Inference for the Lee-Carter Model With An AR(2) Process

Researchers in studying longevity risk often employ the Lee-Carter model with a unit root AR(1) process for unobserved mortality indexes. When one models the mortality index by a stationary AR(1) process, the widely used two-step inference in Lee and Carter (1992) is inconsistent. Some mortality datasets reject the unit root hypothesis. This paper develops consistent statistical inferences for a modified Lee-Carter model using an AR(2) process to model unobserved mortality indexes. It also provides a simulation study to examine their finite sample performance before applying them to the US mortality rates.