Forecasting of cohort fertility under a hierarchical Bayesian approach
The main reason for modelling fertility rates is to generate population estimates and forecasts. Previously deterministic in nature, the current fertility literature is favouring stochastic approaches, making models within a Bayesian framework very appealing. In keeping with the recent literature, our aim is to develop a hierarchical Bayesian model for modelling and forecasting cohort fertility rates. Building on the work of Schmertmann et al. (Journal of the American Statistical Association, 2014, pages 500-513), we propose a hierarchical Bayesian approach, using state-of-the-art Hamiltonian Monte Carlo methods and a dataset taken largely from the Human Fertility Database. Obtaining fertility forecasts for 41 countries using the data available in 2010 and 33 countries using the data available in 2000, we use scoring rules to quantitatively assess the predictive accuracy of the latter. The forecasts generated from our model are plausible with appropriate levels of uncertainty, particularly for countries with stable fertility histories in recent years. We illustrate the benefits of taking a hierarchical Bayesian approach to modelling cohort fertility. The flexibility of the approach allows us to incorporate the natural structure of fertility data indexed by age and cohort, and the underlying assumptions in both dimensions, intuitively and transparently. In addition, it demonstrates how advanced computational methods can be used to fit hierarchical Bayesian models with an atypical setup. This not only cements the position of hierarchical Bayesian methods at the forefront of population forecasting methods, but also makes a valuable contribution to the fertility modelling and forecasting literature.