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題名 小區域人口推估研究：臺北市、雲嘉兩縣、澎湖縣的實證研究
A study of small area population projection in Taiwan
作者 陳政勳
貢獻者 余清祥
陳政勳
關鍵詞 小區域人口推估
人口老化
人口變動要素合成法
電腦模擬
Small Area Population Projection
Population Aging
Cohort Component Method
Computer Simulation
日期 2009
上傳時間 5-Sep-2013 15:10:56 (UTC+8)
摘要 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.
參考文獻 中文部分
行政院經濟建設委員會人力規劃處 (2008), "中華民國臺灣97年至145年人口推計" 臺北
何正羽 (2006). "高齡人口 Gompertz 死亡率推估模型的建構與應用" 東吳大學商用數學系碩士論文.
郭孟坤與余清祥 (2007). "電腦模擬, 隨機方法與人口推估的實證研究" 人口學刊 36: 67－98.
曾奕翔與余清祥 (2002). "Lee-Carter 估計模式與死亡率推估研究" 中華民國人口學會學術研討會.
歐長潤與余清祥 (2008). "APC 模型估計方法的模擬與實證研究" 國立政治大學統計學系碩士論文.

英文部分
Alho, J. and B. D. Spencer (2005). Statistical demography and forecasting, Springer Verlag.
Alonso, A. M., a. Peña, D., et al. (2003). "On sieve bootstrap prediction intervals." Statistics & Probability Letters 65(1): 13－20.
Bühlmann., P. (2002). "Bootstraps for time series." Statistical Science: 52－72.
Bell, W. R. (1992). ARIMA and Principal Component Models in Forecasting Age-Specific Fertility. National Population Forecasting in Industrialized Countries. N. Keilman and H. Cruijsen, Amsterdam: Swets and Zeitlinger.
Bell, W. R. (1997). "Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates." Journal of Official Statistics 13(3): 279－304.
Cannan, E. (1895). "The probability of a cessation of the growth of population in England and Wales during the next century." The Economic Journal 5(20): 505－515.
Denton, F. T., C. H. Feaver, et al. (2005). "Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy." Journal of Population Economics 18(2): 203－227.
Efron, B. (1979). "Bootstrap methods: another look at the jackknife." The annals of statistics 7(1): 1－26.
Hall, P. (1985). "Resampling a coverage pattern." Stochastic Processes and their Applications 20(2): 231－246.
Hyndman, R. J., S. Ullah, et al. (2007). "Robust forecasting of mortality and fertility rates: A functional data approach." Computational Statistics & Data Analysis 51(10): 4942－4956.
Künsch., H.R. (1989). "The jackknife and the bootstrap for general stationary observations." The Annals of Statistics: 1217－1241.
Kanaroglou, P. S., H. F. Maoh, et al. (2009). "A demographic model for small area population projections: an application to the Census Metropolitan Area of Hamilton in Ontario, Canada." Environment and Planning A 41(1).
Keilman, N., D. Q. Pham, et al. (2002). "Why population forecasts should be probabilistic-illustrated by the case of Norway." Demographic Research 6: 410－454.
Koissi, M. C., A. F. Shapiro, et al. (2006). "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval." Insurance: Mathematics and Economics 38(1): 1－20.
Lawson, C. L. and R. J. Hanson (1974). Solving least squares problems, Prentice-Hall, EngleWood Cliffs, NJ.
Lee, R. D. (1998). "Probabilistic approaches to population forecasting." Population and Development Review 24: 156－190.
Lee, R. D. and L. R. Carter (1992). "Modeling and forecasting US mortality." Journal of the American Statistical Association 87(419): 659－671.
Lee, W. C. (2003). "A Partial SMR Approach to Smoothing Age-specific Rates." Annals of epidemiology 13(2): 89－99.
Li, N., R. Lee, et al. (2004). "Using the Lee-Carter method to forecast mortality for populations with limited data." International Statistical Review: 19－36.
Lutz, W., W. C. Sanderson, et al. (1998). "Expert-based probabilistic population projections." Population and Development Review 24: 139－155.
Lutz, W. and S. Scherbov (1998). "An expert-based framework for probabilistic national population projections: The example of Austria." European Journal of Population 14(1): 1－17.
Mammen, E. and S. Nandi (2004). Bootstrap and Resampling.
Neumaier, A. and T. Schneider (2001). "Estimation of parameters and eigenmodes of multivariate autoregressive models." ACM Transactions on Mathematical Software (TOMS) 27(1): 57.
Politis, D. N. and J. P. Romano (1994). "The Stationary Bootstrap." Journal of the American Statistical Association 89(428).
Ramsay, J. and B. Silverman (2005). Functional data analysis, Springer Verlag.
Rao, J. (2003). Small area estimation, Wiley-Interscience.
Rees, P., P. Norman, et al. (2004). "A framework for progressively improving small area population estimates." Journal of the Royal Statistical Society. Series A (Statistics in Society) 167(1): 5－36.
