Non-Existence of Steady State Equilibrium in the Neoclassical Growth Model with a Longevity Trend

Longevity has been increasing in the developed countries for almost two centuries and further increases are expected in the future. In the neoclassical growth models the case of population growth driven by fertility is well-known, whereas the properties of population growth caused by persistently declining mortality rates have received little attention. Furthermore, the economic literature on the consequences of changing longevity has relied almost entirely on analysis applying a once and for all change in the survival probability. This paper raises concern about such an approach of comparison of steady state equilibrium when considering the empirically observed trend in longevity. We extend a standard continuous time overlapping generations model by a longevity trend and are thereby able to study the properties of mortality-driven population growth. This turns out to be exceedingly complicated to handle, and it is shown that in general no steady state equilibrium exists. Consequently analytical results and long run implications cannot be obtained in a setting with a realistic demographic setup.