Bayesian Ridge Estimation of Age-Period-Cohort Models

Minle Xu, University of Texas at Austin
Daniel A. Powers, University of Texas at Austin

Age-Period-Cohort (APC) models offer a useful framework to study trends of time-specific phenomena. Yet the perfect linear relationship among age, period, and cohort brings about the identification issue. Multiple methods have been proposed to cope with the identification issue, e.g., the intrinsic estimator (IE) and the ridge estimator. This study views the ridge estimator from a Bayesian perspective by introducing a prior distribution(s) for the ridge parameter(s). Results indicate that a Bayesian ridge model with a common prior for the ridge parameter yields estimates of age, period, and cohort effects similar to those based on the IE and a ridge estimator. The performance of Bayesian models with distinctive priors for the ridge parameters of age, period, and cohort effects is affected more by the choice of prior distributions. In sum, a Bayesian ridge model provides an effective way to deal with the identification problem of APC model.