑖𝑖,𝑊𝑊𝑖𝑖 | 𝑋𝑋𝑖𝑖 =𝑥𝑥].
𝑖𝑖

𝑖𝑖

𝑖𝑖

In this setting, a scoring function 𝜓𝜓(∙) can be defined as(6)

𝑍𝑍 (𝑌𝑌 − 𝑊𝑊𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥))𝜓𝜓𝜏𝜏(𝑥𝑥),𝜇𝜇(𝑥𝑥) (𝑌𝑌𝑖𝑖 , 𝑊𝑊𝑖𝑖 , 𝑍𝑍𝑖𝑖 ) = � 𝑖𝑖 𝑖𝑖
�.
𝑌𝑌𝑖𝑖 − 𝑊𝑊𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥)Then, 𝜏𝜏(𝑥𝑥) is estimated via moment functions 𝔼𝔼�𝑍𝑍𝑖𝑖 �𝑌𝑌𝑖𝑖 − 𝑊𝑊𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥)��𝑋𝑋𝑖𝑖 =𝑥𝑥] = 0 and 𝔼𝔼[𝑌𝑌𝑖𝑖 − 𝑊𝑊𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥)|𝑋𝑋𝑖𝑖 = 𝑥𝑥] = 0 . Biewen and Kugler (2021)
extended IV forests to a multiple IVs setting (i.e., 𝑍𝑍𝑖𝑖 is a 𝑀𝑀 × 1 vector) by defining𝜓𝜓(∙) as(7)

𝑊𝑊̇ (𝑌𝑌 − 𝑊𝑊̇𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥))⎡ 𝑖𝑖 𝑖𝑖⎤
𝑌𝑌𝑖𝑖 − 𝑊𝑊̇𝑖𝑖 𝜏𝜏(𝑥𝑥) − 𝜇𝜇(𝑥𝑥) ⎥⎢𝜓𝜓𝜏𝜏(𝑥𝑥),𝜇𝜇(𝑥𝑥),𝛾𝛾1(𝑥𝑥),𝛾𝛾0(𝑥𝑥) (𝑌𝑌𝑖𝑖 , 𝑊𝑊𝑖𝑖 , 𝑍𝑍𝑖𝑖 ) = ⎢⎥,′⎢𝑍𝑍𝑖𝑖 (𝑊𝑊𝑖𝑖 − 𝑍𝑍′ 𝑖𝑖 𝛾𝛾1(𝑥𝑥) − 𝛾𝛾0 (𝑥𝑥))⎥⎣ 𝑊𝑊𝑖𝑖 − 𝑍𝑍𝑖𝑖 𝛾𝛾1 (𝑥𝑥) − 𝛾𝛾0 (𝑥𝑥) ⎦where 𝑊𝑊̇𝑖𝑖 = 𝛾𝛾0 (𝑥𝑥) + 𝑍𝑍𝑖𝑖′ 𝛾𝛾1 (𝑥𝑥). The estimates of a conditional local averagetreatment effect 𝜏𝜏̂ (𝑥𝑥) can be obtained by solving 𝑀𝑀 + 3 moment conditions, alongwith weights 𝛼𝛼𝑖𝑖 (𝑥𝑥).

14

B. Statistical Analysis
Our IV forests developed 2000 trees and tuned their parameters 4 through cross3F

validation. To summarize the effect of retirement on cognitive function obtainedusing IV forests, we estimated the local average treatment effect on the overlap
population (LATO). We define the conditional mean of the outcome as 𝑦𝑦(𝑥𝑥) =𝔼𝔼[𝑌𝑌𝑖𝑖 |𝑋𝑋𝑖𝑖 = 𝑥𝑥], the propensity score of the treatment as 𝑤𝑤(𝑥𝑥) = 𝔼𝔼[𝑊𝑊𝑖𝑖 |𝑋𝑋𝑖𝑖 = 𝑥𝑥], andthe propensity score of the instrument as 𝑧𝑧(𝑥𝑥) = 𝔼𝔼[𝑍𝑍𝑖𝑖 |𝑋𝑋𝑖𝑖 = 𝑥𝑥]. The IV forests yieldout-of-bag estimates (i.e., the prediction of the 𝑖𝑖th observation is obtained via trees

fitted without using the 𝑖𝑖 th observation) of these marginal expectations,𝑦𝑦� (−𝑖𝑖) , 𝑤𝑤� (−𝑖𝑖) , 𝑧𝑧̂ (−𝑖𝑖) , which recover √𝑛𝑛 consistency of estimates using a machinelearning-based method (Chernozhukov et al. 2018). Then, we limited samples tothe overlap population 𝒫𝒫 by trimming the estimated propensity score of treatment𝑤𝑤� (−𝑖𝑖) to a value between 0.1 and 0.9 (Crump et al. 2009). To obtain the LATO

