The Evolution of Output and the Precision of Signals in Time when
ψ >1
0.56
0.55
0.54
0.53
60
time
100 120
Figure 5: The Evolution of Output and the Precision of Signal in Time when
ψ > 1.
divergent path errors made with the naive predictor become large and their vari-
ance becomes high, i.e., the predictor becomes less and less reliable. Economic
agents fearing sizable losses due to suboptimal behavior along the intertemporal
margin decide to learn and purchase informative signals, i.e., they, as equation
31 indicates, increase the value of q2. This, however, changes the nature of the
dynamic process of xt. Specifically, xt is put on a convergent path. Therefore,
errors made with the naive predictor become smaller. Expectations based on
the naive predictor do not lead to serious inefficiencies along the intertemporal
margin and allow to save on the information gathering and processing costs.
Consequently economic agents turn towards the naive predictor and stop learn-
ing. However, as a result the nature of the dynamic process is changed again
and the economy enters a divergence regime. This leads to a loss of accuracy
of the naive predictor and learning starts again. The process continues and the
economy permanently oscillates between convergence and divergence regimes
and never settles into a steady state. Figure (5) presents sample dynamics.
The paper up to this point has in effect limited the set of feasible expec-
tation formation technologies to convex combinations of perfect foresight ex-
pectation and a naive expectation. Specifically, priors have been assumed to
be formed with a very simple predictor. However, the assumption may be too
restrictive. It is reasonable to assume that learning, simple trend and pattern
extraction, based on past realized data does not involve significant costs. The
paper, therefore, relaxes the previous restriction and permits economic agents
to select expectation formation technologies from a richer set.
Specifically, it is assumed that economic agents can freely process informa-
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