Convergence of Recursive Learning Mechanisms to Steady States and Cycles in Stochastic Nonlinear Models

We examine recursive algorithms for learning steady states and cycle in dynamic nonlinear models. Simple generically necessary and sufficient conditions for local convergence, based on easily computable expectational-stability conditions, are established for both both stochastic and nonstochastic frameworks. The results are applied to steady-state and cycle equilibria in the standard overlapping generations model. The same methods are also used to study convergence to steady states in statistic models, as illustrated by the Lucas "island" and the "cobweb market" models.

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