the above process allow for a perfect identification of all relevant coefficients,
i.e., allow economic agents to learn the model. However, the shape of the model
depends on the specific form of the expectation formation technology. Therefore,
if economic agents were to use their knowledge of the model in the process of
expectation formation they would change the nature of the model. Specifically,
if economic agents were to start forming expectations according to the true
model then the underlying equilibrium equation would take the form
' ,2 (1 - ⅛) '
x+ =-ψ • .■ x"
i.e., the process would change. Naturally, the new process is also perfectly
identifiable from data, however, an attempt to use the new model for assessments
of xt+1 would change the model again. In general after i steps of learning of
procedure the "true” model would take the form
'
xt + 1
(-ψ)t
(ɪ - ¾2)
1 + ⅜t2
'
xt∙
Not only the process would be different from all previous processes, but also for
i large enough the coefficient in front of xt must be necessarily greater than one.
Therefore, the process of learning not only fails to identify a rule that would
allow economic agents to form expectations correctly, but also destabilizes the
economy. Note that the initial process led to a steady state whereas the process
obtained after i stages of learning does not.
The above example illustrates that while past data can be used for identifi-
cation of analytic relationships the relationships need not have practical impor-
tance as an attempt to use a relationship changes the nature of the relationship
and invalidates the original relationship. The model, thus, provides a version of
the Lucas Critique [31] in the context of expectation formation and its impact
on the coefficients of the underlying model.
5 Policy Considerations
Professional economists while considering high frequency fluctuations in macro-
economic variables to be a matter of fact differ as to their significance. Some
economists maintain that oscillations while present are either virtually harmless,
most notably Lucas [30], when one considers their impact on welfare or adhere
to the view that any attempts to counteract them must necessarily be welfare
worsening, RBC theory proponents. Therefore, they argue, governments should
restrain themselves from activists policies since, given the presence of lags and
uncertainty, any policy aimed at mitigating fluctuations is bound to cause more
harm than good. On the other hand there are plenty of arguments, most recent
those of Gali, Gertler and Lopez-Salido [19] and of Caballero and Hammour [8],
that note potential sizable costs of recessions, and at the minimum, advocate
caution in dealing with movements in macroeconomic variables. Furthermore,
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