Smooth Projection of Mortality Improvement Rates: A Bayesian Two-dimensional Spline Approach
This paper proposes a flexible spline mortality model for generating smooth forecasts of mortality improvement rates. In particular, we follow the two-dimensional B-spline approach developed by Currie et al. (2004), and adapt the Bayesian estimation method and LASSO penalty to overcome the limitations of spline models in forecasting mortality rates. The resulting Bayesian spline model not only provides measures of stochastic and parameter uncertainties, but also allows external opinions on future mortality to be consistently incorporated as prior beliefs. The mortality improvement rates projected by the proposed model are smoothly transitioned from historical values containing short-term shocks in recent observations to long-term terminal rates suggested by external opinions. Our technical work is complemented by empirical illustrations that use industry mortality improvement standards and demonstrate the impact of different prior beliefs on mortality forecasts.