Lumpy Investment, Sectoral Propagation, and Business Cycles

Table 1: Simulated business cycle statistics

have to have precise information about the capital configuration of the entire economy.
When the economy has attained the stationary level, a noisy information would not
contribute to the accuracy of prediction very much in our setting. We also tried another
expectation formulation based on an AR(1) estimate of the past investment path. We
confirmed that the basic property of the fluctuations does not change, although we
noted that the convergence to the rationally expected AR(1) parameters can be fragile
depending on the fundamental parameters. Another issue in the simulation is the
finiteness of the agents. The existence of equilibrium is shown in the previous section
as an asymptotic property when the number of sectors N tends to infinity. When
N is finite, with a positive probability the best response dynamics does not reach an
equilibrium. We impose a rule that the dynamics stops either when all the sectors
adjust upward or all the sectors which adjust at the initial step re-adjust downward.
This case happens in the early periods of simulated paths. We did not observe this
case once the equilibrium path is converged to a stationary state level.

Table 1 summarizes the simulation result on the second moments. The standard
deviations of the estimated second moments in 500 runs are shown in parentheses.
The parameter values are set as σ = 0.01, ν = 0, labor share (1 — 1∕ξ)(1 — α) = 0.58,
mark-up rate 1∕(ξ — 1) = 1/3, and annual discount rate β = 0.96. Although the
correlation between production and investment is not strong enough, the simulation
captures the basic feature of business cycles such as the magnitude of fluctuations in
GDP, investment, and consumption, strong autocorrelations in GDP, positive correla-
tions between production and demand components and input components, and small
wage fluctuations.

Figure 3 shows typical paths of the simulated production and investment for the
same parameter set. The variables are normalized by the stationary level GDP after
convergence. The top left panel shows the entire paths of the GDP and the aggregate

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