Panel Data Research Center at Keio University
DISCUSSION PAPER SERIES
DP2016-008
March, 2017

Use it Too Much and Lose it? The Effect of Working Hours on Cognitive Ability
Shinya Kajitani＊
Colin McKenzie＊＊
Kei Sakata＊＊＊【Abstract】
Using data from Wave 12 of the Household Income and Labour Dynamics in Australia(HILDA) Survey, we examine the causal impact of working hours on the cognitive abilityof people living in Australia aged 40 years and older. Three measures of cognitive ability
are employed: the Backward Digit Span; the Symbol Digits Modalities; and a 25-item
version of the National Adult Reading Test. In order to capture the potential non-linear
dependence of cognitive ability on working hours, the models for cognitive ability include
working hours and its square. We deal with the potential endogeneity of the decision of
how many hours to work by using the instrumental variable estimation technique. Ourfindings show that there is a non-linearity in the causal effect of working hours on
cognitive functioning. For working hours up to around 22–26 hours a week for men andfor 22–30 hours a week for women, an increase in working hours has a positive impact
on cognitive functioning. However, when working hours exceed these hours per week, anincrease in working hours has a negative impact on cognition. Working in excess of 44–
52 hours for men and 44–60 hours for women leads to cognitive scores that are worse
than a person does not work at all. Interestingly, there is no statistical difference in thecausal effects of working hours on cognitive functioning between men and women.
＊

Associate Professor, Meisei University＊＊

Professor, Faculty of Economics, Keio University＊＊＊

Professor, Ritsumeikan University

Panel Data Research Center at Keio University
Keio University

Use it Too Much and Lose it?
The Effect of Working Hours on Cognitive Ability
Shinya Kajitania
Faculty of Economics, Meisei University
Colin McKenzieb
Faculty of Economics, Keio University
Kei Sakatac
Faculty of Economics, Ritsumeikan University

We would like to thank Yoko Ibuka, Daiji Kawaguchi, and Jongsay Yong for their helpfulcomments and suggestions, and Michele Summerfield for providing information about
HILDA’s interviewing procedures. Earlier versions of this paper have been presented at aworkshop at Meisei University, the Tokyo Labor Economics Workshop (Sophia University),the 2016 Spring Meeting of the Japan Economic Association (Nagoya University), the 21stInternational Congress on Modelling and Simulation (Gold Coast), the 30th Annual
Conference of the European Society for Population Economics (Berlin), the Ageing andLongevity in the UK and Japan: Perspectives from the Health and Social Sciences Workshop(Kings College London), the Globalization and the Building of a High Quality Economic
System Conference (Keio University), and the 10th International Conference of the Thailand
Econometric Society 2017 (Chiang Mai University). We also would like to thank theparticipants of these conferences and seminars for their useful suggestions. The first author
gratefully acknowledges the research support provided by the Melbourne Institute ofApplied Economic and Social Research, The University of Melbourne while he was onsabbatical. This paper uses unit record data from the Household, Income and Labour
Dynamics in Australia (HILDA) Survey. The HILDA Project was initiated and is funded by
the Australian Government Department of Social Service (DSS) and is managed by the
Melbourne Institute of Applied Economic and Social Research (Melbourne Institute). The

Shinya Kajitani, Faculty of Economics, Meisei University, 2-1-1, Hodokubo, Hino-shi,
Tokyo 191-8506, JAPAN. Email: kajitani@econ.meisei-u.ac.jp
b Corresponding author: Colin McKenzie, Faculty of Economics, Keio University, 2-15-45
Mita, Minato-ku, Tokyo 108-8345, Japan. Email: mckenzie@z8.keio.jp
c Kei Sakata, Faculty of Economics, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu,
Shiga 525-8577, JAPAN. Email: ksakata@ec.ritsumei.ac.jpafindings and views reported in this paper, however, are those of the authors and should not
be attributed to either DSS or the Melbourne Institute.

Declarations
The authors declare they do not have any actual or potential conflict of interest in relation tothis research. No ethic approval was required for this study.

Funding
This research was supported by: (i) JSPS KAKENHI Grant Number JP24330093 for a
project on “Retirement Behaviour of the Aged and their Cognitive Ability and Health” (P.I.:
Kei Sakata) (Kajitani and Sakata); (ii) a grant from the Meisei University Special Research
Leave Program Fund for a project on “The Impact of the Working Hours on Health andCognitive Functioning for Middle-aged and Older Australians” (Kajitani); (iii) a grant fromthe Fund to Promote Academic Research for a project on “Empirical Research on Responses
to the Aging Problems of Japan’s Economy” (McKenzie), and (iv) a grant from the Japanese
Ministry of Education, Culture, Sports, Science and Technology supported Program for theStrategic Research Foundation at Private Universities for a project on “Globalization and the
Building of a High Quality Economic System” (McKenzie).

2

Abstract
Using data from Wave 12 of the Household Income and Labour Dynamics in Australia(HILDA) Survey, we examine the causal impact of working hours on the cognitive abilityof people living in Australia aged 40 years and older. Three measures of cognitive ability
are employed: the Backward Digit Span; the Symbol Digits Modalities; and a 25-item
version of the National Adult Reading Test. In order to capture the potential non-linear
dependence of cognitive ability on working hours, the models for cognitive ability include
working hours and its square. We deal with the potential endogeneity of the decision of how
many hours to work by using the instrumental variable estimation technique. Our findings
show that there is a non-linearity in the causal effect of working hours on cognitive
functioning. For working hours up to around 22–26 hours a week for men and for 22–30
hours a week for women, an increase in working hours has a positive impact on cognitive
functioning. However, when working hours exceed these hours per week, an increase inworking hours has a negative impact on cognition. Working in excess of 44–52 hours formen and 44–60 hours for women leads to cognitive scores that are worse than a person does
not work at all. Interestingly, there is no statistical difference in the causal effects of working
hours on cognitive functioning between men and women.

Keywords: cognitive ability, endogeneity, gender differences, retirement, working hours
JEL Classification Numbers: I10, J22, J26
Highlights


A non-linear relationship between working hours and cognitive ability is observed.



Cognitive ability peaks somewhere between 22–30 hours of work for both men andwomen.



Working more than 44–60 hours can be worse than not working at all.



Significant gender differences are not observed.

