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School of Geographical Sciences
The (im)possibility of separating
age, period and cohort effects
Andrew Bell
[email protected]
NCRM Research Methods Festival, Oxford, July 2014
Summary
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Age, period and cohort (APC) effects
The APC identification problem
The HAPC model
Why it doesn’t work
Example: mental wellbeing
APC effects
• A: I can’t seem to shake off this tired feeling. Guess I’m just
getting old. [Age effect]
• B: Do you think it’s stress? Business is down this year, and
you’ve let your fatigue build up. [Period effect]
• A: Maybe. What about you?
• B: Actually, I’m exhausted too! My body feels really heavy.
• A: You’re kidding. You’re still young. I could work all day
long when I was your age.
• B: Oh, really?
• A: Yeah, young people these days are quick to whine. We
were not like that. [Cohort effect]
(From Suzuki 2012:452)
APC identification problem
• Age = Period – Cohort
• “the term [confounded] is not used in the
traditional design sense of experimentally
confounded but in the stronger sense of
logically or mathematically confounded”
(Goldstein, 1979, 19)
Impossible to isolate effects
• Cannot hold age and cohort constant and vary
period (without time travel – Suzuki 2012)
– Goldstein 1979: “there is no direct evidence for
three distinct types of causal factors”
– Glenn 2005: “One of the most bizarre instances in
the history of science of repeated attempts to do
something that is logically impossible”
• If you have age in your model, you also have
period and cohort, and vice versa (whether
you like it or not)
Consider these DGPs
𝐻𝑒𝑎𝑙𝑡ℎ = (1 ∗ 𝐴𝑔𝑒) + (1 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑) + (1 ∗ 𝐶𝑜ℎ𝑜𝑟𝑡)
𝐻𝑒𝑎𝑙𝑡ℎ = (2 ∗ 𝐴𝑔𝑒) + (2 ∗ 𝐶𝑜ℎ𝑜𝑟𝑡)
𝐻𝑒𝑎𝑙𝑡ℎ = (2 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑)
• All will produce exactly the same data
• Given that dataset, there is no logical way of telling which
DGP created the dataset
• Exact collinearity from putting all three into a regression
model – model will not run.
• Grouping of one of APC breaks this collinearity, but
produces arbitrary results (that depend on the chosen
grouping)
Consider these DGPs
𝐻𝑒𝑎𝑙𝑡ℎ = (1 ∗ 𝐴𝑔𝑒) + (1 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑) + (1 ∗ 𝐶𝑜ℎ𝑜𝑟𝑡)
𝐻𝑒𝑎𝑙𝑡ℎ = (2 ∗ 𝐴𝑔𝑒) + (2 ∗ 𝐶𝑜ℎ𝑜𝑟𝑡)
𝐻𝑒𝑎𝑙𝑡ℎ = 0 ∗ 𝐴𝑔𝑒 + (2 ∗ 𝑃𝑒𝑟𝑖𝑜𝑑)
• All will produce exactly the same outcome variable
• Given that dataset, there is no logical way of telling which
DGP created it
• Exact collinearity from putting all three into a regression
model – model will not run.
• Grouping of one of APC breaks this collinearity, but
produces arbitrary results (that depend on the chosen
grouping)
Yang and Land’s HAPC model
Multilevel model for individuals nested in cohort groups and periods
Period Cohort
Individual (Age)
Health = Intercept
+ Age linear trend + Age quadratic trend
+ Cohort residual
+ Period residual
+ individual residual
Yang and Land’s HAPC model
• Claimed that this breaks the colinearity by
– Including an age-squared term, and/or
– Treating age in a different way to periods/cohorts
• “the underidentification problem of the classical APC accounting
model has been resolved by the specification of the quadratic function
for the age effects” Yang and Land (2006:84)
• "An HAPC framework does not incur the identification problem
because the three effects are not assumed to be linear and additive at
the same level of analysis" Yang and Land (2013:191)
• "This contextual approach ...helps to deal with (actually completely
avoids) the identification problem" Yang and Land (2013:71)
• Unfortunately this is not the case
– See Bell, A and Jones, K (2014) Another futile quest? A simulation study of Yang
and Land’s Hierarchical age-period-cohort model. Demographic Research, 30, 11,
333-360. DOI: 10.4054/DemRes.2014.30.11
Obesity epidemic
apparently the
result of periods,
not cohorts
Bell, A and Jones, K (2014) Don’t birth cohorts matter? A commentary and simulation
exercise of Reither, Hauser and Yang’s age-period-cohort study of obesity. Social Science
and Medicine, 101, 176-180
Bell, A and Jones, K (2014) Don’t birth cohorts matter? A commentary and simulation
exercise of Reither, Hauser and Yang’s age-period-cohort study of obesity. Social Science
and Medicine, 101, 176-180
Why model is enticing
• Intuitive
– Aging occurs within individuals
– Cohorts are external – we belong to them
– Periods are external – we pass from one into another
• Multilevel model, so has all the extensions that
go with that
– Other covariates at all levels
– Additional levels (eg individuals, neighbourhoods)
– Random coefficients
Our view
• HAPC framework is valuable, but……
• Decision as to which of APC most likely caused the data
should be made based on intuition and theory
• Assumptions constraining one of the parameters (often
to zero) should be made explicitly (so it can be
challenged)
• E.g. to constrain the period effect to zero:
Health = Intercept
+ Age linear trend + Age quadratic trend …
+ Cohort linear trend + cohort quadratic trend …
+ Cohort residual
+ Period residual
+ individual residual
Example – mental wellbeing
• Previous consensus: life course of mental
wellbeing is U-shaped, worsening to the ‘midlife
crisis’ and then improving into old age
• I argue that linear period trends are unlikely, and
so constrain continuous period trends to zero
• Mental wellbeing measured by GHQ score, using
data from the BHPS 1991-2008.
