Lumpy Investment, Sectoral Propagation, and Business Cycles



at which wage and interest rate are determined independently from the product market.
This proposition assures that any plausible magnitude of aggregate fluctuation can be
obtained in our model when the price response to aggregate product is sufficiently slow.

Another line of research on investment fluctuations focused on the endogenous
fluctuations which result from non-linearity of economic dynamics. The models of
multiple equilibria, chaos, or self-fulfilling expectation show the possibility that the
aggregate fluctuations occur in a deterministic environment of economic fundamentals
if the non-linearity is sufficiently strong. This paper explores a new approach along this
line, in which an interaction of many small non-linear behaviors causes a deterministic
fluctuation. We suppose that individual sectors follow a deterministic pattern of capital
oscillations with occasional large adjustments and periods of inertial depreciation. The
sectors monopolistically compete each other, so an increase in production in a sector
induces other sectors to increase their production (and cut prices). Thus the timing of
occasional capital adjustments may be endogenously synchronized. This interrelation
makes the product markets a multi-dimensional non-linear dynamical system which
in principle is capable of generating an endogenous complex fluctuation. The result
obtained here can be seen as a generalization of the critical fluctuations demonstrated
by Bak, Chen, Scheinkman, and Woodford (1993) in particular. They show a power-law
distribution of production propagation in a network of locally interacting producers.
We implement a similar propagation mechanism in an equilibrium model of globally
interacting sectors. We find that a power-law distribution appears at a limiting case,
and near the limit any magnitude of fluctuation is observed for a system of a large
number of individuals.

This paper addresses the question of whether a micro discrete choice, in partic-
ular an (S,s) behavior, is relevant in aggregate fluctuations. The seminal paper by
Doms and Dunne (1998) found that an establishment level capital is adjusted only
occasionally but by a jump in size. A series of research, among others Cooper, Halti-
wanger, and Power (1999), has stressed the role of the lumpy adjustments played in
business cycles. Theoretical and numerical studies on aggregation of (S,s) behaviors,
for example Caplin and Spulber (1987) and Caballero and Engel (1991), have largely
found that such an individual lumpiness does not contribute to aggregate fluctuations.
Again, the law of large number is the logic: the individual lumpiness tends to cancel
out each other. To the contrary, this paper shows that the (S,s) behavior can generate
a considerable magnitude of aggregate fluctuations. In fact, the fluctuation is scale
free, in the sense that the variance does not depend on the number of agents, at the
limiting case when the wage and interest rate are determined independently from the
product markets. The propagation size exhibits a power-law distribution whose mean
and variance diverge. This implies that, if there are numerous establishments in an



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