We first provide a nonparametric inference of the relationship between life expectancy and economic growth using historical data for 18 countries over the period 1820–2005. The obtained shape indicates convexity for low enough values of life expectancy and concavity for large enough values. We then study this relationship using a benchmark model combining “perpetual youth” and learning-by-investing. The generated relationship between life expectancy and economic growth is shown to be strictly increasing and concave. We finally examine two models departing from “perpetual youth” by assuming successively age-dependent earnings and age-dependent survival probabilities. With age-dependent earnings, the obtained relationship is hump-shaped, whereas age-dependent survival laws reproduce the convex–concave shape detected in prior empirical study.