由於許多國家死亡率下降快速、壽命延長幅度超乎預期，加上生育率持續低於替代水準，人口老化現象愈發明顯，近年來個人生涯規劃及政府施政，都格外強調退休後經濟生活及老年相關社會資源分配的比重。以臺灣為例，行政院經濟建設委員會 (簡稱經建會) 從1990年代開始，每兩年公布一次未來的人口推估，但過去十年來經建會屢次修正歷年的推估假設，以因應生育率及死亡率變化快速，適時提醒臺灣日益加速的人口老化。正因為人口推估可能受到人口數、社會變遷、資料品質等因素，影響統計分析的可靠性，常用於國家層級的推估方法，往往無法直接套用至縣市及其以下的層級 (即小區域)，使得小區域人口推估較為棘手，需要更加謹慎面對。 本文延續王信忠等人 (2012) 的研究，以小區域人口推估為目標，著重在生育率推估研究，結合隨機模型與修勻方法，尋找適合臺灣縣市層級的小區域人口推估方法。本文考量的隨機模型計有區塊拔靴法 (Block Bootstrap) 和 Lee-Carter 模型 (Lee and Carter 1992)，以預測未來的生育率和死亡率，並套用年輪組成推計法 (或稱為人口要素合成法；Cohort Component Method) 及修勻 (Graduation) 方法，探討這些方法與人口規模之間的關係，評估用於小區域人口推估之可行性。 本文首先以電腦模擬，探討生育率的推估，討論是否可直接推估總生育率，類似增加樣本數的概念，取代各縣市的年齡別生育率，以取得較為穩定的推估。根據模擬結果，發現人口規模對出生數的推估沒有明顯的關係，只要使用總生育率、再結合區塊拔靴法，就足以提供穩定的推估結果。實證研究方面，以臺灣縣市層級的人口及其年齡結構 (例如：0-14歲、15-64歲、65歲以上) 為驗證對象，發現分析結果也與電腦模擬相似，發現以區塊拔靴法推估臺灣各縣市的總生育率、年齡組死亡率，其推估精確度不因人口規模而打折扣，顯示以區塊拔靴法推估總生育率、年齡組死亡率，可用於推估臺灣小地區的未來人口。 / Due to the rapid mortality reduction, prolonging human longevity is a common phenomenon and longevity risk receives more attention in 21st century. Many developed countries encounter many problems brought up by prolonging life, such as poor community infrastructure and insufficient financial pension funds for the elderly. Population Projection thus becomes essential in government planning in dealing with the population aging. However, rapid changes in mortality and fertility make the projection very tricky. It would be even more difficult to project areas with fewer populations (i.e., small areas) since it takes extra efforts to deal with the larger fluctuations in small population. The objective of the study is to construct a standard operating procedure (SOP) for small population projection. Unlike the previous study, e.g., Wang et al. (2012), we will take both the fertility and mortality into account (but set migration aside for simplicity). First, for the fertility projection, we evaluate if total fertility rates (TFR) are more appropriate than the age-specific fertility rates for small population. Also, we compare two fertility projection methods: Lee-Carter model and block bootstrap, and check which shows better results. Based on the computer simulation, we found that TFR performs better and the block bootstrap method is more sensitive to rapid fertility changes. As for mortality rate projection, we also recommend the standard operating procedure by Wang et al. (2012). However, the smoothing methods have limited impacts on mortality projection and can be ignored. In addition to simulation, we also apply the SOP for projecting the small population to Taiwan counties and it achieves satisfactory results. However, due to the availability of data, our method can only be used for short-term projection (at most 30 years) and these results might not apply to long-term projection. Also, similar to the previous work, the fertility rates have the larger impact on small population projection, although we think that the migration has large impact as well. In this study, only the stochastic projection is considered and we shall consider including expert opinions as the future study.

人口政策的制定需要人口推估作基礎。近年世界各國人口推估逐漸從專家意見推估走向機率推估，常見的機率推估分成三大類，隨機推估、模擬情境、推估誤差三種，本文所使用的人口推估方法為隨機推估法結合生育率之模擬情境方法，在人口變動要素組合法 (Cohort Component Method) 之下輔以電腦模擬的區塊拔靴法 (Block Bootstrap)，針對台灣地區與台灣北、中、南、東四地區進行人口推估。另外，本文試圖在隨機模型人口推估中加入遷移人口之考量，以期針對遷移人口在數量與其影響上都能有較深入的了解，比較區塊拔靴法與經建會推估之差異後發現遷移之考量確實會影響人口推估之結果。 / 針對與全區相符的小區域人口推估，本文亦提出可使得推估一致的方法，但其缺點為限制了生育、死亡人口要素之變動性。此推估在總數上與隨機推估方法差異不大，但在人口結構上則有明顯的差別，此差別可能是來自於死亡率在四區間差異造成。 / Population projection is important to policy making, and only with accurate population projection can the government achieve suitable policy planning and improve the welfare of the society. The most popular and well-known population projection method is the Cohort Component method, proposed since 1930’s. The trends of future fertility, mortality and migration are required, in order to apply the cohort component method. Currently in Taiwan, these trends are determined according to experts’ opinions (or scenario projection) and three future scenarios are assumed: high, median and low scenarios. One of the drawbacks in applying experts’ opinions is that the projection results of these three scenarios do not have the meaning in probability. / To modify the expert’ opinions and let the projection results carry the meaning in probability, many demographic researchers have developed stochastic projection methods. The proposed stochastic methods can be categorized into three groups: stochastic forecast, random scenario and ex post methods. In this study, we introduce these stochastic methods and evaluate the possibility of applying the methods in projecting the population in Taiwan. / In this study we use block bootstrap, a computer simulation and stochastic forecast method, to determine the trends of future fertility, mortality and migration in Taiwan, and combine it with the cohort component method for population projection in Taiwan. We compare the projection results with those from the Council for Economic Planning and Development (a scenario projection). We found that the block bootstrap is a possible alternative to the scenario projection in population projection, and the numbers of migration is small but have a non-ignorable influence on the future population. However, we also found that the block bootstrap alone might not be appropriate for population projection in small areas.