Self-Organized Criticality and Economic Fluctuations

Abstract

Economists have long been interested in explaining the observed instability of economic aggregates. Though several reasons for variation in the pace of production are easily given, such as exogenous variation in tastes or in production possibilities, it is hard to see why there should be large variations in those factors that are synchronized across the entire economy. Instead, it seems more likely to suppose that variations in demand or in production costs in different parts of the economy should be largely independent and hence that a law of large numbers would imply that significant variations in aggregate activity (relative to the typical size of aggregate activity) are not likely to occur. An alternative approach proposes that economies possess intrinsically unstable dynamics, which even in the absence of external shocks would result in persistent deterministic fluctuations. This type of model implies, however, that aggregate fluctuations should involve motion on a low-dimensional attractor, while analysis of economic time series has not revealed structure of this kind.' Another alternative proposes that the economy possesses multiple equilibria and that it can therefore switch between equilibria for arbitrary reasons. This possibility suffers, however, from the difficulty that one must explain how people succeed in coordinating their expectations about the times at which a shift should occur. Here we explore another type of explanation, which relies on an entirely different mechanism. Our proposal is that the effects of many small independent shocks to different sectors of the economy need not cancel out in the aggregate, due to the presence of significantly nonlinear, strongly localized interactions between different parts of the economy. The type of macroscopic instability that can result has been studied by condensed-matter physicists, under the name of self-organized criticality (Per Bak and Kan Chen, 1991). Physicists have noted, in several contexts, the possibility of a state, in which independent microscopic fluctuations can propagate so as to give rise to instability on a macroscopic scale. This is a state in which chain reactions initiated by local disturbances neither damp out over a short distance (the subcritical case) nor propagate explosively so that the system cannot remain in that state (the supercritical case), as in the controlled nuclear fission that allows a reactor to generate power without exploding. Often this has seemed to depend upon parameters being carefully tuned to exactly their critical values. (In the case of a reactor, an elaborate control mechanism is required to keep it near criticality.) More recently, it has been argued that some systems may spontaneously evolve toward a critical state and return to it even if perturbed by an external shock. The prototypical example of such selforganized criticality is a sandpile. When the slope of the pile is nowhere too steep, dropping on additional grains of sand at randomly chosen sites has no macroscopic effects, as at most small numbers of grains will shift position in each case. However, randomly dropping on additional sand will eventually result in the slope of the pile increasing to a critical slope, at which point large avalanches can occur in response to the dropping of a single additional grain of sand. A sandpile with a slope that is initially greater than the critical slope also evolves toward it. in this case through an immediate * Department of Economics, University of Chicago, 1126 East 59th St., Chicago, IL 60637. We thank Per Bak, Buz Brock, Boyan Jovanovic, and Paul Krugman for discussions and the Santa Fe Institute and the NSF for research support. 1Scheinkman (1990) surveys empirical work on this