• Additionally add higher levels (individuals, local
authority districts, households), random
coefficients, covariates, interactions (for more details see
Bell, 2014)
Example – mental wellbeing
Predicted GHQ Score
14.0
12.6
1920
1960
1970
1910
1950
1930
1940
11.2
1980
9.8
19
38
57
Age
76
Example – mental wellbeing
Predicted GHQ Score
14.0
12.6
1920
1960
1970
1910
1950
1930
1940
11.2
1980
9.8
19
U-shape? But
currently cohort
is not controlled
in this graph
38
57
Age
76
Example – mental wellbeing
Female
14
Male
Predicted GHQ score
No U-shape found
• Other findings of Ushape result from
older cohorts having
better mental
wellbeing (i.e.
cohorts were not
appropriately
controlled
• Find mental
wellbeing worsens
throughout the life
course.
12
10
8
20
40
60
Age
80
Example – mental wellbeing
13.5
Female
12.0
Predicted GHQ Score
• Cohort effects
combine
quadratic trend
with stochastic
variation
• Those brought up
during recessions
have generally
better mental
health
throughout their
life course?
Male
10.5
9.0
1896
1920
1944
Birth Year
1968
Conclusions
• Be careful. If you are interested in any of APC,
be aware of the APC identification problem.
• If you have age in your model, you also have
period and cohort (and vice versa)
• There is no mechanical solution to the
problem
• Assumptions about APC need to be made, be
based on theory, and stated explicitly
For more information
• Bell, A and Jones, K (2014) Another futile quest? A simulation study of Yang
and Land’s Hierarchical age-period-cohort model. Demographic Research, 30,
11, 333-360. DOI: 10.4054/DemRes.2014.30.11
• Bell, A and Jones, K (2014) Don’t birth cohorts matter? A commentary and
simulation exercise of Reither, Hauser and Yang’s age-period-cohort study of
obesity. Social Science and Medicine, 101, 176-180
• Bell, A and Jones, K (2013) Bayesian informative priors with Yang and Land’s
Hierarchical age-period-cohort model. Quality and Quantity. DOI:
10.1007/s11135-013-9985-3
– For constraining parameters to something other than zero
• Bell, A (2014) Life course and cohort trajectories of mental wellbeing in the
UK, 1991- 2008 – a multilevel age-period-cohort analysis. Under review,
available on researchgate.net
• Bell, A and Jones, K (forthcoming) Age, period and cohort processes in
longitudinal and life course analysis: a multilevel perspective. In A life course
perspective on health trajectories and transitions, edited by Claudine BurtonJeangros, Stéphane Cullati, Amanda Sacker and David Blane. Springer.
Periods or Cohorts?
• For obesity –changing diets/exercise
regimes/technologies etc
– Period effect – changes in culture affect everyone
the same
– Cohort effect – changes effect the young in their
formative years
– Could look at age effect – which is the most likely?
(I think the one associated with cohorts)
– A cohort effect could cause a period effect? (eg
parents/overall culture influenced by their
children)
Periods or Cohorts?
• For mental wellbeing – changes in pace of
life/working patterns/level of stigma/narcissism
– Period effect – changes in culture affect everyone the
same
– Cohort effect – changes effect the young in their
formative years
– Eg has everyone become more narcissistic? Or is
increasing narcissism in society the result of
narcissism amongst newer cohorts?
• I think the later is more plausible / has a clearer causal
mechanism