A Generalization of the Mechanism-based Approach for Age-Period-Cohort Models

Age-period-cohort models have a long history in epidemiology, social science, and econometrics. An important feature of these models is that they suffer from an inherent identifiability problem, due to the deterministic linear relation between age, period, and cohort. A proposed solution to this problem is the mechanism-based approach, which uses sets of mediators to identify the causal age, period, and cohort effects. Although this approach is conceptually general, previous literature has been limited to special cases and parametric identification. We derive a general nonparametric identification result, which is valid under explicit assumptions about the underlying data-generating mechanism and the set of mediators used for identification. We show how this identification result lends itself naturally to parametric estimation of the causal age, period, and cohort effects similar to the parametric G-formula estimation in causal inference.