The hierarchical age–period–cohort model: why does it find the results that it finds?

Andrew Bell*, Kelvyn Jones

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

68 Citations (Scopus)
363 Downloads (Pure)


It is claimed the hierarchical-age–period–cohort (HAPC) model solves the age–period–cohort (APC) identification problem. However, this is debateable; simulations show situations where the model produces incorrect results, countered by proponents of the model arguing those simulations are not relevant to real-life scenarios. This paper moves beyond questioning whether the HAPC model works, to why it produces the results it does. We argue HAPC estimates are the result not of the distinctive substantive APC processes occurring in the dataset, but are primarily an artefact of the data structure—that is, the way the data has been collected. Were the data collected differently, the results produced would be different. This is illustrated both with simulations and real data, the latter by taking a variety of samples from the National Health Interview Survey (NHIS) data used by Reither et al. (Soc Sci Med 69(10):1439–1448, 2009) in their HAPC study of obesity. When a sample based on a small range of cohorts is taken, such that the period range is much greater than the cohort range, the results produced are very different to those produced when cohort groups span a much wider range than periods, as is structurally the case with repeated cross-sectional data. The paper also addresses the latest defence of the HAPC model by its proponents (Reither et al. in Soc Sci Med 145:125–128, 2015a). The results lend further support to the view that the HAPC model is not able to accurately discern APC effects, and should be used with caution when there appear to be period or cohort near-linear trends.

Original languageEnglish
Pages (from-to)783-799
Number of pages17
JournalQuality and Quantity
Issue number2
Early online date24 Feb 2017
Publication statusPublished - 1 Mar 2018


  • Age–period–cohort
  • Hierarchical age period cohort model
  • Obesity
  • MCMC
  • Identification
  • Multilevel modelling

Cite this