relying on the non-parametric estimation, we computed conditionally centered�𝑖𝑖 = 𝑊𝑊𝑖𝑖 − 𝑤𝑤outcomes 𝑌𝑌�𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝑦𝑦� (−𝑖𝑖) (𝑋𝑋𝑖𝑖 ) , 𝑊𝑊� (−𝑖𝑖) (𝑋𝑋𝑖𝑖 ) , and 𝑍𝑍�𝑖𝑖 = 𝑍𝑍𝑖𝑖 − 𝑧𝑧̂ (−𝑖𝑖) (𝑋𝑋𝑖𝑖 ) ,and then ran residual-on-residual two-stage least squares (2SLS) regression using
�𝑖𝑖 , 𝑍𝑍�𝑖𝑖 }𝑛𝑛𝑖𝑖=1 ∈ 𝒫𝒫. 5 For the purpose of comparison, we also
centered outcomes {𝑌𝑌�𝑖𝑖 , 𝑊𝑊
4F

performed parametric ordinary least squares (OLS) and 2SLS regressions adjustingfor 10 covariates selected based on variable importance in trained IV forests (i.e.,
covariates most frequently used to split samples) among the overlap population. In
addition, we ran causal forests without an IV.

4

Namely, the fraction of the data used to build each tree, the number of variables tried for each split, a target for theminimum number of observations in each leaf, the fraction of data that will be used for determining splits, whether to prune
the estimation sample tree such that no leaves are empty, a parameter that controls the maximum imbalance of a split, and aparameter that controls how harshly imbalanced splits are penalized.
5
Robinson (1988) showed that this orthogonal transformation yields √𝑛𝑛 consistent estimates, even if nuisance estimatessuch as 𝑦𝑦(𝑥𝑥), 𝑤𝑤(𝑥𝑥), 𝑧𝑧(𝑥𝑥) converge at a slower rate.

15

To see how well our IV forests captures effect heterogeneity, we drew acalibration plot according to the ranking of the estimated conditional local averagetreatment effect on the overlap population (CLATO) 𝜏𝜏̂ (𝑥𝑥). To obtain the valid

inference of 𝜏𝜏̂ (𝑋𝑋𝑖𝑖 ) for the 𝑖𝑖th observation based on the “honesty” property, we

should fit trees without using the 𝑖𝑖th observation. Hence, we divided the sample

into 10 folds. Then, IV forests were fitted using nine folds, and the remaining fold

was used to predict 𝜏𝜏̂ (𝑥𝑥). According to the quintile of the 𝜏𝜏̂ (𝑥𝑥) ranking within theheld-out fold, we categorized observations into five groups from Q1 (the lowest

CLATO; subgroup of individuals who received the least benefits from retirement)
to Q5 (the highest CLATO; subgroup of individuals who received the most benefits

from retirement). This procedure was repeated for each iteration. 6 Finally, we
5F

estimated LATOs for each quintile subgroup. Furthermore, to assess theheterogeneity of each covariate, we compared the mean values of covariates acrossgroups. For continuous variables, we also depicted a partial dependence plot withthe continuous variable on the x-axis and the out-of-bag prediction of CLATO𝜏𝜏̂ (−𝑖𝑖) (𝑋𝑋𝑖𝑖 ) on the y-axis.

Building on the LATO estimates for the quintile groups, we estimated themonetary costs of dementia care induced by increasing ORA from the age of 65 to
66 years in the United States and the United Kingdom. 7 We relied on a previous
6F

study that indicated that a one-word increase in the word recall test predicts 0.85
times lower odds of dementia in five years (Tierney, Moineddin, and McDowell2010). Additionally, we predicted increases in the number of workers aged 66 by
estimating the reduced probabilities of retirement attributable to increases in ORA
using HRS and ELSA samples. Hurd et al. (2013) and Wittenberg et al. (2019)

6
7

Namely, we performed a 10-fold cross-fitting procedure.

The United States and the United Kingdom increased their ORA to age 66 for those born after 1943 and those born after
1954, respectively. Both countries have plans to further increase their ORA to age 67.

16

provided monetary cost estimates for dementia care per patient and their projectionsfor 2030 in the United States and the United Kingdom, respectively. By multiplying
these components, we estimated the changes in the total cost of dementia care in
2030.
In all analyses, missing values were imputed using a random forests-basedalgorithm (Mayer 2021) 8 , assuming that the data were missing at random.
7F

Appendix E reports the imputed values for each variable.
IV. Results
A. Descriptive Statistics
After trimming the samples based on the propensity score for retirement, ouranalytical sample comprised 7,432 individuals, including 5,267 (70.9%) workers
and 2,165 (29.1%) retirees in the second wave. Table 2 presents descriptive
statistics. Workers had higher cognitive function than retirees in the third wave. In
the first wave, we found unbalanced characteristics even though all of them had
been working. Those who continued working were younger and had a higher
education and were more likely to be foreign-born, professional workers, and selfemployed at baseline than those who retired in the second wave. However, workers
were less likely to engage in manual labor and part-time jobs than retirees.
Furthermore, workers had higher baseline cognitive function, self-rated health, andhearing ability and were less likely to have health problems, including
hypertension, diabetes, lung disease, stroke, arthritis, health limitations in working,difficulties in activities of daily living, pain-related problems, and smoking habits,
than retirees. We also found differences between workers and retirees in the8

We set the number of candidate non-missing values to sample from in the predictive mean matching steps to 3 and thenumber of trees to 100.

