Another 'futile quest'? A simulation study of Yang and Land's Hierarchical Age-Period-Cohort model

BACKGROUND Whilst some argue that a solution to the age-period-cohort (APC), identification problem. is impossible, numerous methodological solutions have been proposed, including Yang and Land's Hierarchical-APC (HAPC) model: a multilevel model considering periods and cohorts as cross-classified contexts in which individuals exist.

OBJECTIVE To assess the assumptions made by the HAPC model, and the situations in which it does and does not work.

METHODS Simulation study. Simulation scenarios assess the effect of (a) cohort trends in the Data Generating Process (DGP) (compared to only random variation), and (b) grouping cohorts (in both DGP and fitted model).

RESULTS The model only works if either (a) we can assume that there are no linear (or non-linear) trends in periods or cohorts, (b) we control any cohort trend in the model's fixed part and assume there is no period trend, or (c) we group cohorts in such a way that they exactly match the groupings in the (unknown) DGP. Otherwise, the model can arbitrarily reapportion APC effects, radically impacting interpretation.

CONCLUSIONS Since the purpose of APC analysis is often to ascertain the presence of period and/or cohort trends, and since we rarely have solid (if any) theory regarding cohort groupings, there are few circumstances in which this model achieves what Yang and Land claim it can. The results bring into question findings of several published studies using the HAPC model. However, the structure of the model remains a conceptual advance that is useful when we can assume the DGP has no period trends.