Lumpy Investment, Sectoral Propagation, and Business Cycles

explain the economic aggregate fluctuations quantitatively.

3 Business Cycle Simulation

In this section we examine quantitative properties of the equilibrium fluctuation by
numerical simulations. We ask whether the sectoral oscillations of magnitude exhibited
by the U.S. manufacturing sectors would add up in our model to the observed aggregate
fluctuations and generate the business cycle patterns. The answer is affirmative when
the intertemporal substitutions of consumption and leisure are close to perfect. If this
is the case, the (S,s) policy at the individual level generates an endogeneous fluctuation
of the aggregates.

In the previous section we demonstrate the possibility that an individual determin-
istic (S,s) policy generates aggregate fluctuations. The result is obtained by assuming a
simple behavioral rule of consumer decisions and the stationarity of the cross-sectional
distribution of producers’ positions in the (S,s) band. We no longer impose these
assumptions. The consumer’s behavior is derived from a representative household’s
choice. By this we can analyze the impact of preference structure on the aggregate
fluctuations. Moreover, the fluctuation is calculated by simulations without setting
the cross-sectional distribution of producers’ positions at the stationary distribution.
Whereas simulations show that the distribution converges to a uniform distribution
quickly, they can also exhibit interesting dynamics such as the echo-effect or mode-
locking when a large deviation from the stationary state is present. We will study the
dynamics which could not be examined in the setup of the previous section.

Our aim is to reproduce the second moment structure of business cycles. In par-
ticular, we attempt to explain the mechanism for the positive autocorrelation of the
business cycle variables and the positive correlation between production and demand
components. The parameter range we work in is in the vicinity of the fixed price
regime. In this way we quantify the dampening general equilibrium effect and test the
robustness of the fluctuation results we obtained in the partial equilibrium setting.

Let us start from estimating the fluctuation magnitude of U.S. manufacturing sec-
tors. We use the 4-digit SIC annual data compiled by Bartelsman and Gray (1996).
We remove the trend by Hodrick-Prescott filter with smoothing parameter λ = 100.
We estimate a second order autoregressive process of the detrended log sectoral capital
as:

yj,t = ^φ1,j ^yj,t-1 ^{+ φ}2,j ^yj,t-2 ^{+ 6}j,t                             (²³)

The regression shows that 434 sectors out of total 459 sectors exhibit a damped oscil-
lation phase φ₁²_,j + 4φ_2,j < 0. A second order autoregressive process with a damped

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