Sunspot Fluctuations: A Way Out of a Development Trap?

In dynamic general-equilibrium economic models, equilibrium may be indeterminate, so a continuum of equilibrium trajectories may converge to the same steady state. Often, those mechanisms leading to indeterminacy, like increasing returns to scale, may also lead to multiple steady states and possible underdevelopment traps. But indeterminacy often allows construction of rational sunspot equilibrium as a randomization over different equilibrium trajectories or equilibria. This paper studies "rescuing" an economy from a development trap through sunspot-driven self-fulfilling expectations. The problem is stated as stochastic stability of a system of stochastic differential equations with white noise perturbations from sunspot-driven self-fulfilling expectations. The framework of, Benhabib and Farmer (1994) is used. This deterministic continuous-time model with infinitely lived agents is characterized by increasing social returns to scale due to an imperceived externality in the production function. There are two steady states. One has zero capital and zero consumption (the origin); the other has positive capital and consumption. 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. If a sunspot variable - white noise - is added to the model, agents could take it into account when making their decisions. 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. The question of asymptotic stochastic stability is studied by the Lyapunov method.