3

1. Introduction
Many countries have already increased their retirement ages by delaying the age at
which people are eligible to start receiving government pension payments. This means that
more people continue to work in the later stages of their life. Some claim that delaying theretirement age can potentially help reduce the deterioration of cognitive functioning becauseof the continued intellectual stimulation that work provides (Potter et al., 2008; Small, 2002).
The relationship between retirement and cognitive functioning has attracted much attention
in recent years, but recent studies have not reached consensus on whether the so called ‘use
it or lose it’ hypothesis is valid. The ‘use it or lose it’ hypothesis argues that not working(not using the brain) leads to a loss of cognitive functioning. After controlling for theendogeneity of retirement, Mazzonna and Peracchi (2012, 2017) and Rohwedder and Willis(2010) find that there was a significant and negative effect of retirement on cognitive skills,
while Coe and Zamarro (2011) do not find such a causal effect. Bonsang et al. (2012) findthat the effects of retirement on cognitive function appeared with a lag, and conclude that
there were positive externalities of a delayed retirement for older individuals.
Although these previous studies provide important insights into the relationshipbetween retirement and cognitive functioning, they do not examine the impact of the quality
or quantity of work on cognitive functioning. Work can be a double-edged sword, in that it
can stimulate brain activity, but at the same time, long working hours and certain types oftasks can cause fatigue and stress which potentially damage cognitive functions. Thus, thedegree of intellectual stimulation of work may depend on the required tasks and working
hours, that is, the quality and quantity of work. There are number of studies which examine
the effects of the quality of work (job type and job tasks) on cognitive functioning (Schooler
et al., 1999; Bosma et al., 2003; Potter et al., 2008; Finkel et al., 2009; Marquié et al., 2010;
Smart et al., 2014; Kajitani et al., 2016).
However, there seem to be very few studies discussing the impact of the quantity ofwork (working hours) on cognitive functioning. Working individuals with longer hours ofwork have more incentive to invest in cognitive repair activities in order to maintain their
cognition while working longer. In contrast, longer hours of work per se could reduce their
cognitive performance. Using the Whitehall II Study sample of British civil servants,
Virtanen et al. (2009) examine the relationship between long working hours and cognitive
skills in middle age. They find that vocabulary test scores which measure crystallized
intelligence are relatively lower among workers with long working hours, and point out thatlong working hours may have a negative effect on cognition in middle age. However, their4

sample is limited to working civil servants. Moreover, Virtanen et al. (2009) do not compare
the level of cognitive skills of workers and non-workers. Middle aged and elderly persons
tend to retire or decrease their working hours by being employed as a non-regular worker,
so it is important to examine the impact of working hours on cognitive functioning among
middle-aged and older adults.
What are the channels through which labor hours might affect cognitive functioning?
One of the channels is physical and/or psychological stress. Medical research suggests thatstress affects cognitive functioning. McEwen and Sapolsky (1995) indicate that stress affects
cognition rapidly via catecholamines, and more slowly via glucocorticoids. Martin et al.
(2011) find that chronic stress has effects on cognition, and increases the vulnerability tomental illness. Proctor et al. (1996) indicate that long working hours have adverse effects on
the mental health of workers in the automobile industry. In an analysis across 15 European
countries, Cottini and Lucifora (2013) also find that long working hours increase stress. Thus,
although engaging in work by stimulating the brain may help reduce the pace of cognitive
impairment, such positive effects may be offset by the negative impacts caused by mental
and physical stress associated with long labor hours. An alternative possibility is that as anindividual’s wage rate becomes higher, he/she has a stronger incentive to engage in activities
that restore damage to his/her brain, and this incentive may be stronger as he/she works more
hours.
We examine the causal impact of working hours on cognitive functioning for middleaged and older adults living in Australia using a cross section sample from Wave 12 of theHousehold, Income and Labour Dynamics in Australia (HILDA) Survey. In contrast to the‘use it or lose it’ hypothesis, we examine what we term the ‘use it too much and lose it’hypothesis, namely, that in terms of cognitive ability working too much can be worse than
not working at all. In examining this hypothesis, it is important to deal with the potential
endogeneity of decisions on working hours by using an instrumental variable estimation
technique. One potential problem in using working hours as the explanatory variable ofinterest is that the working hours are left censored, that is, for individuals who are retired or
who are not in education, employment or training (NEET), working hours are treated as zero.
In order to take account of these zero values in the reported working hours, we apply a Tobit
model and then use the nonlinear fitted values from the Tobit model as the new instrument
for working hours when the model for cognitive functioning is estimated by an instrumental
variable estimator.

5

Our empirical evidence shows that there is non-linearity in the effects of working hours
on cognitive functioning. More precisely, there is an inverted U-shaped relationship. When
working hours are less than around 22 hours a week, working hours have a positive impact
on cognitive functioning. However, when working hours are more than 26 hours per week
for men and 30 hours per week for women, working hours have negative impacts on
cognition. These results suggest that compared to not work at old people in old age could
maintain or improve their cognitive ability by working in a part-time job that requires them
to work around 22 hours per week.
We estimate our models on samples of males and females separately as Matud (2004)
suggests that there are differences in the extent to which males and females suffer stress andcope with stress. Since stress is suggested in the medical literature as one of the reasons forlabor hours affecting cognitive functioning, Matud’s evidence suggests a possible differencein the connection between working hours and cognitive functioning for men and women.
However, we find that there is no statistically significant gender difference in the effects ofworking hours on cognitive functioning.
The rest of this paper is organized as follows: Section 2 presents the empiricalframework used in this paper. Section 3 describes the data, and Section 4 reports the resultsof estimation and discusses their implications. The last section concludes this paper.

2. Estimation model and identification strategy
Our identification strategy exploits the variation in working hours, while controlling forindividual characteristics. In order to capture a possible non-linearity in the effects ofworking hours on cognitive functioning, we consider the following model1:

,

where

denotes a cognitive test score,

is working hours.

