Ageing & Society30, 2010, 000-000. 2010 Cambridge University Press DOI: 10.1017/S0144686X09990626 Printed in the United Kingdom
Social involvement, behavioural risks and cognitive functioning among the aged
HENRIETTE ENGELHARDT *, ISABELLA BUBER §, VEGARD SKIRBEKK † and ALEXIA PRSKAWETZ ‡§ * Department of Population Studies, Otto Friedrich University Bamberg, Germany § Vienna Institute of Demography, Vienna, Austria † Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria ‡ Institute for Mathematical Methods in Economics, Vienna University of Technology, Austria ABSTRACT
In this study we analyse the relationship between cognitive performance, social participation
and behavioural risks taking into account the influence of age and educational attainment. We
examine individual data from 11 European countries and Israel that were collected in the first
wave of SHARE. The methodology proposed, a stochastic frontier approach, allows us to
identify the effects of the different sources of plasticity on cognitive functioning while
explicitly taking into account the age-related decline in cognitive performance. Social
involvement variables are employment status, attending educational courses, doing voluntary
or charity work, providing help to family, friends or neighbours, participating in a sports,
social or other club, participating in a religious organisation and participating in a political or
community organisation. We control for age, education, income, physical activity, BMI,
smoking and drinking. In the pooled sample, the results clearly show that all kinds of social
involvement enhance cognitive functions, in particular the continuation of occupational
activities. Moreover, behavioural risks such as physical inactivity, obesity, smoking or
drinking are clearly detrimental to cognitive performance. Models for men and women were
run separately. For both genders, all social involvement indicators were found to be associated
with better cognitive performance. Country-specific results, however, vary across countries
with respect to signs for a number of indicators of social involvement and behavioural risks.
KEY WORDS – cognitive ageing, cognitive reserve, social involvement, behavioural risks, social engagement Introduction
It is now well accepted that in the future in most industrialised countries, the labour force will
become smaller and older. To counteract the shrinkage of the working-age population and to
reduce the number of social security beneficiaries, increasing employment at older ages is
called for. Senior workers’ productivity levels are important in determining whether policies
to extend the length of the working life will be successful. Strategies for encouraging older
workers to remain longer in the workforce need to be evaluated in tandem with the
development of the productivity profile of older workers. It is well known that workers of
different ages have different levels of productivity (as well as learning abilities), although the
size of the age effect is still highly disputed and strongly dependent on the occupation,
technological progress and possible cohort effects that work through schooling levels. Studies
of the influence of age on individual productivity use different measures, including
supervisors’ evaluations, piece-rate studies, analyses of employer-employee datasets, age-
earnings profiles and entrepreneurial activity (cf. Prskawetz et al. 2005; Prskawetz, Mahlberg
and Skirbekk 2007; McEvoy and Cascio 1993; Skirbekk 2008; Warr 1994). An important
cause of variability in productivity at higher ages is likely to be the variation in the age-related
decline of cognitive abilities. Some abilities, such as perceptual speed, show relatively large
decrements from young ages, while others, like verbal abilities, exhibit only small changes
throughout the working life. Older individuals learn at a slower pace and have reductions in
their memory and reasoning abilities. In particular, senior workers are likely to have
difficulties in adjusting to new ways of working (Verhage and Salthouse 1997; Schaie 1996;
Skirrbekk 2008; McEvoy and Cascio 1989).
Previous studies have indicated the plasticity of ageing by focusing on the role of
behavioural risk factors and social involvement on individuals’ cognitive reserves in old age
(for a survey see Le Carret et al. 2003). Based on the Survey on Health, Ageing and
Retirement in Europe (SHARE), we study the role of these intervening factors on cognitive
functioning in old age, and focus on the fluid abilities that are more likely to deteriorate with
age. Our approach is to model cognitive abilities as a function of age and education, and to
study the loss in efficiency depending on behavioural risk factors (like smoking and obesity)
as well as social involvement at old age. Differently from the study by Adam et al. (2006),
we study the cognitive decline of a single indicator of fluid abilities that shows clear decline
in old age. Moreover, we model the best possible cognitive performance as a function of age
and education, and perform country-specific analysis to test the generality of the results.
The paper is organised as follows. Theories of cognitive ageing are reviewed in the
next section, and the data, methods and variables are discussed in the next. The descriptive
univariate and multivariate results based on the stochastic frontier concept are presented in the
fourth section, and the fifth sets out our conclusions.
Cognitive ageing and cognitive reserve
During the last three decades, a great deal of evidence has accumulated that increased age is
accompanied by ‘cognitive ageing’ – the term describes a pattern of age-related variation in
cognitive functioning including reasoning, spatial orientation, numerical capabilities, verbal
abilities, memory and problem solving. These cognitive abilities are closely correlated with
performance in several areas of life, in particular job performance (Schmidt and Hunter 1998;
Skirbekk 2008; Warr 1994). Different mental abilities follow different paths across the life
cycle. Crystallised abilities tend to increase or remain at a high functional level until late in
life, while fluid abilities tend to decline substantially over the adult life span (Blum, Jarvik
and Clark 1970; Horn and Cattell 1966, 1967; Schaie 1994; Schwartzman et al. 1987;
Verhaegen and Salthouse 1997). Crystallised abilities include accumulated knowledge and
skills, such as the meaning of words and size of vocabulary, while fluid abilities concern
performance in learning and processing new material—and also comprise perceptual speed
A longitudinal study by Schwartzman et al. (1987) found that verbal skills remain
virtually unchanged across the life cycle, while reasoning and speed decline with age. The
study of twins by Blum et al. (1970) provided similar findings: vocabulary size remained
constant from youth to old age, despite a general reduction in other cognitive abilities.
Verhaegen and Salthouse (1997) analyses 91 different studies and conclude that important
fluid abilities, such as reasoning and speed decline significantly by the age of 50 years. The
decline with age in fluid abilities has been shown across countries, for both men and women,
and for individuals with different ability levels (Park, Nisbett and Hedden 1999; Deary et al.
2000; Maitland et al. 2000). It is important to stress that intra-individual variations increase
with age—following the long-term impact of different lifestyles and health behaviour over the
life cycle. Educational, family and occupational choices in addition to behavioural factors
such as eating, smoking and drinking habits imply that mental health is increasingly variant at
older ages. One example is the greater variation in depression, dementia or activities of daily
life in the latter half of life, implying a greater overall variation in mental health at older ages
(Christensen et al. 1999; Wilson et al. 2002).
