Shi, J., Shi, Y., Wang, P., Zhu, D. (2024). Multi-population mortality modelling: a Bayesian hierarchical approach. ASTIN Bulletin: The Journal of the IAA, 54(1), 46-74.
He, L., Huang, F., Shi, J., Yang, Y. (2021). Mortality forecasting using factor models: Time-varying or time-invariant factor loadings?. Insurance: Mathematics and Economics, 98, 14-34.
A Sparse Dynamic Factor Model for Clustered High-dimensional Time Series: An Application to Mortality Modelling (with Catherine Forbes and Dan Zhu)
Abstract: Dynamic factor models are widely-used in the field of mortality modeling, where the Lee-Carter model (Lee and Carter, 1992) is recognized as the most prominent example. While it is always desirable to employ a minimal number of factors to attain high forecasting accuracy, empirical evidence suggests that many factors may be required to capture the complex dynamics observed in the mortality data. However, permitting a large number of factors will often lead to statistical problems, particularly in limited data contexts. In this article, we develop a new sparse dynamic factor model that substantially reduces the number of parameters, and caters for high-dimensional time series data containing heterogeneous pat- terns including clustering. In particular, our method provides a data-driven classification of the clustered high-dimensional time series with a single-factor model within each class. While each factor drives its own intra-cluster co-movement, the joint evolution of the factors induces inter-cluster dependency. In an application to French mortality data, our proposed model demonstrates superior forecasting performances when compared to a class of dynamic factor models, providing valuable insights for longevity risk management.
Decoding Mortality Trends: A Bayesian Approach With Instrumental Variables (with Catherine Forbes, Hong Li and Dan Zhu). Submitted to Demography
Abstract: In recent decades, the downward trend in U.S. mortality rates has slowed, with certain age groups experiencing an increase in death rates. Existing mortality models often focus on forecasting rates using latent factors, but the interpretation of these changes remains unclear. This paper enhances the Lee-Carter framework by incorporating covariates into the dynamic process of the leading latent factor to improve interpretability. To address potential endogeneity bias, we use the instrumental variable approach to estimate regression coefficients for these covariates. A comprehensive empirical analysis of U.S. and UK mortality data investigates the relationships between mortality trends and various drivers. We find that recent U.S. adult mortality exhibits a counter-cyclical trend and is significantly affected by hot temperatures and tobacco consumption. These findings provide possible explanations of the mortality deterioration in the U.S. over the last decade.
Mortality and Macro-economic Conditions: A Bayesian Mixed-frequency FAVAR Approach (with Catherine Forbes and Dan Zhu)
Abstract: Age-specific mortality data are typically released on an annual basis, yet eco- nomic and financial decision-making often necessitates more timely updates. This paper explores the dynamic interrelationships between age-specific mortality rates and macroeconomic conditions through a Mixed-Frequency Factor-augmented Vector Autoregression (MF-FAVAR) model, accommodating various data release frequencies. In particular, we develop an efficient simulation approach for handling high-dimensional, mixed-frequency data under the Bayesian MF-FAVAR model. Focusing on U.S.-based mortality data and corresponding quarterly macroeconomic indicators, we employ the proposed model to estimate and provide nowcasts of quarterly age-specific mortality rates using the most recent macroeconomic information. Additionally, a comprehensive structural analysis is conducted to unravel the complex interdependencies between macroeconomic conditions and mortality trends using different identification strategies. Specifically, a Bayesian proxy structural Vector Autoregression (BP-SVAR) model is employed to investigate the impacts of health expenditure shocks on mortality rates with the aid of an external instrumental variable. Our findings indicate that a positive, unexpected shock in health expenditures contributes to a short-term reduction in the overall mortality trend.
A Sensitivity Approach for Understanding Mortality and Interest Rate Risks of Annuities
A Smoothing Spline based Mortality Learning
Beyond Linearity: A Bayesian Non-parametric VAR Approach to Mortality Modelling