Should selection of the optimum stochastic mortality model be based on the original or the logarithmic scale of the mortality rate?

Stochastic mortality models seek to forecast future mortality rates; thus, it is apparent that the objective variable should be the mortality rate expressed in the original scale. However, the performance of stochastic mortality models-in terms, that is, of their goodness-of-fit and prediction accuracy-is often based on the logarithmic scale of the mortality rate. In this article, we examine whether the same forecast outcomes are obtained when the performance of mortality models is assessed based on the original and log scales of the mortality rate. We compare four different stochastic mortality models: the original Lee-Carter model, the Lee-Carter model with (log)normal distribution, the Lee-Carter model with Poisson distribution and the median Lee-Carter model. We show that the preferred model will depend on the scale of the objective variable, the selection criteria measure and the range of ages analysed.