Forecasting Mortality using Imputed Data: The Case of Taiwan

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.