Sensitivity and uncertainty in the Lee-Carter mortality model

BACKGROUND: The Lee-Carter model (LC) is widely used in research and applications for forecasting age specific mortality, and typically performs well regardless of the uncertainty and often the limited quality of mortality data. OBJECTIVE: Why dose LC perform well regardless of the uncertainty and the limited data quality? METHODS: We analyze the robustness of LC using sensitivity analyses based on matrix perturbation theory, coupled with simulations that examine the effect of unavoidable randomness in mortality data. The combined effects of sensitivity and uncertainty determine the robustness of LC. RESULTS: We find that the sensitivity of LC and the uncertainty of death rates both have nonuniform patterns across ages and years. The sensitivities are small in general, with largest sensitivities at both ends of the period. The uncertainty of death rates are high in young ages (5-19) and old ages (90+) with rising in young ages but dropping in old ages. CONCLUSIONS: The sensitivity and uncertainty analyses indicate that the randomness hardly interrupts the prediction of LC. The divergence of long term prediction in LC is likely due to structural changes in the age-year specific mortality, which is associated with the development of public health policy, medical innovations and chronic disasters. CONTRIBUTION: Our results reveal that LC is robust against random perturbation and sudden short term changes. ### Competing Interest Statement The authors have declared no competing interest.