For some parameter values, both steady states are indeterminate, and the parameter space is separated into two regions of attraction. The region of attraction at the origin is a development trap. If the economy starts in the development trap, it is possible to select a level of consumption to push the system into the positive steady-state region of attraction. However, no individual agent has an incentive to experiment, and everyone coordinates on a trajectory leading to the origin. This could be corrected if agents could form expectations corresponding to a trajectory converging to a positive steady state.
Agents are unaware of such a trajectory because the externality is assumed to be unknown.
Coordinating on a sunspot white noise allows exploring new regions of the state space and can eventually move the trajectory of the system out of the trap. This happens if a zero steady state is stochastically unstable under sunspot fluctuations or if an initial condition lies outside a region of stochastic stability that may not coincide with the development trap of a deterministic system. When the economy eventually leaves the trap, it is possible to calculate the expected first-exit times from the region of attraction to a zero steady state depending on the initial conditions and magnitude of a sunspot process. This paper uses numerical simulations of stochastic differential equations to calculate the expected times of escape. Boundaries of the stochastic stability region are calculated using a stochastic averaging method.