電腦模擬、隨機方法與人口推估的實證研究

An Empirical Study of Simulation and Stochastic Methods on Population Projections

10.6191/jps.2008.3

郭孟坤(Meng-Kung Kuo)；余清祥(Jack C. Yue)

人口推估 ； 人口變動要素合成法 ； 區塊拔靴法 ； 預測 ； 電腦模擬 ； population projection ； cohort component method ； block bootstrap ； forecast ； computer simulation

人口學刊

36期（2008 / 06 / 01）

67 - 98

繁體中文

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)，可歸類為情境推估(Scenario Forecast)的一種，作法是在參酌專家意見之後，以決定性模型(Deterministic Model)的方式，提供未來生育、死亡、遷移三要素的變動範圍。除了情境推估外，近年為了決定三要素的未來趨勢而發展出三種新的隨機方法：一為隨機推估(Stochastic Forecast)、一為模擬情境(Random Scenario Method)、一為推估誤差(ex post Method)。近十餘年美國及聯合國的推估仍以人口變動要素合成法為主，但未來生育、死亡、遷移趨勢的決定，隨機方法的使用比例逐漸增加。 為探討隨機方法的實用性，本文使用區塊拔靴法(Block Bootstrap)電腦模擬，代入生育、死亡、遷移變化不盡相同的臺灣、美國、日本、法國四國資料，以交叉驗證評估隨機方法的限制，並探討如何修正既有方法。另外，由於缺乏機率詮釋是傳統專家意見的缺點之一，本文採用Stoto (1983)提出的推估誤差法，給予區塊拔靴法和人力規劃處的推估在機率上的詮釋，彌補傳統情境推估的缺點，以提供使用專家意見與隨機方法的參考。研究發現區塊拔靴法在未來變化類似過去趨勢時，穩定性及準確性都相當不錯；傳統依賴專家意見的高、中、低三種推計，藉由推估誤差法發現高、低推計接近68%的預測區間，區塊拔靴法的推估也有類似的詮釋。

Population Projection is essential to policy planning, especially to social welfare. The cohort component method is the most popular method for population projection. The future trends of fertility, mortality, and immigration are often determined by the experts' opinions, which are also known as scenario forecasts, and then plugged into the cohort component method. However, the projections derived via the experts' opinions are deterministic and do not have implications in probability. To let the population projections possess the meaning of probability by renovating the scenario forecasts, researchers have developed three types of probabilistic forecasting methods, including the stochastic forecast method, random scenario method, and ex post method. In this paper, we study the block bootstrap method, a computer simulation method and also a stochastic forecast method, and evaluate the possibility of applying this method in population projection. Specifically, employing data from Taiwan, the U.S., Japan, and France, we use cross-validation and computer simulation to explore the limitations of the block bootstrap, and check if this method can produce reasonable projections. Based on the empirical results, we found that the block bootstrap is a feasible method and can produce stable population projections. In addition, we also study the ex post method proposed by Stoto (1983) and give the probability implications to projections from the Council for Economic Planning and Development (a scenario forecast).

1. 行政院經濟建設委員會建會網站
2. 內政部統計資訊網
3. Alho, J.M.,B.D. Spencer.(2006).Statistical Demography and Forecasting, Springer.
4. Betz, F.,O. Lipps.(2004).Stochastic Population Projection for Germany-based on the QS-approach to Modeling Age Specific Fertility Rates.MEA Discussion Paper Series from Mannheim Research Institute for the Economics of Aging, University of Mannheim.
5. Bühlmann, P.(2002).Bootstraps for Time Series.Statistical Science,17(1),52-72.
6. Denton, F.T.,C. H. Feaver,B.G. Spencer.(2005).Time Series Analysis and Stochastic Forecasting An Econometric Study of Mortality and Life Expectancy.Journal of Population Economics,18,203-227.
7. Hall, P.(1985).Resampling a Coverage Pattern.Stochastic Processes Applications,20,231-246.
8. Künsch, H.R.(1989).The Jackknife and the Bootstrap for General Stationary Observations.The Annuals of Statistics,17,1217-1261.
9. Lee, R.D.(1998).Population and Development Review 24.Supplement:Frontiers of Population Forecasting.
10. Lee, R.D.,L. Carter.(1992).Modeling and Forecasting U. S. Mortality.Journal of the American Statistical Association,87,659-671.
11. Lee, R.D.,S. Tuljapurkar.(1994).Stochastic Population Forecasts for the United States: Beyond High, Medium and Low.Journal of the American Statistical Association,89,1175-1189.
12. Lutz, W.,P. Saariluoma,W. Sanderson,S. Scherbov(2000).New Developments in the Methodology of Expert- and Argument-Based Probabilistic Forecasting.IIASA Interim Report.
13. Lutz, W.,W. Sanderson,S. Scherbov.,W. Lutz(edited),Revised Edition(1996).The Future Population of the World- What Can We Assume Today?.London:Earthscan.
14. Politis, D.N.,J.P. Romano(1994).The Stationary Bootstrap.Journal of the American Statistical Association,89,1303-1313.
15. Sanderson, W.C.,S. Scherbov,B.C. O''Neill\W. Lutz.(2004).Conditional Probabilistic Population Forecasting.International Statistical Review,72(2),157-166.
16. The Methods and Materials of Demography
17. Stoto, M.A.(1983).The Accuracy of Population Projections.Journal of the American Statistical Association,78,13-20.
18. Tuljapurkar, S.,R.D. Lee,Q. Li.(2004).Random Scenario Forecasts Versus Stochastic Forecasts..International Statistical Review,72(2),185-199.
19. World Population Prospects: The 2006 Revision Population Database
20. Wilmoth, J.(1993).Technical Report, Department of Demography.University of California-Berkeley.
21. 內政部(1949)。中華民國台閩地區人口統計。內政部。
22. 何正羽(2006)。東吳大學商用數學系碩士論文。東吳大學商用數學系。
23. 曾奕翔、余清祥(2002)。中華民國人口學會年會研討會論文。台北:政治大學。

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