IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
Which of the following is a known identifiability issue in the age-period-cohort model log m(x,t) = a(x) + b(t) + c(t-x), and how is it usually handled?
Because year of birth equals period minus age, the three effects are linearly dependent and a linear trend cannot be uniquely assigned among them. This is resolved by imposing constraints on the parameters, such as fixing sums or linear components of the effects.
- AAge, period and cohort are linearly dependent because cohort = period - age, so a linear trend cannot be uniquely attributed; constraints are imposed on the parametersCorrect
- BThe model cannot be fitted by maximum likelihood because the Poisson assumption is violated; a normal model is required
- CCohort effects are always zero for lives older than 65, so they are dropped
- DThere are too few parameters, so extra age terms are added
- Period effects are perfectly correlated with age effects, so period is removed entirely
Explanation
Since cohort = period - age, any linear trend can be shifted between the three effects, so the parameters are not uniquely determined. Extra constraints (for example on sums or linear trends of the cohort and period terms) are imposed. The other options misstate the issue.
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