Convergence of Adaptive Learning Models of Pure Exchange
This paper develops an adaptive learning scheme for a standard version of the overlapping generations model with pure exchange using the notion of an error function. Trajectories generated by this scheme converge globally to the monetary steady state for arbitrary consumers' savings behavior. The resulting learning dynamics is therefore globally asymptotically stable. This shows that with the efficient use of structural knowledge on the market mechanism, learning schemes which generate complex dynamics with non-vanishing forecast errors such as ordinary least squares can be avoided. This finding holds for all possible parameterizations guaranteeing the existence of a monetary steady state and generalizes to all one-dimensional models of the Cobweb type.
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