Two-sample Age-period-cohort Models

Age-period-cohort analysis is often done in the context of two samples. This could be samples for women and men or for two countries. It is of interest to ask if some time effects could be common across samples. We clarify how the well-known age-period-cohort problem for one sample carries over to the two sample situation. This is done through a reparametrization in terms of parameters that are invariant to the identification issues. The new parametrization shows which hypotheses can be tested and their degrees of freedom. Testable hypotheses can be formulated for non-linear effects, but not for the linear parts of the individual time effects. This conclusion remains when imposing cross-sample restrictions. The analysis is extended to the mixed frequency situation where age and period are measured at different scales. As an empirical illustration a study of Swiss suicide rates is revisited.