Comparing strategies for matching mortality forecasts to the most recently observed data: exploring the trade-off between accuracy and robustness

Background

Given the increased link between retirement age and payments to the development in life expectancy, a precise and regular forecast of life expectancy is of utmost importance. The choice of the jump-off rates, i.e. the rates in the last year of the fitting period, is essential for matching mortality forecasts to the most recently observed data. A general approach to the choice of the jump-off rates is currently lacking.

Objective

We evaluate six different options for the jump-off rates and examine their effects on the robustness and accuracy of the mortality forecast.

Data and methods

Death and exposure numbers by age for eight European countries over the years 1960–2014 were obtained from the Human Mortality Database. We examined the use of model values as jump-off rates versus observed values in the last year or averaged over the last couple of years. The future life expectancy at age 65 is calculated for different fitting periods and jump-off rates using the Lee-Carter model and examined on accuracy (mean absolute forecast error) and robustness (standard deviation of the change in projected e65).

Results

The choice for the jump-off rates clearly influences the accuracy and robustness of the mortality forecast, albeit in different ways. For most countries using the last observed values as jump-off rates resulted in the most accurate method, which relates to the relatively high estimation error of the model in recent years. The most robust method is obtained by using an average of observed years as jump-off rates. The more years that are averaged, the better the robustness, but accuracy decreases with more years averaged.

Conclusion

Carefully considering the best choice for the jump-off rates is essential when forecasting mortality. The best strategy for matching mortality forecasts to the most recently observed data depends on the goal of the forecast, the country-specific past mortality trends observed, and the model fit.