I analyze how changes in life expectancy affect retirement age, education time, and growth rates of economies. I set up a continuous time, overlapping generations model of endogenous growth with externalities in human capital production. I find that increases in life expectancy give rise to first, higher retirement ages and second, higher education spans. A threshold level for life expectancy exists such that per capita growth rates follow an inverted U pattern.
In this article I analyze how changes in life expectancy may affect optimal education time, retirement age, and the growth rates of economies. To this end I set up a continuous time, overlapping generations growth model with human capital accumulation that I solve numerically. The issue of the effects of the reduction in mortality rates and the resulting increases in life expectancy on economic growth rates has been recently addressed in the literature through both empirical and theoretical studies. Along these lines I focus on human capital acquisition and its transmission across generations as the force driving the growth rate.
Concerning empirical studies, the hypothesis that the reduction in mortality rates has caused higher levels of investment in human capital and therefore augmented growth rates is partially supported for various economies. Thus, Kalemli-Ozcan et al. (2000) show an increase in life expectancy at birth along with an increase in average numbers of years of schooling in England. They claim that after averaging across lower-income countries, there is apparently a connection between increases in life expectancy at birth and increases in gross secondary school enrollment that is positively connected with higher growth rates observed. Preliminary data from Latin American and Caribbean countries show that gross domestic product (GDP) growth is statistically associated with life expectancy: For instance, estimates based on data from Mexico suggest that for any additional year of life expectancy there will be an additional 1% increase in GDP 15 years later (see World Health Organization 1999, box 1.2, 9). Along the same lines, Rodriguez and Sachs (1999) also find a positive effect of life expectancy on GDP growth for the case of Venezuela. Barro and Sala-i-Martin (1995) estimate for a sample of 97 countries that a 13-year increment in life expectancy would increase the per capita growth rate by 1.4% per year. They also find, however, some exceptions where increments in life expectancy have not resulted in higher growth, even though all of them exhibited higher schooling levels in the period 1960-85. Malmberg (1994) gives another exception: Higher growth was achieved when middle-aged persons were numerous, whereas increases in dependent age groups led to lower per capita growth in Sweden. Finally, some other studies find mixed evidence, so that increments in life expectancy result in higher growth rates for low levels of life expectancy but in lower growth rates for high levels of life expectancy (see Zhang et al. 2003 and references therein).
A common result in most theoretical studies that include some sort of human capital is that an increase in life expectancy lengthens the period needed to recover investment in human capital, which translates into higher returns to individual education or human capital investment. This augmented return will give rise to higher levels of investment in human capital, which in turn will raise growth rates. Ehrlich and Lui (1991) show in a three overlapping generations model how improvements in longevity lower fertility, thus raising educational investment and long-term growth. Meltzer (1995) finds that mortality reductions may favor economic growth by increasing educational investment. Kalemli-Ozcan et al. (2000) show in an overlapping generations model a la Blanchard that if mortality drops, life expectancy increases, so that an augmented life horizon to enjoy the return to human capital investment gives rise to higher schooling (human capital investment), although growth is not affected because the growth rate in their model is identically equal to zero. …