Using Graduation to Modify the Estimation of Lee–Carter Model for Small Populations

Abstract

Many mortality models, such as the Lee–Carter model, have unsatisfactory estimation in the case of small populations. Increasing population size is a natural choice to stabilize the estimation, if we can find a larger reference population that has a mortality profile similar to that of the small population. Aggregating historical data of the small populations is a fine candidate for the reference population. However, it is often not feasible in practice and we need to rely on other reference populations. In this study, we explore whether graduation methods can be used if the mortality profile of a small population differs from that of the reference population. To explore the appropriate occasion to use graduation methods, we create several mortality scenarios and similarity types between small and reference populations. We propose combining the graduation methods and mortality models, either graduating mortality rates first or applying the mortality model first, and determine whether they can improve the model fit. We use computer simulation to determine whether the proposed approach has better mortality estimation than the Lee–Carter model and the the Li–Lee model. We found that the Li–Lee model always has smaller estimation errors than the Lee–Carter model, and the proposed approach has smaller estimation errors than the Li–Lee model in most cases.