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Evaluating and extending the Lee - Carter model for mortality forecasting: bootstrap confidence interval. (English) Zbl 1098.62138

Summary: This paper first studies the performance of the R. D. Lee and L. R. Carter [J. Am. Stat. Assoc. 419, No. 87, 659–675 (1992)] model for mortality forecasting on the Nordic countries. Three approaches for computing the model parameters are compared: Singular Value Decomposition, Weighted Least Squares and Maximum Likelihood Estimation. Hypothetical projections are also made, based on variable period intervals. Secondly, the paper addresses an extension to the Lee-Carter method: a residual bootstrapped technique is used to construct confidence intervals for forecasted life expectancies. Uncertainties produced with this method incorporate the variability from all parameters in the model, while the original Lee–Carter method focuses on the variability in the time-varying parameter.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91D20 Mathematical geography and demography
62F25 Parametric tolerance and confidence regions
62N02 Estimation in survival analysis and censored data

Software:

itsmr; SPSS
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References:

[1] Alho, J., 2003. Predictive Distribution of Adjustment for Life Expectancy Change. Finnish Centre for Pensions. Working Papers 3.
[2] Alho, J., Discussion of Lee R., 2000, North American actuarial journal, 4, 91-93, (2000)
[3] Alho, J., 1998. A stochastic forecast of the population of Finland, Tilastokeskus, Reviews 1998/4.
[4] Bell, W.R., Comparing and assessing time series methods for forecasting age specific demographic rates, Journal of official statistics, 13, 279-303, (1997)
[5] Bongaarts, J., Population aging and the rising cost of public pensions, Population and development review, 30, 1, 1-23, (2004)
[6] Booth, H.; Maindonald, J.; Smith, L., Applying lee – carter under conditions of variable mortality decline, Population studies, 56, 325-336, (2002)
[7] Box, G.E.; Jenkins, G.M., Time series analysis: forecasting and control, (1976), Holden-Day San Francisco · Zbl 0363.62069
[8] Brillinger, D.R., The natural variability of vital rates and associated statistics, Biometrics, 42, 4, 693-734, (1986) · Zbl 0611.62136
[9] Brockwell, P., Davis, R., 1996. Introduction to Time Series and Forecasting. Springer Texts in Statistics. · Zbl 0868.62067
[10] Brouhns, N.; Denuit, M.; Van Keilegom, I., Bootstrapping the Poisson log-bilinear model for mortality forecasting, Scandinavian actuarial journal, 3, 212-224, (2005) · Zbl 1092.91038
[11] Brouhns, N.; Denuit, M.; Vermunt, J., A Poisson log-linear regression approach to the construction of projected life tables, Insurance: mathematics and economics, 31, 373-393, (2002) · Zbl 1074.62524
[12] Brown, R.L., Introduction to the mathematics of demography, (1997), Actex Publications
[13] Efron, B., Bootstrap methods: another look at the jackknife, The annals of statistics, 7, 1-26, (1979) · Zbl 0406.62024
[14] Efron, B., Tibshirani, R., 1998. An Introduction to the Bootstrap. CRC Press, Boca Raton, FL. · Zbl 0835.62038
[15] England, P.; Verrall, R., Analytic and bootstrap estimates of prediction errors in claims reserving, Insurance: mathematics and economics, 25, 281-293, (1999) · Zbl 0944.62093
[16] Golub, G.; Van Loan, C., Matrix computations, (1983), John Hopkins Baltimore · Zbl 0559.65011
[17] Hoedemakers, T.; Beirlant, J.; Goovaerts, M.; Dhaene, J., Confidence bounds for discounted loss reserves, Insurance: mathematics and economics, 33, 297-316, (2003) · Zbl 1103.91367
[18] Keilman, N., How accurate are the united nations world population projections?, Population and development review, 24, 15-41, (1998)
[19] Kelley, C., Solving nonlinear equations with Newton’s method. fundamentals of algorithms, (2003), Society for Industrial and Applied Mathematics Philadelphia · Zbl 1031.65069
[20] Kharab, A.; Guenther, R., An introduction to numerical methods: A MATLAB approach, (2002), Chapman & Hall/CRC · Zbl 0993.65001
[21] Lawson, C.; Hanson, R., Solving least squares problems, (1974), Prentice-Hall EngleWood Cliffs, NJ · Zbl 0860.65028
[22] Lee, R.D., The lee – carter method for forecasting mortality, with various extensions and applications, North American actuarial journal, 1, 4, 80-91, (2000) · Zbl 1083.62535
[23] Lee, R.D.; Carter, L.R., Modeling and forecasting U.S. mortality, Journal of the American statistical association, 419, 87, 659-675, (1992) · Zbl 1351.62186
[24] Lee, R.D.; Miller, T., Evaluating the performance of the Lee Carter mortality forecasts, Demography, 38, 4, 537-549, (2001)
[25] Lee, R.D.; Rofman, R., Modeling and forecasting mortality in Chile, Notas, 22, 59, 182-213, (1994)
[26] Levene, H., (), 278-292
[27] Li, N.; Lee, R.; Tuljapurkar, S., Using the lee – carter method to forecast mortality for population with limited data, International statistical review, 72, 1, 19-36, (2004) · Zbl 1330.62349
[28] Lin, J., Changing kinship structure and its implications for old-age support in urban and rural China, Population studies, 49, 1, 127-145, (1995)
[29] Lundström, H.; Qvist, J., Mortality forecasting and trend shifts: an application of the lee – carter model to swedish mortality data, International statistical review, 72, 1, 37-50, (2004) · Zbl 1330.62437
[30] Marques de Sá, J.P., Applied statistics using spss, statistica and Matlab, (2003), Springer · Zbl 1028.62082
[31] Preston, S.; Heuveline, P.; Guillot, M., Demography: measuring and modeling population processes, (2001), Blackwell Publishers
[32] Quenouille, M., Notes on biais in estimation, Biometrika, 43, 353-360, (1956) · Zbl 0074.14003
[33] Renshaw, A.E.; Haberman, S., On the forecasting of mortality reduction factors, Insurance: mathematics and economics, 32, 3, 379-401, (2003) · Zbl 1025.62041
[34] Renshaw, A.; Haberman, S., Lee – carter mortality forecasting with age-specific enhancement, Insurance: mathematics and economics, 33, 255-272, (2003) · Zbl 1103.91371
[35] Stewart, G.W., 1998. Matrix Algorithms Volume 2: Eigensysytems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
[36] Stoto, M., Accuracy of population projections, Journal of the American statistical association, 78, 13-20, (1983)
[37] Tuljapurkar, S.; Nan, L.; Boe, C., A universal pattern of mortality decline in the G7 countries, Nature, 405, 789-792, (2000)
[38] Wilmoth, J.R., 1993. Computational Methods for Fitting and Extrapolating the Lee-Carter Model of Mortality Change. Technical Report. University of California, Berkeley, USA.
[39] Wilmoth, J.R., ()
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