Global stability in spite of "local instability" with learning in general equilibrum models

It is known through earlier work that deterministic temporary equilibrium dynamics with least squares learning are locally divergent from a steady state whenever the initial parameter estimates of the agents is high. This paper establishes that the learning dynamics may be globally stable in spite of displaying "locally unstable" behavior in realistic economic models. We identify a simple property of nonlinear temporary equilibrium maps that guarantees that all trajectories converge to the steady state under the global dynamics with learning -in particular, the locally divergent trajectories are also driven back to the steady state. These seemingly contradictory results can be reconciled by observing that the dynamics with least squares learning are discontinuous at the steady state. We also identify temporary equilibrium maps for which an open set of local1y divergent trajectories escapes to infinity while another open set returns to the steady state.An application of each result to OLG economies is provided.