When searching for a solution to the age, period and cohort (APC) identification problem, applied researchers sometimes consider Bayesian methods as a potential answer, with its focus on distributions rather than point estimates and the use of prior knowledge to inform which estimates are used. I argue that many of the methods sold as solutions to the identification problem (such as the Hierarchical APC model or ridge regression) can in fact be formulated in a Bayesian framework, with priors that make the model identified. However, these prior distributions are implicit, obscuring the fact that very strong priors over the linear trends are required for identification.

In this chapter the author I demonstrate a general framework for Bayesian APC modeling, and examines several major types of Bayesian APC models based on four main kinds of priors over the temporal trends. The advantage of this framework is that, by introducing (presumably realistic or theory-driven) priors, we can avoid the problems with imposing (often) arbitrary priors via methods that are not explicitly Bayesian. Moreover, various priors can be combined and contrasted to evaluate competing theories. He I demonstrate this approach by applying informative priors to temporal trends in political party identification in the United States. The framework outlined brings theoretical considerations and assumptions to the front and center, so they can be evaluated transparently.