Selection effect modification to the Lee-Carter model

Although other risk factors can be used, depending on feasibility, marketing, and data availability, age and gender are the two most common risk factors considered in life insurance products. Previous studies have shown that the newly insured, who passed certain health examinations, tend to have lower mortality rates than those already insured. Insurance companies often use select and ultimate tables to handle mortality discrepancies between the insured in different policy years (i.e., the selection effect). However, the selection effect is easily confused with mortality improvement, and its estimate is likely to be influenced by the annual reduction in mortality rates. In this study, we propose modifying the Lee-Carter model, including the selection effect and mortality improvement. We first use a simulation to evaluate the parameter estimation of the proposed approach and then apply it to experienced data from Taiwan’s largest insurance company, Cathay Life Insurance Company Ltd. The results of our simulation and empirical studies support the newly proposed approach, which provides stable and accurate estimates of the selection effect and mortality improvement. We also find that the size of the selection effect concerning policy year was larger than the difference in mortality rates between smokers and non-smokers; this is particularly noticeable for older age groups.