Using the Heterogeneity Model and the Lee-Carter Method to Estimate Mortality Surfaces at Old Ages

Nan Li, United Nations
James W. Vaupel, Max Planck Institute for Demographic Research

Death rates cannot be measured reliably at old ages, yet their values are necessary in studies such as population forecasts. In estimating the true values of death rates at old ages, general smoothing techniques cannot apply to extremely old ages at which there are too few survivors, and they also involve arbitrary choice between smoothness and fitting. To avoid the arbitrariness, we call for the Lee-Carter method that is designed to distinguish persistent trends and disturbances in mortality change. To extend estimates to any age, we utilize the heterogeneity-mortality model. Composing cohorts born in long periods, we obtain the robust estimate of heterogeneity variance, and subsequently the targets are extended from mortality curves to surfaces. Identifying the baseline mortality surface, we eliminate disturbances using the Lee-Carter method and derive estimates of the true values of cohort mortality. We provide examples using data from 17 low-mortality countries.