The decline in cognitive functioning is associated with structural changes in the brain
(Raz 2004). Even early in the ageing process, cerebral atrophy, ventricular enlargement and
hippocampal atrophy may be evident in many individuals (Meyer et al. 1999; Coffrey et al.
1992). In addition, the underlying pathologic basis of cognitive decline would be the loss of
synapses, neurons, neurochemical inputs and neuronal networks (Honig und Rosenberg
2000). The large variation in cognitive decline implies that many individuals experience
strong declines in cognitive functioning, often related to poor health. Fillit et al. (2002)
suggested that many individuals have a high functional reserve and therefore the potential to
keep learning and adapting in spite of age-related declines in health and mental capacities
(Baltes and Baltes 1990). Scarmeas and Stern (2003) developed this view with the concept of
cognitive reserve, the notion that innate intelligence or life experience as evinced by
educational or occupational attainment creates a cognitive reserve that to some extent
counteracts the cognitive decline associated with normal ageing. Hence, as age development
is similar for those with high and low abilities, those with higher initial ability levels may
simply have ‘more left’—a greater cognitive reserve (Baltes and Mayer 1999; Park, Nisbett
Scarmeas and Stern (2003) explored what constituted cognitive reserve and proposed
that there are both active and passive components. Active components include the experience
acquired from a high level of education, from complex occupations that require continuing
education and sustained intellectual involvement. Passive components are the brain structures
(synaptic density and number of neurons) that are associated with an enhanced capacity to
process information, retrieve memories and solve problems. Recent studies have tried to
identify the parameters that contribute to the development of cognitive reserve and influence
the cognitive performance of elderly people. Epidemiological studies have established low
educational attainment and low occupational status as important risk factors for reduced
cognitive functioning and Alzheimer’s disease (Launer et al. 1999; Cullum et al. 2000). A
significant effect of education on cognitive ageing was reported by Le Carret et al. (2003) –
they found that education protected psychological performance in late life and related this to
occupational complexity and the acquisition of a lifelong ability to sustain attention and
conceptionalise problems. Bennett et al. (2003) found that (more) education modified the
deleterious effect of senile plaque density on cognitive performance. Similarly, lower
childhood intelligence (Whalley et al. 2000; Richards et al. 2004) and lower linguistic ability
in early life (Snowdon et al. 1996) appear to be a reliable proxy for lower cognitive reserves.
Moreover, cognitive training is frequently found to improve cognitive functioning among
elderly persons (Schaie and Willis 1986; Ball et al. 2002). Katzman (1993) suggested that
educational courses can increase the synaptic density in the neocortical association cortex and
therefore delay the onset of dementia by up to five years.
A positive association between cognition and participation in intellectual, social and
physical activities has been reported by several studies. Low-skilled occupations have been
identified as risk factors for age-related cognitive decline (Capurso et al. 2000). On the other
hand, individuals who are/were involved in complex work, with freedom to decide how to
organise their working day, could be expected to experience less cognitive decline (Schooler,
Mulatu and Oates 1999). Salokangas and Joukamaa (1991), Bosse et al. (1987) and Dave,
Rashad and Spasojevic (2006) found that working longer associated with better cognitive
functioning, but because those who experience health impairments retire early (McGarry
2004; Belgrave, Haug and Gomez-Bellenge 1987), it is uncertain to what extent later
retirement actually improves health levels. Moreover, a follow-up study by Sugisawa et al.
(1997) found that cognitive functions among those who retired early did not differ
significantly from their age peers in work, while Mein et al. (2003) found that among British
civil servants in high employment grades, an extended career actually worsened the cognitive
functions relative to those who had retired. Adam et al. (2006) studied the relationship
between cognitive performance and occupational activities, defined in a broad sense that
included professional, leisure, physical and other activities. Their results confirmed the
positive impact of occupational activities on the cognitive functioning of older people.
Several studies have found that a more active lifestyle is protective of late-life
cognitive function (Elwood et al. 1999; Dik et al. 2003; Newson and Kemps 2005), consistent
with a report that cognitive function in mid-life is associated with greater physical activity in
childhood (Richards et al. 2003). Leisure pursuits are often chosen because they require
mental effort and are cognitively stimulating. In a study of a religious order (Wilson et al.
2002), longitudinal data were collected from 801 elderly Catholic nuns, priests and brothers
without dementia. On recruitment, their cognitive activities were rated and subsequently
shown to be associated with retention of cognitive function and reduced risk of dementia after
controlling for age, sex and education. The effect sizes in the sub-analysis of cognitive ageing
were sufficient to suggest that continued demanding cognitive activity in later life might
Leisure activities, irrespective of the extent of cognitive effort involved, surveyed in a
non-demented general population sample were also found to have a cumulative effect on the
risk of incident dementia (Scarmeas et al. 2001). In the British 1946 cohort study (Richards,
Hardy and Wadsworth 2003), leisure activities were associated with better cognitive
performance at age 43 years and physical exercise at age 36 years was linked to a
significantly slower rate of memory decline from age 43 to 53 years. In a Swedish twin study,
Crowe et al. (2003) compared leisure activities between same-sex twin pairs discordant for
dementia. Factor analyses of activity reports obtained 20 years earlier identified three activity
factors: intellectual/cultural, self-improvement and domestic. The authors concluded that
greater participation in intellectual-cultural leisure activities was associated with a lower risk
of Alzheimer’s disease in women, but not men. Studies of physical activity find that regular
exercise improves the working memory function among older men (James and Coyle 1998;
Other risk factors have also been shown to affect cognitive performance among older
adults. In a follow-up of Irish smokers and non-smokers, where initial intelligence levels
were controlled for, a negative effect of smoking was found (Deary et al. 2003). Excessive
alcohol consumption is related to higher morbidity and mortality, but moderate consumption
may be weakly positively related to longevity and mental functioning at older ages (Bond et al. 2001; McDougall, Becker and Areheart 2006). Obesity has been found to have negative
effects on cognitive performance, net of education, occupation, cigarette smoking, alcohol
consumption, total cholesterol and a diagnosis of type II diabetes (Elias et al. 2003).
Living arrangements are another factor that might influence cognition, because social
isolation is related to more rapid decline in cognitive abilities (Wilson et al. 2007). In more
developed countries, the percentage of older people living alone generally rose rapidly
between 1960 and the late 1970s; in some North American and European countries the trend
continued through the 1990s, but in others it slowed or halted around 1980 (Tomassini et al.
