# 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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