Rogers, A. (1995). Multiregional demography: principles, methods and extensions, John Wiley & Son Ltd.
Sanderson, W. C., S. Scherbov, et al. (2004). "Conditional probabilistic population forecasting." International Statistical Review: 157－166.
Smith, S. K. (1987). "Tests of forecast accuracy and bias for county population projections." Journal of the American Statistical Association 82(400): 991－1003.
Stoto, M. A. (1983). "The accuracy of population projections." Journal of the American Statistical Association: 13－20.
Tiao, G. and G. Box (1981). "Modeling multiple times series with applications." Journal of the American Statistical Association 76(376): 802－816.
Tuljapurkar, S., R. D. Lee, et al. (2004). "Random scenario forecasts versus stochastic forecasts." International Statistical Review: 185－199.
Whelpton, P. (1928). "Population of the United States, 1925 to 1975." American Journal of Sociology: 253－270.
Wilson, T. and M. Bell (2004a). "Australia`s uncertain demographic future." Demographic Research 11(8): 195－234.
Wilson, T. and M. Bell (2004b). "Comparative empirical evaluations of internal migration models in subnational population projections." Journal of Population Research 21(2): 127－160.
描述 碩士
國立政治大學
統計研究所
97354015
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354015
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.author (Authors) 陳政勳zh_TW
dc.creator (作者) 陳政勳zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 5-Sep-2013 15:10:56 (UTC+8)-
dc.date.available 5-Sep-2013 15:10:56 (UTC+8)-
dc.date.issued (上傳時間) 5-Sep-2013 15:10:56 (UTC+8)-
dc.identifier (Other Identifiers) G0097354015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60433-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 97354015zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 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。		zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents 誌謝 i
中文摘要 ii
英文摘要 iii
目錄 iv
表目錄 v
圖目錄 vi
第一章 緒論 1
第一節 研究動機 1
第二節 研究目的 3
第二章 文獻回顧 5
第一節 人口變動要素合成法 5
第二節 機率人口推估方法 7
一、 隨機推估法 8
二、 模擬情境法 10
三、 推估誤差法 11
第三節 小區域人口推估的困難 11
第三章 資料介紹與研究方法 13
第一節 資料來源及處理 13
第二節 研究方法 17
一、 區塊拔靴法 17
二、 死亡率比較的其他方法 19
第三節 死亡率推估方法比較 22
第四章 實證研究 24
第一節 估計聻測試 24
一、 出生、死亡及遷移之推估假設 24
二、 推估假設所代表的意義 31
三、 總人口數 31
四、 誤差分析 40
第二節 雲嘉地區未來小區域人口推估 42
一、 推估假設所代表的意義 42
二、 總人口數 44
第三節 臺北市及澎湖縣的實證研究 51
一、 臺北市 51
二、 澎湖縣 54
第四節 實證結果討論 58
第五章 區塊拔靴法的考量 64
第一節 死亡率模型測試 64
一、 推估結果比較 67
二、 區塊拔靴法的相對差異 67
第二節 臺北市測試結果 69
第三節 情境推估 72
第六章 結論 75
參考文獻 77
附錄一：歷年淨遷移人口數 82
附錄二：三種基底函數圖形 83
附錄三：臺北市的實證研究結果 84
附錄四：雲嘉地區的實證研究結果 94
附錄五：澎湖縣的實證研究結果 96
附錄六：區塊拔靴法的考量 106		zh_TW
dc.format.extent 2956550 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097354015en_US
dc.subject (關鍵詞) 小區域人口推估zh_TW
dc.subject (關鍵詞) 人口老化zh_TW
dc.subject (關鍵詞) 人口變動要素合成法zh_TW
dc.subject (關鍵詞) 電腦模擬zh_TW
dc.subject (關鍵詞) Small Area Population Projectionen_US
dc.subject (關鍵詞) Population Agingen_US
dc.subject (關鍵詞) Cohort Component Methoden_US
dc.subject (關鍵詞) Computer Simulationen_US
dc.title (題名) 小區域人口推估研究：臺北市、雲嘉兩縣、澎湖縣的實證研究zh_TW
dc.title (題名) A study of small area population projection in Taiwanen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 中文部分
行政院經濟建設委員會人力規劃處 (2008), "中華民國臺灣97年至145年人口推計" 臺北
何正羽 (2006). "高齡人口 Gompertz 死亡率推估模型的建構與應用" 東吳大學商用數學系碩士論文.
郭孟坤與余清祥 (2007). "電腦模擬, 隨機方法與人口推估的實證研究" 人口學刊 36: 67－98.
曾奕翔與余清祥 (2002). "Lee-Carter 估計模式與死亡率推估研究" 中華民國人口學會學術研討會.
歐長潤與余清祥 (2008). "APC 模型估計方法的模擬與實證研究" 國立政治大學統計學系碩士論文.