17

composition of countries. The outcomes appeared to be normally distributed, as
shown in Appendix F.
TABLE 2—DESCRIPTIVE STATISTICS OF THE OVERLAP POPULATION
Variables, n (%)

Workern = 5267 (70.9%)

Retireen = 2165 (29.1%)

P-value

11.1 (3.21)

10.8 (3.19)<0.001

OutcomeCognitive function, mean (SD)
Characteristics
Age, year, mean (SD)63.9 (3.86)

65.8 (4.27)<0.001

Men

2667 (50.6)

1063 (49.1)

0.23

Foreign-born

707 (13.4)

230 (10.6)<0.001

Education, mean (SD)

2.2 (0.68)

2.1 (0.69)<0.001Married4059 (77.1)

1663 (76.8)

0.81

Living alone

934 (17.7)

406 (18.8)

0.30

No children

544 (10.3)

200 (9.2)

0.15≥3 children

1885 (35.8)760 (35.1)

0.58

Asset, z-score, mean (SD)

0.1 (1.21)

0.0 (0.79)

0.48

Income, z-score, mean (SD)

0.1 (1.14)

0.0 (0.91)

0.67

Professional

2272 (43.1)

878 (40.6)

0.04

Clerk

793 (15.1)

329 (15.2)

0.88Service & sales

1067 (20.3)

446 (20.6)

0.74

Manual labor

1140 (21.6)

515 (23.8)

0.04

Physical demand, mean (SD)

2.3 (1.07)

2.3 (1.05)

0.91

Part-time job

1298 (24.6)

775 (35.8)<0.001

Self-employed

1151 (21.9)

368 (17.0)<0.001Baseline cognition, mean (SD)11.3 (3.19)

11.0 (3.26)<0.001

Self-rated health, mean (SD)

3.4 (0.98)

3.3 (0.95)<0.001

Depression, z-score, mean (SD)

0.0 (1.01)

0.0 (0.97)

0.58

Health & BehaviorsLife satisfaction, z-score, mean (SD)

0.0 (1.00)

0.1 (0.98)

0.06

Hypertension

2064 (39.2)

982 (45.4)<0.001Diabetes

626 (11.9)

311 (14.4)

0.003

Cancer372 (7.1)

177 (8.2)

0.10

Lung disease

231 (4.4)

122 (5.6)

0.02

Heart disease

571 (10.8)

265 (12.2)

0.08

Stroke107 (2.0)

69 (3.2)

0.003

Arthritis

1633 (31.0)

800 (37.0)<0.00118

Psychiatric problems

542 (10.3)

244 (11.3)

0.21

Hyperlipemia

1534 (29.1)

634 (29.3)

0.89

Health limitations in working

526 (10.0)

291 (13.4)<0.001

Difficulty in ADL

205 (3.9)

137 (6.3)<0.001

Difficulty in IADL

129 (2.4)

45 (2.1)

0.34

Distance eyesight, mean (SD)

3.8 (0.94)

3.8 (0.92)

0.96

Near eyesight, mean (SD)

3.6 (0.98)

3.6 (0.97)

0.21

Hearing, mean (SD)

3.6 (1.00)

3.5 (0.99)

0.01

Pain problems

1702 (32.3)

783 (36.2)

0.001

Obesity1515 (28.8)

612 (28.3)

0.67

Physical activity

4629 (87.9)

1888 (87.2)

0.42

Heavy drinking

524 (9.9)237 (10.9)

0.20

Smoking

795 (15.1)

369 (17.0)

0.04

Austria50 (0.9)37 (1.7)

0.006

Belgium

99 (1.9)58 (2.7)

0.03Countries

Croatia37 (0.7)

14 (0.6)

0.79

Czech Republic

147 (2.8)

126 (5.8)<0.001

Denmark

291 (5.5)

92 (4.2)

0.02

Estonia379 (7.2)

93 (4.3)<0.001

France123 (2.3)

86 (4.0)<0.001

Germany

262 (5.0)

128 (5.9)

0.10

Greece182 (3.5)

49 (2.3)

0.007

Israel100 (1.9)30 (1.4)

0.13

Italy

121 (2.3)

37 (1.7)

0.11

Luxembourg

44 (0.8)

27 (1.2)

0.10

Poland31 (0.6)

13 (0.6)

0.95

Slovenia

94 (1.8)60 (2.8)

0.007

Spain

108 (2.1)

61 (2.8)

0.04

Sweden263 (5.0)

152 (7.0)<0.001

Switzerland

276 (5.2)

115 (5.3)

0.90

England974 (18.5)

403 (18.6)

0.90

United States

1686 (32.0)

584 (27.0)<0.001

Notes: ADL and IADL stand for activities of daily living and instrumental activities of daily living, respectively.
Imputed data are used.

