Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

Abstract

Evaluating the predictive ability of mortality forecasts is important yet difficult. Death rates and mean lifespan are basic life table functions typically used to analyze to what extent the forecasts deviate from their realized values. Although these parameters are useful for specifying precisely how mortality has been forecasted, they cannot be used to assess whether the underlying mortality developments are plausible. We therefore propose that in addition to looking at average lifespan, we should examine whether the forecasted variability of the age at death is a plausible continuation of past trends. The validation of mortality forecasts for Italy, Japan, and Denmark demonstrates that their predictive performance can be evaluated more comprehensively by analyzing both the average lifespan and lifespan disparity-that is, by jointly analyzing the mean and the dispersion of mortality. Approaches that account for dynamic age shifts in survival improvements appear to perform better than others that enforce relatively invariant patterns. However, because forecasting approaches are designed to capture trends in average mortality, we argue that studying lifespan disparity may also help to improve the methodology and thus the predictive ability of mortality forecasts.

Keywords: Average lifespan; Evaluation; Forecasting performance; Lifespan disparity.

Fig. 1

Scatterplot of life expectancy at birth and average life years lost at birth due to death for women in Denmark, Italy, and Japan from 1950 to 2012

Fig. 2

Life expectancy at birth (left panels) and life years lost at birth (right panels) for women in Italy, Japan, and Denmark: Observed data, forecasted data using the Lee-Carter model, the Lee-Carter rotating variant (proposed by Li et al. 2013), and the Bohk and Rau model. Forecast years are 1991–2009. Reference period is 1965–1990