(1)is the square of working hours, anddenotes a vector of control variables which consists of a constant, the1

An alternative to the parametric model in equation (1) to account for the non-linear effectof working hours on cognitive functioning would be to estimate a semi-parametric or nonparametric model. However, such an approach makes it rather difficult to deal with thepotential endogeneity between working hours and cognitive functions. Here, we put priority
on dealing with the potential endogeneity of working hours.
6respondent’s age, age squared, dummy variables which indicate his/her years of education,
dummy variables which indicate the type of his/her educational qualification, and his/her
previous work experience. We also include a dummy variable which takes the value unity if
the respondent has a spouse and zero otherwise. This variable is included because
communications and interactions with other family members may prevent declines incognitive functioning. Moreover, in order to control the effects of space between the day ofinterview and the previous weekend, we include dummy variables which indicate what dayof the week the respondent was interviewed. To take account of regional variations, we also
include four 0–1 regional dummies. The unknown parameters to be estimated are
,

and .

coefficientis an error term, and the subscript

refers to the th individual. The

captures the non-linear effect of working hours on cognitive functioning.

Given the discussion in section 1 that some work is better than no work, and that too muchwork may be worse than some work, it is expected that0 and

0. Holding

everything else constant, it is easy to see that the cognitive test score is maximized when
/ 2/

, and that forthe cognitive test score is the same as it

would be if individual was not working.
The possibility of the endogeneity of the respondents’ working hours in equation (1) isa major obstacle to estimating the causal impact of working hours on cognitive functioning.
Individuals whose cognitive abilities are lower (or higher) may decide to leave the workforce
earlier (or later). On the other hand, the reverse causality between cognitive skills andworking hours can be more ambiguous. Previous studies observe that a high wage rate is
associated with cognitive skills (for example, Wooden, 2013; Capatina, 2014). In aneoclassical model of consumer behavior where there is a trade-off between consumption
and leisure, and leisure is a normal good, the impact of the wage rate (and thus cognitive
skills) on working hours depends on whether the substitution effect dominates the income
effect or vice versa. Individuals whose cognitive abilities are higher, who tend to earn a
relatively higher wage, could decide to reduce their hours of work even further.
For equation (1), the standard two stage least squares (2SLS) procedure is to findvariables which are correlated with an individual’s labor supply, but unrelated to their
cognitive skills. However, we have another issue in examining the effects of labor hours on
cognitive functioning, that is, labor hours are censored (for example, retirees reporting zeroworking hours). Rather than directly using variables which correlate with hours worked, but
do not correlate with cognitive functioning, we use these variables for creating the fitted

7

values for squared of working hours and working hours that are then used as instruments.
The following model is assumed to explain observed working hours:
∗

,
0

if
∗

where

∗

∗

2

0,

if 0

3
∗

,

denotes an unobserved latent variable which is connected to the observed

working hours

through equation (3).

is a 0–1 dummy

variable which takes the value one if the respondent is interviewed in July or August, andzero otherwise. This variable is intended to capture seasonal variation in labour supply which
may be due to school holidays occurring in July.

is the difference

between the respondent’s age at the time of the survey,
respondent is eligible for a pension,,

the age at which the. In the existing literature, the age at

which an individual is eligible for a pension is one of the standard instruments used toanalyze the causal relationship between retirement and cognitive functioning (Bonsang et al.
2012, Coe and Zamarro 2011, Mazzonna and Peracchi 2012 & 2017, Rohwedder and Willis,2010). Here, we use a measure of the respondent’s ‘distance’ from their retirement. These
instruments,

,

, and

, are designed to capture the factors which impact on the labor supply ofa respondent, but not on his/her cognitive abilities.
variables as is used in equation (1), andis exactly the same vector of control

is a disturbance which is assumed to be normally,

independently and identically distributed with a zero mean and variance. For a retiree oran unemployed person, we observe his/her working hours per week as zero.
Table I summarizes the ages at which males and females are eligible for pensions at thetime of Wave 12 of the HILDA survey. As can be seen from this Table, there is much morevariation in the pension eligibility ages for women than there is for men. Table I also
indicates the distribution of our sample across the ages for pension eligibility. Although theeligibility age for men born before or on 30 June, 1952 is 65, the proportion of our sample
in this category is just 40.8%. In contrast, the proportion of men whose pension eligibility
age is 67 is 46.2% of our sample.
[Table I around here]

8Given the left censoring of working hours, we estimate equations (2) and (3) using a
1, 2, 3 and ,Tobit estimator to obtain estimates ofand , respectively. Fromequations (2) and (3), and the assumptions about the distribution of
expectation of

can be computed as
|

where

, the conditional

Φ

,

4

and are the vectors of regressors and parameters in equation (2), respectively,and Φ ∙ and∙ are the cumulative distribution and probability distribution functions of

the standard normal distribution, respectively (see Greene 2008, p. 871). Given the estimatesof the parameters of equation (2), the estimates of the conditional expectation in equation(4) are denoted by. Then,andare used as instruments forand,respectively, in equation (1) in a 2SLS procedure (see Wooldridge 2010, p. 268).

3. Data: Overview of the HILDA Survey
Our data are drawn from Wave 12 of the HILDA Survey which is conducted by the
Melbourne Institute of Applied Economics and Social Research, and is a broad social andeconomic longitudinal survey. Since 2001 when Wave 1 was collected, the HILDA Survey
has asked people living in Australia about their economic and subjective well-being, family
structures, and labor market dynamics. Households included in this survey were selectedusing a three-stage approach.2 First, a sample of 488 Census Collection Districts (CDs) wererandomly selected from across Australia. Second, within each of these CDs, a sample ofdwellings was selected based on expected response rates and occupancy rates. Finally,
within each dwelling, up to three households were selected to be part of the sample. In
addition, the sample was replenished in between July 2011 and mid-February 2012 in Wave
11.
Although most questions in the HILDA Survey are repeated every year, there arequestions on several topics that are not repeated every year or are only asked once.
Information on the respondent’s cognitive ability has only been collected in Wave 12 of the
HILDA Survey3. Wave 12 which was collected in between July 2012 and mid-February
Detailed information on the sample design of the HILDA Survey is available in Wooden etal. (2002) and Watson and Wooden (2013).
3
Wooden (2013) discusses in detail the measurement of cognitive ability in Wave 12 of the
HILDA Survey.
2

