Endogenous age structure in descriptive macroeconomic growth models: a general framework and steady state analysis

Many phenomena in population economics, such as demo-economic oscillations, are the dynamical outcome of the interplay between demographic and economic forces. Age structure plays a key role as it is the conveyor belt through which economic shocks that impact on demographic behaviour, such as fertility crisis or explosions, feed-back on the economic system. In this paper we provide a fully realistic endogenisation of the age structure of the population in descriptive continuous-time macro-economic growth models, such as the neoclassical model (Solow 1956) or Goodwin’s (1967) growth cycle. We first develop a general framework, by considering a generic model of descriptive macro-economic growth, and the fundamental equation for the dynamics of a closed age structured population, Von Foerster partial differential equation, and by integrating them through a suitable modelling of the main link function between the economic sytem and the demographic one, i.e. the rate of change of the labour supply. Next we initiate to study the properties of our framework by investigating the existence of joint balanced growth paths of the population and the economy through some noteworthy examples. In particular we consider a Solow-type model with fertility endogenised according to a “demographic transition” pattern. The model shows the possibility of many equilibria, some of which essentially induced by age structure. This gives insight on the issues of the optimum population growth rate and the overall structure of balanced growth equilibria in growth models.