Dynamic modelling and coherent forecasting of mortality rates: a time-varying coefficient spatial-temporal autoregressive approach

Existing literature argues that the mortality rate of a specific age is affected not only by its own lags but by the lags of neighbouring ages, known as cohort effects. Although these effects are assumed constant in most studies, they can be dynamic over a long timespan. Consequently, popular mortality models with time-invariant age-dependent coefficients, including the Lee-Carter (LC) and vector autoregression (VAR) models, are incapable of modelling these dynamic cohort effects. To capture such dynamic patterns, we propose a time-varying coefficient spatial-temporal autoregressive (TVSTAR) model that allows for flexible time-dependent parameters. The proposed TVSTAR model is compatible with multi-population modelling and enjoys sound statistical properties. Using empirical results of mortality data from the United Kingdom (UK) and France over the period 1950–2016, we show that the TVSTAR model consistently outperforms the LC (Li-Lee, or LL) and the original STAR model under the single-population (multi-population) modelling framework. Finally, our empirical results suggest that cohort effects strengthen over time for very old ages in both the UK and France. Using simulation evidence, we argue that this observed upward trend can be caused by the overall advancement in the mortality evolution of the same cohort.