This paper aims to analyze the overlooked link between catastrophic events and sustainability through a limit cycle analysis. We use and extend a well known Calvo and Obstfeld (1988, Optimal Time Consistent Fiscal Policy with Finite Lifetimes, Econometrica) framework in order to distinguish individual’s and social planner’s discount rates and show that Hopf bifurcation occurs at two critical values for individual discount rate, only if the economy is exposed to catastrophic event risk. This result is important because the role of individual discount rate on aggregate long-term dynamics has been overlooked in the literature. More importantly, the existence of limit cycles implies that consumption and natural resource stock are exposed to cycles in the long run, meaning that the path of utility does not conform to the prominent Sustainable Development criterion. Lastly, we analyze the economic reasons behind limit cycles and show that protecting the environment decreases the likelihood that limit cycles will occur.
What can catastrophic events tell us about sustainability ?
9 May 2019