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The authors first provide a nonparametric inference of the relationship between life expectancy and economic growth on an historical data for 18 countries over the period 1820-2005. The obtained shape shows up convexity for low enough values of life expectancy and concavity for large enough values. They then study this relationship on a benchmark model combining "Perpetual youth" and learning-by-investing. In such a benchmark, the generated relationship between life expectancy and economic growth is shown to be strictly increasing and concave.
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