Indeterminacy, sunspots, and development traps

The model considered here belongs to a class of models, related to the model of Benhabib and Farmer (J. Econ. Theory 63(1) (1994) 19), which could be transformed into a two-dimensional system of Lotka-Volterra differential equations. This allows complete characterization of the global dynamics of the deterministic and stochastic versions of the model. In particular, in this class of models limit cycles do not exist, and exact regions of attraction of indeterminate steady states can be obtained. We study the stochastic stability of the poverty trap steady state subject to sunspot fluctuations, and demonstrate an approximate method of estimating escape probability as a function of initial conditions and the model's parameters.