4.3 Inferences from Past Data
Rational expectations approach to modelling decision making under uncertainty
defines a benchmark in economic theory. In a very minimalist sense the rational
expectations approach assumes that economic agents use the true distributions
functions of the underlying variables in the decision making process. Conse-
quently, the approach assumes that economic agents know the ’’model,” i.e., are
aware of the structure of the economy they operate in. The intuitive justification
for the assumption invokes the law of large numbers, which allows to identify
the relevant distribution functions and the interdependence between economic
variables.
Economic literature normally imposes exogenous uncertainty on determin-
istic models. Such an approach is consistent with the assumption of rational
expectations. Indeed, time evolving uncertainty resolution should eventually
identify the true distribution functions as these are not affected by behavior
of economic agents. In other words, even if economic agents at some point use
incorrect distributions functions they are eventually able to identify the frequen-
cies of all states of nature as these are not affected by their actions based on
incorrect distributions. Consequently, economic literature nearly never focuses
on the approach path towards a given rational expectations equilibrium, i.e.,
nearly universally starts by assuming that learning, if any, must have already
occurred. Naturally, the route followed by the literature is sound and consistent,
however, it does not comprise all possibilities.
In the model of this paper there are no stochastic disturbances at all. All vari-
ables are generated by deterministic processes. Therefore, the issue of economic
agents knowing the true distribution functions becomes superfluous. However,
it still remains to be verified whether it is reasonable to assume that economic
agents know the ’model.”
The underlying dynamic equation in the model takes the form
x't+ι = -ψχte+ι-
Naturally, the true realized value of xt+1 depends on expectations formed at time
t with regard to variable xt+1. Therefore, the realized outcome in period t + 1
depends on actions taken by economic agents at time t. This differs the model of
this paper from the benchmark normally present in the literature. The difference
affects in a profound manner the learning process. In the current context errors
affect the realized values whereas in the main stream of the literature they do
not. Therefore, economic agents in the learning process must take into account
the fact that their mistakes affect equilibrium outcomes.
In a special case when economic agents form expectations given a prior Fχ∣
formed from a naive predictor and a signal of quality q. the underlying process
takes the form
' I (1 - qt2) ' ZQδλ
*t + 1 = -ψ ■ . . *t <
and for q2 large enough it is a convergent process. Naturally, data generated by
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