Forecasting life expectancy in an international context

Over the past two centuries, the life expectancy has more than doubled in many countries, for both males and females. The levels of the countries with the highest life expectancies have risen almost linearly. We exploit this regularity by using the classic univariate ARIMA model to forecast future levels of best-practice life expectancy. We then compare two alternative stochastic models for forecasting the gap between the best-practice level and life expectancy in a particular population. One of our approaches is based on the concept of discrete geometric Brownian motion; our other approach relies on a discrete model of geometric mean-reverting processes. A key advantage of our strategy is that the life expectancies forecast for different countries are positively correlated because of their tie to the forecast best-practice line. We provide illustrations based on Italian and US data.