Convergence of adaptive learning and expectational stability: The case of multiple rational-expectations equilibria

This paper analyzes the relationship between the expectational stability of rational expectations solutions and the possible convergence of adaptive l earning processes. Both concepts are used as selection criteria in the case of multiple rational expectations solutions. Results obtained using recurs ive least squares lead to the conjecture that there exists a general one-to -one correspondence between these two selection criteria. On the basis of a simple linear model and a stochastic gradient algorithm as an alternative learning procedure, it is demonstrated that such a conjecture would be inco rrect: There are cases in which stochastic gradient learning converges to r ational expectations solutions that are not expectationally stable.