Multi-population Mortality Projection: The Augmented Common Factor Model with Structural Breaks

Abstract

Multi-population mortality forecasting has become an increasingly important area in actuarial science and demography, as a means to avoid long-run divergence in mortality projection. This paper aims to establish a unified state-space Bayesian framework to model, estimate and forecast mortality rates in a multi-population context. In this regard, we reformulate the augmented common factor model to account for structural breaks in the mortality indexes. Further, we conduct a Bayesian analysis to make inferences and generate forecasts so that process, parameter and model uncertainties can be considered simultaneously and appropriately. The square-root-form of the Kalman Filter is exploited to improve robustness when sampling latent states. We illustrate the efficiency of our methodology through two distinctive case studies. The first uses Australian two-gender mortality data. The second projects mortality for a list of selected Eurozone countries, where the hierarchical clustering approach on principal components is utilised to group countries with similar mortality characteristics together. Both point and probabilistic forecast evaluations are considered in the empirical analysis. The derived results support the fact that the incorporation of stochastic drifts mitigates the impact of the structural change in the time indexes on mortality projection.

Keywords: Multi-population mortality projection; Augmented Common Factor (ACF) model; Structural change; Bayesian statistics

JEL Classification: G22; J11; C11; C51; C53