IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
In the Age-Period-Cohort (APC) model log m(x,t) = a(x) + b(t−x) + c(t) style formulation, which identifiability problem arises when the age, period and cohort effects are all included as free parameters?
The identifiability problem arises because cohort year equals period minus age, making the three effects linearly dependent. Linear trends can be shifted among age, period and cohort terms without changing fitted mortality, so extra constraints are required to obtain unique parameter estimates.
- ACohort year equals period minus age, so the three effects are linearly dependent and linear trends cannot be separatedCorrect
- BThe model has more observations than parameters so it is overdetermined
- CAge effects cannot be estimated without a period effect
- DPoisson assumptions fail whenever a cohort effect is present
- Cohort effects always sum to zero automatically
Explanation
Because cohort = period − age exactly, a linear trend can be moved between the age, period and cohort terms without changing fitted rates. Hence constraints are needed to identify the parameters. The other statements are not the source of the problem.
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