A Bayesian Method for Forecasting Mortality Rates by Health State: LONGEVITY 13： International Longevity Risk and Capital Markets Solutions Conference 2017 A Bayesian Method for Forecasting Mortality Rates by Health State: with Rising Life Expectancy Atsuyuki Kogure Keio University, Japan Shinichi Kamiya Nanyang Technological University, Singapore Takahiro Fushimi Stanford University, USA September 21-22, 2017 1

Aging and mortality forecasting heavy burdens on long-term care cost 2

Japan has been and will be aging　very fast ! Population Pyramid of Japan from 1920 to 2050

Subpopulation mortality forecasting 4

Our objectives 5

Mortality forecasting for total population Death numbers for age x at time t Exposures (population sizes) for age x at time t Dxt Ext Force of mortality

Subpopulations by health state Death numbers for age x at time t in state j Exposures (subpopulation sizes) for age x at time t in state j Dxt0 Health state 0 (no problem) Ext0 Health state 1 (least severe) Ext1 Dxt1 ．．． ．．． ．．． Health state J (most severe) ExtJ DxtJ

Lee-Carter structure by health state

Mortality forecasting for subpopulations

Force of mortality for total population

Mixture Lee-Carter model

Identifiability of the mixture LC model

Bayesian estimation: parameter uncertainty

Priors for observation equation 14

Priors for health factors 15

Priors for State Equation 16

Hyperparameters

Application: Public Long-term Care Insurance System in Japan

Japanese Public Long-term Care System

Source: Monthly Report on the Status of Long-term Care Insurance Trends of Persons Certified As Requiring Long-term Care Total number of certified persons in 2015 is 608 (in 10, 000’s) increased by a factor of 2.79 for the past 15 years. total In 10,000’s Care levels Transitional Care levels levels Support 2000 2005 2010 2015 Source: Monthly Report on the Status of Long-term Care Insurance

Health states

Sizes of LTC subpopulations

Bayes Computation: MCMC

Posterior distributions for η，γ65，β65，κ2001: male

Summary statistics of posterior distributions: male

Changes in posterior means of γx，βx，κt over x or t male

Posterior distributions for η，γ65，β65，κ2001: female

Summary statistics of posterior distributions: female

Chanes in posterior means of γx， βx ，κt over x or t female

Gender difference in health effects male ηj ｈealth effect femae j=health state

Future mortality rates by health status

Future mortality rates by health status ｊ=5 ｊ=4 ｊ=3 ｊ=2 ｊ=1 ｊ=0 Male Female

Survival rates by health status

Future survival rates by health status Male Female

Conclusions (1)

Conclusions (2)

References

References