A Spatial Approach to Model Mortality Rates

Human longevity has been experiencing its largest increase since the end of World War II, and modeling the mortality rates is often the focus of many studies. Among all mortality models, the Lee–Carter model is a popular approach since it is easy to use and has good accuracy in predicting mortality rates. However, empirical studies from several countries have shown that the age parameters of the Lee–Carter model are not constant in time. Many modifications of the Lee–Carter model have been proposed to deal with this problem, including adding an extra cohort effect and adding another period effect. In this study, we propose a spatial modification of the Lee–Carter model and use simulation results to explain why the proposed approach can be used to deal with the problem of the age parameters. Mortality rates are usually recorded by age and time, and thus we can treat mortality rates as two‐dimensional values and apply tools of spatial analysis to them. For example, clusters are areas with unusually higher (or lower) mortality rates than their neighbors and we use popular cluster detection methods, such as Spatial scan statistics, to evaluate where there are locations with mortality rates that cannot be described well by the Lee–Carter model. We first use computer simulation to demonstrate that the cluster effect is a possible source causing the problem of the age parameters not being constant and adding the cluster effect can solve the nonconstant problem. We also apply the proposed approach to mortality data from several countries including Japan, France, the United States, and Taiwan. The empirical results show that our approach has better fitting results and smaller mean absolute percentage errors than the Lee–Carter model.