Bayesian local clustering of age-period mortality surfaces across multiple countries

Abstract

Although classical mortality modelling literature has focused on single countries in isolation, recent contributions have progressively moved toward joint statistical models for multiple countries. Besides favouring borrowing of information to improve age-period forecasts, this perspective has also potential to infer local similarities among countries’ mortality patterns in specific age classes and periods, which could unveil unexplored demographic trends, while guiding the design of targeted policies. Advancements along this direction are undermined by the lack of multi-country models capable of incorporating the core structures of age-period mortality surfaces together with clustering patterns among countries that are not global, but rather vary locally across the different combinations of ages and periods. We cover this gap by developing a Bayesian model for log-mortality rates that characterizes the age structure of mortality through a B-spline expansion whose country-specific dynamic coefficients encode both changes of this age structure across periods and also local clustering patterns among countries under a time-dependent random partition prior for these country-specific dynamic coefficients. While flexible, this formulation facilitates tractable posterior inference leveraging a suitably designed Gibbs sampler. The application to mortality data from 14 countries unveils local similarities which highlight both previously recognized demographic phenomena and also yet unexplored patterns.