2004; United Nations Organization 2007). In a study of 550 Scots whose IQ was tested in
1932 and retested in 1999-2001, Gow et al. (2005) found that those living with more people
in later life, and thus experiencing less loneliness, had higher cognitive performance.
Loneliness accounted for three per cent of the variance in later-life cognition (once prior
abilities and sex were controlled for), such that those experiencing increased levels of
loneliness displayed poorer cognitive performance in later life. A lack of social interaction, as
follows retirement for some people, sets off cognitive function problems (Cohen 2004; Cole,
Schaninger and Harris 2002; Glass et al. 1999; Melchior et al. 2003). Cognitive decline as a
result of reduced socialisation after retirement is most evident among men (Sugisawa et al.
1997). Maier and Klumb (2005) found that in Germany spending time with friends improved
health and survival at older ages. Bassuk, Glass and Berkman (1999) used longitudinal
United States data from 1982 to 1994 and found that those who had no social contacts
suffered from more severe cognitive decline than the rest of the population. A weakening of
the degree of activity is related to stronger decline relative to older individuals who manage to
uphold their level of cognitive functioning (Mackinnon et al. 2003).
Beland et al. (2005) found that participation in community activities mattered for
women in a study of community-dwelling older people and that its effects were more
significant at advanced ages. Barnes et al. (2004) showed that the level of social involvement
and social network size were positively correlated with initial level of cognitive functions and
associated with a reduced rate of cognitive decline. A high number of people in a person’s
social network reduced the rate of decline by 39 per cent when compared to a low number,
and high social involvement reduced decline by 91 per cent. These relationships remained
after controlling for socio-economic status, cognitive activity, physical activity, depressive
symptoms and chronic medical conditions. Zhang (2006) looked at cognitive impairment
over two years, and after controlling for age, activities of daily living disability and rural
residence found that women’s disadvantages in social networks and participation in leisure
activities partially accounted for gender differentials in impairment. In a longitudinal study of
4,603 Taiwanese from 1989 to 2000, Glei et al. (2005) found that older people who
participated in one or two social activities failed 13 per cent fewer cognitive tasks than those
with no social activities; while those who engaged in three or more activities failed 33 per cent
The findings for the effect of social involvement on cognition are nevertheless
contradictory. McGue and Christensen (2007) found in a study of Danish twins that social
activity was significantly and moderately heritable, raising the possibility that late-life
cognition functioning might reflect selection processes. Aside from this, social activity did
not predict changes in functioning, and in monozygotic twins discordant for their levels of
social activity, the more socially-active twin was not any less susceptible to age decreases in
physical and cognitive functioning and increases in depression symptoms. To summarise,
these findings on cognitive reserve may have important implications for the role of continued
education, social involvement and structure of retirement at older ages. These factors may
indeed help to keep up cognitive abilities at older ages, thus increasing the feasibility and
practicability of increasing labour-force participation at higher ages. This literature review
has revealed that numerous studies have identified factors that contribute to the development
of cognitive reserve and to reduced cognitive decline with increasing age. If this is the case,
the impact should be the same in all countries, or at least the sign of the effect should be the
same. Using large-scale samples from 12 different countries, we proceed to test the
hypothesis that the association between cognition on the one hand and social involvement and
behavioural risks on the other hand is the same in each country.
Data, method and variables
The empirical analysis is based on data from the Survey of Health, Ageing and Retirement in Europe (SHARE), the overall aim of which is to increase understanding of ageing processes
and their implications in Europe. SHARE includes detailed cross-national information,
among other things on health, well-being, economic circumstances and social networks for 11
European countries: Austria, Belgium, Denmark, France, Germany, Greece, Italy, The
Netherlands, Sweden, Switzerland and Spain, and Israel. The data were collected between
2004 and 2006. SHARE covers the non-institutional population aged 50 or more years. Since
the spouses of the respondents were also interviewed, some were younger than 50. Release
2.0.1 of the data was for 31,115 individuals in 21,176 households. The weighted average
response rate was 61.6 per cent (Börsch-Supan and Jürges 2005).
In order to exclude greater declines in cognitive functioning as a result of poor health,
the analysis was restricted to ‘healthy’ respondents aged 50-79 years, and we excluded those
who reported a stroke or cerebral vascular disease, Parkinson’s disease or cancer. Anti-cancer
drugs decrease cognitive ability levels (Falleti et al. 2006; Wincour et al. 2006), and
Parkinson’s disease (Norman et al. 2002; Rasquin et al. 2004), stroke and cerebral vascular
disease may severely reduce cognitive functioning (Schatz and Buzan 2006; Schmidt et al.
1993). We also excluded respondents who were taking drugs for anxiety or depression or
who had been treated in a mental hospital or psychiatric ward. These selection criteria are
similar to those of Adam et al. (2006), but whereas that team excluded only people with brain
cancer, we excluded all persons diagnosed with any kind of cancer, because cancer
medication is very likely to affect cognitive functioning. Missing or unreliable data for one of
the variables retained in the analysis was another criterion for exclusion. The final analysis
sample had 22,949 people (10,902 men and 12,047 women), with a mean age for men of 62
We used the ‘stochastic frontier approach’ for the multivariate analysis, which emanates from
econometric studies of production functions. It will be helpful to many readers to begin with
a short account of the method. There are two ways to estimate a fully efficient production
function: (1) Data Envelopment Analysis (DEA), a non-parametric technique that assumes all
deviations from the efficient frontier to be a realisation of inefficiency, and (2) Stochastic
Frontier Analysis (SFA), a parametric technique which assumes that deviations from the
efficient frontier can be either a realisation of inefficiency or a random shock. Aigner, Lovell
and Schmidt (1977) and Meeusen and van den Broeck (1977) simultaneously introduced
stochastic production frontier models. Their models allow for technical inefficiency but also
acknowledge the fact that random shocks outside the control of producers can effect output.
The great virtue of stochastic production frontier models is that the impact of shocks on
output can, at least in principle, be separated from the influence of variation in technical
The application of this terminology to the association between age and cognitive
functioning implies that there a stochastic frontier function represents an ‘optimal’ curve (or
age relationship) depending on various factors. The basic assumption is that age and
educational level are the main explanatory factors of an individual’s cognitive functions.
Therefore, the main ‘input factors’ or predictors for cognition are age and education. Not all
individuals attain the optimal cognitive abilities for their age and educational level, however,
for some are ‘inefficient’ in that their cognitive functioning is poorer than the optimal value.
