consumption and production rather stems from the fluctuations of accumulated capi-
tal. We also obtain (dyt∕yt)∕(dkt∕kt) = (1 + ν)α(ct∕yt)∕(σ(1 — α) + (α + ν)(ct∕yt)) at
equilibrium. This takes values between zero and one, and is close to one when σ and ν
are close to zero, agreeing with our benchmark simulation. Since the investment is de-
termined partly by an independent process of best response dynamics across producers
which the representative household cannot predict deterministically, large production
due to large capital can result in large consumption. The Keynesian multiplier effect
would increase the correlations between production and demand components. This
would be the case when the consumption function is more sensitive to income than
our baseline model. If a significant number of consumers face liquidity constraint, for
example, it would contribute to more synchronous movements between production and
demands.
The autocorrelation of production is generated by the demand-smoothing effect of
the real interest rate. In the previous section we saw that an increase in the interest
rate sensitivity θr lowers φ and dampens the instantaneous investment propagation. In
a dynamic setting, this dampening effect only postpones the investment propagation to
the subsequent periods. Suppose that the interest rate is now above the time average
level due to a large concentration of sectors near the adjustment threshold. In the next
period, the interest rate would decrease to the time average level if the investment
is at the time average level. This decrease in interest rate increases the threshold for
capital adjustment. Hence the investment in the next period tends to be larger than the
time average level. This is the mechanism for the autocorrelation in investment when
σ = 0.01 in Figure 6. In this mechanism, the effect of delaying the investment is strong
when the sensitivity parameter θr is large, and a large θr follows a small intertemporal
substitution in consumption, 1∕σ. The autocorrelation in investment generates the
autocorrelation in production in two routes: a contemporaneous effect on aggregate
demand and subsequent effects on aggregate supply via capital accumulation.
It is helpful to examine our economy’s smooth counterpart to understand the fun-
damental condition when the fluctuations occur. Suppose that there is no discreteness
constraint (4); then any capital level can be chosen. The producers’ optimal choice of
capital yields an optimality condition which is linear in aggregate capital as in (13).
By aggregating the optimality condition, we find that the aggregate capital level kt
is indeterminate in the product market. The capital level is thus solely determined
by the consumer’s choice between leisure and consumption. In our model, the time
average capital level (normalized by the total factor productivity) is also determined
independently from technology. However, the investment is determined uniquely in
the best response dynamics across producers. We saw that the propagation exhibits
an extreme variance when the wage and interest rate are fixed. This corresponds to
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