  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.