Moreover, we also consider measurement errors (statistical noise and random shocks) such as
the daily constitution of a person. Adam et al. (2006) studied the relationship between
cognitive performances and occupational activities using the stochastic frontier approach.
They assumed age to be the driving factor (input) and the cognitive test score to be the output.
We follow their approach but have specified a different model, and we have run the models
Let us consider a production function for the cognitive functioning of an individual i:
q = f (x ; β ) (1)
where x is a vector of inputs (e.g. age and education), q is the output (e.g. cognitive test
score such as ‘number of words recalled’), and β is a [k × ]
estimated. We can think of efficiency being measured as ς multiplied by a theoretical norm
ς = , individuals are fully efficient and ‘produce’ or recall the highest number of words
they can (according to their age and educational level). In this case, their cognitive
performance lies exactly on the optimal or frontier curve f (x ;β ) . If ς < 1 then individuals
are not fully efficient, their cognitive performance is below the optimal curve. Figure 1
graphically represents the mathematical reasoning. Imagine individual A who is ‘fully
efficient’ according to his/her age and educational level. His/her cognitive performance will
lie on the optimal or frontier curve f (x ;β ) . Then imagine individual B who is not ‘fully
efficient’. His/her cognitive performance will lie below the curve. Put differently, in the
stochastic frontier conception, the distance to the optimal or frontier curve is modelled as a
function of various explanatory factors. Adding a two-sided error term (Aigner, Lovell and
q = f (x ; β )ς exp(v ) (3)
ln q = ln f x ; β + ln ς + v (4)
ln q = ln f x ; β + v − u (5)
, where v is the two-sided measurement error
(random factors like the daily constitution of a person), and u is the one-sided technical
inefficiency. The last is a key term in the frontier analysis method, for it corresponds to the
distance to best practice as represented by the stochastic frontier ln( f (x ; β + v . Hence u
requires an assumption about the distribution of u . For this analysis, we assumed for the
inefficiency component a truncated-normal distribution u ~ iidN + (
non-negative disturbance was specified to be half-normally distributed with u ~ N + (
The estimated coefficients slightly differed but remained stable and comparable to the
truncated-normally distributed inefficiency.
The inefficiency term can be modelled as a function of other covariates. This idea was
first introduced by Battese and Ceolli (1995).1 According to their specification, we modelled
the inefficiency term u as u = Z δ where Z is a set of variables thought to influence
inefficiency. The applied software provided an extension to the truncated normal model by
allowing the mean of the inefficiency term to be modelled as a linear function of a set of
covariates. Summing up, the mathematical model applied in the current paper is:
where q represents the cognitive performance measured by the number of words recalled, x
represents age, the square of age, and educational level, and Zi incorporates the measures of
social participation, behavioural risks, economic situation and chronic diseases. The analysis
software estimates the coefficients β (effect of age and education) as well asδ (effect of
social participation and control variables).
SHARE includes five different measures for cognitive functions: orientation, memory, verbal
fluency, numeracy and recall. Orientation for time (date, month, year and day of the week) is
a basic cognitive functioning indicator, and was not included in the analysis because it shows
little variation by age (and is most appropriate for detecting very severe cognitive deficits).
Memory indicates the number of words the interviewee can recall from a list of 10 items:
butter, arm, letter, queen, ticket, grass, corner, stone, book, stick. Recall is the number of
words from this list that the interviewee can recall after a certain delay—dependent on the
time to answer another seven questions, but generally about five minutes. The scales for
memory and recall both range from ‘0’ to ‘10’. Verbal fluency is the number of different
animals that the interviewee can name within one minute, with the values ranging from ‘0’ to
‘80’ in the current sample. Numeracy measures the performance in calculating percentages.2
The respondents achieved scores from ‘1’ to ‘5’—the higher the score, the better the
These measures of cognitive functioning are an assessment more of fluid than
crystallised intelligence. A measure of crystallised intelligence would not involve any
processing of new information, only recall or the performance of learned information and
skills. A vocabulary test or a general knowledge test would be more appropriate. Fluency is
commonly used as a measure of the efficiency of the central executive of working memory,
since it uses the ability to sustain attention on a given task (goal) and to thwart intrusions.
The variables memory and recall involve a timing aspect and a processing speed component.
We report briefly the descriptive evidence from SHARE on the decline with age of the four
measures memory, recall, verbal fluency and numeracy, and then concentrates on recall, as
verbal skills might remain unchanged across the life cycle (Schwartzman et al. 1987). For all
four dimensions, the decline with age was almost linear, which allows the application of
linear regression. The mean number of words remembered declined from 5.5 words at age 50
years to 4.0 words at age 80, and the mean number of words recalled dropped from 4.0 to 2.0.
Respondents aged 50 years named on average 21 animals, while those aged 80 named about
15 animals. Finally, the numerical ability score decreased from 3.8 to 3.0. Using
standardised scores for memory, recall, verbalfluency and numeracy our results clearly
demonstrate that memory and recall decreased more strongly than verbal fluency and
numeracy (for more details see Engelhardt et al. 2008). Since the decline of cognitive
functioning was most pronounced for memory and recall, further analysis concentrated on
those two aspects of cognitive ability. The decline of the standardised scores was almost
identical for both and we chose to examine only recall.
It might be argued that the number of words recalled reflects a ceiling effect
(Rasmussen et al. 2001) since the value of recall cannot exceed 10, as only 10 words were
read out and available for recall. A respondent able to remember more words was unable to
show their superior cognitive ability. It was found that 97.8 per cent of the respondents
recalled up to seven words, another 1.5 per cent eight, 0.5 per cent remembered nine and only
0.2 per cent recalled all the words. Therefore the distribution of recall scores indicates that
the distribution was not distorted by a ceiling effect.