9

2013 contains three measures of cognitive ability: the Backward Digit Span (BDS); theSymbol Digits Modalities (SDM); and a 25-item version of the National Adult Reading Test
(NART25). We use BDS, SDM, and NART25 scores as measures of a respondent’s
cognitive ability. BDS is a test of working memory span and is used in many traditional
intelligence tests. After reading out longer strings of numbers, the respondent is required torepeat those strings in reverse order. The shortest and longest sequence administered are twoand eight digits, respectively. In the BDS test, questions are divided into seven levels, andthere are two trials at each level. When the respondent’s response for the first trial for a given
level is correct, he/she is allocated a score of two for that level, and then moves on to thenext level. When his/her response on the first trial is incorrect, he/she moves on the second
trial. If the respondent’s answer on the second trial is correct, he/she is allocated a score of
one for that level, and then moves onto the next level. If his/her answer on the second trial
is also incorrect, he/she is allocated a score of zero for that level, and this test is discontinued;that is, he/she is allocated a score of zero for all the subsequent questions. Finally, the BDS
score is the sum of the scores at each level, so the maximum possible score for the respondentis 14, and the minimum possible score is zero. BDSscore denotes the respondent’s BDS testscore. SDM is a general test for divided attention, visual scanning, and motor speed. The
respondent is required to match symbols to numbers using a printed key.4 SDMscore is the
respondent’s score on the SDM test, and is defined as the number of items correctly matchedwithin a 90 second time interval. NART25 is a reading test, and provides a measure of mainly
crystallized intelligence. In the NART25 test, the respondent is required to correctly read 25
irregularly spelled words which are listed roughly in order of difficulty. NART25score is
his/her score on the NART25 test, and is also defined as the number of words correctly
pronounced. Definitions of these variables and the other variables used in the analysis that
follows are provided in Appendix I.
Table 1 in Melbourne Institute (2014, p. 9) provides details of the distribution ofinterviews across months of the year for Waves 1–12, and indicates that for the recurrent
sample in Wave 12 interviews were conducted over the period July 2012 to February 2013
with the vast majority of interviews being conducted in either August 2012 (42.5%) or
September (38.1%). Interviewers do not randomly choose an interview month for a
respondent. The fieldwork for each wave is split into 3 periods - starting end of July–early
October (Period 1), end October–early December (Period 2) and early January–earlyFebruary (Period 3) and the interviewers are issued households to approach in each of these4

Strauss et al. (2006) provide details of the SDM test.
10

periods. If a respondent is too busy or away overseas, or temporarily incapable, theinterviewer returned at a time that is more appropriate for the respondent. In the second andsubsequent waves, although respondents were free to choose when they were interviewed
however most respondents were interviewed within 1 month anniversary of their interview
in the previous wave5.
The sample used in this paper is restricted to individuals who meet all of the following
five criterion for Wave 12 of the HILDA data set: (i) males and females aged 40 and over;(ii) all three scores relating to cognitive ability are available; (iii) English is their first
language; (iv) their reported working hours are not deemed to be outliers, namely, thosevalues that are not in the top 1 percentile6; and (v) information on all the relevant variables
is available. For individuals meeting these five criterion, Table II shows descriptive statistics
for all the variables used in the analysis. In our sample, the maximum values of BDSscore,
SDMscore, and NART25score for males (females) are 14 (14), 95 (104) and 24 (24),respectively. Working hours is defined as being the respondent’s usual or average hours ofwork per week, and it can be seen from Table II that the mean values of Working hours formales and females are 27.2 and 16.9 hours, respectively.
[Table II around here]

Table III provides information on the current employment status of respondents bygender and age group. For all age groups, a higher percentage of males are working full-timethan females, and for both males and females as age rises the proportion of full-time workers
falls.
[Table III around here]

4. Estimation results
All regression results reported in this section are estimated using STATA version 14(StataCorp 2015). Table IV presents estimates of the coefficients of the three variables thatare included in equation (2) but not equation (1), that is, the variables that are used to5

Summerfield et al. (2016) contains further information on the HILDA's data collection
process.
6
We have investigated the robustness of our results by dropping observations where thereported working hours are in the top 5% percentile, and found that are results are largely
unchanged.
11

generate exclusion restrictions. The results in Table IV indicate that the three instruments
are all individually statistically significant, and that the null hypothesis that the exclusion
restriction variables are jointly irrelevant in explaining working hours is rejected for bothmales (F-statistics is 14.95) and females (F-statistic is 7.28). The value of the Cragg-Donald(1993) Wald F-statistic for males (16.5) and females (13.8) which are shown in Table V,suggest that there is not a problem of “weak” instruments.
[Table IV around here]

Table V reports the results of estimating equation (1) taking account of the endogeneityof working hours. As shown in columns (1A)–(1C), after controlling for the respondent’s
human capital and demographic variables, the estimated coefficients of Working hourssquared are significantly negative, and the estimated coefficients of Working hours are alsosignificantly positive for males. As can be seen from the results in columns (2A)–(2C), thesame is true for females except for the SDM score.
[Table V around here]

These results indicate that, for both males and females, there is an inverse U relationshipbetween cognitive ability and working hours. As the number of working hours increases
from zero, the magnitude of the positive impact of working hours on their cognitive ability
is decreasing until working hours reaches a threshold. Above that threshold, further increases
in working hours have a negative impact on their cognitive functioning. As Wooden et al.
(2012) point out, BDM and SDM are measures of fluid intelligence, while NART25 is ameasure of crystallized intelligence. It has been argued that crystallized intelligence tends tobe maintained through occupational or cultural experiences, so that assuming hours of work
are associated with the degree of occupational experiences, working hours per se could
potentially be regarded as cognitive repair activities Similarly, although fluid intelligence issubject to a decline as people get older, fluid intelligence could be also maintained byworking hours closer to the threshold.
If we compare the estimated coefficients for men and women associated with working
hours and the square of working hours reported in Table V, there is no statistical difference
between these coefficients for any of the cognitive scores. The t-values for these tests are 0.15 and 0.00 for BDS, 1.35 and -1.28 for SDM, -0.48 and 0.55 for NART25, respectively.

