A Curve-Fitting Approach to Modeling and Projecting Global Mortality Rates

曲線配適方法在各國死亡率曲線預測的應用

黃孝慈(Hsiao-Tzu Huang)；宮可倫(Ko-Lun Kung)；郭維裕(Weiyu Kuo)；蔡政憲(Chenghsien Tsai)

Mortality rate ； Modeling ； Forecasting ； 死亡率 ； 模型 ； 預測

經濟論文

44卷4期（2016 / 12 / 01）

537 - 578

英文

We introduce a curve-fitting model to reduce the dimension of age parameters and allow additional degrees of freedom to be used for the period effect. Large-scale comparisons are carried out against the benchmark Lee-Carter model. The results reveal robust improvements in forecasting accuracy across 23 sampled countries. Our approach is superior in 96 percent of male cases and 88 percent of female cases, with an average RMSE improvement of 14.8 percent and 8.4 percent respectively. The panel Diebold-Mariano test indicates that these improvements are significant. The application in insurance pricing suggests the forecasting model has significant impact on annuity price.

本文研究曲線配適模型在死亡率模型上的應用。我們利用曲線配適模型來減少死亡率模型參數的數目，使得在同樣的參數數目下可以更好的估計與預測死亡率曲線。在實證上我們使用23個國家的死亡率資料，與文獻上常見的Lee-Carter模型比較預測的準確性。我們所提出的模型在男性死亡率預測上在96%的比較中有較好的成績，女性則是88%；平均的RMSE改善率分別是14.8%與8.4%。Panel Diebold-Mariano統計檢定同樣顯示我們的模型具有較佳的預測能力，最後我們將死亡率曲線的預測應用在年金商品的定價上，並說明其對年金價格的影響程度。

1. (1996).Mortality Projection for Japan: A Comparison of Four Methods.New York:Oxford Univerity Press.
2. Human Mortality Database (2011), The Human Mortality Database, University of California, Berkeley (USA) and the Max Planck Institute for Demographic Research (Germany), data accessed on 20 June 2011..
3. BIS(2005).,Bank for International Settlements.
4. Booth, H.(2006).Demographic Forecasting: 1980 to 2005 in Review.International Journal of Forecasting,22(3),547-581.
5. Booth, H.,Maindonald, J.,Smith, L.(2002).Applying Lee-Carter under Conditions of Variable Mortality Decline.Population Studies,56(3),325-336.
6. Booth, H.,Tickle, L.,Smith, L.(2005).Evaluation of the Variants of the Lee-Carter Method of Forecasting Mortality: A Multi-Country Comparison.New Zealand Population Review,31(1),13-34.
7. Brouhns, N.,Denuit, M.,Vermunt, J. K.(2002).A Poisson Log-Bilinear Regression Ap- proach to the Construction of Projected Lifetables.Insurance: Mathematics and Economics,31(3),373-393.
8. Cairns, A. J.,Blake, D.,Dowd, K.,Coughlan, G. D.,Epstein, D.,Khalaf-Allah, M.(2011).Mortality Density Forecasts: An Analysis of Six Stochastic Mortality Models.Insurance: Mathematics and Economics,48(3),355-367.
9. Carter, L. R.,Prskawetz, A.(2001).MPIDR Working PaperMPIDR Working Paper,Rostock, Germany:Max Planck Institute for Demographic Research.
10. Christensen, J. H. E.,Diebold, F. X.,Rudebusch, G. D.(2009).An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model.Econometrics Journal,12(3),C33-C64.
11. Coelho, E.,Nunes, L. C.(2011).ForecastingMortality in the Event of a Structural Change.Journal of the Royal Statistical Society: Series a (Statistics in Society),174(3),713-736.
12. Currie, I.,Durban, M.,Eilers, P.(2004).Smoothing and Forecasting Mortality Rates.Statistical Modelling,4,279-298.
13. De Rezende, R. B.(2008).,Brasilia:ANPEC - Associac, ?ao Nacional dos Centros de P’os-Graduac, ?ao em Economia.
14. Deb´on, A.,Montes, F.,Puig, F.(2008).Modelling and Forecasting Mortality in Spain.European Journal of Operational Research,189(3),624-637.
15. Diebold, F. X.,Li, C.(2006).Forecasting the Term Structure of Government Bond Yields.Journal of Econometrics,130(2),337-364.
16. Diebold, F. X.,Mariano, R. S.(1995).Comparing Predictive Accuracy.Journal of Business & Economic Statistics,13(5),253-263.
17. Dowd, K.,Cairns, A. J.,Blake, D.,Coughlan, G. D.,Epstein, D.,Khalaf-Allah, M.(2010).Evaluating the Goodness of Fit of Stochastic Mortality Models.Insurance: Mathematics and Economics,47(3),255-265.
18. Girosi, F.,King, G.(2007).,Santa Monica, CA:RAND Corporation.
19. Koissi, M.-C.,Shapiro, A. F.,H¨ogn¨as, G.(2006).Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Interval.Insurance: Mathematics and Economics,38(1),1-20.
20. Lee, R.(2000).The Lee-Carter Method for Forecasting Mortality, with Various Extensions and applications.North American Actuarial Journal,4(1),80-91.
21. Lee, R.,Carter, L.(1992).Modeling and Forecasting US Mortality.Journal of the American Statistical Association,87(419),659-675.
22. Lee, R.,Miller, T.(2001).Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality.Demography,38(4),537-549.
23. Lundstr¨om, H.,Qvist, J.(2004).Mortality Forecasting and Trend Shifts: An Application of the Lee-Carter Model to Swedish Mortality Data.International Statistical Review,72,37-50.
24. Nelson, C.,Siegel, A.(1987).Parsimonious Modeling of Yield Curves.Journal of Business,60,473-489.
25. Pesaran, M. H.,Schuermann, T.,Smith, L. V.(2009).Forecasting Economic and Financial Variables with Global VARs.International Journal of Forecasting,25,642-675.
26. Renshaw, A.,Haberman, S.(2003).Lee-Carter Mortality Forecasting with Age-Specific Enhancement.Insurance Mathematics and Economics,33,255-272.
27. Shang, H. L.,Booth, H.,Hyndman, R.(2011).Point and Interval Forecasts of Mortality Rates and Life Expectancy: A Comparison of Ten Principal Component Methods.Demographic Research,25,173-214.
28. Svensson, L. E.(1994).NBER Working PaperNBER Working Paper,未出版
29. Tuljapurkar, S.,Li, N.,Boe, C.(2000).A Universal Pattern of Mortality Decline in the G7 Countries.Nature,405,789-792.