19

B. Average Treatment Effects
Table 3 compares the LATO estimated using IV forests with the estimates of theconventional OLS, 2SLS, and non-IV forests. The OLS test showed a nonsignificant negative association between retirement and cognitive functioning. The
first-stage estimates of the 2SLS indicated that reaching the ERA and ORA
significantly increased the probability of retirement. The F-statistic showed a strong
correlation between IVs and retirement, and the over-identification test did not
reject the null hypothesis, suggesting that our IVs were valid. In the second-stage
estimates, retirement was significantly associated with increased cognitive
function. Similar to the OLS results, non-IV forests showed a non-significant
negative association. However, the IV forests indicated that retirees could recall
1.348 more words than workers, and the point estimate was statistically significant.
TABLE 3—AVERAGE TREATMENT EFFECTS OF RETIREMENT ON COGNITIVE FUNCTION

Retirement(1) OLSa(2) 2SLSa-0.013(0.070)

ERA (1st stage)(3) Non-IV Forests(4) IV Forests

0.962***-0.031

1.348**(0.344)(0.071)(0.528)0.091***(0.011)

ORA (1st stage)

0.249***(0.015)Observations

7432

7432

7432

7432

R squared

0.313

0.295

0.000

-0.051

F statistic

163.037***

Sargan statistic

1.177
Notes: OLS stands for ordinary least squares, 2SLS stands for two-stage least squares, IV stands for instrumental variable,
ERA stands for early retirement age, and ORA stands for official retirement age. Standard errors are shown in parentheses.
The model is adjusted for the following covariates selected based on variable importance in trained IV forests:
assets, age, income, baseline cognition, depression, life satisfaction, self-rated health, hearing, degree of physicaldemands of the job, and distance eyesight.

a*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.

20

C. Heterogeneous Treatment Effect of Retirement
Figure 3 shows the distribution of the conditional average treatment effects
comparing the non-IV and IV forests. While the estimates for non-IV forests wereconcentrated around zero, those for IV forests appeared to be heterogeneously
distributed.

FIGURE 3. DISTRIBUTION OF CONDITIONAL AVERAGE TREATMENT EFFECTS
Notes: IV stands for an instrumental variable. The estimand of non-IV forests is the conditional average treatment effect on
the overlap population (CATO), while that of IV forests is the conditional local average treatment effect on the overlap
population (CLATO).

21

Figure 4 shows the calibration plot for CLATO. As the CLATO ranking
increased, the estimated LATOs in these categories increased monotonically,suggesting that our IV forests correctly captured the heterogeneity in the effect ofretirement on cognitive function. The point estimate of retirement indicated aharmful effect on cognitive function in the lowest CLATO group (Q1), whereas itshowed protective effects in the other groups, although the 95% confidence interval
included a value of 0.

FIGURE 4. CALIBRATION PLOT FOR CLATO
Notes: CLATO stands for the conditional local average treatment effect on the overlap population.

Figure 5 shows the heterogeneity of individual characteristics. Individuals in thehighest CLATO group (Q5) tended to be older, female, and born in the country and22had fewer than three children, higher education, assets, and income than those in
the lowest group (Q1). Those who worked as clerks and whose jobs were
professional or part-time tended to be categorized into the highest group, whereas
those who worked in service and sales and manual jobs and whose jobs were
physically demanding or self-employed tended to be categorized into the lowest
group.
Figure 6 suggests that those with better health and well-being received more
benefits from retirement. Specifically, those in the highest CLATO group tended tohave better self-rated health, life satisfaction, and eyesight and hearing abilities thanthose in the lowest CLATO group. In contrast, those in the lowest group were more
likely to have depressive symptoms, hypertension, diabetes, lung and heartdiseases, arthritis, psychiatric problems, hyperlipidemia, health limitations inworking, difficulties in activities of daily living and instrumental activities of dailyliving, and pain-related problems. Furthermore, while obese individuals tended tobe categorized into the lowest group, those who frequently engaged in physicalactivity tended to be in the highest group.
Figure 7 shows the heterogeneity across countries. People in Denmark andGreece tended to fall into higher CLATO groups, whereas those in Estonia andFrance tended to fall into lower CLATO groups.

23

FIGURE 5. HETEROGENEITY IN INDIVIDUAL CHARACTERISTICS
Notes: CLATO stands for the conditional local average treatment effect on the overlap population. Asset and income arestandardized to z-scores. Q1 is the group with the lowest CLATO, while Q5 is the group with the highest CLATO. Each tile
indicates the mean value of a covariate within the group and its standard deviation in parentheses. P-values of F-statistics arecorrected using the Bonferroni method.

24

FIGURE 6. HETEROGENEITY IN HEALTH AND BEHAVIORS
Notes: ADL and IADL stand for activities of daily living and instrumental activities of daily living, respectively. Depression
and life satisfaction are standardized to z-scores. Q1 is the group with the lowest CLATO, while Q5 is the group with thehighest CLATO. Each tile indicates the mean value of a covariate within the group and its standard deviation in parentheses.
P-values of F-statistics are corrected using the Bonferroni method.

25

FIGURE 7. HETEROGENEITY IN COUNTRIES
Notes: Q1 is the group with the lowest CLATO, while Q5 is the group with the highest CLATO. Each tile indicates the meanvalue of a covariate within the group and its standard deviation in parentheses. P-values of F-statistics are corrected using
the Bonferroni method.

