Non-self-averaging and the statistical mechanics of endogenous macroeconomic fluctuations Masanao Aoki a, ⁎, Raymond J. Hawkins b a Department of Economics, University of California, Los Angeles, CA, 90095, USA b College of Optical Sciences, University of Arizona, Tucson, AZ, 85721, USA abstract article info Keywords: Macoeconomic models Dynamics Non-self-averaging Strong fluctuation phenomena are an endogenous feature of economic systems if they are non-self- averaging. We show that an important consequence of non-self-averaging is that current forms of economic policy can be rendered useless. We also find non-self-averaging both to exist in microeconomic models of cluster development within economies and to be consistent with observed economic power laws. These results suggest the need for straightforward identification of non-self-averaging in economic systems and to this end we present a sufficient condition for non-self-averaging in terms familiar to financial risk management. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Self-averaging behavior is a core, albeit unappreciated, assumption of mainstream macroeconomics. Comparatively well-known in physics, this notion that “the effects of the individual events add up to produce an almost deterministic outcome …essentially without fluctuations” (Kadanoff, 2000), parallels on many levels Adam Smith's “invisible hand” metaphor and underpins much of what is seen in the macroeconomics literature including that of growth and business cycles (Romer, 1986; Lucas, 1988; Grossman and Helpman, 1991; Aghion and Howitt, 1992). Recent events in the world economy and the ubiquity of multiplicative random processes in economic analysis suggest, however, that the assumption of self-averaging is both theoretically suspect and empirically counterfactual. Indeed, non-self-averaging behavior (Derrida, 1997; Kadanoff, 2000; Sornette, 2000) which both follows from multiplicative random processes and “can have huge and (mostly) unpredictable price swings” (Kadanoff, 2000) is far more consistent with recent observations of the economy than any mainstream economic theory. Of particular interest in this regard is the important role that agent heterogeneity plays in non-self-averaging behavior (Kadanoff, 2000). Mainstream macroeconomics, by contrast, employs the notion of a “representative agent” which strips the economy of heterogeneity. While problems with this notion were recognized in the mainstream economics literature as early as the 1920s (Sraffa, 1926; Schumpeter, 1928; Young, 1928) and the list of shortcomings has only increased with time (Kirman, 1992; Hartley, 1996; Hartley, 1997; Schohl, 1999), analytic tractability has, together with the belief that economic fluctuations are of exogenous origin, given this notion remarkable longevity. Recently observed economic fluctuations, however, suggest an endogenous origin consistent with the multiplicative random processes typically employed in economic analysis. This further suggests that the use of the representative agent replaces the actual non-self-averaging behavior of the economy with self-averaging behavior and in so doing assumes away dynamics crucial for the development of responsible risk management in economic policy. Alternatively, one can develop macroeconomics from the perspec- tive of both statistical mechanics and combinatorial stochastic processes (Aoki and Yoshikawa, 2007) and the purpose of this paper is to show that with this perspective the notion of non-self- averaging is revealed to be a central issue in macroeconomics. Our indicator for the nature of “averaging” will be the comparatively simple coefficient of variation CV which is the ratio of the standard deviation σ to the mean μ, or CV =σ / μ. When a process is self- averaging CV =0 in the limit. If CV is nonzero in the limit then the process is non-self-averaging. A highly instructive example of the economic issues raised with non-self-averaging is the question posed by Solomon of whether it makes sense to invest in a system with an average growth rate of -10%/month (Solomon, 2001). On its face the answer might be no. The investment, however, turns out to be diversified with an equal weight in two assets; one with a negative growth rate of -70%/month and one with a positive growth rate of +50%/month. The asset with the positive return gives the investment a return of over 100 times and illustrates a number of challenges with the typical self-averaging approach in economics. First, the notion of “average behavior” is tricky as Solomon observes: “the difference between the exponential of the Economic Modelling 27 (2010) 1543–1546 ⁎ Corresponding author. E-mail address: aoki@econ.ucla.edu (M. Aoki). 0264-9993/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2010.07.008 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod