Lumpy Investment, Sectoral Propagation, and Business Cycles

Figure 7: Distribution of GDP growth rates

on σ and ν. The autocorrelation is estimated by taking an average of 15 runs for
each parameter set. The other parameters are set at the benchmark level. The left
panel shows that the GDP autocorrelation is decreasing in ν. The right panel shows
that the investment autocorrelation is not sensitive to the change in ν . This implies
that the intertemporal substitution of labor affects the production autocorrelation not
through the investment propagation but through the contemporaneous labor decisions.
In contrast, σ affects the autocorrelation of investment quite sensitively. This suggests
that the large part of the decrease in autocorrelation of production from σ = 0.01 to
the other values results from the decrease in autocorrelation in investment (and thus
in capital). In the U.S. data, the autocorrelation of investment is about 0.12 for the
post-war periods. To match this, σ has to be in between 0.01 and 0.02. It is a narrow
range, but the other statistics for this level of σ are consistent with the data as seen in
Table 1.

Finally, Figure 7 shows an inverse cumulative distribution of the growth rates in
GDP. The probability shown in the vertical axis is cumulated from above. The plot is
displayed in a semi-log scale, so a linear line would express an exponential distribution.
We plot by the dashed circle the real distribution calculated by quarterly GDP from
1958 to 2002. The real line shows the simulated distribution. The dotted lines show
several simulated distributions when the sample size is equal to that of the GDP data.
Because of the small sample size, the distribution fluctuates across the simulation

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