26

Appendix G presents the partial dependence plots for the continuous variables.
The estimates of CLATO tended to increase with age until age 65 and then flattened
after age 65. Those with average or below average assets and income showed large
variations in CLATO, whereas those with higher assets and income tended to havehigher CLATO.
D. Monetary Cost Estimation of Increasing ORA
Based on the LATO estimates for the quintile groups shown in Figure 4, we
estimate that the total monetary cost of dementia care will increase by 5.0 billion
dollars (1.4%) in the United States and 3.3 billion pounds (5.2%) in the United
Kingdom in 2030 due to an increase in their ORA from age 65 to 66 (See Appendix
H for details). In the United States, the impact of increasing the ORA will be limited
because a large proportion of workers retire at the ERA of 62 years. In contrast, theimpact of increasing the ORA in the United Kingdom will not be negligible because
most workers consider retirement at the ORA, given that its pension system has noearly retirement scheme. Our findings suggest that delayed retirement owing toincreased ORA use increases the monetary costs of dementia care.
E. Robustness Checks
Table 4 displays the results of the robustness checks comparing the LATO
estimated using different models. Column (1) indicates the estimates from a modelthat restricts participants to individuals aged 55–75 years. Column (2) shows amodel that excludes those who mentioned retirement but worked in the second
wave (i.e., partly retired) and examines the impact of full retirement on cognitive
function. Column (3) shows a model that excludes those who engaged in part-timejobs or were self-employed in the first wave and studied only full-time employees.
Column (4) shows a model that excludes data from the United States, given that it27

has the largest sample size in our dataset. As shown in Table 4, all the LATO
estimates are similar to our main results, which suggests that our findings arerobust, even in different settings.
TABLE 4—ROBUSTNESS CHECKS

Retirement

(1)

(2)

(3)

(4)

1.377***(0.528)1.334**

1.366*

1.348**(0.578)(0.718)(0.599)Observations
7268
6128
4582
5218
Notes: Column (1) is for a model that restricted participants to individuals aged from 55 to 75 years. Column (2) is for amodel that excluded those who mentioned retirement but worked in the second wave. Column (3) is for a model that excluded
those who engaged in a part-time job or were self-employed in the first wave. Column (4) is for a model that excluded datafrom the United States.
*** Significant at the 1 percent level.
** Significant at the 5 percent level.
* Significant at the 10 percent level.

V. Discussion and Conclusions
This study investigated the heterogeneous treatment effects of retirement on
cognitive function using data from 19 countries. We found that retirees had better
cognitive function than workers on average and that the conditional averagetreatment effects varied depending on the individual’s characteristics.
Our findings on ATE were consistent with those of previous studies suggestingthat retirement improves cognitive function (de Grip et al. 2015; Bianchini and
Borella 2016). We found that the estimates of the OLS and non-IV forests indicatednon-significant associations, but they could be negatively biased because of healthselection for retirement. After eliminating potential endogeneity using IV methods,
both the conventional 2SLS and IV forests showed beneficial associations withretirement and cognitive function. The estimate of 1.348 words in the IV forests islarge, given that it corresponds to a 0.42 standard deviation of the distribution of28

the cognitive function score. 9 Improvements in cognitive function after retirement
8F

can be explained through several pathways. First, job strain is a potential risk factor
for decreased cognitive function (Elovainio et al. 2009; Agbenyikey et al. 2015),
but retirement releases individuals from psychosocial stress. Second, retirees caninvest more time in their health than workers. Many studies have shown that
retirement is associated with healthy behaviors such as increased physical activity,
sleep quality, and smoking cessation (Kämpfen and Maurer 2016; Myllyntausta etal. 2018; Müller and Shaikh 2018; Celidoni and Rebba 2017; Kesavayuth,
Rosenman, and Zikos 2018; Eibich 2015; Syse et al. 2017; Insler 2014), which
protect against cognitive decline.
This study presented the heterogeneous treatment effect of retirement on
cognitive function depending on individuals’ characteristics. For example, we
found that women tended to have higher CLATO. This gender difference is in linewith the evidence that women are more likely to engage in exercise to maintaintheir physical and mental health after retirement than men, which could induce
disparities in cognitive function (Sato and Noguchi 2023; Atalay, Barrett, andStaneva 2019). Additionally, individuals who engaged in physical activity before
retirement tended to have a higher CLATO. We assumed that they had a habit ofexercising and maintained it after retirement, which was beneficial to their
cognitive function. Thus, some heterogeneity may be explained by post-retirement
health behaviors.
Furthermore, our findings regarding heterogeneity are consistent with those of
the Grossman model (Grossman 1972). We found that people with higher levels of
education, assets, and income tended to receive more benefits from retirement.
According to this model, retirees have more time, but a lower budget, to invest in

9

Kraft (2020) reviewed 747 randomized control trials for cognitive interventions and proposed that the effect size of over
0.2 standard deviation can be interpreted as large.

