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.

中文部份
中華民國內政部統計資訊網，http://www.moi.gov.tw/W3/stat/。
中華民國臺灣民國 95 年至民國 140 年人口推計，行政院經濟建設委員會人力
規劃處，http://www.cepd.gov.tw/index.jsp。
中華民國台灣地區民國 84 年至民國 140 年人口推計，行政院經濟建設委員
會，http://www.cepd.gov.tw/index.jsp 。
內政部 (1949 ~ 2005)，中華民國台閩地區人口統計，內政部編印。
陳紹馨 (1979)，「中國社會文化研究的實驗室 – 台灣」，台北聯經出版事業
公司。
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。
余清祥與藍銘偉 (2003)，“台灣地區生育率模型之研究”，人口學刊，Vol. 27,
105-131。
黃意萍與余清祥 (2002)，“台灣地區生育率模式的推估研究”，人口學刊，
Vol. 25, 145-171。
曾奕翔與余清祥 (2002)，“台灣地區死亡率推估的實證方法之研究”，中華民
國人口學年會學術研討會。
賴思帆與余清祥 (2006)，“台灣與各國生育率模型之實證與模擬比較”，人口
學刊， Vol. 33, 33-59。
郭孟坤與余清祥 (2007)，“電腦模擬與隨機方法在人口推估的應用”，國立政
治大學統計學系碩士論文。
Alho, J. M. (1990b), “Stochastic Methods in Population Forecasting.” International J.
Forecasting, Vol.6, 521-530.
Alho, J. M. (2002), “The Population of Finland in 2050 and Beyond.” The Research
Institute of the Finnish Economy, Discussion Papers, No.826.
Alho, J., Alders, M., Cruijsen, H., Keliman, N., Nikander, T. and Pham. D.Q. (2006),
“New Forecast:Population Decline Postponed in Europe.” Statistical Journal of
the United Nations ECE, Vol.23, 1-10.
Alho, J.M. and Spencer, B.D. (1997), “The Practical Specification of the Expected
Error of Population Forecasts.” Journal of Official Statistics, Vol.13(3), 203-225.
Alho, J.M. and Spencer, B.D. (2005), Statistical Demography and Forecasting,
Springer, New York.
Armstrong, J.S. (2001), “Principles of Forecasting: A Handbook for Researchers and
Practitioners.” Kluwer Academic Publishers, Boston.
Bongarrts, J. and Feeney G. (1998), “On the Quantum and Tempo of Fertility.”
Population And Development Review, Vol.24(2), 271-291.
Bühlmann, P. (2002), “Bootstraps for Time Series.” Statistical Science, Vol. 17(1),
52-72.
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.
Chatfield, C. (2000), Time-Series Forecasting Chapman & Hall/CRC, New York.
Cushing, B. and Poot, J. 2004, “Crossing boundaries and borders: regional science
advances in migration modelling.” Regional Science 83: 317–338.
Denton, F.T., Feaver, C.H., and Spencer, B.G. (2005), “Time Series Analysis and
Stochastic Forecasting: An Econometric Study of Mortality and Life
Expectancy.” Journal of Population Economics, Vol.18, 203-227.
Efron, B. (1979), “ Bootstrap Method : Another Look at Jackknife. ”, Ann Statist, Vol.
7, 1-26.
Gullickson, A. (2001), “Multiregional probabilistic forecasting.” Paper presented at
the Young Scientists Summer Program Midsummer Workshop, International
Institute for Applied Systems Analysis, July 2001,Vienna, Austria.
Gullickson, A., and Moen, J. (2001), “The Use of Stochastic Methods in Local Area
Population Forecasts.”
Hall, P. (1985), “Resampling a Coverage Pattern.” Stochastic Processes Applications,
Vol. 20, 231-246.
Keilman, N., Pham, D.Q., and Hetland, A. (2002), “Why Population Forecasts should
be Probabilistic - Illustrated by the Case of Norway”, Demographic Research,
Vol. 6, 410-454.
Künsch, H.R. (1989), “The Jackknife and the Bootstrap for General Stationary
Observations.” The Annuals of Statistics, Vol. 17, 1217-1261.
Kupiszewski, M. and Kupizewska, D. (2003), “Internal migration component in subnational
population projections in member states of the European Union.”
Working Paper 2/2003, Central European Forum for Migration Research,
Warsaw.
Lee, R.D. (1974), “Forecasting Births in Post-Transition Populations: Stochastic
Renewal with Serially Correlated Fertility.” Journal of American Statistical
Association, Vol.69, 607-617.
Lee, R.D. (1998), “Probabilistic Approaches to Population Forecasting.” Population
and Development Review, Vol. 24, Supplement: Frontiers of Population
Forecasting. 156-190.
Lee, R.D. and Carter, L (1992), “Modeling and Forecasting U. S. Mortality.” Journal
of the American Statistical Association, Vol. 87, 659-671.
Lee, R.D. and Tuljapurkar, S. (1994), “Stochastic Population Forecasts for the United
States : Beyond High, Medium and Low.” Journal of the American Statistical
Association, Vol. 89, 1175-1189.
Lee, R.D. and Miller, T. (2001), “Estimating the Performance of the Lee-Carter
Method for Forecasting Mortality.” Demography, Vol.38, 537-549.