英文部分
Alho, J. and B. D. Spencer (2005). Statistical demography and forecasting, Springer Verlag.
Alonso, A. M., a. Peña, D., et al. (2003). "On sieve bootstrap prediction intervals." Statistics & Probability Letters 65(1): 13－20.
Bühlmann., P. (2002). "Bootstraps for time series." Statistical Science: 52－72.
Bell, W. R. (1992). ARIMA and Principal Component Models in Forecasting Age-Specific Fertility. National Population Forecasting in Industrialized Countries. N. Keilman and H. Cruijsen, Amsterdam: Swets and Zeitlinger.
Bell, W. R. (1997). "Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates." Journal of Official Statistics 13(3): 279－304.
Cannan, E. (1895). "The probability of a cessation of the growth of population in England and Wales during the next century." The Economic Journal 5(20): 505－515.
Denton, F. T., C. H. Feaver, et al. (2005). "Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy." Journal of Population Economics 18(2): 203－227.
Efron, B. (1979). "Bootstrap methods: another look at the jackknife." The annals of statistics 7(1): 1－26.
Hall, P. (1985). "Resampling a coverage pattern." Stochastic Processes and their Applications 20(2): 231－246.
Hyndman, R. J., S. Ullah, et al. (2007). "Robust forecasting of mortality and fertility rates: A functional data approach." Computational Statistics & Data Analysis 51(10): 4942－4956.
Künsch., H.R. (1989). "The jackknife and the bootstrap for general stationary observations." The Annals of Statistics: 1217－1241.
Kanaroglou, P. S., H. F. Maoh, et al. (2009). "A demographic model for small area population projections: an application to the Census Metropolitan Area of Hamilton in Ontario, Canada." Environment and Planning A 41(1).
Keilman, N., D. Q. Pham, et al. (2002). "Why population forecasts should be probabilistic-illustrated by the case of Norway." Demographic Research 6: 410－454.
Koissi, M. C., A. F. Shapiro, et al. (2006). "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval." Insurance: Mathematics and Economics 38(1): 1－20.
Lawson, C. L. and R. J. Hanson (1974). Solving least squares problems, Prentice-Hall, EngleWood Cliffs, NJ.
Lee, R. D. (1998). "Probabilistic approaches to population forecasting." Population and Development Review 24: 156－190.
Lee, R. D. and L. R. Carter (1992). "Modeling and forecasting US mortality." Journal of the American Statistical Association 87(419): 659－671.
Lee, W. C. (2003). "A Partial SMR Approach to Smoothing Age-specific Rates." Annals of epidemiology 13(2): 89－99.
Li, N., R. Lee, et al. (2004). "Using the Lee-Carter method to forecast mortality for populations with limited data." International Statistical Review: 19－36.
Lutz, W., W. C. Sanderson, et al. (1998). "Expert-based probabilistic population projections." Population and Development Review 24: 139－155.
Lutz, W. and S. Scherbov (1998). "An expert-based framework for probabilistic national population projections: The example of Austria." European Journal of Population 14(1): 1－17.
Mammen, E. and S. Nandi (2004). Bootstrap and Resampling.
Neumaier, A. and T. Schneider (2001). "Estimation of parameters and eigenmodes of multivariate autoregressive models." ACM Transactions on Mathematical Software (TOMS) 27(1): 57.
Politis, D. N. and J. P. Romano (1994). "The Stationary Bootstrap." Journal of the American Statistical Association 89(428).
Ramsay, J. and B. Silverman (2005). Functional data analysis, Springer Verlag.
Rao, J. (2003). Small area estimation, Wiley-Interscience.
Rees, P., P. Norman, et al. (2004). "A framework for progressively improving small area population estimates." Journal of the Royal Statistical Society. Series A (Statistics in Society) 167(1): 5－36.
Rogers, A. (1995). Multiregional demography: principles, methods and extensions, John Wiley & Son Ltd.
Sanderson, W. C., S. Scherbov, et al. (2004). "Conditional probabilistic population forecasting." International Statistical Review: 157－166.
Smith, S. K. (1987). "Tests of forecast accuracy and bias for county population projections." Journal of the American Statistical Association 82(400): 991－1003.
Stoto, M. A. (1983). "The accuracy of population projections." Journal of the American Statistical Association: 13－20.
Tiao, G. and G. Box (1981). "Modeling multiple times series with applications." Journal of the American Statistical Association 76(376): 802－816.
Tuljapurkar, S., R. D. Lee, et al. (2004). "Random scenario forecasts versus stochastic forecasts." International Statistical Review: 185－199.
Whelpton, P. (1928). "Population of the United States, 1925 to 1975." American Journal of Sociology: 253－270.
Wilson, T. and M. Bell (2004a). "Australia`s uncertain demographic future." Demographic Research 11(8): 195－234.
Wilson, T. and M. Bell (2004b). "Comparative empirical evaluations of internal migration models in subnational population projections." Journal of Population Research 21(2): 127－160.		zh_TW