Fluctuations in aggregate variables like output, prices, and employment pervade economic dynamics at all time scales: from minute-to-minute change in a stock price, monthly swings in industrial production, and annual variations in GDP to the longer phases of structural change like those identified by Angus Maddison (1991). Fluctuations in the same variables happen also at spatial scale: spreading from single industry sectors to national economies, to regions, and up to the world economy. To explain why economic activities produce instabilities and to find consistent patterns in a flux of change has always been at the core of macroeconomic research and theorizing. In a previous work (Matutinovic 2005) I dealt tentatively with the first question in the context of microeconomic origins of business cycles. Here, I will address the second one, namely, one statistical pattern--the power law--that emerges in the U.S. business cycle and in other economic phenomena and which is probably pertinent to all market economies. Power-law distributions, also known as Pareto and Zipf distributions (Adamic 2003), show the inverse relationship between the size of an observable and its frequency. As such, they have been known for quite a long time in economics: distribution of income and wealth (Pareto law), size distribution of firms (Simon and Bonini 1958), and size distribution of cities (Zipf's law) are among the most famous instances. Referring to the latter phenomenon, Paul Krugman remarked that "rank-size rule is a major embarrassment for economic theory: one of the strongest statistical relationships we know, lacking any clear basis in theory" (1997, 44). (1)
In the absence of proper economic theory, we can look in other fields of research for explanations of power laws and see if these may apply to the economic context. Thanks to the renewed interest in transdisciplinarity sparked by the complexity theory, which left its mark also on economics (Arthur et al. 1997; Rosser 1999; Arthur 1999), economists began to consider certain meta-theories that originated in natural sciences. Probably the most famous is the self-organized criticality (SOC) developed by the late physicist Per Bak and his co-workers (Bak and Chen 1991). In a nutshell, SOC theory states that any large system composed of many agents, like an economy, spontaneously evolves via local interactions to a state where the size distribution of internal events produced by agent's interactions (e.g., severity of recessions) is power-law distributed, in other words, there is an inverse relationship between the size and frequency of an event. Recently there appeared a competing theory--the highly optimized tolerance (HOT)--which bases its explanation of power laws on design for efficient performance--either by natural selection (in biological systems) or by human intervention (in engineering) (Carlson and Doyle 1999). According to their theory, complex systems are inherently prone to cascading failures because they consist of a large number of different, interrelated parts which may span several hierarchical levels. It is thanks to a goal-oriented design process aimed at preventing major system breakdowns (which would undermine its functionality) that a majority of failures are small sized with only occasional large ones. Therefore the system becomes robust to anticipated perturbations and accounted-for uncertainties in its environment but fragile to design failures and unanticipated perturbations (Carlson and Doyle 1999). Epistemologically, these two theories bring into focus the relative relevance of self-organization versus design in complex systems structure and dynamic behavior. In the context of economics, it is the relationship between "invisible hand" market forces and institutional design, and their respective influence on economic evolution and its large-scale fluctuations.
Because theories considered in this work come from physics, part of the discussion material comes from the new field of econophysics. Over the past ten years econophysicists have been providing a fresh perspective on economic issues, and their formal models, computer simulations, and insights are generally challenging orthodox economics. Their works are rarely published in economic journals and are, therefore, mostly unknown to the wider economic public. However, one may ask why their theories and models, which rely on tools developed for analysis of physical, nonliving systems, would have any relevance for institutional and evolutionary economics. After all, if we look after physicist theories, are we not going to repeat the "original sin" of economic science when it embraced classical physics as its methodological ideal, the only difference being that the emphasis is now on far-from-equilibrium dynamics? In my opinion this danger of replacing the old mechanistic approach with a new one is real and this work will, among other things, address its theoretical weaknesses. (2) Closely related is the issue of the appropriateness of mechanical models in explaining socioeconomic phenomena. Such models are based exclusively on the intrinsic properties of agents and in most cases disregard the cultural context in which the agents operate (Dupre 2001). However, goal orientation and intentionality do not stop at the level of agents but extend to the society as a whole, involving norms and whole paradigms which entrain behavior at the lower, individual level. Consequently, I will argue that any model which wishes to explain nontrivial economic dynamics, like that of business cycles, must go beyond the intrinsic properties of agents and provide an explicit reference to institutions.
