Mortality forecasting using a modified Continuous Mortality Investigation Mortality Projections Model for China I: methodology and country-level results

Abstract

In this paper, we project future mortality rates for actuarial use with Chinese data using a modified Continuous Mortality Investigation (CMI) Mortality Projections Model. The model adopts a convergence structure from “initial” to “long-term” rates of mortality improvement as the process of projection. The initial rates of mortality improvement are derived using two-dimensional P-spline methodology. Given the short history of Chinese data, the long-term rates of mortality improvement are determined by borrowing information from international experience. K-means clustering with dynamic time warping distance is used to classify populations, which is novel in the actuarial mortality research field. The original CMI approach is deterministic, however, in this paper we make it stochastic using techniques outlined by Koller and described by Browne et al. Comparing our results with a pure extrapolative approach, we find that the CMI Mortality Projections Model is more suitable for long-term projections for China.

A Bayesian Approach to Developing a Stochastic Mortality Model for China

“…With such estimates of β x , the projected future mortality rates do not have a smooth, logical age pattern. The same problem was also encountered in the work of Huang and Browne (), page 42, who applied the Lee–Carter model to a portion of the Chinese mortality data set. The abnormally jagged pattern of β x is in part because the length of the data set is too short and in part because some exposure counts (those in the years for which the data are obtained from surveys) are too small.…”

“…Furthermore, the work of Li et al (2004) takes no account of parameter uncertainty and therefore does not meet criterion 2. This category of methods has been considered by other researchers including Jiang et al (2013), who also used three years of census data, Huang and Browne (2017), who considered only the data from 1997 to 2011, and Wang and Huang (2011), who used only the data from 1994 to 2008. Their contributions also do not meet criterion 1.…”

Credible Regression Approaches to Forecast Mortality for Populations with Limited Data

“…For instance, Li et al (2004) extended the Lee-Carter model to be applied for Chinese and South Korean mortality data, which are available at only a few points in time and at unevenly spaced intervals. Zhao (2012) modified the Lee-Carter model by incorporating linearized cubic splines and other additive functions to approximate the model parameters and forecast mortality for short-base-period Chinese data and Huang and Browne (2017) presented a stochastic modification of the CMI (Continuous Mortality Investigation) model to project mortality improvement rates for limited Chinese data using clustering analysis techniques.…”

Bayesian Hierarchical Multi-Population Mortality Modelling for China’s Provinces

“…Zhao (2012 and Zhao et al (2013) apply a modified Lee-Carter model based on census and sample survey data for China. Huang and Browne (2017) and Huang (2017) modify the continuous mortality investigation method of the UK's Institute and Faculty of Actuaries and apply it to China's mortality using data from 1997-2011. Apart from stochastic modelling, Bayesian methods have also been introduced into mortality modelling in China.…”