Lumpy Investment, Sectoral Propagation, and Business Cycles



runs. However, the mean behavior of the distribution matches the data well. Yet, this
should not be taken as a distinctive evidence for our distribution shown in Proposition
1. The distribution declines faster than an exponential distribution, hence a normal
distribution would also fit well. Thus the distribution data by itself does not reject any
aggregative model that results in a normal distribution by the central limit theorem.
The plot only confirms that the propagation distribution exhibited in simulation is
compatible with the data.

Let us now interpret the simulation results by our analytics. In the previous sec-
tion we introduce the parameter
φ to characterize the relation between the propagation
fluctuations and the strategic complementarity across producers. The fluctuation ex-
hibits an extreme variance when
φ = 1. In a static setup where the capital is replaced
with intermediate input, we can derive when this critical fluctuation occurs under the
same utility specification (Nirei (2003)). One case is
σ = ν = 0. In this case, the
utility function is linear in consumption and labor, and thus both of the real wage and
interest rate are fixed. Another case of criticality occurs when
α = 1 and the interest
rate is fixed. Namely, the production is adjusted only by capital. In this extreme
case of “production of commodities by means of commodities,” there is no longer an
aggregate resource constraint of labor. Thus the propagation lacks a dampening mech-
anism in which an increase in production is suppressed by a rising wage. In a general
equilibrium, a rising interest rate still serves as a dampening factor. If we study the
fluctuation of stationary level production, however, the interest rate is not a dampen-
ing factor since the stationary interest rate is given by fundamental parameters. Thus
the fluctuation is still critical in a long run. This is because a rise in interest rate has
to be followed by a decline to the time average level eventually, which serves as an
accelerator of the fluctuations.

It is not trivial in our model to have correlations between production and demand
components. In the standard real business cycle model, the fluctuation in total factor
productivity causes the procyclical movement of both consumption and investment.
Instead, the investment fluctuates relatively independently from the economic envi-
ronment in our model. This aspect gives the model a different mechanism for the
procyclical movement of the consumption and investment. An increase in investment
demand induces the monopolistic producers to produce more on one hand. On the
other hand, since the capital level is predetermined, an increase in investment com-
petes with the contemporaneous consumption given the production level. By using the
equilibrium relations given
kt, we obtain dyt∕dit = 1/(1 + (α + ν)(σ(1 — α)(ct∕yt))),
which is always between 0 and 1. Hence, given the capital level, an investment has
a positive effect on production, but the effect is no more than 1. Hence there is no
multiplier effect of the investment demand on the production. The correlation between

23



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