We selected several indicators that are potential sources of plasticity of cognitive
reserve, namely social participation and behavioural risks. The activities of social
participation captured in SHARE include voluntary and charity work, care provided for sick
or disabled adults, help provided to family, friends and neighbours, educational training,
participation in a sports, social or other kind of club, participation in a religious organisation,
and participation in a political or community organisation. The corresponding questions
referred to activities undertaken within only the previous month and did not elicit how long a
person had engaged in these activities. Additionally, SHARE collected information on
frequency and on the motivation for taking part in the various activities. Our analysis does
not consider those frequencies which are restricted to the preceding month only but might
vary during a year. This restriction of activities to the last month before time of interview is
certainly a limitation to the quality of our data. Thus, for instance, persons who have been
involved in certain activities for many years except for the preceding month would not be
Additionally, the following behavioural risks were included in the analyses: being
employed, carrying out moderate or vigorous physical activities, being overweight or obese,
as well as smoking and drinking habits. If respondents said they engaged in vigorous activity
(such as sports, heavy housework or a job that involves physical labour) at least one to three
times a month, then we coded them as engaged in vigorous activities. If a respondent
answered ‘less than once a month’, he/she was coded as not being engaged in vigorous
activities. The same definition was applied for moderate activities: persons who engaged in
activities that require a low or moderate level of energy (such as gardening, cleaning the car,
or doing a walk) a least one to three times a month were categorised as being engaged in
moderate activities. Persons were coded as overweight or obese if their body mass index
(BMI) was greater than 25. They were coded as smoking if they had ever smoked cigarettes,
cigars, cigarillos or pipes daily for at least one year, and as drinking if they had more than two
glasses of any alcohol almost every day of five to six days a week during the last six months.
Alternatively, we distinguished people who never smoked, former smokers and current
Moreover, we controlled for economic situation and health—specifically, for chronic
diseases. As an economic indicator, a measure generated at the household level and adjusted
for purchasing power parity (ppp) was included, which is especially appropriate for
comparisons of countries with different levels of income. The ppp-adjusted total gross
income (i.e. the nominal gross income at the household level divided by the purchasing power
parity) was included as a control to quantify the association between economic wealth and
cognitive ability. In order to be able to distinguish countries with different income levels,
each country’s quartiles of ppp-adjusted total gross income were calculated. Imputations for
Israel were not available, so Israel was not included in the final pooled model, but only at the
country level, where the final model excluding the income variable was estimated. In order to
control for various chronic diseases, a three-level-variable was included that distinguished: (1)
no chronic diseases, (2) mild chronic diseases (i.e. high blood pressure, high blood
cholesterol, diabetes, asthma, osteoporosis, stomach, duodenal or peptic ulcer, cataracts or hip
fracture), and (3) severe chronic diseases (heart attack and chronic lung disease). These
categories of ill health might affect cognitive performance and central executive function.
Age and education were input factors for the stochastic frontier function. Age was
measured in years. The educational level of each respondent was measured by the
International Standard Classification of Education (ISCED-97) of the amount received
(United Nations Educational, Scientific and Cultural Organization 1997). The ISCED-97
classification has seven levels (0 to 6), ranging from pre-primary level of education (e.g.
kindergarten) to the second stage of tertiary education (Ph.D.). We recoded the ISCED codes
into four broader education levels: ‘low’ (pre-primary education, ISCED 0 and 1), ‘medium’
(lower secondary education, ISCED 2), ‘high’ (upper secondary or post-secondary non
tertiary education, ISCED 3 and 4) and ‘very high’ (first and second stage of tertiary
The descriptive results for number of words recalled clearly indicate a decline of cognitive
functioning with increasing age (see Engelhardt et al. 2008). To see whether the association
between age and recall was similar in all countries, the mean numbers of words recalled for
all countries were plotted separately. Figure 2 depicts the decline with age and shows that the
decline was observed in all countries but that the level at age 50 years and the magnitude of
the decline varied. The recall score was especially low in Italy, Spain and Greece, which
might reflect the relatively low educational level among older people in these countries.
Figure 2 shows the greater variation with increasing age in cognitive performance in Austria,
Denmark, Sweden and Italy, as well as generally large variation in Switzerland and Denmark.
The larger variation is partly explained by the small number of respondents in the
corresponding age groups and countries. For example, the Swiss sample was the smallest
with 713 respondents, followed by Denmark with 1,171. The country with the largest
analysed sample was Belgium, with 2,713 men and women aged 50-79 years.
To estimate the basic stochastic frontier function for the variable recall, at the first step
we included age-squared and the level of education. The estimated coefficients of this first
model (Model 1) are shown in Table 1. Both age and education had a significant effect on the
frontier function. As expected, education was an important factor for cognitive performance
among the aged. The estimated coefficients were highly significant and indicated that the
better the cognitive functioning, the higher the educational level. Summing up, the cognitive
reserve frontier estimated as a function of age and educational level can be considered as a
good benchmark with respect to which individual cognitive performance can be assessed.
The one-sided test for the presence of an inefficiency term detected a statistically significant
effect, so inefficiency was modelled as a function of behavioural risks, social participation
and control variables for economic circumstances and health, as described above.
Model 2 of Table 1 includes a relative income measure and chronic diseases as well as
the following four aspects of behavioural risks: physical activities, BMI, smoking and
drinking. The additionally included coefficients for relative economic situation and chronic
diseases as well as those for behavioural risks were significant. It has to be stressed that
estimated negative coefficients can be interpreted as the actual cognitive performance being
closer to the stochastic frontier and therefore indicating a better cognitive performance.
Conversely, positive coefficients indicate a greater distance to the optimal curve, i.e. to the
best practice curve, and thus indicate inferior cognitive performance. Contrary to the notation
in regression models, the coefficients of the factors explaining the distance to the optimal
curve have different signs. This is because the term Z δ is subtracted in Equation 6.
Income was significantly associated with cognitive functioning: the higher the income
quartile of a respondent, the better their cognitive ability and the lower the distance to the
optimal performance given age and education. As described earlier, the quartiles refer to the
ppp-adjusted total gross income within a country and not to quartiles for the total sample of
12 countries. Chronic diseases, especially severe chronic disease were also significantly
correlated with lower cognitive performance. Physical activities were associated with better
cognitive functioning as individuals who kept up some moderate or even vigorous activities
were also closer to the frontier function compared to those with no physical activities. The
estimated coefficients for a BMI of 25 or higher and for drinking more than the recommended
levels of alcohol (i.e. drinking more than two glasses of any alcohol almost every day or five
to six days a week) indicated that being overweight or obese as well as elevated alcohol
consumption increased the distance to the frontier function of optimal cognitive functioning.
Surprisingly, smoking had a slight positive and even highly significant effect on cognition.
