Population Dynamics and Labour Force Participation within Goodwin Type Growth-Cycle Models

Several efforts in the area of demo-economic interactions have been motivated by the need to provide sound mathematical foundations for the very popular "Easterlin cycle". Among these we recall the classical contributions by Lee (1974) and Samuelson (1976), and the more recent efforts by Feichtinger et al. (1988, 1992, 1994), Chu Lu (1995). In all these works the "economic side" is based on a neoclassical framework, as in Feichtinger et al. or is only implicit through some complicated nonlinear demographic relationship, as in Lee, Samuelson, Feichtinger and Dockner, and Chu Lu. All these last models are in fact purely "demographic": the demo-economic interactions are handled through some clever modelling trick. In this paper we try to offer a different perspective by setting demo-economic interactions within the framework of the classical Goodwin (1967) growth-cycle model. Our aim is to investigate the effects on the Goodwin cycle of a realistic treatment of the labour-supply process embedding (i) age structure, (ii) wage dependent fertility, and (iii) a participation schedule dependent on the state of the labour market. To this end we derive a very general Goodwin-type model based on a stage representation of the full age structure mechanism, which appears to be a suitable and parsimonious tool for these types of problems (a similar framework is used in Feichtinger and Dockner 1989). Our analysis permits us to display several general features of the demo-economic interaction, such as the effects of different fertility schedules and different patterns of age of entry into the labour market, on the structure of the equilibria of the system. Analysis of selected subcases leads to interesting dynamical results, such as the appearance of sustained "labour-market induced" demo-economic oscillations via the Hopf bifurcation mechanism. The stability properties of the emerging cycle are investigated via numerical simulations. Our analysis displays, therefore, a demo-economic fluctuation not necessarily due to the Easterlinian mechanism.