Fading memory learning in a class of forward-looking models with an application to hyperinflation dynamics

We analyze a class of non-linear deterministic forward-looking economic mod els (the state today is affected by today's and tomorrow's expectation) und er bounded rationality learning. The learning mechanism proposed in this pa per defines the expected state as a geometric average of past observations. We show that the memory of the learning process plays a stabilizing role: it enlarges the local stability parameters region of the perfect foresight stationary equilibria and it eliminates non-perfect foresight cycles-attrac tors generated through local bifurcations. In a hyperinflation economy with two stationary equilibria we show that only one of the two equilibria can be stable under bounded rationality learning provided that agents have a 'l ong memory'. We can also have convergence towards non-perfect foresight cyc les and even chaotic dynamics. If the debt financing quota is small enough then no restriction on the agent's memory is needed. The equilibrium with t he higher inflation rate is stable under bounded rationality for a small la nd not really significant) set of economies. (C) 2001 Elsevier Science B.V. All rights reserved.