12

The lack of a gender difference is perhaps surprising since women tend to engage in morework in the household that may matter here.
Where does the threshold occur? In other words, when does the impact of working
hours on cognitive ability change from being positive to negative? Using the coefficientestimates reported in Table V for men, the peaks occur at 23 hours for BDS, 26 hours for
SDM, and 22 hours for NART25. For women, the peaks also occur at 22 hours for BDS, 29
hours for SDM7, and 22 hours for NART25.
In Figure 1, using the estimated coefficients presented in Table V, we plot the estimatedrelationship between working hours and cognitive ability for the three test scores theevaluating other control variables at their sample means. The inverted U shape relationshipbetween cognitive ability and working hours is clear from this Figure. Figure 1 also suggeststhat the cognitive ability of those working extremely long hours can be lower than those whoare not working at all. For example, the BDS score of those who usually work 60 hours per
week is lower than the BDS score of those who are not working both for males and females(Panel A). This suggests that longer working hours can lead to a deterioration of cognitive
functioning.
There is a possibility that the functional relationship between cognitive scores andworking hours could be more complicated than the quadratic form assumed in equation (1).
In order to examine this possibility, we added the cube of Working hours to equation (1) andtested its significance. The estimated coefficients associated with the Working hours-cubic
and their standard errors are reported at the bottom of Table V. None of these coefficientsare statistically significant. These results support our use of a quadratic functional form.
[Figure 1 around here]

The results presented in Table V and graphed in Figure 1 indicate that there is a nonlinearity in the effects of working hours on cognitive functioning for middle aged and older
males and females living in Australia. Even after including retirees and taking account of theendogeneity and censoring of working hours, our findings are consistent with Virtanen etal.’s (2009) findings, that is, long working hours have a negative effect on cognition in

The reader should keep in mind that for women the working hours and its square are notstatistically significant for SDM.
7

13

middle age. Our results indicate that part-time work is an effective way to maintain cognitive
functioning relative to retirement or unemployment.
Using the estimated working hours where the cognitive scores are maximized andwhere cognitive scores are the same as when working hours are zero, Table VI indicates foreach cognitive score the proportion of the sample working more than the threshold andworking so much (for ease of exposition referred at as “working too much”) that their
cognitive scores are worse than people not working at all. Depending on the score, 11% to
28% of men are “working too much”, whereas only 2% to 8% of women “work too much”.
[Table VI around here].

5. Concluding remarks
We examine the causal impact of working hours on the cognitive ability of middle-aged
and older aged males and females living in Australia using Wave 12 of the HILDA Survey
dataset. This study is unique in that it focuses on not only the extensive margin (labor force
participation) but also the intensive margin (working hours) and investigates the optimallevel of working hours for the cognitive levels of middle aged and older workers. Using thetest scores of memory span and cerebral dysfunction for the respondents, it is found thatworking hours up to 22–26 hours per week have a positive impact on cognition for males
depending on the measure and up to 22–30 hours for females. After that, working hours havea negative impact on cognitive functioning. This indicates that the differences in working
hours is an important factor explaining differences in the level of cognitive functioning for
middle and older adults. In other words, in middle age and old age, working part-time could
effective in maintaining cognitive ability compared to not working at all. It is worth notingthat our findings did not show any statistically significant gender differences in the effects
of working hours on cognitive functioning.
Our study also highlights that too much work can have adverse effects on cognitive
functioning to the extent that for cognitive function scores working too much can be worse
than not working at all. We find support for the ‘Use it too much and lose it hypothesis’.
Although our study deals with Australian data, there is good reason to believe that asimilar relationship between cognitive functioning and working hours will be found in othercountries. The exact number of working hours at which cognitive functioning peaks may
differ across countries due to institutional, cultural and other differences. Our study has
focused on the impact of working hours, but what a person does in their non-working time,14

for example, housework and sleep, may also have an important impact on cognitive
functioning. These issues are left for future research.
[Appendix I around here]

References
Atalay K, Barrett GF. 2015. The impact of age pension eligibility age on retirement andprogram dependence: Evidence from an Australian experiment. Review of Economics
and Statistics 97(1): 71–87. DOI:10.1162/REST_a_00443
Bonsang E, Adam S, Perelman S. 2012. Does retirement affect cognitive functioning?
Journal of Health Economics 31 (3): 490–501.
DOI: 10.1016/j.jhealeco.2012.03.005
Bosma H, van Boxtel MP, Ponds RW, Houx PJ, Burdorf A, Jolles J. 2003. Mental work
demands protect against cognitive impairment: MAAS prospective cohort study.
Experimental Aging Research 29(1): 33–45. DOI: 10.1080/03610730303710
Capatina E. 2014. Skills and the evolution of wage inequality. Labour Economics 28: 41–
57. DOI: 10.1016/j.labeco.2014.03.003
Coe NB, Zamarro G. 2011. Retirement effects on health in Europe. Journal of Health
Economics 30(1): 77–86. DOI: 10.1016/j.jhealeco.2010.11.002
Commonwealth of Australia 2009. Securable and Sustainable Pensions. Accessed 4
December 2016. Available at URL:
http://www.budget.gov.au/200910/content/glossy/pension/download/pensions_overview.pdf#search='Securable+and+sustainable+pensions'
Cottini E, Lucifora C. 2013. Mental health and working conditions in European countries.
Industrial & Labor Relations Review 66(4): 958–987.
DOI: 10.1177/001979391306600409
Cragg JG, Donald SG. 1993. Testing identifiability and specification in instrumental
variable models. Econometric Theory 9(2): 222–240.
Finkel D, Andel R, Gatz M, Pedersen NL. 2009. The role of occupational complexity intrajectories of cognitive aging before and after retirement. Psychology and Aging
24(3): 563–573. DOI: 10.1037/a0015511
Greene WH. 2008. Econometric Analysis, 6th edition. Pearson: New Jersey.