29

their health. However, people with a high socioeconomic status can afford healthinvestments to improve their cognitive function. The tendency for people with
better health before retirement to have higher cognitive function after retirement
was also consistent with the model, because healthy people have more time to spend
on health investments than sick people. The association between health limitations
before retirement and cognitive function after retirement is consistent with thefindings of an empirical study (Denier et al. 2017).
Regarding the characteristics of the pre-retirement job in relation to cognitive
decline, people who retired from a professional occupation tended to have a higher
CLATO, whereas those who retired from manual labor and physically demanding
jobs tended to have a lower CLATO. This finding was consistent with many studies
showing an association between retirement from highly complex and mentally
demanding jobs and a slower rate of cognitive decline (Fisher et al. 2014; Andel etal. 2015; Kajitani, Sakata, and Mckenzie 2017; Romero Starke et al. 2019; Carr etal. 2020; Vélez-Coto et al. 2021). These findings suggest that a mentally demanding
job has a protective effect on cognitive function, which gets carried over into
retirement.
This study had several limitations. First, we only investigated the short-term
effects of retirement, given that cognitive function was measured two years after
retirement. Further studies are required to examine the long-term effects. Second,
our analysis of heterogeneity based on specific covariates was exploratory. For
example, we found that people with higher education and a professional job tended
to have higher CLATO, but these characteristics could be confounded (i.e., people
with higher education were likely to have a professional job). Therefore,
confirmatory studies are necessary to determine the causal heterogeneity of specificcovariates. Third, we could not capture the heterogeneity stemming fromunmeasured covariates, although we included 60 candidate variables. Other factors,
such as traumatic brain injury, social isolation, and air pollution, may modify the30effect of retirement on cognitive function (Livingston et al. 2020). Fourth, themeasured variables may have been subject to measurement errors because they
were collected through self-reported interviews. However, it has been shown thatthe word recall test can predict the onset of dementia (Tierney, Moineddin, andMcDowell 2010). Additionally, asking for self-recognition of labor force status ismeaningful because it can influence individuals’ behavior (Eibich 2015). Fifth, thegeneralizability of our findings may be limited to Western countries. Given that
Asian countries face more rapid population aging than Western countries and arealso increasing their SPA, analyses using harmonized data such as the China Healthand Retirement Longitudinal Study and the Korean Longitudinal Study of Aging
will provide essential and comparable evidence for these countries. Sixth, althoughdata harmonization was performed by field experts (Angrisani and Lee 2012a;
2012b; Hu and Lee 2012; Shih, Lee, and Das 2012; Zamarro and Lee 2012),
discrepancies across surveys may remain. However, our pooling analysis provided
important insights into the heterogeneity across countries.
In summary, we found that the impact of retirement on cognitive function varied
depending on the individual’s characteristics. Therefore, we recommend thatpolicymakers provide options for early retirement in the pension system to allow
individuals to decide when to retire. Given that retirement improves cognitive
function, the balance between the social benefits of increasing the state pension age
and the individual cost of increasing dementia risk due to delayed retirement should
be considered.
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Appendixes
A. Sample Flowchart
HRS 2014(n = 18,747)

ELSA 2014(n = 9,666)
Not followed in 2016(n = 2,839)
Not followed in 2018
(n = 3,176)

SHARE 2015
(n = 66,411)
Not followed in 2016(n = 1,578)
Not followed in 2018
(n = 1,188)

Not followed in 2017(n = 15,086)
Not followed in 2019(n = 21,402)

Individuals participated in all the three waves(n = 49,555)
Over 80 years old(n = 6,503)
Not worked in the 1st wave(n = 29,519)
Neither worked nor retired in the 2nd wave(n = 722)
Participants involved to develop trees(n = 12,811)
Propensity score out of 0.1–0.9(n = 5,379)
Analytic overlapped population(n = 7,432)
FIGURE A. SAMPLE FLOWCHART
Notes: HRS stands for the Health and Retirement Study, ELSA stands for the English Longitudinal Study on Ageing, andSHARE stands for the Survey of Health, Ageing and Retirement in Europe.

B. Measurement of Labor Force Status
The Health and Retirement Study (HRS).—Participants in HRS provided
information on their labor force status at several time points in an interview. First,
HRS asks the participants to select all applicable options from a list that includes
1) working now, 2) unemployed and looking for work, 3) temporarily laid off, on

38

sick or other leave, 4) disabled, 5) retired, 6) homemaker, or 7) other (specify). It
also asks them whether they are currently working for payment, the usual numberof hours per week if applicable, and whether they consider themselves partly retired,completely retired, or not retired.
If the participant reports working full-time (i.e. working 35+ hours per week or
36+ weeks per year), the harmonized variable is set to “working full-time”. If theparticipant is working part-time and does not mention retirement, it is set to“working part-time”. If the participant is working part-time and mentions
retirement, it is set to “partly retired”. If the participant is not working but is looking
for a job, it is set to “unemployed”. If the participant is not looking for a job andthere is any mention of retirement, it is set to “retired”. If retirement is not
mentioned and disabled employment status is given, it is set to “disabled”.
Otherwise, the variable is set to “not in the labor force”.
The English Longitudinal Study on Ageing (ELSA).—ELSA asks participants,“Which of these, would you say, best describes your situation?” They then choose
the best description of their current labor force status from a list of options: 1)
employed, 2) self-employed, 3) unemployed, 4) partly retired, 5) retired, 6)
permanently sick or disabled, or 7) looking after home or family. The harmonizedvariable was constructed based on responses to this direct question.
The Survey of Health, Ageing and Retirement in Europe (SHARE).—SHARE asks
participants, “In general, how would you describe your current situation?” They
then choose the best description of their current labor force status from a list of
options: 1) retired, 2) employed or self-employed (including working for a familybusiness), 3) unemployed and looking for work, 4) permanently sick or disabled,5) homemaker, or 6) other (renter, living off own property, student, or doing39

voluntary work). The harmonized variable was constructed based on responses tothis direct question.
TABLE A—SUMMARY OF THE HARMONIZED VARIABLE OF LABOR FORCE STATUS
This study
Included as workers