This result may be due to selection bias in the cross-sectional dataset. Selection could be
caused by an increasingly higher mortality of smokers with age and a positive selection of the
smokers in the survey with respect to cognitive ability. With the additional control of social
involvement (Model 3), the effect of smoking turned in the expected direction. A different
measurement for smoking that distinguished between: (1) people who never smoked over a
period of one year at least one cigarette, cigar or pipe, (2) former smokers, and (3) current
Finally, different dimensions of social involvement were added. More exactly, we
included indicators for being employed, attending educational courses, doing voluntary or
charity work, providing help to family, friends or neighbours, participating in a sports, social
or other club, participating in a religious organisation and participating in a political or
community organisation. The estimated coefficients of the seven dimensions of social
involvement were significantly negative and therefore indicated that individuals engaged in
social activities were closer to the optimal frontier curve as compared to those not engaged
(Table 1, Model 3). In addition, the estimates for the standard deviations of the two error
σ indicated that most of the variation was through technical
inefficiency u , not measurement error v , as the corresponding standard deviation 2
0 04 . In other words, most of the variation was through systematic
inefficiency and not due to measurement errors.
In order to detect possible gender differences in the association between behavioural
risks as well as social involvement and the variable recall, models for men and women were
run separately (Table 2). For both sexes, all coefficients for the social involvement indicators
were negative, thus indicating that social involvement is associated with better cognitive
performance. Except for being employed and doing voluntary work, the association between
social involvement and cognition was stronger among women than among men, the
corresponding coefficients being larger in absolute value. Turning to behavioural risks, the
estimates indicate that the association between cognitive ability and overweight was stronger
among women, whereas the association with excessive consumption of alcohol was more
pronounced among men. Moreover, the surprisingly positive association between smoking
and cognitive ability was partly neutralised by the findings that it applied only for women.
For men, the association between smoking or having smoked over a period of at least one year
at least one cigarette, cigar or pipe daily on the one hand and the number of words recalled on
the other, was negative in the sense that smoking associated with worse cognitive
performance. The estimated coefficient was positive, indicating a greater distance to the
optimal frontier for smokers. Interestingly, smoking decreased the distance to the frontier
Turning to the control variables for health, mild chronic diseases seem to have a
stronger impact among women than men. The diseases included into this category are: high
blood pressure, high blood cholesterol, diabetes, asthma, osteoporosis, stomach, duodenal or
peptic ulcer, cataracts or hip fracture. The descriptive results show that mild chronic diseases
were more frequent among women than men (55 compared to 45 per cent). Severe chronic
diseases (heart attack and chronic lung disease) were more frequent among men than women
(16 versus 11 per cent) and to a higher degree associated with low cognitive performance.
The association between income and cognitive performance was evident among men with a
ppp-adjusted total gross income above the median. The stepwise inclusion of the variables
showed that part of the effect of income was absorbed by social involvement among men,
indicating an interaction between income, social involvement and cognition. Among women,
the association between income and cognition was less pronounced in size and direction.
Finally, the stochastic frontier approach was run for all countries separately. Unfortunately,
the models did not converge for Denmark and Sweden. Nevertheless, the graphs representing
the mean number of words recalled (Figure 1) show for Denmark and Sweden a pattern
similar to the other countries. Despite the different signs of the coefficients for age and
education, we found a decline in cognitive performance with age in all countries. The
estimated effects were significant for all countries. Moreover, we found the expected higher
cognitive performance with higher educational levels, except in Israel and Switzerland for
people in the ISCED 3-4 group. In all countries these coefficients are highly significant.
Concerning the potential factors affecting individuals’ sub-optimal performance, or
distances to the estimated frontier, we found for all countries with the exception of Israel
significant negative effects for being employed. Thus, in almost all countries, being
employed reduced the individual distance from the best possible performance given a certain
age and educational level. Also the exercise of physical activities, whether vigorously or
moderately, had a positive effect on cognitive reserve, again with Israel being the only
exception. As regards being overweight or obese, smoking and drinking, the country-specific
results were generally consistent with the general expectation. In Austria, a high BMI
appeared significantly to favour cognitive performance. For smokers, cognitive performance
seemed to be closer to the optimal level in Belgium and Italy, while it appeared significantly
In accordance with our expectations, the employed and those with further training
showed cognitive performances closer to the optimal level than those who were not employed
(with the exception of Israel for employment, where we did not find a significant effect). The
other forms of social involvement had more disparate effects on cognitive performance.
Voluntary or charity work did not bring about the expected results in Austria, Greece and
Switzerland. Giving help to family, friends or neighbours had no positive effect on cognitive
reserve in Spain. Taking part in a sports or social club did not seem to help in Spain or
Switzerland, and being active in a religious organisation associated with significantly sub-
optimal performance in Austria, Spain and Switzerland. Finally, being active in a political
organisation increased the distance to the cognitive frontier in Germany, Italy and The
Netherlands. Thus although we obtained the expected signs for the pooled sample, the
country-specific results differed and need further consideration.
Discussion
Emerging research is increasing our understanding of the potentially modifiable factors
associated with cognitive decline in later life, and several interventions for preventing
cognitive decline and dementia in old age are being evaluated: early detection, lifestyle
factors, management of medical morbidities as well as pharmaceutical approaches (Filit et al.
2002). The idea of lifestyle management is to promote brain reserve through lifelong
learning, social involvement and occupational complexity. Social detachment is an
independent risk factor for cognitive decline among cognitively intact older people (Bassuk,
Glass and Berkman 1999). Berkman et al. (2000) suggested that social involvement most
likely challenges individuals to communicate and participate in exchanges that stimulate
cognitive capacities. Maintenance of social involvement and avoidance of social isolation
may be important in maintaining cognitive vitality in old age.
In this paper we have used a parametric stochastic frontier approach to estimate the
impact of social involvement as well as behavioural risk factors on cognitive reserve and
vitality in ageing among persons aged 50 or more years in 11 European countries and Israel.
For this purpose we used the individual data collected during the first wave of SHARE in
2004. Using large-scale samples, we tested the hypothesis that the association between
cognitive ability on the one hand and social involvement and behavioural risks on the other
hand is the same in different countries. Using comparable data for the 12 different countries,
the results support this hypothesis. In this respect, our comparative study adds significantly to
In the pooled sample, the results clearly show that individuals’ cognitive reserve is
driven mainly by age and by educational level. At the same time, all different forms of social
involvement increase cognitive functioning, in particular the continuation of occupational
activities. Moreover, behavioural risks such as physical inactivity, being overweight or obese,
smoking or drinking clearly do not favour cognitive performances. The country-specific
results, however, vary for single countries with respect to signs for most indicators of social
involvement and behavioural risks. Cultural differences are clearly important in any
international and cross-cultural analysis. Although cross-cultural surveys allow comparative
ageing research, problems of comparability of behavioural and psychological phenomena may
arise (Tesch-Römer and von Kondratowitz 2006). People from different cultural backgrounds
might understand and interpret terms and concepts differently, which might cause variation
across the participating countries (Bardage et al. 2005). The current study takes into account
various aspects and therefore the differences in cognitive functioning might be due to
methodological or cultural biases, but of course they could also indicate true differences
between countries. In the context of cross-cultural analysis, Börsch-Supan, Hank and Jürges
(2005), and in more detail Jürges (2007), have addressed the role of reporting styles, their
impact on cross-country differences in self-assessed health and comparability of health
measures. Using a standardised health index, they found that Scandinavians (Danes and
Swedes in particular) have a more positive attitude towards their health and tend to
systematically overrate their health as compared to the SHARE average.
