Dynamics of Death in the Lee-Carter Model

Shripad Tuljapurkar, Stanford University

The Lee-Carter model is widely used, both in its original form and newer extensions of the original formulation. It has often been remarked that life expectancy under this model seems to increase linearly over multi-year projections but it is not clear why. We also know that the variance in age at death has fallen over time in many countries but we don't know if and why the Lee-Carter model shows this trend. We study the dynamics of life expectancy and variance in age at death when mortality follows a Lee-Carter model. We present analytical results to show under what circumstances the model predicts linear increases in life expectancy. We also describe conditions under which the variance in age at death will decrease and/or increase overtime. We show that these results illuminate what happens in the data, and also the performance of the model.