SFB 303 Discussion Paper No. B - 133

Author: Kottmann, Thomas
Title: Learning to Become Rational in Simultaneous Equations Linear Models with Forecast Feedback
Abstract: Although considerable work has been done on learning procedures towards rational expectations in linear single equation models with forecast feedback, virtually nothing has been known up to now for simultaneous equations systems. In this paper, instead of assuming rational expectations, we stipulate that present or future values of the endogenous variables are predicted by means of observed auxiliary variables which are fitted to the observations (e.g. by ordinary least squares (OLS)) without knowledge of any model parameters. We investigate to what extent and under what conditions convergence of these forecasts to rational expectations is possible. Under the assumption of stationary ergodic auxiliary variables for a class of learning procedures (including OLS learning) sufficient and in a sense necessary convergence conditions are given. These conditions simply impose bounds on the linear parameters of the model's forecast terms, thereby requiring that the forecast part does not become dominant. Furthermore, in case of convergence the limit expectations are shown to be rational with respect to the employed variables; if the latter coincide with the correct exogenous variables of the model, the limit expectations are fully rational. For some classes of models (e.g. recursive models) the results are particularly persuasive.
Keywords: simultaneous equations; rational expectations; least squares prediction
JEL-Classification-Number: 132
Creation-Date: January 1990 
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