Working Papers

Qian Lu, Katja Hanewald and Xiaojun Wang

Abstract: China has experienced large improvements in mortality rates, but there remain substantial variations at the provincial level. This paper develops new models to project mortality at both the national and provincial levels in China. We propose two models in a Bayesian hierarchical framework based on principal components and a random walk process, and compile a new comprehensive database containing mortality data for 31 provinces over the period 1982–2010. The baseline two-level model with a national–province hierarchy allows for information pooling across provinces, common national factors and consistency conditions. The extended three-level model with a national–region–province hierarchy pools information in the region and also allows for common factors within the region. Both models provide good estimates and reasonable forecasts for China and its provinces. The baseline two-level model provides good fit and reasonable forecasts with equal width intervals for the provinces. The three-level model has a better fit with a lower deviance information criterion and provides forecast intervals reflecting regional uncertainty. The sensitivity analyses show that the forecasts are robust when changing the trend assumptions and regional groups.

Keywords: Mortality modelling, Bayesian framework, Hierarchical models, Coherent mortality projection, China

Sisi Yang and Katja Hanewald

Abstract: The Chinese government has launched a series of health reforms to establish universal health insurance coverage, particularly for vulnerable groups, including older adults. However, the current public health insurance system is highly fragmented, consisting of different programs with different levels of premiums and benefits. We analyse whether the universal health insurance system increases the life satisfaction of middle-aged and older Chinese people and to what extent the type of health insurance affects the life satisfaction of this group. Our study is based on data from the China Health and Retirement Longitudinal Study, a nationally representative longitudinal survey of Chinese aged 45 and above, in 2011, 2013, and 2015. We find that the life satisfaction of middle-aged and older adults does not depend on having any health insurance coverage but varies with the type of health insurance coverage, controlling for potential confounding variables such as health status, occupation, hukou status, education, and other demographic variables. Individuals covered by the most generous program, the Government Medical Insurance, reported a higher life satisfaction. In comparison, individuals covered by the Urban Employee Medical Insurance, the Urban Resident Medical Insurance, and the New Rural Cooperative Scheme reported a lower life satisfaction by 0.155, 0.106, and 0.112 standard deviations, respectively. Our results suggest that establishing a more equitable health insurance system should be the next step in health reforms in China.

Keywords: Life satisfaction, Health insurance, Older adults, Health, China

Zhiping Huang, Michael Sherris, Andrés M Villegas and Jonathan Ziveyi

Abstract: This paper assesses and compares multi-factor continuous time ane mortality models applied to age-cohort mortality curves that are well suited for theoretical and practical application in nance and insurance. Models based on Gaussian distributed mortality rates, as well as the Cox-Ingersoll-Ross (CIR) process allowing for Gamma distributed mortality rates, are compared, also quantifying the probability of negative rates in the Gaussian models. In particular, we introduce the Gaussian Arbitrage-Free Nelson-Siegel (AFNS) mortality model incorporating level, slope and curvature factors. The models have appealing features including ecient estimation and computation. We estimate models using age-cohort data to capture cohort eects more eectively and in order to explain the variability in cohort mortality curves in the continuous time framework. The models allow for Poisson variation in the model estimation using the Kalman lter. The ane mortality models facilitate the derivation of closed-form survivor curves allowing for ecient valuation of mortality-linked claims. The models can also incorporate factor dependence allowing for age-dependence in the mortality curves. Importantly we show that the Gaussian independent factor AFNS model performs very well in explaining and forecasting cohort mortality.

Keywords: mortality models, continuous time, cohort curve, affine rates, Kalman filter

Michael Sherris and Pengyu Wei

Abstract: This paper proposes a multi-state model of both functional disability and health status in the presence of systematic trend and uncertainty. We classify each individual observation along two dimensions: health status (other than disability) and disability and use the multi-state latent factor intensity (MLFI) model to estimate the transitions rates. The model is then used to calculate (healthy) life expectancy and price a variety of insurance products. We illustrate the importance of various factors and quantify the potential losses from model misspecification. Our results suggest that insurers should pay great attention to health status, trend, and systematic uncertainty in disability/mortality modeling and insurance pricing. We also find that integrating LTC insurance with life annuity can help to reduce the systematic uncertainties.

Keywords: functional disability; health status; trend; systematic uncertainty