An Extended Linear Difference Model for Mortality Projection, with Applications to Japan
- Author(s): Ishii, Futoshi
- Advisor(s): Wachter, Kenneth W
- Wilmoth, John R
- et al.
In this dissertation, we propose the Tangent Vector Field (TVF) model for Japanese mortality projection, which is an extended Linear Difference (LD) model, and show its applications.
In the two chapters following the introduction, we describe the mortality trends in Japan and review the mortality projection models for Japan.
Then, in the following two chapters, we describe the data and methods for the mortality models, show the results of fitting, and discuss them with special emphasis on the LD model. We describe the mathematical formulations for decline-type and shift-type models, and discuss the inverse function of log mortality and differential forms of mortality models. We discuss five models: two decline-type models (the Proportional Hazard (PH) and Lee--Carter (LC) models), and three shift-type models (the Horizontal Shifting (HS), Horizontal Lee--Carter (HL), and LD models). In particular, we compare the LC and LD models from a statistical viewpoint. The result guides better construction of a mortality projection model, namely, a blended model with LC properties in youth and LD properties in older age.
In the last chapter, we propose the TVF model applying the idea of tangent vector fields on the log mortality surface. We show a fully specified example of the projection procedure of the TVF model with all constants and coefficients applied for Japanese mortality projection. Then, we compare the TVF and LC models' results of mortality projection. From the observation of the relative mortality rates, we see that the LC model expresses mortality improvement only in a vertical direction, whereas the TVF model succeeds in expressing a shifting of mortality improvement in the direction of older ages that are observed in the actual mortality. In addition, we compare the projected mx curves. The mx by the LC model exhibits an unnatural pattern because the slope of the curve diminishes once around the age of 60 years and becomes much steeper after 80 years. The curve of the TVF model is more plausible. As a whole, we observe that the TVF model has many advantages for Japanese mortality projection compared with the LC model.
We show that the TVF model proposed in this dissertation is not only quite useful for Japanese mortality projection but also has various applicability. At this point in time, there may be few countries with such strong shifting features for old age mortality as Japan. However, some countries are likely to experience the same mortality situation as Japan in the future through the extension of life expectancy. Thus, the TVF model will be a useful tool for projections in such situations.