Lee, R., Miller, T. and Edwards, R.D. (2003), “The Growth and Aging of California’s
Population: Demographic and Fiscal Projections, Characteristics and Service
Needs.” California Policy Research Centre, University of California, Berkeley,
CA.
Isserman, A. (1985), “The Right People, the Right Rates: Making Population
Estimates and Forecasts with an Interregional Cohort-Component Model.”
Journal of the American Planning Association 59, 45–64.
Long, J.F. and Hollmann, F.W. (2004), “Developing Official Stochastic Population
Forecasts at the US Census Bureau.” International Statistical Review, Vol. 72(2),
201-208.
Lutz, W., Sanderson, W., and Scherbov, S. (1996), “Probabilistic Population
Projections Based on Expert Opinion.” The Future Population of the World.
What Can We Assume Today? ,Ed. W. Lutz, 397-428, Revised Edition, London,
Earthscan.
Lutz, W., Saariluoma P., Sanderson, W., and Scherbov, S. (2000), “New
Developments in the Methodology of Expert- and Argument-Based Probabilistic
Forecasting.” IIASA Interim Report, IR-00-020.
Lutz, W., Sanderson, W., and Scherbov, S. (2001), “The End of World Population
Growth.” Nature, Vol. 412, 543-545.
Lutz, W., Sanderson, W., and Scherbov, S. (2004), “The End of World Population
Growth.” The End of World Population Growth in the 21st Century, 17-83,
London, Earthscan.
Lutz, W. and Scherbov, S. (1998), “An Expert-Based Framework for Probabilistic
National Population Projections: The Example of Austria.” European Journal of
Population, Vol. 14, 1-17.
Mammen, E. and Nandi, S. (2004), “Bootstrap and Resampling.” Handbook of
Computational Statistics Concepts and Methods, Ed. Gentle, J. E., Härdle, W.
and Mori, Y., 468-495, Springer, Heidelberg.
Maarten, A. and Joop, D.B. (2002),“An Expert Knowledge Approach to Stochastic
Mortality Forecasting in the Netherlands.”
Miller, T. (2002), “California’s uncertain population future.” Unpublished paper,
Department of Demography, University of California, Berkeley, US.
O'Neill, B.C., Balk, D., Brickman, M., and Ezra, M. (2001), “A Guide to Global
Population Projections.” Demographic Research, Vol. 4, 203-288.
Politis, D.N. and Romano J.P. (1994), “The Stationary Bootstrap.” Journal of the
American Statistical Association, Vol. 89, 1303-1313.
Rees, P., and Turton, I. (1998), “Investigation of the effects of input uncertainty on
population forecasting.” Paper prepared for the GeoComputation 98 Conference,
Bristol, UK, 17–19 September 1998.
Rogers, A. (1975), “Introduction to Multiregional Mathematical Demography.” New
York: John Wiley and Sons.
Rogers, A. (1985), “Regional Population Projection Models.” Beverly Hills, CA:
Sage.
Rogers, A. and Castro, L. (1984), “Model migration schedules. In Migration,
Urbanization, and Spatial Population Dynamics.” Chapter 2, pp. 41{91. Boulder:
Westview Press.
Rogers, A., Willekens, F., Little, J. and Raymer, J. (2002), “Describing Migration
Spatial Structure.” Regional Science 81, 29–48.
Sanderson, W.C., Scherbov, S., O’Neill, B.C., and Lutz, W. (2004), “Conditional
Probabilistic Population Forecasting.” International Statistical Review, Vol.
72(2), 157-166.
Smith, S.K. (1997), “Further Thoughts on Simplicity and Complexity in Population
Projection Models.” International Journal of Forecasting, Vol. 13, 557-565.
Smith, S.K., and Tayman, J. (2004), “Confidence Intervals for Population Forecasts:
A Case Study of Time Series Models for states.” Paper prepared for the
Population Association of America Meeting, Boston, April 1–3, 2004.
Smith, S.K. (1986), “Accounting for Migration in Cohort-Component Projections of
State and Local Populations.” Demography , Vol. 23, No. 1. (Feb., 1986), pp.
127-135.
Stoto, M.A. (1983), “The Accuracy of Population Projections.” J.A.S.A., Vol. 78
(381), 13-20.
Tuljapurkar, S., Lee, R.D., and Li, Q. (2004), “Random Scenario Forecasts Versus
Stochastic Forecasts.” International Statistical Review, Vol. 72(2), 185-199.
Van Imhoff, E., Van derGaag, N., Van Wissen, L. and Rees, P. (1997), “The
Selection of Internal Migration Models for European Regions.” International
Journal of Population Geography 3, 137–59.
Whelpton, P.K. (1928), “Population of the United States, 1925 to 1975.” American
Journal of Sociology, Vol. 34, 253-270.
Whelpton, P.K. (1954), “On Stationary Processes in the Plane.” Biometrika, Vol. 41,
434-449.
Wilson, T. and Bell, M. (2004a), “Australia’s Uncertain Demographic Future.”
Demographic Research 11–8.
Wilson, T. and Bell, M. (2004b), “Comparative Empirical Evaluations of Internal
Migration Models in Subnational Population Projections.” Journal of Population
Research 21.2, 127–60.
Wilson, T. and Rees, P. (2005), “Recent Developments in Population Projection
Methodology : A Review.” Population, Space and Place, Vol. 11, 337-360.