Extensions of the Lee–Carter model to project the data‐driven rotation of age‐specific mortality decline and forecast coherent mortality rates

Accurate forecasts and analyses of mortality rates are essential to many operational practices, such as the designing of pension schemes. Recent studies have focused on the age coherent forecasts, such that long‐term predictions will not diverge infinitely among ages. Although intuitively and biologically reasonable, this age coherence property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. Those include the famous Li–Lee (LL) model, which is argued to produce coherent forecasts of mortality rates across populations, but not ages. In this paper, we progressively explore two effective frameworks with three extensions, by applying the LL specification to the single‐population model (LC‐S) and by introducing time‐dependent age patterns of mortality declines in the forecasting steps with fixed (LC‐VF) and variant (LC‐V) intercepts when modeling those patterns. In particular, the recommended LC‐V model is motivated from the intermediate LC‐S and LC‐VF and resolves all remaining issues of both models. Also, the final LC‐V model is easy to implement, incorporates the dynamic and rotating age‐specific patterns of mortality decline, provides age‐coherent forecasts of mortality rates in the long run, and is straightforwardly extensible to multi‐population cases. Using a large sample of 15 countries, we show that the LC‐V model and its multipopulation counterpart can consistently improve the forecasting accuracy of the competing LC, LL and other extensions in both single‐population and multipopulation scenarios. Long‐term analyses up to 2100 further demonstrate the existence of age coherence when forecasting with the proposed LC‐V model.