oscillation displays a pseudo-periodic behavior. The pseudo-periodicity is calculated as
1∕μj∙ ≡ 2π∕ cos-1(φ1,j∙/(2ʌ/-φ2,j∙)), following the procedure similar to Yoshikawa and
Ohtake (1987).
We emulate this oscillation by our lumpy behavior of sectoral investments. The
presumption is that a sector has to commit to a sizable investment if it invests at
all. If it does not invest, then the gap between the actual and desired level of capital
increases as capital depreciation and technological progress takes effect. The lumpy
adjustment generates a non-harmonic oscillation which is familiar in the (S,s) literature
such as the Baumol-Tobin cash balance dynamics. It is more likely that the committed
amount of investment is executed in several periods, if we consider the time to build.
By incorporating the time to build, the sectoral oscillation exhibits a more realistic
harmonic oscillation, but the basic properties of aggregate behavior does not change by
this modification. Individual sectors may fluctuate for various reasons in reality such as
technological improvement or strategic complementarity among firms’ behaviors within
the industry. It is for convenience of analysis that we assume the lumpy behavior of
monopolists.
We derive λj∙ and δj∙ from the observed oscillations μj∙ and σj∙ in the way that the
periodicity and magnitude of oscillation the data shows are maintained. From the
periodicity we have a relation 1∕μj∙ = log λj∙∕∣ log((1 — δj∙)∕g)∣. Also, we numerically
calculate the standard deviation of the model oscillation for log λ = 1 and δj . Then
log λj is derived by dividing σj by the calculated standard deviation. Thus we obtain
λj and (1 — δj)∕g.
Figure 2 shows the estimated periodicity in the first panel. The periodicity is
distributed with mean 8.2 years and standard deviation 3.3. The second and third
panels show the calibrated discreteness λj and the annual depreciation rate δj that
match with the estimated parameters for oscillations. The mean of λj is 2.5 and
standard deviation is 2, and the mean of δj is 0.09 and standard deviation 0.07. Let us
notice the considerable heterogeneity shown in the periodicity. It casts a doubt on the
view that the sectoral fluctuation is merely a reflection of aggregate fluctuations. It is
worth exploring the possibility that a pseudo-random propagation effect across sectors
causes the aggregate fluctuations.
We will show that our model of investment propagation is capable of reproduc-
ing the basic business cycle structure: the standard deviation of GDP around 1.7%,
the positive correlations between production and demand components, and the strong
autocorrelations of the production and demand components. To do so, we explicitly
solve the representative household’s choice between leisure and consumption. We dis-
cuss how the approximated parameters θw and θr in the previous section relate to the
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