An alternative procedure to obtain the mortality rate with non-linear functions: Application to the case of the Spanish population

by Marcos Postigo-Boix, Ramón Agüero, José L. Melús-Moreno

This paper presents an alternative calculation procedure to calculate the mortality rate, exploiting the data available in the Eurostat demography database for Spain. This methodology has been devised based on two of the most widely known and widespread models to establish the mortality rate: The Gompertz-Makeham (GM) and Lee-Carter (LC) models. Our main goal is to obtain a model yielding a similar accuracy than LC or GM, but able to capture the variation of their parameters over time and ages. The method proposed herewith works by applying simple or double fitting, with non-linear functions, to the values of the parameters considered by each one of such models. One of the main advantages of our approach is that we considerably reduce the amount of data that is required to establish the mortality rate, with respect to what would be needed if the traditional models were used. On the other hand, it also allows analyzing the evolution of the mortality rate, even if no real data was available for a particular year. The results evince that, besides fulfilling the two aforementioned goals, the proposed scheme yields an estimation error that is comparable with that offered by the traditional approach.