小區域生命表編製與死亡率模型估計

Abstract

死亡率模型可用於推估人們的未來壽命，有助於政府擬定社福政策及產業發展計畫，以及個人安排退休生活的規劃，然而臺灣各地人口特性差異不小，用於全國的方法未必可直接套用至縣市、鄉鎮市區等小區域。以常見的Lee-Carter死亡率模型（Lee and Carter, 1992）為例，這個模型用於全國層級時相當準確，但當人數較少時參數估計值有明顯偏誤，甚至產生不收斂的現象，必須適度調整以取得較為穩定的估計值。有鑑於此，本文以臺灣縣市、鄉鎮市區層級為研究目標，希冀可修正Lee-Carter模型在人數少時的估計偏誤，並將研究結果應用至估計臺灣人數較少之縣市或鄉鎮市區等行政區域層級，解決死亡人數為零的死亡率震盪問題，以利小區域生命表的編製。\nLee-Carter模型的參數估計偏誤多半導因於死亡觀察人數為零，通常發生在死亡率較低的年齡層（如5～19歲），傳統修勻方法未必適用，本文引進修勻方法穩定小區域死亡率，藉由人口數較多的參考地區，降低死亡模型的估計偏誤。本文以臺灣鄉鎮市區的人口資料為依據，透過電腦模擬評估修勻方法的優劣，考慮方法包含部分標準死亡比（Partial Standard Mortality Ratio）、Whittaker比值法等方法，藉此調整死亡人數為零（或偏低）的現象。研究發現修勻方法確實可以降低死亡模型的估計偏差，人口數越少時扮演角色越重，以20～49歲年齡層的參數改善最為顯著。此外，參考地區與小區域是否類似、參考地區的人口數都與降低偏誤有關，且兩者彼此會相互影響死亡率估計的準確度。

Mortality models can be used to predict future life expectancy and help governments to design welfare policies and national development plans, as well as providing information for planning individuals’ retirement lives. However, the population characteristics of local areas, such as counties and townships, are very different and the methods used in the national level may not be applicable to small areas. Taking Lee-Carter model as example, it may not be feasible to small populations since its parameters’ estimates are likely to be under-biased. Thus, we aim to explore the possible modifications for reducing the bias of estimates, if the Lee-Carter model is applied to small populations.\nThe bias of parameters’ estimates is likely caused zero number of deaths, which usually occurs in age groups with low mortality rates (e.g., ages 5-19), and the traditional smoothing method may not be applicable. In this paper, we consider a larger population as the reference population, together with graduation methods, such as Partial Standard Mortality Ratio (PSMR) and Whittaker method, to reduce the estimation bias of the mortality model. Based on Taiwan’s data at county and township level to evaluate the proposed approach. We found the proposed approach can reduce the bias of estimates, especially for the cases of smaller populations and age groups 20-49. In addition, both the similarity between the reference population and small population and the size of reference population have a impact on the accuracy of mortality estimation.