I strongly believe that there is a potential value in putting economic issues in a wider system-theoretic context and then looking for insights and analogies that may be useful in understanding a particular economic problem. This may be especially interesting if the "new context" claims to have "universal" theoretical dimension. Therefore, we will examine here two such "universal" theories--self-organized criticality and highly optimized tolerance--which both address power-law distributions in complex systems but provide quite different explanations for their occurrence. I will use them to discuss the "nature" of power laws in business cycles and the respective roles of self-organization and design in a capitalist economy. Last but not the least, the kind of empirical findings presented here largely bypass economic journals regardless of their theoretic orientation. Therefore, this work may be also an opportunity to initiate a wider discussion among economists.
The paper is organized as follows: the next section will introduce self-organized criticality and highly optimized tolerance theories and their relationship to economic dynamics; the third section will present empirical findings related to power laws in the U.S. business cycle; the fourth section will discuss self-organization and design in market economies, and the fifth will close with conclusions.
Meta-Theories of Large-Scale Fluctuations
Self-organized criticality (SOC) is a theory of behavior of large systems with many interacting units originally developed by Per Bak and his co-workers as a general interpretation of a famous relationship known as 1/f noise, (3) which is ubiquitous in nature and therefore of particular interest for natural scientists (Bak et al. 1988; Bak and Chen 1991). The theory is known for its universal or holistic dimension (Bak 1994; Stanley 1995), and it attempts to explain dynamics in widely different contexts: from earthquakes (Bak 1996), mass extinctions in evolutionary time (Sneppen et al. 1995), forest fires and war casualties (Roberts and Turcotte 1998), economic fluctuations (Bak et al. 1993; Schneikman and Woodford 1994; Bak 1996; Andergassen 2001; Buchanan 2001; Stanley et al. 2002), historical turbulences (Buchanan 2001), up to the evolution of the universe (Smolin 1997, 211-214). (4)
In a nutshell, SOC theory states that interactive systems with large numbers of components spontaneously evolve into a "critical state" where minor events may cause "avalanches" of all sizes (Bak 1996, 1-2). For an outside observer such a dynamics makes detailed behavior of a system largely unpredictable, in a way analogous to deterministic chaos. However, unlike in chaotic systems, aggregate temporal observations of events in systems in a critical state yield a particular statistical pattern--a power law--with an important general prediction: the probability of occurrence of an event is inversely proportional to its size.
There are several models of SOC, the "forest fire" model, the "slider-block" model, and the "sand pile," which is also its most popular metaphor (Bak 1996; Roberts and Turcotte 1998). In the sand-pile model, individual grains drip randomly on the surface and the characteristic conic shape arises as a result of friction and long-range correlation of individual grains. During the formation of the pile (the subcritical state) a grain fall can cause only small avalanches. As grain dripping continues and the slope of the pile reaches a critical value, we observe intermittent avalanches of all sizes, triggered by a single grain. These avalanches are power-law distributed: N(s) ~ [s.sup.-[alpha]] (where N(s) is the number of avalanches of size s and [alpha] is a critical exponent). The experiments showed that at the supra-critical state avalanches are much greater than at the critical state and the slope adjusts itself spontaneously to the critical state. Therefore, both sub-critical and supra-critical states in the sand-pile model are naturally attracted toward a critical state (Bak and Chen 1991). The systemic consequence of such a scaling of avalanches is that it allows for a constant change on the pile while preserving its overall identity (the conic shape). Power-law distribution is the...