I probably need to start doing Ken-Ken puzzles for the numeracy portion. Your doctor better cure your aphasia so you can read as needed.
This really tells me nothing. Nothing on what reading and amounts to do or types of math problems to do. Useless!
Age and cognitive skills: Use it or lose it
Science Advances
5 Mar 2025
Vol 11, Issue 10
Abstract
Cross-sectional
age-skill profiles suggest that cognitive skills start declining by age
30 if not earlier. If accurate, such age-driven skill losses pose a
major threat to the human capital of societies with rapidly aging
populations. We estimate actual age-skill profiles from individual
changes in literacy and numeracy skills at different ages. We use the
unique German longitudinal component of the Programme of the
International Assessment of Adult Competencies (PIAAC-L) that retested a
large representative sample of adults after 3.5 years. Our empirical
approach separates age from cohort effects and corrects for measurement
error from reversion to the mean. Two main results emerge. First,
average skills increase strongly into the forties before decreasing
slightly in literacy and more strongly in numeracy. Second, skills
decline at older ages only for those with below-average skill usage.
White-collar and higher-educated workers with above-average usage show
increasing skills even beyond their forties. Women have larger skill
losses at older age, particularly in numeracy.
INTRODUCTION
The commonly accepted conclusion that cognitive skills decline with age starting rather early in adult life (1)
has increasingly important potential economic implications. Cognitive
skills measured by literacy and numeracy are closely related to
individual earnings (2–4) and national growth rates (5, 6), implying that the steady and marked changes in the age composition of societies (7)
might directly affect the economic well-being of nations. However, this
assumed skill pattern has largely come from cross-sectional data that
necessarily incorporate not only aging patterns but also cohort
differences in skills. If the negative age pattern is simply due to
conflating age and cohort effects, the economic concerns are
considerably lessened. Recently developed individual longitudinal skill
tests for a representative population of adults allow us to provide
evidence on actual changes in skills with age and on their relationship
with adult skill usage.
We study the
inevitability of age-driven skill decline using exceptional longitudinal
data for the German adult population. Administered by the Organization
for Economic Co-operation and Development (OECD), the Programme for the
International Assessment of Adult Competencies (PIAAC) tested literacy
and numeracy skills that are relevant for participation in social life
and work, and surveyed economic and social conditions for random samples
of the population aged 16 to 65 in 39 countries (8).
Germany, unique among all participating countries, created a panel of
participants from the PIAAC sample who were re-surveyed and retested 3.5
years after the original survey.
We use the
panel dimension of the data to estimate credible average age-skill
profiles for the adult population. Observing actual changes in adult
skills over the full age spectrum allows us to break the confounding of
age and cohort patterns that has been ubiquitous in general
cross-sectional analyses of adult skills. We estimate the average
annualized marginal changes in skills for each age and concatenate them
across individuals of different ages to derive full age-skill profiles.
However, the panel data introduce new methodological problems that must
be addressed before the analysis of age-skill patterns.
Creating
reliable age-skill patterns based on individual aging requires
addressing the bias from measurement errors that inevitably accompany
testing of skills over time. Observations of test scores include a
combination of true scores and measurement errors, leading to systematic
errors when looking at individual changes with age. Intuitively, low
observed test scores are more likely to include negative errors. When we
observe another assessment for an initially low-scoring individual, the
measurement error is unlikely to be as negative as the first time,
implying that the change in true test scores is biased upward for
low-scoring individuals. For initially high-scoring individuals, the
opposite will be true. This reversion to the mean will bias the overall
age-skill relationship when skills vary by age. Thus, we correct the
observed change in test scores throughout for reversion to the mean (9) to obtain error-adjusted age-skill patterns.
We
find that average (error-corrected) skills increase substantially into
the forties for both literacy and numeracy. Subsequently, average skills
decline slightly in literacy and strongly in numeracy. The averages,
however, mask important heterogeneity.
With
the appropriately adjusted age-skill profiles, we can further
investigate the role of skill usage. Previous analyses have considered
whether individual background or occupations influence the evolution of
age-skill patterns. These investigations of heterogeneity in age
patterns are generally motivated by assumed differences in skill usage
across groups, but data on skill usage have not typically been
available. Because the background data from the PIAAC survey provide
information on the detailed nature and frequency of participants’ skill
usage at work and at home, we are able to explore the demographic aging
patterns in greater depth.
Individuals with
above-average skill usage at work and home on average never face a skill
decline (at least until the limit of our data at age 65). Consistent
with the assumptions of prior studies, usage interacts closely with a
variety of background characteristics. Thus, both literacy and numeracy
skills keep increasing for white-collar and tertiary-educated workers in
the second half of their working life if they have above-median skill
usage, but not if skill usage is below the median. Skill evolution also
varies by gender: Women show steeper skill decline at older ages,
especially in numeracy.
The primary
contribution of our analysis to the literature on cognitive aging is the
development of rich age-skill profiles for literacy and numeracy
skills, skills which have been shown to have economic payoffs in the
labor market, using longitudinal variation in a large representative
sample. The data allow us to go beyond averages to consider important
dimensions of heterogeneity and to describe the connection of profile
differences with individual behavior and background. The studies closest
to our analysis use different large-scale representative surveys with
literacy and numeracy skills (1, 10),
but these do not track actual skill changes of individuals over time. A
parallel set of psychological and neuroscience studies offer related
estimates of age patterns and their sources, albeit for different
dimensions of skills and for nonrepresentative samples (11–16), but evidence on their relationship to the economic outcomes that motivate our work is lacking.
RESULTS
Average age-skill profiles
The starting point for our analysis comes from the cross-sectional picture of how cognitive skills vary with age. Figure 1Opens in image viewer
depicts adult literacy and numeracy skills by age in the PIAAC test for
representative population samples of all participating OECD countries
[see also (8, 17)].
In the cross section, average literacy and numeracy scores start
declining in the late twenties to early thirties. This pattern is
duplicated qualitatively for Germany, our analysis country, where
average literacy scores steadily fall from age 20, while numeracy scores
rise slightly before beginning to decline in the late thirties (fig.
S1).
Fig. 1. Cross-sectional age-skill profiles (OECD countries).
Cross-sectional
association between age and skills in PIAAC (2012). Dots: Average
skills by age. Line: Quadratic fit (estimated over 21 to 65 age range).
Skills measured in SD units. Sample: 25 OECD countries with continuous
age data; full population, ages 16 to 65, weighted by sampling weights (N = 147,667). Data source: PIAAC.
However,
it is difficult to interpret these cross-sectional patterns because
they conflate age and cohort effects. Individuals across different ages
also come from different cohorts and have thus experienced different
histories of skill determinants, implying that these charts fail to
describe the true patterns of the age-skill relationship over time for
any individual. As a result, they also cannot reliably be used to
understand the factors that feed into skill changes by age without
introducing strong assumptions about the nature of cohort and individual
time patterns.
The changes in observed
numeracy and literacy skills for individuals over time show a very
different pattern than suggested by the cross-sectional data. Figure 2BOpens in image viewer
depicts the annualized marginal changes in scores with age for
individuals at each age for the full German population sample (3263
observations). The analysis corrects for reversion to the mean, and it
includes a quadratic fit and 95% confidence intervals. The quadratic
prediction indicates increases in skills for individuals up to age 45 in
literacy and up to age 40 in numeracy. Skill changes turn negative
beyond these ages, with notably stronger declines for numeracy than for
literacy. In both subjects, the marginal change in skills declines
steadily with age. Initially, this decline is close to linear but
ultimately gets flatter.
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