15

Kajitani S, Sakata K, McKenzie C. 2016. Occupation, retirement and cognitive functioning.
Accepted for publication in Ageing & Society. DOI: 10.1017/S0144686X16000465
Marin MF, Lord C, Andrews J, Juster RP, Sindi S, Arsenault-Lapierre G, Fiocco AJ, Lupien
SJ. 2011. Chronic stress, cognitive functioning and mental health. Neurobiology of
Learning and Memory 96(4): 583–595. DOI: 10.1016/j.nlm.2011.02.016
Marquié JC, Duarte LR, Bessières P, Dalm C, Gentil C, Ruidavets JB. 2010. Higher mental
stimulation at work is associated with improved cognitive functioning in both young
and older workers. Ergonomics 53(11): 1287–1301.
DOI: 10.1080/00140139.2010.519125
Matud MP. 2004. Gender differences in stress and coping styles. Personality and Individual
Differences 37(7): 1401–1415. DOI: 10.1016/j.paid.2004.01.010
Mazzonna F, Peracchi F. 2012. Ageing, cognitive abilities and retirement. European
Economic Review 56(4): 691–710. DOI: 10.1016/j.euroecorev.2012.03 .004
Mazzonna F, Peracchi F. 2017. Unhealthy retirement? Journal of Human Resources, 52(1):
128–151. DOI:10.3368/jhr.52.1.0914-6627R1
McEwen BS, Sapolsky RM. 1995. Stress and cognitive function. Current Opinion in
Neurobiology 5(2): 205–216. DOI: 10.1016/0959-4388(95)80028-X
Melbourne Institute 2014. Household, Income and Labour Dynamics in Australia (HILDA)
Survey Annual Report 2013. Accessed 4 December 2016. Available from URL:
https://www.melbourneinstitute.com/hilda/reports/annual_report.html
Potter GG, Helms MJ, Plassman BL. 2008. Association of job demands and intelligencewith cognitive functioning measures among men in late life. Neurology 70(19, part2):
1803–1808. DOI: 10.1212/01.wnl.0000295506.58497.7e
Proctor SP, White RF, Robins TG, Echeverria D, Rocskay AZ. 1996. Effect of overtime
work on cognitive function in automotive workers. Scandinavian Journal of Work,
Environment & Health 22(2): 124–132.
Rohwedder S, Willis RJ. 2010. Mental retirement. Journal of Economic Perspectives 24(1):119–138. DOI: 10.1257/089533010797456247
Schooler C, Mulatu MS, Oates G. 1999. The continuing effects of substantively complex
work on the intellectual functioning of older workers. Psychology and Aging 14(3):483–506. DOI: 10.1037/0882-7974.14.3.483
Small GW. 2002. What we need to know about age related memory loss. British Medical
Journal 324(7352): 1502–1505.
Smart EL, Gow AJ, Deary IJ. 2014. Occupational complexity and lifetime cognitive
abilities. Neurology 83(24): 2285–2291. DOI: 10.1212/WNL.0000000000001075
16

StataCorp. (2015). Stata Glossary and Index: Release 14. College Station, TX: StataCorp
LP.
Strauss E, Sherman EMS, Spreen O. 2006. A Compendium of Neuropsychological Tests:
Administration, Norms, and Commentary, 3rd edition. Oxford University Press: Oxford.
Summerfield M, Freidin S, Hahn M, Li N, Macalalad N, Mundy L, Watson N, Wilkins R,
Wooden M. 2016. HILDA USER Manual - Release 14. Faculty of Business andCrommerce, The University of Melbourne. Accessed 4 December 2016. Available
from URL: http://www.melbourneinstitute.com/hilda/doc/doc_hildamanual.html
Virtanen M, Singh-Manoux A, Ferrie JE, Gimeno D, Marmot MG, Elovainio M, Jokela M,
Vahtera J, Kivimäki M. 2009. Long working hours and cognitive function: The
Whitehall II study. American Journal of Epidemiology 169(5): 596–605.
DOI: 10.1093/aje/kwn382
Watson N, Wooden M. 2013. Adding a top-up sample to the Household, Income and Labour
Dynamics in Australia Survey. Australian Economic Review 46(4): 489–498. DOI:
10.1111/1467-8462.12027
Wooden M, Freidin S, Watson N. 2002. The Household, Income and Labour Dynamics inAustralia (HILDA) Survey: Wave 1. Australian Economic Review 35(3): 339–348.
DOI: 10.1111/1467-8462.00252
Wooden M. 2013. The measurement of cognitive ability in wave 12 of the HILDA Survey.
HILDA Project Discussion Paper no. 1/13, Melbourne Institute of Applied Economic
and Social Research, The University of Melbourne. Accessed 7 December 2016.
Available at the following URL:
https://www.melbourneinstitute.com/downloads/hilda/Bibliography/Hilda_Discussio
n_Papers/hdps113.pdf
Wooden M, Mackinnon A, Rodgers B, Windsor T. 2012. The development of cognitive
ability measures in the HILDA Survey. HILDA Project Discussion Paper no. 1/12,
Melbourne Institute of Applied Economic and Social Research, The University of
Melbourne. Accessed 7 December 2016. Available at the following URL:
https://www.melbourneinstitute.com/downloads/hilda/Bibliography/HILDA_Technic
al_Papers/htec112.pdf
Wooldridge J. 2010. Econometric Analysis of Cross Section and Panel Data, 2nd edition,
MIT Press: Cambridge.

17

Table I: Australian Age Pension Eligibility Age and the Sample Distribution
Males
FemalesPensionPensionSampleSampleeligibility age
eligibility age
Before 1 July, 1935
65
9.3%
60
10.5%
1 July, 1935 to December 31, 1936
65
2.7%
60.5
2.4%
1 January, 1937 to 30 June, 1938
65
1.2%
61
1.6%
1 July, 1938 to December 31, 1939
65
2.9%
61.5
2.9%
1 January, 1940 to 30 June, 1941
65
1.5%
62
1.9%
1 July, 1941 to December 31, 1942
65
3.6%
62.5
3.2%
1 January, 1943 to 30 June, 1944
65
1.7%
63
2.1%
1 July, 1944 to December 31, 1945
65
4.1%
63.5
3.7%
1 January, 1946 to 30 June, 1947
65
2.7%
64
2.7%
1 July, 1947 to December 31, 1948
65
4.4%
64.5
4.5%
1 January, 1949 to 30 June, 1952
65
6.8%
65
6.7%
1 July 1952 to 31 December 1953
65.5
5.6%
65.5
5.0%
1 January 1954 to 30 June 1955
66
1.9%
66
2.7%
1 July 1955 to 31 December 1956
66.5
5.5%
66.5
5.8%
From 1 January 1957
67
46.2%
67
44.5%
Total
100.0%
100.0%
Total sample size
3174
3698
Source: For pension eligibility ages: see Atalay and Barrett (2015), p. 73, Table 1, andCommonwealth of Australia (2009), p. 9. Sample proportions in each group are computed by theauthor using data from Wave 12 of the HILDA Survey.
Birth Cohort

Table II: Descriptive Statistics

BDSscore
SDMscore
NART25score

Males (obs.=3174)
Mean Std. Dev. Min Max
7.19
2.60
0
14
43.66
12.26
0
95
14.46
5.30
0
24

Females (obs.=3698)
Mean Std. Dev. Min Max
7.22
2.54
2
14
46.39
12.82
2 104
14.67
4.83
0
24

Working hours
Working hours-squared
Age
Age-squared/100
School years 7–10
School years 11 and over
University
Technical college
Other school
Non-indigenous origin
MarriedInterview Sunday
Interview Saturday
Number of dependent children
Parent is still alive
Ownhouse
Work experience
Inner regional
Outer regional
RemoteVery remote

