Complex equilibrium dynamics in a simple OLG model of neoclassical growth with endogenous retirement age and public pensions

We analyse the steady-state equilibrium dynamics of the conventional overlapping generations economy à la Diamond (1965) with pay-as-you-go public pensions and second period of life divided between working and retirement time in a proportion dependent on the individual health status (a rather realistic assumption especially in the current world with high longevity). In contrast to an economy without public health spending – which is always stable with monotonic trajectories –, an economy with tax-financed health care services (which in turn affect the individual health status and hence the length of the retirement time) may experience complex equilibrium dynamics with deterministic chaotic business cycles and, in particular, complicated dynamical phenomena, such as multiple “bubblings” may occur when crucial economic parameters change. Interestingly, it is shown that increasing the size of PAYG pensions, although initially may trigger chaotic cycles, eventually works for stability.