Lumpy Investment, Sectoral Propagation, and Business Cycles

0.1         0.2        0.3        0.4        0.5         0.6

Mark-up rate

0         0.01        0.02       0.03       0.04       0.05

ν

Figure 4: Admissible range of parameters

investment. The simulated path converges to a certain level quickly and exhibits per-
sistent fluctuations thereafter. The investment-production rate converges to a realistic
9.6%. The bottom left panel shows the capital paths of individual sectors. We observe
an (S,s) behavior of the sectors. The right panels show the magnified plots of the same
aggregate paths in a shorter time horizon. We observe a chaotic fluctuation (in the
sense that the deterministic path appears random) with a certain degree of periodicity.
Also we see a strong correlation between the production and investment.

The correlation structure shown in Table 1 exhibits a limited robustness in pa-
rameters. Figure 4 shows the admissible range of parameters. For each parameter
alignment, we take an average of estimates from 15 simulation runs. We plot a circle
when the standard deviation of GDP is more than 1% and less than 3%, a cross when
investment correlates with production, and a plus when consumption correlates with
production. The plots show that our results depend on the preference specifications
(σ and ν) sensitively but not on the markup rate (1∕(ξ — 1)). In the left panel, there
exists an admissible range of σ for the markup rate larger than 30% (which corresponds
to ξ ≤ 4). The larger the markup rate is, the larger and the broader the admissible
range of σ is. We observed that the business cycle patters obtain also for a smaller
markup rate (ξ ≥ 10). It is not certain, however, if the business cycle pattern in

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