A hierarchical copula-based sparse VECM for cause-of-death mortality rates: modeling, forecasting, and connectedness

Recent advances in healthcare and rising life expectancy intensify longevity risk, motivating a deeper understanding of how cause-of-death (COD) rates interact. Using male COD data from 1978 to 2018 in the United States, we develop a copula-based hierarchical framework for seven major causes: cancer, diabetes, external causes, influenza, mental disorders, nephritis, and vascular disease. The framework integrates reconciliation, hierarchical dependence, and long-run equilibrium using a Lee–Carter (LC) setting. More specifically, the LC period indices are estimated under reconciliation penalties and are modeled through a sparse vector error correction model, with dependence captured by a hierarchical Archimedean copula. Two applications illustrate the value of our approach. In out-of-sample forecasting, the framework outperforms the standard LC model by improving the accuracy of aggregate mortality rates. In structural analysis, fitted connectedness reveals that diabetes and vascular disease act as net transmitters of mortality shocks, while cancer and external causes are net receivers. These insights help actuaries, demographers, clinicians, and policymakers enhance mortality forecasting to assess whether prioritizing government interventions for high-transmission causes could potentially maximize overall mortality improvements for society.