Education Projections using Age-Period-Cohort Models: Classical and Bayesian Approaches

Abstract

The APC framework for modeling and forecasting the education profile of Brazilian males and females is considered from both classical and Bayesian perspectives. For a classical analysis, I calculate maximum likelihood estimates of APC parameters. For the Bayesian analysis, I estimate posterior means and credible intervals. Both methods are simple and computationally efficient. Results show that both classical and Bayesian methods are able to provide very good forecasts in the short term. However, the Bayesian method performed best for in-sample and out-of-sample forecasts. On the other hand, in a Bayesian setting, uncertainty indeed becomes an issue for long-term forecasts because of the rapidly increasing width of the intervals as the length of the projection increases. A number of enhancements of the classical and Bayesian methods proposed here are suggested for a future research agenda. Foremost is an investigation into an integrated approach to account for uncertainty in the classical multinomial APC model and refined ways of eliciting prior information in the Bayesian framework.