Observe that the intratemporal problem is unaffected by the characteristics of
the expectation formation technology, therefore, the equilibrium level of output,
measured in terms of the price of the consumption good, at time t is still given
by
_ (1 - φβt) ,a (25)
yt (1 - βt)α kt, (25)
where βt is given by (24). Also recall that in equilibrium kt _ βt-∙∖. Note that
in this case output need not be constant. Any change in xf+ι leads to a move
of βt and consequently affects the level of output. Therefore, if in equilibrium
economic agents choose to modify their expectations the change will result in
an innovation in the level of output.
In summary expectations affect aggregate activity because they affect the
marginal propensity to save. Optimism leads economic agents to devote a
smaller fraction of their incomes toward savings and in turn to high output.
Conversely, pessimistic expectations cause economic agents to save a higher
fraction of their incomes, which leads to low demand for consumption good and
in turn to low output.
4 Optimal Expectation Formation
An ability to predict the future with certainty presents economic value as it al-
lows for optimal behavior along the intertemporal margin. However, normally,
economic agents do not have enough capacity to formulate correct point esti-
mates of future economic variables. In reality, economic decision making relies
only on imperfect, second best, assessments of future outcomes. Specifically,
economic agents at any point in time decide which or what combination of fore-
casting tools to develop and to rely on. Similarly, economic agents decide what
information sets to base their decisions on. The mainstream of the literature
either assumes that information regarding future variables arrives exogenously
and economic agents use that information to improve their assessments of the
future, or it assumes that agents willing to sharpen their assessments of the
future need to purchase informative signals at some costs. This paper follows
the latter approach and assumes that economic agents incur a cost in the form
of utility when they attempt to enhance their estimation of the future.
4.1 Rational Selection of an Expectation Formation Tech-
nology
The intertemporal problem of an agent at time t involves an assessment of
Xt+1. Therefore, a particular assessment leads to a particular behavior along
the intertemporal margin. The paper develops a framework in which agents are
allowed decide on the quality of assessments of relevant future variables. In other
words, the paper refrains from imposing any specific expectations formation
technology. On the contrary, it treats the process of expectation formation as a
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