27.21
1251.31
57.88
35.02
0.45
0.53
0.30
0.27
0.10
0.99
0.67
0.09
0.13
0.59
0.52
0.81
35.26
0.27
0.13
0.01
0.00

0
80
0 640040
94
16 88.36
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
7
0
1
0
1
0
72
0
1
0
1
0
1
0
1

16.86
631.59
58.36
35.68
0.48
0.50
0.28
0.17
0.16
0.98
0.57
0.07
0.12
0.52
0.51
0.81
26.01
0.28
0.11
0.01
0.00

18.64
873.10
12.72
15.83
0.50
0.50
0.45
0.37
0.37
0.13
0.49
0.26
0.33
0.94
0.50
0.40
11.86
0.45
0.32
0.10
0.04

0
70
0 490040 10016 100
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
7
0
1
0
1
0
72
0
1
0
1
0
1
0
1

Age minus Aged pension eligibility age
-8.18
13.18
-27
29
Squared of (Age minus Aged pension
240.60220.430841
eligibility age)
Interview July or August
0.45
0.50
0
1
Source: Authors' calculations using data from Wave 12 of the HILDA Survey.

-6.59

15.12

-27

271.93238.570.25 1600

0.46

0.50

22.61
1258.44
12.35
15.19
0.50
0.50
0.46
0.44
0.30
0.12
0.47
0.28
0.34
1.02
0.50
0.39
10.51
0.44
0.33
0.10
0.04

0

40

1

Table III: Current Employment Status by Age and Gender
Full-timePart-time
Non participants/ Total Sample
35 hours and more 34 hours and less
Unemployed
Size
Males
Aged 40–54
83.6%
7.0%
9.4%
Aged 55–69
44.4%
17.1%
38.6%
Aged 70 and over
2.9%
5.5%
91.6%
Total
54.4%
10.1%
35.4%
Females
Aged 40–54
41.5%
38.9%
19.6%
Aged 55–69
22.2%
24.1%
53.7%
Aged 70 and over
0.7%
3.5%
95.8%
Total
26.3%
26.4%
47.2%
Source: Authors' calculations using data from Wave 12 of the HILDA Survey.

1467
1089
618
3174
1647
1284
767
3698

Table IV: Check of the exclusion restriction variables
Dependent variable

Age minus Aged pension eligibility age
Squared of (Age minus Aged pension eligibility age)
Interview July or AugustWorking hours
Males
Females(1)(2)-16.963 ***-4.393 **[2.740][2.151]-0.801 ***0.079 **
[0.137][0.036]-1.604 **-1.767 **[0.797][0.832]3174
3698

Sample size
F-test H0: the coef. on the exclusion restriction variables are jointly
14.95 ***
7.28 ***
zero
Notes:
1) *, ** and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
2) The models are estimated using a Tobit estimator. Figures reported in square brackets are robust
standard errors adjusted for heterogeneity.
3) The first step models reported also include the explanatory variables (excluding the variables related toworking hours) that are reported in Table V. Coefficient estimates associated with these control variables
are not reported.

Table V: Impacts of Working hours on Cognitive Skills Estimated Using an IV Estimator

Variables
Working hours-squared
Working hours
Age-squared/100
Age
School years 7–10
School years 11 and over
University
Technical college
Other school
Non-indigenous origin
MarriedInterview Sunday
Interview Saturday
Number of dependent children
Parent is still alive
Ownhouse
Work experience
Inner regional
Outer regional
RemoteVery remote
Constant(1A)
BDSscore-0.003 ***[0.001]0.147 **
[0.061]-0.027[0.032]0.012[0.049]0.663 **
[0.266]
1.378 ***
[0.277]0.928 ***
[0.150]-0.035[0.130]0.296 *
[0.174]0.930 **
[0.409]0.183[0.120]-0.075[0.192]0.033[0.160]0.137 *
[0.078]0.292 **
[0.147]0.124[0.142]0.005[0.011]
0.144[0.133]0.258[0.198]0.510[0.490]0.118[1.207]4.549 ***
[1.701]

Males
(1B)
(1C)
(2A)
SDMscore NART25score BDSscore-0.015 ***-0.004 **-0.003 *[0.005][0.002][0.002]0.779 ***
0.182 *
0.133 **
[0.227][0.099][0.067]-0.265 *-0.104 *-0.110 ***[0.138][0.060][0.029]-0.146
0.192 **
0.141 ***
[0.197][0.083][0.041]
5.219 ***
2.663 ***
0.775 ***
[1.259][0.644][0.293]9.424 ***
6.076 ***
1.288 ***
[1.291][0.655][0.303]3.425 ***
3.460 ***
0.771 ***
[0.539][0.231][0.152]0.390
0.315-0.159[0.514][0.232][0.142]
1.772 ***
0.906 ***
-0.024[0.685][0.314][0.128]2.358
1.392 **
0.397
[1.517][0.648][0.301]1.641 ***
0.160
-0.031[0.478][0.215][0.097]0.918
0.712 **
0.067
[0.751][0.316][0.210]0.320
0.545 **
0.133
[0.583][0.254][0.134]0.610 **
0.228 *
0.061
[0.287][0.128][0.091]
0.863
0.368
0.075
[0.542][0.230][0.121]0.959 *
0.557 **
0.030
[0.555][0.250][0.138]0.115 **
0.005
0.000
[0.048][0.021][0.005]-0.790-0.667 ***-0.082[0.510][0.220][0.104]-1.234-1.003 ***-0.156[0.776][0.326][0.138]-0.322-1.628 *-0.105[1.879][0.853][0.444]12.187 ***1.416-0.215[4.671][2.839][0.849]41.679 ***-0.593
0.949[6.576][2.718][1.414]3174-11992-9366-8765

