Public Expenditure on Health and Private Old-Age Insurance in an OLG Growth Model with Endogenous Fertility: Chaotic Dynamics Under Perfect Foresight

Abstract

This study analyses the dynamics of an economy with overlapping generations, endogenous population (fertility and adult mortality), logarithmic preferences and Cobb–Douglas technology. We show that the public provision of health investments and the existence of a private system of old-age insurance (i.e., transfers from children to parents) may cause the birth and death of multiple (three) steady states, deterministic chaos and bubbling phenomena when individuals have perfect foresight. Interestingly, however, we show that periodic dynamics (cycles) or complex dynamics (chaos) and global stability of the economy can endogenously be reconciled in the model, because the rise either in public health investments or transfers from young to old people can have the potential to smooth and ultimately suppress endogenous fluctuations in the cases of existence of both a single steady state or multiple steady states.