In the current study, the explanatory variable (cognition) but also the control variables
(behavioural risks, health) might also be distorted by cultural biases. Tesch-Römer and
Kondratowitz (2006) referred to the translation problem and the possibility of transferability
of meaning for cross-cultural analyses. Our study focused on cognitive functioning, more
exactly on the number of words recalled out of a list of the following ten items: butter, arm,
letter, queen, ticket, grass, corner, stone, book, stick. Although these items occur in everyday
life, they might be perceived differently in the various countries. It is conceivable that the
connotation, occurrence and frequencies, and the associations among these words vary by
country (and language). For example, the word ‘queen’ might have distinctive connotations
in countries like The Netherlands, Spain and Sweden, where monarchs still have
constitutional functions and living exemplars. The association with a living person might
make it easier to remember the word ‘queen’ in the cognitive function test. Another example
is hat in Spain butter is hardly ever used and therefore the word might be more difficult to
recall. Then again, it might have been that when the SHARE data were collected, the price of
butter was in the news more in some countries than others, and therefore the word ‘butter’
might be more easily remembered in those countries. Ideally, test conditions should be
identical at each session at the same time of day in the same room (Rasmussen et al. 2001),
but in an international project involving over 30.000 respondents, such conditions cannot be
achieved. There may also be variation at the interviewer level, as through different accents,
reading tempos and audibility. Although interviewers had strict instructions in SHARE, total
exclusion of personal traits and characteristics was impossible. To sum up, distortions and
biases may occur at the level of the respondent, of the interviewer and of the country.
The current study might include cohort effects, especially with regard to education.
Older cohorts might have lower scores in cognition due to a higher percentage of persons with
low education. The increasing access to higher education during recent decades might have
resulted in better cognitive performance of younger cohorts. Therefore, it has to be
underlined that the study is based on cross-sectional data and not on longitudinal data, the
association between age and cognitive performance might partly be explained by cohort
effects and the decrease with age might be smaller compared to the current estimation. Given
the cross-sectional framework of the study, we have to be careful with causal inferences.
Thus we can not say whether socially more active persons have better cognitive performance
or whether persons with better cognitive performance are socially more active. Longitudinal
studies, however, clearly indicate that the relationship between social participation and
cognitive capabilities works in the former way. SHARE is a longitudinal project and further
waves will enable us to produce a causal statement regarding social participation and
cognitive ageing. Further longitudinal analysis may also help us to disentangle some of the
Despite these caveats, the results of the presented analyses clearly indicate that
increased variation of cognitive decline at older ages may not be an argument against
encouraging older workers to remain longer in the workforce. Our results suggest that social
involvement—in particular occupational activities—positively correlate with cognitive
ability. Though we cannot discern any causality from the cross-sectional results, the findings
encourage a focus on the underlying correlates of cognitive variability in old age. The
variation of social involvement and behavioural risk factors will in the end determine the
feasibility of more people working to older ages.
These results so far indicate that all kinds of social involvement increase cognitive
functions. It is in particular the continuation of occupational activities that illustrates the
potential effect on personal cognitive functions of reforms trying to encourage aged workers
to remain active in most European countries. Besides, behavioural risks such as physical
inactivity, obesity, smoking or drinking are clearly detrimental to cognitive performance. A
tentative conclusion of our study is that investing in continued education and fostering social
involvement at older ages may indeed help to keep up cognitive abilities at older ages, thus
increasing the feasibility and practicability of increasing labour force participation at higher
Acknowledgements
SHARE data collection was funded primarily by the European Commission through the 5th
Framework Research and Development Programme (project QLK6-CT-2001-00360 in the
thematic programme Quality of Life). Additional funding came from the United States
National Institute on Aging (NIA) (U01 AG09740-13S2, P01 AG005842, P01 AG08291, P30
AG12815, Y1-AG-4553-01 and OGHA 04-064). Data collection in Austria (through the
Austrian Science Foundation, FWF, grant number P-15422), Belgium (through the Belgian
Science Policy Office) and Switzerland (through BBW/OFES/UFES) was nationally funded.
The SHARE data collection in Israel was funded by NIA (R21 AG025169), by the German-
Israeli Foundation for Scientific Research and Development (G.I.F) and by the National
Insurance Institute of Israel. Further support by the European Commission through the 6th
Framework Programme (projects SHARE-I3, RII-CT-2006-062193 and COMPARE, 028857)
In the STATA analysis software (see http://www.stata.com/), this option can only be
used with the truncated normal which can have a zero mean. A comparison between
the basic model (with age and education only) for half-normally distributed and
truncated-normally distributed technical inefficiency reveals almost identical results.
Therefore the results are stable and do not depend on a specific distribution of the
inefficiency. Moreover, in the model with half-normally distributed technical
inefficiency we also included heteroscedasticity—for the measurement error v as
well as for the technical inefficiency component—based on the log of age in years
which implies different variance over age. Both for the error term and for technical
inefficiency we found heteroscedasticity in the data, therefore the error term and
technical inefficiency have no constant variance and cognitive functioning displays a
greater variability with increasing age. In the case of a truncated-normal distribution,
Stata does not allow the heteroscedasticity to be specified.
