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| Title: | Lee-Carter模型於小區域人口的探討
A Study of Lee-Carter Model in Small Areas |
| Authors: | 張君瑋
Jhang, Jyun-Wei |
| Contributors: | 余清祥
Yu,Cing-Siang
張君瑋
Jhang, Jyun-Wei |
| Keywords: | 壽命延長
死亡率模型
小區域估計
Lee-Carter 模型
修勻
Life Prolonging
Small Area Estimation
Mortality Models
Lee-Carter Model
Graduation |
| Date: | 2023 |
| Issue Date: | 2023-09-01 14:57:30 (UTC+8) |
| Abstract: | 臺灣居民的平均壽命逐年提升，並未隨時間而有明顯減緩的趨勢，預期我國高齡人口將大幅增加，推估未來壽命成為各界關注的議題。死亡模型常用於壽命推估，過去研究發現Lee-Carter模型用於全國等人數較多的層級時，估計結果相對穩定、準確度也相當不錯，因此Lee-Carter模型廣為各國歡迎。然而這個模型套用在人口數較少的地區時，參數估計值有明顯偏誤，有不少學者提出修正作法，但使用時仍有不少限制。另外，Lee-Carter模型有三種參數估計方法：奇異值分解法（SVD法）、近似法、最大概似估計法（MLE法），這三種方法各有特色，但過去並無相關研究比較這些方法在人數少時的估計結果。
有鑑於此，本研究以比較Lee-Carter模型三種估計方法為目標，特別聚焦於人數少時的估計結果，透過電腦模擬比較三種估計方法，評估各方法較為適用的時機。除了探討人口數與估計偏誤之間的關係，我們也提出了可能的調整方式，並與其他常見的修正模型（例如：Li-Lee模型）進行比較。此外，本研究還探討了如何改善在小區域使用Lee-Carter模型的問題，包括降低觀察死亡人數對估計結果的影響，以及納入參考區的小區域死亡率修勻等方法，並評估了不同改善方法對參數估計與預測結果的影響。研究結果顯示隨著人口數的減少，Lee-Carter模型各估計方法的偏誤增大。在三種估計方法中，MLE法的死亡率估計結果最為準確，但即便將死亡人數為零以較小數值（例如：106）替換，該問題仍然無法解決；雖然MLE法在估計上優於其他方法，但預測結果卻最不穩定，尤其是人數較少時。另外，近似法較為穩定，如果結合Partial SMR則更為準確，不論是參數估計或預測的結果都最佳。
Life expectancy of Taiwanese residents continues to increase and there are no signs of slowing down. Taiwan’s elderly population is expected to increase significantly and forecasting life expectancy is important for policy planning. Mortality models are often used to predict life expectancy and Lee-Carter is popular choice. Past studies show that it is fairly stable and has high estimation the accuracy in the case of large population. However, it would create biased estimation if the model is applied to the case of small population. Many scholars proposed modification models to correct the bias but they still have quite a few limitations in usage. Note that the Lee-Carter model has three parameter estimation methods: singular value decomposition (SVD), approximation, and maximum likelihood estimation (MLE). These estimation methods have their own advantages, but no studies have compared the differences between them in the case of small population.
The purpose of this study is to compare the three estimation methods of the Lee-Carter model, especially focusing on the small population case, and evaluate the estimation results through computer simulation. We want to explore the relationship between population size and estimation bias and propose modification methods, in order to compare them with other common correction models (e.g., Li-Lee model). We found that the bias of all estimation methods of the Lee-Carter model increases as the population size decreases. The estimation results of the MLE method are the most accurate but it becomes unstable when the population size is small. Even using a small value (for example: 10-6) to replace zero deaths, the estimation results of MLE are still the least stable and accurate. On the other hand, the approximation method is relatively stable, and it will be more accurate if combined with Partial SMR, and the results of both parameter estimation and prediction are the best. |
| Reference: | 一、中文文獻
王信忠、金碩、余清祥（2012）。「小區域死亡率推估之研究」，《人口學刊》，45，121-154。
余清祥（1997）。《修勻：統計在保險的應用》，臺北：雙葉書廊。
余清祥、王信忠、陳譽騰（2021）。「年輪變動比用於小區域人口推估的探討」，《人口學刊》，63，99-133。
林志軒（2014）。「小區域死亡率模型的探討」。國立政治大學商學院統計學系碩士論文。
陳政勳、余清祥（2010）。「小區域人口推估研究：臺北市、雲嘉兩縣、澎湖縣的實證分析」，《人口學刊》，41，153-183。
曾奕翔（2002）。「臺灣地區死亡率推估的實證方法之研究與相關年金問題之探討」，國立政治大學商學院風險管理與保險學系碩士班碩士論文。
謝靖惟（2022）。「小區域生命表編製與死亡率模型估計」，國立政治大學商學院風險管理與保險學系碩士論文。
二、英文文獻
Brouhns, N., M. Denuit, and J. K. Vermunt (2002). “A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables”, Insurance: Mathematics and Economics, Volume 31, Issue 3, 373-393.
Coulomb, J.-B., Salhi, Y., & Thérond, P.-E. (2020). Credibility Adjustment of the Lee-Carter Longevity Model for Multiple Populations. Retrieved from hal.archives-ouvertes.fr/hal-02557208
Jarner, S. F., & Kryger, E. M. (2011). Modelling Adult Mortality in Small Populations: The Saint Model. Astin Bulletin, 41(2), 377-418.
Henderson, R. (1924). “A New Method of Graduation”, Transactions of the Actuarial Society of America, Volume 25, 29-40.
Henderson, R. (1925). “Further Remarks on Graduation,” Transactions of the Actuarial Society of America, Volume 26, 52-57.
Lee, R.D. and Carter, L.R. (1992). “Modeling and Forecasting US Mortality”, Journal of the American Statistical Association, Volume 87, Issue 419, 659-671.
Lee, W.C. (2003). “A Partial SMR Approach to Smoothing Age-specific Rates”, Annals of Epidemiology, Volume 13, Issue 2, 89-99.
Lee, R.D. (2000). The Lee-Carter Method For Forecasting Mortality, with various extensions and applications. North American actuarial journal, 4(1), 80-91.
Li, N., and Lee, R. (2005). Coherent mortality forecasts for a group of populations : An extension of the Lee-Carter method. Demography U.S. male mortality.
Renshaw, A and Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics 38(3):556-570.
Wiśniowski, A., Smith, P. W. F., Bijak, J., Raymer, J., & Forster, J. J. (2015). Bayesian Population Forecasting: Extending the Lee-Carter Method. Demography, 52, 1035–1059.
Wang, H.-C., Yue, C. J., and Chong, C.-T. (2018). Mortality Models and Longevity Risk for Small Populations. Insurance: Mathematics and Economics, Volume 78, 351-359.
Mantal, N. and Myers, M. (1971). “Maximum Likelihood Iterative Procedures in Multiparameter Situations,” Volume 66, Issue 335, 484-491.
Wang, H.-C., Yue, C. J., and Wang, T.-Y. (2019). Do Domestic Immigrants Live Longer? An Approach for Estimating the Life Expectancy of Small Populations. Migration Letters, Volume 16, Issue 3, 399-416.
Yue, C.J., Wang, H.-C.. and Wang, T. (2021). “Using Graduation to Modify the Estimation of Lee-Carter Model for Small Populations,” North American Actuarial Journal, Volume 25, S410-S420. |
| Description: | 碩士
國立政治大學
統計學系
110354022 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110354022 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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