this region is generated by the mechanism we analytically identified.3 The right panel
shows that the admissible range for preference specifications (σ and ν). We obtain the
aggregate fluctuations large enough when σ + ν is small enough. To obtain a mean-
ingful stochastic propagation effect, the representative household needs to be sensitive
enough to interest rate or wage. We also observe in the plot that σ needs to be small
for the correlation between production and investment to obtain. When σ is larger, an
investment by a sector increases the interest rate more, and dampens the propagation
effect.
The simulation replicates well the mean behavior of the pairwise correlation be-
tween sectoral production and GDP. The comovement of the sectoral production (and
hence sectoral and aggregate production) is a defining characteristic of business cycles.
However, the comovement is far from a perfect mode locking. The left panel of Figure
5 shows the histogram of the correlations in data (shown by a bar). The correlation
between a sector and aggregate is only modest. This fact agrees with another fact we
noted that the periodicity of sectoral oscillations varies much. These suggest contrary
to the view that the business cycles are mainly driven by an aggregate factor and the
sectoral movements are only a noise-ridden version of the same cycles. The modest
correlation between the sectoral and aggregate production is captured by our simula-
tion well. The histogram of the simulated correlations under our benchmark parameter
set (as for Table 1) is drawn by a real line. The simulated histogram is more centered
than the real histogram, which is a natural consequence of our symmetric modeling of
sectoral interactions. The real input-output matrix is far from symmetric, as Horvath
(2000) emphasized, and the asymmetric input-output relation will generate more het-
erogeneity in the comovement structure across sectors. The mean of the correlation
(0.24) is reproduced well by our simulation, however. This suggests that the symmetric
modeling may be satisfactory insofar as the aggregate fluctuations is concerned. The
right panel of Figure 5 shows the histograms of sector size in data (bar) and in sim-
ulation (line). The only source of heterogeneity in the model is depreciation rate (δj)
and lumpiness (λj). The heterogeneity of the sector size is reproduced fairly well. This
excludes the case in which the different variety in comovement stems from the different
sector size distributions. Also this assures that the model fluctuation we observe does
not result from an unrealistic distribution of sector size.
Figure 6 shows that the autocorrelations of production and investment depend
3 For a small markup, the production goods are easily substitutable and the firms are competitive.
Hence the price responds sensitively to the initial shock in the best response dynamics. The subsequent
adjustment process occurs not in the direction to amplify the initial shocks but in the direction to
mitigate the initial response. Hence our analysis does not apply to this case. It is nonetheless
interesting that a competitive setting also generates an endogeneous fluctuation.
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