Life Expectancy, Labor Supply, and Long-Run Growth: Reconciling Theory and Evidence

We set up a three-period overlapping generation model in which young individuals allocate their time to schooling and work, healthy middle aged individuals allocate their time to leisure and work and their income to consumption and savings for retirement, and old age individuals live off their savings. The three period setup allows us to distinguish between longevity and active life expectancy (i.e. the expected length of period 1 and 2). We show that individuals optimally respond to a longer active life by educating more and, if the labor supply elasticity is high enough, by supplying less labor. We calibrate the model to US data and show that the historical evolution of increasing education and declining labor supply can be explained as an optimal response to increasing active life expectancy. We integrate the theory into a unified growth model and reestablish increasing life expectancy as an engine of long-run economic development.