The exact wording of the four questions was: (1) ‘If the chance of getting a disease is
10 per cent, how many people out of 1,000 (one thousand) would be expected to get
the disease?’ (2) ‘In a sale, a shop is selling all items at half price. Before the sale, a
sofa cost €300. How much will it cost in the sale?’ (3) ‘A second-hand dealer is
selling a car for €6,000. This is two-thirds of what it costs new. What is the cost of a
new car? (4) ‘Let’s say you have €2,000 in a savings account. The account earns 10
per cent interest each year. How much would you have in your account at the end of
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Henriette Engelhardt-Woelfler, Department of Population Studies, Otto Friedrich University Bamberg, Lichtenhaidestr. 11, D-96045 Bamberg, Germany E-mail: henriette.engelhardt-woelfler@uni-bamberg.de
Figure 1. The stochastic frontier function
Figure 2. Mean number of words recalled by age and country
Source: SHARE 2004 Release 2.0.1, weighted data, own calculations
TABLE 1. Estimated coefficients of a stochastic frontier model including behavioural risks and social involvementFrontier:
ln(age) 4.75*** 3.79*** 4.33*** (ln(age))² -0.65*** -0.52*** -0.58*** ISCED 0-1
Factors explaining the distance: Notes: Reference categories: ISCED 5-6; 1st income quartile; no chronic diseases; hardly ever or never vigorous or moderate activities; BMI<25; never smoking over a period of one year at least one cigarette, cigar or pipe a day; drinking less than two glasses of alcohol almost every day or 5-6 days a week; not employed; not attending an educational course; not engaged in voluntary or charity work; no provision of help to family, friends or neighbours; no involvement in sports or other social club; no participation in a religious organisation; no participation in a political organisation. * significant at the 5 per cent level, ** significant at the 1 per cent level, *** significant at the 0.1 per cent level. Since income at the household level is not yet available for Israel, Models 2 and 3 do not include Israel, explaining the lower number of absolute records in Models 2 and 3. Significance level: *** p < 0.01 Data source: SHARE 2004 Release 2.0.1, weighted data, own calculations.
TABLE 2. Estimated coefficients of a stochastic frontier model, by gender Frontier:
ln(age) 0.26*** 6.62*** 0.58*** 7.16*** (ln(age))² -0.09*** -0.86*** -0.12*** -0.92*** ISCED 0-1
Constant 2.51*** -10.54*** 1.60*** -11.79***
Factors explaining the distance:
Smoking 0.16*** -0.76*** 0.19*** -0.57*** Drinking 0.43*** 0.20*** 0.31*** 0.14***
Constant -1.16*** -1.37*** -0.56*** -0.74***
Notes: Reference categories: ISCED 5-6 (see text); 1st income quartile; no chronic diseases; hardly ever or never vigorous or moderate activities; BMI<25; never smoking over a period of one year at least one cigarette, cigar or pipe a day; drinking less than two glasses of alcohol almost every day or 5-6 days a week; not employed; not attending an educational course; not engaged in voluntary or charity work; no provision of help to family, friends or neighbours; no involvement in sports or other social club; no participation in a religious organisation; no participation in a political organisation. Income at the household level was not available for Israel, which explains the lower number of absolute records in Models 2 and 3. Significance level: *** p < 0.01
Data source: SHARE 2004 Release 2.0.1 (see text). Weighted data, own calculations.
TABLE 3. Estimated coefficients of a stochastic frontier approach by country
1.66 3.62 3.54 -2.38 13.60 -4.22 8.38 8.20 18.26 -1.11
-0.27 -0.50 -0.49 0.24 -1.72 0.41 -1.10 -1.02 -2.31 0.10
-1.04 -0.18 -0.16 -0.24 -0.18 0.00 -0.28 -0.18 -0.28 -0.10
-0.13 -0.05 -0.08 -0.16 -0.15 -0.03 -0.21 -0.03 -0.19 -0.04
-0.02 -0.06 -0.05 -0.10 -0.03 0.06 -0.18 -0.01 -0.09 0.01
-4.52 -4.35 7.73 -24.89 12.29 -13.85 -14.40 -33.90 4.82
-0.21 -0.06 -0.07 1.07 0.10 0.18 -0.15 -0.33 -0.04 1.66
0.59 0.23 0.38 1.13 2.01 0.59 -0.02 -0.14 0.17 1.30
-1.90 -0.48 -0.56 -2.53 -1.12 0.40 -0.07 -1.15 -0.20 -3.35
-1.65 -0.57 -1.19 -4.43 -1.44 0.32 -0.23 -1.62 -0.42 -2.48
-0.18 0.11 0.20 1.71 0.77 0.07 0.21 0.43 0.04 3.53
0.17 -0.17 0.26 0.94 0.29 0.06 -0.19 0.52 0.02 4.87
0.33 0.03 0.06 2.09 1.18 0.12 0.10 0.54 -0.00 5.90
-0.43 -0.91 -0.14 -1.85 -1.28 0.00 -0.34 -1.88 -0.17 -10.39
-0.56 -1.85 -0.80 -2.84 -0.13 -0.75 -1.51 -2.52 -0.64 -0.37
-0.53 -0.57 1.48 -1.11 -0.08 -1.65 -0.17 1.57
Help to family, friends or neighbours -0.07
-0.34 -0.53 -0.92 -0.44 -0.06 -0.13 -1.13 -0.01 -3.00
-0.88 -1.09 -0.13 -0.92 -1.78 0.17 -4.69
0.48 -0.75 -0.70 -3.17 0.00 -0.01 -0.89 -1.40 0.10 5.05
-0.93 -0.19 -1.09 1.49 -2.14 -0.75 0.39 1.31 -0.80 -3.52
-1.16 -0.89 -0.77 -5.71 -3.78 -0.92 -0.31 -3.57 0.47 -23.43
1,433 2,612 2,008 2,308 2,120 1,905 1,986 2,146 1,649 685
Notes: D: Germany. NL: Netherlands. CH: Switzerland. Reference categories: ISCED 5-6 (see text); 1st income quartile; no chronic diseases; hardly ever or never vigorous or moderate activities; BMI<25; never smoking over a period of one year at least one cigarette, cigar or pipe a day; drinking less than two glasses of alcohol almost every day or 5-6 days a week; not employed; not attending an educational course; not engaged in voluntary or charity work; no provision of help to family, friends or neighbours; no involvement in sports or other social club; no participation in a religious organisation; no participation in a political organisation. Since income at the household level was not available for Israel, that analysis did not include an economic variable. Significance levels: All non-zero coefficients are significant at p <0.01, except one: the frontier constant for Austria (-0.29) is not significant.
Data source: SHARE 2004 Release 2.0.1 (see text and Acknowledgements). Weighted data, own calculations.
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Figure 1. The stochastic frontier function
Figure 2. Mean number of words recalled by age and country
Source: SHARE 2004 Release 2.0.1, weighted data, own calculations
TABLE 1. Estimated coefficients of a stochastic frontier model including behavioural risks and social involvement
Frontier: