Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes

This study analyses the dynamics of a two-dimensional overlapping generations economy with endogenous labour supply à la Reichlin (1986) and aspirations, i.e. effective consumption by individuals of the current generation depends on the standard of living (based on consumption experience) of those that belong to the previous generation. We show that the relative importance of aspirations in utility is responsible for the existence of either one (normalised) steady state or two steady states. In particular, when the relative degree of aspiration is fairly high, the supply of labour becomes higher than those corresponding to the normalised steady state because individuals want to increase the amount of time spent at work when they are young in order to increase consumption possibilities when they are old, since the relative importance of past consumption is high in such a case. As regards local stability, the normalised steady state can be determinate or indeterminate and can undergo either a transcritical bifurcation or supercritical flip bifurcation depending on the intensity of the taste externality. Moreover, some interesting global dynamic properties emerge: indeed, when the relative importance of aspirations is strong enough, cyclical or quasi-cyclical behaviour and/or coexistence of attractors may occur. In particular, this last phenomena may cause global indeterminacy even if the stationary equilibria are locally determinate.