Inference pitfalls in Lee-Carter model for forecasting mortality

Forecasting mortality is of importance in managing longevity risks for insurance companies and pension funds. Some widely employed models are the so-called Lee-Carter model and its extensions, which involve a two-step estimation procedure. Empirical findings from using the Lee-Carter model and its extensions prefer an ARIMA(p,1,q) model for modeling the dynamics of the logarithms of mortality rates, which is called mortality index and is a key element in forecasting mortality rates and managing longevity risks. In this paper we prove that the proposed two-step estimation procedure in Lee and Carter (1992) cannot detect the true dynamics of the mortality index in general, which means that future mortality projections based on the two step inference procedure for Lee-Carter model and its extensions are questionable.