The ( im )possibility of separating age, period and cohort effects - PowerPoint Presentation

1. The (im)possibility of separating age, period and cohort effectsAndrew BellAndrew.bell@bristol.ac.ukSchool of Geographical SciencesNCRM Research Methods Festival, Oxford, July 2014

2. SummaryAge, period and cohort (APC) effectsThe APC identification problemThe HAPC modelWhy it doesn’t workExample: mental wellbeing

3. APC effectsA: 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)

4. APC identification problemAge = 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)

5. Impossible to isolate effectsCannot 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)

6. Consider these DGPsAll will produce exactly the same dataGiven that dataset, there is no logical way of telling which DGP created the datasetExact 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) 

7. Consider these DGPsAll will produce exactly the same outcome variableGiven that dataset, there is no logical way of telling which DGP created itExact 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) 

8. Multilevel model for individuals nested in cohort groups and periodsYang and Land’s HAPC modelCohortPeriodIndividual (Age)Health = Intercept + Age linear trend + Age quadratic trend + Cohort residual + Period residual + individual residual

9. Yang and Land’s HAPC modelClaimed that this breaks the colinearity byIncluding an age-squared term, and/orTreating 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 caseSee 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

10. 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, 176-180Obesity epidemic apparently the result of periods, not cohorts

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

12. Why model is enticingIntuitiveAging occurs within individualsCohorts are external – we belong to themPeriods are external – we pass from one into anotherMultilevel model, so has all the extensions that go with thatOther covariates at all levelsAdditional levels (eg individuals, neighbourhoods)Random coefficients

13. Our viewHAPC framework is valuable, but……Decision as to which of APC most likely caused the data should be made based on intuition and theoryAssumptions 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

14. Example – mental wellbeingPrevious consensus: life course of mental wellbeing is U-shaped, worsening to the ‘midlife crisis’ and then improving into old ageI argue that linear period trends are unlikely, and so constrain continuous period trends to zeroMental 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)

15. Example – mental wellbeing191019201930194019501960197019809.811.212.614.019385776Predicted GHQ ScoreAge

16. Example – mental wellbeing191019201930194019501960197019809.811.212.614.019385776Predicted GHQ ScoreAgeU-shape? But currently cohort is not controlled in this graph

17. MaleFemale810121420406080Predicted GHQ scoreAgeNo U-shape foundOther findings of U-shape result from older cohorts having better mental wellbeing (i.e. cohorts were not appropriately controlledFind mental wellbeing worsens throughout the life course.Example – mental wellbeing

18. Cohort effects combine quadratic trend with stochastic variationThose brought up during recessions have generally better mental health throughout their life course?MaleFemale9.010.512.013.51896192019441968Predicted GHQ ScoreBirth YearExample – mental wellbeing

19. ConclusionsBe 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 problemAssumptions about APC need to be made, be based on theory, and stated explicitly

20. For more informationBell, 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.2014.30.11Bell, 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, 176-180Bell, A and Jones, K (2013) Bayesian informative priors with Yang and Land’s Hierarchical age-period-cohort model. Quality and Quantity. DOI: 10.1007/s11135-013-9985-3For constraining parameters to something other than zeroBell, 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.netBell, 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 Burton-Jeangros, Stéphane Cullati, Amanda Sacker and David Blane. Springer.

21. Periods or Cohorts?For obesity –changing diets/exercise regimes/technologies etcPeriod effect – changes in culture affect everyone the sameCohort effect – changes effect the young in their formative yearsCould 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)

22. Periods or Cohorts?For mental wellbeing – changes in pace of life/working patterns/level of stigma/narcissismPeriod effect – changes in culture affect everyone the sameCohort effect – changes effect the young in their formative yearsEg 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