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.
Over the course of human history we observe a strong positive correlation between income and life expectancy as well as between income and education (Preston, 1975, Bils and Klenow, 2000, Krueger and Lindahl, 2001). These aggregates showed no visible trend for millennia and then, in most developed countries, began to rise jointly and permanently roughly at the same time, for example around the year 1800 in England. The observed positive correlation is thus undisputed, constituting basically a stylized fact of successful human development. Yet there exists a lively debate about the interpretation of the correlation.
One popular hypothesis, built upon human capital theory and the life cycle of earnings (Becker, 1962, Ben-Porath, 1967), argues that increasing life expectancy leads to more education and thereby to faster income growth. With contrast to the second link in this chain of causation, which has been debated for quite a while, the first link, the effect of increasing life expectancy on education, was long considered to be self-evident. Recently, however, this link gained scholarly attention as the so called the Ben-Porath mechanism (Hazan, 2009). It is also at the center of the present paper.