Table 1.
Key papers (and arguments made) in the debate around the HAPC model
| Paper | Argument |
|---|---|
| Yang (2006) | Argues the HAPC model can be used in a Bayesian framework. Uses real data on verbal test scores, and simulations (note that the latter’s DGPs have only independent and identically distributed Normal random variation to generate the period and cohort effects). [51 cites in Google Scholar as of 8th Feb 2017] |
| Yang and Land (2006) | Argues the treatment of age as quadratic in the HAPC model solves the identification problem. Example using real data on verbal test scores [233] |
| Yang and Land (2008) | Uses the Hausman test (on multiple parameters) to test if fixed or random effects should be used for the period and cohort terms. Example using real data on verbal test scores [237] |
| Yang and Land (2013a) | Book argues the different treatment of age (fixed) and period/cohort (random) “completely avoids” (p. 70) the identification problem. Uses various real data sources to illustrate this [132] |
| Bell and Jones (2014a) | Argues with simulations that the HAPC model is not good at recovering DGPs in the presence of linear effects |
| Bell and Jones (2014c) | Argues that results can be reproduced using a completely different DGP do that suggested by those results |
| Reither et al. (2015b) | Argues that linear effects do not occur in real-life data, and thus that the model works for real data (this is illustrated, ironically, with simulations) |
| Bell and Jones (2015b) | Argues with simulations that even when the DGP does not include exactly linear effects, the HAPC model does not work |
| Reither et al. (2015b) | Argues that model fit statistics, and descriptive and modelled graphics, should be used to judge whether the HAPC model is appropriate for use |
| Luo and Hodges (2016) | Argues that grouping cohorts in different ways can produce arbitrarily different results, using simulations |
| O’Brien (2016) | Demonstrates why treating one or more of APC as random effects allows models to be identified, but shows that the solution that is arrived at is an artefact of the way the log likelihood is maximized |
| Fienberg et al. (2015) | Responding to a positive book review they contend that “Yang and Land’s approaches really are no different from previous attempts to resolve the APC identification problem insofar as they impose constraints on the estimated age, period, or cohort effects; the constraints are simply hidden in the technical details of their methodology” (p. 457) |
Papers with Reither or Yang as first author are proponents of the model, others are for the most part critical of it
A somewhat parallel debate also exists on Yang and Land’s Intrinsic estimator as a means of tackling the problem (see Pelzer et al. 2015; Te Grotenhuis et al. 2016; Yang and Land 2013b; Luo 2013a, b; Luo et al. 2016)