小區域死亡率推估之研究

A Simulation Study of Small Area Mortality Projection

10.6191/jps.2012.11

王信忠(Hsin-Chung Wang)；金碩(Shuoh Jin)；余清祥(Jack C. Yue)

小區域死亡率推估 ； 人口老化 ； 修勻 ； 標準死亡比 ； 電腦模擬 ； small area mortality projection ； population aging ； smoothing methods ； standard mortality ratio ； computer simulation

人口學刊

45期（2012 / 12 / 01）

77 - 110

繁體中文

臺灣人口結構漸趨老化，由於老年人使用較多醫療等社會資源，人口老化勢必牽動政府政策與資源分配，然而臺灣各縣市的人口老化速度不一（陳政勳、余清祥2010），因此有必要針對各地方特性發展適當的小區域人口推估方法。小區域推估面臨的問題可歸納為四個方向：「資料品質」、「地區人數」、「資料年數」與「推估年數」，資料品質有賴資料庫與制度的建立，而後三者則與過去資料與推估未來的變異程度有關。本文考量在上述後三個問題的影響下，探討修勻（graduation）相關方法是否可提高小區域死亡率推估的穩定性。本文使用屬於隨機推估的區塊拔靴法（block bootstrap），以電腦模擬評估推估結果，因為小區域人口數較少，本文也使用Whittaker及標準死亡比（standard mortality ratio）等修勻方法，降低因為地區人數較少引起的震盪。另外，小區域推估通常可用的資料時間較短，未來推估結果的震盪也較大，本文針對需要過去幾年資料，以及未來可推估年數等兩項因素進行研究，希冀結果可提供臺灣各地方政府的推估參考。除了電腦模擬外，本文也以實證分析檢驗修勻的成效，將修勻套用至臺南縣、臺東縣等縣市層級的死亡率。研究發現，修勻方法可降低小區域死亡率推估的震盪，如有過去十五年資料可獲得較可信的推估結果，而未來推估年數盡量不超過二十年；相對而言，與人口數比較，小區域與大區域的死亡率差異對修勻的影響較為有限。

The population size plays a very important role in statistical estimation, and it is difficult to derive a reliable estimate for small areas. The estimation is even more difficult if the geographic and social attributes within the small areas vary widely. However, although population aging is a common phenomenon globally, the problem is not the same for different countries. The aim of this study is to explore the mortality projection for small areas, with the consideration of the small area's distinguishing characteristics. In addition to data quality, the difficulties for small area population and mortality projection are threefold: population size, number of base years, and projection horizon. Smoothing methods can be applied to improve the stability and accuracy of small area estimation. In this study, the block bootstrap and smoothing methods are combined to project the mortality of small areas in Taiwan, using the cohort component method. We found that the smoothing methods can reduce the fluctuation of estimates and projections in general, and the improvement is especially noticeable for areas with smaller population sizes. To obtain a reliable mortality projection for small areas, we suggest using at least fifteen years of historical data for projection and a projection horizon of not more than twenty years. Also, the population size has a bigger influence than the discrepancy of mortality rates between small and large areas.

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