Expectation Formation and Endogenous Fluctuations in Aggregate Demand

part of equilibrium and allows agents to decide what expectations to hold with
regard to given variables.

Observe that there are no stochastic disturbances in the model. All out-
comes are purely deterministic. However, economic agents need not have the
ability or desire to discriminate between deterministic and stochastic dynamics.
Accordingly, it is assumed that economic agents treat observed values as being
realizations of some underling random variables. Specifically, economic agents
consider realizations of x_t as random draws from some distribution. The distri-
bution can be conditional on past realized values and can assumes an extreme
form of the delta (Dirac) function.

Recall that the level of utility of a representative agent can be expressed as

Wt - St         f ^rt + -∖ τk + ^πt + lλ

^U Kt,¾t + _l) = ⅛(-⅛-^t)⁺ Io₈     ^t+,    ) ■

Note that under the assumption of logarithmic utility the real value of future
profits x_t+1 = -^—1- is the only, even in the presence of uncertainty, future vari-
able relevant for the determination of the level of savings. Naturally, apart from
x_t+, both future rental price of capital r_t+, and the future price of consump-
tion p_t+, influence the level of realized utility. However, beliefs pertaining to
variables p_t+, and r_{t +} , do not affect the intertemporal problem . Therefore, the
paper focuses solely on expectation formation with respect to variable x_t+,.

Let Ft be the prior distribution of x_t+1 at time t. In addition, let E_tx_t+,
be the expected value of x_{t +} 1 at time t and let σX be the corresponding vari-
ance. In the literature there are two mainstream approaches normally followed
in the context of decision making under uncertainty. Expected utility maximiza-
tion is the dominant one while certainty equivalence approach remains a tool
of convenience. This paper follows the latter approach, i.e., it is assumed that
economic agents treat random variables as if they were equal to their means.
This simplification allows for a complete analytic tractability of the model. The
results are qualitatively unchanged. However, with a certainty equivalence ap-
proach an important channel is absent. There is no precautionary saving motive,
which when present enriches the equilibrium dynamics.

At any point in time economic agents need an assessment of x_t+1 to decide
on the level of savings. It is assumed that the prior Ft is available to economic
agents free of any costs. However, economic agents are not constrained to this
specific piece information. In addition, each agent can purchase a signal of the
true value of a given future variable. Specifically, signals are assumed to be of
the following form
where F_xt-1 denotes the prior distribution of variable x_t+,. In other words,
it is assumed that with a chance q the signal reveals the true value of the
variable and with a chance 1 — q the signal gives a random draw from the

14

<<   <   11   12   13   14   15   16   17   >   >>