Age, period, and cohort models. Non-overlapping cohorts don't resolve the identification problem

Age, period, and cohort models have generally been applied to rates from tabulated national statistics, and it is known that such models suffer from an identification problem. When individual records, including date of birth, are available, however, a unique solution has been proposed which uses non-overlapping cohorts. We have shown that the identification problem exists in continuous time, so that even perfect information on the three variables will fail to resolve it. It is important to recognize clearly the assumptions that are implicit in the non-overlapping cohort formulation of the age-period-cohort model. The value of the solution proposed depends critically on their appropriateness or otherwise. It should always be remembered that the assumptions determine much of the final solution, including the apportionment of trend to the different components, age, period, or cohort.