HRS
1. working full-time

ELSA
1. employed

2. working part-time

2. self-employed

4. partly retired

4. partly retired

5. retired

5. retired

3. unemployed

3. unemployed

3. unemployed

6. disabled

6. disabled

7. not in the labor force

7. looking after home orfamily6. permanently sick or
disabled
8. homemaker

Included as retirees

Excluded from analyses

SHARE
1. employed or selfemployed

5. retired

Notes: HRS stands for the Health and Retirement Study, ELSA stands for the English Longitudinal Study on Ageing, andSHARE stands for the Survey of Health, Ageing and Retirement in Europe. Retirement status was determined based on thevariable of labor force status (RwLBRF) in the harmonized datasets.

C. Early and Official Retirement Age
TABLE B—EARLY AND OFFICIAL RETIREMENT AGE
Men

Women

Country

Year

ERA

ORA

ERA

ORA

Austria

2017

NA

65

NA

60

Belgium

2017

62.5

65

62.5

65

Croatia

2017

60

65

56.75

61.75

Czech Republica

2017

60

63.17

59.33

62.33

Denmark

2017

NA

65

NA

65

England

2016

NA

65

NA

63

Estonia

2017

60

63

60

63

France

2017

62

67

62

67

Germany

2017

63

65.5

63

65.5

Greece

2017

62

67

62

67

Israel

2017

NA

67

NA

62

Italy

2017

62

66.58

62

66.58

40

Luxembourg

2017

57

65

57

65

Poland

2017

NA

65

NA

60

Slovenia

2017

59.67

65

59.33

63.5

Spain

2017

61.42

65.42

61.42

65.42

Sweden

2017

61

65

61

65

Switzerland

2017

63

65

62

64

United States

2016

62

66

62

66

Notes: ERA and ORA stand for early and official retirement age, respectively. NA denotes not applicable.
Source: The United States Social Security Administration "Social Security Programs Throughout the World";
OECD "Pensions at a Glance"; websites of the authorities of each country.
ORA for women is determined according to the number of raised children. ORA of 62 years and 4 months is for
women without children in 2017.

aD. Occupational Codes
TABLE C—OCCUPATIONAL CODESThis study

HRS

ELSA

SHARE
1988 International Standard
Classification of Occupations
0. Armed forces

2. Business and financial
specialists

Standard Occupational
Classification (2000)
1. Managers and senior
officials
2. Managers and proprietors inagriculture and services

3. Computer and mathematicaloccupations

3. Science and technology
professionals

2. Professional

4. Architecture and engineering
occupations

4. Health professionals

3. Technician or associate
professional

5. Life, physical, and social
science occupations

5. Teaching and researchprofessionals

6. Community and social
services occupations

6. Business and public service
professionals

7. Legal occupations

7. Science and technology
associate professionals

8. Education, training, andlibrary occupations

8. Health and social welfare
associate professionals

9. Arts, design, entertainment,
sports, and media occupations

10. Culture, media, and sports
occupations

10. Healthcare practitioners andtechnical occupations

11. Business and public service
associate professionals

The 2010 Census
Professional

Clerk

1. Management occupations

11. Healthcare support
occupations
23. Military-specificoccupations
17. Office and administrative
support occupations

12. Administrative occupations

41

1. Legislator, senior official,or manager

4. Clerk

Service & sales

Manual labor

12. Protective service
occupations

13. Secretarial and related
occupations
9. Protective service
occupations

13. Food preparation andserving occupations

18. Caring personal service
occupations

14. Building and grounds
cleaning and maintenanceoccupations
15. Personal care and service
occupations

19. Leisure and other personal
service occupations

16. Sales occupations

21. Customer service
occupations
25. Elementary administrationand service occupations

18. Farming, fishing, andforestry occupations

14. Skilled agricultural trades

6. Skilled agricultural or
fishery worker

19. Construction and extraction
occupations

15. Skilled metal and electrical
trades7. Craft and related trades
worker

20. Installation, maintenance,and repair workers

16. Skilled construction andbuilding trades

8. Plant and machine operator
or assembler

21. Production occupations

17. Textiles, printing, and otherskilled trades

9. Elementary occupation

22. Transportation and material
moving occupations

22. Process, plant, and machine
operatives

5. Service worker and shopand market sales worker

20. Sales occupations

23. Transport and mobile
machine drivers and operatives
24. Elementary trades, plant,
and storage-related occupations
Notes: HRS stands for the Health and Retirement Study, ELSA stands for the English Longitudinal Study on Ageing, andSHARE stands for the Survey of Health, Ageing and Retirement in Europe.