Females(2B)(2C)
SDMscore NART25score-0.005-0.006 **[0.006][0.003]0.314
0.255 **
[0.258][0.115]-0.675 ***-0.188 ***[0.114][0.051]0.384 **
0.331 ***
[0.154][0.069]4.918 ***
4.326 ***
[1.334][0.565]7.473 ***
6.707 ***
[1.366][0.580]1.128 **
3.561 ***
[0.558][0.244]0.292
0.509 **
[0.532][0.252]-0.1130.783 ***
[0.470][0.224]1.656
1.388 **
[1.193][0.566]0.474-0.195[0.371][0.167]0.137
0.566 *
[0.770][0.329]-0.2370.450 **
[0.515][0.223]0.495
0.045[0.344][0.148]0.961 **
0.044
[0.430][0.202]2.000 ***
0.657 ***
[0.512][0.240]0.071 ***
0.014
[0.020][0.009]-0.178-0.319 *[0.401][0.174]-0.577-1.296 ***[0.486][0.233]-2.651-0.912[1.684][0.852]0.084
1.285 *
[4.348][0.768]33.741 ***-7.400 ***[5.318][2.360]3698-13616-10676

Sample size
Log likelihood-7765
F-test H0: all the coefficients except
16.20 ***
99.38 ***
72.33 ***
13.48 ***
133.8 ***
72.48 ***
the constant are jointly zero
Working hours-cubic-0.036-0.075-0.053-0.051-0.0360.021[0.026][0.078][0.038][0.163][0.338][0.137]
Cragg-Donald Wald F statistic for
16.45
13.77
weak instruments
Notes:
1) *, ** and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
2) These models are estimated by instrumental variable estimation. Figures reported in square brackets are robust standard
errors adjusted for heterogeneity.
3) The Cragg-Donald Wald F statistic is computed using the "ivreg2" command in STATA 14.

Table VI: Proportion of the Sample Above the Threshold and Working "Too Much"
Males
Females
Proportion of the
Proportion of the
Proportion of the
Proportion of the
Sample Working
Sample Working
Sample Working
Sample Working
More than theMore than the"Too Much""Too Much"
ThresholdThreshold
BDSscore
59.0%
21.0%
40.0%
7.9%
SDMscore
57.7%
11.1%
33.2%
1.6%
NART25score
59.1%
28.1%
40.0%
5.8%
Source: Authors' computations based on the estimated results in Table V and data from Wave
12 of the HILDA survey.

Figure 1 : Estimated impacts of working hours on cognitive skills
Panel A

Panel B

Symbol Digits Modalities (SDM)

0

0

10

2

20

4

Score

Score
30

6

40

8

50

10

60

Backward Digit Span (BDS)

0

5

10

15

20

25

30 35 40 45
Working hours
Males

50

55

60

65

70

Females

0

5

10

15

20

25

30 35 40 45
Working hours
Males

50

55

60

65

70

Females

Panel C

0

5

Score
10

15

20

National Adult Reading Test (NART25)

0

5

10

15

20

25

30 35 40 45
Working hours
Males

50

55

60

65

70

Females

Note: The fitted values of these scores are computed using the estimated coefficients reported in Columns (1A)–(2C) in Table V where all variables except
Working hours-squared and Working hours are evaluated at their sample mean values.

Appendix I: Definitions of Variables
Name

SDMscore

Definition
The question consists of seven levels. At each level the respondent has a maximum of
two trials. When the respondent gets the answer correct on the first trial he/she isawarded a score of two, and moves on to the next level. When the respondent's answer on
the first trial is incorrect, he/she moves onto the second trial. If his/her response on thesecond trial is correct, he/she is awarded a score of one and moves on to the next level.
When both his/her responses at the same level are incorrect, he/she is awarded a score ofzero and this test is finished at that point. The sum of the scores at each level is the BDS
score
The number of items correctly matched within a 90 second time interval.

NART25score

The number of words the respondent correctly pronounces.

Working hours

The number of usual or average working hours per week the respondent works.

Working hours-squared
Age=(Working hours)2
Respondent's age in years at the time of the survey

Age-squared/100=(The squared of Age)/100

BDSscore

School years 7–10
0–1 dummy variable taking the value unity if the respondent's highest years of school(benchmark: the respondent's highest years of completed are between 7 and 10, and 0 otherwise.
school completed are under 7)
School years 11 and over
0–1 dummy variable taking the value unity if the respondent's highest years of school(benchmark: the respondent's highest years of completed are 11 and over, and 0 otherwise.
school completed are under 7)
University
0–1 dummy variable taking the value unity if an educational institution where the(benchmark: the respondent did not obtain
respondent obtained his/her highest post-school qualification is a University, Teachers'
post-school qualification)college/College of Advanced Education, Institute of Technology, and 0 otherwise.
Technical college
0–1 dummy variable taking the value unity if an educational institution where the(benchmark: the respondent did not obtain
respondent obtained highest post-school qualification is Technical college/TAFE/College
post-school qualification)of Technical and Further Education , and 0 otherwise.
Other school
0–1 dummy variable taking the value unity if an educational institution where the(benchmark: the respondent did not obtain
respondent obtained highest post-school qualification is other organizations, and 0
post-school qualification)otherwise.
Non-indigenous origin
0–1 dummy variable taking the value unity if the respondent is not of Aboriginal or
Torres Strait Islander origin, and 0 otherwise.
Married
0–1 dummy variable taking the value unity if the respondent is currently married, and 0
otherwise.
Interview Sunday
0–1 dummy variable taking the value unity if interview date is Sunday, and zerootherwise.
Interview Saturday
0–1 dummy variable taking the value unity if interview date is Saturday, and zerootherwise.
Number of dependent children
The number of children who reside with the parent or guardian and who are aged 0 to 24.
Parent is still alive
Ownhouse
Work experience
Inner regional
Outer regional
RemoteVery remote
Age minus Aged pension eligibility age
Squared of (Age minus Aged pension
eligibility age)
Interview July or August

0–1 dummy variable taking the value unity if the respondent's parent is still alive, andzero otherwise.
0–1 dummy variable taking the value unity if the respondent owns his/her own house oris currently paying off a mortgage, and zero otherwise.
=Total years the respondent is(was) in paid work
0–1 dummy variable taking the value unity if the respondent lives in inner regional
Australia, and 0 otherwise.
0–1 dummy variable taking the value unity if the respondent lives in outer regional
Australia, and 0 otherwise.
0–1 dummy variable taking the value unity if the respondent lives in remote Australia,
and 0 otherwise.
0–1 dummy variable taking the value unity if the respondent lives in very remote
Australia, and 0 otherwise.
=(Respondent's age in years at the time of the survey)-(Aged pension eligibility age)
2=(Age minus Aged pension eligibility age)

0–1 dummy variable taking the value unity if the respendent is interviewed in July or
August, and zero otherwise.