Temporary equilibrium with learning: The stability of random walk beliefs

This paper examines the stability of deterministic steady-states with a one dimensional state-variable and a smooth, recursive updating rule. It is shown that the only possibly stable steady states are those associated with random walk beliefs, provided there is motion on a center manifold, which is the case when a key parameter is non-zero; In the extant literature, there is no motion on the center manifold (the parameter is zero), a consequence of the specific assumption that the expected value of the state variable next period determines its current value. The stability properties are seen to be robust with respect to small misspecifications in the agents fixed perception of the steady state.