The sectors are linked each other by derived factor demand when each sector uses
other sectors’ product as intermediate inputs. Their interaction forms a positive feed-
back in capital adjustments in the network of input-output relations. Suppose that
a capital adjustment takes a form of discrete decision. Then there is a chance of a
chain-reaction of investment in which an investment in one sector triggers an invest-
ment in another sector, and so on. This chain-reaction turns out to be represented by
a branching process in a partial equilibrium of product markets. We then find that
the total size of the chain-reaction can exhibit a very large variance in some parameter
range.
Quantitatively, we ask the following question: given the magnitude of sectoral os-
cillations in the U.S. economy, how do the sectoral fluctuations add up to the aggregate
fluctuations? It is immediately clear that just summing up the independent series of
the sectoral oscillations do not amount to the aggregate fluctuations observed in the
U.S. production. There must be some sectoral comovements. Simulations show that
the general equilibrium path of our model matches the magnitude and pattern of the
aggregate fluctuations observed in the U.S. when the responses of real wage and real
intrest rate to aggregate production are modest.
This paper casts a new perspective on the much discussed issue of investment fluctu-
ations. Traditional macroeconomics as well as the benchmark real business cycle theory
supposes the aggregate shocks, such as money supply, aggregate productivity, or animal
spirits of investers, as the fundamental shock. Without apparent evidence of such aggre-
gate shocks as the consistence cause of business cycles (Cochrane (1994),Christiano and
Fitzgerald (1998)), however, the literature is in search of the mechanism which prop-
agates and amplifies the shocks on disaggregated parts of economies (Shleifer (1986),
Horvath (2000), Gabaix (2004)). The disaggregated model of the aggregate fluctuations
turns out to face the law of large numbers: the tendency that disaggregated shocks can-
cel out each other. In many models the tendency is so strong that a realistic magnitude
of an individual shock does not generate aggregate fluctuations large enough to match
the data. For example, Long and Plosser (1983) show that a general equilibrium model
can in principle generate comovement across sectors when sectors bear idiosyncratic
productivity shocks. In a successive research, however, Dupor (1999) establishes that
their model cannot generate the aggregate fluctuations unless the individual shock is
of order the size of the number of individuals in the economy.
This paper shows that the law of large numbers can be overcome. We show that the
propagation distribution in our model has a heavier tail than the normal distribution
which characterizes a large class of aggregative models. The propagation also exhibits
critical fluctuations in which the variance of aggregate growth rates does not converge
to zero when the number of sectors in the economy tends to infinity in the limiting case