Sensitivity and uncertainty in the Lee–Carter mortality model

Abstract

The Lee–Carter model (LC) is widely used for forecasting age-specific mortality, and typically performs well regardless of the uncertainty and often limited quality of mortality data. Why? 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. We find that the sensitivity of LC and the uncertainty of death rates both have non-uniform patterns across ages and years. The sensitivities are small in general, with the largest sensitivities at both ends of the period. The uncertainties of death rates are high in young ages (5–19 years) and old ages (90+ years), rising in young ages but dropping in old ages. Our results reveal that LC is robust against random perturbation and sudden short-term changes.