Systematic simulation of age-period-cohort analysis: Demonstrating bias of Bayesian regularization

Age-period-cohort (APC) analysis is one of the fundamental time-series analyses used in the social sciences. This paper evaluates APC analysis via systematic simulation in term of how well the artificial parameters are recovered. We consider three models of Bayesian regularization using normal prior distributions: the random effects model with reference to multilevel analysis, the ridge regression model equivalent to the intrinsic estimator, and the random walk model referred to as the Bayesian cohort model. The proposed simulation generates artificial data through combinations of the linear components, focusing on the fact that the identification problem affects the linear components of the three effects. Among the 13 cases of artificial data, the random walk model recovered the artificial parameters well in 10 cases, while the random effects model and the ridge regression model did so in 4 cases. The cases in which the models failed to recover the artificial parameters show the estimated linear component of the cohort effects as close to zero. In conclusion, the models of Bayesian regularization in APC analysis have a bias: the index weights have a large influence on the cohort effects and these constraints drive the linear component of the cohort effects close to zero. However, the random walk model mitigates underestimating the linear component of the cohort effects.