高齡死亡率模型的探討

A Study of Elderly Mortality Models

王信忠(Hsin-Chung Wang) ； 余清祥(Jack C. Yue) ； 陳怡萱(Yi-Xuan Chen)

《人口學刊》 52期 (2016/06) Pp. 1-42

https://doi.org/10.6191/JPS.2016.52.01

摘要

隨著醫藥科技等因素的發展，我國國民平均壽命逐年上升，高齡人口的死亡率下降尤為明顯，人口老化速度愈發明顯，國人對於退休生活、醫療需求更形殷切。為了因應老化及長壽的需求，近年政府提出不少政策都和老年人有關，包括全民健保、勞退新制、長期照護等，這些社會保險制度需要對未來人口及其結構，包括高齡人口的死亡率及其平均餘命等數值的推估，這些需求使得高齡死亡模型受到國內外各界的重視。本文探討高齡死亡模型，主要分為兩類：關係模型、隨機模型，比較哪些模型適合用於因應長壽風險，考慮的模型包括Gompertz（1825）、Coale and Kisker（1990）、Lee and Carter（1992）、Renshaw and Haberman（2006）、Cairns et al.（2006a）以及王信忠、余清祥（2011）提出的折扣數列模型（discount sequence, DS），其中後者結合工程上可靠度函數Weibull分布，另外提出折扣數列比值韋伯模型（DSW）。本文以實證資料評估兩類模型的優劣，使用臺灣、日本、美國三國五齡組及單齡組死亡率資料，除了估計效果的比較，也以交叉驗證檢驗預測結果，分析發現DSW與DS關係模型分別在配適與預測上，也能如同隨機模型一樣得到高精確的預測結果。

關鍵字

長壽風險 ； 高齡死亡模型 ； 交叉驗證 ； Lee-Carter模型 ； 折扣數列

並列摘要

A decrease in mortality among the elderly is particularly evident since the end of the 20th century. As a result, the living arrangements after retirement, including as financial planning and health needs, become more important. In recent years, Taiwan’s government has issued varies social policies and a social insurance system to face the rapid population ageing. The National Health Insurance and National Pension Insurance systems are two famous examples. However, the financial solvency of these social insurance systems depends on reliable planning and prediction of future mortality rates, in particular, those of the elderly. Hence, many studies focus on building mortality models for the elderly. The goal of this study is to evaluate popular mortality models for the elderly via empirical data. There are two types of mortality models: relational and stochastic. The former includes the Gompertz, Coale-Kisker, and Discount Sequence models (Wang and Yue 2015), and the latter includes the Lee-Carter (1992), Renshaw and Haberman (2006), and CBD models (2006). For this empirical study, we consider short-term and longterm forecasts, and the evaluation is via cross validation for 5 age groups and single age data from the Human Mortality Database. We found that the Discount Sequence model has about the same prediction accuracy as stochastic models.

並列關鍵字

longevity risk ； elderly mortality models ； cross-validation ； Lee- Carter model ； discount sequence

參考文獻

王信忠、金碩、余清祥(2012)。小區域死亡率推估之研究。人口學刊。45，77-110。

王信忠、余清祥(2011)。規律折扣數列與高齡死亡率。人口學刊。43，37-70。

內政部統計處（n.d.）臺閩地區簡易生命表。http://sowf.moi.gov.tw/stat/Life/quary-1age.htm（取用日期：2014年8月15日）。

Continuous Mortality Investigation Bureau. 1999. “Mortality Improvement Model for Use with the 92' Series of Mortality Tables.” Continuous Mortality Investigation Reports No 17. https://www.actuaries.org.uk/documents/cmi-report-17-whole-volume (Date visited: July 28, 2014).

Gompertz, B. 1825. “On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London 115: 513-583.