Coherent Mortality Forecasting with a Model Averaging Approach: Evidence from Global Populations

Accurate forecasts and analyses of mortality rates are essential to many economic and finance practices, such as the designing of pension schemes. Recent studies have proposed advanced mortality models with age coherent forecasts, such that long-term predictions will not diverge infinitely among ages. Despite their effectiveness, individual models are inevitably misspecified in the empirical analysis, which reduces the reliableness. In this article, we propose a model averaging approach (MAA) that allows for age-specific weights and asymptotically achieves age coherence. Relevant technical details are also provided. The proposed method balances both the in-sample fitting and out-of-sample forecasting, with a uniquely designed smoothness penalty to resolve the potential overfitting and thus avoid abrupt changes in the long-term mortality forecasting. Using a large empirical dataset of 10 countries including 0 to 100 ages and spanning 1950 to 2018, the outstanding forecasting performance of MAA is presented. This robustly holds in various sensitivity analyses and is supported by simulation evidence. A case study is further conducted to discuss the improved forecasting efficiency of MAA, as well as its usefulness in economic and finance applications such as the annuity pricing. The proposed MAA approach is therefore a useful tool in forecasting mortality data for other practices.