Forecast mortality rates with copula-based approaches: Novel evidence from integrated reconciliation

Mortality data exhibit a hierarchical structure, where total death counts equal the sum of sex-specific death counts. While hierarchical forecasting reconciliation methods have improved mortality forecasts at aggregate levels, they typically address only the out-of-sample stage and overlook reconciliation during in-sample modelling. To bridge this gap, we propose three copula-based approaches within the standard Lee–Carter (LC) framework to reconcile total mortality rates using sex-specific rates. By incorporating reconciliation at the in-sample stage, these methods aim to improve parameter estimation and thereby enhance out-of-sample forecast accuracy. Using data from Australia, the United Kingdom, the United States, France, and Japan for ages 65–100 over the period 1950–2020, we demonstrate that our approaches outperform both the traditional LC model and LC-based hierarchical reconciliation. The proposed perfect reconciliation method, which achieves finite-sample reconciliation, consistently delivers the best performance across a range of sensitivity analyses. We further illustrate the practical utility of this integrated approach in forecasting life expectancy and pricing fixed-term annuities, highlighting its broader applicability in actuarial practice.