Forecasting Mortality using Imputed Data: The Case of Taiwan
-
Sheng-Feng Luo
and
Yu-Hsuan Lee
Abstract
Mortality forecasting plays an essential role in designing welfare policies and pricing aged-related financial derivatives. However, most prevailing models do not perform well in mortality forecasting particularly for the elder people. Indeed, the problem of missing category for the elderly is a typical feature in developing countries, because people are shorter-lived in earlier times and hence the mortality is recorded up to fewer age categories. For example, in Taiwan, the mortality is recorded up to an age of 95 before 1997, but as the improvement of life expectancy, the mortality is recorded up to an age of 100 afterwards. This paper proposes several approaches for data imputation to alleviate this systematic missing data problem of the mortality data. Motivated by Lee, and Carter. 1992. “Modelling and Forecasting the Time Series of US Mortality.” Journal of the American Statistical Association 87:659–71 and Renshaw, and Haberman. 2006. “A Cohort-Based Extension to the Lee-Carter Model for Mortality Reduction Factors.” Insurance: Mathematics and Economics 38:556–70, we employ factor models, in which age, period, and cohort are employed as useful effects. Simulation study and an empirical study using mortality data of Taiwan demonstrate the improvement in forecasting using a suitable data augmentation technique.
Funding statement: Funding: Ministry of Science and Technology, Taiwan (Grant / Award Number: “102-2410-H-033-053”, “103-2633-M-008-001”.
References
Booth, H., J. Maindonald, and L. Smith. 2002. “Applying Lee-Carter under Conditions of Variable Mortality Decline.” Population Studies 56 (3):325–36.10.1080/00324720215935Search in Google Scholar
Butt, Z., and S. Haberman. 2009. “ilc: A collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms,” Actuarial Research Paper No.190.Search in Google Scholar
Cairns, A., D. Blake, and K. Dowd. 2006. “A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” Journal of Risk and Insurance 73:687–718.10.1111/j.1539-6975.2006.00195.xSearch in Google Scholar
Cairns, A., D. Blake, K. Dowd, G. Coughlan, D. Epstein, A. Ong, and I. Balevich. 2009. “A Quantitative Comparison of Stochastic Mortality Models Using Data From England & Wales and the United States.” North American Actuarial Journal 13:1–35.10.1080/10920277.2009.10597538Search in Google Scholar
Cairns, A., D. Blake, K. Dowd, G. Coughlan, and M. Khalaf-Allah. 2011. “Bayesian Stochastic Mortality Modelling for Two Populations.” Astin Bulletin 41:29–59.Search in Google Scholar
Coale, A., and G. Gao. 1989. “Revised Regional Model Life Tables at Very Low Levels of Mortality.” Population Index 55:613–43.10.2307/3644567Search in Google Scholar
Coale, A., and E. Kisker. 1990. “Defects in Data on Old-Age Mortality in the United States: New Procedures for Calculating Schedules and Life Tables at the Highest Ages.” Asian and Pacific Population Forum 4:1–31.Search in Google Scholar
Denuit, M., and A. -C. Goderniaux. 2005. “Closing and Projecting Lifetables Using Log-Linear Models.” Bulletin de l‘Association Suisse des Actuaires, 1:29–49.Search in Google Scholar
Dowd, K., D. Blake, A. Cairns, G. Coughlan, D. Epstein, and M. Khalaf-Allah. 2010. “Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts.” North American Actuarial Journal 14:281–98.10.2139/ssrn.1396201Search in Google Scholar
Efron, B., and R. J. Tibshirani. 1993. An Introduction to the Bootstrap. New York: Chapman & Hall/CRC.10.1007/978-1-4899-4541-9Search in Google Scholar
Gompertz, B. 1825. “On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London 115:513–83.10.1098/rstl.1825.0026Search in Google Scholar
Hyndman, R. J., and M. S. Ullah. 2007. “Robust Forecasting of Mortality and Fertility Rate: A Functional Data Approach.” Computational Statistics and Data Analysis 51:4942–56.10.1016/j.csda.2006.07.028Search in Google Scholar
Jarner, S., and E. Kryger. 2011. “Modelling Adult Mortality in Small Populations: The Saint Model.” Astin Bulletin 41:377–418.Search in Google Scholar
Kupper, L. L., J. M. Janis, A. Karmous, and B. G. Greenberg. 1985. “Statistical Age-Period-Cohort Analysis: A Review and Critique.” Journal of Chronic Diseases 38:811–30.10.1016/0021-9681(85)90105-5Search in Google Scholar
Lee, R., and L. R. Carter. 1992. “Modelling and Forecasting the Time Series of US Mortality.” Journal of the American Statistical Association 87:659–71.10.1080/01621459.1992.10475265Search in Google Scholar
Lee, R., and T. Miller. 2001. “Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality.” Demography 38:537–49.10.1353/dem.2001.0036Search in Google Scholar
Li, N., and R. Lee. 2005. “Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee-Carter Method.” Demography 42:575–94.10.1353/dem.2005.0021Search in Google Scholar
Makeham, W. 1860. “On the Law of Mortality.” Journal of the Institute of Actuaries 13:325–58.10.1007/978-3-642-81046-6_31Search in Google Scholar
Renshaw, A. E., and S. Haberman. 2006. “A Cohort-Based Extension to the Lee-Carter Model for Mortality Reduction Factors.” Insurance: Mathematics and Economics 38:556–70.10.1016/j.insmatheco.2005.12.001Search in Google Scholar
Tuljapurkar, S., N. Li, and C. Boe. 2000. “A Universal Pattern of Mortality Decline in G7 Countries.” Nature 405:789–92.10.1038/35015561Search in Google Scholar
Wilmoth, J. R. 1996. “Mortality Projections for Japan: A Comparison of Four Methods.” In Health and Mortality among Elderly Populations, edited by G. Caselli and A. D. Lopez, eds., International Studies in Demography, 266–87. New York: Oxford University Press, chapter 13.Search in Google Scholar
Yang, S. S., J. C. Yue, and H. C. Huang. 2010. “Modeling Longevity Risks Using a Principal Component Approach: A Comparison With Existing Stochastic Mortality Models.” Insurance.” Mathematics and Economics 46:254–70.10.1016/j.insmatheco.2009.09.013Search in Google Scholar
Zhou, R., J. S. -H. Li, and K. S. Tan. 2013. “Pricing Standardized Mortality Securitizations: A Two-Population Model with Transitory Jump Effects.” Journal of Risk and Insurance 80:733–74.10.1111/j.1539-6975.2013.12015.xSearch in Google Scholar
©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Featured Articles
- Forecasting Mortality using Imputed Data: The Case of Taiwan
- On the Bayesian Risk Evaluation of Minimum Guarantees in Variable Annuities
- On the Use of Long-Term Risk Measures as an Approach to Communicating Risks
- Effective Structure of Reinsurance Function for Disaster Risk in the Asia-Oceania Region
- Forecasting Thai Mortality by Using the Lee-Carter Model
- Long-Term Care: Is There Crowding Out of Informal Care, Private Insurance as Well as Saving?
Articles in the same Issue
- Frontmatter
- Featured Articles
- Forecasting Mortality using Imputed Data: The Case of Taiwan
- On the Bayesian Risk Evaluation of Minimum Guarantees in Variable Annuities
- On the Use of Long-Term Risk Measures as an Approach to Communicating Risks
- Effective Structure of Reinsurance Function for Disaster Risk in the Asia-Oceania Region
- Forecasting Thai Mortality by Using the Lee-Carter Model
- Long-Term Care: Is There Crowding Out of Informal Care, Private Insurance as Well as Saving?