E. Number of Imputed Values
TABLE D—NUMBER OF IMPUTED VALUES
Variable
Cognitive function
Retirement
Age
Men
Foreign-born
Education
MarriedLiving alone
No children≥3 children
Asset
IncomeImputed values
793
0
0
0
8
210
5
0
24
24
66
955

42

Professional
Clerk
Service & sales
Manual labor
Physical demand
Part-time job
Self-employed
Baseline cognition
Self-rated health
Depression
Life satisfaction
Hypertension
Diabetes
CancerLung disease
Heart disease
StrokeArthritis
Psychiatric problems
Hyperlipemia
Health limitations in working
Difficulty in ADL
Difficulty in IADL
Distance eyesight
Near eyesight
Hearing
Pain problems
Obesity
Physical activity
Heavy drinking
Smoking

1490
1490
1490
1490
1715
223
13
268
93
170
470
2
2
2
2
2
2
2
2
8
136
2
2
95
99
8
102
844
14
331
470

Notes: ADL and IADL stand for activities of daily living and instrumental activities of daily living, respectively.

43

F. Distribution of Cognitive Function

FIGURE B. DISTRIBUTION OF COGNITIVE FUNCTION

44

G. Partial Dependence Plot for Continuous Variables

FIGURE C. PARTIAL DEPENDENCE PLOT FOR CONTINUOUS VARIABLES
Notes: CLATO stands for the conditional local average treatment effect on the overlap population.

45

H. Details in Monetary Cost Estimation
TABLE E—MONETARY COST ESTIMATION IN THE UNITED STATESRanking

Q1

Q2

Q3

Q4

Q5

Note

(1) EstimatedCLATO-0.579

0.767

1.163

1.379

1.662

From our estimates(2) % ofparticipants

20.04%

19.87%

19.96%

19.91%

20.22%

From our estimates

0.763

exp(ln(0.85) * (1)). Tierney et al.
(2010) showed that a one-word
increase in the RAVLT shortdelayed verbal recall was
associated with 0.85 (95% CI:
0.78-0.92) times lower odds ofdementia in five years.

(3) Odds ratio
for dementia
risk

1.099

0.883

0.828

0.799

U.S. Census Bureau, the 2020
Census Demographic andHousing Characteristics File
(DHC)

(4) Population
aged 55-59 in
2020

22,359,065(5) % ofworkers at age
65

29.18%RAND HRS in 2018(6) Estimated# of workers attheir age of 65

6,524,375(4) * (5)709,708(6) / 9.2. Reaching the ORA
increases the probability ofretirement by 10.9% points indata from HRS. One out of 9.2 (=1/0.109) workers would retire if
they reached the ORA.

(7) Expected
increase in #of workers atage 66(8) Expected #of newly
developed
dementia-14,036

16,525(9) Monetary
cost ofdementia per
patient(10) Estimatedadditional cost(11) Total
monetary cost

24,392

28,37333,968Hurd et al. (2013) estimated themonetary cost of dementia was$56,290 (95% CI: $42,746$69,834) per person.

$56,290
$790M

$930M

$1,373M(1 - (3)) * (2) * (7)$1,597M$1,912M(8) * (9)Hurd et al. (2013) estimated a
total cost of $361B in 2030.

$5.0B (1.4%)

Notes: RAVLT stands for Rey Auditory Verbal Learning Test, CI denotes confidence interval, HRS stands for
the Health and Retirement Study, and ORA stands for official retirement age.

46

TABLE F—MONETARY COST ESTIMATION IN THE UNITED KINGDOM
Ranking

Q1

Q2

Q3

Q4

Q5

Note

(1) EstimatedCLATO-0.579

0.767

1.163

1.379

1.662

From our estimates(2) % ofparticipants

20.48%

20.55%

20.12%

19.83%

19.03%

From our estimates

0.763

exp(ln(0.85) * (1)). Tierney et al.
(2010) showed that a one-word
increase in the RAVLT shortdelayed verbal recall was
associated with 0.85 (95% CI:
0.78-0.92) times lower odds ofdementia in five years.

(3) Odds ratio
for dementia
risk

1.099

0.883

0.828

0.799

(4) Population
aged 55-59 in
2021

4,573,856

Office for National Statistics,
Mid-Year Population Estimates
June 2021(5) % ofworkers at age
65

27.73%ELSA in 2018(6) Estimated #of workers attheir age of 65

1,268,330(4) * (5)552,727(6) / 2.3. Reaching the ORA
increases the probability ofretirement by 43.6% points in datafrom ELSA. One out of 2.3 (=1/0.436) workers would retire if
they reached the ORA.

(7) Expected
increase in # ofworkers at age
66(8) Expected #of newly
developed
dementia-11,169

13,313(9) Monetary
cost ofdementia per
patient(10) Estimatedadditional cost(11) Total
monetary cost

19,14922,001

24,893£59,200M / 1,233,400. Wittenberg
et al. (2019) estimated the numberof people with dementia and its
total cost in 2030.

£47,997

£536M

£639M

£919M

(1 - (3)) * (2) * (7)£1,056M£1,195M(8) * (9)Wittenberg et al. (2019) estimateda total cost of £59.2B in 2030.

£3.3B (5.2%)

Notes: RAVLT stands for Rey Auditory Verbal Learning Test, CI denotes confidence interval, ELSA stands for
the English Longitudinal Study on Ageing, and ORA stands for official retirement age.

47