Expectation Formation and Endogenous Fluctuations in Aggregate Demand



0.61

The Evolution of Output when

ψ <1.

Figure 3: The Evolution of Output when ψ1.

variables. The situation is different when condition (34) is violated. This case
is dealt with next.

Case 2 Assume that the parameters of the model satisfy the following inequality

ψ 1,                                  (35)

i.e., assume that whenever agents choose to form expectations in an adaptive
manner the level of capital stock, and hence the marginal propensity to save,
follow an explosive path.
4

Condition (35) implies that at any time the economy can be in either of two
regimes. For
q'f sufficiently close to one it follows a process that converges to an
equilibrium, i.e., the economy could be in a convergence regime. On the other
hand for q
2 sufficiently close to zero the economy follows a process that does not
converge to an equilibrium, i.e., the economy is in a divergence regime. Figure
(4) illustrates sample dynamics in the two regimes.

In general, the economy could be in either of the two regimes depending
on the precise value of q
2. Recall that q2 does not constitute a parameter of
the economy, but it depends on actions taken by economic agents and is itself
determined as an equilibrium outcome. In particular, if economic agents choose
q
2 to be large enough then the economy will follow a convergent path, on the
other hand, if they choose q
2 to be small then the economy will proceed on a
divergent path.

4Assumption of case 2 can be derived rather than imposed in a model in which optimization
costs accrue in the form of forgone pro
fits rather than in the form of utility costs.

20



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