人口推估(Population Projection)涉及國家的政策及規劃，精確的結果可協助國家適時制訂政策，提高國民福祉。臺灣現在使用的方法為人口變動要素合成法(The Cohort Component Method)，可算是情境推估(Scenario Forecast)的一種，其起源可追溯至1920年代(Whelpton, 1928)，參酌專家意見之後，使用高、中、低三種推計來描述其變動範圍。除了情境推估外，近年在人口變動要素合成方法上發展出的新方法大致可以分成三種：一為隨機推估(Stochastic Forecast Method)、一為模擬情境(Random Scenario Method)、一為推估誤差(ex post Method)，美國及聯合國已經不單單依賴專家提供的傳統高、中、低推計，轉而使用這些新的推估方法。 由於近年來生育率快速降低、平均餘命延長以及外籍新娘增多等因素，大為提高人口推估的難度，因此本文將機率的概念併入人口推估中，以預測區間（Prediction Interval）來捕捉人口各項特性的可能變動範圍。除了回顧幾種在人口變動要素合成法中發展出的隨機推估方法及合併專家意見的方針外，也使用區塊拔靴法(Block Bootstrap)電腦模擬，進行臺灣、美國、日本、法國四個國家的人口推估。另外，本文也採用以Stoto(1983)提出的預測誤差估計，評估區塊拔靴法和人力規劃處推估結果之異同，以提供使用專家意見與隨機方法的參考。最後則是比較臺灣以北中南東小區域推估和臺灣整體的推估結果，並合併專家意見進行臺灣地區人口推估。

國家政策之制定須配合未來人口總數及其結構等特性，藉以達到提高國民福 祉的願景，因此各國均定期公佈人口推估(Population Projection)的結果，目前臺 灣官方人口推估為每兩年公布一次。人口推估主要考量三個要素：出生、死亡、 遷移，以國家層級而言，通常遷徙對未來人口的影響遠小於出生與死亡，所以過 去行政院經濟建設委員會的官方全國人口推估一般專注於出生與死亡。然而，各 國研究發現遷徙是小區域人口推估為最重要的因素，人口數愈少、影響程度有愈 大的傾向，但文獻中較缺乏臺灣內部遷移的研究。如能掌握臺灣小區域人口遷徙 的變遷，將能使政策因地制宜，有助地方政府提高推行政策的有效性，也是本研 究之目標。 由於缺乏完整的縣市、鄉鎮市區層級的詳細遷移資料，本研究以人口平衡公 式反推淨遷移人數，找出各地區的遷移特性後，代入人口變動要素合成法(Cohort Component Method)，搭配屬於機率推估的區塊拔靴法(Block Bootstrap)，推估小 區域的未來人口。關於出生及死亡的推估，過去研究發現使用區塊拔靴法用於小 區域的生育率（曹育欣，2012）及死亡率（金碩，2011），皆有不錯的推估結果。 本研究以臺北市為範例，討論區塊拔靴法在小區域遷徙人口數、年齡別遷徙人口 的推估效果，及是否適合運用在其他不同縣市。 / The population projection is used to provide information for the policy planning of governments. In Taiwan, the Council for Economic Planning and Development is in charge of the official population projection and it release projection results every two years. Basically, three factors are considered in population projection: birth, death, and migration. Since the migration has little impacts in country-level projection, many countries (including Taiwan) assume the future migration is zero or close to zero, and the focus of projection is usually on the birth and death. However, for the projection of small area (such as county- or township-level), past studies found that the effect of migration cannot be ignored. But, partly due to the limitation of migration data, there are not many studies explore the migration patterns of counties or townships in Taiwan. In this study, we use the population records (births and deaths) and the population equation to derive the county-level records of internal migration in Taiwan. We use these data to explore the migration patterns of all counties in Taiwan, and then applying block bootstrap method to modify the county-level population projection. Note that, the block bootstrap is shown to be reliable in forecasting fertility (Tsao, 2012) and mortality (Jin, 2011) for small areas. In this study, we also use the Taipei City to demonstrate the population projection which includes the internal migration, and the result is promising.

一個國家對全國人口有充分瞭解，方能依據國情制定適合的政策，地方發展更是如此，更須洞悉各地的人口結構，以善用有限的資源。台灣近年人口老化日益明顯，各縣市的老化速度及人口問題也不盡相同，若可獲得各地區未來的人口相關數值 (亦即人口推估)，當能減輕未來人口老化對台灣造成的衝擊。本文以縣市層級的人口推估，也就是小區域人口推估為研究目標，探討需注意的事項，尋找適合台灣地區的小區域推估方法。 本文整理小區域人口推估方法，並使用人口要素變動合成法 (Cohort Component Method)，以雲嘉兩縣、臺北市、澎湖縣為範例，測試縣市層級的人口推估。人口推估與生育、死亡、遷移三者的假設有密切關係，我們以死亡率為目標，比較不同模型的優劣，考慮的模型包括 Lee-Carter 模型、區塊拔靴法 (Block Bootstrap)、篩網拔靴法 (Sieve Bootstrap) 以及泛函資料分析 (Functional Data Analysis) 中的主成份分析 (Principle Component Analysis)，以估計誤差為衡量方法優劣的標準。分析發現篩網拔靴法、區塊拔靴法、Lee-Carter 模型三者的結果較佳，因此在小區域推估中使用較簡便的區塊拔靴法。研究發現對小區域的人口推估而言，遷移假設扮演非常重要的角色，此與全國規模的人口推估結果截然不同。研究過程亦發現人口三要素對人口推估有明顯的影響，若假設三要素間互相獨立 (也就是傳統推估時的假設)，推估結果的預測區間遠小於三要素不獨立。 / The government can make policy according to the population change in this country, while the local government can develop their district by using their limited resources well after realizing the populaton structure. The population ageing is becoming more serious and being more different among every counties in Taiwan day by day. If we can get the relative numbers of population in the future (population projection), we can decrease the attack of population ageing for Taiwan. The aim of this paper is to find an appropriate method and some notations of small area population projection in Taiwan. The paper includes the summary of methods of small area population projection and the results by using cohort component method on three areas in Taiwan, YunLin & ChiaYi, Taipein City and PengHu. Population projection is highly related with birth, death and migration, hence we test the mortality rate by using several methods, Lee-Carter, block bootstrap, sieve bootstrap and principal component analysis of functional data analysis are included. We found that the result of sieve bootstrap, block bootstrap and Lee-Carter are much better than the others, therefore, we take block bootstrap which is much simpler than the other two to analysis the effect of birth, death and migration in population projection. The sutdy found that, in small area population projecton, migration plays an important role, which is totally different from the whole country population projection.

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.